Anomalies in b → s transitions and metastability of the two Higgs doublet model: two global analyses

Abstract

Recent years in B physics have witnessed the emergence of a conspicuous pattern of flavour anomalies, arriving from multiple independent sources of data on rare b → s transitions. Of singular importance are: one angular observable of the decay B → K∗ ` +` −, denoted as P 0 5 , the ratio of branching fractions RK ≡ BR(B+ → K+µ +µ −) BR(B+ → K+e+e−) , (1) and another ratio, recently measured by LHCb: RK∗ ≡ BR(B → K∗µ +µ −) BR(B → K∗e+e−) . (2) In this thesis, we developed and made use of the publicly available package HEFfit to perform a global fit to possible shifts in Standard Model currents due to New Physics (NP) contributions, taking into account state-of-the-art theoretical predictions and experimental information, including the LHCb and BELLE measurements of P 0 5 , the LHCb measurement of RK, and, for the first time ever, R∗ K. The analysis was carried out in an effective field theory framework, with the fits being performed using two different approaches to the non-factorizable hadronic contributions: the first approach, labelled PMD, relies completely on a phenomenological model from Khodjamirian et al. (JHEP 1009, 089), and corresponds to the choice that is more widely used in literature; the second one, labelled PDD, imposes the result of Khodjamirian et al. only in the region of very large recoil, allowing the current data to drive the hadronic contributions for invariant dilepton masses above 1 GeV2 . From our analysis of several benchmark scenarios of NP contributions, it is possible to identify two viable classes that fit the aforementioned flavour anomalies: the widely studied scenario with vector muonic currents, as we find a remarkable & 5σ evidence in favour of non-zero muonic vector shifts in the PMD approach, while in the more conservative PDD approach, however, the significance drops to about 3σ, driven mainly by the lepton flavour universality violation observables; an alternative scenario with nonvanishing electronic axial currents, which emerges in the presence of large hadronic corrections to the infinite mass limit, namely our PDD approach. This last NP scenario was yet to be presented in the literature, since it does not provide a satisfactory description of the angular observables within the commonly used PMD approach. 1 A second venture consisted in the analysis of metastability in the Two Higgs Doublet Model (2HDM) with a softly-broken Z2 symmetry. In the last years, numerical methods have been used to discover in supersymmetric models extra minima competing for stability with the minimum we live in, taking loop corrections, and in some cases even thermal effects, into account. Output concerning loop vacuum stability in the Z2-symmetric 2HDM had not come out until Florian Staub (Phys. Lett. B776, 407) set out to perform the first analysis of vacuum stability in this model with radiative corrections included. We set out to use the capabilities of HEPfit to offer, not only a second look, which is always obligatory in science, but also a more polished and, in agreement with the theme of this thesis, more globally informed analysis, imposing many theoretical and experimental constraints. We focused on type-II of the 2HDM, and devised three scenarios: the first one, PT, provides a set of points that comply with positivity, next to-leading order perturbative unitarity, and perturbativity of the 2HDM quartic couplings; the second, PE, trades perturbative unitarity for experimental constraints, which comprise electroweak precision observables, and two flavour observables – the mass difference in Bs − B¯ s mixing and the branching fraction of B → Xsγ; the third and final fit, PTE, corresponds to the simultaneous imposition of the constraints from PT and PE. Stability at the one-loop level is assessed by making use of the effective one-loop Hamiltonian with Coleman-Weinberg contributions. Metastability, on the other hand, is evaluated by computing the vac uum tunnelling rate in the O(4) bounce formalism. For the PT scenario we find theory to favour a region with small tan β, the ratio between the vacuum expectation values of the two doublets, and with just a few metastable or unstable points, due to a small region where the 2HDM quadratic coupling m2 12 is allowed to be negative. This preponderance for the sign of m2 12 to dictate the stability of the potential is also found for PE, where a bigger region of m2 12 < 0 and large tan β is also allowed, yielding huge sectors of instability all over the parameter space. In both cases, however, we observe that either by loop corrections, or by decay rates being larger that the age of the universe, a considerable amount of points are always being rescued from what would be a classification of instability and removal from the accepted regions of parameters, which goes along the lines of the rates of misidentification put forward by Florian Staub. PE produces a bi-modal distribution, and for the mode with small tan β these constraints cut out any possibility of having negative values for m2 12. This means that when both sets of constraints are put together, PTE, the Markov Chain Monte Carlo of HEPfit results in a sample with m2 12 > 0, such that the last global fit finds absolutely nothing but stability in both the tree- and the one-loop level