Luca Di Luzio, Alexander Keshavarzi, Antonio Masiero, Paride Paradisi
The hadronic vacuum polarization (HVP) contributions to the muon $g$$-$$2$ are the crucial quantity to resolve whether new physics is present or not in the comparison between the Standard Model (SM) prediction and experimental measurements at Fermilab. They are commonly and historically determined via dispersion relations using a vast catalogue of experimentally measured, low-energy $e^+e^-to ,rm{hadrons}$ cross section data as input. These dispersive estimates result in a SM prediction that exhibits a muon $g$$-$$2$ discrepancy of more than $5sigma$ when compared to experiment. However, recent lattice QCD evaluations of the HVP and a new hadronic cross section measurement from the CMD-3 experiment favor a no-new-physics scenario and, therefore, exhibit a common tension with the previous $e^+e^-to ,rm{hadrons}$ data. This study explores the current and future implications of these two scenarios on other observables that are also sensitive to the HVP contributions in the hope that they may provide independent tests of the current tensions observed in the muon $g$$-$$2$.
{"title":"Model Independent Tests of the Hadronic Vacuum Polarization Contribution to the Muon $g$$-$$2$","authors":"Luca Di Luzio, Alexander Keshavarzi, Antonio Masiero, Paride Paradisi","doi":"arxiv-2408.01123","DOIUrl":"https://doi.org/arxiv-2408.01123","url":null,"abstract":"The hadronic vacuum polarization (HVP) contributions to the muon $g$$-$$2$\u0000are the crucial quantity to resolve whether new physics is present or not in\u0000the comparison between the Standard Model (SM) prediction and experimental\u0000measurements at Fermilab. They are commonly and historically determined via\u0000dispersion relations using a vast catalogue of experimentally measured,\u0000low-energy $e^+e^-to ,rm{hadrons}$ cross section data as input. These\u0000dispersive estimates result in a SM prediction that exhibits a muon $g$$-$$2$\u0000discrepancy of more than $5sigma$ when compared to experiment. However, recent\u0000lattice QCD evaluations of the HVP and a new hadronic cross section measurement\u0000from the CMD-3 experiment favor a no-new-physics scenario and, therefore,\u0000exhibit a common tension with the previous $e^+e^-to ,rm{hadrons}$ data.\u0000This study explores the current and future implications of these two scenarios\u0000on other observables that are also sensitive to the HVP contributions in the\u0000hope that they may provide independent tests of the current tensions observed\u0000in the muon $g$$-$$2$.","PeriodicalId":501191,"journal":{"name":"arXiv - PHYS - High Energy Physics - Lattice","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Andreas Athenodorou, Ed Bennett, Georg Bergner, Pietro Butti, Julian Lenz, Biagio Lucini
We provide an extended lattice study of the SU(2) gauge theory coupled to one Dirac fermion flavour ($N_{mathrm{f}} =1$) transforming in the adjoint representation as the continuum limit is approached. This investigation is supplemented by numerical results obtained for the SU(2) gauge theory with two Dirac fermion flavours ($N_{mathrm{f}} =2$) transforming in the adjoint representation, for which we perform numerical investigations at a single lattice spacing value, which is analysed together with earlier calculations. The purpose of our study is to advance the characterisation of the infrared properties of both theories, which previous investigations have concluded to be in the conformal window. For both, we determine the mass spectrum and the anomalous dimension of the fermion condensate using finite-size hyperscaling of the spectrum, mode number analysis of the Dirac operator (for which we improve on our previous proposal) and the ratio of masses of the lightest spin-2 particle over the lightest scalar. All methods provide a consistent picture, with the anomalous dimension of the condensate $gamma_*$ decreasing significantly as one approaches the continuum limit for the $N_{mathrm{f}} = 1$ theory towards a value consistent with $gamma_* = 0.174(6)$, while for $N_{mathrm{f}} = 2$ the anomalous dimension decreases more slowly with $beta$. A chiral perturbation theory analysis show that the infrared behaviour of both theories is incompatible with the breaking of chiral symmetry.
