# Precision Predictions for Flavour-Changing Neutral Current Decays

**Principal Investigator:** Gudrun Hiller (Dortmund)

**Participating Researchers: ** Thorsten Feldmann (Siegen), Tobias Huber (Siegen), Alexander Khodjamirian (Siegen), Joachim Brod (Dortmund)

Flavour-changing neutral current (FCNC) decays of heavy quarks involving dileptons and photons have an enhanced sensitivity to physics beyond the SM (BSM). These decays provide one of the most important tools for studies at the *high-precision frontier* in contemporary particle physics. The role of precision measurements in quark-flavour physics will be further growing in the future, complementing searches at the *high-energy frontier* where direct production of new particles is probed, currently at the LHC. Exclusive FCNC decays of *B*-mesons and *b*-baryons are particularly interesting because they are already accessible with high statistics at current collider experiments, notably at LHCb. These processes will also be intensively considered at high-luminosity super-flavour factories planned in the future.

The effective Hamiltonian for low-energy weak interactions in the SM provides a firm and wellestablished basis for the theoretical description of FCNC process, and it can be easily extended and generalised to systematically include BSM effects. On top of this, continuous progress in QCD-based calculations of hadronic matrix elements (decay constants, form factors and nonfactorizable matrix elements) allow for predictions of hadronic amplitudes in FCNC decays with constantly improving accuracy.

The aim of this project is a comprehensive theoretical study of exclusive FCNC decays which will allow us to establish a clean separation between the SM contributions and possible BSM effects in the decay amplitudes. The set of FCNC processes includes the most frequently studied decay channels *B _{s}* → π

^{+}π

^{-},

*B*→

*K*

^{(∗)}

*l*

*l*, and

*B*→

*K*

^{∗}γ , as well as the related channels

*B*→ ϕ

_{s}*l*

^{ +}

*l*

^{ -},

*B*→

*K*

^{(J P= 0+, 2+)}

*l*

^{ +}

*l*

^{ -}, and Λ

_{b}→ Λ

^{(∗)}

*l*

^{ +}

*l*

^{ -}together with the corresponding Cabibbo-suppressed

*b*→

*d*

*l*

^{ +}

*l*

^{ -}and

*b*→

*d*γ

^{ }modes. A very promising and not yet fully explored avenue of research is related to the charm sector, where the exclusive

*c*→

*u*

*l*

^{ +}

*l*

^{ -}and

*c*→

*u*γ transitions, inducing rare

*D*-meson and charm-baryon decays, may also reveal BSM effects in future precision measurements.

Nowadays, we face a broad spectrum of various new physics (NP) models, and different implementations and scenarios related to flavour effects are being discussed. The theoretical foundations of these models — such as supersymmetric (SUSY) extensions of the SM, 4th generation (4G) of flavours, little Higgs (LH) schemes, models with extra space-time dimensions (ED), or models with composite particles — are quite different. Nevertheless, as a common feature, they in general predict new heavy particles with a certain mass spectrum in the TeV range and flavourspecific couplings to the SM degrees of freedom. At low energies, the NP effects in FCNC decays can be encoded in a set of generic effective operators with short-distanceWilson coefficients that depend on the particular NP model. Certain limitations for the latter already exist from lower limits on the new heavy-particle masses and/or upper limits on their couplings. A comprehensive analysis of BSM contributions to FCNC decay amplitudes thus requires to single out the relevant effective operators (with mass dimension six or higher) for the particular FCNC decays under 1study, and to create an efficient mapping of the allowed NP parameter spaces onto the relevant Wilson coefficients. Most interesting will be operators that are absent (or whose coefficients are highly suppressed) in the SM or its minimally flavour-violating (MFV) extensions. This includes effects from fundamental flavour-changing interactions involving right-handed vector currents, scalar currents or tensor currents.

The ultimate goal of this project is to produce a set of theoretical master formulas for several observables in different FCNC decays, with deviations from the SM encoded in such a way that NP parameters can easily be studied in a correlated manner. In addition to already intensively explored observables, such as the forward-backward asymmetry in *b* → *s* *l*^{ +} *l*^{ -} transitions, special attention has to be paid to more “subtle” observables, like CP- and isospin-asymmetries, angular observables in *B* → *K*^{∗}(*K*π) *l*^{ +} *l*^{ -} decays, as well as at “null-tests”, i.e. observables that are vanishingly small in the SM. An interesting and not yet fully explored version of this approach will involve not only FCNCs but also charged flavour-violating electroweak γdecays, such as *B* → τ ν_{τ} or *B* → *D*^{(∗)} τ ν_{τ} . In view of future experiments at super-flavour facilities, also the FCNC channels with neutrinos and tau leptons will be studied such as *B* → *K*^{(∗)} ν ν and *B* → *K*^{(∗)} τ^{ +} τ^{ -} . Finally, correlations emerging in specific BSM scenarios between the NP contributions in FCNC processes and lepton-flavour violating modes will be looked for.

An important issue, which will be clarified in the course of this project, is how to diminish the existing theoretical uncertainties in the hadronic input parameters. To this end, dedicated studies will be performed to find optimised combinations of decay observables and convenient regions of phase space with minimal sensitivity to hadronic uncertainties. One promising direction is to look at the low hadronic-recoil region in *b* → *s* *l*^{ +} *l*^{ - }decays, and to fully exploit the powerful theoretical techniques related to the operator product expansion (OPE). Aiming at high-precision in theoretical predictions for rare *B*-decays, also electromagnetic corrections will be considered where relevant. This includes investigations of final states with additional photons, such as *B _{s}* → π

^{+}π

^{-}γ , which may play a more important role than commonly expected, first as a background to SM observables (for the case of soft photons), and secondly as an independent NP trigger (in the case of hard photons).