Large-momentum effective theory (LaMET) provides an approach to directly calculate the $\textit{x}$-dependence of generalized parton distributions (GPDs) on a Euclidean lattice through power expansion and a perturbative matching. When a parton’s momentum becomes soft, the corresponding logarithms in the matching kernel become non-negligible at higher orders of perturbation theory, which requires a resummation. But the resummation for the off-forward matrix elements at nonzero skewness $\textit{ξ}$ is difficult due to their multi-scale nature. In this work, we demonstrate that these logarithms are important only in the threshold limit, and derive the threshold factorization formula for the quasi-GPDs in LaMET. We then propose an approach to resum all the large logarithms based on the threshold factorization, which is implemented on a GPD model. We demonstrate that the LaMET prediction is reliable for [−1 + $\textit{x}$ $\textit{,}$ −$\textit{ξ}$ − $\textit{x}$ ] ∪ [−$\textit{ξ}$ + $\textit{x}$ $\textit{, ξ}$ − $\textit{x}$ ] ∪ [$\textit{ξ}$ + $\textit{x}$ $\textit{,}$ 1 − $\textit{x}$ ], where $\textit{x}$ is a cutoff depending on hard parton momenta. Through our numerical tests with the GPD model, we demonstrate that our method is self-consistent and that the inverse matching does not spread the nonperturbative effects or power corrections to the perturbatively calculable regions.

United States

Jack Holligan

Huey-Wen Lin

Rui Zhang

Yong Zhao

Resummation for lattice QCD calculation of generalized parton distributions at nonzero skewness

This paper introduces a novel systematic construction of gapped domain walls (GDWs) within the Levin-Wen (LW) model. By gluing two LW models along their open sides in a compatible way, we achieve a complete GDW classification by subsets of bulk input data, which encompass the classifications in terms of bimodule categories. A generalized bimodule structure is introduced to capture domain-wall excitations. Furthermore, we demonstrate that folding along any GDW yields a gapped boundary (GB) described by a Frobenius algebra of the input UFC for the folded model, thus bridging our GDW classification and the GB classification in [1].

China

Yanyan Chen

Siyuan Wang

Yu Zhao

Yuting Hu

Yidun Wan

Classification of gapped domain walls of topological orders in 2+1 dimensions: a Levin-Wen model realization

We develop a new methodology for extracting Compton form factors (CFFs) from deeply virtual exclusive reactions such as the unpolarized DVCS cross section using a specialized inverse problem solver, a variational autoencoder inverse mapper (VAIM). The VAIM-CFF framework not only allows us access to a fitted solution set possibly containing multiple solutions in the extraction of all 8 CFFs from a single cross section measurement, but also accesses the lost information contained in the forward mapping from CFFs to cross section. We investigate various assumptions and their effects on the predicted CFFs such as cross section organization, number of extracted CFFs, use of uncertainty quantification technique, and inclusion of prior physics information. We then use dimensionality reduction techniques such as principal component analysis to visualize the missing physics information tracked in the latent space of the VAIM framework. Through re-framing the extraction of CFFs as an inverse problem, we gain access to fundamental properties of the problem not comprehensible in standard fitting methodologies: exploring the limits of the information encoded in deeply virtual exclusive experiments.

Saudi Arabia

Manal Almaeen

Tareq Alghamdi

Brandon Kriesten

Douglas Adams

Yaohang Li

Simonetta Liuti

VAIM-CFF: a variational autoencoder inverse mapper solution to Compton form factor extraction from deeply virtual exclusive reactions

We present a comparison of different quantum state preparation algorithms and their overall efficiency for the Schwinger model with a theta term. While adiabatic state preparation is proved to be effective, in practice it leads to large cnot gate counts to prepare the ground state. The quantum approximate optimization algorithm (QAOA) provides excellent results while keeping the cnot counts small by design, at the cost of an expensive classical minimization process. We introduce a “blocked” modification of the Schwinger Hamiltonian to be used in the QAOA that further decreases the length of the algorithms as the size of the problem is increased. The rodeo algorithm (RA) provides a powerful tool to efficiently prepare any eigenstate of the Hamiltonian, as long as its overlap with the initial guess is large enough. We obtain the best results when combining the blocked QAOA ansatz and the RA, as this provides an excellent initial state with a relatively short algorithm without the need to perform any classical steps for large problem sizes.

