The $KD$, $ηD_s$ interaction in finite volume and the nature of the $D_{s^* 0}(2317)$ resonance

Abstract

An SU(4) extrapolation of the chiral unitary theory in coupled channels done to study the scalar mesons in the charm sector is extended to produce results in finite volume. The theory in the infinite volume produces dynamically the D s * 0 (2317) resonance by means of the coupled channels KD, ηD s . Energy levels in the finite box are evaluated and, assuming that they would correspond to lattice results, the inverse problem of determining the bound states and phase shifts in the infinite volume from the lattice data is addressed. We observe that it is possible to obtain accurate KD phase shifts and the position of the D s * 0 (2317) state, but it requires the explicit consideration of the two coupled channels in the analysis if one goes close to the ηD s threshold. We also show that the finite volume spectra look rather different in case the D s * 0 (2317) is a composite state of the two mesons, or if it corresponds to a non molecular state with a small overlap with the two meson system. We then show that a careful analysis of the finite volume data can shed some light on the nature of the D s * 0 (2317) resonance as a KD molecule or otherwise.

Unitarized Chiral Perturbation Theory in a finite volume: Scalar meson sector

“…Recently, the problem of extracting continuum quantities from synthetic lattice data has also been also discussed in Ref. [31] in the context of meson-meson interaction with charm and the D s * 0 (2317) resonance. The extraction of continuum quantities, at higher energies, may also be performed using dynamical coupled-channels approaches as shown in Ref.…”

$DDK$ system in finite volume

“…This pole is interpreted as the DK bound state, D * s0 (2317) which has been supported by both lattice QCD [35][36][37][38][39][40][41][42][43] and phenomenological studies [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. Based on the DD interaction potential, Eq.…”

“…The discovery of the D * s0 (2317) [1][2][3] and subsequent phenomenological studies [4][5][6][7][8][9][10][11][12][13][14][15][16][17] imply that there is a strongly attractive interaction between D and K. The prevailing idea that the D * s0 (2317) can be understood as a molecular state has been confirmed by many Weinberg-Tomozawa potential calculations [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] and lattice QCD simulations [35][36][37][38][39][40][41][42][43]. It is also found that there is a long-range attractive potential between D and D * s0 (2317).…”

Hidden charm pentaquark with strangeness $P_{cs}^*(4739)$ as a $Σ_{c}\bar{D}\bar{K}$ bound state

“…MeV respectively [14], thus D * s0 (2317) is difficult to be interpreted as a conventional cs meson. On the other hand, due to the strongly attractive DK interaction predicted by chiral perturbation theory and lattice QCD [15,16], D * s0 (2317) can be easily explained as a DK molecule [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. The same molecular picture is adopted to study the pentaquark states, i.e., P c (4312), P c (4440), and P c (4457), discovered by the LHCb Collaboration [34].…”