Inequality of pseudoscalar-meson wave function renormalization constants and its experimental consequences

1975 ◽  
Vol 13 (8) ◽  
pp. 297-301 ◽  
Author(s):  
A. Ebrahim
Keyword(s):  
Wave Function ◽  
Pseudoscalar Meson ◽  
Wave Function Renormalization ◽  
Meson Wave Function ◽  
Renormalization Constants

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 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.

Lattice pseudoscalar-meson wave-function properties

1988 ◽  
Vol 38 (3) ◽  
pp. 954-961 ◽  
Author(s):  
Thomas A. DeGrand ◽  
Richard D. Loft
Keyword(s):  
Wave Function ◽  
Pseudoscalar Meson ◽  
Meson Wave Function
Sign in / Sign up

Export Citation Format

Share Document