Atmospheric Neutrinos Can Make Beauty Strange Page: 4 of 33
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Using this machinery we discuss the contribution of a large mixing between
right-handed squarks to the CP-violating parameter SOK. We also use this
formalism to address the constraints on the SUSY contribution that come
from the b -+ s7 radiative decay.
2.1 Effective Hamiltonian
The b -+ s transitions of interest can be described by the following AB = 1
effective Hamiltonian:
6
Ieff = (Ci0i+Ci0i)+C,0,+C0''+ C909 +C'', (1)
where
01 = (s.y"PLcj)(cj 7pPLbi) (2)
02 = (97"PL c)(7,,PL b) (3)
03 = (977 PL b) (97p PL s) (4)
04 = (.i7'PLbj)(j 7p PLsi) (5)
05 = (sy"PLb (7p/,PRS) (6)
06 - (.i7'PLbj)(j7/PRSi) (7)
0 e
Or = m(si6""PRbi)Fy (8)
Om = 8b(sia""TjPRb)G. (9)
Here i and j are color indices (suppressed in color singlet terms), PR,L = (1
75)/2, and op" = 2[y, yv]. The primed operators, which are not generated
at leading order in the Standard Model, are obtained by taking L ++ R
everywhere. Here we have ignored the electroweak penguin operators 07_10
and the contributions to the dipole operators proportional to the s-quark
mass, ms.
Following the standard procedure for incorporating QCD corrections we
match the Wilson coefficients at a high scale to loop diagrams containing
heavy particles present in the full theory, and then use the renormalization
group equations (RGE) to run the coefficients to the low scale where mesons
decay. We incorporate leading order QCD corrections using the anomalous
dimension matrices given in [14]. The initial conditions for the standard3
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Harnik, Roni; Larson, Daniel T.; Murayama, Hitoshi & Pierce, Aaron. Atmospheric Neutrinos Can Make Beauty Strange, article, December 1, 2002; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc780333/m1/4/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.