Search

A key issue in making precise predictions in QCD is the uncertainty in setting the renormalization scale $\mu_R$ and thus determining the correct values of the QCD running coupling $\alpha_s(\mu_R^2)$ at each order in the perturbative expansion of a QCD observable. It has often been conventional to simply set the renormalization scale to the typical scale of the process $Q$ and vary it in the range $\mu_R \in [Q/2,2Q]$ in order to estimate the theoretical error. This is the practice of Conventional Scale Setting (CSS). The resulting CSS prediction will however depend on the theorist's choice of renormalization scheme and the resulting pQCD series will diverge factorially. It will also disagree with renormalization scale setting used in QED and electroweak theory thus precluding grand unification. A solution to the renormalization scale-setting problem is offered by the Principle of Maximum Conformality (PMC), which provides a systematic way to eliminate the renormalization scale-and-scheme dependence in perturbative calculations. The PMC method has rigorous theoretical foundations, it satisfies Renormalization Group Invariance (RGI) and preserves all self-consistency conditions derived from the renormalization group. The PMC cancels the renormalon growth, reduces to the Gell-Mann--Low scheme in the $N_C\to 0$ Abelian limit and leads to scale- and scheme-invariant results. The PMC has now been successfully applied to many high-energy processes. In this article we summarize recent developments and results in solving the renormalization scale and scheme ambiguities in perturbative QCD. [full abstract is in the paper]., Comment: 79 pages ; 21 figures; Review article submitted to Prog. Part. Nucl. Phys

The relation between the gluon density in a hadron and entanglement entropy can shed a new light on the high energy scattering behavior of hadrons: The growth above the classical geometric cross section is directly related to the increase of the internal quantum entropy from the entangled parton distribution in hadrons. A rather consistent picture emerges from the scale dependence of the Pomeron from the QCD evolution of the gluon distribution function $g(x, \mu)$, the rising of the integrated cross section in photoproduction of vector mesons, the deep inelastic scattering (DIS) experiments at HERA, hadron multiplicity and entropy. We also point out a possible analogy between parton entanglement entropy and the black-hole entropy of Bekenstein and Hawking., Comment: 17 pages, 4 figures, possible analogy between parton entanglement and the black-hole entropy added, new references included

