Heck, Dieter

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  KIT SCIENTIFIC WORKING PAPERS Production of Vector Mesons by Photonuclear Interactions in the Program CORSIKA  by Dieter Heck1 6   1 Institute for Nuclear Physics, Karlsruhe Institute of Technology (KIT)    Impressum Karlsruher Institut für Technologie (KIT) www.kit.edu    Diese Veröffentlichung ist im Internet unter folgender Creative Commons-Lizenz  publiziert: http://creativecommons.org/licenses/by-nc-nd/3.0/de  2013  ISSN: 2194-1629  IIIAbstractProduction of Vector Mesons by Photo-Nuclear Interactions in the ProgramCORSIKAThis report describes the production of vector mesons by photonuclear inter-actions in the air shower simulation program CORSIKA. These vector mesons ρ0and ω are produced also at the highest γ-energies and decay to only two chargedpions (for ω two charged and one neutral pion), which in turn by decay may leadto muons in the TeV-energy range. Details of the used parameterizations for theproduction process are given.ZusammenfassungProduktion von Vektor-Mesonen durch photonukleare Wechselwirkungenim Programm CORSIKADieser Bericht beschreibt die Produktion von Vektormesonen durch photo-nukleare Wechselwirkungen in dem Luftschauer-Simulationsprogramm CORSI-KA. Diese Vektormesonen ρ0 und ω werden auch bei den ho¨chsten γ-Energienproduziert und zerfallen in nur zwei geladene Pionen (fu¨r ω zwei geladene undein neutrales Pion), die ihrerseits durch Zerfall zu Myonen im TeV-Energiebereichfu¨hren ko¨nnen. Details der benutzten Parametrisierungen fu¨r den Produktions-prozess werden angegeben.IVVContents1 Introduction 12 Cross-Section Data 22.1 Parameterizations of total gamma-air cross-section . . . . . . . . 22.2 Vector meson production at C, N, and O . . . . . . . . . . . . . . 33 Vector Meson Fraction of Photonuclear Interaction 54 Decay of Vector Mesons 65 Higher Mass Vector Mesons 7References 9VI11 IntroductionIn the generalized vector dominance model [1, 2] a γ-ray is assumed to fluctu-ate into a quark-antiquark pair. Due to the interaction this off-mass shell pair ismoved to the mass shell of a vector meson (VM) or a diffractively excited stateof it. If a single VM is produced then this particle carries the quantum numbersof the incoming photon. In other words, the quark pair forms a (qq)J=1 boundstate of a neutral VM which subsequently interacts by elastic scattering off a nu-cleon. Predominantly the VMs ρ0 and ω have to be considered. The productionof higher-mass neutral VMs is strongly suppressed as with increasing quark massthe probability to fluctuate into a ss-pair leading to a φ-meson or into a cc-pairleading to a J/ψ-meson decreases.With extremely short lifetimes the VMs decay into two charged pions (ρ0)rsp. three pions (ω) which by the Lorentz-boost are emitted in the very forewarddirection of the incoming γ-ray:γ +N→ ρ0 +N→ pi+ + pi− +Nγ +N→ ω +N→ pi+ + pi− + pi0 +NThus the γ-ray energy is distributed only onto very few charged pions.In the higher atmosphere above some ten km where the air density is low thepion decay dominates over the pion interaction and energetic muons (and neu-trinos) will emerge and carry away a large fraction of the primary γ-ray. Thisunderlines the importance of the VM production process for muon generation inthe develoment of cosmic ray air showers and therefore the VM production byγ-rays is implemented in the air shower simulation program CORSIKA [3].2 2 CROSS-SECTION DATA2 Cross-Section DataIn CORSIKA the interactions of γ-rays are treated by the custom-made routinesof the EGS4-package [4]. The γ-rays may initiate different processes and theirbranching ratios are defined by the ratios of the cross-sections. The total inelasticγ-ray cross-section (defining the mean free path to the next interaction) and thebranching ratios leading to the different interaction processes are tabulated in theEGSDAT data files which are read in when starting