Recent theoretical results for electromagnetically induced ultraperipheral reactions of heavy ions
aa r X i v : . [ nu c l - t h ] O c t Recent theoretical results for electromagnetically inducedultraperipheral reactions of heavy ions ∗ A. Szczurek
Institute of Nuclear Physics, PANul. Radzikowskiego 152, PL-31-342 Krak´ow, Polandalso at Faculty of Mathematics and Natural Sciences,University of Rzesz´ow, PolandWe briefly review our works on ultraperipheral heavy ion collisions. Wediscuss both γγ and rescattering of hadronic photon fluctuation induced byone nucleus in the collision partner. Production of one and two leptonicand pionic and p ¯ p pairs is discussed as an example of photon-photon pro-cesses. The production of single vector mesons ( ρ or J/ψ ) is an exampleof the second category. The double-scattering mechanisms of two ρ mesonproduction is discussed in addition.PACS numbers: 25.20.Lj,25.75.Cj
1. Introduction
The ultraperipheral collisions is a class of processes that were studiedexperimentally only recently at RHIC and the LHC. The process can beviewed as a scattering of two clouds of photons or a process of scattering ofa photon (or photon hadronic fluctuations) emitted by one nucleus on thesecond colliding nucleus. In general, one is interested rather in processeswith small particle multiplicity which automatically means that the impactparameter is greater than the sum of the radii of colliding nuclei. Some ofsuch processes were suggested long ago [1]. Only recently some experimentalresults were presented. In the following we will present some results. Inaddition we will show some other processes that could be also studied atthe LHC.A schematic view of the photon induced processes is shown in Fig.1and the situation in the impact parameter space is illustrated in Fig.2. ∗ Presented at the XIII Workshop on Particle Correlations and Femtoscopy, 22-26 May2018, Krak´ow, Poland (1) template printed on October 16, 2018 b R R Fig. 1. A schematic view of the γγ induced processes. b b b Fig. 2. The situation in the impact parameter space.
When calculating the cross section in the equivalent photon approximationin the impact parameter space ultraperipheral collisions mean that the twocircles, representing heavy ions, do not overlap ( b > R A + R B ) [1]. Itdoes not mean, however, that the processes of photoproduction disapear insuch a case. In this case they may also contribute and compete with otherprocesess characteristic for standard ( b < R A + R B ) heavy ion collisions.The situation/physics then strongly depends on the reaction.Our detailed studies were presented in Refs.[2-16]. In this presentationwe discuss different processes except light-by-light processes that were dis-cussed in [17]. Here we only sketch some selected results. emplate printed on October 16, 2018
2. A brief review of our results for UPC
We start presentation of our results for dilepton production. In Fig.3we present our results for dielectron invariant mass together with ALICEexperimental data [18]. A good agreement is achieved without free param-eters. [GeV] - e + e M b / G e V ] µ [ - e + e / d M σ d - e + PbPbe → PbPb =2.76 TeV NN s [GeV] - e + e M b / G e V ] µ [ - e + e / d M σ d
10 ALICE data - e + PbPbe → PbPb =2.76 TeV NN s Fig. 3. Dielectron invariant mass for the
P bP b → P bP be + e − for the ALICE ex-perimental cuts [18]. In Fig.4 we present our results together with the ATLAS data [19] for the
P b + P b → P b + P b + µ + + µ − reaction. Experimental cuts were includedin our calculations. In contrast to the P bP b → P bP be + e − reaction theagreement here is much worst. (GeV) µµ M b / G e V ) µ ( µµ ) / d M - µ + µ P b P b → ( P b P b σ d − − − − - µ + + µ + (*) +Pb (*) Pb → Pb+PbATLAS Preliminary |<2.4 µµ |Y |<2.4 µµ =5.02 TeV NN s >4 GeV µ t, p |<2.4 µ η | µµ Y − − b ) µ ( µµ ) / d Y - µ + µ P b P b → ( P b P b σ d − − − - µ + + µ + (*) +Pb (*) Pb → Pb+PbATLAS Preliminary <20 GeV µµ µµ µµ |<2.4 µ η >4 GeV, | µ t, =5.02 TeV, p NN s Fig. 4. Cross section for dimuon production in UPC of Pb+Pb together with AT-LAS experimental data [19].
