These notes are based on a series of lectures on staggered fermions given at the Centre de Physique Th'eorique, Luminy, in Marseille, France, January 17-25, 2024.
这些笔记基于2024年1月17-25日在法国马赛卢米尼物理中心（Centre de Physique Th'eorique, Luminy）举行的一系列关于交错费米子的讲座。
{"title":"Staggered fermions","authors":"Maarten Golterman","doi":"arxiv-2406.02906","DOIUrl":"https://doi.org/arxiv-2406.02906","url":null,"abstract":"These notes are based on a series of lectures on staggered fermions given at\u0000the Centre de Physique Th'eorique, Luminy, in Marseille, France, January\u000017-25, 2024.","PeriodicalId":501191,"journal":{"name":"arXiv - PHYS - High Energy Physics - Lattice","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141521244","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}
M. Engelhardt, N. Hasan, S. Krieg, S. Liuti, S. Meinel, J. Negele, A. Pochinsky, M. Rodekamp, S. Syritsyn
Quark orbital angular momentum in the proton is evaluated via a Lattice QCD calculation of the second Mellin moment of the twist-3 generalized parton distribution $widetilde{E}_{2T} $ in the forward limit. The connection between this approach to quark orbital angular momentum and approaches previously utilized in Lattice QCD calculations, via generalized transverse momentum-dependent parton distributions and via Ji's sum rule, is reviewed. This connection can be given in terms of Lorentz invariance and equation of motion relations. The calculation of the second Mellin moment of $widetilde{E}_{2T} $ proceeds via a finite-momentum proton matrix element of a quark bilocal operator with a straight-line gauge connection and separation in both the longitudinal and transverse directions. The dependence on the former component serves to extract the second Mellin moment, whereas the dependence on the latter component provides a transverse momentum cutoff for the matrix element. Furthermore, a derivative of the matrix element with respect to momentum transfer in the forward limit is required, which is obtained using a direct derivative method. The calculation utilizes a clover fermion ensemble at pion mass 317 MeV. The resulting quark orbital angular momentum is consistent with previous evaluations through alternative approaches, albeit with greater statistical uncertainty using a comparable number of samples.
{"title":"Quark orbital angular momentum in the proton from a twist-3 generalized parton distribution","authors":"M. Engelhardt, N. Hasan, S. Krieg, S. Liuti, S. Meinel, J. Negele, A. Pochinsky, M. Rodekamp, S. Syritsyn","doi":"arxiv-2406.00845","DOIUrl":"https://doi.org/arxiv-2406.00845","url":null,"abstract":"Quark orbital angular momentum in the proton is evaluated via a Lattice QCD\u0000calculation of the second Mellin moment of the twist-3 generalized parton\u0000distribution $widetilde{E}_{2T} $ in the forward limit. The connection between\u0000this approach to quark orbital angular momentum and approaches previously\u0000utilized in Lattice QCD calculations, via generalized transverse\u0000momentum-dependent parton distributions and via Ji's sum rule, is reviewed.\u0000This connection can be given in terms of Lorentz invariance and equation of\u0000motion relations. The calculation of the second Mellin moment of\u0000$widetilde{E}_{2T} $ proceeds via a finite-momentum proton matrix element of a\u0000quark bilocal operator with a straight-line gauge connection and separation in\u0000both the longitudinal and transverse directions. The dependence on the former\u0000component serves to extract the second Mellin moment, whereas the dependence on\u0000the latter component provides a transverse momentum cutoff for the matrix\u0000element. Furthermore, a derivative of the matrix element with respect to\u0000momentum transfer in the forward limit is required, which is obtained using a\u0000direct derivative method. The calculation utilizes a clover fermion ensemble at\u0000pion mass 317 MeV. The resulting quark orbital angular momentum is consistent\u0000with previous evaluations through alternative approaches, albeit with greater\u0000statistical uncertainty using a comparable number of samples.","PeriodicalId":501191,"journal":{"name":"arXiv - PHYS - High Energy Physics - Lattice","volume":"102 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141255303","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 study complex Langevin simulations of a toy model as well as QCD, supplemented with a dynamical stabilization (DS) term, which was proposed to regularize the complexified process at lower temperatures. We compare the results to reweghting from zero chemical potential to measure the bias that the inclusion of the stabilization term causes, depending on its strength. At high temperatures the stabilization term is not needed. At low temperatures (below deconfinement transition) the DS term has a beneficial stabilizing effect, but too strong DS term causes phase quenching on the system. We observed that the bias of the dynamical stabilization can be to a good accuracy removed by extrapolating to zero dynamical stabilization force using a sigmoid fit.
