Pion distribution amplitude from lattice QCD

Zhang, Jian Hui; Chen, Jiunn-Wei; Ji, Xiangdong; Jin, Luchang; Lin, Huey‐Wen

doi:10.1103/physrevd.95.094514

Cited by 171 publications

(186 citation statements)

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“…If one takes z = (z − , z ⊥ ) in the α = + component of M α , the z α -part drops out, and one can introduce a TMD F(x, k 2 ⊥ ) that is related to M p (ν, z 2 ⊥ ) by the scalar formula (6). For quasi-distributions, the easiest way to remove the z α contamination is to take the time component of M α (z = z 3 , p) and define…”

Section: B Quantum Chromodynamics (Qcd) Casementioning

confidence: 99%

Quasi-parton distribution functions, momentum distributions, and pseudo-parton distribution functions

2017

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We show that quasi-PDFs may be treated as hybrids of PDFs and primordial rest-frame momentum distributions of partons. This results in a complicated convolution nature of quasi-PDFs that necessitates using large p3 3 GeV momenta to get reasonably close to the PDF limit. As an alternative approach, we propose to use pseudo-PDFs P(x, z 2 3 ) that generalize the light-front PDFs onto spacelike intervals and are related to Ioffe-time distributions M(ν, z 2 3 ), the functions of the Ioffe time ν = p3z3 and the distance parameter z 2 3 with respect to which it displays perturbative evolution for small z3. In this form, one may divide out the z 2 3 dependence coming from the primordial rest-frame distribution and from the problematic factor due to lattice renormalization of the gauge link. The ν-dependence remains intact and determines the shape of PDFs.

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Section: B Quantum Chromodynamics (Qcd) Casementioning

confidence: 99%

Quasi-parton distribution functions, momentum distributions, and pseudo-parton distribution functions

2017

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“…In contrast, in the LaMET-based approach of [5] formally a Fourier transform over all values of z is taken, and smallness of perturbative and higher twist corrections is achieved indirectly by considering the asymptotic expansion of the amplitude at large values of the pion momentum for a fixed quark momentum fraction u, which is the Fourier conjugate of p · z. Thus |p| → ∞ implies that the integration region in the Fourier integral shrinks to |z| ∼ 1/|p| → 0.…”

Section: Introductionmentioning

confidence: 99%

“…The same DA has recently been studied using the quasidistribution approach in Ref. [5]. We consider a correlation function of renormalized scalar and pseudoscalar operators at equal times…”

Section: Introductionmentioning

confidence: 99%

“…These models and the corresponding Fourier-transformed position space DAs The main difference of our technique [1] to the approach of Ref. [5] is that the smallness of higher twist and perturbative corrections (for arbitrary pion momentum) is guaranteed by keeping the distance |z| between the currents sufficiently small. A large pion momentum is needed not in order to suppress the corrections, but because it provides the necessary lever arm in the dimensionless variable p · z that is mandatory to distinguish between pion DAs of different shape, see Fig.…”

Section: Introductionmentioning

confidence: 99%

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Pion distribution amplitude from Euclidean correlation functions

et al. 2018

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Following the proposal in (Braun and Müller. Eur Phys J C55:349, 2008), we study the feasibility to calculate the pion distribution amplitude (DA) from suitably chosen Euclidean correlation functions at large momentum. In our lattice study we employ the novel momentum smearing technique (Bali et al. Phys Rev D93:094515, 2016; Bali et al. Phys Lett B774:91, 2017). This approach is complementary to the calculations of the lowest moments of the DA using the Wilson operator product expansion and avoids mixing with lower dimensional local operators on the lattice. The theoretical status of this method is similar to that of quasidistributions (Ji. Phys Rev Lett 110:262002, 2013) that have recently been used in (Zhang et al. Phys Rev D95:094514, 2017) to estimate the twist two pion DA. The similarities and differences between these two techniques are highlighted.

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“…Finally, for completeness we mention that Ji's approach can also be used to compute distribution amplitudes (DAs), as shown in Refs. [25,26].…”

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Progress in computing parton distribution functions from the quasi-PDF approach

et al. 2018

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Abstract. We discuss the current developments by the European Twisted Mass Collaboration in extracting parton distribution functions from the quasi-PDF approach. We concentrate on the non-perturbative renormalization prescription recently developed by us, using the RI ′ scheme. We show results for the renormalization functions of matrix elements needed for the computation of quasi-PDFs, including the conversion to the MS scheme, and for renormalized matrix elements. We discuss the systematic effects present in the Z-factors and the possible ways of addressing them in the future.

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Pion distribution amplitude from lattice QCD

Cited by 171 publications

References 58 publications

Quasi-parton distribution functions, momentum distributions, and pseudo-parton distribution functions

Quasi-parton distribution functions, momentum distributions, and pseudo-parton distribution functions

Pion distribution amplitude from Euclidean correlation functions

Progress in computing parton distribution functions from the quasi-PDF approach

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