On P-wave meson decay constants in the heavy quark limit of QCD

Abstract

In previous work it has been shown that, either from a sum rule for the subleading Isgur-Wise function ${\xi }_3(1)$ or from a combination of Uraltsev and Bjorken SR, one infers for $P$-wave states $|{\tau }_{1/2}(1)|\ll |{\tau }_{3/2}(1)|$. This implies, in the heavy quark limit of QCD, a hierarchy for the {\it production} rates of $P$-states $\Gamma ({\bar{B}}_d\to D(\frac{1}{2})\ell \nu )\ll \Gamma ({\bar{B}}_d\to D(\frac{3}{2})\ell \nu )$ that seems at present to be contradicted by experiment. It was also shown that the decay constants of $j=\frac{3}{2}$ $P$-states vanish in the heavy quark limit of QCD, $f_{3/2}^{(n)}=0$. Assuming the {\it model} of factorization in the decays ${\bar{B}}_d\to {\bar{D}}_s^{\ast \ast }D$, one expects the opposite hierarchy for the {\it emission} rates $\Gamma ({\bar{B}}_d\to {\bar{D}}_s(\frac{3}{2})D)\ll \Gamma ({\bar{B}}_d\to {\bar{D}}_s(\frac{1}{2})D)$, since $j=\frac{1}{2}$ $P$-states are coupled to vacuum. Moreover, using Bjorken SR and previously discovered SR involving heavy-light meson decay constants and IW functions, one can prove that the sums $\sum _n(\frac{f^{(n)}}{f^{(0)}}{)}^2$, $\sum _n(\frac{f_{1/2}^{(n)}}{f^{(0)}}{)}^2$ (where $f^{(n)}$ and $f_{1/2}^{(n)}$ are the decay constants of $S$-states and $j=\frac{1}{2}$ $P$-states) are divergent. This situation seems to be realized in the relativistic quark models à la Bakamjian and Thomas, that satisfy HQET and predict decays constants $f^{(n)}$ and $f_{1/2}^{(n)}$ that do not decrease with the radial quantum number $n$.

7 pages, Latex

References in corpus (4)

• QCD factorization for exclusive, non-leptonic B meson decays: General arguments and the case of heavy-light final states
• New Exact Heavy Quark Sum Rules
• Uraltsev Sum Rule in Bakamjian-Thomas Quark Models
• One Interesting New Sum Rule Extending Bjorken's to order {1/m_Q}

Cited by in corpus (9)

• The Physics of the B Factories
• Dynamics and Decay of Heavy-Light Hadrons
• Masses and decay constants of the $D_{s0}^{\ast }(2317)$ and $D_{s1}(2460)$ from $N_f=2$ lattice QCD close to the physical point
• Ds0*(2317) and Ds1(2460) mesons in two-body B-meson decays
• Decay constants of $P$-wave mesons
• Understanding the nature of $D_s(2317)$ and $D_s(2460)$ through nonleptonic B Decays
• Nonleptonic $B\to D^{(\ast )}{D}_{sJ}^{(\ast )}$ decays and the nature of the orbitally excited charmed-strange mesons
• Probing $D_{s0}^{\ast }(2317)$ in the decays of $B$ to two charmed mesons
• The $B^{+(0)}\to {\bar{D}}^{0(-)}{D}_{s0}^{\ast }(2317{)}^{+}$ decays and the molecular structure of $D_{s0}^{\ast }(2317)$