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We report on our finite temperature 2+1 flavor lattice QCD simulation to study the thermodynamic properties of QCD near the (pseudo) critical point employing $N_T=12$ and $16$. The simulation points are chosen along the lines of constant physics. The quark mass for M\"obius domain-wall fermion are tuned by taking into account the residual mass either by fine-tuning the input quark masses or by post-process using reweighting. In this talk, we focus on simulation details and present some preliminary results., Comment: 8 pages, contribution to the 39th International Symposium on Lattice Field theory (LATTICE2022), 8th-13th August, 2022, Bonn, Germany

We perform a non-perturbative lattice calculation of the decay rates for inclusive semi-leptonic decays of charmed mesons. In view of the long-standing tension in the determination of the CKM matrix elements $|V_{ub}|$ and $|V_{cb}|$ from exclusive and inclusive processes, recently, the use of lattice QCD has been extended towards the description of inclusive decays. Since the determination of hadronic input parameters from QCD based methods require independent tests, we focus on the charm sector, since it not only offers experimental data, but also well determined CKM parameters. We carry out a pilot lattice simulation for the $D_s \rightarrow X_s \ell\nu$ and explore the improvement of existing techniques. Our simulation employs M\"obius domain-wall charm and strange quarks whose masses are tuned to be approximately physical and we cover the whole kinematical region. We report on our progress in analyzing different sources of systematic effects, such as the extrapolation of the kernel function chosen for the Chebsyhev approximation as well as the influence on the analysis in the region close to the kinematical limit., Comment: 9 pages, 6 figures, Proceedings of the 39th International Symposium on Lattice Field Theory, 8th-13th August 2022, Bonn, Germany

Utilizing the approach recently proposed for the $\ell N$ inclusive scattering cross section on the lattice, we compute the differential scattering cross section for the charged current process $\ell p \rightarrow \nu n $ for various kinematical channels. The simulation is carried out on the 2+1 flavor $16^3 \times 32 $ ensemble with Iwasaki and Domain Wall Fermion action. The lattice results are compared with MINER$\nu$A result for the equivalent process., Comment: 9pages, LATTICE 2021

Simulations for the thermodynamics of the 2+1 flavor QCD are performed employing chiral fermions. The use of M\"obius domain-wall fermions with stout-link smearing is more effective on the finer lattices where all the relevant chiral symmetries are realized more accurately. We report on the initial simulations near the (pseudo) critical point using the line of constant physics with an average $ud$ quark mass slightly heavier than physical at $a\lesssim 0.1$ fm., Comment: 9 pages, 8 figures, 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July, 2021 Zoom/Gather@MIT

Utilizing the approach recently proposed for the inclusive semi-leptonic decay rate on the lattice, we compute the differential decay rate of a $B_s$ meson for various kinematical channels. The results are compared with the contributions from the ground states (D and D^*) as well as from the orbitally excited states (D^**'s). The computation so far is carried out with an unphysically light bottom quark and strange spectator quark., Comment: 8 pages, 3 figures; contribution to The 38th International Symposium on Lattice Field Theory, LATTICE2021, 26th-30th July, 2021

We present the lattice QCD calculation of inclusive semileptonic $B_s$-meson decays. We follow a recently proposed method, which is based on the extraction of smeared spectral densities from Euclidean correlation functions and on the numerical reconstruction of the integration kernel relevant for the inclusive decay rate calculation. We compute four-point Euclidean correlation functions using JLQCD and ETM gauge ensembles with unphysically light $b$-quark masses, and apply two different methods for the integration kernel reconstruction. Finally, we show that the lattice results obtained in this work are in good agreement with the analytic predictions of the operator-product-expansion. This opens the path for a future full lattice QCD calculation to be used as theoretical input for the determination of the magnitude of the CKM element $V_{cb}$., Comment: 10 pages, 4 figures, contribution to the 39th International Symposium on Lattice Field Theory, 8th-13th August, 2022, Bonn, Germany. arXiv admin note: substantial text overlap with arXiv:2209.15494

We present an ab initio study of inclusive semileptonic decays of heavy mesons from lattice QCD. Our approach is based on a recently proposed method, that allows one to address the study of these decays from the analysis of smeared spectral functions extracted from four-point correlators on the lattice, where the smearing is defined in terms of the phase-space integration relevant to the inclusive decays. We present results obtained from gauge-field ensembles from the JLQCD and ETM collaborations, and discuss their relation with theoretical predictions from the operator-product expansion., Comment: 51 pages, 27 figures and 4 tables. Clarifications added, v2 to appear in JHEP

We perform a numerical computation of the anomalous magnetic moment ($g-2$) of the electron in QED by using the stochastic perturbation theory. Formulating QED on the lattice, we develop a method to calculate the coefficients of the perturbative series of $g-2$ without the use of the Feynman diagrams. We demonstrate the feasibility of the method by performing a computation up to the $\alpha^3$ order and compare with the known results. This program provides us with a totally independent check of the results obtained by the Feynman diagrams and will be useful for the estimations of not-yet-calculated higher order values. This work provides an example of the application of the numerical stochastic perturbation theory to physical quantities, for which the external states have to be taken on-shell., Comment: 35 pages, 5 figures, 2 tables, the version to appear in JHEP

We propose a method to use lattice QCD to compute the Borel transform of the vacuum polarization function appearing in the Shifman-Vainshtein-Zakharov QCD sum rule. We construct the spectral sum corresponding to the Borel transform from two-point functions computed on the Euclidean lattice. As a proof of principle, we compute the $s \bar{s}$ correlators at three lattice spacings and take the continuum limit. We confirm that the method yields results that are consistent with the operator product expansion in the large Borel mass region. The method provides a ground on which the OPE analyses can be directly compared with nonperturbative lattice computations., 27 pages, 13 figures, 1 table; data updated, 1 figure added; version to appear in PRD

