Monte Carlo calculations in the framework of lattice field theory provide non-perturbative access to the equilibrium physics of quantum fields. When applied to certain fermionic systems, or to the calculation of out-of-equilibrium physics, these methods encounter the so-called sign problem, and computational resource requirements become impractically large. These difficulties prevent the calculation from first principles of the equation of state of quantum chromodynamics, as well as the computation of transport coefficients in quantum field theories, among other things. This thesis details two methods for mitigating or avoiding the sign problem. First, via the complexification of the field variables and the application of Cauchy's integral theorem, the difficulty of the sign problem can be changed. This requires searching for a suitable contour of integration. Several methods of finding such a contour are discussed, as well as the procedure for integrating on it. Two notable examples are highlighted: in one case, a contour exists which entirely removes the sign problem, and in another, there is provably no contour available to improve the sign problem by more than a (parametrically) small amount. As an alternative, physical simulations can be performed with the aid of a quantum computer. The formal elements underlying a quantum computation - that is, a Hilbert space, unitary operators acting on it, and Hermitian observables to be measured - can be matched to those of a quantum field theory. In this way an error-corrected quantum computer may be made to serve as a well controlled laboratory. Precise algorithms for this task are presented, specifically in the context of quantum chromodynamics.
{"title":"Sign Problems in Quantum Field Theory: Classical and Quantum Approaches","authors":"S. Lawrence","doi":"10.13016/U5EG-X7Y6","DOIUrl":"https://doi.org/10.13016/U5EG-X7Y6","url":null,"abstract":"Monte Carlo calculations in the framework of lattice field theory provide non-perturbative access to the equilibrium physics of quantum fields. When applied to certain fermionic systems, or to the calculation of out-of-equilibrium physics, these methods encounter the so-called sign problem, and computational resource requirements become impractically large. These difficulties prevent the calculation from first principles of the equation of state of quantum chromodynamics, as well as the computation of transport coefficients in quantum field theories, among other things. \u0000This thesis details two methods for mitigating or avoiding the sign problem. First, via the complexification of the field variables and the application of Cauchy's integral theorem, the difficulty of the sign problem can be changed. This requires searching for a suitable contour of integration. Several methods of finding such a contour are discussed, as well as the procedure for integrating on it. Two notable examples are highlighted: in one case, a contour exists which entirely removes the sign problem, and in another, there is provably no contour available to improve the sign problem by more than a (parametrically) small amount. \u0000As an alternative, physical simulations can be performed with the aid of a quantum computer. The formal elements underlying a quantum computation - that is, a Hilbert space, unitary operators acting on it, and Hermitian observables to be measured - can be matched to those of a quantum field theory. In this way an error-corrected quantum computer may be made to serve as a well controlled laboratory. Precise algorithms for this task are presented, specifically in the context of quantum chromodynamics.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87259673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, employing an all-to-all quark propagator technique, we investigate the kaon-nucleon interactions in lattice QCD. We calculate the S-wave kaon-nucleon potentials at the leading order in the derivative expansion in the time-dependent HAL QCD method, using (2+1)-flavor gauge configurations at the lattice spacing $a approx 0.09$ fm on $32^3 times 64$ lattices and the pion mass $m_{pi} approx 570$ MeV. We take the one-end trick for all-to-all propagators, which allows us to put the zero momentum hadron operators at both source and sink and to smear quark operators at the source. We find the stronger repulsive interaction in the $I=1$ channel than in the $I=0$. The phase shifts obtained by solving the Schrodinger equations with the potentials qualitatively reproduce the energy dependence of the experimental phase shifts, and have the similar behavior to the previous results from lattice QCD without all-to-all propagators. Our study demonstrates that the all-to-all quark propagator technique with the one-end trick is useful to study interactions for meson-baryon systems in the HAL QCD method, so that we will apply it to meson-baryon systems which contain quark-antiquark creation/annihilation processes in our future studies.
