  It has been postulated that partonic orbital angular momentum can lead to a
significant double-helicity dependence in the net transverse momentum of
Drell-Yan dileptons produced in longitudinally polarized p+p collisions.
Analogous effects are also expected for dijet production. If confirmed by
experiment, this hypothesis, which is based on semi-classical arguments, could
lead to a new approach for studying the contributions of orbital angular
momentum to the proton spin. We report the first measurement of the
double-helicity dependence of the dijet transverse momentum in longitudinally
polarized p+p collisions at sqrt(s) = 200 GeV from data taken by the PHENIX
experiment in 2005 and 2006. The analysis deduces the transverse momentum of
the dijet from the widths of the near- and far-side peaks in the azimuthal
correlation of the dihadrons. When averaged over the transverse momentum of the
triggered particle, the difference of the root-mean-square of the dijet
transverse momentum between like- and unlike-helicity collisions is found to be
-37 +/- 88(stat) +/- 14(syst) MeV/c.
