Solving the SUSY Flavour and CP Problems with SU (3) Family

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These previous analyses of the SUSY flavour and CP issues were based on the gravity mediated or SUGRA type of SUSY breaking, together with SU (3) family symmetry. At this point, it is worth commenting on the would-be higher-order corrections due to multiple φ3 and/or φ̄3 insertions, that (due to the relatively large associated expansion parameters ε3 and ε̄3 ) could in principle alter the leading order structure of the expansion above. In these analyses, it is not clear how much of the suppressions are arising from SUGRA and how much are from the SU (3) family symmetry. 4 × (500 GeV/hm̃ i 2 tan β effects are negligible for tan β ∼ 10) |(δRR 12 u RR ) × ε ε̄ ∼ u ) | ∼ 0. an extra relative phase between the two SU (2)R components of the φ3 VEV) does not work in the current model because the net effect of such an extra phase on the diagonalization matrices can be reabsorbed upon getting the resulting CKM matrix into the standard form. Note also that there is in principle at least two distinct types of messengers entering the formula (2. 55) A22 U22 A12 U22 + U12 A21 U12 + U11 A11 U12 + U12 Im(Ã)12 = Im U11 Taking into account the hierarchical nature of the SCKM rotations, A11 = 0 is very welcome as the potentially dangerous first terms in (3. Such parametrizations have been proposed based on symmetric Yukawa matrices with the (1, 1) elements being zero, allowing the successful fermion mass relations to emerge. Once electroweak symmetry is broken, the SU (2)L doublets QL , LL decompose into uL , dL and νL , eL components and so do the corresponding superpartners Q̃ and L̃. In the real world where SU (3) family symmetry is spontaneously broken by flavons VEVs, non-universal soft masses and CP violating effects may be expanded as powers of the symmetry breaking flavon VEVs, leading to suppressed and calculable effects. 50) yields the canonically normalized charged sector Yukawa matrices in the form: u ε2 ε̄ y u ε2 ε̄ O(ε4 ε̄3 ) y12 13 u 2 u ε2 y u ε2 + . In the present section we shall see that SU (3) family symmetry provides an alternative resolution to the SUSY flavour problem, in which the non-universal soft masses are proportional to Yukawa couplings, leading to small violations of universality involving the first and second families, and larger violations of universaility involving the third family, consistently with the constraints in the Tables. 44)) which obeys: Ã ≈ A0 cos θ2 eiρ sin θ2 − sin θ2 eiφ ei(φ+ρ) cos θ2 !† 0 γ1 γ2 δeiψ ! cos θ1 eiφ ei(φ+ρ) sin θ1 − sin θ1 eiρ cos θ1 ! (3. 19) 23 y3u ε23 y3u ε23 c c c y2u y2u 1 y2u k2u 1 2 k3u 1 2 k3u u,R u,R = u , t13 = u 2 1 + ε3 uc , t31 = 1 + ε3 uc , c y4 2 k0 2 y4u k0u 2 k0 y3 ε3 uc u uc u c c u u u y4 1 k3 y4 k2 2iφ3 y4 2iφ3 1 k3 y4 2iφ3 k2u u,R = u 2+ − − ce e − uc , t32 = − u 2 e c c 2 k0u y3u k0 y3 ε3 2 k0u y3u k0u y3 ε3 tu,L = 12 tu,R 12 tu,R 23 y1u , y4u tu,L 13 = while the corresponding down-quark (and charged lepton) sector quantities are readily obc c c u tained from UL,R upon replacing ε → ε̄, ε3 → ε̄3 , kiu → kid (kiu ), yiu → yid (yie ) respectively. However predicted EDMs in the effective SU (3) family symmetry approach are in fact smaller than those predicted in mSUGRA or CMSSM, being suppressed by approximately one further power of the Cabibbo angle. 29), the strong hierarchy of the Yukawas and soft masses therein renders their running strongly suppressed with respect to the effects induced on the diagonal elements by means of the first term. 57) hence bi ∝ ki and all the nonuniversal bij coefficients in (2. One can again appreciate the similarity of the canonically normalized Yukawa and trilinear couplings (2. In the Super-CKM basis, this possible additional suppression effect is seen most manifestly. M f φ f after the hidden sector field X̂ develops a SUSY-breaking F -term