Nuclear Commons^™

Real-Time Estimators For Scattering Observables: A Full Account Of Finite-Volume Errors For Quantum Simulation, Ivan M. Burbano, Marco A. Carrillo, Rana Urek, Anthony N. Ciavarella, Raul A. Briceno

Physics Faculty Publications

The real-time correlators of quantum field theories can be directly probed through new approaches to simulation, such as quantum computing and tensor networks. This provides a new framework for computing scattering observables in lattice formulations of strongly interacting theories, such as lattice quantum chromodynamics. In this paper, we prove that the proposal of real-time estimators of scattering observables is universally applicable to all scattering observables of gapped quantum field theories. All finite-volume errors are exponentially suppressed, and the rate of this suppression is controlled by the regulator considered, namely, a displacement of the spectrum of the theory into the complex …

Inverse Problem In The Large Momentum Effective Theory Framework, Herve Dutrieux, Joe Karpie, Christopher J. Monahan, Kostas Orginos, Anatoly Radyushkin, David Richards, Savvas Zafeiropoulos

Physics Faculty Publications

One proposal to compute parton distributions from first principles is the large momentum effective theory (LaMET), which requires the Fourier transform of matrix elements computed nonperturbatively. Lattice quantum chromodynamics (QCD) provides calculations of these matrix elements over a finite range of Fourier harmonics that are often noisy or unreliable in the largest computed harmonics. It has been suggested that enforcing an exponential decay of the missing harmonics helps alleviate this issue. Using nonperturbative data, we show that the uncertainty introduced by this inverse problem in a realistic setup remains significant without very restrictive assumptions, and that the importance of the …

Relativistic Three Particle Scattering, Md Habib E Islam

Physics Theses & Dissertations

In this dissertation, we develop and apply a relativistic framework for studying three-body scattering amplitudes, their analytic structure, and the emergence of universal phenomena such as the Efimov effect. The work integrates three complementary components.

First, we introduce a systematically improvable numerical method for solving relativistic three-body integral equations in momentum space. By discretizing the continuum problem into finite matrix equations and extrapolating to the continuum limit, we obtain stable partial-wave amplitudes in the presence of a two-body bound state. Two complementary treatments of the pole contribution are implemented and shown to reproduce previous finite volume results, with controlled estimates …

Nonlocal Nucleon Matrix Elements In The Rest Frame, Joe Karpie, Christopher Monahan, Anatoly Radyushkin

Physics Faculty Publications

Extracting parton structure from lattice quantum chromodynamics (QCD) calculations requires studying the coordinate scale 𝑧3 dependence of the matrix elements of bilocal operators. The most significant contribution comes from the 𝑧3 dependence induced by ultraviolet (UV) renormalization of the Wilson line. We demonstrate that the next-to-leading order perturbative calculations of the renormalization factor can describe, to a few percent accuracy, the logarithm of the lattice QCD rest frame matrix elements with separations up to distances of 0.6 fm on multiple lattice spacings. The residual discrepancies can be modeled by a leading effect from the structure of the nucleon.

The Energy Spectrum Of Kaon From Lattice Qcd, Arunangshu Bora, Anirban Mandal, Shreya Mittal, Mihir N. Pandey, Rohan Rana, Harsh Saxena, Priyajit Jana, Rijul Dhumane, Tanmoy Bhowmik

2024 REYES Proceedings

This study presents the analysis of data related to the two-point function of kaon generated from lattice QCD simulations. Using gauge configurations of twisted-mass fermions, we obtain the correlation functions for 6 values of momentum for the kaon between 0 and 2 GeV (both inclusive), we use statistical techniques such as jackknife resampling to derive the energy of the particle. The lattice results are compared to the continuum dispersion relation for the particle, to assess systematic uncertainties in the lattice data. We establish consistency with theory by comparing our results with the theoretical predictions.

Coulomb Confinement In The Hamiltonian Limit, Sebastian M. Dawid, Wyatt A. Smith, Arkaitz Rodas, Robert J. Perry, César Fernández-Ramírez, Eric S. Swanson, Adam P. Szczepaniak

Physics Faculty Publications

The Gribov-Zwanziger scenario attributes the phenomenon of confinement to the instantaneous interaction term in the QCD Hamiltonian in the Coulomb gauge. For a static quark-antiquark pair, it leads to a potential energy that increases linearly with the distance between them. Lattice studies of the SU(2) Yang-Mills theory determined the corresponding (Coulomb) string tension for sources in the fundamental representation, 𝜎_𝐶, to be about 3 times larger than the Wilson loop string tension, 𝜎_𝐹. It is far above the Zwanziger variational bound, 𝜎_𝐶 ≥𝜎_𝐹. We argue that the value often reported in the literature …

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 …

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 …

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. …

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.

