Bound on the curvature of the Isgur-Wise function of the baryon semileptonic decay Lambda_b -> Lambda_c + l + nu

Abstract

In the heavy quark limit of QCD, using the Operator Product Expansion, the formalism of Falk for hadrons or arbitrary spin, and the non-forward amplitude, as proposed by Uraltsev, we formulate sum rules involving the Isgur-Wise function ${\xi }_{\Lambda }(w)$ of the baryon transition ${\Lambda }_b\to {\Lambda }_c\ell {\overline{\nu }}_{\ell }$, where the light cloud has $j^P=0^{+}$ for both initial and final baryons. We recover the lower bound for the slope ${\rho }_{\Lambda }^2=-{\xi }_{\Lambda }^{\prime }(1)\ge 0$ obtained by Isgur et al., and we generalize it by demonstrating that the IW function ${\xi }_{\Lambda }(w)$ is an alternate series in powers of $(w-1)$, i.e. $(-1{)}^n{\xi }_{\Lambda }^{(n)}(1)\ge 0$. Moreover, exploiting systematically the sum rules, we get an improved lower bound for the curvature in terms of the slope, ${\sigma }_{\Lambda }^2=\xi {"}_{\Lambda }(1)\ge \frac{3}{5}[{\rho }_{\Lambda }^2+({\rho }_{\Lambda }^2{)}^2]$. This bound constrains the shape of the Isgur-Wise function and it will be compelling in the analysis of future precise data on the differential rate of the baryon semileptonic decay ${\Lambda }_b\to {\Lambda }_c\ell {\overline{\nu }}_{\ell }$, that has a large measured branching ratio, of about 5%.

16 pages

References in corpus (2)

• Perturbative corrections to curvature sum rules
• Explicit form of the Isgur-Wise function in the BPS limit

Cited by in corpus (5)

• Precision Model-Independent Bounds from Global Analysis of $b\to c\ell \nu$ Form Factors
• Heavy baryon wave functions, Bakamjian-Thomas approach to form factors, and observables in ${\Lambda }_b\to {\Lambda }_c\left({\frac{1}{2}}^{\pm }\right)\ell \overline{\nu }$ transitions
• Isgur-Wise functions and unitary representations of the Lorentz group : the baryon case j = 0
• Searching for New Physics in Semi-Leptonic Baryon Decays
• On the form factors of semileptonic baryon decays in Heavy Quark Effective Theory