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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Improving the Precision of First-Principles Calculation of Parton Physics from Lattice Quantum Chromodynamics

Large momentum effective theory (LaMET) provides a general framework for computing the multi-dimensional partonic structure of the proton from first principles using lattice quantum chromodynamics (QCD). In this effective field theory approach, LaMET predicts parton distributions through a power expansion and perturbative matching of a class of Euclidean observables—quasi-distributions—evaluated at large proton momenta. Recent advances in lattice renormalization, such as the hybrid scheme with leading renormalon resummation, together with improved matching kernel that incorporates higher-loop corrections and resummations, have enhanced both the perturbative and power accuracy of LaMET, enabling a reliable quantification of theoretical uncertainties. Moreover, the Coulomb-gauge correlator approach further simplifies lattice analyses and improves the precision of transverse-momentum-dependent structures, particularly in the non-perturbative region. State-of-the-art LaMET calculations have already yielded certain parton observables with important phenomenological impact. In addition, the recently proposed kinematically enhanced lattice interpolation operators promise access to unprecedented proton momenta with greatly improved signal-to-noise ratios, which will extend the range of LaMET prediction and further suppress the power corrections. The remaining challenges, such as controlling excited-state contamination in lattice matrix elements and extracting gluonic distributions, are expected to benefit from emerging lattice techniques for ground-state isolation and noise reduction. Thus, lattice QCD studies of parton physics have entered an exciting stage of precision control and systematic improvement, which will have a broader impact for nuclear and particle experiments.

Zhao, Yong [Argonne National Laboratory (ANL), Arg↗
NASA NTRS1978

Theory of the classical electron gas

In a previous paper Cohen and Murphy (1969) used the Meeron resummation (1958) of the Mayer diagrams (1950) to calculate the pair correlation for the classical electron gas in thermal equilibrium. They found that successive terms in the expression for the pair correlation were more and more singular for small interparticle spacing, actually dominating the Debye-Hueckel result for sufficiently small distances. This led to apparent divergence in the higher order contributions to the internal energy. The present paper shows that the apparent anomalies in the Cohen-Murphy results can be removed without further resummation by a more careful treatment of the region of small interparticle spacing. It is shown that there is really no anomalous behavior at short range in any order and all integrals in the expression for the internal energy converge.

Guernsey, R. L.↗
DOE OSTI2025

Non-linear dynamics of jet quenching

We develop a comprehensive analytic framework for jet quenching in QCD media, based on a medium-induced parton cascade sourced by collinear virtual splittings. We show that the energy flow out of the jet cone, driven by turbulent gluon cascades, is governed by a non-linear rate equation that resums gluon splittings at arbitrary angles and is enhanced by the medium length, L. The solution of this equation sets the initial condition for a non-linear DGLAP-like evolution equation, which describes the collinear early vacuum cascade resolved by the medium at angles exceeding the medium resolution angle, θ c . For asymptotic jet energies, the medium-induced cascade displays an exponential behavior that generalizes the Poisson-like distribution of parton energy loss. This formulation enables the resummation of leading contributions in α s ln(1/R), and α s ln(R/θ c ), and powers of α s L. We briefly explore the limit of strong quenching, where analytic treatments are feasible, offering insights into the impact of parton cascades on jet quenching. These results provide guidance for future numerical simulations and analytical investigations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Transverse momentum-dependent heavy-quark fragmentation at next-to-leading order