We propose a new method to renormalize lattice operators. The method is based on the technique to compute the spectral sum appearing in the Shifman-Vainshtein-Zakharov QCD sum rule from lattice correlators. The application of this technique to the light quark system is useful for operator renormalization as well as for the test of perturbative QCD and OPE. We determine the renormalization constant of the vector current and discuss extensions to other current operators., Comment: 8 pages, 2 figures, 1 table, talk presented at The 38th International Symposium on Lattice Field Theory (LATTICE2021), 26th-30th July, 2021, Zoom/Gather@Massachusetts Institute of Technology

We propose a fully non-perturbative method to compute inelastic lepton-nucleon ($\ell N$) scattering cross sections using lattice QCD. The method is applicable even at low energies, such as the energy region relevant for the recent and future neutrino-nucleon ($\nu N$) scattering experiments, for which perturbative analysis is invalidated. The basic building block is the forward Compton-scattering amplitude, or the hadronic tensor, computed on a Euclidean lattice. Total cross section is constructed from the hadronic tensor by multiplying a phase space factor and integrating over the energy and momentum of final hadronic states. The energy integral that induces a sum over all possible final states is performed implicitly by promoting the phase space factor to an operator written in terms of the transfer matrix on the lattice. The formalism is imported from that of the inclusive semileptonic B meson decay [P. Gambino, S. Hashimoto, arXiv:2005.13730]. It can be generalized to compute the $\ell N$ scattering cross sections and their moments, as well as the virtual correction to the nuclear $\beta$-decay. Necessary quark-line contractions for two current insertions corresponding to the Compton amplitude to be computed on the lattice are summarized., Comment: 44 pages, 16 figures; minor corrections, a few refs added

We develop a method to compute inclusive semi-leptonic decay rate of hadrons fully non-perturbatively using lattice QCD simulations. The sum over all possible final states is achieved by a calculation of the forward-scattering matrix elements on the lattice, and the phase-space integral is evaluated using their dependence on the time separation between two inserted currents. We perform a pilot lattice computation for the B_s -> X_c l nu decay with an unphysical bottom quark mass and compare the results with the corresponding OPE calculation. The method to treat the inclusive processes on the lattice can be applied to other processes, such as the lepton-nucleon inelastic scattering., 5 pages, 4 figures

Recently, via calculation of spatial correlators of $J=0,1$ isovector operators using a chirally symmetric Dirac operator within $N_F=2$ QCD, it has been found that QCD at temperatures $T_c - 3 T_c$ is approximately $SU(2)_{CS}$ and $SU(4)$ symmetric. The latter symmetry suggests that the physical degrees of freedom are chirally symmetric quarks bound by the chromoelectric field into color singlet objects without chromomagnetic effects. This regime of QCD has been referred to as a Stringy Fluid. Here we calculate correlators for propagation in time direction at a temperature slightly above $T_c$ and find the same approximate symmetries. This means that the meson spectral function is chiral-spin and $SU(4)$ symmetric., 10 pages, 3 figures. Version published by PLB

We investigate the high-temperature phase of QCD using lattice QCD simulations with $N_f = 2$ dynamical M\"obius domain-wall fermions. On generated configurations, we study the axial $U(1)$ symmetry, overlap-Dirac spectra, screening masses from mesonic correlators, and topological susceptibility. We find that some of the observables are quite sensitive to lattice artifacts due to a small violation of the chiral symmetry. For those observables, we reweight the M\"obius domain-wall fermion determinant by that of the overlap fermion. We also check the volume dependence of observables. Our data near the chiral limit indicates a strong suppression of the axial $U(1)$ anomaly at temperatures $\geq$ 220 MeV., Comment: 7 pages, 4 figures, 1 table; Proceedings of the 37th International Symposium on Lattice Field Theory (Lattice 2019), 16-22 June 2019, Wuhan, China

We propose a renormalization scheme that can be simply implemented on the lattice. It consists of the temporal moments of two-point and three-point functions calculated with finite valence quark mass. The scheme is confirmed to yield a consistent result with another renormalization scheme in the continuum limit for the bilinear operators. We apply a similar renormalization scheme for the non-perturbative renormalization of four-fermion operators appearing in the weak effective Hamiltonian., 7 pages, 3 figures, 2 tables; Proceedings of the 37th annual International Symposium on Lattice Field Theory (Lattice 2019), 16-22 June 2019, Wuhan, China

We propose a method to reconstruct smeared spectral functions from two-point correlation functions measured on the Euclidean lattice. Arbitrary smearing function can be considered as far as it is smooth enough to allow an approximation using Chebyshev polynomials. We test the method with numerical lattice data of Charmonium correlators. The method provides a framework to compare lattice calculation with experimental data including excited state contributions without assuming quark-hadron duality., Comment: 23 pages

Based on a complete set of $J = 0$ and $J=1$ spatial isovector correlation functions calculated with $N_F = 2$ domain wall fermions we identify an intermediate temperature regime of $T \sim 220 - 500$ MeV ($1.2T_c$--$2.8T_c$), where chiral symmetry is restored but the correlators are not yet compatible with a simple free quark behavior. More specifically, in the temperature range $T \sim 220 - 500$ MeV we identify a multiplet structure of spatial correlators that suggests emergent $SU(2)_{CS}$ and $SU(4)$ symmetries, which are not symmetries of the free Dirac action. The symmetry breaking effects in this temperature range are less than 5%. Our results indicate that at these temperatures the chromo-magnetic interaction is suppressed and the elementary degrees of freedom are chirally symmetric quarks bound into color-singlet objects by the chromo-electric component of the gluon field. At temperatures between 500 and 660 MeV the emergent $SU(2)_{CS}$ and $SU(4)$ symmetries disappear and one observes a smooth transition to the regime above $T \sim 1$ GeV where only chiral symmetries survive, which are finally compatible with quasi-free quarks., A new figure and discussion added. Accepted for publication in PRD

