Constraining the hidden-charm pentaquark predictions and discriminating the Pc(4440) and Pc(4457) spins through the effective range expansion

Abstract

The Weinberg compositeness criterion dictates that a pure shallow bound state is characterized by a large scattering length a0≫O(1/β) and a positive effective range r0 that naturally scales to the size of O(1/β), where 1/β signifies the interaction range. In constructing the contact-range effective field theory (EFT) up to the next-to-leading order to describe the pentaquarks Pc(4312), Pc(4440), and Pc(4457) observed by the LHCb collaboration in 2019, we match the effective range r0 at single-channel situation for these pentaquarks with the low-energy couplings within the EFT framework. Three different schemes are used to connect the couplings with the effective range. We find positive effective ranges r0 of the natural size of O(1/β) for the spin configurations JP=32− for Pc(4440) and JP=12− for Pc(4457) within the molecular D¯*Σc description. Additionally, predictions from the power counting for low-energy couplings or Wilsonian coefficients suggest that, under heavy quark spin symmetry, the broad Pc(4380) resonance, discovered by the LHCb collaboration in 2015, when considered as part of the single-channel D¯(*)Σc(*) molecular system alongside Pc(4312), Pc(4440), and Pc(4457), has a mass of approximately 4376  MeV. Published by the American Physical Society 2025