  We study the factorization and resummation prediction on the jet mass
spectrum in one-jet inclusive production at the LHC based on soft-collinear
effective theory. The soft function with anti-$k_T$ algorithm is calculated at
next-to-leading order and its validity is demonstrated by checking the
agreement between the expanded leading singular terms with the exact
fixed-order result. The large logarithms $\ln^{n} (m_J^2/p_T^2)$ and the global
logarithms $\ln^{n} (s_4/p_T^2)$ in the process are resummed to all order at
next-to-leading logarithmic and next-to-next-to-leading logarithmic level,
respectively. The cross section is enhanced by about 23% from the
next-to-leading logarithmic level to next-to-next-to-leading logarithmic level.
Comparing our resummation predictions with those from Monte Carlo tool PYTHIA
and ATLAS data at the 7 TeV LHC, we find that the peak positions of the jet
mass spectra agree with those from PYTHIA at parton level, and the predictions
of the jet mass spectra with non-perturbative effects are in coincidence with
the ATLAS data. We also show the predictions at the future 13 TeV LHC.
