scholarly journals Multiplicative renormalizability and quark propagator

2002 ◽  
Vol 66 (3) ◽  
Author(s):  
J. C. R. Bloch
Keyword(s):  
Quark Propagator ◽  
Multiplicative Renormalizability

NONPERTURBATIVE QUARK PROPAGATOR APPROACH TO QCD AT LARGE DISTANCES

1994 ◽  
Vol 09 (05) ◽  
pp. 759-793 ◽  
Author(s):  
V. SH. GOGOHIA
Keyword(s):  
Gluon Propagator ◽  
Chiral Limit ◽  
Renormalization Constant ◽  
Quark Propagator ◽  
Quark Confinement ◽  
Quark Sector ◽  
Symmetry Breakdown ◽  
Gauge Fixing ◽  
Covariant Gauge ◽  
Multiplicative Renormalizability

A nonperturbative approach to QCD at large distances in the context of the Schwinger-Dyson equations and corresponding Slavnov-Taylor identity in the quark sector is presented. Making only one widely accepted assumption that the full gluon propagator becomes an infrared singular like (q2)−2 in the arbitrary covariant gauge, we find three and only three confinement-type solutions for the quark propagator (quark confinement theorem). Two of them vanish after the removal of the infrared regulation parameter. The third solution does not depend on this latter parameter, but it has no pole and it implies dynamical chiral symmetry breakdown (DCSB), which means a close connection between quark confinement and DCSB. We also show that multiplication solely by the quark infrared renormalization constant would make all the Green’s functions infrared finite (multiplicative renormalizability). The final forms of the renormalized (infrared finite) quark SD equations do not explicitly depend on a gauge-fixing parameter (“gauge invariance”). Our approach is free of ghost complications despite the fact that they play an essential role in nonperturbative dynamics. Our approach also implies the existence of a characteristic scale at which confinement, DCSB and other nonperturbative effects become essential. We solve explicitly the SD equation with corresponding ST identity for the above-mentioned IR finite quark propagator in the chiral limit and apply an effective potential in order to determine completely this solution.

scholarly journals Dynamical quark mass generation in QCD3 within the Hamiltonian approach in Coulomb gauge

2020 ◽  
Vol 229 (22-23) ◽  
pp. 3351-3361
Author(s):  
Felix Spengler ◽  
Davide Campagnari ◽  
Hugo Reinhardt
Keyword(s):  
Mass Function ◽  
Quark Propagator ◽  
Coulomb Gauge ◽  
Hamiltonian Approach ◽  
Mass Generation ◽  
Gap Equation ◽  
Spatial Dimensions ◽  
Dynamical Quark Mass ◽  
Static Quark ◽  
Multiplicative Renormalizability

AbstractWe investigate the equal-time (static) quark propagator in Coulomb gauge within the Hamiltonian approach to QCD in d = 2 spatial dimensions. Although the underlying Clifford algebra is very different from its counterpart in d = 3, the gap equation for the dynamical mass function has the same form. The additional vector kernel which was introduced in d = 3 to cancel the linear divergence of the gap equation and to preserve multiplicative renormalizability of the quark propagator makes the gap equation free of divergences also in d = 2.

scholarly journals Contribution of the Darwin operator to non-leptonic decays of heavy quarks

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Alexander Lenz ◽  
Maria Laura Piscopo ◽  
Aleksey V. Rusov
Keyword(s):  
Standard Technique ◽  
Quark Propagator ◽  
Leptonic Decay ◽  
Leptonic Decays ◽  
Interference Contribution ◽  
The Standard Model ◽  
Strength Tensor ◽  
Quark Flavour ◽  
Quark Decay ◽  
B Quark

