Physics Commons^™

Counting Linearly Polarized Gluons With Lattice Qcd, Shuai Zhao

Physics Faculty Publications

We outline an approach to calculate the transverse-momentum-dependent distribution of linearly polarized gluons inside an unpolarized hadron on the lattice with the help of large momentum effective theory. To achieve this purpose, we propose calculating a Euclidean version of the degree of polarization for a fast-moving hadron on the lattice, which is ultraviolet finite, and no soft function subtraction is needed. It indicates a practical way to explore the distribution of the linearly polarized gluons in a proton and the linearly polarized gluon effects in hadron collisions on the lattice.

Non-Singlet Quark Helicity Pdfs Of The Nucleon From Pseudo-Distributions, Robert Edwards, Colin Egerer, Joseph Karpie, Nikhil Karthik, Christopher Monahan, Wayne Morris, Kostas Orginos, Anatoly Radyushkin, David Richards, Eloy Romero, Raza Sabbir Sufian, Savvas Zafeiropoulos, On Behalf Of The Hadstruc Collaboration

Physics Faculty Publications

The non-singlet helicity quark parton distribution functions (PDFs) of the nucleon are determined from lattice QCD, by jointly leveraging pseudo-distributions and the distillation spatial smearing paradigm. A Lorentz decomposition of appropriately isolated space-like matrix elements reveals pseudo-distributions that contain information on the leading-twist helicity PDFs, as well as an invariant amplitude that induces an additional z² contamination of the leading-twist signal. An analysis of the short-distance behavior of the space-like matrix elements using matching coefficients computed to next-to-leading order (NLO) exposes the desired PDF up to this additional z² contamination. Due to the non-conservation of the axial current, …

Prospects For 𝛾*𝛾* → 𝜋𝜋 Via Lattice Qcd, Raúl Briceño, Andrew W. Jackura, Arkaitz Rodas, Juan V. Guerrero

Physics Faculty Publications

The 𝛾*𝛾* → 𝜋𝜋 scattering amplitude plays a key role in a wide range of phenomena, including understanding the inner structure of scalar resonances as well as constraining the hadronic contributions to the anomalous magnetic moment of the muon. In this work, we explain how the infinite-volume Minkowski amplitude can be constrained from finite-volume Euclidean correlation functions. The relationship between the finite-volume Euclidean correlation functions and the desired amplitude holds up to energies where 3𝜋 states can go on shell, and is exact up to exponentially small corrections that scale like 𝒪(e^−m𝜋L), where L is the spatial extent …

Gluon Transverse-Momentum-Dependent Distributions From Large-Momentum Effective Theory, Ruilin Zhu, Yao Ji, Jian-Hui Zhang, Shuai Zhao

Physics Faculty Publications

We demonstrate that gluon transverse-momentum-dependent parton distribution functions (TMDPDFs) can be extracted from lattice calculations of appropriate Euclidean correlations in large-momentum effective theory (LaMET). Based on perturbative calculations of gluon unpolarized and helicity TMDPDFs, we present a matching formula connecting them and their LaMET counterparts, where the latter are renormalized in a scheme facilitating lattice calculations and converted to the MS ¯ scheme. The hard matching kernel is given up to one-loop level. We also show that the perturbative result is independent of the prescription used for the pinch-pole singularity in the relevant correlations. Our results offer a guidance for …

Analytic Continuation Of The Relativistic Three-Particle Scattering Amplitudes, Sebastian M. Dawid, Md Habib E. Islam, Raúl A. Briceño

Physics Faculty Publications

We investigate the relativistic scattering of three identical scalar bosons interacting via pair-wise interactions. Extending techniques from the nonrelativistic three-body scattering theory, we provide a detailed and general prescription for solving and analytically continuing integral equations describing the three-body reactions. We use these techniques to study a system with zero angular momenta described by a single scattering length leading to a bound state in a two-body subchannel. We obtain bound-state-particle and three-particle amplitudes in the previously unexplored kinematical regime; in particular, for real energies below elastic thresholds and complex energies in the physical and unphysical Riemann sheets. We extract positions …

