Search

We present a new approach to determining the strong coupling $\alpha_s(Q)$, over the entire range of validity of perturbative QCD, for scales above $\Lambda_{\mathrm{QCD}}$ and up to the Planck scale $\sim1.22\cdot10^{19}$\,GeV, with the highest precision and using the data of a single experiment. In particular, we use the results obtained for the thrust ($T$) and $C$-parameter ($C$) distributions in $e^+e^-$ annihilation at a single annihilation energy $\sqrt{s}=M_Z$ (i.e.\ at the $Z^0$ peak). This new method is based on the \emph{intrinsic conformality} (iCF) and on the Infinite-Order Scale Setting, using the Principle of Maximum Conformality (i.e.\ the PMC$_\infty$), which allows a rigorous determination of the renormalization scales for the event-shape variable distributions satisfying all of the requirements of Renormalization Group Invariance, including renormalization-scheme independence and consistency with Abelian theory in the $N_C \to 0$ limit. This new method is based on the scale-invariance of the iCF, which allows determination of $\alpha_s(\mu_0)$ at any scale $\mu_0$, and on the Maximum Likelihood statistical approach. We introduce a novel approach to determining the best-fitting range based on the most-likely-lowest $\chi^2$ calculated considering all possible intervals among the entire range of bins available in the perturbative region. This new method improves the precision and leads to results that are statistically more reliable. In particular, we obtain the following results for the running coupling: $\alpha_s(M_Z)=0.1170^{+0.0012}_{-0.0010}$ from thrust and $\alpha_s(M_Z)=0.1181^{+0.0013}_{-0.0009}$ for $C$-parameter in the $\overline{\mathrm{MS}}$ scheme at NNLO..., Comment: 10 pages, 4 figures

In quantum field theory, the vacuum is widely considered to be a complex medium populated with virtual particle + antiparticle pairs. To an observer experiencing uniform acceleration, it is generally held that these virtual particles become real, appearing as a gas at a temperature which grows with the acceleration. This is the Unruh effect. However, it can be shown that vacuum complexity is an artifact, produced by treating quantum field theory in a manner that does not manifestly enforce causality. Choosing a quantization approach that patently enforces causality, the quantum field theory vacuum is barren, bereft even of virtual particles. We show that acceleration has no effect on a trivial vacuum; hence, there is no Unruh effect in such a treatment of quantum field theory. Since the standard calculations suggesting an Unruh effect are formally consistent, insofar as they have been completed, there must be a cancelling contribution that is omitted in the usual analyses. We argue that it is the dynamical action of conventional Lorentz transformations on the structure of an Unruh detector. Given the equivalence principle, an Unruh effect would correspond to black hole radiation. Thus, our perspective has significant consequences for quantum gravity and black hole physics: no Unruh effect entails the absence of black hole radiation evaporation., Comment: 17 pages, 3 figures

We use analytic continuation to extend the gauge/gravity duality nonperturbative description of the strong force coupling into the transition, near-perturbative, regime where perturbative effects become important. By excluding the unphysical region in coupling space from the flow of singularities in the complex plane, we derive a specific relation between the scales relevant at large and short distances; this relation is uniquely fixed by requiring maximal analyticity. The unified effective coupling model gives an accurate description of the data in the nonperturbative and the near-perturbative regions., Comment: 15 pages, 4 figures

In this paper, we clarify a serious misinterpretation and consequent misuse of the Principle of Maximum Conformality (PMC). In a recently published article~\cite{Stevenson:2023isz}, P.~M. Stevenson has claimed that ``the PMC is ineffective and does nothing to resolve the renormalization-scheme-dependence problem", concluding incorrectly that the success of PMC predictions is due to the PMC being a ``laborious, \emph{ad hoc}, back-door" version of the principle of minimum sensitivity (PMS). We show that such conclusions are incorrect, deriving from a misinterpretation of the PMC and overestimation of the applicability of the PMS. The purpose of the PMC is to achieve precise fixed-order pQCD predictions, free from conventional renormalization-scheme and renormalization-scale ambiguities. We demonstrate that the PMC predictions satisfy all of the self-consistency conditions of the renormalization group and standard renormalization-group invariance; the PMC predictions are thus independent of any initial choice of renormalization scheme and scale. The scheme independence of the PMC is also ensured by Commensurate Scale Relations which relate different observables to each other. Owing to the elimination of the factorially-divergent renormalon terms, the PMC series has better convergence behavior than the conventional series; it substantially suppresses any residual scale dependence due to unknown higher-order terms; and it thus provides a reliable basis for estimating the contributions of unknown higher-order terms. Thus, the PMC, based on the standard renormalization group invariance, has a rigorous foundation, eliminates the factorially divergent renormalon contributions, as well as eliminating unnecessary systematic errors which underly high-precision pQCD predictions. The PMC can thus be rigorously applied to virtually all high-energy hadronic processes., Comment: 9 pages, no figures

