$X(3872)$ Relevant $D\bar{D}^*$ Scattering in $N_f=2$ Lattice QCD

TL;DR

This study uses lattice QCD to analyze $Dar{D}^*$ scattering at various pion masses, revealing a bound state and a resonance near 4.0 GeV, consistent with the $ ext{chi}_{c1}(4010)$ observed by LHCb.

Contribution

First lattice QCD analysis of $Dar{D}^*$ scattering revealing a bound state and resonance near 4.0 GeV, supporting the existence of $ ext{chi}_{c1}(4010)$.

Findings

Identified a shallow bound state below the $Dar{D}^*$ threshold.

Detected a resonance near 4.0 GeV with a width of 40-60 MeV.

Results are compatible with the $ ext{chi}_{c1}(4010)$ observed experimentally.

Abstract

We study the $S$-wave $D\bar{D}^*(I=0)$ scattering at four different pion masses $m_\pi$ ranging from 250 MeV to 417 MeV from $N_f=2$ lattice QCD. Three energy levels $E_{2,3,4}$ are extracted at each $m_\pi$. The analysis of $E_{2,3}$ using the effective range expansion (ERE) comes out with a shallow bound state below the $D\bar{D}^*$ threshold, and the phase shifts at $E_{3,4}$ indicate the possible existence of a resonance near 4.0 GeV. We also perform a joint analysis to $E_{2,3,4}$ through the $K$-matrix parameterization of the scattering amplitude. In this way, we observe a $D\bar{D}^*$ bound state whose properties are almost the same as that from the ERE analysis. At each $m_\pi$, this joint analysis also results in a resonance pole with a mass slightly above 4.0 GeV and a width around 40-60 MeV, which are compatible with the properties of the newly observed $\chi_{c1}(4010)$ by LHCb. More scrutinized lattice QCD calculations are desired to check the existence of this resonance.