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DOE OSTI2026

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 $\overline{MS}$ 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}$$^{u-d}_2$⁡(2 GeV) =0.0024⁢(46) at next-to-leading order in $\overline{MS}$. 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 $\overline{MS}$ 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 ∈[0.25,0.75]. The end-point regions are then parametrized, combined with the LaMET prediction at moderate 𝑥, and fitted to the short-distance matrix elements in coordinate space.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

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 Letter establishes a first-principles benchmark for TMDPDFs, offering valuable input for ongoing and future experimental efforts to map the proton’s three-dimensional structure.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Combination of Measurements of the Top Quark Mass from Data Collected by the ATLAS and CMS Experiments at s = 7 and 8 TeV

A combination of fifteen top quark mass measurements performed by the ATLAS and CMS experiments at the LHC is presented. The datasets used correspond to an integrated luminosity of up to 5 and 20 fb − 1 of proton-proton collisions at center-of-mass energies of 7 and 8 TeV, respectively. The combination includes measurements in top quark pair events that exploit both the semileptonic and hadronic decays of the top quark, and a measurement using events enriched in single top quark production via the electroweak t channel. The combination accounts for the correlations between measurements and achieves an improvement in the total uncertainty of 31% relative to the most precise input measurement. The result is m t = 172.52 ± 0.14 ( stat ) ± 0.30 ( syst ) GeV , with a total uncertainty of 0.33 GeV. © 2024 CERN, for the CMS and ATLASs Collaboration 2024 CERN

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Combination of measurements of the top quark mass from data collected by the ATLAS and CMS experiments at $\sqrt{s}=7$ and $8~\mathrm{TeV}$

A combination of fifteen top quark mass measurements performed by the ATLAS and CMS experiments at the LHC is presented. The data sets used correspond to an integrated luminosity of up to 5 and $20~\mathrm{fb}^{-1}$ of proton-proton collisions at center-of-mass energies of 7 and $8~\mathrm{TeV}$, respectively. The combination includes measurements in top-quark pair events that exploit both the semi-leptonic and hadronic decays of the top quark, and a measurement using events enriched in single top quark production via the electroweak $t$-channel. The combination yields $m_{\mathrm{t}} = 172.52 \pm 0.14~(\mathrm{stat}) \pm 0.30~(\mathrm{syst}) ~\mathrm{GeV}$, with a total uncertainty of $0.33~\mathrm{GeV}$.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Real corrections to Higgs boson pair production at NNLO in the large top quark mass limit

In this paper we consider the next-to-next-to-leading order total cross section of Higgs boson pair production in the large top quark mass limit and compute four expansion terms in 1 $ {m}_t^2 $ . To this end, we analytically compute the real-virtual and double-real contributions to the total cross section and combine them with the existing virtual contribution. Good convergence is observed below the top quark threshold, which makes our results a valuable input for approximation methods which aim for next-to-next-to-leading order corrections over the whole kinematic range. We present details on various steps of our calculation; in particular, we provide results for three- and four-particle phase-space master integrals and describe in detail the evaluation of the collinear counterterms.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Two- and three-meson scattering amplitudes with physical quark masses from lattice QCD

We study systems of two and three mesons composed of pions and kaons at maximal isospin using four CLS ensembles with 𝑎 ≈ 0.063 fm, including one with approximately physical quark masses. Using the stochastic Laplacian-Heaviside method, we determine the energy spectrum of these systems including many levels in different momentum frames and irreducible representations. Using the relativistic two- and three-body finite-volume formalism, we constrain the two- and three-meson K matrices, including not only the leading 𝑠 wave, but also 𝑝 and 𝑑 waves. By solving the three-body integral equations, we determine, for the first time, the physical-point scattering amplitudes for 3⁢𝜋 + , 3⁢𝐾 + , 𝜋 + ⁢𝜋 + ⁢𝐾 + , and 𝐾 + ⁢𝐾 + ⁢𝜋 + systems. These are determined for total angular momentum 𝐽 𝑃 = 0 − , 1 + , and 2 − . We also obtain accurate results for 2⁢𝜋 + , 𝜋 + ⁢𝐾 + , and 2⁢𝐾 + phase shifts. We compare our results to chiral perturbation theory and to phenomenological fits.