Abstract We compute the Darwin operator contribution ($$ 1/{m}_b^3 $$ 1 / m b 3 correction) to the width of the inclusive non-leptonic decay of a B meson (B+, Bd or Bs), stemming from the quark flavour-changing transition b → $$ {q}_1{\overline{q}}_2{q}_3 $$ q 1 q ¯ 2 q 3 , where q1, q2 = u, c and q3 = d, s. The key ideas of the computation are the local expansion of the quark propagator in the external gluon field including terms with a covariant derivative of the gluon field strength tensor and the standard technique of the Heavy Quark Expansion (HQE). We confirm the previously known expressions of the $$ 1/{m}_b^3 $$ 1 / m b 3 contributions to the semi-leptonic decay b → $$ {q}_1\mathrm{\ell}{\overline{\nu}}_{\mathrm{\ell}} $$ q 1 ℓ ν ¯ ℓ , with ℓ = e, μ, τ and of the $$ 1/{m}_b^2 $$ 1 / m b 2 contributions to the non-leptonic modes. We find that this new term can give a sizeable correction of about −4 % to the non-leptonic decay width of a B meson. For Bd and Bs mesons this turns out to be the dominant correction to the free b-quark decay, while for the B+ meson the Darwin term gives the second most important correction — roughly 1/2 to 1/3 of the phase space enhanced Pauli interference contribution. Due to the tiny experimental uncertainties in lifetime measurements the incorporation of the Darwin term contribution is crucial for precision tests of the Standard Model.

scholarly journals THE QUARK CONDENSATE IN THE GELL-MANN-OAKES-RENNER RELATION

1996 ◽  
Vol 11 (16) ◽  
pp. 1331-1337 ◽  
Author(s):  
K. LANGFELD ◽  
C. KETTNER
Keyword(s):  
Quark Propagator ◽  
Quark Condensate ◽  
Usual Definition ◽  
Gluon Exchange ◽  
Current Mass ◽  
Definition Of

The quark condensate which enters the Gell-Mann-Oakes-Renner (GMOR) relation, is investigated in the framework of one-gluon-exchange models. The usual definition of the quark condensate via the trace of the quark propagator produces a logarithmic divergent condensate. In the product of current mass and condensate, this divergence is precisely compensated by the bare current mass. The finite value of the product in fact does not contradict the relation recently obtained by Cahill and Gunner. Therefore the GMOR relation is still satisfied.

scholarly journals Hadronic unquenching effects in the quark propagator

2007 ◽  
Vol 76 (9) ◽  
Author(s):  
Christian S. Fischer ◽  
Dominik Nickel ◽  
Jochen Wambach
Keyword(s):  
Quark Propagator

scholarly journals A machine learning pipeline for autonomous numerical analytic continuation of Dyson-Schwinger equations

2022 ◽  
Vol 258 ◽  
pp. 09003
Author(s):  
Andreas Windisch ◽  
Thomas Gallien ◽  
Christopher Schwarzlmüller
Keyword(s):  
Machine Learning ◽  
Landau Gauge ◽  
Radial Component ◽  
Quark Propagator ◽  
Complex Domain ◽  
Iteration Step ◽  
Integration Contour ◽  
Self Energy ◽  
Contour Deformation ◽  
Branch Cuts

Dyson-Schwinger equations (DSEs) are a non-perturbative way to express n-point functions in quantum field theory. Working in Euclidean space and in Landau gauge, for example, one can study the quark propagator Dyson-Schwinger equation in the real and complex domain, given that a suitable and tractable truncation has been found. When aiming for solving these equations in the complex domain, that is, for complex external momenta, one has to deform the integration contour of the radial component in the complex plane of the loop momentum expressed in hyper-spherical coordinates. This has to be done in order to avoid poles and branch cuts in the integrand of the self-energy loop. Since the nature of Dyson-Schwinger equations is such, that they have to be solved in a self-consistent way, one cannot analyze the analytic properties of the integrand after every iteration step, as this would not be feasible. In these proceedings, we suggest a machine learning pipeline based on deep learning (DL) approaches to computer vision (CV), as well as deep reinforcement learning (DRL), that could solve this problem autonomously by detecting poles and branch cuts in the numerical integrand after every iteration step and by suggesting suitable integration contour deformations that avoid these obstructions. We sketch out a proof of principle for both of these tasks, that is, the pole and branch cut detection, as well as the contour deformation.

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