The transverse momentum-dependent fragmentation functions (TMD FFs) of heavy (bottom and charm) quarks, which we recently introduced, are universal building blocks that enter predictions for a large number of observables involving final-state heavy quarks or hadrons. They enable the extension of fixed-order subtraction schemes to quasi-collinear limits, and are of particular interest in their own right as probes of the nonperturbative dynamics of hadronization. In this paper we calculate all TMD FFs involving heavy quarks and the associated TMD matrix element in heavy-quark effective theory (HQET) to next-to-leading order in the strong interaction. Our results confirm the renormalization properties, large-mass, and small-mass consistency relations predicted in our earlier work. We also derive and confirm a prediction for the large-z behavior of the heavy-quark TMD FF by extending, for the first time, the formalism of joint resummation to capture quark mass effects in heavy-quark fragmentation. Our final results in position space agree with those of a recent calculation by another group that used a highly orthogonal organization of singularities in the intermediate momentum-space steps, providing a strong independent cross check. As an immediate application, we present the complete quark mass dependence of the energy-energy correlator (EEC) in the back-to-back limit at $\mathcal{O}\left({\alpha}_s\right)$.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Lattice QCD calculation of the pion distribution amplitude with domain wall fermions at physical pion mass

We present a direct lattice QCD calculation of the x-dependence of the pion distribution amplitude (DA), which is performed using the quasi-DA in large momentum effective theory on a domain-wall fermion ensemble at physical quark masses and spacing a ≈ 0.084 fm. The bare quais-DA matrix elements are renormalized in the hybrid scheme and matched to $\overline{MS}$ with a subtraction of the leading renormalon in the Wilson-line mass. For the first time, we include threshold resummation in the perturbative matching onto the light-cone DA, which resums the large logarithms in the soft gluon limit at next-to-next-to-leading log. The resummed results show controlled scale-variation uncertainty within the range of momentum fraction x ϵ [0.25, 0.75] at the largest pion momentum P z ≈ 1.85 GeV. In addition, we apply the same analysis to quasi-DAs from a highly-improved-staggered-quark ensemble at physical pion mass and a = 0.076 fm. By comparison we find with 2σ confidence level that the DA obtained from chiral fermions is flatter and lower near x = 0.5.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

The three-point energy correlator in the coplanar limit

Energy correlators are a type of observables that measure how energy is distributed across multiple detectors as a function of the angles between pairs of detectors. In this paper, we study the three-point energy correlator (EEEC) at lepton colliders in the three-particle near-to-plane (coplanar) limit. The leading-power contribution in this limit is governed by the three-jet (trijet) configuration. We introduce a new approach by projecting the EEEC onto the volume of the parallelepiped formed by the unit vectors aligned with three detected final-state particles. Analogous to the back-to-back limit of the two-point energy correlator probing the dijet configuration, the small-volume limit of the EEEC probes the trijet configuration. We derive a transverse momentum dependent (TMD) based factorization theorem that captures the soft and collinear logarithms in the coplanar limit, which enables us to achieve the next-to-next-to-next-to-leading logarithm (N 3 LL) resummation. To our knowledge, this is the first N 3 LL result for a trijet event shape. Additionally, we demonstrate that a similar factorization theorem can be applied to the fully differential EEEC in the three-particle coplanar limit, which provides a clean environment for studying different coplanar trijet shapes.

Effective Field Theories of QCD↗
DOE OSTI2024

Advancing the understanding of energy-energy correlators in heavy-ion collisions

We investigate the collinear limit of the energy-energy correlator (EEC) in a heavy-ion context. First, we revisit the leading-logarithmic (LL) resummation of this observable in vacuum following a diagrammatic approach. We argue that this route allows to naturally incorporate medium-induced effects into the all-orders structure systematically. As an example, we show how the phase-space constraints imposed by the static medium on vacuum-like emissions can be incorporated into the LL result by modifying the anomalous dimensions. On the fixed-order side, we calculate the $\mathcal{O}$(α s ) expansion of the in-medium EEC for a γ → $q\overline{q}$ splitting with arbitrary kinematics including, for the first time, subleading colour corrections. When comparing this result to previously used approximations in the literature, we find up to $\mathcal{O}$(1) deviations in the regime of interest for jet quenching signatures. Energy loss effects are also quantified and further suppress the EEC at large angles. These semi-analytic studies are complemented with a phenomenological study using the jet quenching Monte Carlo JetMed. Finally, we argue that the imprint of medium-induced effects in energy-energy correlators can be enhanced by using an alternative definition that takes as input Lund primary declusterings instead of particles.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Improving resbos for the precision needs of the LHC