{"title":"SU(2) gauge theory with one and two adjoint fermions towards the continuum limit","authors":"Andreas Athenodorou, Ed Bennett, Georg Bergner, Pietro Butti, Julian Lenz, Biagio Lucini","doi":"arxiv-2408.00171","DOIUrl":"https://doi.org/arxiv-2408.00171","url":null,"abstract":"We provide an extended lattice study of the SU(2) gauge theory coupled to one\u0000Dirac fermion flavour ($N_{mathrm{f}} =1$) transforming in the adjoint\u0000representation as the continuum limit is approached. This investigation is\u0000supplemented by numerical results obtained for the SU(2) gauge theory with two\u0000Dirac fermion flavours ($N_{mathrm{f}} =2$) transforming in the adjoint\u0000representation, for which we perform numerical investigations at a single\u0000lattice spacing value, which is analysed together with earlier calculations.\u0000The purpose of our study is to advance the characterisation of the infrared\u0000properties of both theories, which previous investigations have concluded to be\u0000in the conformal window. For both, we determine the mass spectrum and the\u0000anomalous dimension of the fermion condensate using finite-size hyperscaling of\u0000the spectrum, mode number analysis of the Dirac operator (for which we improve\u0000on our previous proposal) and the ratio of masses of the lightest spin-2\u0000particle over the lightest scalar. All methods provide a consistent picture,\u0000with the anomalous dimension of the condensate $gamma_*$ decreasing\u0000significantly as one approaches the continuum limit for the $N_{mathrm{f}} =\u00001$ theory towards a value consistent with $gamma_* = 0.174(6)$, while for\u0000$N_{mathrm{f}} = 2$ the anomalous dimension decreases more slowly with\u0000$beta$. A chiral perturbation theory analysis show that the infrared behaviour\u0000of both theories is incompatible with the breaking of chiral symmetry.","PeriodicalId":501191,"journal":{"name":"arXiv - PHYS - High Energy Physics - Lattice","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141883758","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}
Recent work found that an analysis formalism based on the Lanczos algorithm allows energy levels to be extracted from Euclidean correlation functions with faster convergence than existing methods, two-sided error bounds, and no apparent signal-to-noise problems. We extend this formalism to the determination of matrix elements from three-point correlation functions. We demonstrate similar advantages over previously available methods in both signal-to-noise and control of excited-state contamination through example applications to noiseless mock-data as well as calculations of (bare) forward matrix elements of the strange scalar current between both ground and excited states with the quantum numbers of the nucleon.
{"title":"Lanczos for lattice QCD matrix elements","authors":"Daniel C. Hackett, Michael L. Wagman","doi":"arxiv-2407.21777","DOIUrl":"https://doi.org/arxiv-2407.21777","url":null,"abstract":"Recent work found that an analysis formalism based on the Lanczos algorithm\u0000allows energy levels to be extracted from Euclidean correlation functions with\u0000faster convergence than existing methods, two-sided error bounds, and no\u0000apparent signal-to-noise problems. We extend this formalism to the\u0000determination of matrix elements from three-point correlation functions. We\u0000demonstrate similar advantages over previously available methods in both\u0000signal-to-noise and control of excited-state contamination through example\u0000applications to noiseless mock-data as well as calculations of (bare) forward\u0000matrix elements of the strange scalar current between both ground and excited\u0000states with the quantum numbers of the nucleon.","PeriodicalId":501191,"journal":{"name":"arXiv - PHYS - High Energy Physics - Lattice","volume":"296 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872509","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}
Among countless channels of hard exclusive reactions, the kaon electromagnetic form factors (EMFFs) are of special interest, which have been measured up to $Q^2 sim 50;{rm GeV}^2$ in the timelike domain. The kaon EMFFs thereby serve an ideal platform to critically examine the validity and effectiveness of perturbative QCD (pQCD) in accounting for hard exclusive processes. In this work we confront the pQCD predictions that incorporate the next-to-next-to-leading-order (NNLO) perturbative corrections, with the available kaon EMFFs data set from experimental measurements and from lattice predictions. The inclusion of the NNLO corrections turns out to have a substantial and positive impact. If the profiles of the kaon light-cone distribution amplitudes (LCDAs) are taken from the recent lattice QCD prediction by {tt LPC} Collaboration, the satisfactory agreement between theory and data can be reached for both charged and neutral kaons, in both spacelike and timelike large-$Q^2$ domains.
