Minkowski space pion model inspired by lattice QCD running quark mass

Abstract We perform a lattice study of double parton distributions in the pion, using the relationship between their Mellin moments and pion matrix elements of two local currents. A good statistical signal is obtained for almost all relevant Wick contractions. We investigate correlations in the spatial distribution of two partons in the pion, as well as correlations involving the parton polarisation. The patterns we observe depend significantly on the quark mass. We investigate the assumption that double parton distributions approximately factorise into a convolution of single parton distributions.

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Isospin-1/2 Dπ scattering and the lightest $$ {D}_0^{\ast } $$ resonance from lattice QCD

Journal of High Energy Physics ◽

10.1007/jhep07(2021)123 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Luke Gayer ◽

Nicolas Lang ◽

Sinéad M. Ryan ◽

David Tims ◽

Christopher E. Thomas ◽

...

Keyword(s):

Scattering Amplitudes ◽

Lattice Qcd ◽

Quark Mass ◽

Light Quark ◽

Energy Levels ◽

Experimental Result ◽

Infinite Volume ◽

Resonance Pole ◽

Strongly Coupled ◽

Light Quark Mass

Abstract Isospin-1/2 Dπ scattering amplitudes are computed using lattice QCD, working in a single volume of approximately (3.6 fm)3 and with a light quark mass corresponding to mπ ≈ 239 MeV. The spectrum of the elastic Dπ energy region is computed yielding 20 energy levels. Using the Lüscher finite-volume quantisation condition, these energies are translated into constraints on the infinite-volume scattering amplitudes and hence enable us to map out the energy dependence of elastic Dπ scattering. By analytically continuing a range of scattering amplitudes, a $$ {D}_0^{\ast } $$ D 0 ∗ resonance pole is consistently found strongly coupled to the S-wave Dπ channel, with a mass m ≈ 2200 MeV and a width Γ ≈ 400 MeV. Combined with earlier work investigating the $$ {D}_{s0}^{\ast } $$ D s 0 ∗ , and $$ {D}_0^{\ast } $$ D 0 ∗ with heavier light quarks, similar couplings between each of these scalar states and their relevant meson-meson scattering channels are determined. The mass of the $$ {D}_0^{\ast } $$ D 0 ∗ is consistently found well below that of the $$ {D}_{s0}^{\ast } $$ D s 0 ∗ , in contrast to the currently reported experimental result.

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Quark Mass Functions and Pion Structure in Minkowski Space

Few-Body Systems ◽

10.1007/s00601-014-0863-x ◽

2014 ◽

Vol 55 (8-10) ◽

pp. 705-708 ◽

Cited By ~ 2

Author(s):

Elmar P. Biernat ◽

Franz Gross ◽

M. T. Peña ◽

Alfred Stadler

Keyword(s):

Minkowski Space ◽

Quark Mass ◽

Pion Structure ◽

Mass Functions

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Chiral Fermions Algorithms In Lattice QCD

East European Journal of Physics ◽

10.26565/2312-4334-2019-1-02 ◽

2019 ◽

Keyword(s):

Lattice Qcd ◽

Quark Mass ◽

Optimal Algorithm ◽

Quark Propagator ◽

Critical Slowing Down ◽

Group Symmetry ◽

Inversion Algorithm ◽

Four Dimensions ◽

Slowing Down ◽

Lattice Gauge

The theory that explains the strong interactions of the elementary particles, as part of the standard model, it is the so-called Quantum Chromodynamics (QCD) theory. In regimes of low energy this theory it is formulated and solved in a lattice with four dimensions using numerical simulations. This method it is called the lattice QCD theory. Quark propagator it the most important element that is calculated because it contains the physical information of lattice QCD. Computing quark propagator of chiral fermions in lattice means that we should invert the chiral Dirac operator, which has high complexity. In the standard inversion algorithms of the Krylov subspace methods, that are used in these kinds of simulations, the time of inversion is scaled with the inverse of the quark mass. In lattice QCD simulations with chiral fermions, this phenomenon it is knowing as the critical slowing-down problem. The purpose of this work is to show that the preconditioned GMRESR algorithm, developed in our previous work, solves this problem. The preconditioned GMRESR algorithm it is developed in U(1) group symmetry using QCDLAB 1.0 package, as good “environment” for testing new algorithms. In this paper we study the escalation of the time of inversion with the quark mass for this algorithm. It turned out that it is a fast inversion algorithm for lattice QCD simulations with chiral fermions, that “soothes” the critical slowing-down of standard algorithms. The results are compared with SHUMR algorithm that is optimal algorithm used in these kinds of simulations. The calculations are made for 100 statistically independent configurations on 64 x 64 lattice gauge U(1) field for three coupling constant and for some quark masses. The results showed that for the preconditioned GMRESR algorithm the coefficient k, related to the critical slowing down phenomena, it is approximately - 0.3 compared to the inverse proportional standard law (k = -1) that it is scaled SHUMR algorithm, even for dense lattices. These results make more stable and confirm the efficiency of our algorithm as an algorithm that avoid the critical slowing down phenomenon in lattice QCD simulations. In our future studies we have to develop the preconditioned GMRESR algorithm in four dimensions, in SU (3) lattice gauge theory.

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The goldstone pion in SU(2) lattice QCD at low quark mass: Scaling and finite size effects

Nuclear Physics B ◽

10.1016/0550-3213(86)90327-5 ◽

1986 ◽

Vol 271 (2) ◽

pp. 461-496 ◽

Cited By ~ 2

Author(s):

A. Billoire ◽

R. Lacaze ◽

E. Marinari ◽

A. Morel

Keyword(s):

Lattice Qcd ◽

Size Effects ◽

Quark Mass ◽

Finite Size ◽

Finite Size Effects ◽

Mass Scaling

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QCD Factorization and PDFs from Lattice QCD Calculation

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194515600411 ◽

2015 ◽

Vol 37 ◽

pp. 1560041 ◽

Cited By ~ 20

Author(s):

Yan-Qing Ma ◽

Jian-Wei Qiu

Keyword(s):

Euclidean Space ◽

Minkowski Space ◽

Lattice Qcd ◽

Correlation Functions ◽

Parton Distribution ◽

Distribution Functions ◽

Matrix Elements ◽

Parton Distribution Functions ◽

Qcd Factorization ◽

The Matrix

In this talk, we review a QCD factorization based approach to extract parton distribution and correlation functions from lattice QCD calculation of single hadron matrix elements of quark-gluon operators. We argue that although the lattice QCD calculations are done in the Euclidean space, the nonperturbative collinear behavior of the matrix elements are the same as that in the Minkowski space, and could be systematically factorized into parton distribution functions with infrared safe matching coefficients. The matching coefficients can be calculated perturbatively by applying the factorization formalism on to asymptotic partonic states.

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