Central exclusive production of ρρ pairs in proton collision

We investigate the central exclusive production of ρρ pairs in pp collisions at LHC energies. At low central invariant mass this process can be considered as a possible non-resonant background for glueball searches in four-body final states. Above the resonance region non perturbative production mechanism can be studied. All calculations have been performed using generator GENEX [3], specially designed for effective integration of exclusive processes in restricted phase space.


Introduction
We investigate the central exclusive production of ρρ pairs in pp collisions at LHC energies.At low central invariant mass this process can be considered as a possible non-resonant background for glueball searches in four-body final states.Above the resonance region non perturbative production mechanism can be studied.All calculations have been performed using generator GENEX [3], specially designed for effective integration of exclusive processes in restricted phase space.

General description of the model
The Lebiedowicz & Szczurek model [1] was used in the form where M i j is the elastic pπ scattering amplitude and hadronic form-factor depends on parameter Λ.The following replacements were made: • Replace M i j for pπ amplitude with the amplitude for pρ scattering according to the Vector-Dominance model, see section 5.3 of [2], • In (1) and (2) change m π to m ρ .
The above described matrix element for pp → pp + ρρ after addition of ρ decay amplitude and symmetrization for the identical particles in final state has the following form 1 : where ME LS ρ is the modified Lebiedowicz&Szczurek model [1] with Vector-Dominance model (1) and ρ → 2π is given by the standard Zemach formalism: where ε is a ρ vector polarisation vector and p r = p 1 + p 2 .This simplified model gives similar cross section(to the order of magnitude) as the one recently presented in [5].

Results
Cross sections σ pp→pp+ρρ are calculated for full and restricted phase space corresponding to ATLAS and ALICE detectors at √ (s) = 7 T eV.For ATLAS we assume: • Diffractively scattered protons detected in the ATLAS FORWARD DETECTOR (AFD), • Pions detected in Silicon Central Tracker SCT |η π | < 2.5 and p tπ > 0.1 GeV (enhanced track reconstruction [4]).
W define five phase space regions corresponding to the following event selection setups: • ATLAS-I: Protons in AFD with |t p | < 1 GeV 2 and 4π in SCT, • ATLAS-II: Protons in AFD with |t p | < 1 GeV 2 and two opposite-sign pions in SCT, • ATLAS-III: Protons in AFD with |t p | < 1 GeV 2 and two same-sign pions in SCT, • ALICE: 4π in CB.The results are presented in Table 1 and in Figs. 1 and 2. In the figures the cross section ratio R = σ pp→pp+ρρ /σ pp→pp+ππ was drawn as absorption is to large extent cancelled using this variable.It should be noted that recently presented model calculations for the same process [5] give results differing from ours by more than order of magnitude.This model is based on the tensor pomeron exchange in pρ → pρ.The source of so large differences will be investigated.

Conclusions
The cross section for central exclusive production of ρρ pairs at LHC energies is rather small in comparison with central exclusive production of pion pairs and depends strongly on parameter Λ.The process pp → pp + ρρ → pp + 4π does not contribute to the background of the exclusive production of pion pairs, neither in ALICE nor in the ATLAS experiment.In the resonance region of the central invariant mass M central < 2.0 GeV the effect of the symmetrisation for identical particles (ρρ mixing) is significant, making the signal identification event more difficult.

Figure 1 .Figure 2 .
Figure 1.Left: Symmetrization effect full phase space.Right: Cross section ratio full phase space.