We present the first lattice QCD calculation of the quark transverse spin-momentum correlation, i.e., the naive time-reversal-odd Boer-Mulders function, of the nucleon, using large-momentum effective theory (LaMET). The calculation is carried out on an ensemble with lattice spacing $\textit{a}$ = 0.098 fm and pion mass 338 MeV, at various proton momenta up to 2.11 GeV. We have implemented perturbative matching up to the next-to-next-to-leading order together with a renormalization-group resummation improvement. The result exhibits the expected decay behavior with increasing transverse separation $\textit{b}$ . We also compare the results in the nucleon and pion.

China

Lingquan Ma

Jun Hua

Germany

Andreas Schäfer

Hai-Tao Shu

United States

Yushan Su

Peng Sun

Lisa Walter

Wei Wang

Xiaonu Xiong

Yi-Bo Yang

Jian-Hui Zhang

Qi-An Zhang

Quark transverse spin-momentum correlation of the nucleon from lattice QCD: the Boer-Mulders function

We elaborate on the method introduced in arXiv:2403.02165 for holographic duals of Boundary Conformal Field Theories (BCFTs) with multiple boundaries. Naïvely, as the number of boundaries grow large such a calculation becomes unmanageable. We show that is not always the case. Using these advances we calculate the entanglement entropy as a function of time for 1+1-dimensional CFTs that are split into $\textit{N}$ subsystems. We give explicit results for $\textit{N}$ = 4 and $\textit{N}$ = 17. We find that all qualitative differences that arise for larger $\textit{N}$ are present $\textit{N}$ = 4.

Belgium

Joseph Lap

Berndt Müller

Clemens Seidl

Holography for BCFTs with multiple boundaries: multi-splitting quenches

We present the first lattice QCD calculation of the quark transverse spin-momentum correlation, i.e., the T-odd Boer-Mulders function of the pion, using large-momentum effective theory. The calculation is done at three lattice spacings <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>a</mi><mo>=</mo><mo stretchy="false">{</mo><mn>0.098</mn><mo>,</mo><mn>0.085</mn><mo>,</mo><mn>0.064</mn><mo stretchy="false">}</mo><mtext> </mtext><mtext> </mtext><mi>fm</mi></mrow></math> and pion masses <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><mn>350</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, with pion momenta up to 1.8 GeV. The matrix elements are renormalized in a state-of-the-art scheme and extrapolated to the continuum and infinite momentum limit. We have implemented the perturbative matching up to the next-to-next-to-leading order and carried out a renormalization-group resummation. Our results provide valuable input for phenomenological analyses of the Boer-Mulders single-spin asymmetry.

Sebastian Lahrtz

Hong Kong

Quark transverse spin-momentum correlation of the pion from lattice QCD: The Boer-Mulders function

With the discovery of a Higgs boson with a mass of 125 gigaelectronvolts (GeV) at the Large Hadron Collider (LHC) at CERN in 2012, the Standard Model (SM) is complete, and despite intensive searches, no new fundamental particle has been observed since then. In fact, a discovery can be challenging without a predictive new physics model because different channels and observables cannot be combined directly and unambiguously. Furthermore, without supporting indirect hints, the signal space to be searched is huge, resulting in diluted significances owing to the look-elsewhere effect. Several LHC processes with multiple leptons in the final state point towards the existence of a new Higgs boson with a mass between 140 GeV to 160 GeV decaying mostly to $\textit{W}$ bosons. While the former strongly reduces the look-elsewhere effect, the latter indicates that it could be a Higgs triplet with zero hypercharge. Within this simple and predictive extension of the SM, we simulate and combine different channels of di-photon production in association with leptons, missing energy, jets, $\textit{etc}$... Using the full run-2 results by ATLAS, including those presented recently at the Moriond conference, an increased significance of 4 standard deviations is obtained for a $\approx$ 152 GeV Higgs. Due to the previously predicted mass range, the look-elsewhere effect is negligible, and this constitutes the highest statistical evidence for a new narrow resonance obtained at the LHC. Furthermore, the model predicts a heavier-than-expected $\textit{W}$ boson, as indicated by the global electroweak fit. If further substantiated, the discovery of a new Higgs would overthrow the SM, provide a compelling case for the construction of future particle colliders, and pave the way to a novel understanding of the known shortcomings of the SM. In particular, the triplet Higgs field can lead to a strong first-order phase transition and could thus be related to the matter anti-matter asymmetry in our Universe.