Connecting Matrix Elements To Multi-Hadron Form-Factors, Andrew W. Jackura

Physics Faculty Publications

We discuss developments in calculating multi-hadron form-factors and transition processes via lattice QCD. Our primary tools are finite-volume scaling relations, which map spectra and matrix elements to the corresponding multi-hadron infinite-volume amplitudes. We focus on two hadron processes probed by an external current, and provide various checks on the finite-volume formalism in the limiting cases of perturbative interactions and systems forming a bound state. By studying model-independent properties of the infinite-volume amplitudes, we are able to rigorously define form-factors of resonances.

Flavor-Dependent Radiative Corrections In Coherent Elastic Neutrino-Nucleus Scattering, Oleksandr Tomalak, Pedro Machado, Vishvas Pandey, Ryan Plestid

Physics and Astronomy Faculty Publications

We calculate coherent elastic neutrino-nucleus scattering cross sections on spin-0 nuclei (e.g. ⁴⁰Ar and ²⁸Si) at energies below 100 MeV within the Standard Model and account for all effects of permille size. We provide a complete error budget including uncertainties at nuclear, nucleon, hadronic, and quark levels separately as well as perturbative error. Our calculation starts from the four-fermion effective field theory to explicitly separate heavy-particle mediated corrections (which are absorbed by Wilson coefficients) from light-particle contributions. Electrons and muons running in loops introduce a non- trivial dependence on the momentum transfer due to their relatively light masses. …

Consistency Checks For Two-Body Finite-Volume Matrix Elements: Conserved Currents And Bound States, Raúl A. Briceño, Christopher J. Monahan

Physics Faculty Publications

We present a model-independent framework to determine finite-volume corrections of matrix elements of spatially separated current-current operators. We define these matrix elements in terms of Compton-like amplitudes, i.e., amplitudes coupling single-particle states via two current insertions. We show that the infrared behavior of these matrix elements is dominated by the single-particle pole, which is approximated by the elastic form factors of the lowest-lying hadron. Therefore, given lattice data on the relevant elastic form factors, the finite-volume effects can be estimated nonperturbatively and without recourse to effective field theories. For illustration purposes, we investigate the implications of the proposed formalism for …

Role Of Boundary Conditions In Quantum Computations Of Scattering Observables, Raúl A. Briceño, Juan V. Guerrero, Maxwell T. Hansen, Alexandru M. Sturzu

Physics Faculty Publications

Quantum computing may offer the opportunity to simulate strongly interacting field theories, such as quantum chromodynamics, with physical time evolution. This would give access to Minkowski-signature correlators, in contrast to the Euclidean calculations routinely performed at present. However, as with present-day calculations, quantum computation strategies still require the restriction to a finite system size, including a finite, usually periodic, spatial volume. In this work, we investigate the consequences of this in the extraction of hadronic and Compton-like scattering amplitudes. Using the framework presented in Briceno et al. [Phys. Rev. D 101, 014509 (2020)], we estimate the volume effects for various …

Constraining 1 + 𝒥 → 2 Coupled-Channel Amplitudes In A Finite Volume, Raúl A. Briceño, Jozef J. Dudek, Luka Leskovec

Physics Faculty Publications

Whether one is interested in accessing the excited spectrum of hadrons or testing the standard model of particle physics, electroweak transition processes involving multihadron channels in the final state play an important role in a variety of experiments. Presently the primary theoretical tool with which one can study such reactions is lattice QCD, which is defined in a finite spacetime volume. In this work, we investigate the feasibility of implementing existing finite-volume formalism in realistic lattice QCD calculation of reactions in which a stable hadron can transition to one of several two-hadron channels under the action of an external current. …

The Continuum And Leading Twist Limits Of Parton Distribution Functions In Lattice Qcd, Joseph Karpie, Kostas Orginos, Anatoly Radyushkin, Savvas Zafeiropoulos, For The Hadstruc Collaboration

