Abstract
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.
Highlights
The biggest uncertainties for beyond the SM heavy particle production
In this study, we present continuum limit results for the unpolarized parton distribution function of the nucleon computed in lattice QCD
Since this approach would use the same type of matrix elements as in Large Momentum Effective Theory (LaMET), LaMET and Short Distance Factorization (SDF) are intimately related in their factorization theorems, but provide two distinct limits for approaching the light-cone distributions with their different power corrections
Summary
As described in [118], parton distributions can be described in terms of a boost invariant matrix element called the Ioffe time distribution (ITD), whose Fourier transform gives the standard PDFs. Within this double ratio the renormalization constants all cancel explicitly and nonperturbatively, in a way independent of the renormalization scheme, making the reduced pseudo-ITD a RGI quantity [9] The matching of this object to the MS ITD lacks the scheme dependent systematic errors which have been observed in calculations of the related quasi-PDF quantities [37, 68], which so far have always used different variants of RI-MOM schemes. The higher twist, as well as lattice spacing, finite volume, and unphysical pion mass, systematic errors are all being reduced, and this fact has been observed in [74, 75, 86, 100] This particular choice of ratio cancels correlated fluctuations between the terms in the numerator and denominator for small momenta and for small separation data, leading to a measurable improvement of the signal-to-noise ratio of the pertinent matrix element. With sufficient number of terms, this power series approximates the convolution integrals to numerical precision
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