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1.4 CP Violation in the Standard Model

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1.4 CP Violation in the Standard Model

1.4.1 The CKM Picture of CP Violation

In the Standard Model (SM) [24] of SU(3)C×SU(2)L×U(1)Y gauge symmetry with three fermion generations, CP violation arises fr om a single phase in the mixing matrix for quarks [3]. Each quark generation consists of three multiplets:

QLI=(ULIDLI)=(3,2)+1/6,uRI=(3,1)+2/3,dRI=(3,1)-1/3, (1.62)

where (3, 2)+1/6 denotes a triplet of SU(3)C, doublet of SU(2)L with hypercharge Y=QT3= +1/6, and similarly for the other representations. The interactions of quarks with the SU(2)L gauge bosons are given by

LW=21gQLiI¯γμτa1ijQLjIWμa, (1.63)

where γμ operates in Lorentz space, τa operates in SU(2)L space and 1 is the unit matrix operating in generation (flavor) space. This unit matrix is written explicitly to make the transformation to mass eigenbasis clearer. The interactions ofquarks with the single Higgs scalar doublet φ(1,2)+1/2 ofthe Standard Model are given by

LY=aeijQLiI¯φdRjIFijQLiI¯ũ˜uRjI+ Hermitian conjugate; (1.64)

where G and F are general complex 3×3 matrices. Their complex nature is the source of CP violation in the Standard Model. With the spontaneous symmetry breaking, SU(2)L×U(1)Y U(1)EM due to φ0, the two components of the quark doublet become distinguishable, as are the three members ofthe Wμ triplet. The charged current interaction in (1.63) is given by

(1.65)

gu

ij

Li

Lj

The mass terms that arise fr om the replacement Re(φ0)12(v+H0) in (1.64) are given by

(1.66)

vGd

vFu

Rj + Hermitian conjugate;

Li

Li

Rj

namely

Md=Gv/2,Mu=Fv/2. (1.67)

The phase information is now contained in these mass matrices. To transform to the mass eigen‐ basis, one defines four unitary matrices such that

VdLMdVdR=Mddiag,VuLMuVuR=Mudiag, (1.68)

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