Alexei Bazavov

Brandon Henke

Leon Hostetler

Dean Lee

Germany

Giovanni Pederiva

Andrea Shindler

Efficient state preparation for the Schwinger model with a theta term

We present a first study of the effects of renormalization-group resummation (RGR) and leading-renormalon resummation (LRR) on the systematic errors of the unpolarized isovector nucleon generalized parton distribution in the framework of large-momentum effective theory. This work is done using lattice gauge ensembles generated by the MILC Collaboration, consisting of <math><mrow><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math> flavors of highly improved staggered quarks with a physical pion mass at lattice spacing <math><mi>a</mi><mo>≈</mo><mn>0.09</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> and a box width <math><mi>L</mi><mo>≈</mo><mn>5.76</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>. We present results for the nucleon <math><mi>H</mi></math> and <math><mi>E</mi></math> generalized parton distributions (GPDs) with average boost momentum <math><msub><mi>P</mi><mi>z</mi></msub><mo>≈</mo><mn>2</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> at momentum transfers <math><mrow><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>0.97</mn><mo>]</mo><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> at skewness <math><mi>ξ</mi><mo>=</mo><mn>0</mn></math> as well as <math><msup><mi>Q</mi><mn>2</mn></msup><mo>∈</mo><mn>0.23</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></math> at <math><mi>ξ</mi><mo>=</mo><mn>0.1</mn></math>, renormalized in the modified minimal subtraction (<math><mover><mi>MS</mi><mo>¯</mo></mover></math>) scheme at scale <math><mi>μ</mi><mo>=</mo><mn>2.0</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, with two- and one-loop matching, respectively. We demonstrate that the simultaneous application of RGR and LRR significantly reduces the systematic errors in renormalized matrix elements and distributions for both the zero and nonzero skewness GPDs, and that it is necessary to include both RGR and LRR at higher orders in the matching and renormalization processes.

Systematic improvement of <math><mi>x</mi></math>-dependent unpolarized nucleon generalized parton distributions in lattice-QCD calculation

We present the first calculation of the pion gluon moment from lattice QCD in the continuum-physical limit. The calculation is done using clover fermions for the valence action with three pion masses, 220, 310 and 690 MeV, and three lattice spacings, 0.09, 0.12, and 0.15 fm, using ensembles generated by MILC Collaboration with <math><mrow><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math> flavors of highly improved staggered quarks (HISQ). On the lattice, we nonperturbatively renormalize the gluon operator in RI/MOM scheme using the cluster-decomposition error reduction (CDER) technique to enhance the signal-to-noise ratio of the renormalization constant. We extrapolate the pion gluon moment to the continuum-physical limit and obtain <math><mo>⟨</mo><mi>x</mi><msub><mo>⟩</mo><mi>g</mi></msub><mo>=</mo><mn>0.394</mn><mo>(</mo><mn>58</mn><msub><mo>)</mo><mrow><mrow><mi>stat</mi></mrow><mo>+</mo><mi>NPR</mi></mrow></msub><mo>(</mo><mn>39</mn><msub><mo>)</mo><mtext>mixing</mtext></msub></math> in the <math><mover><mi>MS</mi><mo>¯</mo></mover></math> scheme at 2 GeV, with first error being the statistical error and uncertainties in nonperturbative renormalization, and the second being a systematic uncertainty estimating the effect of ignoring quark mixing. Our pion gluon momentum fraction has a central value lower than two recent single-ensemble lattice-QCD results near physical pion mass but is consistent with the recent global fits by JAM and xFitter and with most QCD-model estimates.

William Good

Kinza Hasan

Allison Chevis

Gluon moment and parton distribution function of the pion from <math><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn></math> lattice QCD

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 <math><mi>a</mi><mo>=</mo><mo>{</mo><mn>0.1207</mn><mo>,</mo><mn>0.0888</mn><mo>,</mo><mn>0.0582</mn><mo>}</mo></math> fm, with <math><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn></math> flavors of highly improved staggered quarks at sea pion mass of <math><msub><mrow><mi>M</mi></mrow><mrow><mi>π</mi></mrow></msub><mo>≈</mo><mn>315</mn></math> MeV. We use clover-improved action for our valence quarks with nucleon boost momentum <math><msub><mrow><mi>P</mi></mrow><mrow><mi>z</mi></mrow></msub><mo>≈</mo><mn>1.75</mn></math> 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 <math><mover><mrow><mtext>MS</mtext></mrow><mo>‾</mo></mover></math> scheme at energy scale <math><mi>μ</mi><mo>=</mo><mn>2.0</mn></math> 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.