Acknowledgments We thank the participants of the FPF meetings and the Snowmass working groups for discussions that have contributed both directly and indirectly to this study. We gratefully acknowledge the invaluable support of the CERN Physics Beyond Colliders study group and the work of CERN technical teams related to civil engineering studies (SCE-DOD), safety discussions (HSE-OHS, HSE-RP, EP-DI-SO), integration (EN-ACE), and discussions on services (EN-CV, EN-EL, EN-AA) and simulations (SY-STI). The work by J Alameddine, W Rhode, T Ruhe, and A Sandrock has been supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Collaborative Research Center SFB 876 and SFB 1491. L A Anchordoqui is supported by the US National Science Foundation (NSF) Grant PHY-2112527. T Araki is supported by JP18H01210. A Ariga is supported by JSPS KAKENHI Grant JP20K23373 and the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme (Grant 101002690). T Ariga acknowledges support from JSPS KAKENHI Grant JP19H01909. K Asai is supported by JSPS KAKENHI Grant JP19J13812 and JP21K20365. A Bacchetta and F G Celiberto acknowledge support from the INFN/NINPHA project. P Bakhti and M Rajaee are supported by the National Research Foundation of Korea (NRF-2020R1I1A3072747). B Barman received funding from the Patrimonio Autónomo—Fondo Nacional de Financiamiento para la Ciencia, la Tecnología y la Innovación Francisco José de Caldas (MinCiencias—Colombia) Grant 80740-465-2020 and the European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement No. 860881-HIDDeN. The work of B Batell is supported by the US Department of Energy (DOE) Grant DE–SC0007914. The work of A Berlin, T J Hobbs, S Hoeche, and J G Morfín was supported by the Fermi National Accelerator Laboratory (Fermilab), a US DOE, Office of Science, HEP User Facility. Fermilab is managed by Fermi Research Alliance, LLC (FRA), acting under Contract DE-AC02-07CH11359. M Becker, E Copello and J Harz acknowledge support from the DFG Emmy Noether Grant HA 8555/1-1. E Copello acknowledges also support from the DFG Collaborative Research Centre 'Neutrinos and Dark Matter in Astro- and Particle Physics' (SFB 1258). E Bertuzzo acknowledges financial support from FAPESP Contracts 2015/25884-4 and 2019/15149-6 and is indebted to the Theoretical Particle Physics and Cosmology group at King's College London for hospitality. The work of J Bian and W Wu is supported in part by US DOE Grant DE-SC0009920 and Heising-Simons Foundation Grant 2022-3319. The work of A Boyarsky and M Ovchynnikov is supported by the ERC under the European Union's Horizon 2020 Research and Innovation Programme (GA 694896). A Carmona acknowledges funding from the European Union's Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie Grant Agreement No. 754446 and UGR Research and Knowledge Transfer Found—Athenea3i. A Carmona also acknowledges partial support by the Ministry of Science and Innovation and SRA (10.13039/501100011033) Grant PID2019-106087GB-C22 and by the Junta de Andalucía Grant A-FQM-472-UGR20. F G Celiberto thanks the Università degli Studi di Pavia for the warm hospitality. The work of G Chachamis was supported by the Fundação para a Ciência e a Tecnologia (Portugal) under Project CERN/FIS-PAR/0024/2019 and Contract 'Investigador auxiliar FCT—Individual Call/03216/2017'. The work of M Citron and D Stuart is supported by US DOE Grant DE-SC0011702. The work of L Darme is supported by the European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement 101028626. P B Denton acknowledges support from the US DOE Grant Contract DE-SC0012704. The work of P S Bhupal Dev was supported in part by the US DOE Grant DE-SC0017987. The research activities of K R Dienes were supported in part by the US DOE Grant DE-FG02-13ER41976/DE-SC0009913 and also by the US NSF through its employee IR/D program. M V Diwan acknowledges support from the US DOE Grant Contract DE-SC0012704. Y Du and J H Yu are supported in part by National Key Research and Development Program of China Grant 2020YFC2201501, and the National Science Foundation of China (NSFC) under Grants 12022514, 11875003 and 12047503, and CAS Project for Young Scientists in Basic Research YSBR-006, and the Key Research Program of the CAS Grant XDPB15. The work of B Dutta and S Ghosh are supported in part by the US DOE Grant DE-SC0010813. The work of S Ghosh is also supported in part by National Research Foundation of Korea (NRF)'s Grants, Grant 6N021413. Y Farzan has received financial support from Saramadan Contract ISEF/M/400279 as well as from the European Union's Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie Grant Agreement 860881-HIDDeN. The work of J L Feng is supported in part by US NSF Grants PHY-1915005 and PHY-2111427, Simons Investigator Award #376204, Simons Foundation Grant 623683, and Heising-Simons Foundation Grants 2019-1179 and 2020-1840. M Fieg is supported in part by US NSF Grant PHY-1915005 and by NSF Graduate Research Fellowship Award DGE-1839285. A L Foguel is supported by FAPESP Contract 2020/00174-2. The work of P Foldenauer is supported by the UKRI Future Leaders Fellowship DARKMAP. The work of S Foroughi-Abari and A Ritz is supported in part by NSERC, Canada. The work of J-F Fortin is supported in part by NSERC, Canada. A Friedland is supported by the US DOE Grant DE-AC02-76SF00515. E Fuchs acknowledges support by the DFG Germany's Excellence Strategy—EXC-2123 'QuantumFrontiers'—390837967. M Fucilla, M M A Mohammed, and A Papa acknowledge support from the INFN/QFT@COLLIDERS project. A Garcia acknowledges support from the European Union's H2020-MSCA Grant Agreement 101025085. C A García Canal and S J Sciutto acknowledge support from CONICET and ANPCyT M V Garzelli acknowledges support the from German BMBF Contract 05H21GUCCA. V P Goncalves was partially financed by the Brazilian funding agencies CNPq, CAPES, FAPERGS and INCT-FNA (Process Number 464898/2014-5). S Goswami acknowledges the J C Bose Fellowship (JCB/2020/000011) of Science and Engineering Research Board of Department of Science and Technology, Government of India. The work of M Guzzi is supported by US NSF Grant PHY-2112025. L Harland-Lang thanks the Science and Technology Facilities Council (STFC) for support via Grant Award ST/L000377/1. The work of S P Harris is supported by the US DOE Grant DE-FG02-00ER41132 as well as the US NSF Grant PHY-1430152 (JINA Center for the Evolution of the Elements). J C Helo acknowledge support from Grant ANID FONDECYT-Chile 1201673 and ANID—Millennium Science Initiative Program ICN2019-044. The work of M Hirsch is supported by the Spanish Grants PID2020-113775GB-I00 (AEI/10.13039/501100011033) and PROMETEO/2018/165 (Generalitat Valenciana). The work of A Hryczuk and M Laletin is supported by the National Science Centre, Poland, research Grant 2018/31/D/ST2/00813. The research activities of F Huang are supported by the International Postdoctoral Exchange Fellowship Program and in part by US NSF Grant PHY-1915005. A Ismail is supported by NSERC (Reference Number 557763) and by US NSF Grant PHY-2014071. Y S Jeong acknowledges support from the National Research Foundation of Korea (NRF) grant funded by the Korea government through Ministry of Science and ICT Grant 2021R1A2C1009296. K Jodlowski and L Roszkowski are supported by the National Science Centre, Poland, research Grant 2015/18/A/ST2/00748. S R Klein is supported in part by the US NSF Grant PHY-1307472 and the US DOE Contract DE-AC-76SF00098. F Kling and P Quílez are supported by the DFG under Germany's Excellence Strategy—EXC 2121 Quantum Universe—390833306. P Ko is supported in part by KIAS Individual Grant PG021403 and by National Research Foundation of Korea (NRF) Grant NRF-2019R1A2C3005009. S Kulkarni is supported by the Austrian Science Fund Elise-Richter Grant V592-N27. The work of J Kumar is supported in part by US DOE Grant DE-SC0010504. J-L Kuo is supported by US NSF Theoretical Physics Program, Grant PHY-1915005. The work of C Le Roux and K Zapp is part of a project that has received funding from the ERC under the European Union's Horizon 2020 Research and Innovation Programme (Grant Agreement 803183, collectiveQCD). The work of H-S Lee was supported in part by the National Research Foundation of Korea (NRF-2021R1A2C2009718). S J Lee was supported by the Samsung Science and Technology Foundation. Ji Li is supported by the National Natural Science Foundation of China Grant 11905149. K-F Lyu and Z Liu are supported in part by the US DOE Grant DE-SC0022345. The work of R Maciula and A Szczurek was partially supported by the Polish National Science Centre under Grant 2018/31/B/ST2/03537. R Mammen Abraham and A Ismail acknowledge support from the US DOE Grant DE-SC0016013. M R Masouminia is supported by the UK Science and Technology Facilities Council (Grant ST/P001246/1). The work of J McFayden was supported by the Royal Society Fellowship Grant URF R1 201519. The work of O Mikulenko is supported by the NWO Physics Vrij Programme 'The Hidden Universe of Weakly Inter-acting Particles' with Project Number 680.92.18.03 (NWO Vrije Programma), which is (partly) financed by the Dutch Research Council (NWO). P Nadolsky and F Olness acknowledge support through US DOE Grant DE-SC0010129. E R Nocera thanks the STFC for support by the Grant Awards ST/P000630/1and ST/T000600/1. The work of N Okada is supported by the US DOE Grant DE-SC0012447. V Pandey acknowledges the support from US DOE Grant DE-SC0009824. The work of D Raut is supported by the US DOE Grant DE-SC0013880. P Reimitz acknowledges financial support from FAPESP Contract 2020/10004-7. M H Reno is supported in part by US DOE Grant DE-SC-0010113. The work of J Rojo is partly supported by the Dutch Research Council (NWO). L Roszkowski and S Trojanowski are supported by the grant 'AstroCeNT: Particle Astrophysics Science and Technology Centre' carried out within the International Research Agendas programme of the Foundation for Polish Science financed by the European Union under the European Regional Development Fund. S Trojanowski is also supported in part by the Polish Ministry of Science and Higher Education through its scholarship for young and outstanding scientists (Decision No. 1190/E-78/STYP/14/2019). S Trojanowski is also supported in part from the European Union's Horizon 2020 Research and Innovation Programme under Grant Agreement No. 952480 (DarkWave 24 project). I Sarcevic is supported by US DOE Grant DOE DE-SC-0009913. The work of L Shchutska is supported by the ERC under the European Union's Horizon 2020 Research and Innovation Programme (GA 758316). The work of T Shimomura is supported by JSPS KAKENHI Grants JP18H01210, JP18K03651, and MEXT KAKENHI Grant JP18H05543. The work of K Sinha is supported in part by US DOE Grant DE-SC0009956. The work of T Sjöstrand is supported by the Swedish Research Council, Contract 2016-05996. J T Sobczyk acknowledges support from NCN Grant UMO-2021/41/B/ST2/02778. D Soldin acknowledges support from the US NSF Grant PHY-1913607. H Song is supported by the International Postdoctoral Exchange Fellowship Program. Y Soreq is supported by grants from the NSF-BSF, BSF, the ISF and by the Azrieli foundation. A Stasto acknowledges support from US DOE Grant DE-SC-0002145. S Su is supported by the US DOE Grant DE-FG02-13ER41976/DE-SC0009913. W Su is supported by a KIAS Individual Grant (PG084201) at Korea Institute for Advanced Study. Y Takubo is supported by JP20K04004. M Taoso acknowledges support from the INFN Grant 'LINDARK', the research grant 'The Dark Universe: A Synergic Multimessenger Approach 2017X7X85' funded by MIUR, and the project 'Theoretical Astroparticle Physics (TAsP)' funded by the INFN. The research activities of B Thomas are supported in part by US NSF Grant PHY-2014104. The work of Y-D Tsai is supported in part by US NSF Grant PHY-1915005. The work of A Sabio Vera has been supported by the Spanish Research Agency (Agencia Estatal de Investigación) through the Grant IFT Centro de Excelencia Severo Ochoa SEV-2016-0597, by the Spanish Government Grant FPA2016-78022-P and from the European Union's Horizon 2020 Research and Innovation Programme under Grant Agreement 824093. The work of Yongchao Zhang is supported by the National Natural Science Foundation of China Grant 12175039, the 2021 Jiangsu Shuangchuang (Mass Innovation and Entrepreneurship) Talent Program JSSCBS20210144, and the 'Fundamental Research Funds for the Central Universities'. Yue Zhang is supported by the Arthur B McDonald Canadian Astroparticle Physics Research Institute. R Zukanovich Funchal is partially supported by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Conselho Nacional de Ciência e Tecnologia (CNPq). The opinions and conclusions expressed herein are those of the authors and do not represent any funding agencies., High energy collisions at the High-Luminosity Large Hadron Collider (LHC) produce a large number of particles along the beam collision axis, outside of the acceptance of existing LHC experiments. The proposed Forward Physics Facility (FPF), to be located several hundred meters from the ATLAS interaction point and shielded by concrete and rock, will host a suite of experiments to probe standard model (SM) processes and search for physics beyond the standard model (BSM). In this report, we review the status of the civil engineering plans and the experiments to explore the diverse physics signals that can be uniquely probed in the forward region. FPF experiments will be sensitive to a broad range of BSM physics through searches for new particle scattering or decay signatures and deviations from SM expectations in high statistics analyses with TeV neutrinos in this low-background environment. High statistics neutrino detection will also provide valuable data for fundamental topics in perturbative and non-perturbative QCD and in weak interactions. Experiments at the FPF will enable synergies between forward particle production at the LHC and astroparticle physics to be exploited. We report here on these physics topics, on infrastructure, detector, and simulation studies, and on future directions to realize the FPF's physics potential., German Research Foundation (DFG) SFB 876 SFB 1491, National Science Foundation (NSF) PHY2112527, Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT) Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research (KAKENHI) JP18H01210 JSPS KAKENHI JP20K23373 JP19H01909 JSPS KAKENHI JP19J13812 JP21K20365 JSPS KAKENHI JP18K03651, European Research Council (ERC) 101002690, National Research Foundation of Korea NRF-2020R1I1A3072747, Patrimonio Autónomo-Fondo Nacional de Financiamiento para la Ciencia Tecnología y la Innovación Francisco José de Caldas (MinCiencias-Colombia) 80740-465-2020, European Commission Joint Research Centre 860881-HIDDeN European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant 754446, United States Department of Energy (DOE) DE-SC0007914, Fermi National Accelerator Laboratory (Fermilab), a US DOE, Office of Science, HEP User Facility, Fermi Research Alliance, LLC (FRA) DE-AC02-07CH11359, German Research Foundation (DFG) HA 8555/1-1, DFG Collaborative Research Centre 'Neutrinos and Dark Matter in Astro-and Particle Physics' SFB 1258, Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP) 2015/25884-4 2019/15149-6, United States Department of Energy (DOE) DE-SC0009920, Heising-Simons Foundation 2022-3319 2019-1179 2020-1840, ERC under the European Union's Horizon 2020 Research and Innovation Programme 694896 803183, UGR Research and Knowledge Transfer Found-Athenea3i, Ministry of Science and Innovation, Spain (MICINN) Spanish Government, SRA Grant PID2019-106087GB-C22, Junta de Andalucía A-FQM-472-UGR20, Fundacao para a Ciencia e a Tecnologia (FCT) CERN/FIS-PAR/0024/2019 03216/2017, United States Department of Energy (DOE) DE-SC0011702 DE-SC0017987 DE-FG02-13ER41976/DE-SC0009913 DE-SC0012704 DE-SC0010813 DE-AC02-76SF00515 DE-FG02-00ER41132 DE-AC-76SF00098 DE-SC0010504 DE-SC0022345 DE-SC0010129, US NSF through its employee IR/D program, National Key Research and Development Program of China 2020YFC2201501, National Natural Science Foundation of China (NSFC) 12022514 11875003 12047503, CAS Project for Young Scientists in Basic Research YSBR-006, Key Research Program of the CAS XDPB15, National Research Foundation of Korea (NRF)'s Grants 6N021413, Saramadan Contract ISEF/M/400279, National Science Foundation (NSF) PHY-1915005 PHY-2111427 PHY1430152 PHY-2014071 PHY-1307472 PHY-2014104, Simons Investigator Award 376204, Simons Foundation 623683, National Science Foundation (NSF) DGE-1839285, FAPESP Contract 2020/00174-2, UKRI Future Leaders Fellowship DARKMAP, Natural Sciences and Engineering Research Council of Canada (NSERC), German Research Foundation (DFG) EXC-2123 390837967, INFN/QFT@COLLIDERS project, European Union's H2020-MSCA Grant Agreement 101025085, Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), ANPCyT, Federal Ministry of Education & Research (BMBF) 05H21GUCCA, Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPQ), Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES), Fundacao de Amparo a Ciencia e Tecnologia do Estado do Rio Grande do Sul (FAPERGS), INCT-FNA 464898/2014-5, J C Bose Fellowship of Science and Engineering Research Board of Department of Science and Technology, Government of India JCB/2020/000011, National Science Foundation (NSF) PHY-2112025, UK Research & Innovation (UKRI) Science & Technology Facilities Council (STFC) Science and Technology Development Fund (STDF) ST/L000377/1, Grant ANID FONDECYT-Chile 1201673, ANID-Millennium Science Initiative Program ICN2019-044, Spanish Grant (AEI) PID2020-113775GBI00, Center for Forestry Research & Experimentation (CIEF) PROMETEO/2018/165, National Science Centre, Poland 2018/31/D/ST2/00813, International Postdoctoral Exchange Fellowship Program, KIAS Individual Grant PG021403, National Research Foundation of Korea NRF-2019R1A2C3005009, Austrian Science Fund Elise-Richter Grant V592-N27, US NSF Theoretical Physics Program PHY-1915005, Samsung, National Natural Science Foundation of China (NSFC) 11905149, Polish National Science Centre 2018/31/B/ST2/03537, UK Research & Innovation (UKRI) Science & Technology Facilities Council (STFC) ST/P001246/1, Royal Society of London URF R1 201519, Netherlands Organization for Scientific Research (NWO) 680.92.18.03 Physics Vrij Programme .The Hidden Universe of Weakly Inter-acting Particles' - Dutch Research Council (NWO), UK Research & Innovation (UKRI) Science & Technology Facilities Council (STFC) ST/T000600/1 ST/P000630/1, Netherlands Organization for Scientific Research (NWO), European Union under the European Regional Development Fund, Polish Ministry of Science and Higher Education through its scholarship for young and outstanding scientists 1190/E-78/STYP/14/2019, European Commission 952480, ERC under the European Union 758316, Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT) Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research (KAKENHI) JP18H05543 MEXT KAKENHI, Swedish Research Council 2016-05996, NCN UMO-2021/41/B/ST2/02778, NSF-BSF, US-Israel Binational Science Foundation, Israel Science Foundation, Azrieli foundation, KIAS Individual Grant at Korea Institute for Advanced Study PG084201, Istituto Nazionale di Fisica Nucleare (INFN), Ministry of Education, Universities and Research (MIUR) 2017X7X85', Spanish Government SEV-2016-0597 Spanish Research Agency (Agencia Estatal de Investigacion) through the Grant IFT Centro de Excelencia Severo Ochoa FPA2016-78022-P, European Union's Horizon 2020 Research and Innovation Programme 824093, National Natural Science Foundation of China (NSFC) 12175039, 2021 Jiangsu Shuangchuang (Mass Innovation and Entrepreneurship) Talent Program JSSCBS20210144, Fundamental Research Funds for the Central Universities, Arthur B McDonald Canadian Astroparticle Physics Research Institute, Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP), United States Department of Energy (DOE) DE-SC0012447 DE-SC0009824 DE-SC0013880 :The US DOE DE-SC-0010113 DOE DE-SC-0009913 US DOE DE-SC0009956 DE-FG02-13ER41976/DESC0009913 US DOE JP20K04004