the EGS4-package.2.1 Parameterizations of total gamma-air cross-sectionThe hadronic interaction processes of γ-rays may happen at energies above thepion production threshold of Eγlab > 0.1482 GeV. At γ-energies below Eγcm ≤19.39 GeV (equivalent Eγlab ≤ 200 GeV) the photonuclear cross-section is de-scribed by a continuous distribution [5]σγp =(73.7 s0.073 + 191.7 s−0.602)√1− s0/s (1)where s is the squared cm-energy (in GeV2) and s0 is the pion production thresh-old energy with √s0 = 1.0761 GeV. The resulting cross-section σγp is given inµb. The root on the rhs. of Eq. 1 cuts down the cross-section at the thresh-old energy. Superimposed on this continuous distribution are three resonancesat squared cm-energies of 1.464, 2.220, and 2.789 GeV2 with width parametersof 0.12705, 0.18774, and 0.19372 GeV2 and amplitude parameters of 54.2, 23.2,and 11.2 µb/GeV2, respectively. How well the experimental data points are de-scribed by this parameterization of the resonance structure of the γ-p cross-sectionis demonstrated in Fig. 7.1 of Ref. [3].Above Eγcm > 19.39 GeV the parameterization of Ref. [6, 7] is used (againσγp in µb):σγp = 59.3 s0.093 + 120.2 s−0.358 . (2)The two slope parameters in the exponents and the amplitude factors are resultsof global fits [6] which include pp and pp measurements and use correspond-ing ratios of the real-to-imaginary part of the forward scattering amplitudes. Thisguarantees a reliable extrapolation of Eq. 2 to highest energies. The smooth transi-tion of the cross-section σγp at Eγcm = 19.39 GeV between the two energy rangesof Eq. 1 and Eq. 2, respectively, has been checked.For a target nucleus of mass number A the total inelastic γ-A cross-section isderived from the γ-p cross-section by scaling with A0.91 according Ref. [5, 8].For the three constituents of air with Nitrogen (A = 14, 75.528%), Oxygen (A =16, 23.166%), and Argon (A = 40, 1.282%) we scale the cross-section for each2.2 Vector meson production at C, N, and O 310-111 10 10 2 10 3 10 4 10 5Ecm  (GeV)σγ-A  (mb)1 10 102 103 104 105 106 107 108 109 1010 1011Elab (GeV)σγ-airtotσVM → NσVM → N*σVM → OσVM → O*σVM → ArσVM → Ar*Figure 1: Total photonuclear cross-section of air (black solid line) and VM pro-duction cross-sections of the different constituents of air leading to ground state(solid coloured lines) or excited state (dashed coloured lines) target nuclei areplotted as function of the cm-energy in the γ-nucleon system.component and form the weighted sum from the three individual elemental cross-sections.The resulting total inelastic γ-air cross-section is shown in Fig. 1 as functionof the cm-energy in the γ-nucleon system.2.2 Vector meson production at C, N, and OThe cross-section for the photoproduction of VMs is parameterized [9, 10] in theformσ(Ecm) = a · E δcm + b · E −²cm (3)where the energy E is used in the cm-system (in GeV) of the γ-nucleon systemand the resulting cross-section is given in mb. The parameters a, δ, b, and ² usedin Eq. 3 for the individual components of air are listed in Table 1 for target nucleiremaining in the ground state or in an excited state.4 2 CROSS-SECTION DATATable 1: Cross-section parameters [9] according Eq. 3 for VM production at theconstituents of air with target nuclei remaining in ground state and excited state(marked by ∗) (after [10]).Reaction a b δ ²γ + N → VM + N 0.0932 1.044 0.2304 1.369± 0.0062 ± 0.509 ± 0.0091 ± 0.319γ + N → VM + N∗ 0.0365 0.372 0.1297 1.230± 0.0023 ± 0.105 ± 0.0084 ± 0.182γ + O → VM + O 0.1076 1.222 0.2292 1.358± 0.0074 ± 0.591 ± 0.0094 ± 0.316γ + O → VM + O∗ 0.0417 0.482 0.1280 1.191± 0.0050 ± 0.222 ± 0.0160 ± 0.291γ + Ar → VM + Ar 0.3074 3.835 0.2010 1.449± 0.0211 ± 1.988 ± 0.0094 ± 0.334γ + Ar → VM + Ar∗ 0.0931 1.475 0.0950 1.435± 0.0144 ± 1.148 ± 0.0211 ± 0.48511 10 10 2 10 3 10 4 10 5Ecm  (GeV)σγ-A  (mb)1 10 102 103 104 105 106 107 108 109 1010 1011Elab (GeV)σγ-airtotσγ-airVMFigure 2: The total photonuclear