Nucleon helicity parton distribution function in the continuum limit with self-renormalization

We present results for the isovector axial vector form factors obtained using thirteen <math><mrow><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math>-flavor highly improved staggered quark (HISQ) ensembles generated by the MILC collaboration. The calculation of nucleon two- and three-point correlation functions has been done using Wilson-clover fermions. In the analysis of these data, we quantify the sensitivity of the results to strategies used for removing excited state contamination and invoke the partially conserved axial current relation between the form factors to choose between them. Our data driven analysis includes removing contributions from multihadron <math><mi>N</mi><mi>π</mi></math> states that make significant contributions. Our final results are <math><mrow><msub><mrow><mi>g</mi></mrow><mrow><mi>A</mi></mrow></msub><mo>=</mo><mn>1.292</mn><mo>(</mo><mn>53</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>stat</mi></mrow></msub><mo>(</mo><mn>24</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>sys</mi></mrow></msub></mrow></math> for the axial charge; <math><mrow><msub><mrow><mi>g</mi></mrow><mrow><mi>S</mi></mrow></msub><mo>=</mo><mn>1.085</mn><mo>(</mo><mn>50</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>stat</mi></mrow></msub><mo>(</mo><mn>103</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>sys</mi></mrow></msub></mrow></math> and <math><msub><mi>g</mi><mi>T</mi></msub><mo>=</mo><mn>0.991</mn><mo>(</mo><mn>21</mn><msub><mo>)</mo><mrow><mi>stat</mi></mrow></msub><mo>(</mo><mn>10</mn><msub><mo>)</mo><mi>sys</mi></msub></math> for the scalar and tensor charges; <math><mrow><mo>⟨</mo><msubsup><mrow><mi>r</mi></mrow><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>⟩</mo><mo>=</mo><mn>0.439</mn><mo>(</mo><mn>56</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>stat</mi></mrow></msub><mo>(</mo><mn>34</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>sys</mi></mrow></msub><mtext> </mtext><mtext> </mtext><mrow><msup><mrow><mi>fm</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow></math> for the mean squared axial charge radius, <math><msubsup><mi>g</mi><mi>P</mi><mo>*</mo></msubsup><mo>=</mo><mn>9.03</mn><mo>(</mo><mn>47</mn><msub><mo>)</mo><mrow><mi>stat</mi></mrow></msub><mo>(</mo><mn>42</mn><msub><mo>)</mo><mi>sys</mi></msub></math> for the induced pseudoscalar charge; and <math><msub><mi>g</mi><mrow><mi>π</mi><mi>N</mi><mi>N</mi></mrow></msub><mo>=</mo><mn>14.14</mn><mo>(</mo><mn>81</mn><msub><mo>)</mo><mrow><mi>stat</mi></mrow></msub><mo>(</mo><mn>85</mn><msub><mo>)</mo><mi>sys</mi></msub></math> for the pion-nucleon coupling. We also provide a parametrization of the axial form factor <math><msub><mi>G</mi><mi>A</mi></msub><mo>(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math> over the range <math><mn>0</mn><mo>≤</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>≤</mo><mn>1</mn><mtext> </mtext><mtext> </mtext><mrow><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> for use in phenomenology and a comparison with other lattice determinations. We find that the various lattice data agree within 10% but are significantly different from the extraction of <math><msub><mi>G</mi><mi>A</mi></msub><mo>(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math> from the <math><mi>ν</mi></math>-deuterium scattering data.

Yong-Chull Jang

Rajan Gupta

Tanmoy Bhattacharya

Boram Yoon

Nucleon isovector axial form factors

We present the first lattice-QCD x-dependent pion valence-quark generalized parton distribution (GPD) calculated directly at physical pion mass using the Large-Momentum Effective Theory (LaMET) with next-to-next-to-leading order perturbative matching correction. We use clover fermions for the valence action on <math><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn></math> flavors of highly improved staggered quarks (HISQ), generated by MILC Collaboration, with lattice spacing <math><mi>a</mi><mo>≈</mo><mn>0.09</mn></math> fm and box size <math><mi>L</mi><mo>≈</mo><mn>5.5</mn></math> fm; the pion two-point measurements number up to <math><mi>O</mi><mo>(</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>6</mn></mrow></msup><mo>)</mo></math> with boost momentum 1.73 GeV. The pion valence distribution is renormalized in hybrid scheme with Wilson-line mass subtraction at large distances in coordinate space, followed by a procedure to match it to the <math><mover><mrow><mtext>MS</mtext></mrow><mo>‾</mo></mover></math> scheme. We focus on the zero-skewness limit, where the GPD has a probability-density interpretation in the longitudinal Bjorken x and the transverse impact-parameter distributions. We take the integral of our GPD functions to generate leading moment so that we can make comparisons with past lattice-QCD and experimental determinations of the pion form factors and found consistent agreement among them. We predict the higher GPD moments and reveal x-dependent tomography of the pion for the first time using lattice QCD.

Pion valence-quark generalized parton distribution at physical pion mass

Levin-Wen string-net models provide a construction of (2+1)D topologically ordered phases of matter with anyonic localized excitations described by the Drinfeld center of a unitary fusion category. Anyon condensation is a mechanism for phase transitions between (2+1)D topologically ordered phases. We construct an extension of Levin-Wen models in which tuning a parameter implements anyon condensation. We also describe the classification of anyons in Levin-Wen models via representation theory of the tube algebra, and use a variant of the tube algebra to classify low-energy localized excitations in the condensed phase.