Bs -> mu mu gamma: novel measurement and litmus test of flavour anomalies – GammaRare

The approach we adopt is a structured exploration of two possible interpretations of the current discrepancies in B meson decays -- new effects, or standard physics not currently taken into account. This exploration starts from the measurement of the rare and radiative decay Bs⁰ → μ⁺μ⁻γ. Concerning this measurement, two members of the present project have proposed a new method (Dettori, Guadagnoli and Reboud, Bs⁰ → μ⁺μ⁻γ from Bs⁰ → μ⁺μ⁻, Phys. Lett. B768 (2017) 163-167) that represents the starting point of the present project. This method suggests measuring the spectrum of Bs⁰ → μ⁺μ⁻γ through the data of Bs⁰ → μ⁺μ⁻, i.e., without the direct detection of the photon. Based on this observation, the project identifies several methodological milestones:

1. Measurement. We aim at a full-fledged experimental analysis of Bs⁰ → μ⁺μ⁻γ following the method by Dettori et al. The measurement will be complementary to the other on-going analysis with direct photon detection. Specifically, the kinematic region accessed by the two analyses are disconnected with one another, and the region concerned by this milestone is the one more sensitive to the operators O_{9,10} directly interesting in the light of present discrepancies.

2. Kinematic variables. If judiciously chosen, additional kinematic variables could be devised to serve a double purpose: enhance the signal vs. background separation and provide further theoretical insights.

3. Method extensions. It would be extremely interesting if the method in Dettori et al. -- which is naturally devised to access the so-called initial-state radiation component of the Bs⁰ → μ⁺μ⁻γ spectrum -- could be adjusted to access also the region which is instead dominated by the final-state radiation component, at the moment `just' subtracted using a MonteCarlo. Comparing with theory the separate measurements potentially amount to a litmus test between new physics and systematics, as explanations of the present-day discrepancies.

4. Theory understanding. The previous milestone greatly benefits from a further corroboration of the present theory picture as concerns the new-physics interpretation. In this respect, we will take specific directions of exploration, both at the effective-theory level and at the level of complete models.

5. QED corrections. We aim at calculating QED corrections due to photons with energy large enough to smear out the weak-interaction vertex over the distance 1/\sqrt{m_B \Lambda_QCD} in the context of Bs⁰ → μ⁺μ⁻γ.

1. Explorations of the coherence of the theory picture (2 articles). One of the key questions in connection with the B anomalies that motivate the ANR project, is whether these discrepancies may be connected to other pieces of evidence of physics beyond the Standard Model. The evidence of Dark Matter (DM) is one of the strongest observational arguments in favor of physics beyond the Standard Model. We explore the question whether DM and the B anomalies may have a common origin. We do so in two contexts:- the so-called 4321 gauge model, a UV-complete and calculable setup that yields a U1 leptoquark, the by far most successful single mediator able to explain the B anomalies.- a model of composite Dark Matter, in which a new QCD-like confining "hypercolor'' sector generates naturally stable hyperbaryons as DM candidates.

2. Further Bs⁰ → μ⁺μ⁻γ observables with reduced theory uncertainty (1 article). We consider the Bs⁰ → μ⁺μ⁻γ effective lifetime, and the related CP-phase sensitive quantity A_{Delta Gamma_s}, as a way to obtain qualitatively new insights on the current B anomalies. We explore the possibility of telling apart scenarios with new CP violation with A_{Delta Gamma_s}, once resonance-modeling and form-factor uncertainties are taken into account. We do so in both regions of low and high invariant di-lepton mass-squared.

3. Further corroborations of present anomalies from data (1 article). In a recent re-analysis of 2018 Belle data, it was found that the forward-backward asymmetry of B ? D^{*}µv vs B ? D^{*}ev disagrees with the SM prediction by about 4sigma, which would be an additional sign of lepton flavor universality violation. The above putative deviation might share a common origin with the other flavor anomalies. We show that a tensor operator is necessary to significantly improve the global fit w.r.t. the SM, which can only be induced by a scalar leptoquark.

4. Extensions of the Dettori et al. method (1 articles). New particles phi in the MeV-GeV range produced at colliders and escaping detection can be searched for at operating b- and tau-factories such as Belle II. A typical search topology involves pair-produced tau's (or mesons), one of which decaying to visibles plus the phi, and the other providing a tag. We observe that such topology lends itself to the use of kinematic variables such as M_2, and we construct a full-fledged measurement strategy. Application of our strategy leads to an improvement by a factor close to 3 in the branching-ratio upper limit for tau ? e phi, with respect to the currently expected limit, assuming m_phi < 1 MeV.

We are working on four complementary directions: (1) Electromagnetic corrections to RK beyond scalar QED; (2) A global fit to B discrepancies: new physics vs. mundane explanations; (3) b ? c anomalies and signals in leptonic heavy-vector decays; (4) Axions in K decays. These directions are designed to address complementary outstanding issues in the project.

Topic (1) is at the core of the ANR proposal. The task is to evaluate leading QED corrections to RK beyond the state-of-the-art approximation of considering point like external mesons, which corresponds to assuming photons with small energy, not larger than the QCD confinement scale. The idea is to use soft-collinear effective theory, with as many collinear directions as the charged external states.

