scholarly journals A semi-analytic method to compute Feynman integrals applied to four-loop corrections to the $$ \overline{\mathrm{MS}} $$-pole quark mass relation

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Matteo Fael ◽  
Fabian Lange ◽  
Kay Schönwald ◽  
Matthias Steinhauser
Keyword(s):  
Quark Mass ◽  
Numerical Evaluation ◽  
Dimensionless Parameter ◽  
Series Expansions ◽  
Analytic Method ◽  
Coefficient Function ◽  
Mass Relation ◽  
Kinematic Range ◽  
Numerical Accuracy ◽  
Feynman Integrals

Abstract We describe a method to numerically compute multi-loop integrals, depending on one dimensionless parameter x and the dimension d, in the whole kinematic range of x. The method is based on differential equations, which, however, do not require any special form, and series expansions around singular and regular points. This method provides results well suited for fast numerical evaluation and sufficiently precise for phenomenological applications. We apply the approach to four-loop on-shell integrals and compute the coefficient function of eight colour structures in the relation between the mass of a heavy quark defined in the $$ \overline{\mathrm{MS}} $$ MS ¯ and the on-shell scheme allowing for a second non-zero quark mass. We also obtain analytic results for these eight coefficient functions in terms of harmonic polylogarithms and iterated integrals. This allows for a validation of the numerical accuracy.

scholarly journals Pentagon functions for scattering of five massless particles

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
D. Chicherin ◽  
V. Sotnikov
Keyword(s):  
Phase Space ◽  
Numerical Evaluation ◽  
Public Library ◽  
Basis Set ◽  
Particle Scattering ◽  
Minimal Basis ◽  
Feynman Integrals ◽  
Analytic Expressions ◽  
Transcendental Functions ◽  
Branch Cuts

Abstract We complete the analytic calculation of the full set of two-loop Feynman integrals required for computation of massless five-particle scattering amplitudes. We employ the method of canonical differential equations to construct a minimal basis set of transcendental functions, pentagon functions, which is sufficient to express all planar and nonplanar massless five-point two-loop Feynman integrals in the whole physical phase space. We find analytic expressions for pentagon functions which are manifestly free of unphysical branch cuts. We present a public library for numerical evaluation of pentagon functions suitable for immediate phenomenological applications.

A new lepton-quark mass relation in a unified theory

1979 ◽  
Vol 86 (3-4) ◽  
pp. 297-300 ◽  
Author(s):  
Howard Georgi ◽  
C. Jarlskog
Keyword(s):  
Quark Mass ◽  
Mass Relation ◽  
Unified Theory

scholarly journals Four-loop corrections to the MSbar-OS quark mass relation and the anomalous magnetic moment of the muon

2016 ◽  
Author(s):  
Matthias Steinhauser ◽  
Alexander Kurz ◽  
Tao Liu ◽  
Peter Marquard ◽  
Alexander Smirnov ◽  
...  
Keyword(s):  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Quark Mass ◽  
Mass Relation

Evaluation of the Wavelike Disturbance in the Kelvin Wave Source Potential

1988 ◽  
Vol 32 (01) ◽  
pp. 44-53 ◽  
Author(s):  
J. J. M. Baar ◽  
W. G. Price
Keyword(s):  
Numerical Evaluation ◽  
Field Component ◽  
Near Field ◽  
Neumann Series ◽  
Series Expansions ◽  
Effective Solution ◽  
Kelvin Wave ◽  
Wave Source ◽  
Series Representations ◽  
Single Integral

This paper discusses the numerical evaluation of the characteristic Kelvin wavelike disturbance trailing downstream from a translating submerged source. Mathematically the function describing the wavelike disturbance is expressed as a single integral with infinite integration limits and a rapidly oscillatory integrand. Numerical integration of such integrals is both cumbersome and time-consuming. Attention is therefore focused on two complementary Neumann-series expansions which were originally derived by Bessho [1].2 Numerically stable algorithms are presented for the accurate and efficient evaluation of the two series representations. When used in combination with the Chebyshev expansions for the nonoscillatory near-field component which were recently obtained by Newman [2], the present algorithms provide an effective solution to the numerical difficulties associated with the evaluation of the Kelvin wave source potential.

scholarly journals Parameter-independent quark mass relation in the U(3) × U(3)′ model

2018 ◽  
Vol 33 (39) ◽  
pp. 1850230
Author(s):  
Yoshio Koide ◽  
Hiroyuki Nishiura
Keyword(s):  
Charged Lepton ◽  
Quark Mass ◽  
Mass Matrix ◽  
Mass Relation ◽  
Family Symmetry ◽  
Quark Masses ◽  
Down Quark ◽  
Mass Matrices ◽  
Additional Input ◽  
Matrix Formula

Recently, we have proposed a quark mass matrix model based on U(3) × U(3)[Formula: see text] family symmetry, in which up- and down-quark mass matrices [Formula: see text] and [Formula: see text] are described only by complex parameters [Formula: see text] and [Formula: see text], respectively. When we use charged lepton masses as additional input values, we can successfully obtain predictions for quark masses and Cabibbo–Kobayashi–Maskawa mixing. Since we have only one complex parameter [Formula: see text] for each mass matrix [Formula: see text], we can obtain a parameter-independent mass relation by using three equations for [Formula: see text], [Formula: see text] and [Formula: see text], where [Formula: see text] ([Formula: see text]). In this paper, we investigate the parameter-independent feature of the quark mass relation in the model.

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 Numerical Evaluation of Feynman Integrals by a Direct Computation Method

2009 ◽  
Author(s):  
Fukuko Yuasa ◽  
Tadashi Ishikawa ◽  
Junpei Fujimoto ◽  
Nobuyuki HAMAGUCHI ◽  
Elise de Doncker ◽  
...  
Keyword(s):  
Numerical Evaluation ◽  
Computation Method ◽  
Direct Computation ◽  
Feynman Integrals

FORMATION OF COMPOSITE HIGGS BOSONS FROM QUARK-ANTIQUARKS AT LOWER ENERGY SCALES

1990 ◽  
Vol 05 (15) ◽  
pp. 1205-1211 ◽  
Author(s):  
MAHIKO SUZUKI
Keyword(s):  
Higgs Boson ◽  
Quark Mass ◽  
Lower Energy ◽  
Energy Scale ◽  
Higgs Bosons ◽  
Mass Relation ◽  
Composite Higgs ◽  
Quark Interaction ◽  
200 Gev ◽  
Simple Mass

We study how the simple predictions of the Nambu-Jona-Lasinio model of composite Higgs bosons are modified when quark interactions more singular than the nonderivative four-quark interaction are added. The t-quark mass is no longer restricted to ≳ 200 GeV, the simple mass relation between the t-quark and the scalar Higgs boson is lost, and the energy scale of the quark couplings can be chosen as low as we wish. Implications in experimental testability of this class of models are briefly discussed.

Sign in / Sign up

Export Citation Format

Share Document