Heavy flavor physics entered a new era when the Belle II experiment observed its first collision. There are several hints found so far by BaBar, Belle, and LHCb in particular, that suggest the physics beyond the Standard Model appearing in the loop processes at short distances. They will be further tested by higher precision experiments in the coming years, while the role of lattice QCD is to understand the long-distance physics quantitatively so that one can unambiguously isolate the short-distance physics from the experimental data. I summarize the status towards this goal and then look at the challenges we are facing., 20 pages, 4 figures, talk presented at the 36th Annual International Symposium on Lattice Field Theory - LATTICE2018, 22-28 July, 2018, Michigan State University, East Lansing, Michigan, USA

cd. autorów: L. Cao48,‡, G. Caria145,‡, G. Casarosa57,‡, C. Cecchi56,‡,D. Cˇ ervenkov10,‡,M.-C. Chang22,‡, P. Chang92,‡, R. Cheaib146,‡, V. Chekelian83,‡, Y. Chen154,‡, B. G. Cheon28,‡, K. Chilikin77,‡, K. Cho70,‡, J. Choi14,‡, S.-K. Choi27,‡, S. Choudhury35,‡, D. Cinabro170,‡, L. M. Cremaldi146,‡, D. Cuesta47,‡, S. Cunliffe16,‡, N. Dash33,‡, E. de la Cruz Burelo9,‡, E. de Lucia52,‡, G. De Nardo54,‡, †Editor. ‡Belle II Collaborator. §Theory or external contributing author. M. De Nuccio16,‡, G. De Pietro59,‡, A. De Yta Hernandez9,‡, B. Deschamps129,‡, M. Destefanis60,‡, S. Dey116,‡, F.Di Capua54,‡, S.Di Carlo75,‡, J. Dingfelder129,‡, Z. Doležal10,‡, I. Domínguez Jiménez125,‡, T.V. Dong30,26,‡, D. Dossett145,‡, S. Duell129,‡, S. Eidelman6,96,77,‡, D. Epifanov6,96,‡, J. E. Fast100,‡, T. Ferber16,‡, S. Fiore18,‡, A. Fodor85,‡, F. Forti57,‡, A. Frey24,‡, O. Frost16,‡, B. G. Fulsom100,‡, M. Gabriel83,‡, N. Gabyshev6,96,‡, E. Ganiev61,‡, X. Gao3,‡, B. Gao23,‡, R. Garg101,‡, A. Garmash6,96,‡, V. Gaur169,‡, A. Gaz90,‡, T. Geßler65,‡, U. Gebauer24,‡, M. Gelb48,‡, A. Gellrich16,‡, D. Getzkow65,‡, R. Giordano54,‡, A. Giri35,‡, A. Glazov16,‡, B. Gobbo61,‡, R. Godang157,‡, O. Gogota110,‡, P. Goldenzweig48,‡, B. Golob141,109,‡,W. Gradl63,‡, E. Graziani59,‡, M. Greco60,‡, D. Greenwald114,‡, S. Gribanov6,96,‡, Y. Guan17,‡, E. Guido60,‡, A. Guo41,‡, S. Halder111,‡, K. Hara30,26,‡, O. Hartbrich138,‡, T. Hauth48,‡, K. Hayasaka94,‡, H. Hayashii91,‡, C. Hearty130,‡, I. Heredia De La Cruz9,‡, M. Hernandez Villanueva9,‡, A. Hershenhorn130,‡, T. Higuchi66,‡,M. Hoek63,‡, S. Hollitt124,‡, N. T. HongVan44,‡, C.-L. Hsu160,‡, Y. Hu41,‡, K. Huang92,‡, T. Iijima89,90,‡, K. Inami90,‡, G. Inguglia40,‡,A. Ishikawa119,‡, R. Itoh30,26,‡, Y. Iwasaki30,‡, M. Iwasaki97,‡, P. Jackson124,‡, W. W. Jacobs37,‡, I. Jaegle137,‡, H. B. Jeon73,‡, X. Ji41,‡, S. Jia3,‡,Y. Jin162,‡, C. Joo66,‡,M. Künzel16,‡, I. Kadenko110,‡, J. Kahn78,‡, H. Kakuno121,‡, A. B. Kaliyar36,‡, J. Kandra10,‡, K. H. Kang73,‡, Y. Kato90,‡, T. Kawasaki68,‡, C. Ketter138,‡, M. Khasmidatul143,‡, H. Kichimi30,‡, J. B. Kim71,‡, K. T. Kim71,‡, H. J. Kim73,‡, D.Y. Kim108,‡, K. Kim172,‡, Y. Kim172,‡, T. D. Kimmel169,‡, H. Kindo30,26,‡, K. Kinoshita135,‡, T. Konno68,‡, A. Korobov6,96,‡, S. Korpar144,109,‡, D. Kotchetkov138,‡, R. Kowalewski165,‡, P. Križan141,109,‡, R. Kroeger146,‡, J.-F. Krohn145,‡, P. Krokovny6,96,‡, W. Kuehn65,‡, T. Kuhr78,‡, R. Kulasiri67,‡, M. Kumar81,‡, R. Kumar101,‡, T. Kumita121,‡, A. Kuzmin6,96,‡, Y.-J. Kwon172,‡, S. Lacaprara55,‡, Y.-T. Lai30,‡, K. Lalwani81,‡, J. S. Lange65,‡, S. C. Lee73,‡, J.Y. Lee106,‡, P. Leitl83,‡, D. Levit114,‡, S. Levonian16,‡, S. Li3,‡, L. K. Li41,‡, Y. Li41,‡,Y. B. Li103,‡, Q. Li103,‡, L. Li Gioi83,‡, J. Libby36,‡, Z. Liptak138,‡, D. Liventsev169,‡, S. Longo165,‡, A. Loos158,‡, G. Lopez Castro9,‡, M. Lubej109,‡, T. Lueck57,‡, F. Luetticke129,‡, T. Luo23,‡, F. Müller16,‡, Th. Müller48,‡, C. MacQueen145,‡, Y. Maeda90,‡, M. Maggiora60,‡, S. Maity33,‡, E. Manoni56,‡, S. Marcello60,‡, C. Marinas129,‡, M. Martinez Hernandez4,‡, A. Martini59,‡, D. Matvienko6,96,77,‡, J. A. McKenna130,‡, F. Meier160,‡, M. Merola54,‡, F. Metzner48,‡, C. Miller165,‡, K. Miyabayashi91,‡, H. Miyake30,26,‡, H. Miyata94,‡, R. Mizuk77,88,87,‡, G. B. Mohanty111,163,‡, H. K. Moon71,‡, T. Moon106,‡,A. Morda55,‡, T. Morii66,‡, M. Mrvar109,‡, G. Muroyama90,‡, R. Mussa60,‡, I. Nakamura30,26,‡, T. Nakano99,‡, M. Nakao30,26,‡, H. Nakayama30,26,‡, H. Nakazawa92,‡, T. Nanut109,‡, M. Naruki72,‡, K. J. Nath34,‡, M. Nayak116,‡, N. Nellikunnummel151,‡, D. Neverov90,‡, C. Niebuhr16,‡, J. Ninkovic84,‡, S. Nishida30,26,‡, K. Nishimura138,‡, M. Nouxman143,‡, G. Nowak93,‡, K. Ogawa94,‡, Y. Onishchuk110,‡, H. Ono94,‡, Y. Onuki162,‡, P. Pakhlov77,88,‡, G. Pakhlova87,‡, B. Pal5,‡, E. Paoloni57,‡, H. Park73,‡, C.-S. Park172,‡, B. Paschen129,‡, A. Passeri59,‡, S. Paul114,‡, T. K. Pedlar80,‡, M. Perelló46,‡, I. M. Peruzzi52,‡, R. Pestotnik109,‡, L. E. Piilonen169,‡, L. Podesta Lerma125,‡, V. Popov87,‡, K. Prasanth111,‡, E. Prencipe21,‡, M. Prim48,‡, M. V. Purohit158,‡, A. Rabusov114,‡, R. Rasheed47,‡, S. Reiter65,‡, M. Remnev6,96,‡, P. K. Resmi36,‡, I. Ripp-Baudot47,‡, M. Ritter78,‡, M. Ritzert139,‡, G. Rizzo57,‡, L. Rizzuto141,109,‡, S. H. Robertson85,‡, D. Rodriguez Perez125,‡, J. M. Roney165,‡, C. Rosenfeld158,‡, A. Rostomyan16,‡, N. Rout36,‡, S. Rummel78,‡, G. Russo54,‡, D. Sahoo111,‡, Y. Sakai30,26,‡, M. Salehi143,78,‡, D. A. Sanders146,‡, S. Sandilya135,‡, A. Sangal135,‡, L. Santelj47,‡, J. Sasaki162,‡, Y. Sato30,‡, V. Savinov151,‡, B. Scavino63,‡, M. Schram100,‡, H. Schreeck24,‡, J. Schueler138,‡,C. Schwanda40,‡,A. J. Schwartz135,‡,R.M. Seddon85,‡,Y. Seino94,‡, K. Senyo171,‡, O. Seon90,‡, I. S. Seong138,‡, M. E. Sevior145,‡, C. Sfienti63,‡, M. Shapkin38,‡, C. P. Shen3,‡,M. Shimomura91,‡, J.