Physics Faculty Publications

In this study, we present continuum limit results for the unpolarized parton distribution function of the nucleon computed in lattice QCD. This study is the first continuum limit using the pseudo-PDF approach with Short Distance Factorization for factorizing lattice QCD calculable matrix elements. Our findings are also compared with the pertinent phenomenological determinations. Inter alia, we are employing the summation Generalized Eigenvalue Problem (sGEVP) technique in order to optimize our control over the excited state contamination which can be one of the most serious systematic errors in this type of calculations. A crucial novel ingredient of our analysis is the …

Unpolarized Gluon Distribution In The Nucleon From Lattice Quantum Chromodynamics, Tanjib Khan, Raza Sabbir Sufian, Joseph Karpie, Christopher J. Monahan, Colin Egerer, Bálint Joó, Wayne Morris, Kostas Orginos, Anatoly Radyushkin, David G. Richards, Eloy Romero, Savvas Zafeiropoulos, On Behalf Of The Hadstruc Collaboration

Physics Faculty Publications

In this study, we present a determination of the unpolarized gluon Ioffe-time distribution in the nucleon from a first principles lattice quantum chromodynamics calculation. We carry out the lattice calculation on a 32³ × 64 ensemble with a pion mass of 358 MeV and lattice spacing of 0.094 fm. We construct the nucleon interpolating fields using the distillation technique, flow the gauge fields using the gradient flow, and solve the summed generalized eigenvalue problem to determine the gluonic matrix elements. Combining these techniques allows us to provide a statistically well-controlled Ioffe-time distribution and unpolarized gluon parton distribution function. We …

Parton Distribution Functions From Ioffe Time Pseudodistributions From Lattice Calculations: Approaching The Physical Point, Bálint Joó, Joseph Karpie, Kostas Orginos, Anatoly V. Radyushkin, David G. Richards, Savvas Zafeiropoulos

Physics Faculty Publications

We present results for the unpolarized parton distribution function of the nucleon computed in lattice QCD at the physical pion mass. This is the first study of its kind employing the method of Ioffe time pseudodistributions. Beyond the reconstruction of the Bjorken-x dependence, we also extract the lowest moments of the distribution function using the small Ioffe time expansion of the Ioffe time pseudodistribution. We compare our findings with the pertinent phenomenological determinations.

B-Meson Light-Cone Distribution Amplitude From Euclidean Quantities, Wei Wang, Yu-Ming Wang, Ji Xu, Shuai Zhao

Physics Faculty Publications

A new method for the model-independent determination of the light-cone distribution amplitude of the B-meson in heavy quark effective theory (HQET) is proposed by combining the large momentum effective theory and the numerical simulation technique on the Euclidean lattice. We demonstrate the autonomous scale dependence of the nonlocal quasi-HQET operator with the aid of the auxiliary field approach, and further determine the perturbative matching coefficient entering the hard-collinear factorization formula for the B-meson quasidistribution amplitude at the one-loop accuracy. These results will be crucial to explore the partonic structure of heavy-quark hadrons in the static limit and to …

Long-Range Electroweak Amplitudes Of Single Hadrons From Euclidean Finite-Volume Correlation Functions, Raúl A. Briceño, Zohreh Davoudi, Maxwell T. Hansen, Matthias R. Schindler, Alessandro Baroni

Physics Faculty Publications

A relation is presented between single-hadron long-range matrix elements defined in a finite Euclidean spacetime and the corresponding infinite-volume Minkowski amplitudes. This relation is valid in the kinematic region where any number of two-hadron states can simultaneously go on shell, so that the effects of strongly coupled intermediate channels are included. These channels can consist of nonidentical particles with arbitrary intrinsic spins. The result accommodates general Lorentz structures as well as nonzero momentum transfer for the two external currents inserted between the single-hadron states. The formalism, therefore, generalizes the work by Christ et al. [Phys. Rev. D 91, 114510 …

Generalized Parton Distributions And Pseudodistributions, Anatoly V. Radyushkin

Physics Faculty Publications

We derive one-loop matching relations for the Ioffe-time distributions (ITDs) related to the pion distribution amplitude (DA) and generalized parton distributions (GPDs). They are obtained from a universal expression for the one-loop correction in an operator form, and will be used in the ongoing lattice calculations of the pion DA and GPDs within the parton pseudodistributions approach.