The resummation calculation (esos) is a widely used tool for the simulation of single vector boson production at colliders. In this work, we develop a significant improvement over the esos code by increasing the accuracy from NNLL + NLO to N 3 LL + NNLO and release the esos v2.0 code. Furthermore, we propose a new nonperturbative function that includes information about the rapidity of the system (IFY). The IFY functional form was fitted to data from fixed target experiments, the Tevatron, and the LHC. We find that the nonperturbative function has mild rapidity dependence based on the results of the fit. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Three-dimensional imaging of pion using lattice QCD: generalized parton distributions

In this work, we report a lattice calculation of x-dependent valence pion generalized parton distributions (GPDs) at zero skewness with multiple values of the momentum transfer −t. The calculations are based on an N f = 2 + 1 gauge ensemble of highly improved staggered quarks with Wilson-Clover valence fermion. The lattice spacing is 0.04 fm, and the pion valence mass is tuned to be 300 MeV. We determine the Lorentz-invariant amplitudes of the quasi-GPD matrix elements for both symmetric and asymmetric momenta transfers with similar values and show the equivalence of both frames. Then, focusing on the asymmetric frame, we utilize a hybrid scheme to renormalize the quasi-GPD matrix elements obtained from the lattice calculations. After the Fourier transforms, the quasi-GPDs are then matched to the light-cone GPDs within the framework of large momentum effective theory with improved matching, including the next-to-next-to-leading order perturbative corrections, and leading renormalon and renormalization group resummations. We also present the 3-dimensional image of the pion in impact-parameter space through the Fourier transform of the momentum transfer −t.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Radiative corrections to superallowed beta decays at $\mathcal{O}\left({\alpha}^2Z\right)$

We compute $\mathcal{O}\left({\alpha}^2Z\right)$ radiative corrections to superallowed β decays with a heavy-particle effective field theory that systematically describes the interactions of low-energy ultrasoft photons with nuclei. We calculate two-loop virtual and one-loop real-virtual amplitudes by reducing the Feynman integrals to a set of master integrals, which we solve analytically using a variety of techniques. These techniques can be applied to other phenomenologically interesting observables. The ultrasoft corrections can then be combined with contributions arising from the exchange of potential photons to obtain the complete $\mathcal{O}\left({\alpha}^2Z\right)$ correction to the decay rate, with resummation of large logarithms of the electron energy times the nuclear radius. We find that $\mathcal{O}\left({\alpha}^2Z\right)$ ultrasoft loops induce a relative correction to the decay rate that ranges from 0.7 ∙ 10 −3 in the decay of 10 C to 3.6 ∙ 10 −3 in the decay of 54 Co, and will thus impact the extraction of V ud at the permille level. We show that the inclusion of these corrections reduces the residual renormalization scale dependence of the decay rate to a negligible level, making missing ultrasoft perturbative corrections a subdominant source of theoretical uncertainty.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Testing real WIMPs with CTAO

We forecast the reach of the upcoming Cherenkov Telescope Array Observatory (CTAO) to the full set of real representations within the paradigm of minimal dark matter. We employ effective field theory techniques to compute the annihilation cross section and photon spectrum that results when fermionic dark matter is the neutral component of an arbitrary odd and real representation of SU(2), including the Sommerfeld enhancement, next-to-leading log resummation of the relevant electroweak effects, and the contribution from bound states. We also compute the corresponding signals for scalar dark matter, with the exception of the bound state contribution. Results are presented for all real representations from the ~ 3 TeV triplet (or wino), a 3 of SU(2), to the ~ 300 TeV tredecuplet, a 13 of SU(2) that is at the threshold of the unitarity bound. Using these results, we forecast that with 500 hrs of Galactic Center observations and assuming background systematics are controlled at the level of $\mathcal{(O)}$(1%), then should no signal emerge, CTAO could exclude all representations up to the 11 of SU(2) in even the most conservative models for the dark-matter density in the inner galaxy, in both the fermionic and scalar dark matter cases. Assuming the default CTAO configuration, the tredecuplet will marginally escape exclusion, although we outline steps that CTAO could take to test even this scenario. In summary, CTAO appears poised to make a definitive statement on whether real WIMPs constitute the dark matter of our universe.

