$B\to X_c\ell \bar{\nu }$ Decay as a Probe of Complex Conjugate Poles

Abstract

In this work, nontrivial analytic structure of the quark propagator is discussed for $B$-meson inclusive decays. Attributed to invalidity of the standard Källén-Lehman spectral representation, complex conjugate poles alter the evaluation of decay rates, which lead to violation of quark-hadron duality. As phenomenological observables, widths in $B\to X_c\ell \bar{\nu }$ decay as well as the lifetime of the $B_d^0$ meson are discussed. In the presence of the mentioned nonanalytical contributions, the possibility for resolving the $|V_{cb}|$ puzzle is addressed. It is demonstrated that there exists a parameter region, which explains $|V_{cb}|$ and $B_d^0$-meson lifetime simultaneously within 1$\sigma$ via the complex conjugate poles from a charm quark.

8 pages, 5 figures; v3: version published in PRD

References in corpus (8)

• FLAG Review 2021
• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of 2021
• Three loop calculations and inclusive $V_{cb}$
• Can the differences in the determinations of $V_{ub}$ and $V_{cb}$ be explained by New Physics?
• Disintegration of beauty: a precision study
• Reconstructing confined particles with complex singularities
• Heavy meson semileptonic differential decay rate in two dimensions in the large Nc
• Is right-handed current contribution to $\bar{B}\to X_{u}l\nu$ decays corrected by non-trivial vacuum in QCD?