scholarly journals Exact results for $$ {Z}_m^{\mathrm{OS}} $$ and $$ {Z}_2^{\mathrm{OS}} $$ with two mass scales and up to three loops

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Matteo Fael ◽  
Kay Schönwald ◽  
Matthias Steinhauser
Keyword(s):  
Wave Function ◽  
Quark Mass ◽  
Numerical Evaluation ◽  
Large Mass ◽  
Equal Mass ◽  
Exact Results ◽  
Loop Order ◽  
Wave Function Renormalization ◽  
Shell Mass ◽  
Renormalization Constants

Abstract We consider the on-shell mass and wave function renormalization constants $$ {Z}_m^{\mathrm{OS}} $$ Z m OS and $$ {Z}_2^{\mathrm{OS}} $$ Z 2 OS up to three-loop order allowing for a second non-zero quark mass. We obtain analytic results in terms of harmonic polylogarithms and iterated integrals with the additional letters $$ \sqrt{1-{\tau}^2} $$ 1 − τ 2 and $$ \sqrt{1-{\tau}^2}/\tau $$ 1 − τ 2 / τ which extends the findings from ref. [1] where only numerical expressions are presented. Furthermore, we provide terms of order $$ \mathcal{O} $$ O (ϵ2) and $$ \mathcal{O} $$ O (ϵ) at two- and three-loop order which are crucial ingredients for a future four-loop calculation. Compact results for the expansions around the zero-mass, equal-mass and large-mass cases allow for a fast high-precision numerical evaluation.

scholarly journals MOMENTUM EXPANSION OF MASSIVE TWO-LOOP FEYNMAN GRAPHS AROUND A FINITE VALUE

2000 ◽  
Vol 15 (07) ◽  
pp. 509-515 ◽  
Author(s):  
ADRIAN GHINCULOV ◽  
YORK-PENG YAO
Keyword(s):  
Wave Function ◽  
Numerical Integration ◽  
Special Functions ◽  
Wave Function Renormalization ◽  
Self Energy ◽  
Feynman Graphs ◽  
Algebraic Reduction ◽  
Standard Set ◽  
B Quark ◽  
Renormalization Constants

We give an algorithm for obtaining expansions of massive two-loop Feynman graphs in powers of the external momentum around a finite, nonzero value of the momentum. Such momentum derivatives are encountered while evaluating physical radiative corrections, such as in wave function renormalization constants. This is based on our general two-loop formalism to reduce massive two-loop graphs with renormalizable interactions into a standard set of special functions. After the algebraic reduction, the final results are obtained by numerical integration. We apply the expansion algorithm to treat the top-dependent corrections of [Formula: see text] to the b-quark self-energy and extract its momentum expansion on-shell.

scholarly journals Non-perturbative determination of cV, ZV and ZS/ZP in Nf = 3 lattice QCD

2018 ◽  
Vol 175 ◽  
pp. 10004 ◽  
Author(s):  
Jochen Heitger ◽  
Fabian Joswig ◽  
Anastassios Vladikas ◽  
Christian Wittemeier
Keyword(s):  
Lattice Qcd ◽  
Quark Mass ◽  
Numerical Evaluation ◽  
Vector Current ◽  
Tree Level ◽  
Gauge Action ◽  
Renormalization Factor ◽  
Preliminary Results ◽  
Renormalization Constants

We report on non-perturbative computations of the improvement coefficient cV and the renormalization factor ZV of the vector current in three-flavour O(a) improved lattice QCD with Wilson quarks and tree-level Symanzik improved gauge action. To reduce finite quark mass effects, our improvement and normalization conditions exploit massive chiral Ward identities formulated in the Schrödinger functional setup, which also allow deriving a new method to extract the ratio ZS/ZP of scalar to pseudoscalar renormalization constants. We present preliminary results of a numerical evaluation of ZV and cV along a line of constant physics with gauge couplings corresponding to lattice spacings of about 0:09 fm and below, relevant for phenomenological applications.

scholarly journals WAVE FUNCTION RENORMALIZATION PRESCRIPTION OF UNSTABLE PARTICLE

2006 ◽  
Vol 21 (36) ◽  
pp. 2763-2777 ◽  
Author(s):  
YONG ZHOU
Keyword(s):  
Wave Function ◽  
Gauge Theory ◽  
Conservation Law ◽  
New Wave ◽  
Wave Function Renormalization ◽  
Reduction Formula ◽  
Renormalization Condition ◽  
Gauge Dependence ◽  
Unstable Particles ◽  
Renormalization Constants

We define four Wave function Renormalization Constants (WRCs) for unstable particles under the LSZ reduction formula. By CPT conservation law we obtain a new wave function renormalization condition and determine the four WRCs. By calculating the gauge dependence of the physical amplitudes we demonstrate the consistency of the current wave function renormalization prescription with the gauge theory in standard model. We also prove that the conventional wave function renormalization prescription leads to physical amplitudes of gauge dependent.

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