Charm Production/Decay Models In Atmosphere (Part I) for Prompt Lepton Study

1. Charm Production/Decay Models In Atmosphere(Part I)for Prompt Lepton Study UW IceCube Group meeting 5/20/2005 Aya Ishihara, Teresa Montaruli and Sean Grullon

2. Atmospheric Neutrino from Charmed Mesons E3f(E) sample Considered as dominant source of very high energy neutrino background Why so? • Short life times, order of c  10-3s and it decays before reaching on the Earth (produceneutrino) • Do not loose energy by colliding the nucleon in the atmosphere (prompt high energy neutrino) - Want to set an upper limit on theoretical uncertainty of atmospheric neutrino models, for physics interest of itself (energy region can not be studied by accelerators) and for the studies of higher energy cosmic neutrino! Problem • Details of production mechanism unknown – scc cross-section uncertainty • Atmospheric neutrino estimation vary by orders in magnitude • Shifts the energy prompt exceeds conventional • New experimental data available from CDF-II, STAR at the energy of interest over last 2 years (beam energy 20 – 2000 TeV) • many models calculated before the data came, need review of models used & update!

3. Atmospheric Neutrino Also Neutrino Yield includes: Atmospheric depth p-A collisions occur Extrapolation from p-N to p-A In this presentation, I only consider the largest uncertainty from charmed meson production cross-section Models considered in part-1 are, from following papers only from pQCD: Thunman, Ingelman and Gondolo (TIG1996) improved version a Gelmini, Gondolo, Varieschi (GGV1999-1) a using different parton distribution function (GGV1999-2, GGV2000), Pasquali, Reno, Sarcevic (PRS1998) Martin, Ryskin, Stasto (MRS2003) Following will be Added in part-2 (phenomenological models, any suggestion?) Fiorentini Naumov Villante (FNV2002) Bugaev, Misaki, Naumov, Sinegovskaya, Sinegovsky, Takahashi (BMNSST1998) Volkova, Fulgione, Galeotti, Saavedra (VFGS1987) etc. …

4. =Review= ref/review * prompt "Prompt Lepton Cookbook" hep-ph0010306-Costa-PromptLeptonCookbook.pdf "Atmospheric Muon Flux at Sea Level, Underground and Underwater" hep-ph9803488-BMNSST.pdf * conventional astro-ph0502380-Gaisser-AtmosphericNeutrino.pdf * for amanda/icecube hep-ph0104039-CostaHalzenSalles-PromptAtmosphericNeutrinoWindow.pdf =pQCD= ref/pqcd-models * GGV hep-ph0209111-GelminiGondoloVarieschi-MeasuringPromptAtmosphericNeutrino.pdf hep-ph9905377-GelminiGondoloVarieschi-DependenceOnGluonDistributionFunction.pdf hep-ph9904457-GelminiGondoloVarieschi-PromptNeutrinoMuonNLO-LOQCDPredictions.pdf "MEASUREMENT OF THE GLUON PDF AT SMALL X WITH NEUTRINO TELESCOPES" By Graciela Gelmini, Paolo Gondolo, Gabriele Varieschi Phys.Rev.D63:036006,2001 e-Print Archive: hep-ph/0003307 0003307.pdf * PRS hep-ph9806428-PasqualiRenoSarcevic-LeptonFluxesFromAtmosphricCharm.pdf * MRS hep-ph0302140-MartinRyskinStasto-PromptNeutrinosFromccbbSmallGluonX.pdf * TIG-PYTHIA(MC) hep-ph9505417-ThunmanIngelmanGondolo-CharmProductionHighEnergyAtmosphericMuonAndNeutrino.pdf ref/pqcd-theory (tutorial) IntroPqcd-long.pdf p-qcd-lecture.pdf cdf4113_qcd_in_hadron_coll..ps Soper.pdf LHC-QCD1.ps =non-pQCD= ref/pheno-models * FNV + QGSM/RQPM hep0106014-FiorentiniNaumovVillante.pdf hep0201310-FiorentiniNaumovVillante.pdf * QGSM and RQPM discussed Atmospheric Muon Flux at Sea Level, Underground and Underwater (BMNSST) 9803488.pdf ref/pheno-theory NuclPhysB405-80.pdf =experimental result= ref/charm-production * pQCDPredictionCharmBottomAtRHIC_hepex-0502203.pdf hep-ph/9702287 Title: Heavy-Quark Production Authors: S. Frixione, M.L. Mangano, P. Nason, G. Ridolfi "Heavy Flavours II", eds. A.J. Buras and M. Lindner, Advanced Series on Directions in High Energy Physics, World Scientific Publishing Co., Singapore. Journal-ref: Adv.Ser.Direct.High Energy Phys. 15 (1998) 609-706 charm-production/9702287.pdf * experimental result in p+p and d+Au collisions at \sqrt{s}=200GeV 0407006-star-charm.pdf * CDF p+pbar collisions at \sqrt{s}=1.96TeV RecentCharmFromCDF2004-Dec.ps.gz hepex0307080_CDFII_2TeV_charm.pdf CharmPhysicsAtTevatronII_Presen.pdf * UA2 (p+pbar@sqrt(s)=630 Gev:Elab~180TeV) physLettB236-448-UA2Charm.pdf * pqcd prediction(for RHIC Elab~20Tev and LHC Elab~12000TeV energy) pQCDPredictionCharmBottomAtRHIC_hepex-0502203.pdf hep-ph0203151-Vogt-HeavyQuarkProduction.pdf hep-ph9411438-HeavyQuarkProductionInPP.pdf … and more! Reference catalog athttp://www.icecube.wisc.edu/~aya/simulation/prompt/index.html