{"title":"Testing dynamical stabilization of Complex Langevin simulations of QCD","authors":"Michael W. Hansen, Dénes Sexty","doi":"arxiv-2405.20709","DOIUrl":"https://doi.org/arxiv-2405.20709","url":null,"abstract":"We study complex Langevin simulations of a toy model as well as QCD,\u0000supplemented with a dynamical stabilization (DS) term, which was proposed to\u0000regularize the complexified process at lower temperatures. We compare the\u0000results to reweghting from zero chemical potential to measure the bias that the\u0000inclusion of the stabilization term causes, depending on its strength. At high\u0000temperatures the stabilization term is not needed. At low temperatures (below\u0000deconfinement transition) the DS term has a beneficial stabilizing effect, but\u0000too strong DS term causes phase quenching on the system. We observed that the\u0000bias of the dynamical stabilization can be to a good accuracy removed by\u0000extrapolating to zero dynamical stabilization force using a sigmoid fit.","PeriodicalId":501191,"journal":{"name":"arXiv - PHYS - High Energy Physics - Lattice","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141255246","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 study the renormalization of a complete set of gauge-invariant gluon nonlocal operators in lattice perturbation theory. We determine the mixing pattern under renormalization of these operators using symmetry arguments, which extend beyond perturbation theory. Additionally, we derive the renormalization factors of the operators within the modified Minimal Subtraction $(rm overline{MS})$ scheme up to one-loop. To enable a non-perturbative renormalization procedure, we investigate a suitable version of the modified regularization-invariant (${rm RI}'$) scheme, and we calculate the conversion factors from that scheme to $rmoverline{MS}$. The computations are performed by employing both dimensional and lattice regularizations, using the Wilson gluon action. This work is relevant to nonperturbative studies of the gluon parton distribution functions (PDFs) on the lattice.
{"title":"Renormalization of nonlocal gluon operators on the lattice","authors":"Demetrianos Gavriel, Haralambos Panagopoulos, Gregoris Spanoudes","doi":"arxiv-2406.15446","DOIUrl":"https://doi.org/arxiv-2406.15446","url":null,"abstract":"We study the renormalization of a complete set of gauge-invariant gluon\u0000nonlocal operators in lattice perturbation theory. We determine the mixing\u0000pattern under renormalization of these operators using symmetry arguments,\u0000which extend beyond perturbation theory. Additionally, we derive the\u0000renormalization factors of the operators within the modified Minimal\u0000Subtraction $(rm overline{MS})$ scheme up to one-loop. To enable a\u0000non-perturbative renormalization procedure, we investigate a suitable version\u0000of the modified regularization-invariant (${rm RI}'$) scheme, and we calculate\u0000the conversion factors from that scheme to $rmoverline{MS}$. The computations\u0000are performed by employing both dimensional and lattice regularizations, using\u0000the Wilson gluon action. This work is relevant to nonperturbative studies of\u0000the gluon parton distribution functions (PDFs) on the lattice.","PeriodicalId":501191,"journal":{"name":"arXiv - PHYS - High Energy Physics - Lattice","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141521239","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}
Nucleon weak matrix elements can be extracted from nucleon correlation functions with lattice QCD simulations. The signal-to-noise ratio prohibits the analysis at large source-sink separations and as a consequence, excited state contamination affects the extraction of the nucleon matrix elements. Chiral perturbation theory (ChPT) suggests that the dominant contamination in some of these channels is due to $Npi$ states where the pion carries the same momentum of the current. In this talk, we report updates on the variational analysis with $qqq$-operators (nucleon-like) and $(qqq)(bar{q}q)$-operators (nucleon-pion-like) where we report for the first time some preliminary results of $langle Npi| mathcal{J}| N rangle $, modulo some kinematic and volume factors, and we compare the results against ChPT. This pilot study is performed on a CLS ensemble with $N_f=3$, $m_pi approx 420~mathrm{MeV}$, $aapprox 0.1~mathrm{fm}$ and $T=2Lapprox 4.8~mathrm{fm}$.
