^{1}

^{1}

^{2}

^{3}

^{1}

^{2}

^{3}

^{3}.

In this work, we study the resonances near the thresholds of the open heavy-flavor hadrons using the effective-range-expansion method. The unitarity, analyticity, and compositeness coefficient are also taken into account in our theoretical formalism. We consider the

Since the discovery of the

By combining the ERE, unitarity, analyticity, and the compositeness coefficients developed in [

The basic staring point of our theoretical formalism is the ERE up to the next-to-leading order:

We mention that a more general expression to write the scattering amplitude near threshold is to include the so-called Castillejo-Dalitz-Dyson (CDD) poles. The standard ERE in (

The partial-wave amplitude given in (

Let us now consider a resonance

The resonance pole corresponds to the zero of the denominator of

Substituting (

In [

In the next section, we proceed to study several near-threshold resonances within the present ERE approach. Let us notice that if this type of ERE study is applied to a near-threshold resonance which is composite of the nearby channel (the so-called elastic one) then

Before entering the detailed discussions, we stress that the theoretical approach developed is based on the elastic

The crossed-channel effects, such as the light-flavor hadron exchanges, are neglected in (

The masses and widths of the

In the second and third columns, the masses and widths of the ~~LHCb~~) and the PDG average. To make a conservative error estimate, the largest error bars are taken for the asymmetric ones in the values from the LHCb and PDG. We assume that the

Resonance | Mass | Width | Threshold | | | |
---|---|---|---|---|---|---|

(MeV) | (MeV) | (MeV) | (fm) | (fm) | ||

| | | | | | |

| ||||||

| | | | | | |

| ||||||

| | | | | | |

| ||||||

| | | | | | |

| ||||||

| | | | | | |

| | | | | | |

| | | | | | |

For the

It is proposed in [

Due to the closeness of the

The quantum numbers of the

We have employed the approach of [

References [

In turn, [

We give in Table

Set of numbers

Asymptotic | |||||
---|---|---|---|---|---|

Resonance | State | | | | |

| | | | | |

| |||||

| | | | | |

| |||||

| | | | | |

| |||||

| | | | | |

| |||||

| | | | | |

| | | | | |

| | | | | |

For the resonance

Let us also mention that the ERE for scattering up to and including the effective range, like in our study here, drives necessarily to purely imaginary values for

In this work, we have combined the effective range expansion, unitarity, analyticity, and the compositeness coefficient to study the resonance dynamics around the threshold energy region. We only focus on the elastic

We have applied the theoretical formalism to the

The data used to support the findings of this study are included within the article.

The authors declare that they have no conflicts of interest.

Zhi-Hui Guo would like to thank En Wang for the informative communication on the

^{±}→K

^{±}

^{+}

^{−}J/

^{0}

_{s}Decays