arXiv subjects

Swagato Mukherjee

Publications and source records attributed to Swagato Mukherjee.

At least 19 recordsLinked to original sources

arXiv2026

QCD Chiral Crossover Line from Lee-Yang Edge Singularities

We propose a universality-based reconstruction of the QCD chiral crossover line from Lee-Yang edge singularities in the complex baryon chemical potential plane. The framework maps lattice-extracted complex Lee-Yang-zero estimates, treated as proxies for edge singularities, to the universal chiral Lee-Yang edge and thereby determines the $\mu_B$ dependence of both the chiral critical line in the light-quark chiral limit and the pseudo-critical crossover line at physical quark masses. As an illustration, we apply the framework to Lee-Yang-zero estimates recently obtained by the Wuppertal-Budapest collaboration from high-statistics lattice QCD simulations. Without imposing the previously determined small-$\mu_B$ expansion of the crossover line as input, the reconstructed curvature is consistent with existing continuum lattice-QCD results at small $\mu_B$. The fitted chiral-limit transition temperature is also compatible with existing chiral-scaling analyses. These results demonstrate that lattice information on Lee-Yang singularities, combined with universal chiral scaling, provides a quantitatively consistent constraint on the QCD crossover line within the present temperature window and establishes a framework that can be systematically improved with future Lee-Yang-zero determinations.

hep-lat↗

arXiv2026

Back-to-back dijet production in DIS at arbitrary Bjorken-x: TMD quark distributions to twist-3 accuracy

We study the contributions of target quark background to quark-gluon and quark-antiquark dijet productions cross sections in deep inelastic scattering (DIS) at arbitrary Bjorken-$x$. Using the background-field method, we organize the leading-order dijet production cross section in terms of bilocal quark and trilocal quark--gluon--quark correlators. The former provides the contributions of the leading-twist as well as the kinematical and dynamical twist-three quark transverse-momentum-dependent (TMD) distributions, while the latter encode contributions of the dynamical twist-three TMD distributions. {Together with the gluon distributions derived in Ref.~\cite{Mukherjee:2026cte}}, these results provide the complete leading-order cross section for back-to-back dijet production in DIS at arbitrary Bjorken-$x$ to twist-three accuracy. This theoretical framework extends the TMD description of the process beyond the small-$x$ eikonal regime and provides the necessary tools for analyzing data from the future Electron--Ion Collider.

hep-ph↗

arXiv2026

Proton isovector helicity PDF at NNLO and the twist-3 moment $\tilde{d}_2$ from lattice QCD at physical quark masses

We present a lattice quantum chromodynamics calculation of the $x$-dependent isovector quark helicity parton distribution function (PDF) of the proton in the large momentum effective theory (LaMET) framework. Through operator product expansion (OPE) we also extract the $\tilde{d}_2$ moment of the twist-3 PDF $g_T(x)$ for the first time in the $\overline{\rm MS}$ scheme, which is proportional to the average color Lorentz force experienced by the quark in the proton. This calculation is performed on a lattice of spacing $a$ = 0.076 fm at physical quark masses. The quasi-PDF matrix elements are measured in proton states boosted to momenta $P_z=\{0, 0.25, 1.02, 1.53\}$ GeV. We first extract the lowest few helicity PDF moments from the renormalization-group (RG) invariant ratios of the matrix elements with OPE. Combined with the matrix elements relevant for $g_T(x)$, we obtain $\tilde{d}_2^{u-d}(2\ {\rm GeV})=0.0024(46)$ at next-to-leading order in $\overline{\rm MS}$. Then, the helicity quasi-PDF matrix elements are renormalized in the hybrid scheme with linear renormalon resummation and Fourier transformed to the $x$-space after an asymptotic extrapolation. The quasi-PDF is perturbatively matched to the $\overline{\rm MS}$ PDF with RG and threshold resummations at next-to-leading power and next-to-next-to-leading logarithmic accuracies. After resummations, we determine the PDF in the region $x\in[0.25,0.75]$ with controlled systematic uncertainties. The end-point regions are then parameterized, combined with the LaMET prediction at moderate $x$, and fitted to the short-distance matrix elements in coordinate space.

hep-lat↗

arXiv2026

Quark-Mass Dependence of Light-Nuclei Masses from Lattice QCD and Trace-Anomaly Contributions to Nuclear Bindings