核子弱矩阵元素可以通过格子 QCD 模拟从核子相关函数中提取出来。由于信噪比的原因，无法在大的源-汇分离条件下进行分析，因此激发态污染影响了核子矩阵元素的提取。手性扰动理论（Chiralperturbation theory，ChPT）表明，其中一些通道中的主要污染是由先驱携带与电流相同动量的$N/pi$态引起的。在本讲座中，我们将报告用$qqq$操作数（类核子）和$(qqq)(bar{q}q)$操作数（类核子-pion）进行变分分析的最新情况，我们将首次报告$langle Npi| mathcal{J}| N rangle $的一些初步结果，并将这些结果与ChPT进行比较。这项试验性研究是在一个CLS集合上进行的，集合参数为：$N_f=3$，$m_pi约为420~mathrm{MeV}$，$a约为0.1~mathrm{fm}$，$T=2L约为4.8~mathrm{fm}$。
{"title":"Progress on nucleon transition matrix elements with a lattice QCD variational analysis","authors":"Lorenzo Barca, Gunnar Bali, Sara Collins","doi":"arxiv-2405.20875","DOIUrl":"https://doi.org/arxiv-2405.20875","url":null,"abstract":"Nucleon weak matrix elements can be extracted from nucleon correlation\u0000functions with lattice QCD simulations. The signal-to-noise ratio prohibits the\u0000analysis at large source-sink separations and as a consequence, excited state\u0000contamination affects the extraction of the nucleon matrix elements. Chiral\u0000perturbation theory (ChPT) suggests that the dominant contamination in some of\u0000these channels is due to $Npi$ states where the pion carries the same momentum\u0000of the current. In this talk, we report updates on the variational analysis\u0000with $qqq$-operators (nucleon-like) and $(qqq)(bar{q}q)$-operators\u0000(nucleon-pion-like) where we report for the first time some preliminary results\u0000of $langle Npi| mathcal{J}| N rangle $, modulo some kinematic and volume\u0000factors, and we compare the results against ChPT. This pilot study is performed\u0000on a CLS ensemble with $N_f=3$, $m_pi approx 420~mathrm{MeV}$, $aapprox\u00000.1~mathrm{fm}$ and $T=2Lapprox 4.8~mathrm{fm}$.","PeriodicalId":501191,"journal":{"name":"arXiv - PHYS - High Energy Physics - Lattice","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141255239","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 construct neural networks that work for any Lie group and maintain gauge covariance, enabling smooth, invertible gauge field transformations. We implement these transformations for 4D SU(3) lattice gauge fields and explore their use in HMC. We focus on developing loss functions and optimizing the transformations. We show the effects on HMC's molecular dynamics and discuss the scalability of the approach.
{"title":"Neural Network Gauge Field Transformation for 4D SU(3) gauge fields","authors":"Xiao-Yong Jin","doi":"arxiv-2405.19692","DOIUrl":"https://doi.org/arxiv-2405.19692","url":null,"abstract":"We construct neural networks that work for any Lie group and maintain gauge\u0000covariance, enabling smooth, invertible gauge field transformations. We\u0000implement these transformations for 4D SU(3) lattice gauge fields and explore\u0000their use in HMC. We focus on developing loss functions and optimizing the\u0000transformations. We show the effects on HMC's molecular dynamics and discuss\u0000the scalability of the approach.","PeriodicalId":501191,"journal":{"name":"arXiv - PHYS - High Energy Physics - Lattice","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141189629","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}
Ethan Baker, Dennis Bollweg, Peter Boyle, Ian Cloët, Xiang Gao, Swagato Mukherjee, Peter Petreczky, Rui Zhang, Yong Zhao
We present a direct lattice QCD calculation of the $x$-dependence of the pion distribution amplitude (DA), which is performed using the quasi-DA in large momentum effective theory on a domain-wall fermion ensemble at physical quark masses and spacing $aapprox 0.084$ fm. The bare quais-DA matrix elements are renormalized in the hybrid scheme and matched to $overline{rm MS}$ with a subtraction of the leading renormalon in the Wilson-line mass. For the first time, we include threshold resummation in the perturbative matching onto the light-cone DA, which resums the large logarithms in the soft gluon limit at next-to-next-to-leading log. The resummed results show controlled scale-variation uncertainty within the range of momentum fraction $xin[0.25,0.75]$ at the largest pion momentum $P_zapprox 1.85$~GeV. In addition, we apply the same analysis to quasi-DAs from a highly-improved-staggered-quark ensemble at physical pion mass and $a=0.076$ fm. By comparison we find with $2sigma$ confidence level that the DA obtained from chiral fermions is flatter and lower near $x=0.5$.