Switzerland

Andreas Crivellin

Saiyad Ashanujjaman

Sumit Banik

Guglielmo Coloretti

India

Siddharth P. Maharathy

South Africa

Bruce Mellado

Growing evidence for a Higgs triplet * The work of Andreas Crivellin is supported by a Professorship Grant from the Swiss National Science Foundation (PP00P21_76884). The work of Saiyad Ashanujjaman is partially supported by the National Natural Science Foundation of China (11835013). Siddharth P. Maharathy acknowledges using the SAMKHYA: High-Performance Computing Facility provided by the Institute of Physics, Bhubaneswar

We calculate the leading-twist light cone distribution amplitudes of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mi>u</mi><mi>d</mi><mi>s</mi><mo stretchy="false">)</mo></math> baryon using lattice QCD methods within the framework of large-momentum effective theory. Our numerical computations are carried out with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn></math> stout smeared clover fermions and a Symanzik gauge action on a lattice with spacing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>a</mi><mo>=</mo><mn>0.077</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> and a pion mass of 303 MeV. To approach the large-momentum region, we simulate the equal-time correlations with the hadron momentum <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>P</mi></mrow><mrow><mi>z</mi></mrow></msup><mo>=</mo><mo stretchy="false">{</mo><mn>2.52</mn><mo>,</mo><mn>3.02</mn><mo>,</mo><mn>3.52</mn><mo stretchy="false">}</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>. We investigate the analytic properties of the baryon quasidistribution amplitude in coordinate space and validate them through our lattice calculations. After renormalization and extrapolation, we present results for the three-dimensional distribution in momentum fractions of the two light quarks. Based on these findings, we briefly discuss the phenomenological impact on weak decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub></math> and outline potential systematic uncertainties that can be improved in the future. This work lays the theoretical foundation for accessing baryon light cone distribution amplitudes from lattice QCD.

Poland

Min-Huan Chu

Haoyang Bai

Jian Liang

Xiangdong Ji

Jun Zeng

Light cone distribution amplitude for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math> baryon from lattice QCD

We develop an approach for calculating heavy quark effective theory (HQET) light-cone distribution amplitudes (LCDAs) by employing a sequential effective theory methodology. The theoretical foundation of the framework is established, elucidating how the quasidistribution amplitudes (quasi-DAs) with three scales can be utilized to compute HQET LCDAs. We provide theoretical support for this approach by demonstrating the rationale behind devising a hierarchical ordering for the three involved scales, discussing the factorization at each step, clarifying the underlying reason for obtaining HQET LCDAs in the final phase, and addressing potential theoretical challenges. The lattice QCD simulation aspect is explored in detail, and the computations of quasi-DAs are presented. We employ three fitting strategies to handle contributions from excited states and extract the bare matrix elements. For renormalization purposes, we apply hybrid renormalization schemes at short and long distance separations. To mitigate long-distance perturbations, we perform an extrapolation in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi><mo>=</mo><mi>z</mi><mo>·</mo><msup><mi>P</mi><mi>z</mi></msup></math> and assess the stability against various parameters. After two-step matching, our results for HQET LCDAs are found in agreement with existing model parametrizations. The potential phenomenological implications of the results are discussed, shedding light on how these findings could impact our understanding of the strong interaction dynamics and physics beyond the standard model. It should be noted, however, that systematic uncertainties have not been accounted for yet.

