The $$ \overline{B} $$ → π form factors from QCD and their impact on |Vub|

We revisit light-cone sum rules with pion distribution amplitudes to determine the full set of local $$ \overline{B} $$ B ¯ → π form factors. To this end, we determine all duality threshold parameters from a Bayesian fit for the first time. Our results, obtained at small momentum transfer q2, are extrapolated to large q2 where they agree with precise lattice QCD results. We find that a modification to the commonly used BCL parametrization is crucial to interpolate the scalar form factor between the two q2 regions. We provide numerical results for the form factor parameters — including their covariance — based on simultaneous fit of all three form factors to both the sum rule and lattice QCD results. Our predictions for the form factors agree well with measurements of the q2 spectrum of the semileptonic decay $$ {\overline{B}}^0\to {\pi}^{+}{\mathrm{\ell}}^{-}{\overline{\nu}}_{\mathrm{\ell}} $$ B ¯ 0 → π + ℓ − ν ¯ ℓ . From the world average of the latter we obtain |Vub| = (3.77 ± 0.15) · 10−3, which is in agreement with the most recent inclusive determination at the 1 σ level.

Chiral dynamics and S-wave contributions in $${\bar{B}}^0/D^0 \rightarrow \pi ^{\pm }\eta \ l^{\mp } \nu $$ decays

In this work, we analyze the semi-leptonic decays $$\bar{B}^0/D^0 \rightarrow (a_0(980)^{\pm }\rightarrow \pi ^{\pm }\eta ) l^{\mp } \nu $$ B ¯ 0 / D 0 → ( a 0 ( 980 ) ± → π ± η ) l ∓ ν within light-cone sum rules. The two and three-body light-cone distribution amplitudes (LCDAs) of the B meson and the only available two-body LCDA of the D meson are used. To include the finite-width effect of the $$a_0(980)$$ a 0 ( 980 ) , we use a scalar form factor to describe the final-state interaction between the $$\pi \eta $$ π η mesons, which was previously calculated within unitarized Chiral Perturbation Theory. The result for the decay branching fraction of the $$D^0$$ D 0 decay is in good agreement with that measured by the BESIII Collaboration, while the branching fraction of the $${\bar{B}}^0$$ B ¯ 0 decay can be tested in future experiments.

Relations between b → cτν decay modes in scalar models

As a consequence of the Ward identity for hadronic matrix elements, we find relations between the differential decay rates of semileptonic decay modes with the underlying quark-level transition b → cτν, which are valid in scalar models. The decay-mode dependent scalar form factor is the only necessary theoretical ingredient for the relations. Otherwise, they combine measurable decay rates as a function of the invariant mass-squared of the lepton pair q2 in such a way that a universal decay-mode independent function is found for decays to vector and pseudoscalar mesons, respectively. This can be applied to the decays $$ B\to {D}^{\ast}\tau v,{B}_s\to {D}_s^{\ast}\tau v,{B}_c\to J/\psi \tau v $$ B → D ∗ τv , B s → D s ∗ τv , B c → J / ψτv and B → Dτv, Bs → Dsτv, Bc → ηcτv, with implications for R(D(*)), $$ R\left({D}_s^{\left(\ast \right)}\right) $$ R D s ∗ , R(J/ψ), R(ηc), and ℬ(Bc → τv). The slope and curvature of the characteristic q2-dependence is proportional to scalar new physics parameters, facilitating their straight forward extraction, complementary to global fits.

Equivalence Between Vector Meson Dominance and Unitarised Chiral Perturbation Theory

It is explicitly shown that either the approximate solution of the integral equation for the inverse of the pion form facto,r or the result of the Pad\(\text{\'e}\) approximant method of resumming the one loop Chiral Perturbation Theory (CPTH) are equivalent to the standard vector meson dominance (VMD) models, using the vector meson coupling to two pseudoscalars given by the KSRF relation. Inconsistencies between the one loop CPTH and its unitarised version (or the VMD model) are pointed out. The situation is better for the CPTH calculation of the scalar form factor and the related S-wave $\pi \pi$ scattering. The branching ratios of \(\tau \to \pi^+ \pi^0 \nu \), \(\tau \to K \pi \nu \), \(\tau \to K^+ \eta \nu\) and $\tau \to K^+ \bar{K^0} \nu\) using only two inputs as the \(\rho\) and \(K^*\) masses, or the two corresponding rms radii, agree with the experimental data. Using the same number of parameters, the corresponding one loop CPTH calculation cannot explain the $\tau$ data.