Exclusive production of χ_{c}(0^{+}) meson and its measurement in the π^{+}π^{-} channel
NNuclear Physics B Proceedings Supplement 00 (2018) 1–4
Nuclear Physics BProceedingsSupplement
Exclusive production of χ c (0 + ) meson and its measurement in the π + π − channel P. Lebiedowicz a , R. Pasechnik b , A. Szczurek a,c a Institute of Nuclear Physics PAN, PL-31-342 Cracow, Poland b Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden c University of Rzesz´ow, PL-35-959 Rzesz´ow, Poland
Abstract
We report on the results of a theoretical study of the central exclusive production of scalar χ c (0 + ) meson via χ c → π + π − decay in high-energy hadron collisions at the RHIC, Tevatron and LHC. The corresponding amplitude forexclusive double-di ff ractive χ c meson production was obtained within the k t -factorization approach including virtual-ities of active gluons and the cross section is calculated with unintegrated gluon distribution functions (UGDFs) knownfrom the literature. The four-body pp → pp π + π − reaction constitutes an irreducible background to the exclusive χ c meson production. We include the absorption e ff ects due to proton-proton interaction and pion-pion rescattering.Several di ff erential distributions for pp ( ¯ p ) → pp ( ¯ p ) χ c process, including the absorptive corrections, were calculated.The influence of kinematical cuts on the signal-to-background ratio is investigated. Keywords: χ c (0 + ) → π + π − decay, di ff ractive processes, two-pion continuum
1. Introduction
The mechanism of exclusive production of mesons athigh energies became recently a very active field of re-search (see [1] and refs. therein). These reactions pp → pM p , where M = σ, ρ , f (980) , φ, f (1270) , f (1500), χ c , provide a valuable tool to investigate in detail theproperties of resonance states at high energies. The re-cent works concentrated on the production of χ c mesons(see e.g. Refs. [2–5]) where the QCD mechanism issimilar to the exclusive production of the Higgs bo-son. Furthermore, the χ c (0 , states are expected to an-nihilate via two-gluon processes into light mesons andmay, therefore, allow the study of glueball productiondynamics. The two-pion background to exclusive pro-duction of f (1500) [6] and χ c [7] mesons was alreadydiscussed. In Ref. [8] a new perturbative mechanismof the ππ production was discussed. Due to reasons ex- Email addresses: [email protected] (P.Lebiedowicz), [email protected] (R. Pasechnik), [email protected] (A. Szczurek) plained in Ref. [8] this mechanism gives relatively smallcontribution in the χ c invariant mass region.The CDF Collaboration has measured the cross sec-tion of CEP χ c mesons in proton-antiproton collisions atthe Tevatron [9]. In this experiment χ c mesons are iden-tified via decay to the J /ψ + γ with J /ψ → µ + µ − channel.The experimental invariant mass resolution was not suf-ficient to distinguish between scalar, axial and tensor χ c .While the branching fractions to this channel for axialand tensor mesons are large [10] ( B = (34 . ± . B = (19 . ± . B = (1 . ± . χ c production obtained within the k t -factorizationis much bigger than that for χ c and χ c . As a conse-quence, all χ c mesons give similar contributions [4] tothe J /ψ + γ decay channel. Clearly, the measurementvia decay to the J /ψ + γ channel cannot provide crosssection for di ff erent χ c .The χ c meson decays into several two-body channels(e.g. ππ , K + K − , p ¯ p ) or four-body hadronic modes (e.g. π + π − π + π − , π + π − K + K − ). We have analyzed a possibility a r X i v : . [ h e p - ph ] A ug Nuclear Physics B Proceedings Supplement 00 (2018) 1–4 to measure χ c via its decay into π + π − channel [7]. Thebranching fraction B ( χ c → π + π − ) = (0 . ± . χ c does not decay to the ππ channeland B ( χ c → π + π − ) = (0 . ± . χ c pro-duction means that in practise only χ c will contributeto the signal. The advantage of this channel is that the π + π − continuum has been studied recently [7, 11] and isrelatively well known.
