A new lepton-quark mass relation in a unified theory

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.

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

Modern Physics Letters A ◽

10.1142/s0217732318502309 ◽

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.

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t-quark mass in a super-unified theory

Physics Letters B ◽

10.1016/0370-2693(79)90249-1 ◽

1979 ◽

Vol 82 (3-4) ◽

pp. 392-394 ◽

Cited By ~ 99

Author(s):

Howard Georgi ◽

D.V. Nanopoulos

Keyword(s):

Quark Mass ◽

Unified Theory

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

Modern Physics Letters A ◽

10.1142/s0217732390001359 ◽

1990 ◽

Vol 05 (15) ◽

pp. 1205-1211 ◽

Cited By ~ 48

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.

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