5. The Strong Coupling Constant s Quark Gluon parton s (Q,nf)=12(33-2nf)log(Q2 /QCD2) nf :number of quark flavor of which masses less than ~ QCD Before stepping into deep --- The basic QCD properties Nucleon xq QCD special features relevant to charmed hadron production • Strong inlarge distance (small momentum transfer), coupling constant exponentially increases ⇒ quark confinement, infrared singularities, factorization and non-perturbative QCD • Weak insmall distance(large momentum transfer), nearly free inside hadron radius ⇒ asymptotic freedom and perturbative QCD • Parton and gluon distribution functions as a function of x - F(x,Q), g(x,Q) small-x QCD momentum fraction x =Q2/2n ~ Q2/s xg

6. Quick view of the hadron production models quark pair production and hadronization • Non-Perturbative phenomenological QCD (dominant for light hadrons and describe it well, historically preferred model for heavy quark production but is partially because of poor agreement of pQCD models) typically Q < 1~2GeV • String Fragmentation • Quark Parton Recombination (Intrinsic Charm) • (Lattice QCD?) • Perturbative QCD – cross-sections in terms of s (Q) - leading O(s2) / next-to-reading O(s3), preferred model for heavy quarks due to its large masses ~ large momentum transferred Q : applicable for charm quark mass of the order of 1.3 GeV? (still argument compared to b-quark mass 4.5-5.6 GeV) • Models describe interaction with large momentum transfer, i.e. Jet Productions very well • Uncertainty in x (fraction of momentum carried by parton, considered to be the ‘momentum resolution’ of the partons) dependences of parton distribution function F2(x,Q2) – at small x, only gluon distribution is relevant … active area of DIS study • Uncertainty in fragmentation function

7. Charge-Dependent (CD) = Like-sign – Unlike-sign q q Color-field string fragments along beam axis (the Lund model of soft-particle production, QM Tunnelling pre-QCD Regge-based approach, fragmentation function) q q beam axis q q proton-proton collisions at 200 GeV (c.m.) How does it look like?? non-pQCD exampleString Fragmentation (QGSM or the Lund Model) consequence in particle correlations as well as the success in predicting low energy hadron yield Negative Gaussian on  (independent of ) • Local momentum, charge, flavor conservation

8. p-p collision mini-jet (back-to-back) strong correlation between jet thrust axis and secondary particles How does it look like?? pQCD exampleParton fragmentation (hard-particle productions) Two-particle correlation proton+proton at 200 GeV (c.m.)

9. soft Produced and thermalized by inelastic scatterings hard elastic process (Jet, mini-jet) 10% p+p like Light hadron production (e.g. p): two-component model • Main two differences for • charmed meson production • large quark masses • quark doesn’t exists in projectile/target hadron (Phys. Rev. Lett. 89, 202301 (2002) )

10. pQCD models for atmospheric charm pQCD – considered to be applicable only for a large momentum transfer interaction Some notes: • pQCD claims soft charm production is negledgeble in the Lund model which predicts quark-pari production ratio uu:dd:ss:cc ~ 1:1:0.3:10-11 • pQCD can study x, Q dependences in principle but NOT absolute normalization. Usually parameter set to some experimental data at lower energy region • Our interest is of energy region 104<E<1012 GeV

11. Heavy quark mass mc QCD renormalization parameter LQCD Renormalization scale parameter for perturbative calculation mr:Factor needed for the expansion of the observable in power of the strong coupling constant which is truncated at a certain order pQCD Factorization scale parameter mf :defines the separation between short-distance QCD processes and long-distance, non-perturbative processes, which are absorbed in the parton distribution Parton distribution function (PDF) in proton F(x, Q) or gluon distribution function g(x, Q) which depends on both x and Q Perturbation Order: Leading-Order (LO) to Next-to-Leading-Order (NLO) b b g g b g q b b b b b q g g g q q Flavor Excitation Flavor Creation (gluon fusion) Flavor Creation (annihilation) Gluon Splitting Important factors for pQCD LO NLO

12. pQCD Model differences TIG(starting point of pQCD calculation for atmospheric prompt leptons, 1996) pythia (Lund) + LO pQCD

13. Fig. 7 Fig. 10 TIG Results Summary (initial pQCD study) Small cross section at high energy region which indicates small fluxes of prompt leptons For nm, Log10(E(fconv=fprompt))~5.7 At lower energy it agrees with experimental results as it is normalized by experimental data Problem on PDF (extrapolation to small x) and K factor (the higher order p correction) • need to be fixed Charm production cross section muon and neutrino distributions