-G. Shiu92,‡, B. Shwartz6,96,‡,A. Sibidanov165,‡, F. Simon83,113,‡, J. B. Singh101,‡, R. Sinha42,‡, S. Skambraks83,‡, K. Smith145,‡, R. J. Sobie165,‡, A. Soffer116,‡, A. Sokolov38,‡, E. Solovieva77,87,‡, B. Spruck63,‡, S. Staniˇc149,‡, M. Stariˇc109,‡, N. Starinsky147,‡, U. Stolzenberg24,‡, Z. Stottler169,‡, R. Stroili55,‡, J. F. Strube100,‡, J. Stypula93,‡, M. Sumihama25,‡, K. Sumisawa30,26,‡, T. Sumiyoshi121,‡, D. Summers146,‡, W. Sutcliffe48,‡, S. Y. Suzuki30,26,‡, M. Tabata13,‡, M. Takahashi16,‡, M. Takizawa107,‡, U. Tamponi60,‡, J. Tan145,‡, S. Tanaka30,26,‡, K. Tanida2,‡, N. Taniguchi30,‡, Y. Tao137,‡, P. Taras147,‡, G. Tejeda Munoz4,‡, F. Tenchini16,‡, U. Tippawan12,‡, E. Torassa55,‡, K. Trabelsi30,26,‡, T. Tsuboyama30,26,‡, M. Uchida120,‡, S. Uehara30,26,‡, T. Uglov77,87,‡, Y. Unno28,‡, S. Uno30,26,‡, Y. Ushiroda30,26,162,‡, Y. Usov6,96,‡, S. E. Vahsen138,‡, R. van Tonder48,‡, G. Varner138,‡, K. E. Varvell160,‡, A. Vinokurova6,96,‡, L.Vitale61,‡,M.Vos46,‡,A.Vossen17,‡,E.Waheed145,‡,H.Wakeling85,‡,K.Wan162,‡, M.-Z.Wang92,‡, X. L. Wang23,‡, B. Wang135,‡, A. Warburton85,‡, J. Webb145,‡, S. Wehle16,‡, C. Wessel129,‡, J. Wiechczynski93,‡, P. Wieduwilt24,‡, E. Won71,‡, Q. Xu41,‡, X. Xu41,‡, B. D. Yabsley160,‡, S. Yamada30,‡, H. Yamamoto119,‡, W. Yan3,‡, W. Yan154,‡, S. B. Yang71,‡, H. Ye16,‡, I. Yeo70,‡, J. H. Yin41,‡, M. Yonenaga121,‡, T. Yoshinobu94,‡, W. Yuan55,‡, C. Z. Yuan41,‡, Y. Yusa94,‡, S. Zakharov77,87,‡, L. Zani57,‡, M. Zeyrek86,‡, J. Zhang41,‡,Y. Zhang23,‡,Y. Zhang154,‡, X. Zhou3,‡, V. Zhukova77,‡, V. Zhulanov6,96,‡, and A. Zupanc141,109,‡ †Editor. ‡Belle II Collaborator. §Theory or external contributing author., "The Belle II Theory Interface Platform (B2TiP) was created as a physics prospects working group of the Belle II collaboration in June 2014. It offered a platform where theorists and experimentalists could work together to elucidate the potential impacts of the Belle II program, which includes a wide scope of physics topics: B physics, charm, τ , quarkonium physics, electroweak precision measurements, and dark sector searches. It is composed of nine working groups (WGs), which 6/654 Downloaded from https://academic.oup.com/ptep/article-abstract/2019/12/123C01/5685006 by Uniwersytet Slaski Biblioteka Glowna user on 20 February 2020 PTEP 2019, 123C01 E. Kou et al. are coordinated by teams of theory and experiment conveners: WG1, Semileptonic and leptonic B Decays; WG2, Radiative and Electroweak Penguins; WG3, φ1 and φ2 (Time-Dependent CP Violation) Measurements; WG4, φ3 Measurement; WG5, Charmless Hadronic B Decay; WG6, Charm; WG7, Quarkonium(-like); WG8, τ and Low-Multiplicity Processes; WG9, New Physics. We organized workshops twice a year from 2014 until 2016, which moved from KEK in Japan to Europe and the Americas, gathering experts in the respective fields for discussions with Belle II members. One of the goals for B2TiP was to propose so-called “golden and silver channels”: we asked each working group to choose, among numerous possible measurements, those that would have the highest potential impact and to focus on them for the writeup. Theorists scrutinized the role of those measurements in terms of understanding the theory behind them, and estimated the theoretical uncertainties now achievable as well as prospects for the future. For flavor physics, having tight control of hadronic uncertainties is one of the most crucial aspects in the field, and this is considered an important criterion in determining the golden or silver channels. Experimentalists, on the other hand, investigated the expected improvements with data from Belle II. For the channels where the errors are dominated by statistical uncertainties, or where systematic errors are reducible, the errors can decrease rapidly as more data becomes available. The impact of the upgraded performance from Belle II is a crucial element in reducing the uncertainties: we therefore include the latest available studies of the detector efficiency using Monte Carlo simulated events.We list the golden and silver channel table in the introductory chapter, as a guide for the chapters that follow. This book is not a collection of reports based on talks given at the workshops. The working group conveners endeavored to construct a coherent document that can be used by Belle II collaborators, and others in the field of flavor physics, as a reference. Two books of a similar type have been produced in the past: The BaBar Book [1] and The Physics of the B Factories [2]. In order to avoid too much repetition with respect to those references, we refer to them wherever possible for introductory material. We would like to thank the section editors and contributing authors for the many stimulating discussions and their tremendous efforts in bringing the book together." (Preface)