Models for Dark Matter↗
DOE OSTI2024

QED corrections to the thermal neutrino interaction rate

Abstract Motivated by precision computations of neutrino decoupling at MeV temperatures, we show how QED corrections to the thermal neutrino interaction rate can be related to the electron-positron spectral function as well as an effective$$\overline{\nu }\nu \gamma $$vertex. The spectral function is needed both in a timelike and in a spacelike domain, and for both of its physical polarization states (transverse and longitudinal with respect to spatial momentum). Incorporating an NLO evaluation of this spectral function, an estimate of the$$\overline{\nu }\nu \gamma $$vertex, and HTL resummation of scatterings mediated by soft Bose-enhancedt-channel photons, we compute the interaction rate as a function of the neutrino momentum and flavour. Effects on the – (0. . .2)% level are found, noticeably smaller than a previous estimate of a related quantity.

Physics↗
DOE OSTI2024

Testing the scalar weak gravity conjecture in no-scale supergravity

We explore possible extensions of the Weak Gravity Conjecture (WGC) to scalar field theories. To avoid charged black hole remnants, the WGC requires the existence of a particle with a mass m ≤ gqM P , with charge q and U(1) gauge coupling g, allowing the decay to shed the black hole charge. Although there is no obvious problem that arises in the absence of a U(1) charge, it has been postulated that gravity must remain the weakest force even when extended to scalar interactions. Quantifying this conjecture may be done by comparing scalar and gravitational amplitudes, or as we advocate here by comparing scattering cross sections. In theories with non-trivial field space geometries, by working out examples with perturbation theory around arbitrary field values and performing tadpole resummations, we argue that the conjecture must be applied only at extrema of the scalar potential (when expressed in locally canonical coordinates). We consider several toy models in the context of no-scale supergravity and also consider examples of inflationary models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Non-perturbative quarkonium dissociation rates in strongly coupled quark-gluon plasma

Heavy quarks and quarkonia are versatile probes of the transport properties of the hot QCD medium produced in ultra-relativistic heavy-ion collisions (URHICs). A robust description of heavy-flavor transport coefficients requires a microscopic approach that treats the open and hidden heavy-flavor sectors on the same footing. Here, we employ the quantum many-body T -matrix formalism to evaluate the dissociation rates of heavy quarkonia in the quark-gluon plasma (QGP). The basic ingredient is the heavy-light T -matrix, which utilizes a nonperturbative driving kernel constrained by lattice-QCD data. Its resummation in a ladder series provides a much enhanced interaction strength compared to a previously used perturbative coupling to the quasiparticle partons in the QGP. The in-medium quarkonium properties, particularly their temperature-dependent binding energies, are obtained from selfconsistent calculations with the same interaction kernel, including interference effects (also referred to as the imaginary part of the heavy-quark potential) as well as off-shell parton spectral functions. We systematically investigate the interplay of these effects and elaborate on the connections to the dipole approximation used in effective field theory.

effective field theories of QCD↗
DOE OSTI2024

Dihadron correlations in small- x DIS at NLO: transverse momentum dependent fragmentation

