On the impact of power corrections in the prediction of B → K *μ+μ− observables

Abstract

Abstract:The recent LHCb angular analysis of the exclusive decay B → K * µ + µ − has indicated significant deviations from the Standard Model expectations. Accurate predictions can be achieved at large K * -meson recoil for an optimised set of observables designed to have no sensitivity to hadronic input in the heavy-quark limit at leading order in α s . However, hadronic uncertainties reappear through non-perturbative Λ QCD /m b power corrections, which must be assessed precisely. In the framework of QCD factorisation we present a systematic method to include factorisable power corrections and point out that their impact on angular observables depends on the scheme chosen to define the soft form factors. Associated uncertainties are found to be under control, contrary to earlier claims in the literature. We also discuss the impact of possible non-factorisable power corrections, including an estimate of charm-loop effects. We provide results for angular observables at large recoil for two different sets of inputs for the form factors, spelling out the different sources of theoretical uncertainties. Finally, we comment on a recent proposal to explain the anomaly in B → K * µ + µ − observables through charm-resonance effects, and we propose strategies to test this proposal identifying observables and kinematic regions where either the charm-loop model can be disentangled from New Physics effects or the two options leave different imprints.

Flavour anomalies after the R K ∗ measurement

“…Recently, great theoretical effort went into the understanding of these aspects, see refs. [7,[14][15][16][17][18][19][20][21][22][23] for an incomplete list of references.…”

On the importance of electroweak corrections for B anomalies

“…All the λ's satisfy 13) so that all the elements |λ ij | should be smaller or equal to one. A useful and general parametrisation of λ f (f = u, d, e) is: 14) where α f and β f are complex numbers.…”

“…In particular, the statistically most significant results are accounted for by the following observables: where = e, µ, which follow from the HFAG averages [1] of Babar [2], Belle [3], and LHCb data [4], combined with the corresponding theory predictions [5,6], and based on combination of LHCb data [7,8] with the SM expectation R µ/e K ( * ) = 1.00 ± 0.01 [9,10]. Moreover, there are additional tensions between the SM predictions and experimental data in b → s differential observables, though large non-perturbative effects can be invoked to explain the observed anomaly [11][12][13][14][15]. Yet, it is interesting that the whole set of b → s data could be reconciled with the theory predictions assuming some NP contributions exclusively in the muonic channels, see e.g.…”

Large hadronic power corrections or new physics in the rare decay B → K ∗ μ + μ −?

“…It is well-known that there is no theoretical description of power corrections existing within this theoretical framework. Power corrections can only be guesstimated and are -depending on the involved assumptions -rather different in size [11][12][13][14]. Thus, it is difficult to unambiguously determine whether the source of the anomaly is due to NP or due to underestimated hadronic effects within these exclusive observables.…”

“…[11] (see also ref. [14]), the factorisable power corrections can be in principle determined using the factorisation formula between soft and full form factors which can be written in a schematic way:…”