<p>The one loop matching kernels between parton distribution functions (PDFs) for parton <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>i</mi><mo>=</mo><mi>u</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>d</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>s</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>g</mi></mrow></math> and their corresponding quasi-PDFs are computed at one loop in the hybrid-ratio scheme. We found that, in addition to the conservation of the quasiquark number for each flavor, the second moment <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">⟨</mo><mi>x</mi><msub><mo stretchy="false">⟩</mo><mover accent="true"><mi>i</mi><mo stretchy="false">˜</mo></mover></msub><mo>=</mo><mo stretchy="false">⟨</mo><mi>x</mi><msub><mo stretchy="false">⟩</mo><mi>i</mi></msub></math> of quasi-PDF of parton <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>i</mi></math> (denoted as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>i</mi><mo stretchy="false">˜</mo></mover></math>) and PDF of parton <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>i</mi></math> is the same in our approach. This is demonstrated numerically using the CTEQ14 global analysis as input.</p>

Taiwan

Yi-Xian Chen

Japan

Jiunn-Wei Chen

One-loop matching factors for singlet quasiparton distribution functions in the hybrid-ratio scheme

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.

China

Fei Yao

Germany

Lisa Walter

Jun Hua

United States

Xiangdong Ji

Luchang Jin

Sebastian Lahrtz

Lingquan Ma

India

Protick Mohanta

Andreas Schäfer

Hai-Tao Shu

Yushan Su

Peng Sun

Xiaonu Xiong

Yi-Bo Yang

Hong Kong

Jian-Hui Zhang

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

Abstract The open N = 2 string theory is defined on the 4D space-time with the split signature (+, +, −, −). The string field theory action of the open N = 2 string theory is described by the 4D Wess–Zumino–Witten (WZW$_{4}$) model. The equation of motion of the WZW$_{4}$ model is the Yang equation, which is equivalent to the anti-self-dual Yang–Mills equation. In this paper, we study soliton-type classical solutions of the WZW$_{4}$ model in the split signature by calculating the action density of the WZW$_{4}$ model. We find that the action density of the one-soliton solutions is localized on a 3D hyperplane. This shows that there would be codimension-one-solitonic objects, or equivalently some kind of three-branes in the open N = 2 string theory. We also prove that, in the asymptotic region of the space-time, the action density of the n-soliton solutions is a “non-linear superposition” of n one-solitons. This suggests the existence of n intersecting three-branes in the N = 2 strings. Finally we make a reduction to a (1 + 2)D real space-time to calculate the energy densities of the soliton solutions. We can successfully evaluate the energy distribution for the two-soliton solutions and find that there is no singularity in the interacting region. This implies the existence of smooth intersecting codimension-one branes in the whole region. Soliton solutions in the Euclidean signature are also discussed.

Masashi Hamanaka

Shan-Chi Huang

Hiroaki Kanno

Solitons in open = 2 String Theory Kahler-Chen-Simons theory A tour through N=2 strings On soliton solutions of the anti-self-dual Yang-Mills equations from the perspective of integrable systems Soliton solutions in an integrable chiral model in 2+1 dimensions On the space-time monopole equation A review on tachyon condensation in open string field theories Soliton equations as dynamical systems on infinite dimensional Grassmann manifold

Detectors with low thresholds for electron recoil open a new window to direct searches of sub-GeV dark matter (DM) candidates. In the past decade, many strong limits on DM-electron interactions have been set, but most on the one which is spin-independent (SI) of both dark matter and electron spins. In this work, we study DM-atom scattering through a spin-dependent (SD) interaction at leading order (LO), using well-benchmarked, state-of-the-art atomic many-body calculations. Exclusion limits on the SD DM-electron cross section are derived with data taken from experiments with xenon and germanium detectors at leading sensitivities. In the DM mass range of 0.1–10 GeV, the best limits set by the XENON1T experiment: <math><mrow><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>e</mi></mrow><mrow><mo>(</mo><mi>SD</mi><mo>)</mo></mrow></msubsup><mo>&lt;</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>41</mn></mrow></msup><mi>–</mi><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>40</mn></mrow></msup><mtext> </mtext><mtext> </mtext><msup><mrow><mi>cm</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>, are comparable to the ones drawn on DM-neutron and DM-proton at slightly bigger DM masses. The detector’s responses to the LO SD and SI interactions are analyzed. In nonrelativistic limit, a constant ratio between them leads to an indistinguishability of the SD and SI recoil energy spectra. Relativistic calculations however show the scaling starts to break down at a few hundreds of eV, where the spin-orbit effects become sizable. We discuss the prospects of disentangling the SI and SD components in DM-electron interactions via spectral shape measurements, as well as having spin-sensitive experimental signatures without SI backgrounds.