The purpose of the Low-$x$ Workshop series is to stimulate discussions between experimentalists and theorists in diffractive hadronic physics, QCD dynamics at low $x$, parton saturation, and exciting problems in QCD at HERA, Tevatron, LHC, RHIC, and the future EIC. The central topics of the workshop, summarized in the current Proceedings, were: Diffraction in ep and e-ion collisions (including EIC physics); Diffraction and photon-exchange in hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions; Spin Physics; Low-$x$ PDFs, forward physics, and hadronic final states. This Workshop has been the XXVIII edition in the series of the workshop., The 2021 edition of the Low-$x$ International Workshop took place from September 26 to October 1 in Elba, Italy. Contains arXiv:2202.03724, arXiv:2111.04515, arXiv:2112.07827, arXiv:2110.05081, arXiv:2112.11054, arXiv:2112.13794, arXiv:2111.13916, arXiv:2201.06948, arXiv:2201.05224, arXiv:2202.04207, arXiv:2205.08785

The Pomeron Regge trajectory underlies the dynamics dependence of hadronic total cross sections and diffractive reactions at high energies. The physics of the Pomeron is closely related to the gluon distribution function and the gluon gravitational form factor of the target hadron. In this article we examine the scale dependence of the nonperturbative gluon distribution in the nucleon and the pion which was derived in a previous article [Phys. Rev. D 104, 114005 (2021)] in the framework of holographic light-front QCD and the Veneziano model. We argue that the QCD evolution of the gluon distribution function $g(x,\mu)$ to large $\mu^2$ leads to a single scale-dependent Pomeron. The resulting Pomeron trajectory $\alpha_P(t, \mu)$ not only depends on the momentum transfer squared $t$, but also on the physical scale $\mu$ of the amplitude, such as the virtuality $Q^2$ of the interacting photon in inclusive diffractive electroproduction. This can explain not only the $Q^2$ evolution of the proton structure function $F_2(x,Q^2)$ at small $x$, but also the observed energy and $Q^2$ dependence of high energy diffractive processes involving virtual photons up to LHC energies., Comment: 22 pages, 6 figures

Recent observations of the angular correlation spectra in the decays $ {\rm ^4He}^*\to {\rm ^4He}+ e^+e^-$ and $ {\rm ^8Be}^*\to {\rm ^8Be}+ e^+e^-$ have been suggested as due to the creation and subsequent decay to an electron-positron pair of a new light particle with a mass of $\sim 17$ MeV. In this work, we present a calculation of the invariant $m_{e^+e^-}$ mass spectrum of the electromagnetic transition of an excited state of helium and estimate the differential and total width of the decay. We investigate the possibility that the source of the signal is an $e^+ e^-$ pair created by a new electromagnetic decay of $\rm ^4He$ caused by a proposed 12-quark hidden-color Fock state in the ${\rm {^4He}}$ nuclear wavefunction, the "hexadiquark.'' We find that we can fit the shape of the signal with the QCD Fock state at excitation energy ${\rm E^*}\simeq 17.9 $ MeV and a Gaussian form factor for the electromagnetic decay. We address the physical issues with the fit parameters using properties of the hexadiquark state. In light of this work, we emphasize the need for independent experimental confirmation or refutation of the ATOMKI results as well as further experiments to detect the proposed new excitation of ${\rm ^4He}$., Comment: Condensed version, 8 pages, 3 figures, comments welcome

I survey recent developments in hadron physics which follow from the application of superconformal quantum mechanics and light-front holography. This includes new insights into the physics of color confinement, chiral symmetry, the spectroscopy and dynamics of hadrons, as well as surprising supersymmetric relations between the masses of mesons, baryons, and tetraquarks. I also will discuss some novel features of QCD -- such as color transparency, hidden color, and asymmetric intrinsic heavy-quark phenomena. The elimination of renormalization scale ambiguities and the modification of QCD sum rules due to diffractive phenomena are also briefly reviewed., Contribution to the Proceedings of the 24th Workshop, "What Comes Beyond the Standard Models", Bled, July 3. - 11., 2021. arXiv admin note: substantial text overlap with arXiv:1512.05100, arXiv:1601.06328, arXiv:1611.07194; text overlap with arXiv:1709.01191, arXiv:1511.04142

Hidden-color configurations are a key prediction of QCD with important physical consequences. In this work we examine a QCD color-singlet configuration in nuclei formed by combining six scalar [ud] diquarks in a strongly bound SU(3)C channel. The resulting hexadiquark state is a charge-2, spin-0, baryon number-4, isospin-0, color-singlet state. It contributes to alpha clustering in light nuclei and to the additional binding energy not saturated by ordinary nuclear forces in He4 as well as the alpha-nuclei sequence of interest for nuclear astrophysics. We show that the strongly bound combination of six scalar isospin-0 [ud] diquarks within the nuclear wave function - relative to free nucleons - provides a natural explanation of the EMC effect measured by the CLAS collaboration's comparison of nuclear parton distribution function ratios for a large range of nuclei. These experiments confirmed that the EMC effect; i.e., the distortion of quark distributions within nuclei, is dominantly identified with the dynamics of neutron-proton (“isophobic”) short-range correlations within the nuclear wave function rather than proton-proton or neutron-neutron correlations.