We present results for the thrust distribution in the electron positron annihilation to the three jet process at NNLO in the perturbative conformal window of QCD, as a function of the number of flavors $N_f$. Given the existence of an infrared interacting fixed point in this region, we can compare the Conventional Scale Setting (CSS) and the Principle of Maximum Conformality (PMC$_\infty$) methods along the entire renormalization group flow from the highest energies to zero energy. We then consider also the QED thrust, obtained as the limit $N_c \rightarrow 0$ of the number of colors and we show analogous comparison. QED in the low energy regime develops an infrared non-interacting fixed point. Using these quantum field theory limits as theoretical laboratories, we arrive at interesting results showing new features of the PMC$_\infty$., Comment: "Submission to SciPost", 14pages, 5 figures, proceedings , conference RADCOR 2023

Dedicated to the memory of our colleague, Harald Fritzsch, who, together with Murray Gell-Mann, introduced the color quantum number as the exact symmetry responsible for the strong interaction, thus establishing quantum chromodynamics (QCD) as a fundamental non-Abelian gauge theory. A basic understanding of hadron properties, however, such as confinement and the emergence of a mass scale, from first principles QCD has remained elusive: Hadronic characteristics are not explicit properties of the QCD Lagrangian and perturbative QCD, so successful in the large transverse momentum domain, is not applicable at large distances. In this article, we shall examine how this daunting obstacle is overcome in holographic QCD with the introduction of a superconformal symmetry in anti de Sitter (AdS) space which is responsible for confinement and the introduction of a mass scale within the superconformal group. When mapped to light-front coordinates in physical spacetime, this approach incorporates supersymmetric relations between the Regge trajectories of meson, baryon and tetraquark states which can be visualized in terms of specific $SU(3)_C$ color representations of quarks. We will also briefly discuss here the implications of holographic models for QCD color transparency in view of the present experimental interest. Based on the invited contribution to the book dedicated to the memory of Harald Fritzsch., Comment: 22 pages, 5 figures, Based on the Invited contribution to the book dedicated to the memory of Harald Fritzsch. Updated references. arXiv admin note: substantial text overlap with arXiv:2212.14028

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. Using the holographic light-front QCD framework 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 quantum 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, updated references

The setting of the renormalization scale ($\mu_r$) in the perturbative QCD (pQCD) is one of the crucial problems for achieving precise fixed-order pQCD predictions. The conventional prescription is to take its value as the typical momentum transfer $Q$ in a given process, and theoretical uncertainties are then evaluated by varying it over an arbitrary range. The conventional scale-setting procedure introduces arbitrary scheme-and-scale ambiguities in fixed-order pQCD predictions. The principle of maximum conformality (PMC) provides a systematic way to eliminate the renormalization scheme-and-scale ambiguities. The PMC method has rigorous theoretical foundations; it satisfies the renormalization group invariance (RGI) and all of the self-consistency conditions derived from the renormalization group. The PMC has now been successfully applied to many physical processes. In this paper, we summarize recent PMC applications, including event shape observables and heavy quark pair production near the threshold region in $e^+e^-$ annihilation and top-quark decay at hadronic colliders. In addition, estimating the contributions related to the uncalculated higher-order terms is also summarized. These results show that the major theoretical uncertainties caused by different choices of $\mu_r$ are eliminated, and the improved pQCD predictions are thus obtained, demonstrating the generality and applicability of the PMC., Comment: 14 pages, 9 figures, an invited review for the special issue "The Quantum Chromodynamics: 50th Anniversary of the Discovery" for Universe, published version

This paper presents a comprehensive review of both the theory and experimental successes of Quantum Chromodynamics, starting with its emergence as a well defined theory in 1972-73 and following developments and results up to the present day. Topics include a review of the earliest theoretical and experimental foundations; the fundamental constants of QCD; an introductory discussion of lattice QCD, the only known method for obtaining exact predictions from QCD; methods for approximating QCD, with special focus on effective field theories; QCD under extreme conditions; measurements and predictions of meson and baryon states; a special discussion of the structure of the nucleon; techniques for study of QCD at high energy, including treatment of jets and showers; measurements at colliders; weak decays and quark mixing; and a section on the future, which discusses new experimental facilities or upgrades currently funded. The paper is intended to provide a broad background for Ph.D. students and postdocs starting their career. Some contributions include personal accounts of how the ideas or experiments were developed., Comment: Invited volume for the EJPC; 567 pages if text/figures and 4783 references occupying about 160 additional pages. arXiv abstract abridged, for the complete abstract please see the full text