C.P. Liu

Canada

Chih-Pan Wu

Hsin-Chang Chi

Mukesh K. Pandey

Lakhwinder Singh

Henry T. Wong

Spin-dependent dark matter-electron interactions

Large-momentum effective theory allows extraction of hadron parton distribution functions in lattice QCD by matching them to quark bilinear matrix elements of hadrons with large momenta. We calculate the matching kernels for the unpolarized, helicity, and transversity-isovector parton distribution functions and skewless generalized parton distributions of all hadrons in the hybrid-regularization-invariant momentum subtraction (RI/MOM) scheme. This renormalization scheme uses RI/MOM when the Wilson line length is less than <math><msub><mi>z</mi><mi>s</mi></msub></math>, otherwise a mass subtraction scheme is used. By design, the nonhybrid scheme is recovered as <math><msub><mi>z</mi><mi>s</mi></msub><mo>→</mo><mi>∞</mi></math>. In the opposite limit, <math><msub><mi>z</mi><mi>s</mi></msub><mo>→</mo><mn>0</mn></math>, the self-renormalization scheme is obtained. When the parameters <math><msubsup><mi>p</mi><mi>z</mi><mi>R</mi></msubsup><mo>=</mo><mn>0</mn></math> and <math><msup><mi>μ</mi><mi>R</mi></msup><msub><mi>z</mi><mi>s</mi></msub><mo>≪</mo><mn>1</mn></math>, the hybrid-RI/MOM scheme coincides with the hybrid-ratio scheme times the charge of the PDF. We also discuss the subtlety related to the commutativity of Fourier transform and <math><mi>ε</mi></math> expansion in the <math><mover><mi>MS</mi><mo>¯</mo></mover></math> scheme.

Chien-Yu Chou

One-loop hybrid renormalization matching kernels for quasiparton distributions

We investigate the renormalon ambiguity from bubble-chain diagrams in the isovector unpolarized quasiparton distribution function (PDF) of a hadron. We confirm the assertion by Braun, Vladimirov, and Zhang [Phys. Rev. D 99, 014013 (2019)] that the leading IR renormalon ambiguity is an <math><mi>O</mi><mo>(</mo><msubsup><mi>Λ</mi><mi>QCD</mi><mn>2</mn></msubsup><mo>/</mo><msup><mi>x</mi><mn>2</mn></msup><msubsup><mi>P</mi><mi>z</mi><mn>2</mn></msubsup><mo>)</mo></math> effect, with <math><mi>x</mi></math> the parton momentum fraction and <math><msub><mi>P</mi><mi>z</mi></msub></math> the hadron momentum, together with a new <math><mi>O</mi><mo>(</mo><mi>δ</mi><mo>(</mo><mi>x</mi><mo>)</mo><msubsup><mi>Λ</mi><mi>QCD</mi><mn>2</mn></msubsup><mo>/</mo><msubsup><mi>P</mi><mi>z</mi><mn>2</mn></msubsup><mo>)</mo></math> contribution such that the quark number is conserved. This implies the convergence of the perturbative matching kernel between a quasi-PDF and a PDF would eventually fail for small <math><mi>x</mi></math>. However, in both the <math><mi>R</mi></math>-scheme designed to cancel the leading IR renormalon and the typically used regularization-independent momentum subtraction scheme in lattice QCD for the same quasi-PDF, we find good convergence in the kernel based on three-loop bubble-chain diagram analyses. These results are encouraging for the quasi-PDF program. However, firm conclusions can only be drawn after the complete higher loop QCD calculations are carried out.

