arXiv subjects
Publications and source records attributed to Swagato Mukherjee.
This report, as part of the 2021 Snowmass Process, summarizes the current status of collider physics at the Energy Frontier, the broad and exciting future prospects identified for the Energy Frontier, the challenges and needs of future experiments, and indicates high priority research areas.
We present lattice QCD calculations of valence parton distribution function (PDF) of pion employing next-to-next-leading-order (NNLO) perturbative QCD matching. Our calculations are based on three gauge ensembles of 2+1 flavor highly improved staggered quarks and Wilson--Clover valance quarks, corresponding to pion mass $m_π=140$~MeV at a lattice spacing $a=0.076$~fm and $m_π=300$~MeV at $a=0.04, 0.06$~fm. This enables us to present, for the first time, continuum-extrapolated lattice QCD results for NNLO valence PDF of the pion at the physical point. Applying leading-twist expansion for renormalization group invariant (RGI) ratios of bi-local pion matrix elements with NNLO Wilson coefficients we extract $2^{\mathrm{nd}}$, $4^{\mathrm{th}}$ and $6^{\mathrm{th}}$ Mellin moments of the PDF. We reconstruct the Bjorken-$x$ dependence of the NNLO PDF from real-space RGI ratios using a deep neural network (DNN) as well as from momentum-space matrix elements renormalized using a hybrid-scheme. All our results are in broad agreement with the results of global fits to the experimental data carried out by the xFitter and JAM collaborations.
In this work, we present a numerical investigation of a novel Lorentz-covariant parametrization to extract $x$-dependent GPDs using off-forward matrix elements of momentum-boosted hadrons coupled to non-local operators. The novelty of the method is the implementation of an asymmetric frame for the momentum transfer between the initial and final hadron state and the parametrization of the matrix elements into Lorentz-invariant amplitudes. The amplitudes can then be related to the standard light-cone GPDs. GPDs are defined in the symmetric frame, which requires a separate calculation for each value of the momentum transfer, increasing the computational cost significantly. The proposed method is powerful, as one can extract the GPDs at multiple values of the momentum transfer at the computational cost of a single value. For this proof-of-concept calculation, we use one ensemble of $N_f=2+1+1$ twisted mass fermions and a clover improvement with a pion mass of 260 MeV to calculate the proton unpolarized GPDs.
We present results on the in-medium interactions of static quark anti-quark pairs using realistic 2+1 HISQ flavor lattice QCD. Focus is put on the extraction of spectral information from Wilson line correlators in Coulomb gauge using four complementary methods. Our results indicate that on HISQ lattices, the position of the dominant spectral peak associated with the real-part of the interquark potential remains unaffected by temperature. This is in contrast to prior work in quenched QCD and we present follow up comparisons to newly generated quenched ensembles.
We present a lattice QCD determination of the distribution amplitude (DA) of the pion and the first few Mellin moments from an analysis of the quasi-DA matrix element within the leading-twist framework. We perform our study on a HISQ ensemble with $a=0.076$ fm lattice spacing with the Wilson-Clover valence quark mass tuned to the physical point. We analyze the ratios of pion quasi-DA matrix elements at short distances using the leading-twist Mellin operator product expansion (OPE) at the next-to-leading order and the conformal OPE at the leading-logarithmic order. We find a robust result for the first non-vanishing Mellin moment $\langle x^2 \rangle = 0.287(6)(6)$ at a factorization scale $μ=2$ GeV. We also present different Ansätze-based reconstructions of the $x$-dependent DA, from which we determine the perturbative leading-twist expectations for the pion electromagnetic and gravitational form-factors at large momentum transfers.
Electron Ion Collider (EIC) is a particle accelerator facility planned for construction at Brookhaven National Laboratory on Long Island, New York by the United States Department of Energy. EIC will provide capabilities of colliding beams of polarized electrons with polarized beams of proton and light ions. EIC will be one of the largest and most sophisticated new accelerator facilities worldwide, and the only new large-scale accelerator facility planned for construction in the United States in the next few decades. The versatility, resolving power and intensity of EIC will present many new opportunities to address some of the crucial and fundamental open scientific questions in particle physics. This document provides an overview of the science case of EIC from the perspective of the high energy physics community.
Contribution from the USQCD Collaboration to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021).
Lattice gauge theory continues to be a powerful theoretical and computational approach to simulating strongly interacting quantum field theories, whose applications permeate almost all disciplines of modern-day research in High-Energy Physics. Whether it is to enable precision quark- and lepton-flavor physics, to uncover signals of new physics in nucleons and nuclei, to elucidate hadron structure and spectrum, to serve as a numerical laboratory to reach beyond the Standard Model, or to invent and improve state-of-the-art computational paradigms, the lattice-gauge-theory program is in a prime position to impact the course of developments and enhance discovery potential of a vibrant experimental program in High-Energy Physics over the coming decade. This projection is based on abundant successful results that have emerged using lattice gauge theory over the years: on continued improvement in theoretical frameworks and algorithmic suits; on the forthcoming transition into the exascale era of high-performance computing; and on a skillful, dedicated, and organized community of lattice gauge theorists in the U.S. and worldwide. The prospects of this effort in pushing the frontiers of research in High-Energy Physics have recently been studied within the U.S. decadal Particle Physics Planning Exercise (Snowmass 2021), and the conclusions are summarized in this Topical Report.
