<p>We report a lattice QCD calculation of the parton distribution function (PDF) of a deuteronlike dibaryon system using large-momentum effective theory. The calculation is done on three Wilson-clover ensembles with a fixed lattice spacing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>a</mi><mo>=</mo><mn>0.105</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></mrow></math> and two pion masses. The lattice matrix elements are computed at proton momenta up to 2.46 GeV, with the signal of high-momentum modes being improved by applying the momentum smearing technique. The state-of-the-art renormalization, matching, and extrapolation are then applied to obtain the final result of the light-cone PDF. A comparison between the result of the dibaryon system and the sum of the proton and neutron PDFs is also given.</p>

China

Chen Chen

Yiqi Geng

Liuming Liu

Peng Sun

Yi-Bo Yang

Hong Kong

Fei Yao

Jian-Hui Zhang

Kuan Zhang

Parton distribution function of a deuteronlike dibaryon system from lattice QCD

We propose two approaches for extracting the total gluon helicity contribution to proton spin from lattice QCD, one from local operator matrix elements in a fixed gauge accessible on lattice with feasible renormalization, and the other from gauge-invariant nonlocal gluon correlators. Neither of these approaches requires a matching procedure when converted to the   <math> <mover> <mi>MS</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\textrm{MS}} $$  scheme. Our proposal resolves a long-standing inconsistency in the literature regarding lattice calculations of the total gluon helicity, and has the potential to greatly facilitate these calculations.

Zhuoyi Pang

Total gluon helicity from lattice without effective theory matching

We report a state-of-the-art lattice QCD calculation of the isovector quark transversity distribution of the proton in the continuum and physical mass limit using large-momentum effective theory. The calculation is done at four lattice spacings <math><mrow><mi>a</mi><mo>=</mo><mo>{</mo><mn>0.098</mn><mo>,</mo><mn>0.085</mn><mo>,</mo><mn>0.064</mn><mo>,</mo><mn>0.049</mn><mo>}</mo><mtext> </mtext><mtext> </mtext><mi>fm</mi></mrow></math> and various pion masses ranging between 220 and 350 MeV, with proton momenta up to 2.8 GeV. The result is nonperturbatively renormalized in the hybrid scheme with self-renormalization, which treats the infrared physics at large correlation distance properly, and extrapolated to the continuum, physical mass, and infinite momentum limit. We also compare with recent global analyses for the nucleon isovector quark transversity distribution.

Germany

Lisa Walter

Taiwan

Jiunn-Wei Chen

Jun Hua

United States

Xiangdong Ji

Luchang Jin

Sebastian Lahrtz

Lingquan Ma

India

Protick Mohanta

Andreas Schäfer

Hai-Tao Shu

Yushan Su

Xiaonu Xiong

Nucleon Transversity Distribution in the Continuum and Physical Mass Limit from Lattice QCD

We present a unified framework for the perturbative factorization connecting Euclidean correlations to light-cone correlations. Starting from nonlocal quark and gluon bilinear correlators, we derive the relevant hard-matching kernel up to the next-to-leading-order, both for the flavor singlet and non-singlet combinations, in non-forward and forward kinematics, and in coordinate and momentum space. The results for the generalized distribution functions (GPDs), parton distribution functions (PDFs), and distribution amplitudes (DAs) are obtained by choosing appropriate kinematics. The renormalization and matching are done in a state-of-the-art scheme. We also clarify some issues raised on the perturbative matching of GPDs in the literature. Our results provide a complete manual for extracting all leading-twist GPDs, PDFs as well as DAs from lattice simulations of Euclidean correlations in a state-of-the-art strategy, either in coordinate or in momentum space factorization approach.

Yao Ji

Connecting Euclidean to light-cone correlations: from flavor nonsinglet in forward kinematics to flavor singlet in non-forward kinematics

In the large-momentum expansion for parton distribution functions (PDFs), the natural physics scale is the longitudinal momentum (<math><msub><mrow><mi>p</mi></mrow><mrow><mi>z</mi></mrow></msub></math>) of the quarks (or gluons) in a large-momentum hadron. We show how to expose this scale dependence through resumming logarithms of the type <math><msup><mrow><mi>ln</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>⁡</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>z</mi></mrow></msub><mo>/</mo><mi>μ</mi></math> in the matching coefficient, where μ is a fixed renormalization scale. The result enhances the accuracy of the expansion at moderate <math><msub><mrow><mi>p</mi></mrow><mrow><mi>z</mi></mrow></msub><mo>&gt;</mo><mn>1</mn></math> GeV, and at the same time, clearly shows that the partons cannot be approximated from quarks with <math><msub><mrow><mi>p</mi></mrow><mrow><mi>z</mi></mrow></msub><mo>∼</mo><msub><mrow><mi>Λ</mi></mrow><mrow><mi>QCD</mi></mrow></msub></math> which are not predominantly collinear with the parent hadron momentum, consistent with power counting of the large-momentum effective theory. The same physics mechanism constrains the coordinate space expansion at large distances z, the conjugate of <math><msub><mrow><mi>p</mi></mrow><mrow><mi>z</mi></mrow></msub></math>, as illustrated in the example of fitting the moments of the PDFs.

Jack Holligan

Rui Zhang

Resumming quark's longitudinal momentum logarithms in LaMET expansion of lattice PDFs

We present a state-of-the-art lattice QCD calculation of the pion and kaon light-cone distribution amplitudes (DAs) using large-momentum effective theory. The calculation is done at three lattice spacings <math><mrow><mi>a</mi><mo>≈</mo><mo>{</mo><mn>0.06</mn><mo>,</mo><mn>0.09</mn><mo>,</mo><mn>0.12</mn><mo>}</mo><mtext> </mtext><mtext> </mtext><mi>fm</mi></mrow></math> and physical pion and kaon masses, with the meson momenta <math><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>z</mi></mrow></msub><mo>=</mo><mo>{</mo><mn>1.29</mn><mo>,</mo><mn>1.72</mn><mo>,</mo><mn>2.15</mn><mo>}</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>. The result is nonperturbatively renormalized in a recently proposed hybrid scheme with self-renormalization, and extrapolated reliably to the continuum as well as the infinite momentum limit. We find a significant deviation of the pion and kaon DAs from the asymptotic form, and a large <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> flavor breaking effect in the kaon DA.

Min-Huan Chu

Fang-Cheng He

Jin-Chen He

Wei Wang

Ji Xu

Qi-An Zhang

Pion and Kaon Distribution Amplitudes from Lattice QCD

To calculate the transverse-momentum-dependent parton distribution functions (TMDPDFs) from lattice QCD, an important goal yet to be realized, it is crucial to establish a viable nonperturbative renormalization approach for linear divergences in the corresponding Euclidean quasi-TMDPDF correlators in large-momentum effective theory. We perform a first systematic study of the renormalization property of the quasi-TMDPDFs by calculating the relevant matrix elements in a pion state at five lattice spacings ranging from 0.03 fm to 0.12 fm. We demonstrate that the square root of the Wilson loop combined with the short distance hadron matrix element provides a successful method to remove all ultraviolet divergences of the quasi-TMD operator, and thus provides the necessary justification to perform a continuum limit calculation of TMDPDFs. In contrast, the popular regularization independent momentum subtraction renormalization (RI/MOM) scheme fails to eliminate all linear divergences.

Renormalization of Transverse-Momentum-Dependent Parton Distribution on the Lattice