We present lattice QCD calculations of the masses of the deuteron, dineutron, Helium-3 and Helium-4 with physical sea quarks and valence quark masses corresponding to pion masses between 140 and 700 MeV. At the physical point, the lowest finite-volume two-nucleon energy levels exhibit the qualitative pattern of a bound deuteron and an unbound dineutron within uncertainties, while at heavier quark masses they indicate the presence of deeply bound states. Compared with expectations from low-energy effective field theories, the observed mass dependence of the binding energies provides first-principles constraints on the quark-mass dependence of two- and three-nucleon interactions. From the quark-mass variation of the nuclear energies, we determine nuclear sigma terms and quantify the response of light-nuclear masses to changes in the light-quark mass. Using the QCD trace anomaly relation, we decompose the nuclear binding energy into quark-mass and gluonic contributions around the deuteron mass scale of $\mu=2$ GeV. We find that the quark-mass contribution to the binding energy is small and approximately additive in nucleon number within current precision, whereas the gluonic component provides the dominant contribution and show milder increases with mass number.

hep-lat↗

arXiv2026

Back-to-back dijet production in DIS at arbitrary Bjorken-x: TMD gluon distributions to twist-3 accuracy

We derive the gluon transverse-momentum-dependent (TMD) operator structure of back-to-back quark-antiquark dijet production in deep inelastic scattering at arbitrary Bjorken-x to twist-3 accuracy. Working at leading order in the strong coupling and in the kinematic regime where the transverse momentum imbalance of the jets is much smaller than their individual transverse momenta, we perform a systematic gradient expansion of the quark propagator in a background gluon field. This expansion organizes multiple interactions with the target in terms of longitudinal Wilson lines and gauge-invariant field-strength insertions, yielding a TMD description valid beyond the strict high-energy eikonal (x -> 0) approximation. We obtain explicit cross sections for longitudinally and transversely polarized virtual photons, identifying all contributing gluon TMD operators up to twist-3, including structures involving F_+-, F_ij, and three-gluon correlators. The full longitudinal phase associated with Bjorken-x is retained throughout. In the small-x limit, our results reproduce the known sub-eikonal expressions obtained in the Color Glass Condensate framework, establishing a direct connection between the general-x TMD expansion and high-energy factorization. We further reduce the operator basis using equations of motion, minimizing the number of independent nonperturbative matrix elements entering the cross section. This work provides a systematic foundation for extending TMD analyses of dijet production beyond leading twist, establishing a unified operator framework valid at arbitrary Bjorken x that smoothly interpolates between moderate- and small-x descriptions of gluon TMDs.

hep-ph↗

arXiv2026

Nucleon Parton Distribution Functions from Boosted Correlations in the Coulomb gauge

Recently, a novel approach has been proposed to compute parton distributions through the use of boosted correlators fixed in the Coulomb gauge from lattice QCD, within the framework of Large-Momentum Effective Theory (LaMET). This approach circumvents the need for Wilson lines, potentially enhancing the efficiency and accuracy of lattice calculations. In this work, we present the first exploratory implementation of the Coulomb gauge method for calculating nucleon unpolarized, helicity, and transversity parton distribution functions (PDFs). The calculations are performed on a Highly-Improved-Staggered-Quark ensemble with lattice spacing $a = 0.06$ fm, volume $L_s^3 \times L_t=48^3\times 64$, and valence pion mass $m_\pi=300$ MeV, employing boosted nucleon states with momenta up to 3.04 GeV. Our lattice predictions for the valence-quark PDFs -- extracted from the real part of the correlators -- show good convergence with increasing nucleon momentum and are compatible with the most recent global analyses for all spin structures. On the other hand, the full-quark-channel PDFs obtained from the imaginary part of the correlators exhibit discrepancies between the two large nucleon momenta considered, although the results at the higher momentum are consistent with phenomenology. The discrepancies are likely driven by stronger excited-state contamination in the imaginary matrix elements, which is consistent with the observation in the literature. Overall, this work demonstrates the efficacy of the Coulomb gauge approach for nucleon PDFs and serves as a benchmark for its broader applications.