{"title":"S-wave kaon–nucleon potentials with all-to-all propagators in the HAL QCD method","authors":"K. Murakami, Yutaro Akahoshi, S. Aoki","doi":"10.1093/PTEP/PTAA118","DOIUrl":"https://doi.org/10.1093/PTEP/PTAA118","url":null,"abstract":"In this paper, employing an all-to-all quark propagator technique, we investigate the kaon-nucleon interactions in lattice QCD. We calculate the S-wave kaon-nucleon potentials at the leading order in the derivative expansion in the time-dependent HAL QCD method, using (2+1)-flavor gauge configurations at the lattice spacing $a approx 0.09$ fm on $32^3 times 64$ lattices and the pion mass $m_{pi} approx 570$ MeV. We take the one-end trick for all-to-all propagators, which allows us to put the zero momentum hadron operators at both source and sink and to smear quark operators at the source. We find the stronger repulsive interaction in the $I=1$ channel than in the $I=0$. The phase shifts obtained by solving the Schrodinger equations with the potentials qualitatively reproduce the energy dependence of the experimental phase shifts, and have the similar behavior to the previous results from lattice QCD without all-to-all propagators. Our study demonstrates that the all-to-all quark propagator technique with the one-end trick is useful to study interactions for meson-baryon systems in the HAL QCD method, so that we will apply it to meson-baryon systems which contain quark-antiquark creation/annihilation processes in our future studies.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74869618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The type IIB matrix model is a promising candidate for a nonperturbative formulation of superstring theory. In the Lorentzian version, in particular, the emergence of (3+1)D expanding space-time was observed by Monte Carlo studies of this model. Here we provide new perspectives on the (3+1)D expanding space-time that have arised from recent studies. First it was found that the matrix configurations generated by the simulation are singular in that the submatrices representing the expanding 3D space have only two large eigenvalues associated with the Pauli matrices. This problem was conjectured to occur due to the approximation used to avoid the sign problem in simulating the model. In order to confirm this conjecture, the complex Langevin method was applied to overcome the sign problem instead of using the approximation. The results indeed showed a clear departure from the Pauli-matrix structure, while the (3+1)D expanding behavior remained unaltered. It was also found that classical solutions obtained within a certain ansatz show quite generically a (3+1)D expanding behavior with smooth space-time structure.
{"title":"New perspectives on the emergence of (3+1)D expanding space-time in the Lorentzian type IIB matrix model","authors":"J. Nishimura","doi":"10.22323/1.376.0178","DOIUrl":"https://doi.org/10.22323/1.376.0178","url":null,"abstract":"The type IIB matrix model is a promising candidate for a nonperturbative formulation of superstring theory. In the Lorentzian version, in particular, the emergence of (3+1)D expanding space-time was observed by Monte Carlo studies of this model. Here we provide new perspectives on the (3+1)D expanding space-time that have arised from recent studies. First it was found that the matrix configurations generated by the simulation are singular in that the submatrices representing the expanding 3D space have only two large eigenvalues associated with the Pauli matrices. This problem was conjectured to occur due to the approximation used to avoid the sign problem in simulating the model. In order to confirm this conjecture, the complex Langevin method was applied to overcome the sign problem instead of using the approximation. The results indeed showed a clear departure from the Pauli-matrix structure, while the (3+1)D expanding behavior remained unaltered. It was also found that classical solutions obtained within a certain ansatz show quite generically a (3+1)D expanding behavior with smooth space-time structure.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73658207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-28DOI: 10.1103/physrevd.102.114513
Yao Ji, Henry Lamm, Shuchen Zhu
Efficient digitization is required for quantum simulations of gauge theories. Schemes based on discrete subgroups use fewer qubits at the cost of systematic errors. We systematize this approach by deriving a single plaquette action for approximating general continuous gauge groups through integrating out field fluctuations. This provides insight into the effectiveness of these approximations, and how they could be improved. We accompany the scheme by simulations of pure gauge over the largest discrete subgroup of $SU(3)$ up to the third order.
{"title":"Gluon field digitization via group space decimation for quantum computers","authors":"Yao Ji, Henry Lamm, Shuchen Zhu","doi":"10.1103/physrevd.102.114513","DOIUrl":"https://doi.org/10.1103/physrevd.102.114513","url":null,"abstract":"Efficient digitization is required for quantum simulations of gauge theories. Schemes based on discrete subgroups use fewer qubits at the cost of systematic errors. We systematize this approach by deriving a single plaquette action for approximating general continuous gauge groups through integrating out field fluctuations. This provides insight into the effectiveness of these approximations, and how they could be improved. We accompany the scheme by simulations of pure gauge over the largest discrete subgroup of $SU(3)$ up to the third order.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73174655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-25DOI: 10.1103/PHYSREVD.102.074504
Z. Fan, Xiang Gao, Rui-Cheng Li, Huey-Wen Lin, Nikhil Karthik, S. Mukherjee, P. Petreczky, S. Syritsyn, Yi-Bo Yang, Rui Zhang
We study isovector unpolarized and helicity parton distribution functions (PDF) of proton within the framework of Large Momentum Effective Theory. We use a gauge ensemble, generated by the MILC collaboration, with a superfine lattice spacing of $0.042$ fm and a pion mass of $310$ MeV, enabling us to simultaneously reach sub-fermi spatial separations and larger nucleon momenta. We compare the spatial dependence of quasi-PDF matrix elements in different renormalization schemes with the corresponding results of the global fits, obtained using 1-loop perturbative matching. We present determinations of first four moments of the unpolarized and helicity PDFs of proton from the Ioffe-time dependence of the isovector matrix elements, obtained employing a ratio-based renormalization scheme.
