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The dynamically generated $h_1$ state by the $K^*\bar{K}^*$ interaction and its $K_1(1270)\bar{K}$ and $b_1(1235)π$ decays

Qing-Hua Shen, Li-Sheng Geng, Xiang Liu, Ju-Jun Xie

Abstract

We investigate the dynamically generated $h_1$ state with spin-parity $J^P = 1^+$ and a mass around 1790~MeV, arising from the $K^* \bar{K}^*$ interaction within the chiral unitary approach. The partial decay widths into the $K_1(1270)\bar{K}$ and $b_1(1235)π$ channels are calculated via a triangular loop mechanism. In this mechanism, the $h_1$ state couples to $K^* \bar{K}^*$, and final-state interactions between $K^*$ and $\bar{K}^*$ proceed through pseudoscalar-meson exchange, leading to the final states $\bar{K}$ (or $π$) and $K_1(1270)$ [or $b_1(1235)$]. We also present the invariant mass distributions of a vector meson and a pseudoscalar meson originating from the decays of $K_1(1270)$ or $b_1(1235)$, along with the corresponding decay widths. Our results show that these decay widths are all of the order of a few MeV. We hope that future experiments can test the predictions presented here, thereby helping to identify this $h_1$ state.

The dynamically generated $h_1$ state by the $K^*\bar{K}^*$ interaction and its $K_1(1270)\bar{K}$ and $b_1(1235)π$ decays

Abstract

We investigate the dynamically generated state with spin-parity and a mass around 1790~MeV, arising from the interaction within the chiral unitary approach. The partial decay widths into the and channels are calculated via a triangular loop mechanism. In this mechanism, the state couples to , and final-state interactions between and proceed through pseudoscalar-meson exchange, leading to the final states (or ) and [or ]. We also present the invariant mass distributions of a vector meson and a pseudoscalar meson originating from the decays of or , along with the corresponding decay widths. Our results show that these decay widths are all of the order of a few MeV. We hope that future experiments can test the predictions presented here, thereby helping to identify this state.
Paper Structure (5 sections, 20 equations, 9 figures, 2 tables)

This paper contains 5 sections, 20 equations, 9 figures, 2 tables.

Table of Contents

  1. Introduction
  2. An $h_1$ state dynamically generated from the $K^*\bar{K^*}$ interaction
  3. The $h_1 \to K_1(1270)\bar{K} \to K^{*+} \pi^0 K^-$ and $h_1 \to b_1(1235)\pi \to \omega(\phi) \pi^+ \pi^-$ decays
  4. Numerical results and discussions
  5. summary

Figures (9)

  • Figure 1: The mechanisms of the $K^*\bar{K}^*$ meson interaction. (a): four-vector-contact term. (b): $t(u)$-channel vector meson exchange. (c): the effective interaction vertex of $K^*\bar{K}^* \to K^*\bar{K}^*$ at tree level.
  • Figure 2: The real (a) and imaginary (b) parts of the pole position of the $K^*\bar{K}^* \to K^* \bar{K}^*$ scattering amplitude as a function of the subtraction constant $a(\mu)$.
  • Figure 3: Coupling constant of the dynamically generated $h_1$ state to the $K^*\bar{K}^*$ channel as a function of the subtraction constant $a(\mu)$.
  • Figure 4: Diagrammatic representation of the triangular loop mechanism for the $h_1 \to K_1(1270)/b_1(1235) P_2 \to V_f P_1 P_2$ decay. $V_f$, $P_1$ and $P_2$ stand for the vector meson and pseudoscalar mesons in the final state.
  • Figure 5: Diagrammatic representation of the decay mechanisms $h_1 \to K_{1}^+(1270)K^- \to K^{*+}\pi^0 K^-$ through the $K^*$-$\bar{K}^*$-$\pi/\eta$ triangle loop.
  • ...and 4 more figures