hep-lat↗

arXiv2026

Lattice-QCD validation of hadron mass and trace-anomaly decomposition sum rules

We present the first lattice-QCD validation of multiple sum rules associated with quark-gluon decomposition of hadron mass by computing all components from first principles. We achieve this through nonperturbative renormalization of the QCD energy-momentum tensor, including its trace, in a gradient-flow scheme, followed by continuum extrapolations, two-loop matching to the $\overline{\mathrm{MS}}$ scheme, and zero-flow-time extrapolations. These ingredients enable a direct and simultaneous verification, in a common renormalization scheme and scale, of multiple energy-density-based and trace-based mass decomposition sum rules proposed in the literature. We demonstrate the framework for the $\eta_c$ and $J/\psi$ charmonia using three fine lattice spacings with a physical strange-quark and near-physical up- and down-quark masses. We present the first lattice-QCD results for the gravitational form factor $\bar{C}$. We find sizable gluonic contributions to charmonia masses at the hadronic scale, $\sim 15\%$ in the Lorc\'e and Metz-Pasquini-Rodini decompositions. The trace-anomaly contribution in the Ji sum rule is $\sim 6\%$, while the gluonic component of the trace anomaly in the Hatta-Rajan-Tanaka sum rule is $\sim 35\%$. The method is general and can be straightforwardly adopted for lattice-QCD calculations of mass and spin decompositions as well as gravitational form factors of other hadrons and nuclei.

hep-lat↗

arXiv2026

QCD Crossover at Low Temperatures from Lee-Yang Edge Singularity

We provide the first lattice-QCD estimate of the crossover line down to $T\simeq108$~MeV. We introduce a new method that combines the Lee-Yang edge in the complex plane of baryon chemical potential $\mu_B$ with universal chiral scaling to determine the $\mu_B$ dependence of the QCD chiral critical and pseudo-critical temperatures. By performing $(2\!+\!1)$-flavor lattice QCD simulations at $T\simeq108$~MeV and purely imaginary $\mu_B$ with a single lattice spacing and two volumes, we compute $\mu_B$-dependent baryon-number susceptibilities and extract the location of the Lee-Yang edge. Together with universal scaling near the QCD chiral transition, it constrains the mapping function between $\{T,\mu_B\}$ and the scaling variable (\textit{i.e.}\ the argument of the universal scaling functions). This mapping function then yields the $\mu_B$ dependence of the critical and pseudo-critical temperatures for $T\gtrsim108$~MeV. While our calculation is performed only at a single value of low temperature without explicit input from small-$\mu_B$ expansion, the resulting $\mu_B$ dependence of the pseudo-critical temperature is consistent with established lattice-QCD determinations at small $\mu_B$ and compatible with chemical freeze-out parameters of heavy-ion collisions down to low temperatures, demonstrating the validity and robustness of the method. Application of this method can be systematically extended to additional temperatures and finer discretizations, opening a pathway to charting the QCD phase diagram in the low-$T$, high-$\mu_B$ regime.

hep-lat↗

arXiv2026

Quantum dynamics of cosmological particle production: interacting quantum field theories with matrix product states

Understanding real-time dynamics of interacting quantum fields in curved spacetime remains a major theoretical challenge. We employ tensor network methods to study such dynamics using interacting scalar and gauge theories in 1+1 spacetime dimensions, subject to a quench modeling a homogeneously expanding gravitational background. The models considered are the scalar $\lambda\phi^4$ theory and the Schwinger model, i.e. a Dirac fermion coupled to a $U(1)$ gauge field which is equivalent via bosonization to a scalar field with a cosine self-interaction. In the free scalar limit, both theories reproduce known analytical results, providing a nontrivial numerical validation of bosonization in curved spacetime for the Schwinger model. Our central finding is that self-interactions lead to a suppression of gravitational particle production compared to the free-field case, as evidenced by two-point functions and the spectra of produced particles. We further examine the behavior of entanglement generation and find that interactions suppress entanglement growth in the $\lambda\phi^4$ theory, while in the Schwinger model, the interplay between suppressed particle production and enhanced inter-particle correlations leads to more complex entanglement behavior. Our results pave the way for further explorations of nonperturbative quantum real-time dynamics of interacting scalar and gauge theories in arbitrary gravitational backgrounds.

hep-th↗

arXiv2025

Skewness-dependent moments of the pion GPD from nonlocal quark-bilinear correlators

