Unitarity Bounds for Semileptonic Decays in Lattice QCD

Abstract

In this work we discuss in detail the non-perturbative determination of the momentum dependence of the form factors entering in semileptonic decays using unitarity and analyticity constraints. The method contains several new elements with respect to previous proposals and allows to extract, using suitable two-point functions computed non-perturbatively, the form factors at low momentum transfer $q^2$ from those computed explicitly on the lattice at large $q^2$, without any assumption about their $q^2$-dependence. The approach will be very useful for exclusive semileptonic $B$-meson decays, where the direct calculation of the form factors at low $q^2$ is particularly difficult due to large statistical fluctuations and discretisation effects. As a testing ground we apply our approach to the semileptonic $D\to K\ell {\nu }_{\ell }$ decay, where we can compare the results of the unitarity approach to the explicit direct lattice calculation of the form factors in the full $q^2$-range. We show that the method is very effective and that it allows to compute the form factors with rather good precision.

66 pages, 13 figures and 10 tables. Minor changes matched to the version accepted by PRD

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Cited by in corpus (15)

• $|V_{cb}|$ and $R(D^{(\ast )})$ using lattice QCD and unitarity
• Constraints for the semileptonic $B\to D^{(\ast )}$ form factors from lattice QCD simulations of two-point correlation functions
• $B\to D\ell {\nu }_{\ell }$ form factors beyond leading power and extraction of $|V_{cb}|$ and $R(D)$
• Exclusive determinations of $|V_{cb}|$ and $R(D^{\ast })$ through unitarity
• Review of Semileptonic $B$ Anomalies
• $|V_{cb}|$, Lepton Flavour Universality and $SU(3{)}_F$ symmetry breaking in $B_s\to D_s^{(\ast )}\ell {\nu }_{\ell }$ decays through unitarity and lattice QCD
• Discriminating $B\to D^{\ast }\ell \nu$ form factors via polarization observables and asymmetries
• Dispersive bounds for local form factors in ${\Lambda }_b\to \Lambda$ transitions
• Relations among $B_c\to J/\psi ,{\eta }_c$ form factors
• Constraining inverse moment of $B$-meson distribution amplitude using Lattice QCD data
• Exclusive semileptonic $B$-meson decays using lattice QCD and unitarity
• Branching Fraction of the Decay $B^{+}\to {\pi }^{+}{\tau }^{+}{\tau }^{-}$ and Lepton Flavor Universality Test via the Ratio $R_{\pi }(\tau /\mu )$
• Transition form factors for $D/B$ to $a_0(980)$ from light-cone QCD sum rules
• Self-consistent optimization of the $z$-Expansion for $B$ meson decays
• Determination of $B$-meson distribution amplitudes from $B\to \pi ,K,D$ transition form factors