Let us discuss now briefly production of charged pion pairs. In Fig.5we demonstrate how well our multicomponent model [5] describes the ele- template printed on October 16, 2018 mentary cross sections: γγ → π + π − and γγ → π π measured in detail bydifferent experiments [5]. These elementary cross sections can be used incalculation of the cross section for nuclear processes AA → AAππ . [GeV] π π = M γ γ W ) [ nb ] - π + π → γ γ ( σ -2 -1 ALEPHBelleCELLOCLEOTwo GammaMark IIVENUS -2 =4 GeV πγ B -2 =6 GeV πγ B [GeV] π π = M γ γ W ) [ nb ] π π → γ γ ( σ -2 -1 Crystal BallBelle - e xc hange ρ + sum Fig. 5. Energy dependence of the elementary cross sections for γγ → ππ reactions. There is a strong competition in the π + π − channel of coherent ρ mesonproduction (see Fig.6) which decays into a π + π − pair. The main mechanismis photon fluctuation into virtual ρ meson and its multiple rescattering inthe collision partner. In Fig.7 we show invariant mass distribution of the π + π − system. Both ρ contribution with effective inclusion of the pho-toproduction continum, called sometimes S¨oding mechanism, and the γγ mechanism were considered. The γγ mechanism becomes sizeable in the re-gion of the f (1270) dipion resonance and its presence improves agreementwith the ALICE experimental data [20]. A Aρ IP / IR A A π + π − IP / IR Fig. 6. Mechanism of coherent ρ production. The cross section for coherent single ρ production is very large. There-fore one could consider also double-scattering cross section for productionof ρ ρ pairs. The underlying mechanisms are sketched in Fig.8. emplate printed on October 16, 2018 [GeV] - π + π M | < . ) [ b / G e V ] - π + π ( | Y - π + π / d M σ d -3 -2 -1 ∑ Soding(res+cont) - π + π→γγ from =2.76 TeV NN sPb-Pb; Fig. 7. Dipion invariant mass together with ALICE experimental data [20]. The ρ → π + π − and γγ → π + π − contributions are shown separately. A AV IP / IR A AV IP / IR A AV IP / IR A AV IP / IR A AV IP / IR A AV IP / IR A AV IP / IR A AV IP / IR Fig. 8. The mechanisms of double ρ production. In Fig.9 we show distribution in four-pion invariant mass for √ s NN =200 GeV together with STAR data [21]. We show the γγ → ρ ρ anddouble-scattering contributions. Clearly the double scattering contributionis larger than the γγ one but insufficient to understand the STAR data [21].Is the disagreement due to coherent production of ρ ′ or ρ ′′ mesons ? Thisis not clear in the moment and requires further studies in future.In Fig.10 we show our predictions for four-pion invariant mass, includingonly double-scattering mechanism for √ s NN = 2.76 TeV. The resultingdistribution strongly depends on the range of rapidity. A longer range ispreferred when one wants to enhance the double-scattering contribution.Another interesting process is AA → AAp ¯ p . The continuum subpro- template printed on October 16, 2018 [GeV] π M [ m b / G e V ] π ) / d M - π + π - π + π A u A u → ( A u A u σ d -4 -3 -2 -1 STARFitDouble scattering, Low energy γγ , VDM Regge γγ = 200 GeV NN s Fig. 9. Four-pion invariant mass distribution calculated by us together with theSTAR experimental data [21]. The contribution of the double scattering mechanismis shown by the blue solid line. In addition we show contribution of single scatteringbased on γγ → ρ ρ subprocess subdivided into two subcontributions described in[4]. [GeV] - π + π - π + π M [ m b / G e V ] π / d M σ d -3 -2 -1 | π η full ||<2.5 π η | |<1.2 π η | = 2.76 TeV PbPb s - π + π - π + π PbPb → PbPb
Fig. 10. Four-pion invariant mass at the LHC for different ranges of pion pseudo-rapidity. cess is shown for example in Fig.11. In our studies we included also someresonances [11]. In Fig.12 we show our predictions for M p ¯ p and rapiditydistributions for P bP b → P bP bp ¯ p process at √ s NN = 5.02 TeV. Predictedcross sections for P bP b → P bP bp ¯ p for different experimental cuts are givenin Tab.1.Double scattering UPC are possible also for production of two leptonpairs as shown in Fig.13. The cross section integrated over phase space isshown in Fig.14 for two different cuts on lepton transverse momenta (the emplate printed on October 16, 2018 γ ( p ) γ ( p ) p ( p )¯ p ( p ) p t γ ( p ) γ ( p ) ¯ p ( p ) p ( p ) p u Fig. 11. Elementary processes γγ → p ¯ p responsible for production of p ¯ p pairs inUPC of heavy ions. (GeV) γγ W ( nb / G e V ) γγ ) / d W p P b P bp → ( P b P b σ d
10 =5.02 TeV NN s z full|z|<0.6 p y -8 -6 -4 -2 0 2 4 6 8 ( nb ) p ) / d y p P b P bp → ( P b P b σ d
10 =5.02 TeV NN s z full|z|<0.6 Fig. 12. Examples of differential cross sections for the
P bP b → P bP bp ¯ p reaction. Experiment Cuts σ [ µ b]ALICE p t,p > | y p | < p t,p > . | y p | < p t,p > . | y p | < p t,p > . < y p < l + A A l − l − l + A A Fig. 13. Double scattering production mechanism of two lepton pairs.
The number of counts for integrated luminosity L int = 1 nb − is given inTab.2. The table shows that some measurements of four leptons are possible. template printed on October 16, 2018 [GeV] NN s P b P b X ) [ nb ] → ( P b P b σ − e + e e + e e + e >0.3 GeV t p [GeV] NN s P b P b X ) [ nb ] → ( P b P b σ − − − − − − − e + e e + e e + e >2.0 GeV t p Fig. 14. Phase-space integrated cross section for e + e − e + e − and e + e − productionfor two different cuts on lepton transverse momenta. Certainly such a test of our predictions of double scattering mechanismwould be new and valueable.(4 µ ), √ s NN = 5 .
02 TeV (4 e ), √ s NN = 5 . | y i | < p t > | y i | < p t > | y i | < p t > | y i | < p t > | y i | < p t > | y i | < p t > | y i | < p t > | y i | < p t > | y i | < p t > ≪ J/ψ quarkonium in [12].In Fig.15 we show the cross section for different bins of centrality. Rathergood description of the data was achieved by imposing special conditionson photon fluxes [12].Another example is the AA → e + e − peripheral and semicentral nucleus-nucleus collisions for small dilepton transverse momenta discussed very re-cently [16]. The photoproduction mechanism is particularly important forsmall dielectron transverse momenta and not too small energies where itcompetes with thermal dielectron production.This work was supported by the National Science Centre, Poland (NCN),grant number 2014/15/B/ST2/02528. emplate printed on October 16, 2018 centrality [%] b ] µ [ Ψ J / / d y σ d ,b) ω ( (0) N ,b) ω ( (1) N ,b) ω ( (2) N Fig. 15. Dependence of the cross section for creation of the
J/ψ meson as a functionof meson centrality together with the ALICE experimental data [22].
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