Properties of QCD matter change significantly around the chiral crossover temperature, and the effects on $U(1)_A$ and topological susceptibilities, as well as the meson spectrum have been studied with much care. Baryons and the effect of parity doubling in this temperature range have been analyzed previously by various other groups employing different setups. Here we construct suitable operators to investigate chiral and axial $U(1)_A$ symmetries in the baryon spectrum. Measurements for different volumes and quark-masses are done with two flavors of chirally symmetric domain-wall fermions at temperatures above the critical one. The possibility of emergent $SU(4)$ and $SU(2)_{CS}$ symmetries is discussed., Comment: 7 pages, 4 figures, talk presented at the 37th International Symposium on Lattice Field Theory (Lattice 2019), 16-22 June 2019, Wuhan, China. Updated numerical data in Fig. 1 and Fig. 2

Using lattice QCD simulations with $N_f = 2$ dynamical fermions, we study the axial $U(1)$ symmetry, topological charge, and Dirac eigenvalue spectra in the high-temperature phase in which the chiral symmetry is restored. Our gauge ensembles are generated with M\"obius domain-wall fermions, but the measurements such as susceptibilities are reweighted to those for the overlap fermions by using overlap/domain-wall reweighting technique. We find that the $U(1)_A$ and topological susceptibilities are strongly suppressed in the small quark mass region, which is related to the reduction of chiral-zero and low-nonzero modes on the Dirac spectra. We also examine their volume dependence., Comment: 10 pages, 4 figures, 1 table; Proceedings of The 9th International Workshop on Chiral Dynamics (CD18), 17-21 September, 2018, Durham, NC, USA. arXiv admin note: text overlap with arXiv:1812.06621

We report on the progress of understanding spatial correlation functions in high temperature QCD. We study isovector meson operators in $N_f=2$ QCD using domain-wall fermions on lattices of $N_s=32$ and different quark masses. It has previously been found that at $\sim 2T_c$ these observables are not only chirally symmetric but in addition approximately $SU(2)_{CS}$ and $SU(4)$ symmetric. In this study we increase the temperature up to $5T_c$ and can identify convergence towards an asymptotically free scenario at very high temperatures., 7 pages, 5 figures, version to appear in proceedings of the LATTICE2018 conference

We compute the Dirac spectral density of QCD in a wide range of eigenvalues by using a stochastic method. We use 2+1 flavor lattice ensembles generated with Mobius domain-wall fermion at three lattice spacings ($a=0.083, 0.055, 0.044$ fm) to estimate the continuum limit. The discretization effect can be minimized by a generalization of the valence domain-wall fermion. The spectral density at relatively high eigenvalues can be matched with perturbation theory. We compare the lattice results with the perturbative expansion available to $O(\alpha_s^4)$., Comment: 8 pages, 4 figures. Proceedings of the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spain