Parton Distribution Functions From Loffe Time Pseudo-Distributions, Bálint Joó, Joseph Karpie, Kostas Orginos, Anatoly V. Radyushkin, David Richards, Savvas Zafeiropoulos

Physics Faculty Publications

In this paper, we present a detailed study of the unpolarized nucleon parton distribution function (PDF) employing the approach of parton pseudo-distribution functions. We perform a systematic analysis using three lattice ensembles at two volumes, with lattice spacings a = 0.127 fm and a = 0.094 fm, for a pion mass of roughly 400 MeV. With two lattice spacings and two volumes, both continuum limit and infinite volume extrapolation systematic errors of the PDF are considered. In addition to the x dependence of the PDF, we compute their first two moments and compare them with the pertinent phenomenological determinations.

Numerical Exploration Of Three Relativistic Particles In A Finite Volume Including Two-Particle Resonances And Bound States, Fernando Romero-López, Stephen R. Sharpe, Tyler D. Blanton, Raúl A. Briceño, Maxwell T. Hansen

Physics Faculty Publications

In this work, we use an extension of the quantization condition, given in ref. [1], to numerically explore the finite-volume spectrum of three relativistic particles, in the case that two-particle subsets are either resonant or bound. The original form of the relativistic three-particle quantization condition was derived under a technical assumption on the two-particle K matrix that required the absence of two-particle bound states or narrow two-particle resonances. Here we describe how this restriction can be lifted in a simple way using the freedom in the definition of the K-matrix-like quantity that enters the quantization condition. With this in hand, …

Finite Volume Matrix Elements Of Two-Body States, Alessandro Baroni, Raúl A. Briceño, Maxwell T. Hansen, Filipe G. Ortega-Gama

Physics Faculty Publications

In this talk, we present a framework for studying structural information of resonances and bound states coupling to two-hadron scattering states. This makes use of a recently proposed finite-volume formalism to determine a class of observables that are experimentally inaccessible but can be accessed via lattice QCD. In particular, we shown that finite-volume two-body matrix elements with one current insertion can be directly related to scattering amplitudes coupling to the external current. For two-hadron systems with resonances or bound states, one can extract the corresponding form factors of these from the energy-dependence of the amplitudes.

Gluon Quasi-Parton-Distribution Functions From Lattice Qcd, Zhou-You Fan, Yi-Bo Yang, Adam Anthony, Huey-Wen Lin, Keh-Fei Liu

Physics and Astronomy Faculty Publications

We present the first attempt to access the x dependence of the gluon unpolarized parton-distribution function (PDF), based on lattice simulations using the large-momentum effective theory approach. The lattice calculation is carried out with pion masses of 340 and 678 MeV on a (2+1)-flavor domain-wall fermion configuration with lattice spacing a = 0.111  fm, for the gluon quasi-PDF matrix element with the nucleon momentum up to 0.93 GeV. Taking the normalization from similar matrix elements in the rest frame of the nucleon and pion, our results for these matrix elements are consistent with the Fourier transform of the global fit …

Proton Mass Decomposition From The Qcd Energy Momentum Tensor, Yi-Bo Yang, Jian Liang, Yu-Jiang Bi, Ying Chen, Terrence Draper, Keh-Fei Liu, Zhaofeng Liu

Physics and Astronomy Faculty Publications

We report results on the proton mass decomposition and also on related quark and glue momentum fractions. The results are based on overlap valence fermions on four ensembles of N_f = 2 + 1 domain wall fermion configurations with three lattice spacings and three volumes, and several pion masses including the physical pion mass. With fully nonperturbative renormalization (and universal normalization on both quark and gluon), we find that the quark energy and glue field energy contribute 32(4)(4)% and 36(5)(4)% respectively in the MS¯ (modified minimal substraction) scheme at μ = 2  GeV. A quarter of the trace anomaly …

