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Register a new userIs there really a $W to tau u$ puzzle?
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According to the Particle Data Group, the measurements of ${cal B}(W^+ to tau^+ u_tau)$ and ${cal B}(W^+ to ell^+ u_ell)$ ($ell = e,mu$) disagree with one another at the $2.3sigma$ level. In this paper, we search for a new-physics (NP) explanation of this $W to tau u$ puzzle. We consider two NP scenarios: (i) the $W$ mixes with a $W$ boson that couples preferentially to the third generation, (ii) $tau_{L,R}$ and $ u_{tau L}$ mix with isospin-triplet leptons. Unfortunately, once other experimental constraints are taken into account, neither scenario can explain the above experimental result. Our conclusion is that the $W to tau u$ puzzle is almost certainly just a statistical fluctuation.
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The heliocentric redshifts ($z_mathrm{hel}$) reported for 150 Type Ia supernovae in the Pantheon compilation are significantly discrepant from their corresponding values in the JLA compilation. Both catalogues include corrections to the redshifts and magnitudes of the supernovae to account for the motion of the heliocentric frame relative to the `CMB rest frame, as well as corrections for the directionally coherent bulk motion of local galaxies with respect to this frame. The latter is done employing modelling of peculiar velocities which assume the $Lambda$CDM cosmological model but nevertheless provide evidence for residual bulk flows which are discordant with this model (implying that the observed Universe is in fact anisotropic). Until recently such peculiar velocity corrections in the Pantheon catalogue were made at redshifts exceeding 0.2 although there is no data on which to base such corrections. We study the impact of these vexed issues on the 4.4 $sigma$ discrepancy between the Hubble constant of $H_0 = 67.4 pm 0.5$ km/s/Mpc inferred from observations of CMB anisotropies by Planck assuming $Lambda$CDM, and the measurement of $H_0 = 73.5 pm 1.4$ km/s/Mpc by the SH0ES project which extended the local distance ladder using Type Ia supernovae. Using the same methodology as the latter study we find that for supernovae whose redshifts are discrepant between Pantheon and JLA with $Delta z_mathrm{hel} > 0.0025$, the Pantheon redshifts favour $H_0 simeq 72$ km/s/Mpc, while the JLA redshifts favour $H_0 simeq 68$ km/s/Mpc. Thus the discrepancies between SNe Ia datasets are sufficient to undermine the claimed `Hubble tension. We further note the systematic variation of $H_0$ by $sim$ 6-9 km/s/Mpc across the sky seen in multiple datasets, implying that it cannot be measured locally to better than $sim$ 10% in a model-independent manner.
We evaluate long-distance electromagnetic (QED) contributions to $bar{B}{}^0 to D^+ tau^{-} bar{ u}_{tau}$ and $B^- to D^0 tau^{-} bar{ u}_{tau}$ relative to $bar{B}{}^0 to D^+ mu^{-} bar{ u}_{mu}$ and $B^- to D^0 mu^{-} bar{ u}_{mu}$, respectively, in the standard model. We point out that the QED corrections to the ratios $R(D^{+})$ and $R(D^{0})$ are not negligible, contrary to the expectation that radiative corrections are almost canceled out in the ratio of the two branching fractions. The reason is that long-distance QED corrections depend on the masses and relative velocities of the daughter particles. We find that theoretical predictions for $R(D^{+})^{tau/mu}$ and $R(D^{0})^{tau/mu}$ can be amplified by $sim4%$ and $sim3%$, respectively, for the soft-photon energy cut in range $20$-$40$ MeV.
We derive the corrections induced by the W-boson propagator to the differential rates of the leptonic decay of a polarized muon and tau lepton. Results are presented both for decays inclusive of inner bremsstrahlung as well as for radiative ones, when a photon emitted in the decay process is measured. The numerical effect of these corrections is discussed. The definition of the Fermi constant is briefly reviewed.
The meson decays $Bto Dtau u$ and $Bto D^* tau u$ are sensitive probes of the $bto ctau u$ transition. In this work we present a complete framework to obtain the maximum information on the physics of $Bto D^{(*)}tau u$ with polarized $tau$ leptons and unpolarized $D^{(*)}$ mesons. Focusing on the hadronic decays $tauto pi u$ and $tautorho u$, we show how to extract seven $tau$ asymmetries from a fully differential analysis of the final-state kinematics. At Belle II with $50~text{ab}^{-1}$ of data, these asymmetries could potentially be measured with percent level statistical uncertainty. This would open a new window into possible new physics contributions in $bto ctau u$ and would allow us to decipher its Lorentz and gauge structure.
In this addendum to arXiv:1811.09603 we update our results including the recent measurement of ${cal R}(D)$ and ${cal R}(D^*)$ by the Belle collaboration: ${cal R}(D)_{rm Belle} = 0.307pm0.037pm0.016$ and ${cal R}(D^*)_{rm Belle}=0.283pm0.018pm0.014$, resulting in the new HFLAV fit result ${cal R}(D) = {0.340pm0.027 pm 0.013}$, ${cal R}(D^*) = {0.295pm0.011 pm 0.008 }$, exhibiting a $3.1,sigma$ tension with the Standard Model. We present the new fit results and update all figures, including the relevant new collider constraints. The updated prediction for ${cal R}(Lambda_c)$ from our sum rule reads ${cal R}(Lambda_c)= mathcal{R}_{rm SM}(Lambda_c) left( 1.15 pm 0.04 right) = 0.38 pm 0.01 pm 0.01$. We also comment on theoretical predictions for the fragmentation function $f_c$ of $bto B_c$ and their implication on the constraint from $B_{u/c}totau u$ data.
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