{"title":"Confronting perturbative QCD with the hardest exclusive reactions: kaon electromagnetic form factors","authors":"Long-Bin Chen, Wen Chen, Feng Feng, Yu Jia","doi":"arxiv-2407.21120","DOIUrl":"https://doi.org/arxiv-2407.21120","url":null,"abstract":"Among countless channels of hard exclusive reactions, the kaon\u0000electromagnetic form factors (EMFFs) are of special interest, which have been\u0000measured up to $Q^2 sim 50;{rm GeV}^2$ in the timelike domain. The kaon\u0000EMFFs thereby serve an ideal platform to critically examine the validity and\u0000effectiveness of perturbative QCD (pQCD) in accounting for hard exclusive\u0000processes. In this work we confront the pQCD predictions that incorporate the\u0000next-to-next-to-leading-order (NNLO) perturbative corrections, with the\u0000available kaon EMFFs data set from experimental measurements and from lattice\u0000predictions. The inclusion of the NNLO corrections turns out to have a\u0000substantial and positive impact. If the profiles of the kaon light-cone\u0000distribution amplitudes (LCDAs) are taken from the recent lattice QCD\u0000prediction by {tt LPC} Collaboration, the satisfactory agreement between\u0000theory and data can be reached for both charged and neutral kaons, in both\u0000spacelike and timelike large-$Q^2$ domains.","PeriodicalId":501191,"journal":{"name":"arXiv - PHYS - High Energy Physics - Lattice","volume":"176 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872412","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}
Saurabh V. Kadam, Aahiri Naskar, Indrakshi Raychowdhury, Jesse R. Stryker
The construction of gauge invariant states of SU(3) lattice gauge theories has garnered new interest in recent years, but implementing them is complicated by the need for SU(3) Clebsch-Gordon coefficients. In the loop-string-hadron (LSH) approach to lattice gauge theories, the elementary excitations are strictly gauge invariant, and constructing the basis requires no knowledge of Clebsch-Gordon coefficients. Originally developed for SU(2), the LSH formulation was recently generalized to SU(3), but limited to one spatial dimension. In this work, we generalize the LSH approach to constructing the basis of SU(3) gauge invariant states at a trivalent vertex - the essential building block to multidimensional space. A direct generalization from the SU(2) vertex yields a legitimate basis; however, in certain sectors of the Hilbert space, the naive LSH basis vectors so defined suffer from being nonorthogonal. The issues with orthogonality are directly related to the `missing label' or `outer multiplicity' problem associated with SU(3) tensor products, and may also be phrased in terms of Littlewood-Richardson coefficients or the need for a `seventh Casimir' operator. The states that are unaffected by the problem are orthonormalized in closed form. For the sectors that are afflicted, we discuss the nonorthogonal bases and their orthogonalization. A few candidates for seventh Casimir operators are readily constructed from the suite of LSH gauge-singlet operators. The diagonalization of a seventh Casimir represents one prescriptive solution towards obtaining a complete orthonormal basis, but a closed-form general solution remains to be found.
