The Baryon Isgur-Wise Function in the Large $N_c$ Limit

Abstract

In the large $N_c$ limit, the $Λ_b$ and $Λ_c$ can be treated as bound states of chiral solitons and mesons containing a heavy quark. We show that the soliton and heavy meson are bound in an attractive harmonic oscillator potential. The Isgur-Wise function for $Λ_b\rightarrowΛ_c\, e^-\,\barν_e$ decay is computed in the large $N_c$ limit. Corrections to the form factor which depend on $m_N/ m_Q$ can be summed exactly ($m_N$ and $m_Q$ are the nucleon and heavy quark masses). We find that this symmetry breaking correction at zero recoil is only $1\%$.