[Paper Review] Charmed scalar mesons and related

K. Terasaki|ArXiv.org|May 16, 2004

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper proposes that the narrow $D_{s0}^{+}(2.32)$ meson is the $I_3 = 0$ component of an iso-triplet four-quark meson multiplet $\hat{F}_I$, composed of $[cq][\bar{q}\bar{q}]$ states. By analyzing decay properties within this multiplet, it predicts additional narrow scalar mesons, including a broad $\hat{D}$ doublet and an extremely narrow $\hat{F}_0^+$, while resolving the long-standing puzzle in charm meson decays through four-quark contributions.

ABSTRACT

Charmed scalar mesons are studied. By assigning the newly observed charmed strange meson with a narrow width to one of the iso-triplet four-quark mesons, decays of the multiplet members are investigated and, as the consequence, existence of additional narrow scalar mesons is predicted. Decays of the ordinary charmed scalar mesons are also studied. In addition, it is demonstrated that four-quark mesons can play an important role in hadronic weak decays of charm mesons.

Motivation & Objective

• To resolve the discrepancy between the low mass of the observed $D_{s0}^{+}(2.32)$ and theoretical predictions for conventional $\{c\bar{s}\}$ states.
• To investigate the decay properties of a proposed iso-triplet four-quark multiplet $\hat{F}_I$ containing $D_{s0}^{+}(2.32)$ as its $I_3=0$ component.
• To examine whether four-quark mesons can consistently explain the observed hadronic weak decays of charm mesons, resolving a long-standing puzzle.
• To compare decay widths of four-quark states with those of conventional scalar $\{c\bar{q}\}$ mesons using $K_0^*(1430)$ as a reference.

Proposed method

• Assigns the $D_{s0}^{+}(2.32)$ to the $I_3 = 0$ component $\hat{F}_I^+$ of an iso-triplet four-quark multiplet $\hat{F}_I \sim [cq][\bar{q}\bar{q}]$, with $q = u,d,s$.
• Uses a potential model framework with $SU(3)$-color symmetric vector meson exchange to describe $[qq][\bar{q}\bar{q}]$ interactions.
• Applies the $^3P_0$ quark pair creation model to estimate decay widths of the $\hat{F}_I$ multiplet members.
• Compares decay rates of $\hat{F}_I$ states with those of conventional $\{c\bar{q}\}$ mesons, using $K_0^*(1430)$ as a benchmark for $\{n\bar{s}\}$ states.
• Analyzes contributions of four-quark states to hadronic weak decays of $D$ and $D_s^+$ mesons, showing consistency with experimental data.
• Evaluates mass and width predictions using effective Lagrangians and symmetry-based arguments, including isospin-violating decays.

Experimental results

Research questions

• RQ1 Can the narrow $D_{s0}^{+}(2.32)$ be consistently explained as a four-quark state rather than a conventional $\{c\bar{s}\}$ meson?
• RQ2 What are the decay properties of the full $\hat{F}_I$ iso-triplet four-quark multiplet, and are they consistent with observed widths?
• RQ3 Can four-quark mesons resolve the long-standing puzzle in charm meson hadronic weak decays, particularly the discrepancy in branching ratios?
• RQ4 How do the decay widths of $[cq][\bar{q}\bar{q}]$ four-quark states compare with those of conventional scalar $\{c\bar{q}\}$ mesons?
• RQ5 What is the role of isospin-violating interactions in suppressing the width of the $\hat{F}_0^+$ state?

Key findings

• The $D_{s0}^{+}(2.32)$ is identified as the $I_3 = 0$ component $\hat{F}_I^+$ of an iso-triplet four-quark multiplet $\hat{F}_I \sim [cq][\bar{q}\bar{q}]$, with a predicted mass of 2.32 GeV.
• The iso-doublet $\hat{D}$ states are predicted to have moderate widths of $\sim 60-90$ MeV, consistent with the broad bump observed at $\sim 2.31$ GeV in the $D\pi$ channel.
• The iso-singlet $\hat{F}_0^+$ is predicted to be extremely narrow due to dominance of isospin-violating decay modes, with a width $\lesssim 10$ MeV.
• The strange partner $\hat{D}^{s}$ is predicted to be near the $D\eta$ threshold, resulting in a suppressed decay width despite being kinematically allowed.
• The ordinary scalar $D_0^*$ is predicted to have a width of $\sim (60-90)$ MeV, and $D_{s0}^{*+}$ a width of $\sim (40-70)$ MeV, based on comparison with $K_0^*(1430)$.
• Four-quark mesons can resolve the long-standing puzzle in charm meson decays by providing consistent contributions to branching ratios, particularly in $D_s^+ \to D_s^{*+} \pi^0$ and $D \to D^* \pi^0$ modes.