A general procedure for obtaining frame-independent three-dimensional light-front coordinate-space wave functions is introduced. The third spatial coordinate z̃ is the boost and Lorentz frame-independent coordinate conjugate to the light-front momentum coordinate x=k+P+ which appears in the momentum-space light-front wave functions underlying generalized parton distributions, structure functions, distribution amplitudes, form factors, and other hadronic observables. These causal light-front coordinate-space wave functions are used to derive a general expression for the quark distribution function of hadrons as an integral over the frame-independent longitudinal distance (the Ioffe time) between virtual-photon absorption and emission appearing in the forward virtual photon-hadron Compton scattering amplitude. Specific examples using models derived from light-front holographic QCD show that the spatial extent of the proton eigenfunction in the longitudinal direction can have a very large extent in z̃.

Heavy fermion pair production in $e^+e^-$ annihilation is a fundamental process in hadron physics and is of considerable interest for various phenomena. In this paper, we will apply the Principle of Maximum Conformality (PMC) to provide a comprehensive analysis of these processes. The PMC provides a systematic, unambiguous method for determining the renormalization scales of the QCD coupling constant for single-scale and multiple-scale applications. The resulting predictions eliminate any renormalization scheme-and-scale ambiguities, eliminate the factorial renormalon divergences, and are consistent with the requirements of the renormalization group. It is remarkable that two distinctly different scales are determined by using the PMC for heavy fermion pair production near the threshold region. One scale is the order of the fermion mass $m_f$, which enters the hard virtual corrections, and the other scale is of order $ v\,m_f$, where $v$ is the quark velocity, which enters the Coulomb rescattering amplitude. The PMC scales yield the correct physical behavior and reflect the virtuality of the propagating gluons (photons) for the QCD (QED) processes. Moreover, we demonstrate the consistency of PMC scale setting from QCD to QED. Perfect agreement between the Abelian unambiguous Gell-Mann-Low and the PMC scale-setting methods in the limit of zero number of colors is demonstrated., 8 pages, 6 figures, published version

Hidden-color configurations are a key prediction of QCD with important physical consequences. In this work we examine a QCD color-singlet configuration in nuclei formed by combining six scalar $[u d]$ diquarks in a strongly bound $\rm SU(3)_C$ channel. The resulting hexadiquark state is a charge-2, spin-0, baryon number-4, isospin-0, color-singlet state. It contributes to alpha clustering in light nuclei and to the additional binding energy not saturated by ordinary nuclear forces in \he as well as the alpha-nuclei sequence of interest for nuclear astrophysics. We show that the strongly bound combination of six scalar isospin-0 $[ud]$ diquarks within the nuclear wave function - relative to free nucleons - provides a natural explanation of the EMC effect measured by the CLAS collaboration's comparison of nuclear parton distribution function ratios for a large range of nuclei. These experiments confirmed that the EMC effect; i.e., the distortion of quark distributions within nuclei, is dominantly identified with the dynamics of neutron-proton (``isophobic'') short-range correlations within the nuclear wave function rather than proton-proton or neutron-neutron correlations., 9 pages. References with positive preliminary results from the MARATHON experiment added, clarifications and minor edits. Version accepted for publication

In the paper, we present QCD predictions for $��_{c} + ��$ production at an electron-position collider up to next-to-next-to-leading order (NNLO) accuracy without renormalization scale ambiguities. The NNLO total cross-section for $e^{+}+e^{-}\to��+��_{c}$ using the conventional scale-setting approach has large renormalization scale ambiguities, usually estimated by choosing the renormalization scale to be the $e^+ e^-$ center-of-mass collision energy $\sqrt{s}$. The Principle of Maximum Conformality (PMC) provides a systematic way to eliminate such renormalization scale ambiguities by summing the nonconformal $��$ contributions into the QCD coupling $��_s(Q^2)$. The renormalization group equation then sets the value of $��_s$ for the process. The PMC renormalization scale reflects the virtuality of the underlying process, and the resulting predictions satisfy all of the requirements of renormalization group invariance, including renormalization scheme invariance. After applying the PMC, we obtain a scale-and-scheme independent prediction, $��|_{\rm NNLO, PMC}\simeq 41.18$ fb for $\sqrt{s}$=10.6 GeV. The resulting pQCD series matches the series for conformal theory and thus has no divergent renormalon contributions. The large $K$ factor which contributes to this process reinforces the importance of uncalculated NNNLO and higher-order terms. Using the PMC scale-and-scheme independent conformal series and the $\rm Pad\acute{e}$ approximation approach, we predict $��|_{\rm NNNLO, PMC+Pade} \simeq 21.36$ fb, which is consistent with the recent BELLE measurement $��^{\rm obs}$=$16.58^{+10.51}_{-9.93}$ fb at $\sqrt{s} \simeq 10.6$ GeV. This procedure also provides a first estimate of the NNNLO contribution., 8 pages, 5 figures. Discussions improved and references updated. Revised version to be published in JHEP

We address the validity of the momentum sum rule for deep inelastic nuclear structure functions., 5 pages, 5 figures

A general procedure for obtaining frame-independent, three-dimensional light-front coordinate-space wave functions is introduced. The third spatial coordinate, $\tilde z$ , is the frame independent coordinate conjugate to the light-front momentum coordinate $x={k^+\over P^+}$ which appears in the momentum-space light-front wave functions underlying generalized parton distributions, structure functions, distribution amplitudes, form factors, and other hadronic observables. These causal light-front coordinate-space wave functions are used to derive a general expression for the quark distribution function of hadrons as an integral over the frame-independent longitudinal distance (the Ioffe time) between virtual-photon absorption and emission appearing in the forward virtual photon-hadron Compton scattering amplitude. Specific examples using models derived from light-front holographic QCD show that the spatial extent of the proton eigenfunction in the longitudinal direction can have very large extent in $\tilde z$., Comment: 6 pages, 6 figures, this version adds references, corrects a typographical error and contains more explanations regarding the use of the variable $\tilde z$

We predict the rate for exclusive double-charmonium production in electron-positron annihilation e+e−→J/ψ+ηc using pQCD and the NRQCD framework for hard, heavy-quarkonium exclusive processes. The cross sections measured at the B-factories Belle and BABAR at s=10.6 GeV disagree with the pQCD leading-order predictions by an order of magnitude. The predictions at next-to-leading order are, however, very sensitive to the choice of the renormalization scale, resulting in an apparent discrepancy between the theoretical prediction and the data. We show that this discrepancy can in fact be eliminated by applying the principle of maximum conformality (PMC) to set the renormalization scale. By carefully applying the PMC to different topologies of the annihilation process, one achieves precise pQCD predictions, together with improved perturbative convergence. We also observe that the single-photon-fragmentation QED correction is important, an effect that increases the total cross section by about 10%. The scale-fixed, scheme-independent cross section predicted by the PMC is σtot|PMC=20.35−3.8+3.5 fb, where the uncertainties come from the squared average of the errors due to the value of the charm mass and the uncertainty from the quarkonium wave functions at the origin. We find that the typical momentum flow of the process is 2.30 GeV, which explains the guessed choice of 2–3 GeV using conventional scale setting. The scale-fixed e+e−→J/ψ+ηc cross section predicted by the PMC shows agreement with the Belle and BABAR measurements.