Nonperturbatively Renormalized Glue Momentum Fraction At The Physical Pion Mass From Lattice Qcd, Yi-Bo Yang, Ming Gong, Jian Liang, Huey-Wen Lin, Keh-Fei Liu, Dimitra Pefkou, Phiala Shanahan

Physics and Astronomy Faculty Publications

We present the first nonperturbatively renormalized determination of the glue momentum fraction ⟨x⟩_g in the nucleon, based on lattice-QCD simulations at the physical pion mass using the cluster-decomposition error reduction technique. We provide the first practical strategy to renormalize the gauge energy-momentum tensor nonperturbatively in the regularization-independent momentum-subtraction (RI/MOM) scheme and convert the results to the MS¯ scheme with one-loop matching. The simulation results show that the cluster-decomposition error reduction technique can reduce the statistical uncertainty of its renormalization constant by a factor of O(300) in calculations using a typical state-of-the-art lattice volume, and the nonperturbatively …

Quark Spins And Anomalous Ward Identity, Jian Liang, Yi-Bo Yang, Terrence Draper, Ming Gong, Keh-Fei Liu

Physics and Astronomy Faculty Publications

We calculate the intrinsic quark spin contribution to the total proton spin using overlap valence quarks on three ensembles of 2 + 1-flavor RBC/UKQCD domain-wall configurations with different lattice spacings. The lowest pion mass of the ensembles is around 171 MeV, which is close to the physical point. With overlap fermions and a topological charge derived from the overlap operator, we verify the anomalous Ward identity between nucleon states with momentum transfer. Both the connected and the disconnected insertions of the axial-vector current are calculated. For the disconnected-insertion part, the cluster-decomposition error reduction technique is utilized for the lattice with …

Measurement Of Unpolarized And Polarized Cross Sections For Deeply Virtual Compton Scattering On The Proton At Jefferson Laboratory With Clas, N. Hirlinger Saylor, B. Guegan, V. D. Burkert, L. Elouadrhiri, M. Garçon, F. X. Girod, M. Guidal, H. S. Jo, V. Kubarovsky, S. Niccolai, P. Stoler, K. P. Adhikari, S. Adhikari, Z. Akbar, M. J. Amaryan, S. Anefalos Pereira, J. Ball, I. Balossino, N. A. Baltzell, L. Barion, M. Battaglieri, V. Batourine, I. Bedlinskiy, A. S. Biselli, S. Boiarinov, W. J. Briscoe, W. K. Brooks, S. Bültmann, F. Cao, S. Carman, Wesley P. Gohn

Physics and Astronomy Faculty Publications

This paper reports the measurement of polarized and unpolarized cross sections for the ep → e′ p′ γ reaction, which is composed of deeply virtual Compton scattering (DVCS) and Bethe-Heitler (BH) processes, at an electron beam energy of 5.88 GeV at the Thomas Jefferson National Accelerator Facility using the Large Acceptance Spectrometer CLAS. The unpolarized cross sections and polarized cross section differences have been measured over broad kinematics, 0.10 < x_B < 0.58, 1.0 < Q² < 4.8GeV², and 0.09 < −t < 2.00GeV². The results are found to be consistent with previous CLAS data, and these new data are discussed in …

Determination Of S- And P-Wave I = 1/2 Kπ Scattering Amplitudes In NF = 2 + 1 Lattice Qcd, Ruairí Brett, John Bulava, Jacob Fallica, Andrew Hanlon, Ben Hörz, Colin Morningstar