In addition to the evaluation of high-order loop contributions, the precision and predictive power of perturbative QCD (pQCD) predictions depends on two important issues: (1) how to achieve a reliable, convergent fixed-order series, and (2) how to reliably estimate the contributions of unknown higher-order terms. The recursive use of renormalization group equation, together with the Principle of Maximum Conformality (PMC), eliminates the renormalization scheme-and-scale ambiguities of the conventional pQCD series. The result is a conformal, scale-invariant series of finite order which also satisfies all of the principles of the renormalization group. In this paper we propose a novel Bayesian-based approach to estimate the size of the unknown higher order contributions based on an optimized analysis of probability distributions. We show that by using the PMC conformal series, in combination with the Bayesian analysis, one can consistently achieve high degree of reliability estimates for the unknown high order terms. Thus the predictive power of pQCD can be greatly improved. We illustrate this procedure for two pQCD observables: $R_{e^+e^-}$ and $R_\tau$, which are each known up to four loops in pQCD. Numerical analyses confirm that by using the scale-independent and more convergent PMC conformal series, one can achieve reliable Bayesian probability estimates for the unknown higher-order contributions., Comment: 14 pages, 4 figures, published version

Quantum chromodynamics (QCD) predicts the existence of both nonperturbative intrinsic and perturbative extrinsic heavy quark contributions to the fundamental structure of hadrons. The existence of intrinsic charm at the 3-standard-deviation level in the proton has recently been established from structure function measurements by the NNPDF Collaboration. Here we revisit the physics of intrinsic heavy quarks using light-front holographic QCD (LFHQCD) - a novel comprehensive approach to hadron structure which provides detailed predictions for dynamical properties of the hadrons, such as form factors, distribution amplitudes, structure functions, etc. We will extend this nonperturbative light-front QCD approach to study the heavy quark-antiquark contribution to the electromagnetic properties of nucleon. Our framework is based on a study of the eigenfunctions of the QCD light-front Hamiltonian, the frame-independent light-front wave functions (LFWFs) underlying hadron dynamics. We analyze the heavy quark content in the proton, induced either directly by the nonperturbative $|uud+Q\bar Q\rangle$ Fock state or by the $|uud+g\rangle$ Fock state, where the gluon splits into a heavy quark-antiquark pair. The specific form of these LFWFs are derived from LFHQCD. Using these LFWFs, we construct light-front representations for the heavy quark-antiquark asymmetry, the electromagnetic form factors of nucleons induced by heavy quarks, including their magnetic moments and radii., Comment: 8 pages, 8 figures

Observations of anomalous angular correlations in electron-positron pairs produced from excited states of $^{4}$He, $^{8}$Be and $^{12}$C nuclei have been suggested as due to the creation and subsequent decay of a new light particle of mass $\sim$17 MeV. In this work, we investigate the possibility that the source of the observed signals is a set of new excitation channels created by the 12-quark hidden-color Fock state within the ${\rm {^4He}}$ nuclear wavefunction dubbed the "hexadiquark." We calculate the invariant $e^+e^-$ mass spectrum for the electromagnetic transition from a new excitation of $^{4}$He, estimating its differential and total decay width. We find that we can fit the shape of the anomalous signal with the QCD Fock state at excitation energy $\rm E^{*} = 17.9 \pm 1$ 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 particular the three weakly repulsive $\rm 6_C$ interactions of $\rm SU(3)_C$ between diquark pairs. Experimental tests of our model are described in detail. In light of this work, we emphasize the need for independent experimental confirmation or refutation of the ATOMKI results as well as dedicated experiments to search for the proposed new excitations of ${\rm ^4He}$ and other $\alpha$-cluster nuclei., Comment: Experimental signatures of the model added, 9 pages, 3 figures, comments welcome

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., Comment: 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

A new approach to nonperturbative QCD, holographic light-front QCD, provides a comprehensive model for hadron dynamics and spectroscopy, incorporating color confinement, a universal hadron mass scale, the prediction of a massless pion in the chiral limit, and connections between the spectroscopy of mesons, baryons and tetraquarks across the full hadron spectrum. In this article we present predictions for the Sivers asymmetry and related transverse momentum distributions for the proton based on the light-front wavefunctions of the baryon eigenstate predicted by holographic QCD., Comment: 9 pages, 10 figures

The color transparency (CT) of a hadron, propagating with reduced absorption in a nucleus, is a fundamental property of QCD (quantum chromodynamics) reflecting its internal structure and effective size when it is produced at high transverse momentum, $Q$. CT has been confirmed in many experiments, such as semi-exclusive hard electroproduction, $e A \to e' \pi X$ for mesons produced at $Q^2 > 3 ~ {\rm GeV}^2$. However, a recent JLab (Jefferson Laboratory) measurement for a proton electroproduced in carbon $e\, {\rm C}\to e' p X$, where $X$ stands for the inclusive sum of all produced final states, fails to observe CT at $Q^2$ up to 14.2 GeV$^2$. In this paper, the onset of CT is determined by comparing the $Q^2$-dependence of the hadronic cross sections for the initial formation of a small color-singlet configuration using the generalized parton distributions from holographic light-front QCD. A critical dependence on the hadron's twist, $\tau$, the number of hadron constituents, is found for the onset of CT, with no significant effects from the nuclear medium. This effect can explain the absence of proton CT in the present kinematic range of the JLab experiment. The proton is predicted to have a "two-stage" color transparency with the onset of CT differing for the spin-conserving (twist-3, $\tau=3$) Dirac form factor with a higher onset in $Q^2$ for the spin-flip Pauli (twist-4) form factor. In contrast, the neutron is predicted to have a "one-stage" color transparency with the onset at higher $Q^2$ because of the dominance of its Pauli form factor. The model also predicts a strong dependence at low energies on the flavor of the quark current coupling to the hadron., Comment: 19 pages, 3 figures, contributed to the MDPI special issue for the special issue "The Future of Color Transparency, Hadronization and Short-Range Nucleon-Nucleon Correlation Studies"