We compute the inclusive dihadron cross-section in Deep Inelastic Scattering at next-to-leading order (NLO) and small x in the Color Glass Condensate. We focus on the kinematic limit where the hadrons are produced at forward rapidities (in the direction of the virtual photon) and back-to-back in the transverse plane. Our calculation demonstrates that the coefficient of the Sudakov double logarithm for this process is –$\frac{αs}{2π}$ [C F + $\frac{Nc}{2}$] instead of –$\frac{αsNc}{4π}$ when back-to-back jets are measured in the final state. To preserve the universality of the Sudakov soft factor associated with the Weizsäcker-Williams transverse momentum dependent (TMD) gluon distribution, we promote the collinear fragmentation functions into TMD fragmentation functions. We then perform the resummation of the Sudakov logarithms through Collins-Soper-Sterman evolution of the TMD fragmentation functions and the Weizsäcker-Williams TMD gluon distribution. Finally, analytic expressions are obtained for the NLO coefficient functions in the $\overline{MS}$-scheme. These results pave the way towards numerically calculating dihadron correlations at small x at the future Electron-Ion Collider with full NLO accuracy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Generalized parton distributions and gravitational form factors at large momentum transfer

Within the soft collinear effective theory (SCET), we derive a factorization theorem which resums Sudakov logarithms (α s ln 2 ( –t)) n to all orders in the quark-in-quark generalized parton distribution (GPD) at large momentum transfer t, and perform a consistency check to one-loop. We show that the same Sudakov factor appears in the ‘Feynman’ contribution to the GPDs of the nucleon. Our result enables the resummation of all the large logarithms ln Q 2 and ln 2 t in exclusive processes with two hard scales Λ$^{2}_{QCD}$ ≪ |t| ≪ Q 2 . We also present a SCET power counting analysis of the Feynman contributions to the GPDs and show that the x-dependence of GPDs factorizes at large-t with controlled corrections. This in particular implies that any ratio of GPD moments such as the electromagnetic and gravitational form factors (GFF) is perturbatively calculable in this approximation. Furthermore, we identify a novel order α s power-law t-dependence in the GPD and the D-type GFF that will dominate over the standard order α$^{2}_{s}$ ‘leading twist’ asymptotic contribution in the phenomenologically relevant region of t.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Understanding parton evolution in matter from renormalization group analysis

We perform a renormalization group (RG) analysis of collinear hadron production in deep inelastic scattering on nuclei. We consider the limit where the parent parton energy E is large, while the medium opacity remains small. We identify the fixed order and leading enhanced medium contributions to the semi-inclusive cross sections and derive RG equations that resum multiple emissions near the endpoints of the splitting functions at first order in opacity. These evolution equations treat the same type of radiation enhancement in matter as the modified Dokshitzer-Gribov-Lipatov-Altarelli-Parisi approach, but differ in the way one regulates the collinear divergences. They provide a unique analytic insight into the problem of resummation and a faster and more efficient path to phenomenology. The new RG evolution framework is applied to study fragmentation in eA reactions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

ν-point energy correletors with F AST EEC: Small-x physics from LHC jets

In recent years, energy correlators have emerged as a powerful tool for studying jet substructure, with promising applications such as probing the hadronization transition, analyzing the quark-gluon plasma, and improving the precision of top quark mass measurements. The projected N-point correlator measures correlations between N final-state particles by tracking the largest separation between them, showing a scaling behavior related to DGLAP splitting functions. These correlators can be analytically continued in N, commonly referred to as ν-correlators, allowing access to non-integer moments of the splitting functions. Of particular interest is the ν → 0 limit, where the small momentum fraction behavior of the splitting functions requires resummation. Originally, the computational complexity of evaluating ν-correlators for M particles scaled as 2 2M , making it impractical for real-world analyses. However, by using recursion, we reduce this to M 2M , and through the FastEEC method of dynamically resolving subjets, M is replaced by the number of subjets. This breakthrough enables, for the first time, the computation of ν-correlators for LHC data. In practice, limiting the number of subjets to 16 is sufficient to achieve percent-level precision, which we validate using known integer-ν results and convergence tests for non-integer ν. We have implemented this in an update to FastEEC and conducted an initial study of power-law scaling in the perturbative regime as a function of ν, using CMS Open Data on jets. The results agree with DGLAP evolution, except at small ν, where the anomalous dimension saturates to a value that matches the BFKL anomalous dimension.

Energy correlators↗