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Register a new userHadronic uncertainties in $Bto K^*mu^+mu^-$: a state-of-the-art analysis
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Bernat Capdevila
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In the absence of direct evidence for New Physics at present LHC energies, the focus is set on the anomalies and discrepancies recently observed in rare $b to sellell$ transitions which can be interpreted as indirect hints. Global fits have shown that an economical New Physics solution can simultaneously alleviate the tensions in the various channels and can lead to a significant improvement in the description of the data. Alternative explanations within the Standard Model for part of the observed anomalies have been proposed in terms of (unexpectedly large) hadronic effects at low dilepton invariant mass and attributing tensions in protected observables to statistical fluctuations or experimental errors. We review the treatment of hadronic uncertainties in this kinematic regime for one of the most important channels, $B to K^*mu^+mu^-$, in a pedagogical way. We provide detailed arguments showing that factorisable power corrections cannot account for the observed anomalies and that an explanation through long-distance charm contributions is disfavoured. Some optimized observables at very low dilepton invariant mass are shown to be protected against contributions from the semileptonic coefficient $C_9$ (including any associated long-distance charm effects), enhancing their sensitivity to New Physics contributions to other Wilson coefficients. Finally, we discuss how the recent measurement of $Q_5$ by Belle (and in the future by LHCb and Belle-II) may provide a robust cross-check of our arguments.
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Theory uncertainties on non-local hadronic effects limit the New Physics discovery potential of the rare decays $Bto K^*mu^+mu^-$. We investigate prospects to disentangle New Physics effects in the short-distance coefficients from these effects. Our approach makes use of an event-by-event amplitude analysis, and relies on the state of the art parametrisation of the non-local contributions. We find that non-standard effects in the short-distance coefficients can be successfully disentangled from non-local hadronic effects. The impact of the truncation on the parametrisation of non-local contributions to the Wilson coefficients are for the first time systematically examined and prospects for its precise determination are discussed. We find that physical observables are unaffected by these uncertainties. Compared to other methods, our approach provides for a more precise extraction of the angular observables from data.
Motivated by the recently improved lattice QCD results on the hadronic matrix elements entering $Delta M_{s,d}$ in $B_{s,d}^0-bar B_{s,d}^0$ mixings and the resulting increased tensions between $Delta M_{s,d}$ and $varepsilon_K$ in the Standard Model and CMFV models, we demonstrate that these tensions can be removed in 331 models based on the gauge group $SU(3)_Ctimes SU(3)_Ltimes U(1)_X$ both for $M_{Z^prime}$ in the LHC reach and well beyond it. But the implied new physics (NP) patterns in $Delta F=1$ observables depend sensitively on the value of $|V_{cb}|$. Concentrating the analysis on three 331 models that have been selected by us previously on the basis of their performance in electroweak precision tests and $varepsilon^prime/varepsilon$ we illustrate this for $|V_{cb}|=0.042$ and $|V_{cb}|=0.040$. We find that these new lattice data still allow for positive shifts in $varepsilon^prime/varepsilon$ up to $6times 10^{-4}$ for $M_{Z^prime}=3~TeV$ for both values of $$|V_{cb}|$ but for $M_{Z^prime}=10~TeV$ only for $|V_{cb}|=0.040$ such shifts can be obtained. NP effects in $B_stomu^+mu^-$ and in the Wilson coefficient $C_9$ are significantly larger in all three models for the case of $|V_{cb}|=0.040$. In particular in two models the rate for $B_stomu^+mu^-$ can be reduced by NP by $20%$ for $M_{Z^prime}=3~TeV$ resulting in values in the ballpark of central values from CMS and LHCb. In the third model a shift in $C_9$ up to $C_9^text{NP}=-0.5$ is possible. We also consider the simplest 331 model, analyzed recently in the literature, in which $X=Y$, the usual hypercharge. We find that in this model NP effects in flavour observables are much smaller than in the three models with $X ot=Y$, in particular NP contributions to the ratio $varepsilon^prime/varepsilon$ are very strongly suppressed.
Following updated and extended measurements of the full angular distribution of the decay $Lambda_bto Lambda(to p,pi^-)mu^+mu^-$ by the LHCb collaborations, as well as a new measurement of the $Lambda to p pi^-$ decay asymmetry parameter by the BESIII collaboration, we study the impact of these results on searches for non-standard effects in exclusive $bto smu^+mu^-$ decays. To this end, we constrain the Wilson coefficients $mathcal{C}_{9}$ and $mathcal{C}_{10}$ of the numerically leading dimension-six operators in the weak effective Hamiltonian, in addition to the relevant nuisance parameters. In stark contrast to previous analyses of this decay mode, the changes in the updated experimental results lead us to find very good compatibility with both the Standard Model and with the $bto smu^+mu^-$ anomalies observed in rare $B$-meson decays. We provide a detailed analysis of the impact of the partial angular distribution, the full angular distribution, and the $Lambda_bto Lambdamu^+mu^-$ branching fraction on the Wilson coefficients. In this process, we are also able to constrain the size of the production polarization of the $Lambda_b$ baryon at LHCb.
A rare decay $K_L to mu^+ mu^- $ has been measured precisely, while a rare decay $K_S to mu^+ mu^- $ will be observed by an upgrade of the LHCb experiment. Although both processes are almost CP-conserving decays, we point out that an interference contribution between $K_L$ and $K_S$ in the kaon beam emerges from a genuine direct CP violation. It is found that the interference contribution can change $K_S to mu^+ mu^-$ standard-model predictions at $mathcal{O}(60%)$. We also stress that an unknown sign of $mathcal{A}(K_L to gamma gamma)$ can be determined by a measurement of the interference, which can much reduce a theoretical uncertainty of $mathcal{B}(K_L to mu^+ mu^-)$. We also investigate the interference in a new physics model, where the $epsilon_K / epsilon_K$ tension is explained by an additional $Z$-penguin contribution.
We investigate the possibility of explaining the enhancement in semileptonic decays of $bar B to D^{(*)} tau bar u$, the anomalies induced by $bto smu^+mu^-$ in $bar Bto (K, K^*, phi)mu^+mu^-$ and violation of lepton universality in $R_K = Br(bar Bto K mu^+mu^-)/Br(bar Bto K e^+e^-)$ within the framework of R-parity violating (RPV) MSSM. Exchange of down type right-handed squark coupled to quarks and leptons yield interactions which are similar to leptoquark induced interactions that have been proposed to explain the $bar B to D^{(*)} tau bar u$ by tree level interactions and $bto s mu^+mu^-$ anomalies by loop induced interactions, simultaneously. However, the Yukawa couplings in such theories have severe constraints from other rare processes in $B$ and $D$ decays. Although this interaction can provide a viable solution to $R(D^{(*)})$ anomaly, we show that with the severe constraint from $bar B to K u bar u$, it is impossible to solve the anomalies in $bto s mu^+mu^-$ process simultaneously.
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