{"title":"Isovector parton distribution functions of the proton on a superfine lattice","authors":"Z. Fan, Xiang Gao, Rui-Cheng Li, Huey-Wen Lin, Nikhil Karthik, S. Mukherjee, P. Petreczky, S. Syritsyn, Yi-Bo Yang, Rui Zhang","doi":"10.1103/PHYSREVD.102.074504","DOIUrl":"https://doi.org/10.1103/PHYSREVD.102.074504","url":null,"abstract":"We study isovector unpolarized and helicity parton distribution functions (PDF) of proton within the framework of Large Momentum Effective Theory. We use a gauge ensemble, generated by the MILC collaboration, with a superfine lattice spacing of $0.042$ fm and a pion mass of $310$ MeV, enabling us to simultaneously reach sub-fermi spatial separations and larger nucleon momenta. We compare the spatial dependence of quasi-PDF matrix elements in different renormalization schemes with the corresponding results of the global fits, obtained using 1-loop perturbative matching. We present determinations of first four moments of the unpolarized and helicity PDFs of proton from the Ioffe-time dependence of the isovector matrix elements, obtained employing a ratio-based renormalization scheme.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75099990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-13DOI: 10.1142/S0217751X20300100
M. Lombardo, A. Trunin
QCD axions are at the crossroads of QCD topology and Dark Matter searches. We present here the current status of topological studies on the lattice, and their implication on axion physics. We outline the specific challenges posed by lattice topology, the different proposals for handling them, the observable effects of topology on the QCD spectrum and its interrelation with chiral and axial symmetries. We review the transition to the Quark Gluon Plasma, the fate of topology at the transition, and the approach to the high temperature limit. We discuss the extrapolations needed to reach the regime of cosmological relevance, and the resulting constraints on the QCD axion.
{"title":"Topology and axions in QCD","authors":"M. Lombardo, A. Trunin","doi":"10.1142/S0217751X20300100","DOIUrl":"https://doi.org/10.1142/S0217751X20300100","url":null,"abstract":"QCD axions are at the crossroads of QCD topology and Dark Matter searches. We present here the current status of topological studies on the lattice, and their implication on axion physics. We outline the specific challenges posed by lattice topology, the different proposals for handling them, the observable effects of topology on the QCD spectrum and its interrelation with chiral and axial symmetries. We review the transition to the Quark Gluon Plasma, the fate of topology at the transition, and the approach to the high temperature limit. We discuss the extrapolations needed to reach the regime of cosmological relevance, and the resulting constraints on the QCD axion.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141205262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-12DOI: 10.5506/aphyspolbsupp.14.93
M. Catillo, M. K. Marinkovi'c, P. Bicudo, N. Cardoso
We present a preliminary computation of potentials between two static quarks in $n_f=2$ QCD with O(a) improved Wilson fermions. We explore different smearing choices (HYP, HYP2 and APE) and their effect on the signal to noise ratio in the computed static potentials. This is a part of a larger effort concerning, at first, a precise computation of the QCD string breaking parameters and their subsequent utilization for the recent approach based on Born-Oppenheimer approximation (Bicudo et al. 2020 cite{Bicudo:2019ymo}) to study quarkonium resonances and bound states.