2. Signal and background amplitudes
Figure 1:
The QCD mechanism of exclusive di ff ractive pro-duction of χ c meson including the absorptive correction. The QCD mechanism for the di ff ractive productionof heavy central system has been proposed by Khoze,Martin and Ryskin (KMR) and developed in collabo-ration with Kaidalov and Stirling for Higgs production(see e.g. Refs. [12]). In the framework of this approachthe amplitude of the exclusive pp → pp χ c process isdescribed by the diagram shown in Fig. 1, where thehard subprocess g ∗ g ∗ → χ c is initiated by the fusionof two o ff -shell gluons and the soft part is representedin terms of the o ff -diagonal unintegrated gluon distribu-tion functions (UGDFs). The formalism used to calcu-late the exclusive χ c meson production is explained indetail elsewhere [2].The dominant mechanism of the exclusive produc-tion of π + π − pairs at high energies is sketched in Fig. 2.The expected non-resonant background can be mod-eled using a ”non-perturbative” framework where thepion pair is produced by Pomeron-Pomeron fusion withan intermediate o ff -shell pion / Reggeon exchanged be-tween the final-state particle pairs (see [7, 11, 13] fordetails). In calculations of the amplitude we follow thegeneral rules of Pumplin and Henyey [14] used recentlyin Ref. [11] where a first estimate of the di ff erentialcross sections for the π + π − pairs production at the LHCenergies has been presented. The Regge parametriza-tion of the π ± p → π ± p and π + π − → π + π − scatter-ing amplitude includes both Pomeron as well as f and Figure 2:
The double-di ff ractive mechanism of exclusive pro-duction of π + π − pairs including the pion and Regge exchanges,the absorptive corrections due to proton-proton interactions aswell as pion-pion rescattering. ρ Reggeon exchanges with the parameters taken fromthe Donnachie-Landsho ff analysis [15] of the total crosssections. The Regge-type interaction applies at higherenergies and at low energies should be switched o ff (see[7, 11, 13]). In Ref. [7] we propose to use a general-ized propagator. The form factors correct for the o ff -shellness of the intermediate pions are parametrized as F π (ˆ t / ˆ u ) = exp (cid:18) ˆ t / ˆ u − m π Λ of f (cid:19) , where the parameter Λ o f f is ob-tained from fit to the experimental data [16] (see [7]).
3. Results
We first show (Fig. 3) the di ff erential cross sectionsof χ c CEP at √ s =
14 TeV without (dashed line) andwith (solid line) absorptive corrections. These calcu-lations were done with GJR NLO [17] collinear gluondistribution, to generate the KMR UGDFs, which al-lows to use low values of the internal gluon transversemomenta Q t ≥ Q cut = . . The bigger the valueof the cut-o ff parameter, the smaller the cross section(see Ref. [2]). In the calculations we take the value ofthe hard scale to be µ = M . The smaller µ , the big-ger the cross section [2]. In all cases the absorption ef-fects lead to a damping of the cross section. In mostcases the shape is almost unchanged. Exception is thedistribution in proton transverse momentum where theabsorption e ff ects lead to a damping of the cross sec-tion at small proton p t and an enhancement of the crosssection at large proton p t . In relative azimuthal angledistribution we observe a dip at φ ∼ π/
2. Transversemomentum distribution of χ c shows a small minimumat p t ∼ ff erential distributions of pi-ons from the χ c decay (see the peak at M ππ (cid:39) . Nuclear Physics B Proceedings Supplement 00 (2018) 1–4 (GeV) t, 1 p b / G e V ) m ( t , / dp s d -5 -4 -3 -2 -1 + (0 c c pp fi pp W = 14 TeVGJR08 NLO (deg) f b ) m ( f / d s d -2 -1 + (0 c c pp fi pp W = 14 TeVGJR08 NLO (GeV) c c t, p b / G e V ) m ( c c t , / dp s d -9 -7 -5 -3 -1 + (0 c c pp fi pp W = 14 TeVGJR08 NLO c c y -8 -6 -4 -2 0 2 4 6 8 b ) m ( c c / dy s d -6 -5 -4 -3 -2 -1
101 ) + (0 c c pp fi pp W = 14 TeVGJR08 NLO Figure 3: Di ff erential cross sections for the pp → pp χ c re-action at √ s =
14 TeV without (dashed line) and with (solidline) absorption e ff ects. with those for the continuum pions. While left panelsshow the cross section integrated over the full phasespace, the right panels show results including the rel-evant pion pseudorapidities restrictions − < η π + , η π − < − . < η π + , η π − < . χ c contribution is calculated with GRV94NLO [18] and GJR08 NLO [17] collinear gluon distri-butions.In Fig. 5 we show distributions in pion transverse mo-menta (left panels). The pions from the χ c decay areplaced at slightly larger transverse momenta. This canbe therefore used to get rid of the bulk of the contin-uum by imposing an extra cut on the pion transversemomenta. In the right panels we show two-pion invari-ant mass distributions with additional cuts on both piontransverse momenta | p t ,π | > . χ c rapidity and transverse momentum. InFig. 6 we show the two-dimensional ratio of the crosssections for the χ c meson in its rapidity and transversemomentum:Ratio( y , p t ) = d σ pp → pp χ c ( → π + π − )with cuts / dyd p t d σ pp → pp χ c / dyd p t . The numerator includes limitations on η π and p t ,π .These distributions provide a fairly precise evaluationof the expected acceptances when experimental cuts are (GeV) pp M b / G e V ) m ( pp / d M s d -3 -2 -1 - p + p pp fi pp = 0.5 TeVsfull phase space c0 c ) p -rescatt. (mes. pp no ) p rescatt. (reg. (GeV) pp M ( nb / G e V ) pp / d M s d - p + p pp fi pp = 0.5 TeVs 1 £ | p h | c0 c (GeV) pp M b / G e V ) m ( pp / d M s d -3 -2 -1 - p + p p p fi pp = 1.96 TeVsfull phase space c0 c (GeV) pp M ( nb / G e V ) pp / d M s d - p + p p p fi pp = 1.96 TeVs 1 £ | p h | c0 c (GeV) pp M b / G e V ) m ( pp / d M s d -3 -2 -1 - p + p pp fi pp = 14 TeVsfull phase space c0 c (GeV) pp M ( nb / G e V ) pp / d M s d - p + p pp fi pp = 14 TeVs 2.5 £ | p h | c0 c Figure 4:
The π + π − invariant mass distribution at √ s = . , . ,
14 TeV integrated over the full phase space (left pan-els) and with the detector limitations in η π (right panels). Re-sults for the ππ continuum with the meson propagator and withthe cut-o ff parameters Λ of f = (lower and upperdashed lines, respectively) as well as with the generalized pionpropagator and ππ -rescattering (solid line) are presented. Weuse GRV94 NLO (dotted lines) and GJR08 NLO (filled areas)collinear gluon distributions. The absorption e ff ects both forthe signal and background were included in the calculations. imposed. The experimental data could be corrected byour two-dimensional acceptance function to recover thedistributions of interest.
