By Andrija Rasin

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44. 58 [2 . 46) The decay p--, K°ei The decay p --* K°ei r(p---_ • . 003GeV z) ( 1301_eV f. )2 ( 101rGeV M_ )2 (1TeV" X X I [UQ(VTUL)'' . 70 12 . 48), and those are given, via UQ and U L, by the flavor structure of the underlying SUSY GUT. 37) h" = 2 hQ = symmetric, If we go to the basis of mass eigenstates h d = h LT = heT. 49) for up quarks (h" -- diag(A,,,Ac, At)) and charged leptons (h e = diag(Ae, A_,,A_)) , hQ also becomes diagonal with the same values as h_, up to two phases (phases cannot be absorbed by redefinition of Q fields: their phases are already fixed by requiring the diagonal h_ to be real), while hd = h LT = h • V_?

The smallnessand hierarchy of fermionmassesand mixingscan be restated in termsofapproximatechiral and flavor symmetrieswhichacton eachfermion type([3]-[5]). 13) become approximate [s_sz31, etc. Hence these approximate sufficient to guarantee alone one finds that the equalities, chiral and flavor symmetries powerful means, for example by some new exact symmetry. 2). These results follow only if the 11, 13 and 31 entries of the Yukawa matrices are constrained . thus [s131 ans_tze, family symmetries by some more In many specific force these to vanish([9],[64],[63],[15]).

41) with winos produces which contribute the effective to nucleon decays[84]: _ -- 1 a q n Mc2_r[U;kU_, - U,QU_](u,_)(uke,)[f(_,_,,) + f(fij,d_)] L=dd_ _ - 1 a rUq r rL M. 38), we generate five are the triangle diagram running through the triangle. 42) matrix (at the weak scale) and of left handed up and down quarks, respectively. factors, which are functions of scalar masses For simplicity we assume all the scalars to be of the same mass, and we set from now on all the f's equal. _, , ,.. 40).

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Flavor symmetries and fermion masses by Andrija Rasin

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