The Pion Form Factor And Momentum And Angular Momentum Fractions Of The Proton In Lattice Qcd, Gen Wang

Theses and Dissertations--Physics and Astronomy

Lattice Quantum Chromodynamics (QCD) provides a way to have a precise calculation and a new way of understanding the hadrons from first principles. From this perspective, this dissertation focuses first on a precise calculation of the pion form factor using overlap fermions on six ensembles of 2+1-flavor domain-wall configurations generated by the RBC/UKQCD collaboration with pion masses varying from 137 to 339 MeV. Taking advantage of the fast Fourier transform, low-mode substitution (LMS) and the multi-mass algorithm to access many combinations of source and sink momenta, we have done a simulation with various valence quark masses and with a range …

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.

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.

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 …

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 …

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 …

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 …

Lattice Calculation Of Nucleon Isovector Axial Charge With Improved Currents, Jian Liang, Yi-Bo Yang, Keh-Fei Liu, Andrei Alexandru, Terrence Draper, Raza Sabbir Sufian

Physics and Astronomy Faculty Publications

We employ dimension-4 operators to improve the local vector and axial-vector currents and calculate the nucleon isovector axial coupling g³_A with overlap valence on 2 + 1-flavor domain wall fermion (DWF) sea. Using the equality of g³_A from the spatial and temporal components of the axial-vector current as a normalization condition, we find that g³_A is increased by a few percent towards the experimental value. The excited-state contamination has been taken into account with three time separations between the source and sink. The improved axial charges g³_A(24I) = 1.22(4)(3) …

Glue Spin And Helicity In The Proton From Lattice Qcd, Yi-Bo Yang, Raza Sabbir Sufian, Andrei Alexandru, Terrence Draper, Michael J. Glatzmaier, Keh-Fei Liu, Yong Zhao

Physics and Astronomy Faculty Publications

We report the first lattice QCD calculation of the glue spin in the nucleon. The lattice calculation is carried out with valence overlap fermions on 2 + 1 flavor domain-wall fermion gauge configurations on four lattice spacings and four volumes including an ensemble with physical values for the quark masses. The glue spin SG in the Coulomb gauge in the modified minimal subtraction (MS¯) scheme is obtained with one-loop perturbative matching. We find the results fairly insensitive to lattice spacing and quark masses. We also find that the proton momentum dependence of S_G in the range 0 ≤ |p …

Locality And Efficient Evaluation Of Lattice Composite Fields: Overlap-Based Gauge Operators, Andrei Alexandru, Ivan Horváth

Physics and Astronomy Faculty Publications

We propose a novel general approach to locality of lattice composite fields, which in case of QCD involves locality in both quark and gauge degrees of freedom. The method is applied to gauge operators based on the overlap Dirac matrix elements, showing for the first time their local nature on realistic path-integral backgrounds. The framework entails a method for efficient evaluation of such nonultralocal operators, whose computational cost is volume independent at fixed accuracy, and only grows logarithmically as this accuracy approaches zero. This makes computation of useful operators, such as overlap-based topological density, practical. The key notion underlying these …

Nonperturbative Evolution Of Parton Quasi-Distributions, A. V. Radyushkin

Physics Faculty Publications

Using the formalism of parton virtuality distribution functions (VDFs) we establish a connection between the transverse momentum dependent distributions (TMDs) F(x,k²_⊥) and quasi-distributions (PQDs) Q(y,p₃) introduced recently by X. Ji for lattice QCD extraction of parton distributions f(x). We build models for PQDs from the VDF-based models for soft TMDs, and analyze the p₃ dependence of the resulting PQDs. We observe a strong nonperturbative evolution of PQDs for small and moderately large values of p₃ reflecting the transverse momentum dependence of TMDs. Thus, the study of PQDs on the lattice …

Disconnected-Sea Quarks Contribution To Nucleon Electromagnetic Form Factors, Raza Sabbir Sufian

Theses and Dissertations--Physics and Astronomy

We present comprehensive analysis of the light and strange disconnected-sea quarks contribution to the nucleon electric and magnetic form factors. The lattice QCD estimates of strange quark magnetic moment G^s_M (0) = −0.064(14)(09) μ_N and the mean squared charge radius ⟨r²_s⟩_E = −0.0043(16)(14) fm² are more precise than any existing experimental measurements and other lattice calculations. The lattice QCD calculation includes ensembles across several lattice volumes and lattice spacings with one of the ensembles at the physical pion mass. We have performed a simultaneous chiral, infinite volume, and continuum extrapolation in …

Negative-Parity Baryon Masses Using An O(A)-Improved Fermion Action, M. Göckeler, R. Horsley, D. Pleiter, P. E. L. Rakow, G. Schierholz, C. M. Maynard, D. G. Richards

Physics Faculty Publications

We present a calculation of the mass of the lowest-lying negative-parity J=1/2− state in quenched QCD. Results are obtained using a non-perturbatively O(a)-improved clover fermion action, and a splitting is found between the mass of the nucleon, and its parity partner. The calculation is performed on two lattice volumes and at three lattice spacings, enabling a study of both finite-volume and finite lattice-spacing uncertainties. A comparison is made with results obtained using the unimproved Wilson fermion action.