  We place observational constraints on a coupling between dark energy and dark
matter by using 71 Type Ia supernovae (SNe Ia) from the first year of the
five-year Supernova Legacy Survey (SNLS), the cosmic microwave background (CMB)
shift parameter from the three-year Wilkinson Microwave Anisotropy Probe
(WMAP), and the baryon acoustic oscillation (BAO) peak found in the Sloan
Digital Sky Survey (SDSS). The interactions we study are (i) constant coupling
delta and (ii) varying coupling delta(z) that depends on a redshift z, both of
which have simple parametrizations of the Hubble parameter to confront with
observational data. We find that the combination of the three databases
marginalized over a present dark energy density gives stringent constraints on
the coupling, -0.08 < delta < 0.03 (95% CL) in the constant coupling model and
-0.4 < delta_0 < 0.1 (95% CL) in the varying coupling model, where delta_0 is a
present value. The uncoupled LambdaCDM model (w_X = -1 and delta = 0) still
remains a good fit to the data, but the negative coupling (delta < 0) with the
equation of state of dark energy w_X < -1 is slightly favoured over the
LambdaCDM model.