We predict the rate for exclusive double-charmonium production in electron-positron annihilation $e^+ e^- \to J/\psi+\eta_c$ using perturbative quantum chromodynamics and the NRQCD framework for hard, heavy-quarkonium exclusive processes. The cross sections measured at the $B$-factories Belle and Babar at $\sqrt{s}=10.6$ GeV disagree with the pQCD leading-order predictions by an order of magnitude. The predictions at next-to-leading order are, however, very sensitive to the choice of the renormalization scale, resulting in an apparent discrepancy between the theoretical prediction and the data. We show that this discrepancy can in fact be eliminated by applying the Principle of Maximum Conformality (PMC) to set the renormalization scale. ... By carefully applying the PMC to different topologies of the annihilation process, one achieves precise pQCD predictions, together with improved perturbative convergence. We also observe that the single-photon-fragmentation QED correction is important, an effect which increases the total cross-section by about $10\%$. The scale-fixed, scheme-independent cross-section predicted by the PMC is $\sigma_{\rm tot}|_{\rm PMC}=20.35 ^{+3.5}_{-3.8}$ fb, where the uncertainties come from the squared average of the errors due to the value of the charm mass and the uncertainty from the quarkonium wavefunctions at the origin. We find that the typical momentum flow of the process is $2.30$ GeV, which explains the guessed choice of $2-3$ GeV using conventional scale-setting. The scale-fixed $e^+ e^- \to J/\psi+\eta_c$ cross-section predicted by the PMC shows excellent agreement with the Belle and Babar measurements, emphasizing the importance of a rigorous renormalization scale-setting procedure., Comment: 5 pages, 3 figures. Accepted for publication in PRD

The next-to-next-to-leading-order (NNLO) pQCD prediction for the γγ*→ηc form factor was evaluated in 2015 using nonrelativistic QCD (NRQCD). A strong discrepancy between the NRQCD prediction and the BABAR measurements was observed. Until now there has been no solution for this puzzle. In this paper, we present a NNLO analysis by applying the Principle of Maximum Conformality (PMC) to set the renormalization scale. By carefully dealing with the light-by-light diagrams at the NNLO level, the resulting high precision PMC prediction agrees with the BABAR measurements within errors, and the conventional renormalization scale uncertainty is eliminated. The PMC is consistent with all of the requirements of the renormalization group, including scheme-independence. The application of the PMC thus provides a rigorous solution for the γγ*→ηc form factor puzzle, emphasizing the importance of correct renormalization scale-setting. The results also support the applicability of NRQCD to hard exclusive processes involving charmonium.

The next-to-next-to-leading order (NNLO) pQCD prediction for the $\gamma\gamma^* \to \eta_c$ form factor was evaluated in 2015 using nonrelativistic QCD (NRQCD). A strong discrepancy between the NRQCD prediction and the BaBar measurements was observed. Until now there has been no solution for this puzzle. In this paper, we present a NNLO analysis by applying the Principle of Maximum Conformality (PMC) to set the renormalization scale. By carefully dealing with the light-by-light diagrams at the NNLO level, the resulting high precision PMC prediction agrees with the BaBar measurements within errors, and the conventional renormalization scale uncertainty is eliminated. The PMC is consistent with all of the requirements of the renormalization group, including scheme-independence. The application of the PMC thus provides a rigorous solution for the $\gamma\gamma^* \to \eta_c$ form factor puzzle, emphasizing the importance of correct renormalization scale-setting. The results also support the applicability of NRQCD to hard exclusive processes involving charmonium., Comment: 5 pages, 4 figures. References updated. To be published in Phys.Rev.D

The measured Bd→π0π0 branching fraction deviates significantly from conventional QCD predictions, a puzzle which has persisted for more than 10 years. This may be a hint of new physics beyond the Standard Model; however, as we shall show in this paper, the pQCD prediction is highly sensitive to the choice of the renormalization scales which enter the decay amplitude. In the present paper, we show that the renormalization scale uncertainties for B→ππ can be greatly reduced by applying the Principle of Maximum Conformality (PMC), and more precise predictions for CP-averaged branching ratios B(B→ππ) can be achieved. Combining the errors in quadrature, we obtain B(Bd→π0π0)|PMC=(0.98−0.31+0.44)×10−6 by using the light-front holographic low-energy model for the running coupling. All of the CP-averaged B→ππ branching fractions predicted by the PMC are consistent with the Particle Data Group average values and the recent Belle data. Thus, the PMC provides a possible solution for the Bd→π0π0 puzzle.

The QCD light-front Hamiltonian equation HLFΨ=M2Ψ derived from quantization at fixed LF time τ=t + z/c provides a causal, frame-independent method for computing hadron spectroscopy as well as dynamical observables such as structure functions, transverse momentum distributions, and distribution amplitudes. The QCD Lagrangian with zero quark mass has no explicit mass scale. de Alfaro, Fubini, and Furlan (dAFF) have made an important observation that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator. If one applies the dAFF procedure to the QCD light-front Hamiltonian, it leads to a color-confining potential κ4ζ2 for mesons, where ζ2 is the LF radial variable conjugate to the qq¯ invariant mass squared. The same result, including spin terms, is obtained using light-front holography, the duality between light-front dynamics and AdS5, if one modifies the AdS5 action by the dilaton eκ2z2 in the fifth dimension z. When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions provide a unified Regge spectroscopy of meson, baryon, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons and baryons and a universal Regge slope. The pion qq¯ eigenstate has zero mass at mq=0. The superconformal relations also can be extended to heavy-light quark mesons and baryons. This approach also leads to insights into the physics underlying hadronization at the amplitude level. I will also discuss the remarkable features of the Poincaré invariant, causal vacuum defined by light-front quantization and its impact on the interpretation of the cosmological constant. AdS/QCD also predicts the analytic form of the nonperturbative running coupling αs(Q2)∝e-Q2/4κ2. The mass scale κ underlying hadron masses can be connected to the parameter ΛMS¯ in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling αs(Q2) defined at all momenta. One obtains empirically viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. Finally, I address the interesting question of whether the momentum sum rule is valid for nuclear structure functions.

The next-to-next-to-leading order (NNLO) pQCD prediction for the $����^* \to ��_c$ form factor was evaluated in 2015 using nonrelativistic QCD (NRQCD). A strong discrepancy between the NRQCD prediction and the BaBar measurements was observed. Until now there has been no solution for this puzzle. In this paper, we present a NNLO analysis by applying the Principle of Maximum Conformality (PMC) to set the renormalization scale. By carefully dealing with the light-by-light diagrams at the NNLO level, the resulting high precision PMC prediction agrees with the BaBar measurements within errors, and the conventional renormalization scale uncertainty is eliminated. The PMC is consistent with all of the requirements of the renormalization group, including scheme-independence. The application of the PMC thus provides a rigorous solution for the $����^* \to ��_c$ form factor puzzle, emphasizing the importance of correct renormalization scale-setting. The results also support the applicability of NRQCD to hard exclusive processes involving charmonium., 5 pages, 4 figures. References updated. To be published in Phys.Rev.D

This document collects the proceedings of the PHOTON 2017 conference ("International Conference on the Structure and the Interactions of the Photon", including the 22th "International Workshop on Photon-Photon Collisions", and the "International Workshop on High Energy Photon Colliders") held at CERN (Geneva) in May 2017. The latest experimental and theoretical developments on the topics of the PHOTON conference series are covered: (i) $\gamma\,\gamma$ processes in e$^+$e$^-$, proton-proton (pp) and nucleus-nucleus (AA) collisions at current and future colliders, (ii) $\gamma$-hadron interactions in e$^\pm$p, pp, and AA collisions, (iii) final-state photon production (including Standard Model studies and searches beyond it) in pp and AA collisions, and (iv) high-energy $\gamma$-ray astrophysics. These proceedings are dedicated to the memory of Maria Krawczyk., Comment: 296 pages. CERN-Proceedings-2018-001 (CERN, Geneva, 2018), to appear. arXiv admin note: substantial text overlap with arXiv:1804.05614, arXiv:1708.06683, arXiv:1709.09044, arXiv:1708.00912, arXiv:1708.07173, arXiv:1709.02985, arXiv:1709.00176, arXiv:1709.05167, arXiv:1708.05756, arXiv:1708.09759, arXiv:1708.07531, arXiv:1703.08450, arXiv:1711.02551, arXiv:1511.07794, arXiv:1712.10104, arXiv:1708.05776, arXiv:1712.10202, arXiv:1709.07110, arXiv:1702.08730, arXiv:1709.02648, arXiv:1411.6397

An unexpected result at the RHIC and the LHC is the observation that high-multiplicity hadronic events in heavy-ion and proton-proton collisions are distributed as two "ridges", approximately flat in rapidity and opposite in azimuthal angle. We propose that the origin of these events is due to the inelastic collisions of aligned gluonic flux tubes that underly the color confinement of the quarks in each proton. We predict that high-multiplicity hadronic ridges will also be produced in the high energy photon-photon collisions accessible at the LHC in ultra-peripheral proton-proton collisions or at a high energy electron-positron collider. We also note the orientation of the flux tubes between the quark and antiquark of each high energy photon will be correlated with the plane of the scattered proton or lepton. Thus hadron production and ridge formation can be controlled in a novel way at the LHC by observing the azimuthal correlations of the scattering planes of the ultra-peripheral protons with the orientation of the produced ridges. Photon-photon collisions can thus illuminate the fundamental physics underlying the ridge effect and the physics of color confinement in QCD., CERN Proceedings, Vol 1 (2018): Proceedings of the PHOTON'17 Conference