We present lattice QCD calculations of the odd Mellin moments of pion valence-quark generalized parton distribution (GPD) up to fifth order, $\langle x^4\rangle$, and for the skewness range $[-0.33, 0]$ using operator product expansion of bilocal quark-bilinear operators. The calculations are performed on an ensemble with lattice spacing $a=0.04~\mathrm{fm}$ and valence pion mass $300$ $\mathrm{MeV}$, employing boosted pion states with momenta up to 2.428 GeV and momentum transfers reaching 2.748 GeV$^2$. We employ ratio-scheme renormalization and next-to-leading-logarithmic resummed perturbative matching. At zero skewness, our results are consistent with previous lattice studies. By combining matrix elements at multiple values of skewness and momentum transfer, skewness-dependent moments are obtained through simultaneous polynomiality-constrained fits.

hep-lat↗

arXiv2025

Thermal modifications of mesons and energy-energy correlators from real-time simulations of a $U(1)$ lattice gauge theory

We investigate thermal properties of a $U(1)$ lattice gauge theory in $1+1$-dimensions through real-time simulations. We extract the spectral functions directly coupling to the pseudoscalar and scalar mesons, demonstrating the thermal modifications of these states with increasing temperatures. Introducing the notion of energy-flow operators, we quantify the temporal build-up of correlations in the energy flows across the lattice. We demonstrate that energy-energy correlators fail to factorize to products of energy flows, both in the vacuum and at nonzero-temperature, indicating the presence of non-trivial correlations in the quantum states. Our results constitute a first real-time \textit{ab-initio} study of bound state thermal broadening and finite temperature energy-flow correlations in a gauge theory, providing a benchmark for future studies of hadronic matter under extreme conditions.

hep-ph↗

arXiv2025

Temperature Dependence of Heavy Quark Diffusion from (2+1)-flavor Lattice QCD

We present a lattice determination of the heavy-quark diffusion coefficient in (2+1)-flavor QCD with almost physical quark masses. The momentum and spatial diffusion coefficients are extracted for a wide temperature range, from $T=163$ MeV to $10$ GeV. The results are in agreement with previous works from the HotQCD collaboration, and show fast thermalization of the heavy quark inside the QGP. Near the chiral crossover temperature $T_c\simeq150$ MeV, our results are close to the AdS/CFT estimation computed at strong coupling.

hep-lat↗

arXiv2025

Lattice QCD Benchmark of Proton Helicity and Flavor-Dependent Unpolarized Transverse Momentum-Dependent Parton Distribution Functions at Physical Quark Masses

We present the first lattice QCD calculations of the isovector helicity transverse momentum-dependent parton distribution function (TMDPDF) and the flavor-dependent unpolarized TMDPDFs for up and down quarks in the proton. Our computations utilize domain-wall fermion discretization with physical quark masses. Employing Coulomb-gauge-fixed quark correlation functions within the large-momentum effective theory framework, we access nonperturbative transverse quark separations $b_T$ up to approximately 1 fm, corresponding to transverse momenta as low as 200 MeV. Based on the quasi-TMD factorization theorem, we construct renormalization-group-invariant ratios that are equal to the corresponding light-cone TMDPDF ratios. At moderate $x$, our results reveal that the isovector helicity and unpolarized TMDPDFs exhibit nearly identical transverse structure up to a normalization factor, and the unpolarized distributions display only mild flavor dependence. These findings not only support key trends observed in recent global analyses but also provide robust, nonperturbative constraints that can distinguish between different parameterizations. This work establishes a first-principles benchmark for TMDPDFs, offering valuable input for ongoing and future experimental efforts to map the proton's three-dimensional structure.

hep-lat↗

arXiv2025

In-medium bottomonium properties from lattice NRQCD calculations with extended meson operators

We calculate the temperature dependence of bottomonium correlators in (2+1)-flavor lattice QCD with the aim to constrain in-medium properties of bottomonia at high temperature. The lattice calculations are performed using HISQ action with physical strange quark mass and light quark masses twenty times smaller than the strange quark mass at two lattice spacings $a=0.0493$ fm and $0.0602$ fm, and temporal extents $N_τ=16-30$, corresponding to the temperatures $T=133-250$ MeV. We use a tadpole-improved NRQCD action including spin-dependent $v^6$ corrections for the heavy quarks and extended meson operators in order to be sensitive to in-medium properties of the bottomonium states of interest. We find that within estimated errors the bottomonium masses do not change compared to their vacuum values for all temperatures under our consideration; however, we find different nonzero widths for the various bottomonium states.

hep-lat↗

arXiv2025

Transverse-momentum-dependent pion structures from lattice QCD: Collins-Soper kernel, soft factor, TMDWF, and TMDPDF

