$B\to X_c\ell \bar{\nu }$ 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.

arXiv comment8 pages, 5 figures; v3: version published in PRD

References in corpus (36)

• Weak Decays Beyond Leading Logarithms
• FLAG Review 2021
• QCD Predictions for Lepton Spectra in Inclusive Heavy Flavour Decays
• Inclusive Semileptonic B and Polarized Lambda_b Decays from QCD
• Dispersive Bounds on the Shape of B -> D^(*) l nu Form Factors
• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of 2021
• Differential Distributions in Semileptonic Decays of the Heavy Flavors in QCD
• Sum Rules for Heavy Flavor Transitions in the SV Limit
• Model-Independent Extraction of |V_{cb}| Using Dispersion Relations
• Heavy Quark Expansion for the Inclusive Decay $\bar{B}\to \tau \bar{\nu }X$
• Spectral functions of confined particles
• Can the differences in the determinations of $V_{ub}$ and $V_{cb}$ be explained by New Physics?
• Three loop calculations and inclusive $V_{cb}$
• Constraining new physics in $b\to c\ell \nu$ transitions
• Operator Product Expansion, Heavy Quarks, QCD Duality and its Violations
• Bayesian fit analysis to full distribution data of $\bar{B}\to D^{(\ast )}\ell \bar{\nu }$: $|V_{cb}|$ determination and New Physics constraints
• Heavy flavor decays, OPE and duality in two-Dimensional 't Hooft model
• Explicit Quark-hadron Duality in Heavy-light Meson Weak Decays in the 't Hooft Model
• Analytical properties of the quark propagator from truncated Dyson-Schwinger equation in complex Euclidean space
• Complex poles and spectral function of Yang-Mills theory
• Precision Studies of Duality in the 't Hooft Model
• Disintegration of beauty: a precision study
• Reconstructing confined particles with complex singularities
• Complex poles and spectral functions of Landau gauge QCD and QCD-like theories
• Violations of Local Duality in the Heavy Quark Sector
• Global duality in heavy flavor decays in the 't Hooft model
• Quark-Hadron Duality in the 't Hooft Model for Meson Weak Decays: Different Quark Diagram Topologies
• Global duality in heavy flavor hadronic decays
• Heavy Quark Expansion and Preasymptotic Corrections to Decay Widths in the 't Hooft Model
• Pauli Interference in the 't Hooft Model: Heavy Quark Expansion and Quark-Hadron Duality
• Heavy meson semileptonic differential decay rate in two dimensions in the large Nc
• Instanton Contribution to $B\to X_{u}e\bar{\nu }$ Decay
• Instantons and the endpoint of the lepton energy spectrum in charmless semileptonic $B$ decays
• Instanton Contribution to $B\to X_s\gamma$ Decay
• Is right-handed current contribution to $\bar{B}\to X_{u}l\nu$ decays corrected by non-trivial vacuum in QCD?
• Extracting a model quark propagator's spectral density