Probing the Energy-Smeared R Ratio Using Lattice QCD.

We present a first-principles lattice QCD investigation of the R ratio between the e^{+}e^{-} cross section into hadrons and into muons. By using the method of Ref. [1], that allows one to extract smeared spectral densities from Euclidean correlators, we compute the R ratio convoluted with Gaussian smearing kernels of widths of about 600 MeV and central energies from 220 MeV up to 2.5 GeV. Our theoretical results are compared with the corresponding quantities obtained by smearing the KNT19 compilation [2] of R-ratio experimental measurements with the same kernels and, by centering the Gaussians in the region around the ρ-resonance peak, a tension of about 3 standard deviations is observed. From the phenomenological perspective, we have not included yet in our calculation QED and strong isospin-breaking corrections, and this might affect the observed tension. From the methodological perspective, our calculation demonstrates that it is possible to study the R ratio in Gaussian energy bins on the lattice at the level of accuracy required in order to perform precision tests of the standard model.

Lattice QCD Study of Transverse-Momentum Dependent Soft Function.

In this work, we perform a lattice QCD study of the intrinsic, rapidity-independent soft function within the framework of large momentum effective theory. The computation is carried out using a gauge ensemble of N_{f}=2+1+1 clover-improved twisted mass fermion. After applying an appropriate renormalization procedure and the removal of significant higher-twist contamination, we obtain the intrinsic soft function that is comparable to the one-loop perturbative result at large external momentum. The determination of the nonperturbative soft function from first principles is crucial to sharpen our understanding of the processes with small transverse momentum such as the Drell-Yan production and the semi-inclusive deep inelastic scattering. Additionally, we calculate the Collins-Soper evolution kernel using the quasi-transverse-momentum-dependent wave function as input.

Flavor Decomposition for the Proton Helicity Parton Distribution Functions.

We present, for the first time, an ab initio calculation of the individual up, down, and strange quark helicity parton distribution functions for the proton. The calculation is performed within the twisted mass clover-improved fermion formulation of lattice QCD. The analysis is performed using one ensemble of dynamical up, down, strange, and charm quarks with a pion mass of 260 MeV. The lattice matrix elements are nonperturbatively renormalized and the final results are presented in the MS[over ¯] scheme at a scale of 2 GeV. We give results for Δu^{+}(x), Δd^{+}(x) Δu^{-}(x), Δd^{-}(x), including disconnected quark loop contributions, as well as for Δs^{+}(x) and Δs^{-}(x). For the latter we achieve unprecedented precision compared to the phenomenological estimates.

Quark and Gluon Momentum Fractions in the Pion from N_{f}=2+1+1 Lattice QCD.

We perform the first full decomposition of the pion momentum into its gluon and quark contributions. We employ an ensemble generated by the Extended Twisted Mass Collaboration with N_{f}=2+1+1 Wilson twisted mass clover fermions at maximal twist tuned to reproduce the physical pion mass. We present our results in the MS[over ¯] scheme at 2 GeV. We find ⟨x⟩_{u+d}=0.601(28), ⟨x⟩_{s}=0.059(13), ⟨x⟩_{c}=0.019(05), and ⟨x⟩_{g}=0.52(11) for the separate contributions, respectively, whose sum saturates the momentum sum rule.

Unpolarized and Helicity Generalized Parton Distributions of the Proton within Lattice QCD.

We present the first calculation of the x dependence of the proton generalized parton distributions (GPDs) within lattice QCD. Results are obtained for the isovector unpolarized and helicity GPDs. We compute the appropriate matrix elements of fast-moving protons coupled to nonlocal operators containing a Wilson line. We present results for proton momenta 0.83,1.25,1.67 GeV, and momentum transfer squared 0.69,1.38 GeV^{2}. These combinations include cases with zero and nonzero skewness. The calculation is performed using one ensemble of two degenerate mass light quarks, a strange quark, and a charm quark of maximally twisted mass fermions with a clover term. The lattice results are matched to the light-cone GPDs using one-loop perturbation theory within the framework of large momentum effective theory. The final GPDs are given in the MS[over ¯] scheme at a scale of 2 GeV.