Implications from clean observables for the binned analysis of B → K ∗ μ + μ − at large recoil

Abstract

Abstract:We perform a frequentist analysis of q 2 -dependent B → K * (→ Kπ)ℓ + ℓ − angular observables at large recoil, aiming at bridging the gap between current theoretical analyses and the actual experimental measurements. We focus on the most appropriate set of observables to measure and on the role of the q 2 -binning. We highlight the importance of the observables P i exhibiting a limited sensitivity to soft form factors for the search for New Physics contributions. We compute predictions for these binned observables in the Standard Model, and we compare them with their experimental determination extracted from recent LHCb data. Analysing b → s and b → sℓ + ℓ − transitions within four different New Physics scenarios, we identify several New Physics benchmark points which can be discriminated through the measurement of P i observables with a fine q 2 -binning. We emphasise the importance (and risks) of using observables with (un)suppressed dependence on soft form factors for the search of New Physics, which we illustrate by the different size of hadronic uncertainties attached to two related observables (P 1 and S 3 ). We illustrate how the q 2 -dependent angular observables measured in several bins can help to unravel New Physics contributions to B → K * (→ Kπ)ℓ + ℓ − , and show the extraordinary constraining power that the clean observables will have in the near future. We provide semi-numerical expressions for these observables as functions of the relevant Wilson coefficients at the low scale.

$$B\rightarrow K^*\mu ^+\mu ^-$$ B → K ∗ μ + μ - optimised observables in the MSSM

“…While all previous experimental results from rare | B| = | S| = 1 processes were pointing to SM like values for the Wilson coefficients, the bounds on dileptonic operators were relatively mild, still allowing |δC 9,10 ( ) /C SM 9,10 ( ) | ∼ O(1) [28]. First measurements of the full angular distribution by the LHCb collaboration [12,13] have changed the situation, presenting a tension in several binned observables, such as P 2 and P 5 .…”

“…From these a number of optimised observables can be constructed, where some hadronic uncertainties are minimised by taking appropriate ratios. A set of such optimised observables have been measured recently by the LHCb collaboration [12,13], these are defined as [28,35,38]: …”

“…[46,47]. In this kinematical region several form-factor relations [48,49] allow one to build the various optimised observables [28,35,38]. At low recoil (large q 2 ) the computation relies on an OPE for the relevant non-local hadronic matrix element, either in full QCD [50] or within the HQET [51].…”

“…We have neglected the tensor operators as they are highly suppressed both in the SM and in the Minimal Supersymmetric Standard Model (MSSM). The corresponding Wilson coefficients are well known in the SM [18][19][20][21][22][23][24], where C SM [25][26][27][28], specially when the latest B → K * μ + μ − data is included [1][2][3][4].…”

“…However, theoretical predictions for the most obvious observables inherit large uncertainties from not-so-well-known hadronic form factors. This has led to the construction of a number of optimised observables as appropriate ratios of angular coefficients where most of the dependence on the form factors cancels, while having high sensitivity to NP effects [28,[33][34][35][36][37]. A complete minimal set of such observables is given by the {P ( ) i } ensemble [28,35].…”