In certain Mott-insulating dimerized antiferromagnets, triplet excitations of
the paramagnetic phase can decay into the two-particle continuum. When such a
magnet undergoes a quantum phase transition into a magnetically ordered state,
this coupling becomes part of the critical theory provided that the lattice
ordering wavevector is zero. One microscopic example is the staggered-dimer
antiferromagnet on the square lattice, for which deviations from O(3)
universality have been reported in numerical studies. Using both symmetry
arguments and microscopic calculations, we show that a non-trivial cubic term
arises in the relevant order-parameter quantum field theory, and assess its
consequences using a combination of analytical and numerical methods. We also
present finite-temperature quantum Monte Carlo data for the staggered-dimer
antiferromagnet which complement recently published results. The data can be
consistently interpreted in terms of critical exponents identical to that of
the standard O(3) universality class, but with anomalously large corrections to
scaling. We argue that the two-particle decay of critical triplons, although
irrelevant in two spatial dimensions, is responsible for the leading
corrections to scaling due to its small scaling dimension.Comment: 14 pages, 7 fig