We present the first lattice quantum chromodynamics (QCD) calculation of the pion valence-quark transverse-momentum-dependent parton distribution function (TMDPDF) within the framework of large-momentum effective theory (LaMET). Using correlators fixed in the Coulomb gauge (CG), we computed the quasi-TMD beam function for a pion with a mass of 300 MeV, a fine lattice spacing of $a = 0.06$ fm and multiple large momenta up to 3 GeV. The intrinsic soft functions in the CG approach are extracted from form factors with large momentum transfer, and as a byproduct, we also obtain the corresponding Collins-Soper (CS) kernel. Our determinations of both the soft function and the CS kernel agree with perturbation theory at small transverse separations ($b_\perp$) between the quarks. At larger $b_\perp$, the CS kernel remains consistent with recent results obtained using both CG and gauge-invariant TMD correlators in the literature. By combining next-to-leading logarithmic (NLL) factorization of the quasi-TMD beam function and the soft function, we obtain $x$-dependent pion valence-quark TMDPDF for transverse separations $b_\perp \gtrsim 1$ fm. Interestingly, we find that the $b_\perp$ dependence of the phenomenological parameterizations of TMDPDF for moderate values of $x$ are in reasonable agreement with our QCD determinations. In addition, we present results for the transverse-momentum-dependent wave function (TMDWF) for a heavier pion with 670 MeV mass.

hep-lat↗

arXiv2025

Towards a Real-Time Computation of Timelike Hadronic Vacuum Polarization and Light-by-Light Scattering: Schwinger Model Tests

Hadronic vacuum polarization (HVP) and light-by-light scattering (HLBL) are crucial for evaluating the Standard Model predictions concerning the muon's anomalous magnetic moment. However, direct first-principle lattice gauge theory-based calculations of these observables in the timelike region remain challenging. Discrepancies persist between lattice quantum chromodynamics (QCD) calculations in the spacelike region and dispersive approaches relying on experimental data parametrization from the timelike region. Here, we introduce a methodology employing 1+1-dimensional quantum electrodynamics (QED), i.e. the Schwinger Model, to investigate the HVP and HLBL. To that end, we use both tensor network techniques, specifically matrix product states, and classical emulators of digital quantum computers. Demonstrating feasibility in a simplified model, our approach sets the stage for future endeavors leveraging digital quantum computers.

hep-ph↗

arXiv2025

Perturbative Corrections to Quark TMDPDFs in the Background-Field Method: Gauge Invariance, Equations of Motion, and Multiple Interactions

We calculate the perturbative corrections in the strong coupling to the unpolarized quark transverse-momentum dependent parton distribution function (TMDPDF) operator within a background-field framework, extending the approach of Ref. [1]. We focus on ensuring gauge invariance, identifying two key components needed: a gauge-invariant TMDPDF operator with a transverse gauge link at spatial infinity, and accounting of the equations of motion (EoM) of the background fields. We go beyond next-to-leading order in strong coupling expansion, considering multiple interactions with the background field at all orders of strong coupling. By examining the interplay between quark and gluon contributions, we show that spurious singularities, proportional to EoM, can be misinterpreted as genuine divergences in QCD factorization unless properly identified and removed.

hep-ph↗

arXiv2025

Quarkonium Spectroscopy in the Quark-Gluon Plasma

The properties of bound states are fundamental to hadronic spectroscopy and play a central role in the transition from hadronic matter to a quark-gluon plasma (QGP). In a strongly coupled QGP (sQGP), the interplay of temperature, binding energy and large collisional widths of the partons poses formidable challenges in evaluating the in-medium properties of hadronic states and their eventual melting. In particular, the existence of heavy quarkonia in the QGP is a long-standing problem that is hard to solve by considering their spectral properties on the real-energy axis. We address this problem by analyzing in-medium thermodynamic quarkonium $T$-matrices in the complex energy plane. We first validate this method in vacuum, where the $T$-matrix poles of observed states are readily identified. When deploying this approach to recent self-consistently calculated $T$-matrices in the QGP, we find that poles in the complex energy plane can persist to surprisingly large temperatures, depending on the strength of the in-medium interactions. While the masses and widths of the pole positions are precisely defined, the notion of a binding energy is not due to the absence of thresholds caused by the (large) widths of the underlying anti-/quark spectral functions. Our method thus provides a new and definitive quantum-mechanical criterion to determine the melting temperature of hadronic states in the sQGP while increasing the accuracy in the theoretical determination of transport parameters.

nucl-th↗