{"title":"Lattice QCD calculation of the pion distribution amplitude with domain wall fermions at physical pion mass","authors":"Ethan Baker, Dennis Bollweg, Peter Boyle, Ian Cloët, Xiang Gao, Swagato Mukherjee, Peter Petreczky, Rui Zhang, Yong Zhao","doi":"arxiv-2405.20120","DOIUrl":"https://doi.org/arxiv-2405.20120","url":null,"abstract":"We present a direct lattice QCD calculation of the $x$-dependence of the pion\u0000distribution amplitude (DA), which is performed using the quasi-DA in large\u0000momentum effective theory on a domain-wall fermion ensemble at physical quark\u0000masses and spacing $aapprox 0.084$ fm. The bare quais-DA matrix elements are\u0000renormalized in the hybrid scheme and matched to $overline{rm MS}$ with a\u0000subtraction of the leading renormalon in the Wilson-line mass. For the first\u0000time, we include threshold resummation in the perturbative matching onto the\u0000light-cone DA, which resums the large logarithms in the soft gluon limit at\u0000next-to-next-to-leading log. The resummed results show controlled\u0000scale-variation uncertainty within the range of momentum fraction\u0000$xin[0.25,0.75]$ at the largest pion momentum $P_zapprox 1.85$~GeV. In\u0000addition, we apply the same analysis to quasi-DAs from a\u0000highly-improved-staggered-quark ensemble at physical pion mass and $a=0.076$\u0000fm. By comparison we find with $2sigma$ confidence level that the DA obtained\u0000from chiral fermions is flatter and lower near $x=0.5$.","PeriodicalId":501191,"journal":{"name":"arXiv - PHYS - High Energy Physics - Lattice","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141189630","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}
Solving discretized versions of the Dirac equation represents a large share of execution time in lattice Quantum Chromodynamics (QCD) simulations. Many high-performance computing (HPC) clusters use graphics processing units (GPUs) to offer more computational resources. Our solver program, DDalphaAMG, previously was unable to fully take advantage of GPUs to accelerate its computations. Making use of GPUs for DDalphaAMG is an ongoing development, and we will present some current progress herein. Through a detailed description of our development, this thesis should offer valuable insights into using GPUs to accelerate a memory-bound CPU implementation. We developed a storage scheme for multiple tuples, which allows much more efficient memory access on GPUs, given that the element at the same index is read from multiple tuples simultaneously. Still, our implementation of a discrete Dirac operator is memory-bound, and we only achieved improvements for large linear systems on few nodes at the JUWELS cluster. These improvements do not currently overcome additional introduced overheads. However, the results for the application of the Wilson-Dirac operator show a speedup of around 3 for large lattices. If the additional overheads can be eliminated in the future, GPUs could reduce the DDalphaAMG execution time significantly for large lattices. We also found that a previous publication on the GPU acceleration of DDalphaAMG, underrepresented the achieved speedup, because small lattices were used. This further highlights that GPUs often require large-scale problems to solve in order to be faster than CPUs
{"title":"Accelerating Lattice QCD Simulations using GPUs","authors":"Tilmann Matthaei","doi":"arxiv-2407.00041","DOIUrl":"https://doi.org/arxiv-2407.00041","url":null,"abstract":"Solving discretized versions of the Dirac equation represents a large share\u0000of execution time in lattice Quantum Chromodynamics (QCD) simulations. Many\u0000high-performance computing (HPC) clusters use graphics processing units (GPUs)\u0000to offer more computational resources. Our solver program, DDalphaAMG,\u0000previously was unable to fully take advantage of GPUs to accelerate its\u0000computations. Making use of GPUs for DDalphaAMG is an ongoing development, and\u0000we will present some current progress herein. Through a detailed description of\u0000our development, this thesis should offer valuable insights into using GPUs to\u0000accelerate a memory-bound CPU implementation. We developed a storage scheme for multiple tuples, which allows much more\u0000efficient memory access on GPUs, given that the element at the same index is\u0000read from multiple tuples simultaneously. Still, our implementation of a\u0000discrete Dirac operator is memory-bound, and we only achieved improvements for\u0000large linear systems on few nodes at the JUWELS cluster. These improvements do\u0000not currently overcome additional introduced overheads. However, the results\u0000for the application of the Wilson-Dirac operator show a speedup of around 3 for\u0000large lattices. If the additional overheads can be eliminated in the future,\u0000GPUs could reduce the DDalphaAMG execution time significantly for large\u0000lattices. We also found that a previous publication on the GPU acceleration of\u0000DDalphaAMG, underrepresented the achieved speedup, because small lattices were\u0000used. This further highlights that GPUs often require large-scale problems to\u0000solve in order to be faster than CPUs","PeriodicalId":501191,"journal":{"name":"arXiv - PHYS - High Energy Physics - Lattice","volume":"133 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141521241","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 present the first lattice calculation of the nucleon isovector helicity parton distribution function (PDF) in the framework of large-momentum effective theory (LaMET) that uses the hybrid scheme with self-renormalization. We use ensembles generated by the MILC collaboration at lattice spacings $a={0.1207,0.0888,0.0582}$ fm, with $N_f=2+1+1$ flavors of highly improved staggered quarks at sea pion mass of $M_{pi}approx 315$ MeV. We use clover-improved action for our valence quarks with nucleon boost momentum $P_zapprox 1.75$ GeV and high-statistics measurements for the LaMET matrix elements. We perform an extrapolation to the continuum limit and improve the handling of systematic errors using renormalization-group resummation (RGR) and leading-renormalon resummation (LRR). Our final nucleon helicity PDF is renormalized in the $overline{text{MS}}$ scheme at energy scale $mu=2.0$ GeV. We compare our results with and without the two systematic improvements of RGR and LRR at each lattice spacing as well as the continuum limit, and we see that the application of RGR and LRR greatly reduces the systematic errors across the whole $x$ range. Our continuum results with both RGR and LRR show a small positive antiquark region for the nucleon helicity PDF as well as a change of as much as a factor of two in the central values compared to results with neither RGR or LRR. By contrast, the application of RGR and LRR only changes the central values by about 5% in the quark region. We compare our lattice results with the global fits by the JAM, NNPDF and DSSV collaborations, and we observe some tension between our results.
