/ 06 03 25 1 v 1 3 0 M ar 2 00 6 DESY 06 - 033 Constraint on Right - Handed Squark Mixings from B s − B̄ s Mass Difference

We point out that the right-handed squark mixings can sizably enhance SUSY contributions to ∆Ms by taking into account renormalization group effects via the CKM matrix. The recent result of ∆Ms from the DØ experiment at the Tevatron thus implies a strong constraint on the right-handed mixings. Effects of the underlying physics at high energy scale are imprinted not only in flavor structures of the matters in the standard model (SM), but also in those of their superpartners by extending the SM to include supersymmetry (SUSY). They evolve from the cutoff scale to a low energy via the renormalization running, and are recognized through signals of the flavor-changing neutral currents (FCNCs). The b̃− s̃ mixings of the right-handed squarks have attracted a lot of interests [1] in the light of the discovery of the neutrino oscillations with large mixing angles [2], and the success of the supersymmetric grand unification. The mixings are parameterized by the flavorchanging components between b̃R − s̃R and b̃L − s̃R in the mass matrices, which are called the RR and RL mixings, respectively. At the weak scale, they contribute to b→ s transition processes. Some golden modes have been already measured precisely in experiments, and their results are compared to the SM predictions. Particularly, the measured branching ratio of the inclusive Bd → Xsγ decay is known to agree well with the SM value [3, 4]. Thus it provides one of the severest constraints on the down-type squark mixings, including the RR and RL mixings. Even with the constraint from Br(b→ sγ), there is still left large possibility to detect sizable effects on some b → s processes, especially, from the right-handed squark mixings. Recently, the DØ collaboration have reported the updated result of the mass difference of the Bs mesons [5]: 17 ps < ∆Ms < 21 ps −1 90% C.L. , (1) which is the first result with a direct two-side bound. Although the data includes large uncertainties, this result is in agreement with the SM predictions, which are estimated as 21.3 ± 2.6 ps by the UTfit group [6] and 20.9 −4.2 ps −1 by the CKMfitter group [7]. In the supersymmetric SM, it is known that a combination of the LL and RR mixings, (m d̃LL )23(m 2 d̃RR )23, can enhance the SUSY contributions to ∆Ms sizably [8]. If the LL mixing is suppressed sufficiently, the current data of ∆Ms remains insensitive to the right-handed mixings [9]. In general supersymmetric SM at the weak scale, we may choose the down-type LL squark mixing to vanish. Rather, in realistic models, the mixing tends to be finite because 1 the CKM matrix contributes to the left-handed mass matrix of the down-type squarks during the renormalization group evolutions. In fact, in a class of supergravity mediations, the LL mixing generally gets a correction of (δ LL)23 ∼ λ , where λ ∼ 0.2 is the Wolfenstein parameter. In this letter, we want to emphasize that this tiny mixing is significant for ∆Ms when we discuss the mixings in the right-handed sector. We will show that without any imprinted LL mixing, the RR squark mixing can affect ∆Ms to the level of the SM value satisfying with the bound from Br(b→ sγ). Let us first review the SUSY contributions to ∆Ms. The Bs−B̄s transition is represented by the transition matrix element, M12 = M SM 12 +M SUSY 12 ≡ M SM 12 (1 +R). (2) In terms of R, which corresponds to the SUSY contributions, the mass difference between Bs and B̄s becomes ∆Ms = ∆M SM s |1 + R|. Although the estimation of the SM value contains large hadronic uncertainties, the ratio ∆Ms/∆Md can be predicted more cleanly. Then R is given by |1 +R| = ∆M d ∆MSM s ∆M s ∆M d = MBd MBs 1 ξ2 ∣