4. Conclusions
It was realized recently that the measurement of ex-clusive production of χ c via decay in the J /ψ + γ chan-nel cannot give production cross sections for di ff erentspecies of χ c . In this decay channel the contributions of χ c mesons with di ff erent spins are similar and experi-mental resolution is not su ffi cient to distinguish them.We have analyzed a possibility to measure the exclu-sive production of χ c meson in the proton-(anti)proton Nuclear Physics B Proceedings Supplement 00 (2018) 1–4 (GeV) p t, p b / G e V ) m ( p t , / dp s d -6 -4 -2 - p + p pp fi pp = 0.5 TeVs 1 £ | p h | GJR08 NLOGRV94 NLO ) p -rescatt. (mes. pp no ) p rescatt. (reg. (GeV) pp M ( nb / G e V ) pp / d M s d - p + p pp fi pp = 0.5 TeVs 1 £ | p h | | > 1.5 GeV p t, |p c0 c (GeV) p t, p b / G e V ) m ( p t , / dp s d -6 -4 -2 - p + p p p fi pp = 1.96 TeVs 1 £ | p h | GJR08 NLOGRV94 NLO (GeV) pp M ( nb / G e V ) pp / d M s d - p + p p p fi pp = 1.96 TeVs 1 £ | p h | | > 1.5 GeV p t, |p c0 c (GeV) p t, p b / G e V ) m ( p t , / dp s d -6 -4 -2 - p + p pp fi pp = 14 TeVs 2.5 £ | p h | GRV94 NLOGJR08 NLO (GeV) pp M ( nb / G e V ) pp / d M s d - p + p pp fi pp = 14 TeVs 2.5 £ | p h | | > 1.5 GeV p t, |p c0 c Figure 5:
Left panels: Di ff erential cross section d σ/ dp t ,π at √ s = . , . ,
14 TeV with cuts on the pion pseudorapidi-ties. The absorption e ff ects both for the signal and backgroundwere included in the calculations. Right panels: The π + π − in-variant mass distribution with the relevant restrictions in thepion pseudorapidities and pion transverse momenta. Figure 6:
Ratio of the two-dimensional cross sections in ( y , p t )for the pp → pp χ c reaction with the relevant limitations onthe pion pseudorapidities for the ATLAS or CMS detectors( | η π | < .
5) and a cuts on the pion transverse momenta p t ,π . collisions at the LHC, Tevatron and RHIC via χ c → π + π − decay channel. Since the cross section for exclu-sive χ c production is much larger than that for χ c and χ c and the branching fraction to the ππ channel for χ c is larger than that for χ c ( χ c does not decay into twopions) the two-pion channel should provide an usefulinformation about the χ c CEP.We have performed detailed studies of several di ff er-ential distributions and demonstrated how to impose ex-tra cuts in order to improve the signal-to-backgroundratio. The two-pion background was calculated in asimple model with parameters adjusted to low energydata (see [7, 11]). We have shown that relevant mea-surements at Tevatron and LHC are possible. At RHICthe signal-to-background ratio is much worse but mea-surements should be possible as well. Imposing cutsdistorts the original distributions for χ c in rapidity andtransverse momentum. We have demonstrated how torecover the original distributions and presented the cor-rection functions for some typical experimental situa-tions. References [1] M.G. Albrow, T.D. Coughlin and J.R. Forshaw, Prog. Part. Nucl.Phys. (2010) 149.[2] R.S. Pasechnik, A. Szczurek and O.V. Teryaev, Phys. Rev. D78 (2008) 014007.[3] R.S. Pasechnik, A. Szczurek and O.V. Teryaev, Phys. Lett.
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