Vector resonance $X_1(2900)$ and its structure

TL;DR

This paper models the $X_1(2900)$ resonance as an exotic vector tetraquark, calculates its properties using QCD sum rules, and compares results with experimental data, suggesting it could be a tetraquark state.

Contribution

It provides a theoretical QCD-based model of the $X_1(2900)$ as a vector tetraquark and computes its mass, width, and couplings, offering insights into its internal structure.

Findings

Calculated mass $m=(2890\,\pm\,122)$ MeV, close to experimental value.

Estimated width $\,(93\pm 13)$ MeV, consistent within errors.

Supports the interpretation of $X_1(2900)$ as a vector tetraquark.

Abstract

The new vector resonance $X_1(2900)$ observed recently by LHCb in the $ D^{-}K^{+}$ invariant mass distribution in the decay $B^{+} \to D^{+}D^{-}K^{+}$ is studied to uncover internal structure of this state, and calculate its physical parameters. In the present paper, the resonance $ X_1(2900)$ is modeled as an exotic vector state, $ J^P=1^- $, built of the light diquark $u^{T}C\gamma_5d$ and heavy antidiquark $\overline{c} \gamma_{\mu}\gamma_5C\overline{s}^{T}$. The mass and current coupling of $ X_1(2900)$ are computed using the QCD two-point sum rule approach by taking into account various vacuum condensates up to dimension $10$. The width of the resonance $X_1(2900)$ is saturated by two decay channels $X_1 \to D^{-}K^{+}$ and $X_1 \to \overline{D}^{0}K^{0}$. The strong couplings $g_1$ and $g_2$ corresponding to the vertices $X_1D^{-}K^{+}$ and $X_1\overline{D} ^{0}K^{0}$ are evaluated in the context of the QCD light-cone sum rule method and technical tools of the soft-meson approximation. Results for the mass of the resonance $X_1(2900)$ $m=(2890~\pm 122)~\mathrm{MeV}$, and for its full width $\Gamma _{\mathrm{full}}=(93\pm 13)~\mathrm{MeV}$ are smaller than their experimental values reported by the LHCb collaboration. Nevertheless, by taking into account theoretical and experimental errors of investigations, interpretation of the state $X_1(2900)$ as the vector tetraquark does not contradict to the LHCb data. We also point out that analysis of the invariant mass distribution $D^{+}K^{+}$ in the same decay $ B^{+} \to D^{+}D^{-}K^{+}$ may reveal doubly charged four-quark structures $ [uc][\overline{s}\overline{d}]$.