Extraction of $ND$ scattering lengths from the ${\Lambda }_b\to {\pi }^{-}p{D}^0$ decay and properties of the ${\Sigma }_c(2800{)}^{+}$

Abstract

The isovector and isoscalar $ND$ $s$-wave scattering lengths are extracted by fitting to the LHCb data of the $p{D}^0$ invariant-mass distribution in the decay ${\Lambda }_b\to {\pi }^{-}p{D}^0$, making use of the cusp effect at the $n{D}^{+}$ threshold. The analysis is based on a coupled-channel nonrelativistic effective field theory. We find that the real part of the isovector $ND$ scattering length is unnaturally large due to the existence of a near-threshold state with a mass around 2.8 GeV. The state is consistent with the ${\Sigma }_c(2800{)}^{+}$ resonance observed at Belle. Our results suggest that it couples strongly to the $ND$ channel in an $s$-wave, and that its quantum numbers are $J^P=1/2^{-}$. The strong cusp behavior at the $n{D}^{+}$ threshold can be verified using updated LHCb data.

Comments: 9 pages, 6 figures; version to be published in Phys. Lett. B