Abstract
In large-momentum effective theory (LaMET), calculating parton physics starts from calculating coordinate-space-z correlation functions h˜(z,a,Pz) in a hadron of momentum Pz in lattice QCD. Such correlation functions involve both linear and logarithmic divergences in lattice spacing a, and thus need to be properly renormalized. We introduce a hybrid renormalization procedure to match these lattice correlations to those in the continuum MS‾ scheme, without introducing extra non-perturbative effects at large z. We analyze the effect of O(ΛQCD) ambiguity in the Wilson line self-energy subtraction involved in this hybrid scheme. To obtain the momentum-space distributions, we recommend to extrapolate the lattice data to the asymptotic z-region using the generic properties of the coordinate space correlations at moderate and large Pz, respectively.
Highlights
Parton physics is important both for understanding the dynamics of highenergy collisions of hadrons and for studying their internal structure [1, 2]
An effective field theory (EFT) approach–large momentum effective theory (LaMET)– has been proposed to extract parton physics from physical properties of hadrons moving at large momentum [4, 5], where the latter can be calculated from systematic approximations to Euclidean quantum chromodynamics (QCD) such as lattice field theory
We address several other issues that are important in extracting parton physics using large-momentum effective theory (LaMET), e.g., how to match appropriately to the continuum scheme near z ∼ 0, and how to utilize the asymptotic behavior of relevant correlation functions at large light-front (LF) distance to remove the unphysical oscillations in the momentum distribution that arise from truncated Fourier transform
Summary
Parton physics is important both for understanding the dynamics of highenergy collisions of hadrons and for studying their internal structure [1, 2]. The main approaches suggested in practical applications include the regularizationindependent momentum subtraction method or RI/MOM [36, 37, 38, 39] and the ratio method [40, 41, 42, 43] The latter relies on the validity of Euclidean operator product expansion (OPE) and can only be applied to correlations at short distances, and cannot be used directly for LaMET applications. We address several other issues that are important in extracting parton physics using LaMET, e.g., how to match appropriately to the continuum scheme near z ∼ 0, and how to utilize the asymptotic behavior of relevant correlation functions at large light-front (LF) distance to remove the unphysical oscillations in the momentum distribution that arise from truncated Fourier transform
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