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Register a new userNew insights on proton structure from lattice QCD: the twist-3 parton distribution function $g_T(x)$
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In this work, we present the first-ever calculation of the isovector flavor combination of the twist-3 parton distribution function $g_T(x)$ for the proton from lattice QCD. We use an ensemble of gauge configurations with two degenerate light, a strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with a clover improvement. The lattice has a spatial extent of 3~fm, lattice spacing of 0.093~fm, and reproduces a pion mass of $260$ MeV. We use the quasi-distribution approach and employ three values of the proton momentum boost, 0.83 GeV, 1.25 GeV, and 1.67 GeV. We use a source-sink separation of 1.12~fm to suppress excited-states contamination. The lattice data are renormalized non-perturbatively. We calculate the matching equation within Large Momentum Effective Theory, which is applied to the lattice data in order to obtain $g_T$. The final distribution is presented in the $overline{rm MS}$ scheme at a scale of 2 GeV. We also calculate the helicity distribution $g_1$ to test the Wandzura-Wilczek approximation for $g_T$. We find that the approximation works well for a broad range of $x$. This work demonstrates the feasibility of accessing twist-3 parton distribution functions from novel methods within lattice QCD and can provide essential insights into the structure of hadrons.
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We report the first-ever calculation of the isovector flavor combination of the chiral-odd twist-3 parton distribution $h_L(x)$ for the proton from lattice QCD. We employ gauge configurations with two degenerate light, a strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with a clover improvement. The lattice has a spatial extent of 3 fm and lattice spacing of 0.093 fm. The values of the quark masses lead to a pion mass of $260$ MeV. We use a source-sink time separation of 1.12 fm to control contamination from excited states. Our calculation is based on the quasi-distribution approach, with three values for the proton momentum: 0.83 GeV, 1.25 GeV, and 1.67 GeV. The lattice data are renormalized non-perturbatively using the RI$$ scheme, and the final result for $h_L(x)$ is presented in the $overline{rm MS}$ scheme at the scale of 2 GeV. Furthermore, we compute in the same setup the transversity distribution, $h_1(x)$, which allows us, in particular, to compare $h_L(x)$ to its Wandzura-Wilczek approximation. We also combine results for the isovector and isoscalar flavor combinations to disentangle the individual quark contributions for $h_1(x)$ and $h_L(x)$, and address the Wandzura-Wilczek approximation in that case as well.
Perturbative matching relates the parton quasi-distributions, defined by Euclidean correlators at finite hadron momenta, to the light-cone distributions which are accessible in experiments. Previous matching calculations have exclusively focused on twist-2 distributions. In this work, we address, for the first time, the one-loop matching for the twist-3 parton distribution function $g_T(x)$. The results have been obtained using three different infrared regulators, while dimensional regularization has been adopted to deal with the ultraviolet divergences. We present the renormalized expressions of the matching coefficient for $g_{T}(x)$ in the $overline{rm MS}$ and modified $overline{rm MS}$ schemes. We also discuss the role played by a zero-mode contribution. Our results have already been used for the extraction of $g_T(x)$ from lattice QCD calculations.
We present lattice results for the isovector unpolarized parton distribution with nonperturbative RI/MOM-scheme renormalization on the lattice. In the framework of large-momentum effective field theory (LaMET), the full Bjorken-$x$ dependence of a momentum-dependent quasi-distribution is calculated on the lattice and matched to the ordinary lightcone parton distribution at one-loop order, with power corrections included. The important step of RI/MOM renormalization that connects the lattice and continuum matrix elements is detailed in this paper. A few consequences of the results are also addressed here.
Twist-3 partonic distributions contain important information that characterizes nucleons structure. In this work, we show our lattice exploration of the twist-3 PDFs $g_T(x)$, and $h_L(x)$. We also present our preliminary results on the twist-3 GPD $tilde{G}_2(x)$. We use the quasi-distribution approach to connect the lattice-extracted matrix elements, renormalized in the RI/MOM scheme, to light-cone distributions, applying the matching procedure that we developed in parallel. We also calculate the twist-2 counterparts of $g_T(x)$ and $h_L(x)$, i.e. $g_1(x)$, and $h_1(x)$, and test the Wandzura-Wilczek approximation.
In this study, we present continuum limit results for the unpolarized parton distribution function of the nucleon computed in lattice QCD. This study is the first continuum limit using the pseudo-PDF approach with Short Distance Factorization for factorizing lattice QCD calculable matrix elements. Our findings are also compared with the pertinent phenomenological determinations. Inter alia, we are employing the summation Generalized Eigenvalue Problem (sGEVP) technique in order to optimize our control over the excited state contamination which can be one of the most serious systematic errors in this type of calculations. A crucial novel ingredient of our analysis is the parameterization of systematic errors using Jacobi polynomials to characterize and remove both lattice spacing and higher twist contaminations, as well as the leading twist distribution. This method can be expanded in further studies to remove all other systematic errors.
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