{"title":"Loop-string-hadron approach to SU(3) lattice Yang-Mills theory: Gauge invariant Hilbert space of a trivalent vertex","authors":"Saurabh V. Kadam, Aahiri Naskar, Indrakshi Raychowdhury, Jesse R. Stryker","doi":"arxiv-2407.19181","DOIUrl":"https://doi.org/arxiv-2407.19181","url":null,"abstract":"The construction of gauge invariant states of SU(3) lattice gauge theories\u0000has garnered new interest in recent years, but implementing them is complicated\u0000by the need for SU(3) Clebsch-Gordon coefficients. In the loop-string-hadron\u0000(LSH) approach to lattice gauge theories, the elementary excitations are\u0000strictly gauge invariant, and constructing the basis requires no knowledge of\u0000Clebsch-Gordon coefficients. Originally developed for SU(2), the LSH\u0000formulation was recently generalized to SU(3), but limited to one spatial\u0000dimension. In this work, we generalize the LSH approach to constructing the\u0000basis of SU(3) gauge invariant states at a trivalent vertex - the essential\u0000building block to multidimensional space. A direct generalization from the\u0000SU(2) vertex yields a legitimate basis; however, in certain sectors of the\u0000Hilbert space, the naive LSH basis vectors so defined suffer from being\u0000nonorthogonal. The issues with orthogonality are directly related to the\u0000`missing label' or `outer multiplicity' problem associated with SU(3) tensor\u0000products, and may also be phrased in terms of Littlewood-Richardson\u0000coefficients or the need for a `seventh Casimir' operator. The states that are\u0000unaffected by the problem are orthonormalized in closed form. For the sectors\u0000that are afflicted, we discuss the nonorthogonal bases and their\u0000orthogonalization. A few candidates for seventh Casimir operators are readily\u0000constructed from the suite of LSH gauge-singlet operators. The diagonalization\u0000of a seventh Casimir represents one prescriptive solution towards obtaining a\u0000complete orthonormal basis, but a closed-form general solution remains to be\u0000found.","PeriodicalId":501191,"journal":{"name":"arXiv - PHYS - High Energy Physics - Lattice","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872413","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}
This study investigates finite-volume effects in physical processes that involve the combination of long-range hadronic matrix elements with electroweak loop integrals. We adopt the approach of implementing the electroweak part as the infinite-volume version, which is denoted as the EW$_infty$ method in this work. A general approach is established for correcting finite-volume effects in cases where the hadronic intermediate states are dominated by either a single particle or two particles. For the single-particle case, this work derives the infinite volume reconstruction (IVR) method from a new perspective. For the two-particle case, we provide the correction formulas for power-law finite-volume effects and unphysical terms with exponentially divergent time dependence. The finite-volume formalism developed in this study has broad applications, including the QED corrections in various processes and the two-photon exchange contribution in $K_Ltomu^+mu^-$ or $etatomu^+mu^-$ decays.
{"title":"Finite-volume formalism for physical processes with an electroweak loop integral","authors":"Xin-Yu Tuo, Xu Feng","doi":"arxiv-2407.16930","DOIUrl":"https://doi.org/arxiv-2407.16930","url":null,"abstract":"This study investigates finite-volume effects in physical processes that\u0000involve the combination of long-range hadronic matrix elements with electroweak\u0000loop integrals. We adopt the approach of implementing the electroweak part as\u0000the infinite-volume version, which is denoted as the EW$_infty$ method in this\u0000work. A general approach is established for correcting finite-volume effects in\u0000cases where the hadronic intermediate states are dominated by either a single\u0000particle or two particles. For the single-particle case, this work derives the\u0000infinite volume reconstruction (IVR) method from a new perspective. For the\u0000two-particle case, we provide the correction formulas for power-law\u0000finite-volume effects and unphysical terms with exponentially divergent time\u0000dependence. The finite-volume formalism developed in this study has broad\u0000applications, including the QED corrections in various processes and the\u0000two-photon exchange contribution in $K_Ltomu^+mu^-$ or $etatomu^+mu^-$\u0000decays.","PeriodicalId":501191,"journal":{"name":"arXiv - PHYS - High Energy Physics - Lattice","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785858","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}
Given a base manifold $M$ and a Lie group $G$, we define $widetilde{cal A}_M$ a space of generalized $G$-connections on $M$ with the following properties: - The space of smooth connections ${cal A}^infty_M = sqcup_pi {cal A}^infty_pi$ is densely embedded in $widetilde{cal A}_M = sqcup_pi widetilde{cal A}^infty_pi$; moreover, in contrast with the usual space of generalized connections, the embedding preserves topological sectors. - It is a homogeneous covering space for the standard space of generalized connections of loop quantization $bar{cal A}_M$. - It is a measurable space constructed as an inverse limit of of spaces of connections with a cutoff, much like $bar{cal A}_M$. At each level of the cutoff, a Haar measure, a BF measure and heat kernel measures can be defined. - The topological charge of generalized connections on closed manifolds $Q= int Tr(F)$ in 2d, $Q= int Tr(F wedge F)$ in 4d, etc, is defined. - On a subdivided manifold, it can be calculated in terms of the spaces of generalized connections associated to its pieces. Thus, spaces of boundary connections can be computed from spaces associated to faces. - The soul of our generalized connections is a notion of higher homotopy parallel transport defined for smooth connections. We recover standard generalized connections by forgetting its higher levels. - Higher levels of our higher gauge fields are often trivial. Then $widetilde{cal A}_Sigma = bar{cal A}_Sigma$ for $dim Sigma = 3$ and $G=SU(2)$, but $widetilde{cal A}_M neq bar{cal A}_M$ for $dim M = 4$ and $G=SL(2, {mathbb C})$ or $G=SU(2)$. Boundary data for loop quantum gravity is consistent with our space of generalized connections, but a path integral for quantum gravity with Lorentzian or euclidean signatures would be sensitive to homotopy data.