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

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., Comment: 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

We address novel features of deep inelastic lepton scattering on nuclei at small Bjorken variable $x_{Bj}$. In this regime the lepton-nuclear cross section involves the interference between the standard lepton-quark scattering amplitude for the deep inelastic scattering (DIS) process on a single nucleon and a two-step process where diffractive scattering on a first nucleon combines with the amplitude for DIS on a second nucleon. The phases associated with the $t$-channel exchanges to the diffractive amplitude can produce either a destructive or constructive quantum-mechanical interference of the one-step and two-step amplitudes. This provides a mechanism regulating the respective amounts of shadowing suppression and anti-shadowing enhancement at low $x_{Bj}$. Furthermore, the standard leading-twist operator product and handbag diagram analyses of the forward virtual Compton amplitude on the nucleus are inapplicable, barring a conventional probabilistic interpretation. A main observable consequence is the impossibility of extracting momentum and spin sum rules from nuclear structure functions. We present numerical predictions supporting this picture and test them against DIS neutrino-nucleus and charged-lepton-nucleus scattering data., Comment: 7 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1908.06317

We show results for Thrust and C-parameter in $e^+ e^-$ annihilation to 3 jets obtained using the recently developed new method for eliminating the scale ambiguity and the scheme dependence in pQCD namely the Infinite-Order Scale-Setting method using the Principle of Maximum Conformality (PMC$_\infty$). This method preserves an important underlying property of gauge theories: intrinsic Conformality (iCF). It leads to a remarkably efficient method to eliminate the conventional renormalization scale ambiguity at any order in pQCD. A comparison with Conventional Scale Setting method (CSS) is also shown., Comment: "Submission to SciPost", 11pages, 3 figures, proceedings , conference RADCOR 2021

The {\it Principle of Maximum Conformality} (PMC), which generalizes the conventional Gell-Mann-Low method for scale-setting in perturbative QED to non-Abelian QCD, provides a rigorous method for achieving unambiguous scheme-independent, fixed-order predictions for physical observables consistent with the principles of the renormalization group. In addition to the original multi-scale-setting approach (PMCm), two variations of the PMC have been proposed to deal with ambiguities associated with the uncalculated higher order terms in the pQCD series, i.e. the single-scale-setting approach (PMCs) and the procedures based on ``intrinsic conformality" (PMC$_\infty$). In this paper, we will give a detailed comparison of these PMC approaches by comparing their predictions for three important quantities $R_{e^+e^-}$, $R_{\tau}$, and $\Gamma(H \to b \bar{b})$ up to four-loop pQCD corrections. The PMCs approach determines an overall effective running coupling $\alpha_s(Q)$ by the recursive use of the renormalization group equation, whose argument $Q$ represents the actual momentum flow of the process. Our numerical results show that the PMCs method, which involves a somewhat simpler analysis, can serve as a reliable substitute for the full multi-scale PMCm method, and that it leads to more precise pQCD predictions with small residual scale dependence., Comment: 17 pages, 6 figures, to be published in Nuclear Physics B

The holographic light-front QCD framework provides a unified nonperturbative description of the hadron mass spectrum, form factors and quark distributions. In this article we extend holographic QCD in order to describe the gluonic distribution in both the proton and pion from the coupling of the metric fluctuations induced by the spin-two Pomeron with the energy momentum tensor in anti--de Sitter space, together with constraints imposed by the Veneziano model{\color{blue},} without additional free parameters. The gluonic and quark distributions are shown to have significantly different effective QCD scales., Comment: Version to be published in Phys. Rev. D

