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Method to measure quarkonium wave function using $B_c$ decay

Yukinari Sumino

Abstract

We propose a method that enables a direct experimental probe of the quarkonium wave function defined in potential nonrelativistic QCD (pNRQCD) using the three-body decay of the $B_c$ meson. We show that the momentum distribution of the spectator $c$-quark in the partonic decay is proportional to the absolute square of the momentum-space wave function of the $B_c$ state. It would provide, for the first time, an experimentally accessible probe of the quarkonium wave function.

Method to measure quarkonium wave function using $B_c$ decay

Abstract

We propose a method that enables a direct experimental probe of the quarkonium wave function defined in potential nonrelativistic QCD (pNRQCD) using the three-body decay of the meson. We show that the momentum distribution of the spectator -quark in the partonic decay is proportional to the absolute square of the momentum-space wave function of the state. It would provide, for the first time, an experimentally accessible probe of the quarkonium wave function.

Paper Structure

This paper contains 1 section, 7 equations, 3 figures.

Table of Contents

  1. Acknowledgements

Figures (3)

  • Figure 1: Feynman diagrams relevant for the process $B_c^+ \to D^+\, D^-\, \pi^+$.
  • Figure 2: Diagram for the partonic decay amplitude eq. \ref{['DecayAmp']}.
  • Figure 3: Absolute square of the momentum-space wave functions of the $1S$ and $2S$$B_c$ states multiplied by the phase-space factor, $p^2 |\phi(p)|^2$. Black solid, blue solid, and red dashed lines, respectively, represent the wave functions calculated with the three-loop static QCD potential, Cornell potential, and Coulomb potential. The height of $p^2|\phi(p)|^2$ is normalized at the first peak position.