A remarkable feature of QCD is that the mass scale which controls color confinement and hadron mass scales does not appear explicitly in the QCD Lagrangian. However, de Alfaro, Fubini, and Furlan have shown that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator. Applying the same procedure to the light-front Hamiltonian leads to a unique confinement potential $\kappa^4 \zeta^2$ for mesons, where $\zeta$ is the LF radial variable conjugate to the invariant mass. The same result, including spin terms, is obtained using light-front holography, the duality between the front form and AdS$_5,$ if one modifies the action by the dilaton $e^{\kappa^2 z^2}$ in the fifth dimension $z$. Generalizing this procedure using superconformal algebra, leads to a unified Regge spectroscopy of meson, baryon, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons and baryons of the same parity. One also predicts observables such as hadron structure functions, transverse momentum distributions, and the distribution amplitudes defined from the hadronic light-front wavefunctions. The mass scale underlying confinement and hadron masses can be connected to the mass parameter in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling defined at all momenta and the determination of a momentum scale which sets the interface between perturbative and nonperturbative hadron dynamics. I also discuss evidence that the antishadowing of nuclear structure functions is non-universal, and why shadowing and antishadowing phenomena may be incompatible with sum rules for nuclear parton distribution functions., Comment: Presented at Light-Cone 2016, Challenges in Experimental and Theoretical Physics on the Light Front, September 5-8, 2015, IST, Universidade de Lisboa, Lisbon, Portugal. arXiv admin note: substantial text overlap with arXiv:1601.06328, arXiv:1606.04638, arXiv:1512.05100, arXiv:1511.04142

We study the exclusive double-photon annihilation processes, $e^+ e^- \to \gamma \gamma^\ast\to \gamma V^0$ and $e^+ e^- \to \gamma^\ast \gamma^\ast \to V^0_a V^0_b,$ where the $V^0_i$ is a neutral vector meson produced in the forward kinematical region: $s \gg -t$ and $-t \gg \Lambda_{\rm QCD}^2$. We show how the differential cross sections $\frac{d\sigma}{dt}$, as predicted by QCD, have additional falloff in the momentum transfer squared $t$ due to the QCD compositeness of the hadrons, consistent with the leading-twist fixed-$\theta_{\rm CM} $ scaling laws. However, even though they are exclusive channels and not associated with the conventional electron-positron annihilation process $e^+ e^- \to \gamma^\ast \to q \bar q,$ these total cross sections $\sigma(e^+ e^- \to \gamma V^0) $ and $\sigma(e^+ e^- \to V^0_a V^0_b),$ integrated over the dominant forward- and backward-$\theta_{\rm CM}$ angular domains, scale as $1/s$, and thus contribute to the leading-twist scaling behavior of the ratio $R_{e^+ e^-}$. We generalize these results to exclusive double-electroweak vector-boson annihilation processes accompanied by the forward production of hadrons, such as $e^+ e^- \to Z^0 V^0$ and $e^+ e^- \to W^-\rho^+$. These results can also be applied to the exclusive production of exotic hadrons such as tetraquarks, where the cross-section scaling behavior can reveal their multiquark nature., Comment: 10 pages

The discovery of extraterrestrial neutrinos in the $\sim$ 30 TeV -- PeV energy range by IceCube provides new constraints on high energy astrophysics. An important background to the signal are the prompt neutrinos which originate from the decay of charm hadrons produced by high energy cosmic-ray particles interacting in the Earth's atmosphere. It is conventional to use the calculations of charm hadroproduction using gluon splitting $g \to c \bar c$ alone. However, QCD predicts an additional "intrinsic" component of the heavy quark distribution which arises from diagrams where heavy quarks are multiply connected to the proton's valence quarks. We estimate the prompt neutrino spectrum due to intrinsic charm. We find that the atmospheric prompt neutrino flux from intrinsic charm is comparable to those calculated using QCD computations not including intrinsic charm, once we normalize the intrinsic charm differential cross sections to the ISR and the LEBC-MPS collaboration data. In future, IceCube will constrain the intrinsic charm content of the proton and will contribute to one of the major questions in high energy physics phenomenology., Comment: v3: 13 pages, 4 figures. Added more details about the calculation. Conclusions unchanged. Accepted in PRD

We study the exclusive double-photon annihilation processes, $e^+ e^- \to ����^\ast\to ��V^0$ and $e^+ e^- \to ��^\ast ��^\ast \to V^0_a V^0_b,$ where the $V^0_i$ is a neutral vector meson produced in the forward kinematical region: $s \gg -t$ and $-t \gg ��_{\rm QCD}^2$. We show how the differential cross sections $\frac{d��}{dt}$, as predicted by QCD, have additional falloff in the momentum transfer squared $t$ due to the QCD compositeness of the hadrons, consistent with the leading-twist fixed-$��_{\rm CM} $ scaling laws. However, even though they are exclusive channels and not associated with the conventional electron-positron annihilation process $e^+ e^- \to ��^\ast \to q \bar q,$ these total cross sections $��(e^+ e^- \to ��V^0) $ and $��(e^+ e^- \to V^0_a V^0_b),$ integrated over the dominant forward- and backward-$��_{\rm CM}$ angular domains, scale as $1/s$, and thus contribute to the leading-twist scaling behavior of the ratio $R_{e^+ e^-}$. We generalize these results to exclusive double-electroweak vector-boson annihilation processes accompanied by the forward production of hadrons, such as $e^+ e^- \to Z^0 V^0$ and $e^+ e^- \to W^-��^+$. These results can also be applied to the exclusive production of exotic hadrons such as tetraquarks, where the cross-section scaling behavior can reveal their multiquark nature., 10 pages

Light-Front Quantization -- Dirac's "Front Form" -- provides a physical, frame-independent formalism for hadron dynamics and structure. Observables such as structure functions, transverse momentum distributions, and distribution amplitudes are defined from the hadronic LFWFs. One obtains new insights into the hadronic mass scale, the hadronic spectrum, and the functional form of the QCD running coupling in the nonperturbative domain using light-front holography. In addition, superconformal algebra leads to remarkable supersymmetric relations between mesons and baryons. I also discuss evidence that the antishadowing of nuclear structure functions is non-universal, i.e., flavor dependent, and why shadowing and antishadowing phenomena may be incompatible with the momentum and other sum rules for the nuclear parton distribution functions., To appear in the Proceedings of the 18th Bled workshop "What Comes Beyond the Standard Models", Bled, Slovenia, July 11-19, 2015. arXiv admin note: substantial text overlap with arXiv:1511.04142

A primary problem for perturbative QCD analyses is how to set the renormalization scale of the QCD running coupling in order to achieve maximally precise fixed-order predictions for physical observables. The Principle of Maximum Conformality (PMC) eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, giving predictions which are independent of the choice of renormalization scheme. The scales of the QCD couplings and the effective number of quark flavors are set order by order in the pQCD series. The PMC has a solid theoretical foundation, satisfying the standard renormalization group invariance and all of the the self-consistency conditions derived from the renormalization group......In this brief report, we summarize the results of our recent PMC applications for a number of collider processes, emphasizing their generality and applicability....... These results demonstrate that the application of the PMC systematically eliminates a major theoretical uncertainty for pQCD predictions, thus increasing the sensitivity of the colliders to possible new physics beyond the Standard Model., 10 pages, 4 figures. The title has been changed. This review, submitted to Frontiers of Physics, is based on a contribution by S.J.B. at the Conference {\it Workshop on Physics at a Future High Intensity Collider @ 2-7 GeV in China} Hefei, China January 14-16, 2015

This document presents the recommendations and scientific conclusions from the Town Meeting on QCD and Hadronic Physics that took place in the period 13-15 September 2014 at Temple University as part of the NSAC 2014 Long Range Planning process. It highlights progress in hadron physics in the seven years since the 2007 Long Range Plan (LRP07), and presents a vision for the future by identifying key questions and plausible paths to solutions which should define our next decade. In defining the priority of outstanding physics opportunities for the future, both prospects for the short (roughly 5 years) and longer term (beyond 10 years) are identified together with the facilities, personnel and other resources needed to maximize the discovery potential in hadronic physics worldwide. In this connection, the potential of an electron ion collider is highlighted., Comment: 48 pages, 19 figures. Summary of the DNP Town Meeting, Temple University, 13-15 September 2014