The cross section for deep inelastic lepton-proton scattering (DIS) $\ell p \to \ell' X$ includes a diffractive deep inelastic (DDIS) contribution $\ell p \to \ell' p' X$, in which the proton remains intact with a large longitudinal momentum fraction $x_F$ greater than 0.9 and small transverse momentum. The DDIS events, which can be identified with Pomeron exchange in the $t$-channel, account for approximately $10\%$ of all of the DIS events. Thus, when one measures DIS, one automatically includes the leading-twist Bjorken-scaling DDIS events as a contribution to the DIS cross section, whether or not the final-state proton $p'$ is detected. In such events, the missing momentum fraction $x_{p'} \sim 0.9$ carried by the final-state proton $p'$ in the DDIS events could be misidentified with the light-front momentum fraction carried by sea quarks or gluons in the protons' Fock structure. As we shall show in this article, the underlying QCD Pomeron-exchange amplitude which produces the DDIS events does not obey the operator product expansion nor satisfy momentum sum rules. Thus we conclude that the quark and gluon distributions measured in DIS experiments will be misidentified, unless the measurements explicitly exclude the DDIS events and that a correct determination of the parton distribution functions (PDFs) derived from the DIS data requires the explicit subtraction of the DDIS contribution from the full DIS cross section., Comment: 8 pages, 4 figures

The breaking of chiral symmetry in holographic light-front QCD is encoded in its longitudinal dynamics with its chiral limit protected by the superconformal algebraic structure which governs its transverse dynamics. The scale in the longitudinal light-front Hamiltonian determines the confinement strength in this direction: It is also responsible for most of the light meson ground state mass consistent with the Gell-Mann-Oakes-Renner constraint. Longitudinal confinement and the breaking of chiral symmetry are found to be different manifestations of the same underlying dynamics as found in 't Hooft large $N_C$ QCD(1 + 1) model., Comment: 10 pages, 4 figures, accepted for publication in PRD

In this paper, we calculate the $t\bar{t}$ pQCD production cross-section at NNLO and determine the top-quark pole mass from recent measurements at the LHC at $\sqrt{S}=13$ TeV center-of-mass energy to high precision by applying the Principle of Maximum Conformality (PMC). The PMC provides a systematic method which rigorously eliminates QCD renormalization scale ambiguities by summing the nonconformal $\beta$ contributions into the QCD coupling constant. The PMC predictions satisfy the requirements of renormalization group invariance, including renormalization scheme independence, and the PMC scales accurately reflect the virtuality of the underlying production subprocesses. By using the PMC, an improved prediction for the $t\bar{t}$ production cross-section is obtained without scale ambiguities, which in turn provides a precise value for the top-quark pole mass. Moreover, the predictive power of PMC calculations that the magnitude of higher-order PMC predictions are well within the error bars predicted from the known lower-order has been demonstrated for the top-quark pair production. The resulting determination of the top-quark pole mass $m_t^{\rm pole}=172.5\pm1.4$ GeV from the LHC measurement at $\sqrt{S}=13$ TeV is in agreement with the current world average cited by the Particle Data Group (PDG). The PMC prediction provides an important high-precision test of the consistency of pQCD and the SM at $\sqrt{S}=13$ TeV with previous LHC measurements at lower CM energies., Comment: 8 pages, 5 figures

In the paper, we present QCD predictions for $\eta_{c} + \gamma$ 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 $e^{+}+e^{-}\to\gamma+\eta_{c}$ 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 $\beta$ contributions into the QCD coupling $\alpha_s(Q^2)$. The renormalization group equation then sets the value of $\alpha_s$ 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, $\sigma|_{\rm NNLO, PMC}\simeq 41.18$ 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 $\sigma|_{\rm NNNLO, PMC+Pade} \simeq 21.36$ fb, which is consistent with the recent BELLE measurement $\sigma^{\rm obs}$=$16.58^{+10.51}_{-9.93}$ fb at $\sqrt{s} \simeq 10.6$ GeV. This procedure also provides a first estimate of the NNNLO contribution., Comment: 8 pages, 5 figures. Discussions improved and references updated. Revised version to be published in JHEP

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., Comment: 9 pages. References with positive preliminary results from the MARATHON experiment added, clarifications and minor edits. Version accepted for publication

We compare light-front quantization and instant-time quantization both at the level of operators and at the level of their Feynman diagram matrix elements. At the level of operators light-front quantization and instant-time quantization lead to equal light-front time commutation (or anticommutation) relations that appear to be quite different from equal instant-time commutation (or anticommutation) relations. Despite this we show that at unequal times instant-time and light-front commutation (or anticommutation) relations actually can be transformed into each other, with it only being the restriction to equal times that makes the commutation (or anticommutation) relations appear to be so different. While our results are valid for both bosons and fermions, for fermions there are subtleties associated with tip of the light cone contributions that need to be taken care of. At the level of Feynman diagrams we show for non-vacuum Feynman diagrams that the pole terms in four-dimensional light-front Feynman diagrams reproduce the three-dimensional light-front on-shell Hamiltonian Fock space formulation in which the light-front energy and light-front momentum are on shell. However, because of circle at infinity contributions we show that this equivalence fails for four-dimensional light-front vacuum tadpole diagrams. Then, precisely because of these circle at infinity contributions, light-front vacuum tadpole diagrams are not only nonzero, they are actually equal to instant-time vacuum tadpole diagrams. Light-front vacuum diagrams are not correctly describable by the on-shell Hamiltonian formalism, and thus not by the closely related infinite momentum frame prescription either. With the transformation from instant-time fields to light-front fields being a spacetime translation, not only are instant-time quantization and light-front quantization equivalent, they are unitarily equivalent., Comment: 72 pages, 2 figures. Expanded version of arXiv:1909.03548, includes discussion of light-front Lehmann representation and connection between light-front and instant-time Hamiltonians