We calculate the scalar and tensor charges of the nucleon in 2+1-flavor lattice QCD, for which the systematics of the renormalization of the disconnected diagram is well controlled. Numerical simulations are performed at a single lattice spacing a = 0.11 fm. We simulate four pion masses, which cover a range of $m_\pi \sim$ 290 - 540 MeV, and a single strange quark mass close to its physical value. The statistical accuracy is improved by employing the so-called low-mode averaging technique and the truncated solver method. We study up, down, and strange quark contributions to the nucleon charges by calculating disconnected diagrams using the all-to-all quark propagator. Chiral symmetry is exactly preserved by using the overlap quark action to avoid operator mixing among different flavors, which complicates the renormalization of scalar and tensor matrix elements and leads to possibly large contamination to the small strange quark contributions. We also study the nucleon axial charge with contribution from the disconnected diagram. Our results are in reasonable agreement with experiments and previous lattice studies., Comment: 39 pages, 17 figures

The axial $U(1)$ symmetry in the high-temperature phase is investigated with $N_f = 2$ lattice QCD simulations. The gauge ensembles are generated with M\"obius domain-wall fermions, and the overlap/domain-wall reweighting is applied. We find that the $U(1)_A$ susceptibility evaluated from the spectrum of overlap-Dirac eigenvalues is strongly suppressed in the chiral limit. We also study its volume dependence., Comment: 7 pages, 2 figures, talk presented at the 36th International Symposium on Lattice Field Theory (Lattice 2018), 22-28 July, 2018, Michigan, USA

The eigenvalue spectrum $\rho(\lambda)$ of the Dirac operator is numerically calculated in lattice QCD with 2+1 flavors of dynamical domain-wall fermions. In the high-energy regime, the discretization effects become significant. We subtract them at the leading order and then take the continuum limit with lattice data at three lattice spacings. Lattice results for the exponent $\partial\ln\rho/\partial\ln\lambda$ are matched to continuum perturbation theory, which is known up to $O(\alpha_s^4)$, to extract the strong coupling constant $\alpha_s$., Comment: 34 pages, 18 figures, and 2 tables

We present our calculation of D \to pi and D \to K semileptonic form factors in Nf = 2+1 lattice QCD. We simulate three lattice cutoffs 1/a \sim 2.5, 3.6 and 4.5 GeV with pion masses as low as 230 MeV. The M\"obius domain-wall action is employed for both light and charm quarks. We present our results for the vector and scalar form factors and discuss their dependence on the lattice spacing, light quark masses and momentum transfer., Comment: 8 pages, 5 figures, talk presented at the 35th International Symposium on Lattice Field Theory (Lattice 2017), 18-24 June 2017, Granada, Spain

We study spatial isovector meson correlators in $N_f=2$ QCD with dynamical domain-wall fermions on $32^3\times 8$ lattices at temperatures $T=220-380$ MeV. We measure the correlators of spin-one ($J=1$) operators including vector, axial-vector, tensor and axial-tensor. Restoration of chiral $U(1)_A$ and $SU(2)_L \times SU(2)_R$ symmetries of QCD implies degeneracies in vector--axial-vector ($SU(2)_L \times SU(2)_R$) and tensor--axial-tensor ($U(1)_A$) pairs, which are indeed observed at temperatures above $T_c$. Moreover, we observe an approximate degeneracy of all $J=1$ correlators with increasing temperature. This approximate degeneracy suggests emergent $SU(2)_{CS}$ and $SU(4)$ symmeries at high temperatures, that mix left- and right-handed quarks., This revised version contains all corrections that will appear in the forthcoming erratum

We compute the topological susceptibility $\chi_t$ of lattice QCD with $2+1$ dynamical quark flavors described by the M\"obius domain wall fermion. Violation of chiral symmetry as measured by the residual mass is kept at $\sim$1 MeV or smaller. We measure the fluctuation of the topological charge density in a `slab' sub-volume of the simulated lattice using the method proposed by Bietenholz {\it et al.} The quark mass dependence of $\chi_t$ is consistent with the prediction of chiral perturbation theory, from which the chiral condensate is extracted as $\Sigma^{\overline{\rm MS}} (\mbox{2GeV}) = [274(13)(29)\mbox{MeV}]^3$, where the first error is statistical and the second one is systematic. Combining the results for the pion mass $M_\pi$ and decay constant $F_\pi$, we obtain $\chi_t = 0.229(03)(13)M_\pi^2F_\pi^2$ at the physical point., Comment: 23pages, 10figures, metadata abstract corrected

We propose a method to non-perturbatively calculate the forward-scattering matrix elements relevant to inclusive semi-leptonic B meson decays. Corresponding hadronic structure functions at unphysical kinematics are accessible through lattice QCD calculation of four-point correlation functions. The unphysical kinematical point may be reached by analytic continuation from the physical differential decay rate. A numerical test is performed for the B_s -> X_c l nu mode in the zero-recoil limit. We use lattice ensembles generated with 2+1 dynamical quark flavors. The valence charm quark mass is tuned to its physical value, while the bottom quark mass is varied in the range (1.56-2.44)m_c. From the numerical results we can identify the contributions of the ground state D_s^(*) meson as well as those of excited states or continuum states., 35 pages, 14 figures

We study the vector and axial-vector current correlators in perturbative and non-perturbative regimes of QCD. The correlators in Euclidean coordinate space are calculated on the lattice using the M\"obius domain-wall fermion formulation at three lattice spacings covering 0.044--0.080~fm. The dynamical quark effects of $2+1$ light flavors are included. The sum $V+A$ and the difference $V-A$ of the vector ($V$) and axial-vector ($A$) current correlators calculated on the lattice after extrapolating to the physical point agree with those converted from the ALEPH experimental data of hadronic $\tau$ decays. The level of the agreement in the $V+A$ channel is about $1.3\sigma$ or smaller in the region of $|x|\ge0.4$~fm, while that in the $V-A$ channel is about $1.8\sigma$ at $|x|=0.74$~fm and smaller at other distances. We also extract the hiral condensate from the short-distance correlators on the lattice using the PCAC relation. Its result extrapolated to the chiral and continuum limit is compatible with other estimates at low energies., Comment: 32 pages, 19 figures

We explore the heavy-quark mass region above the charm mass using M\"obius domain-wall fermions on fine lattices at $a = 0.080$, $0.055$, and $0.044$ fm. We examine masses and decay constants using a series of heavy quark masses up to 3 times the charm quark. We analyze the cutoff effects for heavy quarks above the charm and account for the leading order discretization effects using ideas from HQET. We extrapolate to the bottom quark mass and report preliminary results for $f_{B}$ and $f_{B_s}$.

