Heavy meson semileptonic differential decay rate in two dimensions in the large Nc

Abstract

We study QCD in 1+1 dimensions in the large $N_c$ limit using light-front Hamiltonian perturbation theory in the $1/N_c$ expansion. We use this formalism to exactly compute hadronic transition matrix elements for arbitrary currents at leading order in $1/N_c$. We compute the semileptonic differential decay rate of a heavy meson, $d\Gamma /dx$, and its moments, $M_N$, using the hadronic matrix elements obtained previously. We put some emphasis in trying to understand parity invariance. We also study with special care the kinematic region where the operator product expansion ($1/N\sim 1-x\sim 1$) or non-local effective field theories ($1/N\sim 1-x\sim {\Lambda }_{QCD}/m_Q$) can be applied. We then compare with the results obtained using an effective field theory approach based on perturbative factorization, with the focus to better understand quark-hadron duality. At the end of the day, using effective field theories, we have been able to obtain expressions for the moments with relative accuracy of $O({\Lambda }_{QCD}^2/m_Q^2)$ in the kinematic region where the operator product expansion can be applied, and with relative accuracy of $O({\Lambda }_{QCD}/m_Q)$ in the kinematic region where non-local effective field theories can be applied. These expressions agree, within this precision, with those obtained from the hadronic result using the layer-function approximation plus Euler-McLaurin expansion. Very good numerical agreement for the moments is obtained between the exact result and the result using effective field theories.

arXiv comment52 pages, 30 figures, references added, small modifications, some discussion of the four dimensional case changed, journal version

References in corpus (18)

• An effective field theory for collinear and soft gluons: heavy to light decays
• Soft-Collinear Factorization in Effective Field Theory
• Asymptotic expansion of Feynman integrals near threshold
• Summing Sudakov logarithms in B -> X_s + gamma in effective field theory
• Effective field theories for heavy quarkonium
• Soft-collinear effective theory and heavy-to-light currents beyond leading power
• The Zero-Bin and Mode Factorization in Quantum Field Theory
• Factorization and Endpoint Singularities in Heavy-to-Light decays
• Heavy flavor decays, OPE and duality in two-Dimensional 't Hooft model
• Power corrections to B\to X_u l ν(X_sγ) decay spectra in the "shape-function" region
• Explicit Quark-hadron Duality in Heavy-light Meson Weak Decays in the 't Hooft Model
• Soft-Collinear Messengers: A New Mode in Soft-Collinear Effective Theory
• Precision Studies of Duality in the 't Hooft Model
• Infrared regulators and SCETII
• Analytical Heavy Quark Expansion in the 't Hooft Model
• Effective hamiltonians for 1/N expansion in two-dimensional QCD
• Neural network parametrization of the lepton energy spectrum in semileptonic B meson decays
• Path Integral Approach to Two-Dimensional QCD in the Light-Front

Cited by in corpus (8)

• 1/N_c and 1/n preasymptotic corrections to Current-Current correlators
• Deep inelastic scattering and factorization in the 't Hooft Model
• Quark-hadron duality for heavy meson mixings in the 't Hooft model
• The neural network approach to parton distribution functions
• Breakdown of the operator product expansion in the 't Hooft model
• Is right-handed current contribution to $\bar{B}\to X_{u}l\nu$ decays corrected by non-trivial vacuum in QCD?
• $B\to X_c\ell \bar{\nu }$ Decay as a Probe of Complex Conjugate Poles
• Heavy meson semileptonic decays in two dimensions in the large Nc