我们提出了一个用O(a)改进的威尔逊费米子在$n_f=2$ QCD中两个静态夸克之间的势的初步计算。我们探讨了不同的涂抹选择(HYP, HYP2和APE)及其对计算静态电位信噪比的影响。这是一项更大的努力的一部分，首先是精确计算QCD弦断裂参数，并随后将其用于基于Born-Oppenheimer近似(Bicudo et al. 2020 cite{Bicudo:2019ymo})的最新方法，以研究夸克粒子共振和束缚态。
{"title":"From String Breaking to Quarkonium Spectrum","authors":"M. Catillo, M. K. Marinkovi'c, P. Bicudo, N. Cardoso","doi":"10.5506/aphyspolbsupp.14.93","DOIUrl":"https://doi.org/10.5506/aphyspolbsupp.14.93","url":null,"abstract":"We present a preliminary computation of potentials between two static quarks in $n_f=2$ QCD with O(a) improved Wilson fermions. We explore different smearing choices (HYP, HYP2 and APE) and their effect on the signal to noise ratio in the computed static potentials. This is a part of a larger effort concerning, at first, a precise computation of the QCD string breaking parameters and their subsequent utilization for the recent approach based on Born-Oppenheimer approximation (Bicudo et al. 2020 cite{Bicudo:2019ymo}) to study quarkonium resonances and bound states.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86229404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-01DOI: 10.1103/physrevd.102.014510
Y. Taniguchi, S. Ejiri, K. Kanaya, M. Kitazawa, Hiroshi Suzuki, T. Umeda
We study thermodynamic properties of Nf=2+1 QCD on the lattice adopting O(a)-improved Wilson quark action and Iwasaki gauge action. To cope with the problems due to explicit violation of the Poincare and chiral symmetries, we apply the Small Flow-time eXpansion (SFtX) method based on the gradient flow, which is a general method to correctly calculate any renormalized observables on the lattice. In this method, the matching coefficients in front of operators in the small flow-time expansion are calculated by perturbation theory. In a previous study using one-loop matching coefficients, we found that the SFtX method works well for the equation of state, chiral condensates and susceptibilities. In this paper, we study the effect of two-loop matching coefficients by Harlander et al. We also test the influence of the renormalization scale in the SFtX method. We find that, by adopting the mu_0 renormalization scale of Harlander et al. instead of the conventional mu_d=1/sqrt{8t} scale, the linear behavior at large t is improved so that we can perform the t -> 0 extrapolation of the SFtX method more confidently. In the calculation of the two-loop matching coefficients by Harlander et al., the equation of motion for quark fields was used. For the entropy density in which the equation of motion has no effects, we find that the results using the two-loop coefficients agree well with those using one-loop coefficients. On the other hand, for the trace anomaly which is affected by the equation of motion, we find discrepancies between the one- and two-loop results at high temperatures. By comparing the results of one-loop coefficients with and without using the equation of motion, the main origin of the discrepancies is suggested to be attributed to O((aT)^2)=O(1/N_t^2) discretization errors in the equation of motion at N_t =< 10.
{"title":"Nf=2+1\u0000 QCD thermodynamics with gradient flow using two-loop matching coefficients","authors":"Y. Taniguchi, S. Ejiri, K. Kanaya, M. Kitazawa, Hiroshi Suzuki, T. Umeda","doi":"10.1103/physrevd.102.014510","DOIUrl":"https://doi.org/10.1103/physrevd.102.014510","url":null,"abstract":"We study thermodynamic properties of Nf=2+1 QCD on the lattice adopting O(a)-improved Wilson quark action and Iwasaki gauge action. To cope with the problems due to explicit violation of the Poincare and chiral symmetries, we apply the Small Flow-time eXpansion (SFtX) method based on the gradient flow, which is a general method to correctly calculate any renormalized observables on the lattice. In this method, the matching coefficients in front of operators in the small flow-time expansion are calculated by perturbation theory. In a previous study using one-loop matching coefficients, we found that the SFtX method works well for the equation of state, chiral condensates and susceptibilities. In this paper, we study the effect of two-loop matching coefficients by Harlander et al. We also test the influence of the renormalization scale in the SFtX method. We find that, by adopting the mu_0 renormalization scale of Harlander et al. instead of the conventional mu_d=1/sqrt{8t} scale, the linear behavior at large t is improved so that we can perform the t -> 0 extrapolation of the SFtX method more confidently. In the calculation of the two-loop matching coefficients by Harlander et al., the equation of motion for quark fields was used. For the entropy density in which the equation of motion has no effects, we find that the results using the two-loop coefficients agree well with those using one-loop coefficients. On the other hand, for the trace anomaly which is affected by the equation of motion, we find discrepancies between the one- and two-loop results at high temperatures. By comparing the results of one-loop coefficients with and without using the equation of motion, the main origin of the discrepancies is suggested to be attributed to O((aT)^2)=O(1/N_t^2) discretization errors in the equation of motion at N_t =< 10.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76384765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-04-08DOI: 10.1103/physrevd.102.111501
