Across the Present Energy Frontier : Probing the Origin of

mass, Corfu, Greece, 10 - 12 September 2001

Athanasios Dedes

University of Bonn, Germany

Correlation of B_{s} → μ^{+}μ^{−} and (g − 2)_{μ} in Minimal Supergravity

In collaboration with: H. Dreiner and U. Nierste, hep-ph/0108037

We show :

1. the decay B_{s} → μ^{+}μ^{−} is a stringent test of the mSUGRA scenario with large tan β > ∼ 35, in particular when correlated with (g − 2)_{μ}

2. if (g − 2)_{μ} exceeds the Standard Model prediction by 30 · 10^{−10}, B(B_{s} → μ^{+}μ^{−}) is larger by a factor of 100 than in the Standard Model and well within reach of Run-II of the Tevatron.

3. Higgs masses less than 119 GeV are correlated with an enhancement of B(B_{s} → μ^{+}μ^{−}) over the SM value by two orders of magnitude.

4. B(B_{s} → μ^{+}μ^{−}) and (g −2)_{μ} : a threat or discovery for SO(10) GUTS!

Correlation of B_{s} → μ^{+}μ^{−} and (g − 2)_{μ} in Minimal Supergravity,  hep-ph/0108037 1

• Based on Davier-Höcker calculation for the Hadronic contributions to the muon g − 2, BNL reports a 2.6σ deviation from the SM

There are four possible interpretations of this discrepancy :

• a statistical fluctuation with 0.9% probability.

• something is “wrong” with the experiment

• something is “wrong” with the theoretical analysis of the hadronic and/or the light by light contribution to the muon anomalous magnetic moment.

• the by far most exciting possibility:

there is “New Physics” BSM

21.5 × 10^{−10} < ∼ δa_{μ}^{NP} < ∼ 63.7 × 10^{−10} @90% CL

• δa_{μ}^{NP} is positive

• δa_{μ}^{NP} is of the same order of the EW contributions, δa_{μ}^{NP} ∝ \frac{G_{F} m_{μ}^{2}}{4π^{2}\sqrt{2}}

• mSUGRA
(δa_{μ})_{SUSY} ∝ tan β _{\frac{f(M_{0})}{M_{1/2}^{2}}}

invites large tan β > ∼ 10 and M_{1/2} < ∼ 750 GeV

Correlation of B_{s} → μ^{+}μ^{−} and (g − 2)_{μ} in Minimal Supergravity,  hep-ph/0108037 2

• SUSY modifies B-meson observables if tan β is large [⇒ Y_{b} large ]

• Especially sencitive observables : B → X_{s}γ, B → l^{+}l^{−}

• B → X_{s}γ : relies on a cancelation between H^{±} − t and χ̃ − t̃ loops.

• B → l^{+}l^{−} : large for large tan β, almost independent from the sign of μ

B(B_{s} → μ^{+}μ^{−}) ∝ \frac{tan^{6} β}{M_{1/2}^{2}}

So,

B(B_{s} → μ^{+}μ^{−}) ∝ \frac{tan^{5} β (δa_{μ})_{SUSY}}{f(M_{0})}

University of Bonn  2  Athanasios Dedes

Correlation of B_{s} → μ^{+}μ^{−} and (g − 2)_{μ} in Minimal Supergravity,  hep-ph/0108037 3

• Standard Model :

B(B_{s} → μ^{+}μ^{−}) = (3.7 ± 1.2) × 10^{−9} very small!

• Only an experimental bound from CDF Run I

B(B_{s} → μ^{+}μ^{−}) < 2.6 × 10^{−6}, at 95% C.L.

• Future experiment: CDF Run IIa and IIb → 5 × 10^{−7} for 50 events with luminosity 2 fb^{−1} → 5 × 10^{−7} for 250-500 events with luminosity 10-20 fb^{−1}

B(B_{s} → μ^{+}μ^{−}) =

6.0 · 10^{−7} (\frac{|V_{ts}|}{0.040})^{2} (\frac{f_{B_{s}}}{230 MeV})^{2} \frac{m_{μ}^{2}}{m_{B_{s}}^{2}} \sqrt{1 − \frac{4m_{μ}^{2}}{m_{B_{s}}^{2}}}

\{(1 − \frac{4m_{μ}^{2}}{M_{B_{s}}^{2}} ) |\frac{m_{B_{s}}^{2}C_{S}}{m_{μ}} |^{2} + |\frac{m_{B_{s}}^{2}C_{P}}{m_{μ}} − 2C_{A}|^{2}\}.

C_{P}^{self−SUSY} , C_{S}^{self−SUSY} ∝ tan^{3} β

Correlation of B_{s} → μ^{+}μ^{−} and (g − 2)_{μ} in Minimal Supergravity,  hep-ph/0108037 4

C_{A} is tha SM contribution from t − W penguins t − W − ν box. mSUGRA point: M_{1/2} = 450, M_{0} = 350, A_{0} = 0, μ > 0, m_{t} = 175 GeV

Correlation of B_{s} → μ^{+}μ^{−} and (g − 2)_{μ} in Minimal Supergravity,  hep-ph/0108037 7

• Large tan β is well motivated in SO(10)

• In order to avoid various constraints [mainly proton decay, b → sγ, g − 2 and REWSB] it requires : breaking of universality for the Higgs masses, and M_{1/2} << M_{0}.

Example [after a fit] : M_{A} = 110 GeV, tan β ≃ 50, A_{t} > ∼ , 1 TeV, mt̃ < 1 TeV, mχ̃ < 250 GeV implies :

B(B_{s} → μ^{+}μ^{−}) > ∼ 10^{−5} already excluded by CDF

A way out → relax Yukawa unification up to 5-10% and you are just around the corner of the B_{s} → μ^{+}μ^{−} to be discovered at CDF Run IIa !!

Conclusions

√ Striking correlation between the muon anomalous magnetic moment a_{μ} and the branching ratio B(B_{s} → μ^{+}μ^{−}) in mSUGRA scenarios.

√ If the reported excess in a_{μ} is caused by mSUGRA corrections with large tan β, one faces more than an order of magnitude enhancement of B(B_{s} → μ^{+}μ^{−}) over its SM value.

√ Well within reach of Run-II of the Tevatron.

√ The two combined measurements significantly constrain the mSUGRA parameters, allowing a determination of tan β and M_{1/2}.

√ A measurement of B(B_{s} → μ^{+}μ^{−}) will further constrain the mass of the lightest Higgs boson.

√ SO(10) SUSY explanations of the measured a_{μ} are barely compatible with the present upper bound on B(B_{s} → μ^{+}μ^{−}).