We calculate the vector and axial-vector current correlators in the coordinate space and compare them with the experimental information obtained through the spectral functions of hadronic tau decays measured by ALEPH. Lattice data are obtained with 2+1 Mobius domain-wall fermions at three lattice spacings 0.044, 0.055 and 0.080 fm and the continuum limit is taken. The correlators calculated on the lattice after extrapolating to the physical point agree with those converted from the ALEPH data., Comment: 7 pages, 7 figures; talk presented at Lattice 2016 -- 34th International Symposium on Lattice Field Theory, 24-30 July 2016, University of Southampton, UK

We study the topological charge in $N_f=2$ QCD at finite temperature using M\"obius domain-wall fermions. The susceptibility $\chi_t$ of the topological charge defined either by the index of overlap Dirac operator or a gluonic operator is investigated at several values of temperature $T\ (>T_c)$ varying the quark mass. A strong suppression of the susceptibility is observed below a certain value of the quark mass. The relation with the restoration of $U_A(1)$ is discussed., Comment: 8 pages, 8 figures, Proceedings of the 35th International Symposium on Lattice Field Theory, June 18-24, 2017, Granada, Spain

We calculate charmonium correlators on the lattice with 2+1-flavors of sea quarks and charm valence quark both described by the M\"obius domain-wall fermion. Temporal moments of the correlators are calculated and matched to perturbative QCD formulae to extract the charm quark mass $m_c(\mu)$ and strong coupling constant $\alpha_s(\mu)$. Lattice data at three lattice spacings, 0.044, 0.055, and 0.080~fm, are extrapolated to the continuum limit. The correlators in the vector channel are confirmed to be consistent with the experimental data for $e^+e^-\to c\bar{c}$, while the pseudo-scalar channel is used to extract $m_c(\mu)$ and $\alpha_s(\mu)$. We obtain $m_\mathrm{c}(3 \mathrm{\ GeV})$ = 1.003(10)~GeV and $\alpha_s^{\bar{\mathrm{MS}}(4)}(3\mathrm{\ GeV})$ = 0.253(13). Dominant source of the error is the truncation of perturbative expansion at $\alpha_s^3$., Comment: 32 pages, 10 figures, 10 tables

We investigate the properties of the background gauge field configurations that act as disorder for the Anderson localization mechanism in the Dirac spectrum of QCD at high temperatures. We compute the eigenmodes of the M\"obius domain-wall fermion operator on configurations generated for the $SU(3)$ gauge theory with two flavors of fermions, in the temperature range $[0.9,1.9]T_c$. We identify the source of localization of the eigenmodes with gauge configurations that are self-dual and support negative fluctuations of the Polyakov loop $P_L$, in the high temperature sea of $P_L\sim 1$. The dependence of these observations on the boundary conditions of the valence operator is studied. We also investigate the spatial overlap of the left-handed and right-handed projected eigenmodes in correlation with the localization and the corresponding eigenvalue. We discuss an interpretation of the results in terms of monopole-instanton structures., Comment: 27 pages, 16 figures, 2 tables, minor corrections and typos

We determine the renormalization constants for flavor non-singlet fermion bilinear operators of M\"obius domain-wall fermions. The renormalization condition is imposed on the correlation functions in the coordinate space, such that the non-perturbative lattice calculation reproduces the perturbatively calculated counterpart at short distances. The perturbative expansion is precise as the coefficients are available up to $O(\alpha_s^4)$. We employ $2+1$-flavor lattice ensembles at three lattice spacings in the range 0.044--0.080~fm., Comment: 36 pages, 20 figures

We compute the chiral condensate in 2+1-flavor QCD through the spectrum of low-lying eigenmodes of Dirac operator. The number of eigenvalues of the Dirac operator is evaluated using a stochastic method with an eigenvalue filtering technique on the background gauge configurations generated by lattice QCD simulations including the effects of dynamical up, down and strange quarks described by the Mobius domain-wall fermion formulation. The low-lying spectrum is related to the chiral condensate, which is one of the leading order low-energy constants in chiral effective theory, as dictated by the Banks-Casher relation. The spectrum shape and its dependence on the sea quark masses calculated in numerical simulations are consistent with the expectation from one-loop chiral perturbation theory. After taking the chiral limit as well as the continuum limit using the data at three lattice spacings ranging 0.080-0.045 fm, we obtain $\Sigma^{1/3}$(2 GeV) = 270.0(4.9) MeV, with the error combining those from statistical and from various sources of systematic errors. Finite volume effect is confirmed to be under control by a direct comparison of the results from two different volumes at the lightest available sea quarks corresponding to 230 MeV pions., Comment: 21 pages, 9 figures, a revised version to appear in PTEP

By using the overlap-Dirac operator eigenmodes, we investigate spatial distribution of the chiral condensate around static color sources for both quark-antiquark and three quark systems. In the presence of color sources, a characteristic flux-tube structure appears among them, suggesting a linear confining potential. We show that the magnitude of the condensate is reduced inside the color flux, which indicates the partial restoration of chiral symmetry inside the "hadrons." Considering a periodic box containing a static baryon source, which mimics the "nuclear matter," we estimate the chiral symmetry restoration in the presence of finite baryon number density., 7 pages, 6 figures, presented at the 32nd International Symposium on Lattice Field Theory, 23-28 June, 2014, Columbia University New York, NY

We compute the topological susceptibility $\chi_t$ of 2+1-flavor lattice QCD with dynamical M\"obius domain-wall fermions, whose residual mass is kept at 1 MeV or smaller. In our analysis, we focus on the fluctuation of the topological charge density in a "slab" sub-volume of the simulated lattice, as proposed by Bietenholz et al. The quark mass dependence of our results agrees well with the prediction of the chiral perturbation theory, from which the chiral condensate is extracted. Combining the results for the pion mass $M_\pi$ and decay constant $F_\pi$, we obtain $\chi_t$ = 0.227(02)(11)$M_\pi^2 F_\pi^2$ at the physical point, where the first error is statistical and the second is systematic., Comment: 8 pages, 3 figures, talk given at the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spain