We give an overview of recent progress into the infrared structure of QCD based on the gauge/gravity correspondence and light-front quantization, where the color confining interaction for mesons and baryons is determined by an underlying superconformal algebraic structure. This new approach to hadron physics gives remarkable connections and predictions across the entire mass spectrum of hadrons and also describes the infrared behavior of the strong coupling. More recently, an extensive study of form factors, polarized and unpolarized parton distributions and the sea quark contribution to the nucleon has been carried out by extending the holographic formalism to incorporate the nonperturbative structure of Veneziano amplitudes. Contribution to the report "Strong QCD from Hadron Structure Experiments" Jefferson Lab Workshop, 5-9 November, 2019, Comment: 8 pages, 7 figures, Strong QCD from Hadron Structure Experiments, SLAC-PUB-17520. Jefferson Lab Workshop, 5-9 November, 2019

We present the first lattice QCD calculation of the charm quark contribution to the nucleon electromagnetic form factors $G^c_{E,M}(Q^2)$ in the momentum transfer range $0\leq Q^2 \leq 1.4$ $\rm GeV^2$. The quark mass dependence, finite lattice spacing and volume corrections are taken into account simultaneously based on the calculation on three gauge ensembles including one at the physical pion mass. The nonzero value of the charm magnetic moment $\mu^c_M=-0.00127(38)_{\rm stat}(5)_{\rm sys}$, as well as the Pauli form factor, reflects a nontrivial role of the charm sea in the nucleon spin structure. The nonzero $G^c_{E}(Q^2)$ indicates the existence of a nonvanishing asymmetric charm-anticharm sea in the nucleon. Performing a nonperturbative analysis based on holographic QCD and the generalized Veneziano model, we study the constraints on the $[c(x)-\bar{c}(x)]$ distribution from the lattice QCD results presented here. Our results provide complementary information and motivation for more detailed studies of physical observables that are sensitive to intrinsic charm and for future global analyses of parton distributions including asymmetric charm-anticharm distribution., Comment: Published version, Physics Letters B

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., Comment: 8 pages, 6 figures, published version

We identify a property of renormalizable SU(N)/U(1) gauge theories, the intrinsic Conformality ($iCF$), which underlies the scale invariance of physical observables and leads to a remarkably efficient method to solve the conventional renormalization scale ambiguity at every order in pQCD: the PMC$_\infty$. This new method reflects the underlying conformal properties displayed by pQCD at NNLO, eliminates the scheme dependence of pQCD predictions and is consistent with the general properties of the PMC (Principle of Maximum Conformality). We introduce a new method to identify conformal and $\beta$-terms which can be applied either to numerical or to theoretical calculations. We illustrate the PMC$_\infty$ for the thrust and C-parameter distributions in $e^+ e^-$ annihilation and then we show how to apply this new method to general observables in QCD. We point out how the implementation of the PMC$_\infty$ can significantly improve the precision of pQCD predictions; its implementation in multi-loop analysis also simplifies the calculation of higher orders corrections in a general renormalizable gauge theory., Comment: 10 pages, 6 figures

I review applications of superconformal algebra. light-front holography, and an extended form of conformal symmetry to hadron spectroscopy and dynamics. QCD is not supersymmetrical in the traditional sense -- the QCD Lagrangian is based on quark and gluonic fields -- not squarks nor gluinos. However, its hadronic eigensolutions conform to a representation of superconformal algebra. and provide a unified Regge spectroscopy of meson, baryon, and tetraquarks with a universal Regge slope. The pion $q \bar q$ eigenstate is composite but yet has zero mass for $m_q=0.$ Light-Front Holography also predicts the form of the nonperturbative QCD running coupling in agreement with the effective charge determined from measurements of the Bjorken sum rule. One also obtains viable predictions for hadron dynamics such as spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. The combined approach of light-front holography and superconformal algebra also provides insight into the origin of the QCD mass scale and color confinement. A key tool is the dAFF principle which shows how a mass scale can appear in the Hamiltonian and the equations of motion while retaining the conformal symmetry of the action. When one applies the dAFF procedure to chiral QCD, a mass scale $\kappa$ appears which determines the hadron masses in the absence of the Higgs coupling. The result is an extended conformal symmetry which has a conformally invariant action even though an underlying mass scale appears in the Hamiltonian. Although conformal symmetry is strongly broken by the heavy quark mass, the supersymmetric mechanism, which transforms mesons to baryons (and baryons to tetraquarks), still holds and gives remarkable mass degeneracies across the spectrum of light, heavy-light and double-heavy hadrons., Comment: Invited talk presented at Light Cone 2019 - QCD on the light cone: from hadrons to heavy ions - LC2019. 16-20 September 2019. Ecole Polytechnique, Palaiseau, France. To be published in the conference proceedings. arXiv admin note: text overlap with arXiv:1802.08552

