UTfit: First evidence of New Physics in Bs sector

First evidence of New Physics in B_s sector

Reference paper: M. Bona et al. [UTfit Collaboration], "First Evidence of New Physics in b <--> s Transitions" arXiv:0803.0659

We are much indebted to Marco Rescigno, for triggering this analysis and for improving it with several suggestions. We also thank G. Punzi, D. Zieminska and G. Giurgiu for their assistance with the Tevatron experimental results.

We perform an analysis in which New Physics contributions with arbitrary phase is allowed in all sectors (NP in the mixing between the 1-2, 1-3 and 2-3 families), as described in hep-ph/0701204.
We thus obtain a model-independent determination of the CKM parameters ρ and η.
We also determine the |ΔF|=2 amplitudes, which can be used to test any extension of the SM. In particular, combining all the available experimental information, with the UTfit method, we find evidence of a B_s mixing phase larger than what expected in the SM, with a significance exceeding 3σ.

In the following we sketch the method and results which are detailed in arXiv:0803.0659.

The NP contributions to B_s mixing are parametrized using the following general expression:

C_{B_s} e^{2 i φ_{B_s}} =

< B_s|H_eff^full|B_s >

< B_s|H_eff^SM|B_s >

=

A_s^SM e^-2iβ_s+ A_s^NP e^{2i(φ_s^NP-β_s)}

A_s^SM e^-2iβ_s

where H_eff^SM includes only the SM box diagram, while H_eff^full includes also the NP contributions. These definitions imply that the mass differences and the CP asymmetry are related to the SM counterparts by

Δm_s=C_{B_s} ⋅ Δm_s^SM

β_s^exp = β_s - φ_{B_s}

The SM phase β_s is defined as β_s=arg(-(V_tsV_tb^*)/(V_csV_cb^*)) and it is equal to (1.03 ± 0.06)^o in the SM.
Recent experimental developments are now allowing for dramatic improvements in the B_s sector. We use the following experimental inputs:

&Delta m_s measurement (see UTfit page here)
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_{B_s}^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])

We recall here that &Phi_s=2(&beta_s-&phi_{B_s}).

Results
The results of the analysis are summarized in the table below and the 68% and 95% probability regions obtained for C_{B_s}, Φ_{B_s}, C_{B_s} vs Φ_{B_s}, A_s^NP / A_s^SM, Φ_s^NP and A_s^NP / A_s^SM vs Φ_s^NP are shown in the figures.

(EPS) [JPG]

(EPS) [JPG]

RESULT:

C_{B_s} = 1.07 ± 0.29

RESULT:

Φ_{B_s} = (-19.9 ± 5.6)^oU(-68.2 ± 4.9)^o

(EPS) [JPG]

(EPS) [JPG]

(EPS) [JPG]

RESULT:

A_s^NP / A_s^SM= (0.73 ± 0.35)U(1.87 ± 0.06)

RESULT:

Φ_s^NP = (-51 ± 11)^oU(-79 ± 3)^o

(EPS) [JPG]

Results

Parameter	68% probability Region	95% probability Region
&Phi_{B_s}[^o]	(-19.9 ± 5.6)U(-68.2 ± 4.9)	[-30.45,-9.29]U[-78.45,-58.2]
C_{B_s}	1.07 ± 0.29	[0.62,1.93]
&Phi_s^NP[^o]	(-51 ± 11)U(-79 ± 3)	[-69,-27]U[-84,-71]
A_s^NP / A_s^SM	(0.73 ± 0.35)U(1.87 ± 0.06)	[0.24,1.38]U[1.50,2.47]

The result for the phase &Phi_{B_s} deviates from zero at 3.7 σ.
Although the procedure to combine the available measurements still depends on some assumptions, different analyses performed with alternative choices always show a deviation of the value of &Phi_{B_s} from zero of at least 3σ, as it is detailed in arXiv:0803.0659.
We conclude that the combined analysis of the available experimental information gives a stable evidence of NP.