{"title":"A better space of generalized connections","authors":"Juan Orendain, Jose A. Zapata","doi":"arxiv-2407.17400","DOIUrl":"https://doi.org/arxiv-2407.17400","url":null,"abstract":"Given a base manifold $M$ and a Lie group $G$, we define $widetilde{cal\u0000A}_M$ a space of generalized $G$-connections on $M$ with the following\u0000properties: - The space of smooth connections ${cal A}^infty_M = sqcup_pi {cal\u0000A}^infty_pi$ is densely embedded in $widetilde{cal A}_M = sqcup_pi\u0000widetilde{cal A}^infty_pi$; moreover, in contrast with the usual space of\u0000generalized connections, the embedding preserves topological sectors. - It is a homogeneous covering space for the standard space of generalized\u0000connections of loop quantization $bar{cal A}_M$. - It is a measurable space constructed as an inverse limit of of spaces of\u0000connections with a cutoff, much like $bar{cal A}_M$. At each level of the\u0000cutoff, a Haar measure, a BF measure and heat kernel measures can be defined. - The topological charge of generalized connections on closed manifolds $Q=\u0000int Tr(F)$ in 2d, $Q= int Tr(F wedge F)$ in 4d, etc, is defined. - On a subdivided manifold, it can be calculated in terms of the spaces of\u0000generalized connections associated to its pieces. Thus, spaces of boundary\u0000connections can be computed from spaces associated to faces. - The soul of our generalized connections is a notion of higher homotopy\u0000parallel transport defined for smooth connections. We recover standard\u0000generalized connections by forgetting its higher levels. - Higher levels of our higher gauge fields are often trivial. Then\u0000$widetilde{cal A}_Sigma = bar{cal A}_Sigma$ for $dim Sigma = 3$ and\u0000$G=SU(2)$, but $widetilde{cal A}_M neq bar{cal A}_M$ for $dim M = 4$ and\u0000$G=SL(2, {mathbb C})$ or $G=SU(2)$. Boundary data for loop quantum gravity is\u0000consistent with our space of generalized connections, but a path integral for\u0000quantum gravity with Lorentzian or euclidean signatures would be sensitive to\u0000homotopy data.","PeriodicalId":501191,"journal":{"name":"arXiv - PHYS - High Energy Physics - Lattice","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141779101","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 demonstrate that the update of weight matrices in learning algorithms can be described in the framework of Dyson Brownian motion, thereby inheriting many features of random matrix theory. We relate the level of stochasticity to the ratio of the learning rate and the mini-batch size, providing more robust evidence to a previously conjectured scaling relationship. We discuss universal and non-universal features in the resulting Coulomb gas distribution and identify the Wigner surmise and Wigner semicircle explicitly in a teacher-student model and in the (near-)solvable case of the Gaussian restricted Boltzmann machine.
