  It has been observed in the literature that measurements of low-mass
Drell-Yan (DY) transverse momentum spectra at low center-of-mass energies
$\sqrt{s}$ are not well described by perturbative QCD calculations in collinear
factorization in the region where transverse momenta are comparable with the DY
mass. We examine this issue from the standpoint of the Parton Branching (PB)
method, combining next-to-leading-order (NLO) calculations of the hard process
with the evolution of transverse momentum dependent (TMD) parton distributions.
We compare our predictions with experimental measurements at low DY mass, and
find very good agreement.In addition we use the low mass DY measurements at low
$\sqrt{s}$ to determine the width $q_s$ of the intrinsic Gauss distribution of
the PB-TMDs at low evolution scales. We find values close to what has earlier
been used in applications of PB -TMDs to high-energy processes at the Large
Hadron Collider (LHC) and HERA. We find that at low DY mass and low $\sqrt{s}$
even in the region of $p_t/m_{DY} \sim 1$ the contribution of multiple soft
gluon emissions (included in the PB-TMDs) is essential to describe
themeasurements, while at larger masses ($m_{DY} \sim m_{Z}$) and LHC energies
the contribution from soft gluons in the region of $p_t/m_{DY}\sim 1$ is small.
