Accurate standardization of Type Ia supernovae (SNIa) is instrumental to the
usage of SNIa as distance indicators. We analyse a homogeneous sample of 22 lowz
SNIa, observed by the Carnegie Supernova Project (CSP) in the optical and near
infra-red (NIR). We study the time of the second peak in the J-band, t2, as an alternative
standardization parameter of SNIa peak optical brightness, as measured by the
standard SALT2 parameter mB. We use BAHAMAS, a Bayesian hierarchical model
for SNIa cosmology, to estimate the residual scatter in the Hubble diagram.
We find that in the absence of a colour correction, t2 is a better standardization
parameter compared to stretch: t2 has a 1σ posterior interval for the Hubble residual
scatter of σ∆µ = {0.250, 0.257} mag, compared to σ∆µ = {0.280, 0.287} mag when
stretch (x1) alone is used. We demonstrate that when employed together with a colour
correction, t2 and stretch lead to similar residual scatter. Using colour, stretch and
t2 jointly as standardization parameters does not result in any further reduction in
scatter, suggesting that t2 carries redundant information with respect to stretch and
colour. With a much larger SNIa NIR sample at higher redshift in the future, t2 could
be a useful quantity to perform robustness checks of the standardization procedure.