Abelian gauge theory in $d\neq 4$ spacetime dimensions is an example of a scale invariant theory which does not possess conformal symmetry -- the special conformal transformation(SCT) explicitly breaks the gauge invariance of the theory. In this work, we construct a non-local gauge-invariant extension of the SCT, which is compatible with the BRST formalism and defines a new symmetry of the physical Hilbert space of the Maxwell theory for any dimension $d\geqslant 3$. We prove the invariance of the Maxwell theory in $d\geqslant 3$ by explicitly showing that the gauge-invariant two-point correlation functions, the action, and the classical equation of motion are unchanged under such a transformation., Comment: 23 pages

The $12~$GeV electron beam energy at Jefferson Laboratory provides ideal electroproduction kinematics for many novel tests of QCD in both the perturbative and nonperturbative domains. These include tests of the quark flavor dependence of the nuclear structure functions; measurements of the QCD running coupling at soft scales; measurements of the diffractive deep inelastic structure function; measurements of exclusive contributions to the $T-$ odd Sivers function; the identification of ``odderon" contributions; tests of the spectroscopic and dynamic features of light-front holography, as well as ``meson-nucleon supersymmetry"; the production of open and hidden charm states in the heavy-quark threshold domain; and the production of exotic hadronic states such as pentaquarks, tetraquarks and even octoquarks containing charm quarks. One can also study fundamental features of QCD at JLab$12$ such as the ``hidden color" of nuclear wavefunctions, the ``color transparency" of hard exclusive processes, and the ``intrinsic strangeness and charm" content of the proton wavefunction. I will also discuss evidence that the antishadowing of nuclear structure functions is non-universal; i.e., flavor dependent. I will also present arguments why shadowing and antishadowing phenomena may be incompatible with the momentum and other sum rules for the nuclear parton distribution functions. I will also briefly review new insights into the hadron mass scale, the hadron mass spectrum, the functional form of the QCD coupling in the nonperturbative domain predicted by light-front holography, and how superconformal algebra leads to remarkable supersymmetric relations between mesons and baryons., Comment: Presented at the QCD Evolution 2015 Workshop, Jefferson Laboratory, May 26-30, 2015

The valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a relativistic equation of motion with an effective confining potential $U$ which systematically incorporates the effects of higher quark and gluon Fock states. If one requires that the effective action which underlies the QCD Lagrangian remains conformally invariant and extends the formalism of de Alfaro, Fubini and Furlan to light front Hamiltonian theory, the potential $U$ has a unique form of a harmonic oscillator potential, and a mass gap arises. The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the same slope in the radial quantum number $n$ and orbital angular momentum $L$. Only one mass parameter $\kappa$ appears. Light-front holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. We also show how the mass scale $\kappa$ underlying confinement and hadron masses determines the scale $\Lambda_{\overline{MS}} $ controlling the evolution of the perturbative QCD coupling. The relation between scales is obtained by matching the nonperturbative dynamics, as described by an effective conformal theory mapped to the light-front and its embedding in AdS space, to the perturbative QCD regime computed to four-loop order. The result is an effective coupling defined at all momenta. The predicted value $\Lambda_{\overline{MS}} = 0.328 \pm 0.034$ GeV is in agreement with the world average $0.339 \pm 0.010$ GeV. The analysis applies to any renormalization scheme., Comment: Presented by SJB at "Theory and Experiment for Hadrons on the Light-Front" (Light Cone 2014) } May 26 -- 30, 2013, Raleigh, North Carolina

The measured $B_d \to \pi^0\pi^0$ branching fraction deviates significantly from conventional QCD predictions, a puzzle which has persisted for more than 10 years. This may be a hint of new physics beyond the Standard Model; however, as we shall show in this paper, the pQCD prediction is highly sensitive to the choice of the renormalization scales which enter the decay amplitude. In the present paper, we show that the renormalization scale uncertainties for $B\to \pi\pi$ can be greatly reduced by applying the Principle of Maximum Conformality (PMC), and more precise predictions for CP-averaged branching ratios ${\cal B}(B\to\pi\pi)$ can be achieved. Combining the errors in quadrature, we obtain ${\cal B}(B_{d}\to \pi^0\pi^0)|_{\rm PMC} = \left(0.98^{+0.44}_{-0.31}\right) \times10^{-6}$ by using the light-front holographic low-energy model for the running coupling. All of the CP-averaged $B\to\pi\pi$ branching fractions predicted by the PMC are consistent with the Particle Data Group average values and the recent Belle data. Thus, the PMC provides a possible solution for the $B_d \to \pi^0\pi^0$ puzzle., Comment: Comments: 7 pages, 1 figure, to be published at Phys.Lett.B

We present a new dynamical picture that identifies the formation of the exotic $\bar c c$-containing states $XY \! Z$ with the confinement-induced hadronization of a rapidly separating pair of a compact diquark and antidiquark. This picture combines the advantages of diquark-based models, which can accommodate much of the known $XY \! Z$ spectrum, with the experimental fact that such states are both relatively narrow and are produced promptly. It also naturally explains the preference of some of the exotic states to decay to $\psi(2S)$, rather than $J/\psi$, in terms of a simple wave-function overlap effect., Comment: 5 pages, 4 .eps figures, ReVTeX. References added

We briefly review the remarkable connections between light-front QCD, gravity in AdS space, and conformal quantum mechanics. We discuss, in particular, the group theoretical and geometrical aspects of the underlying one-dimensional quantum field theory. The resulting effective theory leads to a phenomenologically successful confining interaction potential in the relativistic light-front wave equation which incorporates relevant non-perturbative dynamical aspects of hadron physics., Comment: 12 pages, 2 figures. Presented by HGD at the International Fall Workshop Geometry and Physics II, Institut Henri Poincare, Paris, November 28 and 29, 2013

We describe a procedure to extend the light-front holographic approach to hadronic physics to include light-quark masses. The proposed framework allows us to extend the formalism of de Alfaro, Fubini and Furlan to the frame-independent light-front Hamiltonian theory in the approximation where the dynamics in the invariant transverse variable is unchanged to first order in the quark masses. The confinement potential follows from an effective theory which encodes the fundamental conformality of the classical QCD Lagrangian and leads to a semiclassical relativistic light-front wave equation for arbitrary spin. In particular, the K meson spectrum is successfully described without modifying the emerging confinement scale. The Wilson loop criteria for confinement is maintained, since for light quark masses a harmonic potential and linear Regge trajectories in the light-front form of dynamics corresponds to a linear potential in the usual instant-form., Comment: 14 pages, 1 figure. Based on an invited talk, presented by GdT at the Rencontres de Moriond, QCD and High Energy Interactions (2014)

A valid prediction for a physical observable from quantum field theory should be independent of the choice of renormalization scheme -- this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance is a challenging problem for perturbative QCD (pQCD), since a truncated perturbation series does not automatically satisfy the requirements of the renormalization group. Two distinct approaches for satisfying the RGI principle have been suggested in the literature. One is the "Principle of Maximum Conformality" (PMC) in which the terms associated with the $\beta$-function are absorbed into the scale of the running coupling at each perturbative order; its predictions are scheme and scale independent at every finite order. The other approach is the "Principle of Minimum Sensitivity" (PMS), which is based on local RGI; the PMS approach determines the optimal renormalization scale by requiring the slope of the approximant of an observable to vanish. In this paper, we present a detailed comparison of the PMC and PMS procedures by analyzing two physical observables $R_{e+e-}$ and $\Gamma(H\to b\bar{b})$ up to four-loop order in pQCD. At the four-loop level, the PMC and PMS predictions for both observables agree within small errors with those of conventional scale setting assuming a physically-motivated scale, and each prediction shows small scale dependences. However, the convergence of the pQCD series at high orders, behaves quite differently: The PMC displays the best pQCD convergence since it eliminates divergent renormalon terms; in contrast, the convergence of the PMS prediction is questionable, often even worse than the conventional prediction based on an arbitrary guess for the renormalization scale. ......, Comment: 20 pages, 5 figures. References updated and discussions improved. To be published in Reports on Progress in Physics as a Review Article

The valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a relativistic equation of motion with an effective confining potential $U$ which systematically incorporates the effects of higher quark and gluon Fock states. If one requires that the effective action which underlies the QCD Lagrangian remains conformally invariant and extends the formalism of de Alfaro, Fubini and Furlan to light front Hamiltonian theory, the potential $U$ has a unique form of a harmonic oscillator potential, and a mass gap arises. The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the same slope in the radial quantum number $n$ and orbital angular momentum $L$. Only one mass parameter $��$ appears. Light-front holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. We also show how the mass scale $��$ underlying confinement and hadron masses determines the scale $��_{\overline{MS}} $ controlling the evolution of the perturbative QCD coupling. The relation between scales is obtained by matching the nonperturbative dynamics, as described by an effective conformal theory mapped to the light-front and its embedding in AdS space, to the perturbative QCD regime computed to four-loop order. The result is an effective coupling defined at all momenta. The predicted value $��_{\overline{MS}} = 0.328 \pm 0.034$ GeV is in agreement with the world average $0.339 \pm 0.010$ GeV. The analysis applies to any renormalization scheme., Presented by SJB at "Theory and Experiment for Hadrons on the Light-Front" (Light Cone 2014) } May 26 -- 30, 2013, Raleigh, North Carolina