Using high-statistics datasets generated in (2+1)-flavor QCD calculations at finite temperature we construct estimators for the radius of convergence from an eighth order series expansion of the pressure as well as the number density. We show that the estimator for pressure and number density will be identical in the asymptotic limit. In the vicinity of the pseudo-critical temperature, $T_{pc}\simeq 156.5$~MeV, we find the estimator of the radius of convergence to be $μ_B/T \gtrsim\ 3$ for strangeness-neutral matter. We also present results for the pole structure of the Padé approximants for the pressure at non-zero values of the baryon chemical potential and show that the pole structure of the [4,4] Padé is consistent with not having a critical point at temperatures larger than $135~$MeV and a baryon chemical potential smaller than $μ_B/T \sim \ 2.5$.
Using high statistics datasets generated in (2+1)-flavor QCD calculations at finite temperature we present results for low order cumulants of net baryon-number fluctuations at non-zero values of the baryon chemical potential. We calculate Taylor expansions for the pressure (zeroth order cumulant), net baryon-number density (first order cumulant) and the variance of the distribution on net-baryon number fluctuations (second order cumulant). We obtain series expansions from an eighth order expansion of the pressure and compare these to diagonal Padé approximants. This allows us to estimate the range of values for the baryon chemical potential in which these expansions are reliable. We find $μ_B/T\le 2.5$, $2.0$ and $1.5$ for the zeroth, first and second order cumulants, respectively. We furthermore, construct estimators for the radius of convergence of the Taylor series of the pressure. In the vicinity of the pseudo-critical temperature, $T_{pc}\simeq 156.5$ MeV, we find $μ_B/T \gtrsim\ 2.9$ at vanishing strangeness chemical potential and somewhat larger values for strangeness neutral matter. These estimates are temperature dependent and range from $μ_B/T \gtrsim\ 2.2$ at $T=135$ MeV to $μ_B/T\ \gtrsim\ 3.2$ at $T=165$ MeV. The estimated radius of convergences is the same for any higher order cumulant.
We report the first lattice QCD calculation of pion valence quark distribution with next-to-next-to-leading order perturbative matching correction, which is done using two fine lattices with spacings $a=0.04$ fm and $0.06$ fm and valence pion mass $m_π=300$ MeV, at boost momentum as large as $2.42$ GeV. As a crucial step to control the systematics, we renormalize the pion valence quasi distribution in the recently proposed hybrid scheme, which features a Wilson-line mass subtraction at large distances in coordinate space, and develop a procedure to match it to the $\overline{\rm MS}$ scheme. We demonstrate that the renormalization and the perturbative matching in Bjorken-$x$ space yield a reliable determination of the valence quark distribution for $0.03\lesssim x \lesssim 0.80$ with 5-20\% uncertainties.
For theories plagued with a sign problem at finite density, a Taylor expansion in the chemical potential is frequently used for lattice gauge theory based computations of the equation of state. Recently, in arXiv:2106.03165, a new resummation scheme was proposed for such an expansion that resums contributions of correlation functions of conserved currents to all orders in the chemical potential. Here, we study the efficacy of this resummation scheme using a solvable low energy model, namely the mean-field quark-meson model. After adapting the scheme for a mean-field analysis, we confront the results of this scheme with the direct solution of the model at finite density as well as compare with results from Taylor expansions. We study to what extent the two methods capture the analytical properties of the equation of state in the complex chemical potential plane. As expected, the Taylor expansion breaks down as soon as the baryon chemical potential reaches the radius of convergence defined by the Yang-Lee edge singularity. Encouragingly, the resummation not only captures the location of the Yang-Lee edge singularity accurately, but is also able to describe the equation of state for larger chemical potentials beyond the location of the edge singularity for a wide range of temperatures.
We study the interactions of a static quark antiquark pair at non-zero temperature using realistic 2+1 flavor lattice QCD calculations. The study consists of two parts: the first investigates the properties of Wilson line correlators in Coulomb gauge and compares to predictions of hard-thermal loop perturbation theory. As a second step we extract the spectral functions underlying the correlators using four conceptually different methods: spectral function fits, a HTL inspired fit for the correlation function, Padé rational approximation and the Bayesian BR spectral reconstruction. We find that our high statistics Euclidean lattice data are amenable to different hypotheses for the shapes of the spectral function and we compare the implications of each analysis method for the existence and properties of a well defined ground state spectral peak.
