To (b)e or not to (b)e: no electrons at LHCb

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Algueró, M 
Biswas, A 
Capdevila, B 
Descotes-Genon, S 
Matias, J 

jats:titleAbstract</jats:title>jats:pWe discuss the impact of the recent LHCb update on the two lepton-flavour universality ratios jats:inline-formulajats:alternativesjats:tex-math$$R_K$$</jats:tex-math><mml:math xmlns:mml=""> mml:msub mml:miR</mml:mi> mml:miK</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> and jats:inline-formulajats:alternativesjats:tex-math$$R_{K^}$$</jats:tex-math><mml:math xmlns:mml=""> mml:msub mml:miR</mml:mi> mml:msup mml:miK</mml:mi> mml:mo∗</mml:mo> </mml:msup> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula>, and the CMS update of jats:inline-formulajats:alternativesjats:tex-math$$B({B_s \rightarrow \mu ^+\mu ^-})$$</jats:tex-math><mml:math xmlns:mml=""> mml:mrow mml:miB</mml:mi> mml:mo(</mml:mo> mml:mrow mml:msub mml:miB</mml:mi> mml:mis</mml:mi> </mml:msub> mml:mo→</mml:mo> mml:msup mml:miμ</mml:mi> mml:mo+</mml:mo> </mml:msup> mml:msup mml:miμ</mml:mi> mml:mo-</mml:mo> </mml:msup> </mml:mrow> mml:mo)</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> regarding the possibility of New Physics in jats:inline-formulajats:alternativesjats:tex-math$$b\rightarrow s\ell ^+\ell ^-$$</jats:tex-math><mml:math xmlns:mml=""> mml:mrow mml:mib</mml:mi> mml:mo→</mml:mo> mml:mis</mml:mi> mml:msup mml:miℓ</mml:mi> mml:mo+</mml:mo> </mml:msup> mml:msup mml:miℓ</mml:mi> mml:mo-</mml:mo> </mml:msup> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> decays. We perform global fits of the New Physics Wilson coefficients defined in the model-independent approach of the Weak Effective Theory at the jats:italicb</jats:italic>-quark mass. We discuss three different frameworks for this analysis: (i) an update limited to the experimental data but using the same theoretical framework as in earlier works, (ii) a full update concerning both the experimental inputs and the theoretical framework, (iii) an analysis without the LHCb results on electron modes. The comparison between these various sets of results allows us to identify the differences stemming from the various components of the analysis: new experimental results, new inputs for the hadronic form factors, the role played by LHCb data on electron modes. As expected, the significance of all New Physics hypotheses gets reduced after the LHCb announcements on jats:inline-formulajats:alternativesjats:tex-math$$R_{K^{()}}$$</jats:tex-math><mml:math xmlns:mml=""> mml:msub mml:miR</mml:mi> mml:msup mml:miK</mml:mi> mml:mrow mml:mo(</mml:mo> <mml:mrow /> mml:mo∗</mml:mo> mml:mo)</mml:mo> </mml:mrow> </mml:msup> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> while the hypothesis of a lepton-flavour-universal contribution to the Wilson coefficient of the semileptonic jats:inline-formulajats:alternativesjats:tex-math$$O_{9\ell }$$</jats:tex-math><mml:math xmlns:mml=""> mml:msub mml:miO</mml:mi> mml:mrow mml:mn9</mml:mn> mml:miℓ</mml:mi> </mml:mrow> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> operators (possibly with a very small lepton-flavour-universality violating component) is clearly reinforced. We also discuss the possibility of a long-distance charm-loop contribution through a mode-by-mode analysis and we find that the preferred values for the jats:inline-formulajats:alternativesjats:tex-math$${\mathcal C}_{9\mu }$$</jats:tex-math><mml:math xmlns:mml=""> mml:msub mml:miC</mml:mi> mml:mrow mml:mn9</mml:mn> mml:miμ</mml:mi> </mml:mrow> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> Wilson coefficient are consistent throughout the different jats:inline-formulajats:alternativesjats:tex-math$$b\rightarrow s\mu ^+\mu ^-$$</jats:tex-math><mml:math xmlns:mml=""> mml:mrow mml:mib</mml:mi> mml:mo→</mml:mo> mml:mis</mml:mi> mml:msup mml:miμ</mml:mi> mml:mo+</mml:mo> </mml:msup> mml:msup mml:miμ</mml:mi> mml:mo-</mml:mo> </mml:msup> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> modes and that there is no significant evidence of non-constant jats:inline-formulajats:alternativesjats:tex-math$$q^2$$</jats:tex-math><mml:math xmlns:mml=""> mml:msup mml:miq</mml:mi> mml:mn2</mml:mn> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula> dependencies, which would indicate the presence of a long-distance charm-loop contribution beyond those already included.</jats:p>


Acknowledgements: This project has received support from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 860881-HIDDeN [S.D.G.]. This study has been carried out within the INFN project (Iniziativa Specifica) QFT-HEP [M.N.B.]. J.M. gratefully acknowledges the financial support from ICREA under the ICREA Academia programme and from the Pauli Center (Zurich) and the Physics Department of University of Zurich. J.M. and A.B. also received financial support from Spanish Ministry of Science, Innovation and Universities (project PID2020-112965GB-I00) and from the Research Grant Agency of the Government of Catalonia (project SGR 1069). The work of B.C. is supported by the Margarita Salas postdoctoral program funded by the European Union-NextGenerationEU. B.C. also thanks the CERN Theory Division, where part of this work was done, for hospitality and the Cambridge Pheno Working Group for helpful discussions.

5106 Nuclear and Plasma Physics, 5107 Particle and High Energy Physics, 51 Physical Sciences
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European Physical Journal C
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Springer Science and Business Media LLC