{"title":"Nucleon Helicity Parton Distribution Function in the Continuum Limit with Self-Renormalization","authors":"Jack Holligan, Huey-Wen Lin","doi":"arxiv-2405.18238","DOIUrl":"https://doi.org/arxiv-2405.18238","url":null,"abstract":"We present the first lattice calculation of the nucleon isovector helicity\u0000parton distribution function (PDF) in the framework of large-momentum effective\u0000theory (LaMET) that uses the hybrid scheme with self-renormalization. We use\u0000ensembles generated by the MILC collaboration at lattice spacings\u0000$a={0.1207,0.0888,0.0582}$ fm, with $N_f=2+1+1$ flavors of highly improved\u0000staggered quarks at sea pion mass of $M_{pi}approx 315$ MeV. We use\u0000clover-improved action for our valence quarks with nucleon boost momentum\u0000$P_zapprox 1.75$ GeV and high-statistics measurements for the LaMET matrix\u0000elements. We perform an extrapolation to the continuum limit and improve the\u0000handling of systematic errors using renormalization-group resummation (RGR) and\u0000leading-renormalon resummation (LRR). Our final nucleon helicity PDF is\u0000renormalized in the $overline{text{MS}}$ scheme at energy scale $mu=2.0$\u0000GeV. We compare our results with and without the two systematic improvements of\u0000RGR and LRR at each lattice spacing as well as the continuum limit, and we see\u0000that the application of RGR and LRR greatly reduces the systematic errors\u0000across the whole $x$ range. Our continuum results with both RGR and LRR show a\u0000small positive antiquark region for the nucleon helicity PDF as well as a\u0000change of as much as a factor of two in the central values compared to results\u0000with neither RGR or LRR. By contrast, the application of RGR and LRR only\u0000changes the central values by about 5% in the quark region. We compare our\u0000lattice results with the global fits by the JAM, NNPDF and DSSV collaborations,\u0000and we observe some tension between our results.","PeriodicalId":501191,"journal":{"name":"arXiv - PHYS - High Energy Physics - Lattice","volume":"97 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170413","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 study the impact of Gribov copies on the quark propagator in lattice 2-colour QCD. We find that the Gribov noise is comparable to the gauge noise for smaller volumes but becomes less significant for larger spatial volumes. The Gribov noise in the quark propagator is found to be comparable to, but smaller than in the gluon propagator on the same ensembles. No correlation is found between the values of either of the quark propagator form factors and the value of the gauge fixing functional, nor between the two form factors.
{"title":"Gribov copies in the quark propagator","authors":"Gerhard Kalusche, Dale Lawlor, Jon-Ivar Skullerud","doi":"arxiv-2405.17301","DOIUrl":"https://doi.org/arxiv-2405.17301","url":null,"abstract":"We study the impact of Gribov copies on the quark propagator in lattice\u00002-colour QCD. We find that the Gribov noise is comparable to the gauge noise\u0000for smaller volumes but becomes less significant for larger spatial volumes.\u0000The Gribov noise in the quark propagator is found to be comparable to, but\u0000smaller than in the gluon propagator on the same ensembles. No correlation is\u0000found between the values of either of the quark propagator form factors and the\u0000value of the gauge fixing functional, nor between the two form factors.","PeriodicalId":501191,"journal":{"name":"arXiv - PHYS - High Energy Physics - Lattice","volume":"130 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170277","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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