The LHCb Collaboration has recently released a new study of <math><msup><mi>B</mi><mo>+</mo></msup><mo>→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> and <math><mi>B</mi><mo>→</mo><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> (<math><mo>ℓ</mo><mo>=</mo><mi>e</mi></math>, <math><mrow><mi>μ</mi></mrow></math>) decays, testing lepton universality with unprecedented accuracy using the whole Run 1 and 2 dataset. In addition, the CMS Collaboration has reported an improved analysis of the branching ratios <math><msub><mi>B</mi><mrow><mo>(</mo><mi>d</mi><mo>,</mo><mi>s</mi><mo>)</mo></mrow></msub><mo>→</mo><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math>. While these measurements offer, per se, a powerful probe of new physics, global analyses of <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> transitions also rely on the assumptions about nonperturbative contributions to the decay matrix elements. In this work, we perform a global Bayesian analysis of new physics in (semi)leptonic rare <math><mi>B</mi></math> decays, paying attention to the role of charming penguins which are difficult to evaluate from first principles. We find data to be consistent with the Standard Model once rescattering from intermediate hadronic states is included. Consequently, we derive stringent bounds on lepton universality violation in <math><mo>|</mo><mi>Δ</mi><mi>B</mi><mo>|</mo><mo>=</mo><mo>|</mo><mi>Δ</mi><mi>S</mi><mo>|</mo><mo>=</mo><mn>1</mn></math> (semi)leptonic processes.

Italy

Marco Ciuchini

Germany

Marco Fedele

Enrico Franco

United States

Ayan Paul

Luca Silvestrini

Mauro Valli

Constraints on lepton universality violation from rare <math><mi>B</mi></math> decays

The LHCb experiment has recently presented new results on Lepton Universality Violation (LUV) in  $$B \rightarrow K^{(*)} \ell ^+ \ell ^-$$  <math> <mrow> <mi>B</mi> <mo>→</mo> <msup> <mi>K</mi> <mrow> <mo>(</mo> <mrow></mrow> <mo>∗</mo> <mo>)</mo> </mrow> </msup> <msup> <mi>ℓ</mi> <mo>+</mo> </msup> <msup> <mi>ℓ</mi> <mo>-</mo> </msup> </mrow> </math>   decays involving  $$K_S$$  <math> <msub> <mi>K</mi> <mi>S</mi> </msub> </math>   in the final state, which strengthen the recent evidence of LUV obtained in  $$B^+ \rightarrow K^{+} \ell ^+ \ell ^-$$  <math> <mrow> <msup> <mi>B</mi> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>K</mi> <mo>+</mo> </msup> <msup> <mi>ℓ</mi> <mo>+</mo> </msup> <msup> <mi>ℓ</mi> <mo>-</mo> </msup> </mrow> </math>   decays and the previous measurements of  $$B \rightarrow K^{*0} \ell ^+ \ell ^-$$  <math> <mrow> <mi>B</mi> <mo>→</mo> <msup> <mi>K</mi> <mrow> <mrow></mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> <msup> <mi>ℓ</mi> <mo>+</mo> </msup> <msup> <mi>ℓ</mi> <mo>-</mo> </msup> </mrow> </math>  . While LUV observables in the Standard Model are theoretically clean, their predictions in New Physics scenarios are sensitive to the details of the hadronic dynamics, and in particular of the charming penguin contribution. In this work, we show how a conservative treatment of hadronic uncertainties is crucial not only to assess the significance of deviations from the Standard Model but also to obtain a conservative picture of the New Physics responsible for LUV. Adopting a very general parameterization of charming penguins, we find that: (i) current data hint at a sizable  $$q^2$$  <math> <msup> <mi>q</mi> <mn>2</mn> </msup> </math>   and helicity dependence of charm loop amplitudes; (ii) conservative NP solutions to B anomalies favour a left-handed or an axial lepton coupling rather than a vector one.

Charming penguins and lepton universality violation in  $$\varvec{b \rightarrow s \ell ^+ \ell ^-}$$  <math> <mrow> <mi>b</mi> <mo>→</mo> <mi>s</mi> <msup> <mi>ℓ</mi> <mo>+</mo> </msup> <msup> <mi>ℓ</mi> <mo>-</mo> </msup> </mrow> </math>   decays

We perform an analysis within the Standard Model of <math><msup><mi>B</mi><mrow><mn>0</mn><mo>,</mo><mo>+</mo></mrow></msup><mo>→</mo><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn><mo>,</mo><mo>+</mo></mrow></msup><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> decays in light of the recent measurements from the LHCb experiment, showing that new data strengthen the need for sizable hadronic contributions and correlations among them. We then extend our analysis to new physics via the Standard Model effective theory, and carry out a state-of-the-art fit of available <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> data, including possible hadronic contributions. We find the case of a fully left-handed operator standing out as the simplest scenario with a significance of almost <math><mn>6</mn><mi>σ</mi></math>.