cross-section of air (black solid line) and the VMproduction cross-section of air (dashed red line) including contributions leadingto ground states and excited states of the air constituents is plotted as function ofthe cm-energy in the γ-nucleon system.5The resulting VM production cross-sections are plotted in Fig. 1. In theseparameterizations the contribution ratio of ρ0 and ω mesons is assumed [11] to be9 : 1, while the production of φ or heavier VMs is neglected, see also Sect. 5.Summing up the weighted contributions of all components of air we arrive atthe total γ-air VM production cross-section which is shown in Fig. 2.3 Vector Meson Fraction of Photonuclear InteractionFrom the two functions plotted in Fig. 2 we form the quotient σVMγair / σtotγair whichis displayed in Fig. 3. Taking typically two points per Ecm-decade and addingsome more points around Ecm ≈ 10 GeV where the VM fraction shows a strongbending of the curve we fit to the 15 selected points the function of Eq. 4 which isof the form of Eq. 3.203040501 10 10 2 10 3 10 4 10 5Ecm  (GeV)fraction (%) 1 10 102 103 104 105 106 107 108 109 1010 1011Elab (GeV)fraction of VM productionfit to fraction of VM productionFigure 3: Fraction of VM production (solid line) calculated from the quotientσVMγair / σtotγair as function of the cm-energy (in the γ-nucleon system). 15 points ofthis distribution have been selected (open circels) and the function (dashed line)of Eq. 4 is fitted to them.6 4 DECAY OF VECTOR MESONSThe final parameters of the fit result in the VM fraction as function of thecm-energy in the γ-nucleon system tofractionVM = 0.17560 · E 0.037303cm + 0.68008 · E −1.3021cm . (4)This function follows rather closely the selected points, see Fig. 3.4 Decay of Vector MesonsThe decay modes of the different VMs are listed in Tabel 2. In CORSIKA in alldecays only modes with a branching ratio ≥ 1 % are respected. All those modesare given for the ρ0, ω and φ-mesons. For the ψ-meson only the mode leading toa high-energy µ+µ−-pair is shown.Table 2: Lifetime and decay modes of vector mesons with branging ratios ≥ 1 %(after [7]). For the ψ-meson only the interesting µ+µ−-decay mode leading tohigh-energy muons is listed.vector meson lifetime (s) decay mode branching ratioρ0 4.50·10−24 pi+ pi− ≈ 100 %pi+ pi− pi0 89.2 %ω 7.75·10−23 pi0 γ 8.28 %pi+ pi− 1.53 %K+ K− 48.9 %K0L K0S 34.2 %φ 1.55·10−22 ρ pi } 15.32 %pi+ pi− pi0η γ 1.309 %. . . . . .ψ 7.01·10−21 µ+ µ− 5.93 %. . . . . .The VMs are produced preferentially by the transverse polarization of the in-coming γ-ray. Therefore the pi+pi−-pair from the two-body decay of the VMs isemitted preferentially in transverse direction with the characteristic dipole angu-lar distribution I ∝ sin2 θcm with θcm denoting the polar angle relative to theVM direction in the cm-system. This is considered in CORSIKA for the decayingρ0-meson using the experimentally found parameter of the ZEUS Collaboration[12]I(θcm) ∝ (1− 0.8836 · cos2 θcm)7The three-body decay of the ω-meson is treated with correct kinematics, butwithout any angular preference. A homogeneous distribution in the correspondingDalitz plot is assumed. Also for the two other respected two-body decays of theω-meson no angular alignments of the decay directions are assumed.The lifetime of the VMs is too short to respect any transport between VM cre-ation and decay. Therefore in the CORSIKA program the VM production positionis taken as vertex point of the decay.5 Higher Mass Vector MesonsIn the SU(6) theory one assumes the photon to couple to the charge of the partic-ipating quarks which determines [13] the photoproduction cross-section ratio toFigure 4: Experimental γ-p cross-sections for different VMs, rescaled into onefigure from Fig. 109 and Fig. 111 of Ref. [14]. Included are tentative extrapola-tions (dashed lines) to higher energies.8 5 HIGHER MASS VECTOR MESONSσρ0 : σω : σφ : σψ = 9 : 1 : 2 : 8 . (5)The greater the