Searching for New Physics with $\overline{\mathcal{B}}(B_{s,d}\to \mu \bar{\mu })/\Delta M_{s,d}$

Abstract

We reemphasize that the ratio $R_{s\mu }\equiv \overline{\mathcal{B}}(B_s\to \mu \bar{\mu })/\Delta M_s$ is a measure of the tension of the Standard Model (SM) with latest measurements of $\overline{\mathcal{B}}(B_s\to \mu \bar{\mu })$ that does not suffer from the persistent puzzle on the $|V_{cb}|$ determinations from inclusive versus exclusive $b\to c\ell \bar{\nu }$ decays and which affects the value of the CKM element $|V_{ts}|$ that is crucial for the SM predictions of both $\overline{\mathcal{B}}(B_s\to \mu \bar{\mu })$ and $\Delta M_s$, but cancels out in the ratio $R_{s\mu }$. In our analysis we include higher order electroweak and QED corrections und adapt the latest hadronic input to find a tension of about $2\sigma$ for $R_{s\mu }$ measurements with the SM independently of $|V_{ts}|$. We also discuss the ratio $R_{d\mu }$ which could turn out, in particular in correlation with $R_{s\mu }$, to be useful for the search for New Physics, when the data on both ratios improves. Also $R_{d\mu }$ is independent of $|V_{cb}|$ or more precisely $|V_{td}|$.

14 pages, 2 figures; v2: updated experimental input and added discussion on top-quark-mass dependence, added references, conclusions unchanged; v3: matches published version, updated LHCb references

References in corpus (7)

• Two-Loop Electroweak Corrections for the K -> pi nu anti-nu Decays
• Probing New Physics via the $B_s^0\to {\mu }^{+}{\mu }^{-}$ Effective Lifetime
• Neutral B Meson Mixing in Unquenched Lattice QCD
• The $V_{cb}$ puzzle: an update
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• Neutral $B$ meson mixings and $B$ meson decay constants with static heavy and domain-wall light quarks
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Cited by in corpus (7)

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• The Exclusive Vision of Rare $K$ and $B$ Decays and of the Quark Mixing in the Standard Model
• New Physics in $B_q^0-{\bar{B}}_q^0$ Mixing: Present Challenges, Prospects, and Implications for $B_q^0\to {\mu }^{+}{\mu }^{-}$
• Loopy Determinations of $V_{ub}$ and $V_{cb}$
• Recent progress in decays of $b$ and $c$ hadrons
• Re-evaluation of the isoscalar mixing angle within selected mesonic nonets
• On the Superiority of the $|V_{cb}|-\gamma$ Plots over the Unitarity Triangle Plots in the 2020s