The CLAS collaboration at Jefferson Laboratory has compared nuclear parton distributions for a range of nuclear targets and found that the EMC effect measured in deep inelastic lepton-nucleus scattering has a strongly "isophobic" nature. This surprising observation suggests short-range correlations between neighboring $n$ and $p$ nucleons in nuclear wavefunctions that are much stronger compared to $p-p$ or $n-n$ correlations. In this paper we propose a definitive experimental test of the nucleon-nucleon explanation of the isophobic nature of the EMC effect: the diffractive dissociation on a nuclear target $A$ of high energy $\rm ^4He$ nuclei to pairs of nucleons $n$ and $p$ with high relative transverse momentum, $\alpha + A \to n + p + A' + X $. The comparison of $n-p$ events with $p-p$ and $n-n$ events directly tests the postulated breaking of isospin symmetry. The experiment also tests alternative QCD-level explanations for the isophobic EMC effect. In particular it will test a proposal for hidden-color degrees of freedom in nuclear wavefunctions based on isospin-zero $[ud]$ diquarks., Comment: 5 pages, references added, clarifications due to helpful referee comments (latexdiff for all changes). Accepted for publication in Physics Letters B

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 propose a unified new approach to describe polarized and unpolarized quark distributions in the proton based on the gauge-gravity correspondence, light-front holography, and the generalized Veneziano model. We find that the spin-dependent quark distributions are uniquely determined in terms of the unpolarized distributions by chirality separation without the introduction of additional free parameters. The predictions are consistent with existing experimental data and agree with perturbative QCD constraints at large longitudinal momentum $x$. In particular, we predict the sign reversal of the polarized down-quark distribution in the proton at $x=0.8\pm0.03$, a key property of nucleon substructure which will be tested very soon in upcoming experiments., Comment: 7 pages, 3 figures, version to appear in Physical Review Letters

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

The QCD light-front (LF) Hamiltonian equation H_{LF}|\Psi> = M^2 |\Psi> derived from quantization at fixed LF time \tau = 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 LF formalism also leads to novel nuclear phenomena, such as "hidden color", "color transparency", "nuclear-bound quarkonium" and the shadowing and antishadowing of nuclear structure functions. For example, there are five distinct color-singlet Fock state representations of the six color-triplet quarks of the deuteron. The hidden color Fock states become manifest when the deuteron is probed when it has small transverse size, as in measurements of the deuteron form factor at large momentum transfer. The QCD Lagrangian with zero quark mass has no explicit mass scale. However, as shown by de Alfaro, Fubini, and Furlan (dAFF), a mass scale can appear in the equations of motion without affecting the conformal invariance of the Action. When one applies the dAFF procedure to the QCD LF Hamiltonian, it leads to a color confining potential \kappa^4 \zeta^2 for mesons, where \zeta^2 is the LF radial variable conjugate to the qbar-q invariant mass squared. The same result, including spin terms, is obtained using LF holography (AdS/QCD) -- the duality between LF dynamics and AdS_5 -- if one modifies the AdS_5 Action by the dilaton exp{+\kappa^2 z^2} in the fifth dimension z. If this procedure is generalized using superconformal algebra, the resulting LF eigensolutions provide unified Regge spectroscopy of mesons, baryons, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons, baryons and tetraquarks with a universal Regge slope..., Comment: 8 pages, 3 figures. Contribution to the proceedings of 13th International Conference on Nucleus-Nucleus Collisions (NN2018) in Omiya, Japan. Plenary talk given by S. J. Brodsky. arXiv admin note: text overlap with arXiv:1802.08552, arXiv:1709.01191, arXiv:1611.0719

