Paper detail

Extraction of $ND$ scattering lengths from the $Λ_b\rightarrowπ^-pD^0$ decay and properties of the $Σ_c(2800)^+$

The isovector and isoscalar $ND$ $s$-wave scattering lengths are extracted by fitting to the LHCb data of the $pD^0$ invariant-mass distribution in the decay $Λ_b\rightarrowπ^-pD^0$, making use of the cusp effect at the $nD^+$ 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 $Σ_c(2800)^+$ 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 $nD^+$ threshold can be verified using updated LHCb data.