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Register a new userLight Resonances and the Low-$q^2$ Bin of $R_{K^*}$
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LHCb has reported hints of lepton-flavor universality violation in the rare decays $B to K^{(*)} ell^+ell^-$, both in high- and low-$q^2$ bins. Although the high-$q^2$ hint may be explained by new short-ranged interactions, the low-$q^2$ one cannot. We thus explore the possibility that the latter is explained by a new light resonance. We find that LHCbs central value of $R_{K^*}$ in the low-$q^2$ bin is achievable in a restricted parameter space of new-physics scenarios in which the new, light resonance decays preferentially to electrons and has a mass within approximately $10$ MeV of the di-muon threshold. Interestingly, such an explanation can have a kinematic origin and does not require a source of lepton-flavor universality violation. A model-independent prediction is a narrow peak in the differential $B to K^* e^+e^-$ rate close to the di-muon threshold. If such a peak is observed, other observables, such as the differential $B to K e^+e^-$ rate and $R_K$, may be employed to distinguish between models. However, if a low-mass resonance is not observed and the low-$q^2$ anomaly increases in significance, then the case for an experimental origin of the lepton-flavor universality violating anomalies would be strengthened. To further explore this, we also point out that, in analogy to $J/psi$ decays, $e^+e^-$ and $mu^+mu^-$ decays of $phi$ mesons can be used as a cross check of lepton-flavor universality by LHCb with $5$ fb$^{-1}$ of integrated luminosity.
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We present the proton and neutron vector form factors in a convenient parametric form that is optimized for momentum transfers $lesssim$ few GeV$^2$. The form factors are determined from a global fit to electron scattering data and precise charge radius measurements. A new treatment of radiative corrections is applied. This parametric representation of the form factors, uncertainties and correlations provides an efficient means to evaluate many derived observables. We consider two classes of illustrative examples: neutrino-nucleon scattering cross sections at GeV energies for neutrino oscillation experiments and nucleon structure corrections for atomic spectroscopy. The neutrino-nucleon charged current quasielastic (CCQE) cross section differs by 3-5% compared to commonly used form factor models when the vector form factors are constrained by recent high-statistics electron-proton scattering data from the A1 Collaboration. Nucleon structure parameter determinations include: the magnetic and Zemach radii of the proton and neutron, $[r_M^p, r_M^n] = [ 0.739(41)(23), 0.776(53)(28)]$ fm and $[r_Z^p, r_Z^n] = [ 1.0227(94)(51), -0.0445(14)(3)]$ fm; the Friar radius of nucleons, $[(r^p_F)^3, (r^n_F)^3] = [2.246(58)(2), 0.0093(6)(1)]$ fm$^3$; the electric curvatures, $[langle r^4 rangle^p_E, langle r^4 rangle^n_E ] = [1.08(28)(5), -0.33(24)(3)]$ fm$^4$; and bounds on the magnetic curvatures, $[ langle r^4 rangle^p_M, langle r^4 rangle^n_M ] = [ -2.0(1.7)(0.8), -2.3(2.1)(1.1)]$ fm$^4$. The first and dominant uncertainty is propagated from the experimental data and radiative corrections, and the second error is due to the fitting procedure.
We identify a single six-dimensional effective operator $O_{ellell}$ that can account for the Cabibbo angle anomaly naturally, without any tension with the electroweak precision observables. The renormalization group running of $O_{ell ell}$ yields the required new couplings of $W$ and $Z$ bosons in exactly the right proportion. When generated as a result of a $Z$ model, the non-universal leptonic coupling needed for this operator can also contribute to the lepton flavor universality violating $R_{K^{(*)}}$ anomaly, generating the preferred relation $C_9=-C_{10}$ between the Wilson coefficients. We find the region in parameter space of $Z$ mass and couplings that offer a simultaneous solution to both these anomalies, and argue that $O_{ell ell}$ is a unique single operator that can offer such a resolution. Our arguments may also be extended to multi-operator scenarios like $U_1$ vector leptoquark, which is known to address multiple anomalies that violate the lepton flavor universality.
The LHCb measurements of the $mu / e$ ratio in $B to K ell ell$ decays $(R_{K^{}})$ indicate a deficit with respect to the Standard Model prediction, supporting earlier hints of lepton universality violation observed in the $R_{K^{(*)}}$ ratio. Possible explanations of these $B$-physics anomalies include heavy $Z$ bosons or leptoquarks mediating $b to s mu^+ mu^- $. We note that a muon collider can directly measure this process via $mu^+ mu^- to b bar s$ and can shed light on the lepton non-universality scenario. Investigating currently discussed center-of-mass energies $sqrt{s} = 3$, 6 and 10 TeV, we show that the parameter space of $Z$ and $S_3$ leptoquark solutions to the $R_{K^{(*)}}$ anomalies can be mostly covered. Effective operators explaining the anomalies can be probed with the muon collider setup $sqrt{s} = 6~{rm TeV}$ and integrated luminosity $L = 4~{rm ab^{-1}}$.
We present a model to explain LHCbs recent measurements of $R_K$ and $R_{K^{ast}}$ based on an anomaly-free, spontaneously-broken $U(1)_F$ gauge symmetry, without any fermionic fields beyond those of the Standard Model (SM). The model explains the hierarchical heaviness of the third family and the smallness of quark mixing. The $U(1)_F$ charges of the third family of SM fields and the Higgs doublet are set equal to their respective hypercharges. A heavy $Z^prime$ particle with flavour-dependent couplings can modify the $[overline{b_L} gamma^rho s_L][overline{mu_L} gamma_rho mu_L]$ effective vertex in the desired way. The $Z^prime$ contribution to $B_s-overline{B_s}$ mixing is suppressed by a small mixing angle connected to $V_{ts}$, making the constraint coming from its measurement easier to satisfy. The model can explain $R_K$ and $R_{K^{(ast)}}$ whilst simultaneously passing other constraints, including measurements of the lepton flavour universality of $Z$ couplings.
The recent measurement of $R_{K^*}$ is yet another hint of new physics (NP), and supports the idea that it is present in $bto smu^+mu^-$ decays. We perform a combined model-independent and model-dependent analysis in order to deduce properties of this NP. Like others, we find that the NP must obey one of two scenarios: (I) $C_9^{mumu}({rm NP}) < 0$ or (II) $C_9^{mumu}({rm NP}) = - C_{10}^{mumu}({rm NP}) < 0$. A third scenario, (III) $C_9^{mumu}({rm NP}) = - C_{9}^{prime mumu}({rm NP})$, is rejected largely because it predicts $R_K = 1$, in disagreement with experiment. The simplest NP models involve the tree-level exchange of a leptoquark (LQ) or a $Z$ boson. We show that scenario (II) can arise in LQ or $Z$ models, but scenario (I) is only possible with a $Z$. Fits to $Z$ models must take into account the additional constraints from $B^0_s$-${bar B}^0_s$ mixing and neutrino trident production. Although the LQs must be heavy, O(TeV), we find that the $Z$ can be light, e.g., $M_{Z} = 10$ GeV or 200 MeV.
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