S. Bhattacharya, K. Cichy, M. Constantinou, A. Metz, Aurora Scapellato, F. Steffens
In this work, we present the first-ever calculation of the isovector flavor combination of the twist-3 parton distribution function $g_T(x)$ for the proton from lattice QCD. We use an ensemble of gauge configurations with two degenerate light, a strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with a clover improvement. The lattice has a spatial extent of 3 fm, lattice spacing of 0.093 fm, and reproduces a pion mass of $260$ MeV. We use the quasi-distribution approach and employ three values of the proton momentum boost, 0.83 GeV, 1.25 GeV and 1.67 GeV. We use a source-sink separation of 1.12 fm to suppress excited-states contamination. The lattice data are renormalized non-perturbatively. We calculate the appropriate matching within Large Momentum Effective Theory, which is applied to the lattice data in order to obtain $g_T$. The final distribution is presented in the $overline{rm MS}$ scheme at a scale of 2 GeV. We also calculate the helicity distribution $g_1$ to test the Wandzura-Wilczek approximation for $g_T$. We find that the approximation works well for a large range in $x$. This work demonstrates the feasibility of accessing twist-3 parton distribution functions from novel methods within lattice QCD, and can provide important insights on the structure of hadrons.
{"title":"Insights on proton structure from lattice QCD: The twist-3 parton distribution function \u0000gT(x)","authors":"S. Bhattacharya, K. Cichy, M. Constantinou, A. Metz, Aurora Scapellato, F. Steffens","doi":"10.1103/physrevd.102.111501","DOIUrl":"https://doi.org/10.1103/physrevd.102.111501","url":null,"abstract":"In this work, we present the first-ever calculation of the isovector flavor combination of the twist-3 parton distribution function $g_T(x)$ for the proton from lattice QCD. We use an ensemble of gauge configurations with two degenerate light, a strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with a clover improvement. The lattice has a spatial extent of 3 fm, lattice spacing of 0.093 fm, and reproduces a pion mass of $260$ MeV. We use the quasi-distribution approach and employ three values of the proton momentum boost, 0.83 GeV, 1.25 GeV and 1.67 GeV. We use a source-sink separation of 1.12 fm to suppress excited-states contamination. The lattice data are renormalized non-perturbatively. We calculate the appropriate matching within Large Momentum Effective Theory, which is applied to the lattice data in order to obtain $g_T$. The final distribution is presented in the $overline{rm MS}$ scheme at a scale of 2 GeV. We also calculate the helicity distribution $g_1$ to test the Wandzura-Wilczek approximation for $g_T$. We find that the approximation works well for a large range in $x$. \u0000This work demonstrates the feasibility of accessing twist-3 parton distribution functions from novel methods within lattice QCD, and can provide important insights on the structure of hadrons.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75565084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigated the origin of the RI'/MOM quark mass under the Landau gauge at the non-perturbative scale, using the chiral fermion with different quark masses and lattice spacings. Our result confirms that such a mass is non-vanishing based on the linear extrapolation to the chiral and continuum limit, and shows that such a mass comes from the spontaneous chiral symmetry breaking induced by the near zero modes with the eigenvalue $lambda<{cal O}(5m_q)$, and is proportional to the quark matrix element of the trace anomaly at least down to $sim $1.3 GeV.
{"title":"Trace anomaly and dynamical quark mass","authors":"Yi-Bo Yang, Jian Liang, Zhaofeng Liu, P. Sun","doi":"10.22323/1.363.0001","DOIUrl":"https://doi.org/10.22323/1.363.0001","url":null,"abstract":"We investigated the origin of the RI'/MOM quark mass under the Landau gauge at the non-perturbative scale, using the chiral fermion with different quark masses and lattice spacings. Our result confirms that such a mass is non-vanishing based on the linear extrapolation to the chiral and continuum limit, and shows that such a mass comes from the spontaneous chiral symmetry breaking induced by the near zero modes with the eigenvalue $lambda<{cal O}(5m_q)$, and is proportional to the quark matrix element of the trace anomaly at least down to $sim $1.3 GeV.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90205037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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