Taylor expansion in powers of baryon chemical potential ($μ_B$) is an oft-used method in lattice QCD to compute QCD thermodynamics for $μ_B>0$. Based only upon the few known lowest order Taylor coefficients, it is difficult to discern the range of $μ_B$ where such an expansion around $μ_B=0$ can be trusted. We introduce a resummation scheme for the Taylor expansion of the QCD equation of state in $μ_B$ that is based on the $n$-point correlation functions of the conserved current ($D_n$). The method resums the contributions of the first $N$ correlation function $D_1,\dots,D_N$ to the Taylor expansion of the QCD partition function to all orders in $μ_B$. We show that the resummed partition function is an approximation to the reweighted partition function at $μ_B\ne0$. We apply the proposed approach to high-statistics lattice QCD calculations using 2+1 flavors of Highly Improved Staggered Quarks with physical quark masses on $32^3\times8$ lattices and for temperatures $T\approx145$-176 MeV. We demonstrate that, as opposed to the Taylor expansion, the resummed version not only leads to improved convergence but also reflects the zeros of the resummed partition function and severity of the sign problem, leading to its eventual breakdown. We also provide a generalization of our scheme to include resummation of powers of temperature and quark masses in addition to $μ_B$, and show that the alternative expansion scheme of [S. Borsányi et al., Phys. Rev. Lett. 126, 232001 (2021).] is a special case of this generalized resummation.
Bottomonium states are key probes for experimental studies of the quark-gluon plasma (QGP) created in high-energy nuclear collisions. Theoretical models of bottomonium productions in high-energy nuclear collisions rely on the in-medium interactions between the bottom and antibottom quarks. The latter can be characterized by the temperature ($T$) dependent potential, with real ($V_R(T,r)$) and imaginary ($V_I(T,r)$) parts, as a function of the spatial separation ($r$). Recently, the masses and thermal widths of up to $3S$ and $2P$ bottomonium states in QGP were calculated using lattice quantum chromodynamics (LQCD). Starting from these LQCD results and through a novel application of deep neural network, here, we obtain $V_R(T,r)$ and $V_I(T,r)$ in a model-independent fashion. The temperature dependence of $V_R(T,r)$ was found to be very mild between $T\approx0-334$~MeV. For $T=151-334$~MeV, $V_I(T,r)$ shows a rapid increase with $T$ and $r$, which is much larger than the perturbation-theory-based expectations.
We present our results on the electromagnetic form factor of pion over a wide range of $Q^2$ using lattice QCD simulations with Wilson-clover valence quarks and HISQ sea quarks. We study the form factor at the physical point with a lattice spacing $a=0.076$ fm. To study the lattice spacing and quark mass effects, we also present results for 300 MeV pion at two different lattice spacings $a=0.04$ and 0.06 fm. The lattice calculations at the physical quark mass appear to agree with the experimental results. Through fits to the form factor, we estimate the charge radius of pion for physical pion mass to be $\langle r_π^2 \rangle=0.42(2)~{\rm fm}^2$.
We investigate the Dirac eigenvalue spectrum ($ρ(λ,m_l)$) to study the microscopic origin of axial anomaly in high temperature phase of QCD. We propose novel relations between the derivatives ($\partial^n ρ(λ,m_l)/\partial m_l^n$) of the Dirac eigenvalue spectrum with respect to the quark mass ($m_l$) and the $(n+1)$-point correlations among the eigenvalues ($λ$) of the massless Dirac operator. Based on these relations, we present lattice QCD results for $\partial^n ρ(λ,m_l)/\partial m_l^n$ ($n=1, 2, 3$) with $m_l$ corresponding to pion masses $m_π=160-55$ MeV, and at a temperature of about 1.6 times the chiral phase transition temperature. Calculations were carried out using (2+1)-flavors of highly improved staggered quarks and the tree-level Symanzik gauge action with the physical strange quark mass, three lattice spacings $a=0.12, 0.08, 0.06$ fm, and lattices having aspect ratios $4-9$. We find that $ρ(λ\to0,m_l)$ develops a peaked structure. This peaked structure, which arises due to non-Poisson correlations within the infrared part of the Dirac eigenvalue spectrum, becomes sharper as $a\to0$, and its amplitude is proportional to $m_l^2$. After continuum and chiral extrapolations, we find that the axial anomaly remains manifested in two-point correlation functions of scalar and pseudo-scalar mesons in the chiral limit. We demonstrate that the behavior of $ρ(λ\to0,m_l)$ is responsible for it.
We have studied finite temperature complex static quark-antiquark potentials for 2+1 flavor QCD using highly improved staggered action with physical strange quark masses and light quark masses corresponding to a pion mass of 161 MeV. We calculated the potential using Wilson line correlators fixed in Coulomb gauge. For the extraction, we have used HTL motivated parametrization of the correlators. We found that the real part of the potential is screened above the crossover temperature and it's close to singlet free energies, whereas the imaginary part is increasing with both distance and temperature.