FOS: Physical sciences↗
DOE OSTI2025

Factorial growth in perturbation theory, power corrections: precise extraction of quark masses and $\alpha_\text{s}$

These proceedings summarize a newly found connection between the factorial growth of coefficients in perturbative QCD and power corrections to the perturbation series, discussed in refs. [1-4]. The improved convergence is shown for three quantities four which four terms in the series are available: the static energy, the quark pole mass, and the polarized Bjorken sum rule. Prospects for determinations of $\alpha_\text{s}$ with controlled truncation uncertainties are discussed, as was found earlier in quark-mass determinations [3,5].

Kronfeld, Andreas S. [Fermilab; TUM-IAS, Munich] (↗
DOE OSTI2024

Determination of crossing-symmetric π π scattering amplitudes and the quark mass evolution of the σ constrained by lattice QCD

Lattice QCD spectra can be used to constrain partial-wave scattering amplitudes that, while satisfying unitarity, do not have to respect crossing symmetry and analyticity. This becomes a particular problem when extrapolated far from real energies, e.g. in the case of broad resonances like the σ , leading to large systematic uncertainties in the pole position. In this manuscript, we will show how dispersion relations can implement the additional constraints, using as input lattice-determined π π partial-wave scattering amplitudes with isospin–0,1,2. We will show that only certain combinations of amplitude parametrizations satisfy all constraints, and that when we restrict to these, the σ pole position is determined with minimal systematic uncertainty. The evolution of the now well-constrained σ pole with varying light quark mass is presented, showing how it transitions from a bound-state to a broad resonance. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Heavy quark mass effects in charged-current deep-inelastic scattering at approximate NNLO in the Aivazis-Collins-Olness-Tung scheme

The approximate SACOT-𝜒 scheme for heavy quark production in deep-inelastic scattering was initially formulated for the neutral current structure functions 𝐹 2 and 𝐹 𝐿 . We extend this approach to the charged current case (also including 𝐹 3 ), and thereby complete the definitions for the most relevant inclusive structure functions. Furthermore, we implement these structure functions in the open-source code APFEL++ which provides fast numerical evaluations over a wide kinematic range; this addition to the APFEL++ code is publicly available, with details provided in the Appendix. This SACOT-𝜒 implementation enables detailed numerical insights on the mass dependence of the structure functions and cross sections in the (𝑥,𝑄 2 )-plane for both neutral and charged current processes. We consider kinematic regions relevant for the experimental measurements from fixed-target 𝜈⁢ DIS experiments (NuTeV, CCFR, and Chorus) and HERA, and also projections for the upcoming EIC. In particular, the 𝜈⁢ DIS experiments reveal a surprisingly strong dependence on the mass effects, offering valuable insights that may help resolve long-standing challenges in accurately describing these datasets.

Risse, P. [Westfälische Wilhelms-Universität Münst↗
DOE OSTI2023

Isospin-breaking corrections to light-meson leptonic decays from lattice simulations at physical quark masses

The decreasing uncertainties in theoretical predictions and experimental measurements of several hadronic observables related to weak processes, which in many cases are now smaller than O(1%), require theoretical calculations to include subleading corrections that were neglected so far. Precise determinations of leptonic and semi-leptonic decay rates, including QED and strong isospin-breaking effects, can play a central role in solving the current tensions in the first-row unitarity of the CKM matrix. In this work we present the first RBC/UKQCD lattice calculation of the isospin-breaking corrections to the ratio of leptonic decay rates of kaons and pions into muons and neutrinos. The calculation is performed at fixed lattice spacing (a –1 ≃ 1.730 GeV) on a 48 3 × 96 volume with N f = 2 + 1 dynamical quarks close to the physical point and domain wall fermions in the Möbius formulation are employed. Long-distance QED interactions are included according to the QED L prescription and the crucial role of finite-volume electromagnetic corrections in the determination of leptonic decay rates, which produce a large systematic uncertainty, is extensively discussed. Finally, we study the different sources of uncertainty on |V us |/|V ud | and observe that, if finite-volume systematics can be reduced, the error from isospin-breaking corrections is potentially sub-dominant in the final precision of the ratio of the CKM matrix elements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Quark mass difference effects in hadronic Fermi matrix elements from first principles

It was recently estimated that the strong isospin-symmetry breaking (ISB) corrections to the Fermi matrix element in free neutron decay could be of the order 10 –4 , one order of magnitude larger than the naïve estimate based on the Behrends-Sirlin-Ademollo-Gatto theorem. To investigate this claim, we derive a general expression of the leading ISB correction to hadronic Fermi matrix elements, which takes the form of a four-point correlation function in lattice gauge theory and is straightforward to compute from first principles. Our formalism paves the way for the first determination of such correction in the neutron sector with fully-controlled theory uncertainties.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