Lessons from the <math><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn><mo>,</mo><mo>+</mo></mrow></msup><mo>→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo><mn>0</mn><mo>,</mo><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> angular analyses

In light of the very recent updates on the $$R_K$$ <math><msub><mi>R</mi><mi>K</mi></msub></math>  and $$R_{K^*}$$ <math><msub><mi>R</mi><msup><mi>K</mi><mo>∗</mo></msup></msub></math>  measurements from the LHCb and Belle collaborations, we systematically explore here imprints of New Physics in $$b \rightarrow s \ell ^+ \ell ^- $$ <math><mrow><mi>b</mi><mo>→</mo><mi>s</mi><msup><mi>ℓ</mi><mo>+</mo></msup><msup><mi>ℓ</mi><mo>-</mo></msup></mrow></math>  transitions using the language of effective field theories. We focus on effects that violate Lepton Flavour Universality both in the Weak Effective Theory and in the Standard Model Effective Field Theory. In the Weak Effective Theory we find a preference for scenarios with the simultaneous presence of two operators, a left-handed quark current with vector muon coupling and a right-handed quark current with axial muon coupling, irrespective of the treatment of hadronic uncertainties. In the Standard Model Effective Field Theory we select different scenarios according to the treatment of hadronic effects: while an aggressive estimate of hadronic uncertainties points to the simultaneous presence of two operators, one with left-handed quark and muon couplings and one with left-handed quark and right-handed muon couplings, a more conservative treatment of hadronic matrix elements leaves room for a broader set of scenarios, including the one involving only the purely left-handed operator with muon coupling.

Portugal

António Coutinho

Spain

CERN

New Physics in $${\varvec{b \rightarrow s \ell ^+ \ell ^-}}$$ <math><mrow><mi>b</mi><mo>→</mo><mi>s</mi><msup><mi>ℓ</mi><mo>+</mo></msup><msup><mi>ℓ</mi><mo>-</mo></msup></mrow></math>  confronts new data on lepton universality

Within the standard approach of effective field theory of weak interactions for $$\varDelta B = 1$$ <math><mrow><mi>Δ</mi><mi>B</mi><mo>=</mo><mn>1</mn></mrow></math>  transitions, we look for possibly unexpected subtle New Physics effects, here dubbed “flavourful Easter eggs”. We perform a Bayesian global fit using the publicly available HEPfit package, taking into account state-of-the-art experimental information concerning these processes, including the suggestive measurements from LHCb of $$R_{K}$$ <math><msub><mi>R</mi><mi>K</mi></msub></math>  and $$R_{K^{*}}$$ <math><msub><mi>R</mi><msup><mi>K</mi><mrow><mrow></mrow><mo>∗</mo></mrow></msup></msub></math> , the latter available only very recently. We parametrise New Physics contributions to $$b \rightarrow s$$ <math><mrow><mi>b</mi><mo>→</mo><mi>s</mi></mrow></math>  transitions in terms of shifts of Wilson coefficients of the electromagnetic dipole and semileptonic operators, assuming CP-conserving effects, but allowing in general for violation of lepton flavour universality. We show how optimistic/conservative hadronic estimates can impact quantitatively the size of New Physics extracted from the fit. With a conservative approach to hadronic uncertainties we find nonzero New Physics contributions to Wilson coefficients at the level of $$\sim 3\sigma $$ <math><mrow><mo>∼</mo><mn>3</mn><mi>σ</mi></mrow></math> , depending on the model chosen. Furthermore, given the interplay between hadronic contributions and New Physics effects in the leptonic vector current, a scenario with nonstandard leptonic axial currents is comparable to the more widely advocated one with New Physics in the leptonic vector current.

On flavourful Easter eggs for New Physics hunger and lepton flavour universality violation

We critically reassess the theoretical uncertainties in the Standard Model calculation of the B → K ∗ ℓ + ℓ − observables, focusing on the low q 2 region. We point out that even optimized observables are affected by sizable uncertainties, since hadronic contributions generated by current-current operators with charm are difficult to estimate, especially for q 2  ∼ 4 m c 2  ≃ 6.8 GeV 2 . We perform a detailed numerical analysis and present both predictions and results from the fit obtained using most recent data. We find that non-factorizable power corrections of the expected order of magnitude are sufficient to give a good description of current experimental data within the Standard Model. We discuss in detail the q 2 dependence of the corrections and their possible interpretation as shifts of the Standard Model Wilson coefficients.