Transverse momentum distributions of quarks in the nucleon from the Chiral Quark Soliton Model

We report the first calculation of the simplest but most fundamental transverse momentum dependent (TMD) distribution of quarks in the nucleon, i.e. the time-reversal-even unpolarized TMD quark and antiquark distribution with isoscalar combination, within the framework of the chiral quark soliton model. The nonperturbative account of the deformed Dirac-sea quarks within the theoretical scheme enables us to make a reliable predictions not only for the quark distribution but also for the antiquark distribution. We found that the predicted average transverse momentum square $<k_\perp^2>$ of quarks and antiquarks depends strongly on their longitudinal momentum fraction $x$, which means that the frequently used assumption of factorization in $x$ and $k_\perp$ is significantly violated. It is also found, somewhat unexpectedly, that the average transverse momentum square of antiquarks is considerably larger than that of quarks.