Xue-Ying Han

Cai-Dian Lü

Ji Xu

Yibo Yang

Shuai Zhao

Calculation of heavy meson light-cone distribution amplitudes from lattice QCD

We analyze the gauge fixing precision dependence of some nonlocal quark-bilinear lattice operators interesting in computing parton physics for several measurements, using five lattice spacings ranging from 0.032 to 0.121 fm. Our results show that gauge-dependent nonlocal measurements are significantly more sensitive to the precision of gauge fixing than anticipated. The impact of imprecise gauge fixing is significant for fine lattices and long distances. For instance, even with the typically defined precision of Landau gauge fixing of <math><msup><mn>10</mn><mrow><mo>−</mo><mn>8</mn></mrow></msup></math>, the deviation caused by imprecise gauge fixing can reach 12%, when calculating the trace of Wilson lines at 1.2 fm with a lattice spacing of approximately 0.03 fm. Similar behavior has been observed in <math><mi>ξ</mi></math> gauge and Coulomb gauge as well. For both quasi-parton-distribution functions (quasi-PDFs) and quasi-transverse-momentum-dependent PDFs operators renormalized using the regularization independent momentum subtraction (RI/MOM) scheme, convergence for different lattice spacings at long distance is only observed when the precision of Landau gauge fixing is sufficiently high. To describe these findings quantitatively, we propose an empirical formula to estimate the required precision.

Kuan Zhang

Yi-Kai Huo

Chun-Jiang Shi

Impact of gauge fixing precision on the continuum limit of nonlocal quark-bilinear lattice operators

Following previous works on that topic, we consider Euclidean hadronic matrix elements in position space of two spatially separated local currents on the lattice, in order to extract the <math><mi>x</mi></math> dependence of parton distribution functions (PDFs). The corresponding approach is often referred to by the term lattice cross section. In this work we will consider valence quark PDFs of an unpolarized proton. We adapt the previously established formalism to our choice of operators. The calculation of the two-current matrix elements requires the evaluation of four-point functions. The corresponding calculation is carried out on a <math><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> gauge ensemble with lattice spacing <math><mi>a</mi><mo>=</mo><mn>0.0856</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math> and pseudoscalar masses <math><msub><mi>m</mi><mi>π</mi></msub><mo>=</mo><mn>355</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> and <math><msub><mi>m</mi><mi>K</mi></msub><mo>=</mo><mn>441</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. The four-point functions have been evaluated in a previous project. The lattice data is converted to the <math><mover><mi>MS</mi><mo>¯</mo></mover></math> scheme at a scale <math><mi>μ</mi><mo>=</mo><mn>2</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> and improved with respect to lattice artifacts. We use a common model as fit ansatz for the lattice data in order to extract the PDFs.

France

Christian Zimmermann

Valence quark PDFs of the proton from two-current correlations in lattice QCD

We study the entanglement entropy of Hamiltonian SU(2) lattice gauge theory in <math><mn>2</mn><mo>+</mo><mn>1</mn></math> dimensions on linear plaquette chains and show that the entanglement entropies of both ground and excited states follow Page curves. The transition of the subsystem size dependence of the entanglement entropy from the area law for the ground state to the volume law for highly excited states is found to be described by a universal crossover function. Quantum many-body scars in the middle of the spectrum, which are present in the electric flux truncated Hilbert space, where the gauge theory can be mapped onto an Ising model, disappear when higher electric field representations are included in the Hilbert space basis. This suggests the continuum (<math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional SU(2) gauge theory does not have such scarred states.

Lukas Ebner

Xiaojun Yao

Entanglement entropy of (<math><mn>2</mn><mo>+</mo><mn>1</mn></math>)-dimensional SU(2) lattice gauge theory on plaquette chains

We present a first lattice QCD calculation of the unpolarized nucleon’s isovector transverse-momentum-dependent parton distribution functions (TMDPDFs), which are essential to predict observables of multiscale, semi-inclusive processes in the standard model. We use a <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> MILC ensemble with valence clover fermions on a highly improved staggered quark (HISQ) sea to compute the quark momentum distributions in a large-momentum nucleon on the lattice. The state-of-the-art techniques in renormalization and extrapolation in the correlation distance on the lattice are adopted. The perturbative kernel up to next-to-next-to-leading order is taken into account, and the dependence on the pion mass and the hadron momentum is explored. Our results are qualitatively comparable with phenomenological TMDPDFs, which provide an opportunity to predict high energy scatterings from first principles.

Jin-Chen He

Unpolarized transverse momentum dependent parton distributions of the nucleon from lattice QCD