masses of the quark constituents of the φ-meson, which con-sists essentially of a ss-pair, and of the ψ-meson, which is formed by a cc-pair,the more suppressed are their photoproduction probabilities thus modifying theratios of Eq. 5. Experimental values for the production cross-section as functionof energy are summarized in Fig. 4.The ψ-meson has only a small decay branching ratio of ≈ 6 % leading to aµ+µ−-pair (see Table 2). In all other modes muons may also be produced finallyin the decay chains leading over charged pions, but in those cases the energy isdistributed to much more particles thus reducing the occurence of high-energymuons. The overall production of high-energy muons via a ψ-meson has to becompared with the direct production of a muon pair according γ → µ+ + µ−,as described in Ref. [15].With the tentative extrapolation of the ψ-production shown in Fig. 4 the muonproduction at Ecm = 104 GeV is about a factor 10 less probable than the directproduction via γ → µ+ + µ−. At lower energies Ecm = 102 GeV this factorreaches ≈ 150 and increases rapidly with decreasing energy because of the steepfall-off of the ψ-production cross-section, see Fig. 4. Therefore the production ofψ-mesons is neglected in CORSIKA.In the present version of CORSIKA (7.350 issued Dec. 2012) also the φ-meson production is not considered. Its cross-section is about 20 % below that ofthe ω-meson. Despite its low decay branching ratio leading to K-mesons – thecharged Kaons (produced in about the half of the φ-decays) lead with 63.5 % to amuon, while only 27.1 % of the long living neutral Kaons decay directly to a muon– the short lifetime of the K-mesons (relative to that of the charged pions) favoursthe production of high-energy muons. Therefore it seems worth to consider theproduction of φ-mesons in future versions of the CORSIKA program.REFERENCES 9References[1] G. Grammer, Jr. and D. Sullivan, in: Electromagnetic Interactions ofHadrons, ed. A. Donnachie and G. Shaw (Plenum Press, New York, 1978)Vol. 2, 195[2] D. Schildknecht, Acta Phys. Polon. B 37 (2006) 595; D. Schildknecht, G.A.Schuler, and B. Surrow, Phys. Lett. B 449 (1999) 328[3] D. Heck et al., Report FZKA 6019 (1998), ForschungszentrumKarlsruhe, available from: http://www-ik.fzk.de/corsika/physics description/corsika phys.html[4] W.R. Nelson, H. Hirayama, and D.W.O. Rogers, ReportSLAC 265 (1985), Stanford Linear Accelerator Center;http://www.slac.stanford.edu/pubs/slacreports/slac-r-265.html; http://www.irs.inms.nrc.ca/inms/irs/EGS4/get egs4.html[5] T. Stanev, T.K. Gaisser, and F. Halzen, Phys. Rev. D 32 (1985) 1244[6] J.R. Cudell et al., Phys. Rev. D 61 (2000) 034019; Erratum: Phys. Rev. D 63(2001) 059901[7] J. Beringer et al. (Particle Data Group), Phys. Rev. D 86 (2012) 010001;http://pdg.lbl.gov/index.html[8] P. Joos, in: Landolt-Bo¨rnstein, New Series, Group I: Nuclear and ParticlePhysics, ed. H. Schopper (Springer, Berlin, 1973) Vol. 8, 306[9] R. Engel, private communication (2001)[10] R. Engel, J. Ranft, and S. Roesler, Phys. Rev. D 55 (1997) 6957[11] A. Mu¨cke et al., Comp. Phys. Comm. 124 (2000) 290[12] M. Derrick et al. (ZEUS Collab.), Z. Phys. C 69 (1995) 39[13] D.W.G.S. Leith, in: Electromagnetic Interactions of Hadrons, ed. A. Don-nachie and G. Shaw (Plenum Press, New York, 1978) Vol. 1, 345[14] H. Abramowicz and A.C. Caldwell, Rev. Mod. Phys. 71 (1999) 1275[15] D. Heck, Report FZKA 7525 (2009), Forschungszentrum Karlsruhe, avail-able from: http://www-ik.fzk.de/˜heck/publications/ KIT Scientific Working Papers ISSN 2194-1629www.kit.eduKIT – University of the State of Baden-Wuerttemberg and National Research Center of the Helmholtz Association

Production of Vector Mesons by Photonuclear Interactions in the Program CORSIKA

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Production of Vector Mesons by Photonuclear Interactions in the Program CORSIKA

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