We present a novel method for precisely determining the running QCD coupling constant $\alpha_s(Q^2)$ over a wide range of $Q^2$ from event shapes for electron-positron annihilation measured at a single annihilation energy $\sqrt{s}$. The renormalization scale $Q^2$ of the running coupling depends dynamically on the virtuality of the underlying quark and gluon subprocess and thus the specific kinematics of each event. The determination of the renormalization scale for event shape distributions is obtained by using the Principle of Maximum Conformality (PMC), a rigorous scale-setting method for gauge theories which satisfies all the requirements of Renormalization Group Invariance, including renormalization-scheme independence and consistency with Abelian theory in the $N_C \to 0$ limit. In this paper we apply the PMC to two classic event shapes measured in $e^+ e^-$ annihilation: the thrust ($T$) and C-parameter ($C$). The PMC renormalization scale depends differentially on the values of $T$ and $C$. The application of PMC scale-setting determines the running coupling $\alpha_s(Q^2)$ to high precision over a wide range of $Q^2$ from $10$ to $250~\rm{GeV}^2$ from measurements of the event shape distributions at the $Z^0$ peak. The extrapolation of the running coupling using pQCD evolution gives the value $\alpha_s(M^2_Z)=0.1185\pm0.0012$ from the thrust, and $\alpha_s(M^2_Z)=0.1193^{+0.0021}_{-0.0019}$ from the C-parameter in the $\bar{\rm{MS}}$ scheme. These determinations of $\alpha_s(M^2_Z)$ are consistent with the world average and are more precise than the values obtained from analyses of event shapes currently used in the world average. The highly-consistent results for the $T$ and $C$ event-shape distributions provide an additional verification of the applicability of the PMC to pQCD., Comment: 6 pages, 6 figures. Published version

We study the structure of scalar field light front quantization vacuum graphs. In instant time quantization both non-vacuum and vacuum graphs can equivalently be described by either the off-shell four-dimensional Feynman diagram approach or the on-shell three-dimensional Fock space approach, with this being the case since the relevant Feynman diagrams are given entirely by pole terms. This is also the case for light front quantization non-vacuum graphs. However this is the not the case for light front vacuum sector diagrams, since then there are also circle at infinity contributions to Feynman diagrams. These non-pole contributions cause vacuum diagrams to be nonzero and to not be given by a light-front Hamiltonian Fock space analysis. The three-dimensional approach thus fails in the light front vacuum sector. In consequence, the closely related infinite momentum frame approach also fails in the light front vacuum sector., Comment: 12 pages

The conventional approach to fixed-order perturbative QCD predictions is based on an arbitrary choice of the renormalization scale, together with an arbitrary range. This {\it ad hoc} assignment of the renormalization scale causes the coefficients of the QCD running coupling at each perturbative order to be strongly dependent on the choice of both the renormalization scale and the renormalization scheme. However, such ambiguities are not necessary, since as a basic requirement of renormalization group invariance (RGI), any physical observable must be independent of the choice of both the renormalization scheme and the renormalization scale. In fact, if one uses the {\it Principle of Maximum Conformality} (PMC) to fix the renormalization scale, the coefficients of the pQCD series match the series of conformal theory, and they are thus scheme independent. It has been found that the elimination of the scale and scheme ambiguities at all orders relies heavily on how precisely we know the analytic form of the QCD running coupling $\alpha_s$. In this review, we summarize the known properties of the QCD running coupling and its recent progresses, especially for its behavior within the asymptotic region. We also summarize the current progress on the PMC and some of its typical applications, showing to what degree the conventional renormalization scheme-and-scale ambiguities can be eliminated after applying the PMC. We also compare the PA approach for the conventional scale-dependent pQCD series and the PMC scale-independent conformal series. We observe that by using the conformal series, the PA approach can provide a more reliable estimate of the magnitude of the uncalculated terms. And if the conformal series for an observable has been calculated up to $n_{\rm th}$-order level, then the $[N/M]=[0/n-1]$-type PA series provides an important estimate for the higher-order terms., Comment: 67 pages, 26 figures. Updated version which has been published as an invited review for Prog.Part.Nucl.Phys. arXiv admin note: text overlap with arXiv:1802.09154

We present a comprehensive and self-consistent analysis for the thrust distribution by using the Principle of Maximum Conformality (PMC). By absorbing all nonconformal terms into the running coupling using PMC via renormalization group equation, the scale in the running coupling shows the correct physical behavior and the correct number of active flavors is determined. The resulting PMC predictions agree with the precise measurements for both the thrust differential distributions and the thrust mean values. Moreover, we provide a new remarkable way to determine the running of the coupling constant $\alpha_s(Q^2)$ from the measurement of the jet distributions in electron-positron annihilation at a single given value of the center-of-mass energy $\sqrt{s}$., Comment: 6 pages, 4 figures, v2: matches published version

In this article a systematic quantitative analysis of the isoscalar bosonic states is performed in the framework of supersymmetric light front holographic QCD. It is shown that the spectroscopy of the $\eta$ and $h$ mesons can be well described if one additional mass parameter -- which corresponds to the hard breaking of chiral $U(1)$ symmetry in standard QCD -- is introduced. The mass difference of the $\eta$ and $\eta'$ isoscalar mesons is then determined by the strange quark mass content of the $\eta'$. The theory also predicts the existence of isoscalar tetraquarks which are bound states of diquarks and anti-diquarks. The candidates for these exotic isoscalar tetraquarks are identified. In particular, the $f_0(1500)$ is identified as isoscalar tetraquark; the predicted mass value 1.52 GeV agrees with the measured experimental value within the model uncertainties., Comment: 20 pages, 2 figures