Combined explanations of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>b</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>s</mml:mi><mml:msup><mml:mi>μ</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>μ</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>b</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>c</mml:mi><mml:msup><mml:mi>τ</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mover accent="true"><mml:mi>ν</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:math> anomalies: A general model analysis

There are four models of tree-level new physics (NP) that can potentially simultaneously explain the $b\ensuremath{\rightarrow}s{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ and $b\ensuremath{\rightarrow}c{\ensuremath{\tau}}^{\ensuremath{-}}\overline{\ensuremath{\nu}}$ anomalies. They are the ${S}_{3}$, ${U}_{3}$ and ${U}_{1}$ leptoquarks (LQs), and a triplet of standard-model-like vector bosons ($VB$'s). Under the theoretical assumption that the NP couples predominantly to the third generation, previous analyses found that, when constraints from other processes are taken into account, the ${S}_{3}$, ${U}_{3}$ and $VB$ models cannot explain the $B$ anomalies, but ${U}_{1}$ is viable. In this paper, we reanalyze these models, but without any assumption about their couplings. We find that, even in this most general case, ${S}_{3}$ and ${U}_{3}$ are excluded. For the ${U}_{1}$ model, constraints from the semileptonic lepton-flavor-violating (LFV) processes $B\ensuremath{\rightarrow}{K}^{(*)}{\ensuremath{\mu}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\tau}}^{\ensuremath{\mp}}$, $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\phi}$ and $\mathrm{\ensuremath{\Upsilon}}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\tau}$, which have been largely ignored previously, are found to be very important. Because of the LFV constraints, the pattern of couplings of the ${U}_{1}$ LQ is similar to that obtained with the above theoretical assumption. Also, the LFV constraints render unimportant those constraints obtained using the renormalization group equations. As for the $VB$ model, it is excluded if the above theoretical assumption is made due to the additional constraints from ${B}_{s}^{0}\text{\ensuremath{-}}{\overline{B}}_{s}^{0}$ mixing, $\ensuremath{\tau}\ensuremath{\rightarrow}3\ensuremath{\mu}$ and $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\nu}\overline{\ensuremath{\nu}}$. By contrast, we find a different set of NP couplings that both explains the $b\ensuremath{\rightarrow}s{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ anomaly and is compatible with all constraints. However, it does not reproduce the measured values of the $b\ensuremath{\rightarrow}c{\ensuremath{\tau}}^{\ensuremath{-}}\overline{\ensuremath{\nu}}$ anomalies---it would be viable only if future measurements find that the central values of these anomalies are reduced. Even so, this $VB$ model is excluded by the LHC bounds on high-mass resonant dimuon pairs. This conclusion is reached without any assumptions about the NP couplings.

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