Physics and Astronomy Faculty Publications

The elastic I = 1/2, s- and p-wave kaon-pion scattering amplitudes are calculated using a single ensemble of anisotropic lattice QCD gauge field configurations with N_f = 2+1 flavors of dynamical Wilson-clover fermions at m_π = 230MeV. A large spatial extent of L = 3.7fm enables a good energy resolution while partial wave mixing due to the reduced symmetries of the finite volume is treated explicitly. The p-wave amplitude is well described by a Breit–Wigner shape with parameters m_K⁎/m_π = 3.808(18) and g^BW_K⁎_Kπ = 5.33(20) which …

Anatomy Of The Ρ Resonance From Lattice Qcd At The Physical Point, Wei Sun, Andrei Alexandru, Ying Chen, Terrence Draper, Zhaofeng Liu, Yi-Bo Yang, Χqcd Collaboration

Physics and Astronomy Faculty Publications

We propose a strategy to access the qq component of the ρ resonance in lattice QCD.

For the remainder of the abstract, please download this article or visit https://doi.org/10.1088/1674-1137/42/6/063102.

Ri/Mom And Ri/Smom Renormalization Of Overlap Quark Bilinears On Domain Wall Fermion Configurations, Yujiang Bi, Hao Cai, Ying Chen, Ming Gong, Keh-Fei Liu, Zhaofeng Liu, Yi-Bo Yang

Physics and Astronomy Faculty Publications

Renormalization constants (RCs) of overlap quark bilinear operators on 2+1-flavor domain wall fermion configurations are calculated by using the RI/MOM and RI/SMOM schemes. The scale independent RC for the axial vector current is computed by using a Ward identity. Then the RCs for the quark field and the vector, tensor, scalar, and pseudoscalar operators are calculated in both the RI/MOM and RI/SMOM schemes. The RCs are converted to the MS¯ scheme and we compare the numerical results from using the two intermediate schemes. The lattice size is 48³ × 96 and the inverse spacing 1/a = 1.730(4)  GeV.

Variance Reduction And Cluster Decomposition, Keh-Fei Liu, Jian Liang, Yi-Bo Yang

Physics and Astronomy Faculty Publications

It is a common problem in lattice QCD calculation of the mass of the hadron with an annihilation channel that the signal falls off in time while the noise remains constant. In addition, the disconnected insertion calculation of the three-point function and the calculation of the neutron electric dipole moment with the θ term suffer from a noise problem due to the √V fluctuation. We identify these problems to have the same origin and the √V problem can be overcome by utilizing the cluster decomposition principle. We demonstrate this by considering the calculations of the glueball mass, the …

Isoscalar Ππ; Kk; Ηη Scattering And The Σ; F0; F2 Mesons From Qcd, Raul A. Briceño, Jozef J. Dudek, Robert G. Edwards, David J. Wilson

Physics Faculty Publications

We present the first lattice QCD study of coupled isoscalar ππ;K ¯K; ηη S- and D-wave scattering extracted from discrete finite-volume spectra computed on lattices which have a value of the light quark mass corresponding to m_π ∼ 391 MeV. In the J^P = 0⁺ sector we find analogues of the experimental σ and f₀ (980) states, where the σ appears as a stable bound-state below ππ threshold, and, similar to what is seen in experiment, the f₀ (980) manifests itself as a dip in the ππ cross section in the vicinity of the …

Sea Quarks Contribution To The Nucleon Magnetic Moment And Charge Radius At The Physical Point, Raza Sabbir Sufian, Yi-Bo Yang, Jian Liang, Terrence Draper, Keh-Fei Liu

Physics and Astronomy Faculty Publications

We report a comprehensive analysis of the light and strange disconnected-sea quarks contribution to the nucleon magnetic moment, charge radius, and the electric and magnetic form factors. The lattice QCD calculation includes ensembles across several lattice volumes and lattice spacings with one of the ensembles at the physical pion mass. We adopt a model-independent extrapolation of the nucleon magnetic moment and the charge radius. We have performed a simultaneous chiral, infinite volume, and continuum extrapolation in a global fit to calculate results in the continuum limit. We find that the combined light and strange disconnected-sea quarks contribution to the nucleon …