14. GGV 1: LO to NLO comparison with MNR routines (charm quark production) + PYTHIA 6.115 (charm quark fragmentation, charm interaction and decay) competitive Perturbation series 1

15. GGV2: the main difference from GGV1 in the extrapolation to x<10-5 Perturbation series 2 (BFKL)

16. Fig. 5 Dependence on different extrapolation Charm production cross section GGV Results Summary Dependence on different PDF Fig. 3 Al l matched at low energies due to fixed parameter at the same energy at 250 GeV Similar glow up to 106~7 but different from TIG above 104 CTEQ3M > other TIG the lowest due to NLO effect, small-x extrapolation Very similar distribution for leptons m, nm, ne. nm and ne are almost equal K factor (NLO/LO ratio) 2.1 ~ 2.5 Adifference is mainly due to Small-x l from 0.08 (TIG) to 0.2 – 0.3 • Charm production cross-section is very much gluon distribution l dependent ! which is a parameter to describe gluon distribution function contribution from small x region • The spectral index of the atmospheric leptonic fluxes depends linearly on the slope of the gluon and distribution function at very small x a suggests prompt lepton to study small-x physics K factor (ratio: NLO/LO) Dependence on different extrapolation Dependence on different PDF

17. PRS98: small-x behavior, factorization and renormalization scale dependence

18. PRS98 summary Cross section Steeper small-x behavior by 0.2 of the parton distribution function enhance cross section by a factor of 2.6 at 108GeV Decreasing renormalization scale from 2mc to mc decreases cross section by 2.1 at 108GeV Flux reflects the differences MRS D- (l=0.5, mr=2mc, mF=mc) PRS-3 m flux CTEQ3 (l~0.3, mr=2mc, mF=mc) PRS-1 CTEQ3 (l~0.3, mr=mc, mF=mc) PRS-2 TIG prompt TIG conventional

19. MRS03: idea of gluon saturation • We have seen that current problem is uncertainty associated with small-x of region which is not accessible by experiments • Gluon distribution behavior at small-x is hot topic in physics, how it saturate, CGC? • This paper study the extrapolation methods from the last known points of x … • New – inclusion of prompt nt (Dsatnt decay), contribution from beauty hadrons which is small but it’s tnt semileptonic decay channel may be important Suggested by DGLAP formalism Non zero c (~0.05-0.2) for triple-Pomeron effect (?)

20. MRS-3 MRS03 summary • ne are essentially equal to nm, thus is ne more visible over its conventional • electrons are negligible, muon 10% less than nm at the surface • nt contribution from beauty decay (~40%) included, still 10 times less than nm, ne • Gluon saturation effect need to be included as MRS-3 which is minimum saturation thus considered to be upper limit of cross section • Flux Although MRS-3 is smaller than the other models MRS-1,2 for example, authors claim that considering saturation effect the MRS-3 would set the upper limits

21. Charm (heavy quark) Productions at accelerators • Hints: • Recent experiments total c-cbar cross section from • CDF-II (PRL2003) @ Tevatron p-pbar at sqrt(s) = 1.96 TeV aElab ~ s/2mp ~ 2000 TeV • STAR (PRL2004) @ RHIC p-p, d-Au sqrt(s) = 200GeV aElab ~ 20 TeV • D0 (preliminary) @ Tevatron • note: direct comparison require additional information In favor of NLO pQCD with PDF: MRST HO, mc=1.2GeV, Renorm. scale: mc, Fact. scale: 2mc STAR 20 TeV(lab)

22. Experimental results at Tevatron CDF-II Elab ~ 2000 TeV Integrated cross sections at CDF-II: CTEQ6M PDF Mc=1.5GeV, Fragmentation: ALEPH measurement Renorm. and fact. Scale: mT=(mc2+pT2)1/2 Theory uncertainty: scale factor 0.5-2.0 Theory prediction: Calculation from M. Cacciari and P. Nason: Resummed perturbative QCD (FONLL) JHEP 0309,006 (2003)

23. Summary of part-I Prompt Lepton Models for the IceCube • pQCD reasonably describe the cross section from experimental data over large energy range • (at least) NLO estimation for heavy quark production is required • Results are very sensitive to PDF especially its small-x behaviour of gluon distribution func. • Stay tuned on small-x saturation problem and results from experiments at RHIC/Tevatron To do --- to be continued in the part-II !! • Non perturbative QCD review • Comparison with experimental results * As direct comparisons of different experiments requires extra caution, in the part-II of presentation, experimental results and models described in the part-I will be compared in indirect way, i.e. study the difference between pQCD theory compared with experimental results (pdf: MRST HO and CTEQ 6M) and pQCD models studied in this presentation and consider the modification needed to it to match to the experimental results. • Comparison of effects other than charm production cross section • Include some reasonable models into IceTray for IceCube prompt study for all nm, ne, nt • Because models only study energy up to 108 or 109 GeV. These model need to be extrapolated to the higher energy region to study upper energy limits on atmospheric neutrino • Heavier (beauty) quark contribution Any suggestion/correction/question/help welcome!