{"title":"Stochastic weight matrix dynamics during learning and Dyson Brownian motion","authors":"Gert Aarts, Biagio Lucini, Chanju Park","doi":"arxiv-2407.16427","DOIUrl":"https://doi.org/arxiv-2407.16427","url":null,"abstract":"We demonstrate that the update of weight matrices in learning algorithms can\u0000be described in the framework of Dyson Brownian motion, thereby inheriting many\u0000features of random matrix theory. We relate the level of stochasticity to the\u0000ratio of the learning rate and the mini-batch size, providing more robust\u0000evidence to a previously conjectured scaling relationship. We discuss universal\u0000and non-universal features in the resulting Coulomb gas distribution and\u0000identify the Wigner surmise and Wigner semicircle explicitly in a\u0000teacher-student model and in the (near-)solvable case of the Gaussian\u0000restricted Boltzmann machine.","PeriodicalId":501191,"journal":{"name":"arXiv - PHYS - High Energy Physics - Lattice","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141779102","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}
Joe Karpie, Christopher Monahan, Anatoly Radyushkin
Extracting parton structure from lattice quantum chromodynamics (QCD) calculations requires studying the coordinate scale $z_3$ dependence of the matrix elements of bilocal operators. The most significant contribution comes from the $z_3$ dependence induced by ultraviolet (UV) renormalization of the Wilson line. We demonstrate that the next-to-leading order perturbative calculations of the renormalization factor can describe, to a few percent accuracy, the lattice QCD rest frame matrix elements with separations up to distances of 0.6~fm on multiple lattice spacings. The residual discrepancies can be modeled by a leading effect from the structure of the nucleon.
{"title":"Non-local Nucleon Matrix Elements in the Rest Frame","authors":"Joe Karpie, Christopher Monahan, Anatoly Radyushkin","doi":"arxiv-2407.16577","DOIUrl":"https://doi.org/arxiv-2407.16577","url":null,"abstract":"Extracting parton structure from lattice quantum chromodynamics (QCD)\u0000calculations requires studying the coordinate scale $z_3$ dependence of the\u0000matrix elements of bilocal operators. The most significant contribution comes\u0000from the $z_3$ dependence induced by ultraviolet (UV) renormalization of the\u0000Wilson line. We demonstrate that the next-to-leading order perturbative\u0000calculations of the renormalization factor can describe, to a few percent\u0000accuracy, the lattice QCD rest frame matrix elements with separations up to\u0000distances of 0.6~fm on multiple lattice spacings. The residual discrepancies\u0000can be modeled by a leading effect from the structure of the nucleon.","PeriodicalId":501191,"journal":{"name":"arXiv - PHYS - High Energy Physics - Lattice","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141779103","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}
This PhD thesis gives a comprehensive treatment of ab initio lattice Monte Carlo simulations of ultracold Bose gases by means of the complex Langevin algorithm. Since the field-theoretic action of non-relativistic bosons is a complex quantity, the corresponding path integral features a complex weight and is not accessible to standard Monte Carlo techniques. The complex Langevin algorithm represents an approach to overcome this obstacle, thereby providing the intriguing possibility of numerically exact simulations of interacting Bose-Einstein condensates within the field-theoretic framework. After reviewing the coherent-state path integral description of ultracold Bose gases as well as the complex Langevin method, we present the results of simulations in several physical scenarios. While parts of the thesis are based on arXiv:2204.10661 and arXiv:2304.05699 that treat the 3D and 2D homogeneous gas with contact interactions, it contains additional material covering external trapping potentials as well as Bose gases with long-range dipolar interactions.
{"title":"Simulation of ultracold Bose gases with the complex Langevin method","authors":"Philipp Heinen","doi":"arxiv-2407.16730","DOIUrl":"https://doi.org/arxiv-2407.16730","url":null,"abstract":"This PhD thesis gives a comprehensive treatment of ab initio lattice Monte\u0000Carlo simulations of ultracold Bose gases by means of the complex Langevin\u0000algorithm. Since the field-theoretic action of non-relativistic bosons is a\u0000complex quantity, the corresponding path integral features a complex weight and\u0000is not accessible to standard Monte Carlo techniques. The complex Langevin\u0000algorithm represents an approach to overcome this obstacle, thereby providing\u0000the intriguing possibility of numerically exact simulations of interacting\u0000Bose-Einstein condensates within the field-theoretic framework. After reviewing\u0000the coherent-state path integral description of ultracold Bose gases as well as\u0000the complex Langevin method, we present the results of simulations in several\u0000physical scenarios. While parts of the thesis are based on arXiv:2204.10661 and\u0000arXiv:2304.05699 that treat the 3D and 2D homogeneous gas with contact\u0000interactions, it contains additional material covering external trapping\u0000potentials as well as Bose gases with long-range dipolar interactions.","PeriodicalId":501191,"journal":{"name":"arXiv - PHYS - High Energy Physics - Lattice","volume":"81 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785860","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：