Wei-Yang Liu

Renormalon effects in quasiparton distributions

Large momentum effective field theory (LaMET) enables the extraction of parton distribution functions (PDF’s) directly on a Euclidean lattice through a factorization theorem that relates the computed quasi-PDF’s to PDF’s. We apply chiral perturbation theory (ChPT) to LaMET to further separate soft scales, such as light quark masses and lattice size, to obtain leading model independent extrapolation formulas for extrapolations to physical quark masses and infinite volume. We find that the finite volume effect is reduced when the nucleon carries a finite momentum. For nucleon momentum greater than 1 GeV and the lattice size <math><mi>L</mi></math> and pion mass <math><msub><mi>m</mi><mi>π</mi></msub></math> satisfying <math><msub><mi>m</mi><mi>π</mi></msub><mi>L</mi><mo>≥</mo><mn>3</mn></math>, the finite volume effect is less than 1% and is negligible for the current precision of lattice computations. This can be interpreted as a Lorentz contraction of the nucleon size in the z-direction which makes the lattice size effectively larger in that direction. We also find that the quark mass dependence in the infinite volume limit computed with nonzero nucleon momentum reproduces the previous result computed at zero momentum, as expected. Our approach can be generalized to other parton observables in LaMET straight forwardly.

Chiral perturbation for large momentum effective field theory

We investigate how entanglement entropy behaves in a non-conformal scalar field system with a quantum phase transition, by the replica method. We study the σ-model in 3+1 dimensions which is O(N) symmetric as the mass squared parameter μ 2 is positive, and undergoes spontaneous symmetry breaking while μ 2 becomes negative. The area law leading divergence of the entanglement entropy is preserved in both of the symmetric and the broken phases. The spontaneous symmetry breaking changes the subleading divergence from log to log squared, due to the cubic interaction on the cone. At the leading order of the coupling constant expansion, the entanglement entropy reaches a cusped maximum at the quantum phase transition point μ 2 = 0, and decreases while μ 2 is tuned away from 0 into either phase.

Shou-Huang Dai

Jin-Yi Pang

Entanglement Entropy and Quantum Phase Transition in the O(N) σ-model

We present the first lattice-QCD calculation of the kaon valence-quark distribution functions using the large-momentum effective theory (LaMET) approach. The calculation is performed with multiple pion masses with the lightest one around 220 MeV, 2 lattice spacings <math><mi>a</mi><mo>=</mo><mn>0.06</mn></math> and 0.12 fm, <math><mo>(</mo><msub><mi>M</mi><mi>π</mi></msub><msub><mo>)</mo><mi>min</mi></msub><mi>L</mi><mo>≈</mo><mn>5.5</mn></math>, and high statistics ranging from 11,600 to 61,312 measurements. We also calculate the valence-quark distribution of pion and find it to be consistent with the FNAL E615 experimental results, and our ratio of the <math><mi>u</mi></math> quark PDF in the kaon to that in the pion agrees with the CERN NA3 experiment. We also make predictions of the strange-quark distribution of the kaon.

Huey-Wen Lin

Zhouyou Fan

Rui Zhang

Valence-quark distribution of the kaon and pion from lattice QCD

Scattering of light dark matter (LDM) particles with atomic electrons is studied in the context of effective field theory. Contact and long-range interactions between dark matter and an electron are both considered. A state-of-the-art many-body method is used to evaluate the spin-independent atomic ionization cross sections of LDM-electron scattering, with an estimated error about 20%. New upper limits are derived on parameter space spanned by LDM mass and effective coupling strengths using data from the CDMSlite, XENON10, XENON100, and XENON1T experiments. Comparison with existing calculations shows the importance of atomic structure. Two aspects particularly important are relativistic effect for inner-shell ionization and final-state free electron wave function which sensitively depends on the underlying atomic approaches.

Chung-Chun Hsieh

Constraints from a many-body method on spin-independent dark matter scattering off electrons using data from germanium and xenon detectors