The recent measurements reported by the Tevatron experiments CDF and D0 allow to perform an analysis for search of NP in the B_s sector. While these constraints do not provide additional information in the context of the Standard Model UT analysis (their impact being limited by the experimental accuracy, compared to the present fit precision), they are very effective in constraining NP effects to the B_s mixing. In our NP analysis we combine the information from the following measurements:

• &Delta m_s measurement
• the semileptonic asymmetry in B_s, A_SL^s ([D0 Collaboration] Phys.Rev.Lett.98:151801,2007)
• the dimuon charged asymmetry, A_SL^&mu&mu ([D0 collaboration] Phys.Rev.D74:092001,2006 ) and CDF collaboration, note 9015.
• the B_s lifetime measurement from flavor specific final states, &tau_Bs^FS ( ALEPH, CDF, DELPHI, D0, OPAL, see ref [19] in arXiv:0803.0659 and HFAG)
• the two-dimensional likelihood ratio for &Delta&Gamma_s and &Phi_s from the time dependent tagged angular analysis of B_s J/&psi &phi ( [CDF collaboration])
• the correlated constraints on &Gamma_s, &Delta&Gamma_s and &Phi_s from the analysis of B_s J/&psi &phi ( [D0 collaboration])

The last two measurements are the most sensitive to NP contributions to the mixing phase. And indeed both the experiments report a (not yet significative) deviation from the SM expecation values. In addition, it is important to stress the very good agreement between the values quoted by the two experiments. Our analysis uses the likelihood shapes as provided by CDF and D0.

• A_SL and New Physics effects
• Dimuon Charge Asymmetry A_CH
• Width Difference ΔΓ_q
• Predictions for Semi-leptonic and Dimuon Charge Asymmetries in SM and in NP scenarios

One can also add the constraint coming from the CP asymmetry in semi-leptonic B decays A_SL, defined as

It has been noted in hep-ph/0202010 that A_SL is a crucial ingredient of the UT analysis once the formulae are generalized as described below, since it depends on both C_Bd and φ_Bd. Infact, we can write:

where Γ₁₂ and M₁₂ are the absorptive and dispersive parts of the B⁰_d-B⁰_d mixing amplitude.

At the leading order, A_SL is independent of penguin operators, but, at the NLO, the penguin contribution should be taken into account. In the SM, the effect of penguin operators is GIM suppressed since their CKM factor is aligned with M₁₂: both are proportional to (V*_tbV_td)². This is not true anymore in the presence of NP, so that the effects of penguins are amplified beyond the SM. We therefore start from the full NLO calculation of hep-ph/0308029, allowing for an additional NP contribution to the penguin term in the |Δ F |=1 amplitude. This introduces two additional parameters C_Pen and φ_Pen that, because of the extra α_s factor, enter as a smearing in the expression of A_SL. The generalized expression of A_SL is given in hep-ph/0509219

BaBar has recently released a new improved A_SL measurement that in association with the quantity A_CH described in the following allows for further constraining the φ_Bd and C_Bd; NP parameters. As can be seen below, the actual measurements of these two observables strongly disfavour the solution with ρ and η in the third quadrant, which now has only 0.4% probability.
Here we show the one-dimensional distributions for this quantity both in the Standard Model fit (left plot) and in the New Physics general scenario (right plot). See the table for the numerical results.

(EPS) [JPG]

(EPS) [JPG]

The charge asymmetry A_CH in dimuon events is a rather unique constraint since it depends on ρ and η and on all ΔB=2 NP parameters (C_Bd, φ_Bd, C_Bs, and φ_Bs). D0 Collaboration has recently announced a new result for this observable. The dimuon charge asymmetry A_CH can be defined as:

using the notation as in the D0 result where the definition and the measured values for the P parameters can be found. We have:

where we have assumed equal semi-leptonic widths for B_d andn B_s mesons, f_d = 0.397 ± 0.010 and f_s = 0.107 ± 0.011 are the production fractions of B_d and B_s mesons respectively and the χ_q and χ_q are given in equation 6 in . They contain the dependence (through equations 7 in the same ref.) on the ΔB=2 NP parameters (C_Bd, φ_Bd, C_Bs, and φ_Bs) as well as the possible NP contributions to ΔB=1 penguins (C_q^Pen, φ_q^Pen).
Here we show the one-dimensional distributions for this quantity both in the Standard Model fit (left plot) and in the New Physics general scenario (right plot) See the table for the numerical results.

(EPS) [JPG]

(EPS) [JPG]

In presence of New Physics, the measurement of ΔΓ_q is related to ρ and η, and to the NP parameters C_Bq and φ_Bq through the value of Δm_q: you can find the relation here (eq. 7 in hep-ph/0605213) A simultaneous use of Δm_q and of the bound from ΔΓ_q allows to constrain the phase of the mixing even without a direct measurement of the mixing phase. This is particularly important in the case of the B_s sector, waiting for the measurement on the time-dependent CP asymmetry in B_s → J/ψ φ Since the available experimental measurements are not directly sensitive to the phase of the mixing amplitude, they are actually a measurement of &Delta&Gamma_q cos2(φ_Bq- β_q) in the presence of NP.

We add here the prediction on the quantities previously described: A_SL, A_CH, ΔΓ_q/Γ_q. These are obtained from the fully model-independent fit without using the given quantities. The values represent the allowed ranges in this generalized framework. For comparison also the SM values are given together with the experimental measurements.