$LoadPhi = True ; $LoadFeynArts = True ;

Needs["HighEnergyPhysics`FeynCalc`"] ;

FeynCalc 4.2.0
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FeynArts 3.1

by Hagen Eck, Sepp Kueblbeck, and Thomas Hahn

last revised 12 Feb 03

patched for use with FeynCalc by Frederik Orellana

•UQuarkMassMatrix

UQuarkMassMatrix is one of the built-in objects of PHI.  It is an iso-matrix, and therefore has head UMatrix.  Since it takes other options than the ones of UMatrix, it is defined by UQuarkMassMatrix[opts] := UMatrix[UQuarkMass[opts],opts], where the relevant options are threaded down to each function.

Options[UMatrix] // StandardForm

{SUNN -> 2, UDimension -> Automatic}

Options[UQuarkMass] // StandardForm

{Explicit -> True, QuarkToMesonMasses -> True, DiagonalToU -> False, SUNN -> 2, UDimension -> Automatic}

The default settings correspond to the SU(2) matrix with a large quark condensate and to lowest order in the quark masses:

UQuarkMassMatrix[SUNN -> 2] // Simplify

((m _ π^(ó  ))^2 ÷¬öé)/(2 !, _ 0^( ))

UTrace[%, SUNN -> 2]

(m _ π^(ó  ))^2/!, _ 0^( )

In SU(3) it is sometimes usefull to split a diagonal matrix up in a linear combination of generator matrices (and the identity matrix):

UQuarkMassMatrix[QuarkToMesonMasses -> False, DiagonalToU -> True, SUNN -> 3]

m _ s^(ó  ) (÷¬öé/3 - σ^8/3^(1/2)) + m _ d^(ó  ) (÷¬öé/3 - σ^3/2 + σ^8/(2 3^(1/2))) + m _ u^(ó  ) (÷¬öé/3 + σ^3/2 + σ^8/(2 3^(1/2)))

UTrace[%, SUNN -> 3]

m _ d^(ó  ) + m _ u^(ó  ) + m _ s^(ó  )

To write out in components use WriteOutIsoVectors and WriteOutUMatrices:

UQuarkMassMatrix[QuarkToMesonMasses -> False, DiagonalToU -> True, SUNN -> 3] // WriteOutIsoVectors // WriteOutUMatrices // Simplify

( ó  ) m u 0 0 ó  m 0 d 0 ó  m 0 0 s

The trace is the same as before:

UTrace[%, SUNN -> 3]

m _ d^(ó  ) + m _ u^(ó  ) + m _ s^(ó  )

Converted by Mathematica  (July 10, 2003)