Resummation and Shower Studies

The transverse momentum of a colour-singlet massive particle produced in a hadronic collision provides important information on perturbative and nonperturbative effects. A process like qq! Z0 corresponds to a p?Z = 0, while higher-order processes provide p? kicks as the Z0 recoils against quarks and gluons. At large p?Z values the bulk of the p? comes from one hard emission, and perturbation theory is a reasonable approach. In the small-p?Z region, on the other hand, many emissions can contribute with p? kicks of comparable size, and so the order-by-order approach is rather poorly convergent. Furthermore, in this region nonperturbative effects may start to become non-negligible relative to the perturbative ones. The traditional solution has been to apply either an analytical resummation approach or a numerical parton-shower one. These methods to some extent are complementary. The norm today is for showers to be based on an improved leading-log picture, while resummation is carried out to next-to-leading logs. However, resummation gives no information on the partonic system recoiling against the Z0, while showers do, and therefore can be integrated into full-fledged event generators, allowing accurate experimental studies. In both approaches the high-p? tail is constrained by fixed-order perturbation theory, so the interesting and nontrivial region is the low-to-medium-p? one. Both also require nonperturbative input to handle the low-p? region, e.g. in the form of a primordial k? carried by the initiator of a shower. One of the disconcerting aspects of the game is that a large primordial k? seems to be required and that the required value of this primordial k? can be dependent on the kinematics of the process being considered. Confinement of partons inside the proton implies a hk?i 0:3 GeV, while fits to Z0 data at the Tevatron favour 2 GeV [1] (actually as a root-mean-square value, assuming a Gaussian distribution). Also resummation approaches tend to require a non-negligible nonperturbative contribution, but that contribution can be determined from fixed-target data and then automatically evolved to the kinematical region of interest. In this note we present updated comparisons and study possible shower modifications that might alleviate the problem. We will use the two cases of qq ! Z0 and gg ! H0 (in the infinite-top-mass limit) to illustrate differences in quark and gluon evolution, and the Tevatron and the LHC to quantify an energy dependence.