Meson Decay Tables

Light meson decays, care of Ted Barnes.

Partial widths of 2³S₁ states (MeV).
Partial widths of 2¹S₀ states (MeV).
Partial widths of 3³S₁ states (MeV).
Partial widths of 3¹S₀ states (MeV).
Partial widths of 2³P_J a_J states (MeV).
Partial widths of 2³P_J f_J states (MeV).
Partial widths of 2¹P₁ b₁ and h₁ states (MeV).
Partial widths of ³D_J rho_J states (MeV).
Partial widths of ³D_J omega_J states (MeV).
Partial widths of ¹D₂ pi₂ and eta₂ states (MeV).
Partial widths of ³F_J a_J states (MeV).
Partial widths of ³F_J f_J states (MeV).
Partial widths of ¹F₃ b₃ and h₃ states (MeV).

These tables are taken from T. Barnes, F.E. Close, P.R. Page, and E.S. Swanson Phys. Rev. D55, 4157 (1997). Please refer to this work if you use these tables in your research.

We quote numerical values for partial widths predicted by the ³P₀ model. The masses used are experimental values of well established candidates, usually taken from the 1996 PDG, otherwise we used an approximate multiplet mass. These are 1750 MeV (2P), 1670 MeV (1D), 2050 MeV (1F), and 1900 MeV and 1800 MeV respectively for the 3³S₁ and 3 $\, {}^1$ S₀. Although we found optimum parameters near $\gamma = 0.5$ and $\beta = 0.4$ GeV in a fit to light 1S and 1P decays, these parameters lead to moderate overestimates of the widths of the well established higher-L states $\pi_2(1670)$ and f₄(2044); with this $\beta$ a value closer to $\gamma = 0.4$ is preferred. Consequently we quote widths for all these higher quarkonia with the parameters

$\begin{displaymath}(\gamma, \beta ) = (0.4, 0.4 \ {\rm GeV} ) \ . \end{displaymath}$

(1)

The tables are largely self explanatory. Except in a few cases the states are specified uniquely by their labels. Exceptions are the $\vert\eta(547)\rangle$ and $\vert\eta'(958)\rangle$ , which we take to be the usual $1/\sqrt{2}$ combinations of $\vert n\bar n \rangle$ and $\vert s\bar s \rangle$ basis states. We assume that the $\vert\eta(1295)\rangle$ and $\vert\eta_2(1645)\rangle$ are pure $\vert n\bar n \rangle$ states. The strange mesons K₁(1273) and K₁(1402) are taken to be the linear combinations

$\begin{displaymath}\vert{\rm K}_1(1273)\rangle = \sqrt{ {2\over 3} } \; \vert {... ...rangle + \sqrt{ {1\over 3} } \; \vert {}^3{\rm P}_1 \rangle \end{displaymath}$

(2)

and

$\begin{displaymath}\vert{\rm K}_1(1402)\rangle = -\sqrt{ {1\over 3} } \; \vert ... ...gle + \sqrt{ {2\over 3} } \; \vert {}^3{\rm P}_1 \rangle \ . \end{displaymath}$

(3)

This gives a zero S-wave ${\rm K}_1(1273)\to {\rm K}^*\pi$ coupling; experimentally D/S = 1.0(0.7), and the small partial width implies a small S-wave amplitude. The orthogonal state ${\rm K}_1(1402)$ is predicted to have a D/S ratio of +0.049 in ${\rm K}^*\pi$ , quite close to the experimental D/S = +0.04(1). The large ${\rm K}_1(1273)\to {\rm K}\rho$ mode is not predicted and is presumably due to a virtual intermediate state such as K $^*_0(1429)\pi$ followed by a final-state interaction.

The tables give partial widths for all nonstrange 2S, 3S, 2P, 1D and 1F quarkonia to all two-body modes allowed by phase space, rounded to the nearest MeV. The predictions of the dominant modes of the ``missing states'' in the quark model, such as the 2^- states and most of the 1F states, are especially interesting. If the ³P₀ model has even moderate accuracy these tables should be very useful in searches for these states.