We show that (a) the conformal properties of Anti-de Sitter (AdS) space, (b) the properties of a field theory in one dimension under the full conformal group found by de Alfaro, Fubini and Furlan, and (c) the frame-independent single-variable light-front Schr\"odinger equation for bound states all lead to the same result: a relativistic nonperturbative model which successfully incorporates salient features of hadronic physics, including confinement, linear Regge trajectories, and results which are conventionally attributed to spontaneous chiral symmetry breaking., Comment: Presented by SJB at the Third Workshop on the QCD Structure of the Nucleon (QCD-N'12), Bilbao, Spain, October 22-26, 2012. This work was supported by the Department of Energy contract DE--AC02--76SF00515

The collisions of high energy photons produced at an electron-positron collider provide a comprehensive laboratory for testing QCD, electroweak interactions, and extensions of the Standard Model. The luminosity and energy of the colliding photons produced by back-scattering laser beams is expected to be comparable to that of the primary $e^+e^-$ collisions. In this overview, we shall focus on tests of electroweak theory in photon-photon annihilation, particularly $\gamma\gamma \rightarrow W^+ W^-$, $\gamma\gamma \rightarrow $ Higgs bosons, and higher-order loop processes, such as $\gamma\gamma \rightarrow \gamma\gamma, Z \gamma$ and $ZZ.$ Since each photon can be resolved into a $W^+ W^-$ pair, high energy photon-photon collisions can also provide a remarkably background-free laboratory for studying $WW$ collisions and annihilation. We also review high energy $\gamma\gamma$ tests of quantum chromodynamics, such as the scaling of the photon structure function, $t \bar t$ production, mini-jet processes, and diffractive reactions., Comment: uses PHYZZX, 52 pages, 30 figures (available upon request), SLAC-PUB-6571

A major contribution to the uncertainty of finite-order perturbative QCD predictions is the perceived ambiguity in setting the renormalization scale $\mu_r$. For example, by using the conventional way of setting $\mu_r \in [m_t/2,2m_t]$, one obtains the total $t \bar{t}$ production cross-section $\sigma_{t \bar{t}}$ with the uncertainty $\Delta \sigma_{t \bar{t}}/\sigma_{t \bar{t}}\sim ({}^{+3%}_{-4%})$ at the Tevatron and LHC even for the present NNLO level. The Principle of Maximum Conformality (PMC) eliminates the renormalization scale ambiguity in precision tests of Abelian QED and non-Abelian QCD theories. In this paper we apply PMC scale-setting to predict the $t \bar t$ cross-section $\sigma_{t\bar{t}}$ at the Tevatron and LHC colliders. It is found that $\sigma_{t\bar{t}}$ remains almost unchanged by varying $\mu^{\rm init}_r$ within the region of $[m_t/4,4m_t]$. The convergence of the expansion series is greatly improved. For the $(q\bar{q})$-channel, which is dominant at the Tevatron, its NLO PMC scale is much smaller than the top-quark mass in the small $x$-region, and thus its NLO cross-section is increased by about a factor of two. In the case of the $(gg)$-channel, which is dominant at the LHC, its NLO PMC scale slightly increases with the subprocess collision energy $\sqrt{s}$, but it is still smaller than $m_t$ for $\sqrt{s}\lesssim 1$ TeV, and the resulting NLO cross-section is increased by $\sim 20%$. As a result, a larger $\sigma_{t\bar{t}}$ is obtained in comparison to the conventional scale-setting method, which agrees well with the present Tevatron and LHC data. More explicitly, by setting $m_t=172.9\pm 1.1$ GeV, we predict $\sigma_{\rm Tevatron,\;1.96\,TeV} = 7.626^{+0.265}_{-0.257}$ pb, $\sigma_{\rm LHC,\;7\,TeV} = 171.8^{+5.8}_{-5.6}$ pb and $\sigma_{\rm LHC,\;14\,TeV} = 941.3^{+28.4}_{-26.5}$ pb. [full abstract can be found in the paper.], Comment: 15 pages, 11 figures, 5 tables. Fig.(9) is corrected

We show that the nonperturbative light-front dynamics of relativistic hadronic bound states has a dual semiclassical gravity description on a higher dimensional warped AdS space in the limit of zero quark masses. This mapping of AdS gravity theory to the boundary quantum field theory, quantized at fixed light-front time, allows one to establish a precise relation between holographic wave functions in AdS space and the light-front wavefunctions describing the internal structure of hadrons. The resulting AdS/QCD model gives a remarkably good accounting of the spectrum, elastic and transition form factors of the light-quark hadrons in terms of one parameter, the QCD gap scale. The light-front holographic approach described here thus provides a frame-independent first approximation to the light-front Hamiltonian problem for QCD. This article is based on lectures at the Niccolo Cabeo International School of Hadronic Physics, Ferrara, Italy, May 2011., Invited lectures presented by GdT at the Niccolo Cabeo International School of Hadronic Physics, Ferrara, Italy, May 2011 (73 pages, 14 figures)

We introduce a generalization of the conventional renormalization schemes used in dimensional regularization, which illuminates the renormalization scheme and scale ambiguities of pQCD predictions, exposes the general pattern of nonconformal {\beta_i}-terms, and reveals a special degeneracy of the terms in the perturbative coefficients. It allows us to systematically determine the argument of the running coupling order by order in pQCD in a form which can be readily automatized. The new method satisfies all of the principles of the renormalization group and eliminates an unnecessary source of systematic error., Comment: 5 pages, 1 figure, revised to match the published version

I discuss several novel and unexpected aspects of quantum chromodynamics. These include: (a) the nonperturbative origin of intrinsic strange, charm and bottom quarks in the nucleon at large light-cone momenta x; the breakdown of pQCD factorization theorems due to the lensing effects of initial- and final-state interactions; (b) important corrections to pQCD scaling for inclusive reactions due to processes in which hadrons are created at high transverse momentum directly in the hard processes and their relation to the baryon anomaly in high-centrality heavy-ion collisions; and (c) the nonuniversality of quark distributions in nuclei. I also discuss some novel theoretical perspectives in QCD: (a) light-front holography -- a relativistic, color-confining, first approximation to QCD based on the AdS/CFT correspondence principle; (b) the principle of maximum conformality -- a method which determines the renormalization scale at finite order in perturbation theory yielding scheme independent results; (c) the replacement of quark and gluon vacuum condensates by "in-hadron condensates" and how this helps to resolves the conflict between QCD vacuum and the cosmological constant., Comment: Invited talk, presented at the International Symposium on Subnuclear Physics: Past, Present and Future, held at the Pontifical Academy of Sciences in the Vatican from 30 Oct. to 2 Nov. 2011

Transversity observables, such as the T-odd single-spin asymmetry measured in deep inelastic lepton scattering on polarized protons, and the distributions which are measured in deeply virtual Compton scattering provide important constraints on the fundamental quark and gluon structure of the proton. In this talk I discuss the challenge of computing these observables from first principles; i.e., quantum chromodynamics, itself. A key step is the determination of the frame-independent light-front wavefunctions (LFWFs) of hadrons -- the QCD eigensolutions which are analogs of the Schrodinger wavefunctions of atomic physics. The lensing effects of initial-state and final-state interactions, acting on LFWFs with different orbital angular momentum, lead to the T-odd transversity observables such as the Sivers, Collins, and Boer-Mulders distributions. The lensing effect also leads to leading-twist phenomena which break leading-twist factorization, such as the breakdown of the Lam-Tung relation in Drell-Yan reactions. A similar rescattering mechanism also leads to diffractive deep inelastic scattering, as well as nuclear shadowing and non-universal antishadowing. It is thus important to distinguish "static" structure functions, the probability distributions computed from the target hadron's light-front wavefunctions, versus "dynamical" structure functions which include the effects of initial- and final-state rescattering. I also discuss related effects, such as the J=0 fixed pole contribution which appears in the real part of the virtual Compton amplitude. AdS/QCD, together with "Light-Front Holography", provides a simple Lorentz-invariant color-confining approximation to QCD which is successful in accounting for light-quark meson and baryon spectroscopy as well as hadronic LFWFs., Presented at Transversity 2011: The 3rd International Workshop On Transverse Polarization Phenomena In Hard Scattering, 29 August - 2 September 2011, Veli Lozinj, Croatia