Topic (2) serves to consolidate the current theory understanding of the anomalies from a perspective which is as model-independent and robust as possible. We aim at a state-of-the-art assessment of the B-decay discrepancies, taking a conservative approach. Within this approach, we allow for large long-distance Standard-Model contributions and address the question to what extent they can describe the data. This project provides the basis for a robust interpretation of the anomalies within an effective-theory approach, i.e. the most general one assuming new physics above the electroweak scale.

Topic (3) goes one step forward with respect to the previous one and attempts to relate the new-physics interpretation found with selected observables at the energy frontier, in particular Drell-Yan di-lepton production. To do so, we need to assume more than just an effective theory, as in the previous project. We consider the case of leptoquarks, which are currently the preferred explanation of the ensemble of anomalies that the ANR proposal aims at interpreting.

Finally, topic (4) is a spin-off of the idea in Dettori, Guadagnoli and Reboud, Bs⁰ → μ⁺μ⁻γ from Bs⁰ → μ⁺μ⁻, Phys. Lett. B768 (2017) 163–167, which initiated the present proposal. Rather than measuring Bs⁰ → μ⁺μ⁻γ from Bs⁰ → μ⁺μ⁻, i.e. with an undetected photon, here the idea is to relate a decay to an undetected new particle, notably an axion, to decays that are well-measured. We do so with selected K decays. The aim is twofold: to constrain a very popular extension of the SM, whereby one introduces an axion-like particle, and to test the limits of applicability of the idea in Dettori et al.

[1] F. Dettori, D. Guadagnoli and M. Reboud, Bs0 ? µ+µ-? from Bs0 ? µ+µ-, Phys. Lett. B 768 (2017) 163–167, [1610.00629].
[2] D. Guadagnoli, M. Reboud and P. Stangl, The Dark Side of 4321, JHEP 10 (2020) 084, [2005.10117].
[3] A. Carvunis, D. Guadagnoli, M. Reboud and P. Stangl, Composite Dark Matter and a horizontal symmetry, JHEP 02 (2021) 056, [2007.11931].
[4] A. Carvunis, F. Dettori, S. Gangal, D. Guadagnoli and C. Normand, On the effective lifetime of Bs ? µµ?, 2102.13390.
[5] A. Carvunis, A. Crivellin, D. Guadagnoli and S. Gangal, The Forward-Backward Asymmetry in B ? D*l?: One more hint for Scalar Leptoquarks?, 2106.09610.
[6] D. Guadagnoli, C. B. Park and F. Tenchini, t ? l+ invisible through invisible-savvy collider variables, Phys. Lett. B 822 (2021) 136701, [2106.16236].

A whole body of data on B-meson decays display persistent deviations from Standard-Model (SM) predictions. These data constitute the single, coherent array of deviations from the SM, and in a set of processes historically sensitive to new effects. Most remarkably, data seem to sit always on a given side with respect to the SM prediction. These data clearly need be scrutinised exploiting the full LHC dataset from Run 2 and beyond. On the theory side, these data find a cogent explanation within an Effective-Theory framework, that per se constitutes a non-trivial result. However, a full-fledged theory able to explain at the same time these anomalies and the absence of deviations in many related datasets poses a major challenge. It is clear that appropriate experimental input will be crucial to improve the theory understanding.

In these circumstances we can neither dismiss the possibility that these anomalies are indeed heralding new effects, nor the alternative possibility of a mundane explanation, for example experimental systematic effects that have hitherto escaped consideration. This project proposes a strategy towards telling apart these two possibilities.

This strategy is based on the detailed investigation of a suitable process, from theory aspects to a complete analysis. The process we will consider is the rare, radiative decay Bs -> mu mu gamma, measured using the Bs -> mu mu dataset, i.e. without detection of the photon. This method, put forth in Dettori, Guadagnoli, Reboud, PLB 768 (2017) 163–167 (Ref. [1]), merges the advantages of both decays: we exploit the rich and ever increasing Bs -> mu mu dataset as a proxy for Bs -> mu mu gamma, which probes the mentioned discrepancies more thoroughly, due to the presence of the final-state photon.

In addition, the radiative nature of the decay allows, while probing new physics, to probe, at the same time, certain crucial sources of systematics, notably from QED, as an alternative explanation of the anomalies. As a consequence, the project tasks leading to the measurement will amount to litmus tests of the anomalies.

Concretely, the project will accomplish 4 groups of objectives: (a) confirm/disprove the present theory picture of the anomalies, using a novel, independent decay channel never measured so far. In doing so, the project will (b) deliver the first measurement (ever) of this channel. Besides, we will (c) carry out a systematic theoretical study of QED corrections to the process in the very kinematical region accessed by our experimental method. This objective will provide a non-trivial test of the understanding of QED effects in a region where they are intertwined with QCD dynamics. Finally, the comparison between the calculated and the measured spectrum will allow to (d) confirm/disprove that certain critical sources of systematic uncertainties in the discrepant measurements are indeed well understood.

All of these 4 groups of objectives include theoretical and experimental facets, intertwined with one another. The tasks towards these objectives will be carried out in a ‘hybrid’ collaboration of theorists and experimentalists. This team has a collaborative record proven by the co-supervision of PhD students as well as by articles, including the `method paper' underlying the project itself, Ref. [1]. Our consortium will also ensure a constant feedback between the theory and experimental facets of the implementation, including theory oversight on specific aspects of the experimental analysis proposed.

The project's success rests on appropriate human resources: a PhD student, co-supervised within our team, and a 3-year postdoc with expertise on effective-theory approaches to flavour observables, on the calculation of photon-inclusive decay distributions, and possibly their coding for experimental applications.