Parton transverse momenta and direct photon production in hadronic collisions at high energies

Abstract

The invariant cross sections for direct photon production in hadron-hadron collisions are calculated for several initial energies (SPS, ISR, SppS, RHIC, Tevatron, LHC) including initial parton transverse momenta within the formalism of unintegrated parton distributions (UPDF). Different approaches from the literature are compared and discussed. A special emphasis is put on the Kimber-MartinRyskin (KMR) distributions and their extension into the soft region. Sum rules for UPDFs are formulated and discussed in detail. We find a violation of naive number sum rules for the KMR UPDFs. An interesting interplay of perturbative (large k 2 t ) and nonperturbative (small k 2 t ) regions of UPDFs in the production of both soft and hard photons is identified. The kt-factorization approach with the KMR UPDFs is inconsistent with the collinear approach at large transverse momenta of photons. Kwieciński UPDFs provide very good description of all world data, especially at SPS and ISR energies. Off-shell effects are discussed and quantified. Predictions for the CERN LHC are given. Very forward/backward regions in rapidity at LHC energy are discussed and a possibility to test unintegrated gluon distributions (UGDF) is presented.

Enhancement of prompt photons in ultrarelativistic proton-proton collisions from nonlinear gluon evolution at smallx

“…Usually the parton distributions in a proton are described by the DGLAP evolution equations [5] and the cross section is calculated using collinear factorization. More recently, the k T -factorization, which takes into account effects of finite virtualities and transverse momenta of the incoming partons, has been applied to calculate the prompt photon production cross section [6,7]. In this case, the cross section is given in terms of the unintegrated parton distributions, which are a solution of the BFKL or CCFM evolution equations, for instance.…”

Associated production of prompt photons and heavy quarks in off-shell gluon–gluon fusion

“…The average value of this k T increases from k T ∼ 1 GeV to more than k T ∼ 3 GeV [13,16] as the √ s increases from UA6 to Tevatron energies 2 . From our point of view, a more adequate solution was found [22][23][24][25] in the framework of the k T -factorization approach [26,27]. This approach is based on the familiar Balitsky-FadinKuraev-Lipatov (BFKL) [28] or Ciafaloni-Catani-Fiorani-Marchesini (CCFM) [29] gluon evolution equations and takes into account the large logarithmic terms proportional to ln 1/x.…”

“…However, an important component of the calculations [22][23][24] is the unintegrated quark distribution in a proton which at present is available in the framework of Kimber-Martin-Ryskin (KMR) [31] approach only 4 . In contrast with [22][23][24], the central part of our previous consideration [25] is the off-shell gluon-gluon fusion subprocess g * + g * → γ + qq. At the price of considering the 2 → 3 rather than 2 → 2 matrix elements, the problem of unknown unintegrated quark distributions has been reduced to the problem of gluon distributions.…”

“…First calculations of the inclusive prompt photon production at the Tevatron within the k T -factorization formalism have been performed in [22][23][24][25]. The calculations [22][23][24] were based on the q + g * → γ + q and q +q → γ + g off-shell matrix elements 3 .…”

“…First calculations of the inclusive prompt photon production at the Tevatron within the k T -factorization formalism have been performed in [22][23][24][25]. The calculations [22][23][24] were based on the q + g * → γ + q and q +q → γ + g off-shell matrix elements 3 . A reasonable agreement was found [24] between the theoretical predictions and the available D⊘ and CDF experimental data [1][2][3][4][5][6] in both the central and forward pseudorapidity η γ regions.…”