We investigate the axial $U(1)_A$ symmetry breaking above the critical temperature in two-flavor lattice QCD. The ensembles are generated with dynamical M\"obius domain-wall or reweighted overlap fermions. The $U(1)_A$ susceptibility is extracted from the low-modes spectrum of the overlap Dirac eigenvalues. We show the quark mass and temperature dependences of $U(1)_A$ susceptibility. Our results at $T=220 \, \mathrm{MeV}$ imply that the $U(1)_A$ symmetry is restored in the chiral limit. Its coincidence with vanishing topological susceptibility is observed., Comment: 8 pages, 4 figures, Proceedings of the 35th International Symposium on Lattice Field Theory, June 18-24, 2017, Granada, Spain

We study spatial isovector meson correlators in $N_f=2$ QCD with dynamical domain-wall fermions on $32^3\times 8$ lattices at temperatures up to 380 MeV with various quark masses. We measure the correlators of spin-one isovector operators including vector, axial-vector, tensor and axial-tensor. At temperatures above $T_c$ we observe an approximate degeneracy of the correlators in these channels, which is unexpected because some of them are not related under $SU(2)_L \times SU(2)_R$ nor $U(1)_A$ symmetries. The observed approximate degeneracy suggests emergent $SU(2)_{CS}$ (chiral-spin) and $SU(4)$ symmetries at high $T$., Comment: 8 pages, 2 tables, 4 figures. Talk presented at the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spain. arXiv admin note: substantial text overlap with arXiv:1707.01881

We investigate the correlators of flavor non-singlet bilinear operators calculated on the lattice at short distances. In the continuum theory, non-perturbative effects are encoded in the form of the operator product expansion (OPE). We test the prediction of OPE by comparing lattice results with those in the continuum theory. We also determine the renormalization factors of quark currents.

We present scaling studies for heavy-quark observables calculated with an $O(a^2)$-improved fermion action on tree-level Symanzik improved gauge configurations. Lattices of $1/a = $ 2.0-3.8 GeV with an equal physical volume 1.6 fm are used. The results are compared with the standard domain-wall and naive Wilson fermions., 7 pages, 3 figures, presented at the 32nd International Symposium on Lattice Field Theory, 23-28 June, 2014, Colombia University, New York, USA

Using the quark eigenmodes computed on the lattice with the overlap-Dirac operator, we investigate the spatial distribution of the chiral condensate around static color sources corresponding to quark-antiquark and three-quark systems. A flux structure of chromo fields appears in the presence of such color charges. The magnitude of the chiral condensate is reduced inside the color flux, which implies partial restoration of chiral symmetry inside hadrons. Taking a static baryon source in a periodic box as a toy model of nuclear matter, we estimate the magnitude of the chiral symmetry restoration as a function of baryon matter density., Comment: 21 pages, 14 figures, published version in Phys. Rev. D

We report on our calculation of the nucleon axial and tensor charges in 2+1-flavor QCD with dynamical overlap quarks. Gauge ensembles are generated at a single lattice spacing 0.12 fm and at a strange quark mass close to its physical value. We employ the all-mode-averaging technique to calculate the relevant nucleon correlation functions, and the disconnected quark loop is efficiently calculated by using the all-to-all quark propagator. We present our preliminary results for the isoscalar and isovector charges obtained at pion masses $m_\pi$ = 450 and 540 MeV., Comment: 7 pages, 10 figures, proceeding of the 33rd International Symposium on Lattice field theory (Lattice 2015), Kobe, Japan, July 2015

We present results showing that Domain Wall fermions are a suitable discretisation for the simulation of heavy quarks. This is done by a continuum scaling study of charm quarks in a M\"obius Domain Wall formalism using a quenched set-up. We find that discretisation effects remain well controlled by the choice of Domain Wall parameters preparing the ground work for the ongoing dynamical $2+1f$ charm program of RBC/UKQCD., Comment: The 32nd International Symposium on Lattice Field Theory

We develop an improved lattice action for heavy quarks based on Brillouin-type fermions, that have excellent energy-momentum dispersion relation. The leading discretization errors of $O(a)$ and $O(a^2)$ are eliminated at tree-level. We carry out a scaling study of this improved Brillouin fermion action on quenched lattices by calculating the charmonium energy-momentum dispersion relation and hyperfine splitting. We present a comparison to standard Wilson fermions and domain-wall fermions., Comment: 33 pages, 23 figures, minor changes are made, a version published in JHEP

We calculate the charmonium correlators on the lattice with $n_f = 2+ 1$ Moebius domain wall fermion, and extract the charm quark mass and the strong coupling constant. Time moments are defined by current-current correlators, which have been calculated in the continuum theory by perturbation theory. We extract the charm quark mass by matching the lattice results with the corresponding perturbative QCD calculations, using the recently generated ensembles by the JLQCD collaboration at lattice spacings $a = 0.083, 0.055$, and $0.044$ fm., Comment: 7 pages, 3 figure, 1 table, presented at 33rd International Symposium on Lattice Field Theory, July 14-18, 2015, Kobe, Japan

The Wilson fermion determinant can be written in the form of a series expansion in fugacity $\xi=\exp(\mu/T)$, provided that the eigenmodes of the temporally reduced operator are obtained. Since the calculation of all eigenmodes rapidly becomes prohibitive for larger volumes, we develop a method to calculate only the low-energy eigenmodes of the reduced matrix using a matrix filetering technique. This provides a basis for an approximation to neglect uninteresting ultraviolet contributions., Comment: 7 pages, 2figures. Proceedings of The 32nd International Symposium on Lattice Field Theory, 23-28 June, 2014 Columbia University New York, NY