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Introduzione alla fisica degli heavy flavour nelle collisioni nucleari ultrarelativistiche

Introduzione alla fisica degli heavy flavour nelle collisioni nucleari ultrarelativistiche. Federico Antinori (INFN, Padova & CERN, Ginevra). LHC is a Heavy Flavour Machine!. system. shadowing. NN x-sect (mb). total multiplicity. pp 14 TeV. 11.2 / 0.5. 1 / 1. 0.16 / 0.007.

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Introduzione alla fisica degli heavy flavour nelle collisioni nucleari ultrarelativistiche

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  1. Introduzione alla fisica degli heavy flavour nelle collisioni nucleari ultrarelativistiche Federico Antinori (INFN, Padova & CERN, Ginevra) FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  2. LHC is a Heavy Flavour Machine! system shadowing NN x-sect (mb) total multiplicity pp 14 TeV 11.2/0.5 1/1 0.16/0.007 Pb-Pb 5.5 TeV (5% cent) 6.6 /0.2 0.65 /0.85 115 /4.6 • cc and bb rates • ALICE PPR (NTLO + shadowing) cc bb PbPb/pp PbPb/pp PbPb PbPb pp pp FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  3. Probing the medium with heavy flavours • c, b produced in early stages of collision, then conserved (neglecting annihilation) production quantitatively under control in pQCD  ideal probes of bulk, strongly interacting phase • energy loss? • thermal production? • no extra production at hadronization  ideal probes of fragmentation • independent string fragmentation vs recombination FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  4. Corso in due parti • Parte prima: • introduzione • heavy flavour in collisioni elementari • Parte seconda: • heavy flavour in collisioni nucleo-nucleo FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  5. Parte prima : introduzione,heavy flavour in collisionielementari FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  6. Heavy Flavour Decays FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  7. Some zoology... • Lower mass heavy flavour hadrons decay weakly • t ~ ps • ct ~ 100’s µm • weakly decaying states from PDG 2006 summary tables: FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  8. In UR limit b ~ Lorentz invariant: ... so b ~ independent of g if cos qCM distribution is flat: so, in space, in projection: so: Impact parameter ~ ct primary vertex decay length = L q decay vertex impact parameter = b y d j x b FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  9. Weak decays of charm W- W+ W+ c c b s’ c s’ e+ µ+ u ne nµ d’ • typically: • large branching ratio to kaons: • D+: • D+  K-+X BR ~ 28 % • “golden” channel: D+ K-p+p+ BR ~ 9% • D0: • D0 K-+X BR ~ 50% • “golden” channels: D0 K-p+ BR ~ 4% ; D0 K-p+p+p- BR ~ 7% • W± branchings: • large semileptonic branching ratio, varies with heavy flavour particle, typical ~ 10% ~ 10% heavy flavour hadrons give in final state an e± (and ~ 10% a µ±) (and with a respectable pT...) C = “Cabibbo angle” (similarly: ) FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  10. Standard experimental tools WA92: Si µstrips primary vertex decay length = L q decay vertex impact parameter = b [Adamovich et al.: NIM A 379 (1996) 252] • Silicon vertex detectors: • so: tracks from heavy flavour weak decays typically “miss” primary vertex by ct ~ 100’s µm • impact parameter resolutions of typical heavy flavour apparatus ~ 10’s µm • e± and/or µ ± identification • charged kaon identification FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  11. Heavy Flavour Production in QCD FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  12. Heavy Flavour hadro-production in pQCD a=q Q b=q Q • Factorization: (at sufficiently large Q2) hadron charmed hadron hadron parton distribution functions xa = momentum fraction of parton a in hadron A cross-section at parton level e.g.: fragmentation z = fraction of c momentum to hadron D cross-section at hadron level FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  13. factorization implies: • PDFs can be measured with one reaction... • say: Drell-Yan: A+B  e+e- + X ... and used to calculate a different one • say: heavy-flavour production • fragmentation independent of the reaction (e.g.: same in pp, e+e-) FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  14. Parton Distribution Functions • PDFs vary depending on momentum transfer scale Q2 • Intuitively: higher Q2 -> higher resolution high-x parton -> lower-x partons • The Q2 evolution of the PDFs can be calculated in pQCD • Altarelli-Parisi evolution (DGLAP) FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  15. Leading-order (LO) q Q Q g g Q g q g Q Q Q Q g Q g • Relevant diagrams: pair creation • qq QQ (quark-antiquark annihilation) • gg QQ (gluon-gluon fusion) FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  16. A few results • the partonic cross-section decreases with energy • faster for qq than for gg (which therefore is expected to dominate, except near threshold) • the parton luminosities near threshold increase with energy, the cross section increases with the energy of the hadron-hadron collision • the pair cross section is proportional to: y (y): rapidity of Q (Q) • Q and Q therefore expected to be close in y • Experimentally: EHS, 360 GeV p-p  DDX FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009 [EHS: PLB 123 (1983) 98]

  17. Next-To-Leading-Order (NTLO) Q Q Q Q Q Q • in absolute value, LO cross sections are typically underestimated by factor 2.5 - 3 (“K factor”) • at NTLO: additional diagrams, such as: higher order corrections to pair creation flavour excitation gluon splitting FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  18. the agreement with experiment for the total cross-section is good (within large bands...) • e.g.: charm cross section at fixed target: FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009 [Mangano: hep-ph/9711337]

  19. results depend on the values of: • mc, µR (renormalization scale), µF (factorization scale) • the result of an exact calculation would be independent of the choice of the scale parameters µR, µF • the residual scale dependence is a measure of the accuracy of the calculation • e.g.: for b production at Tevatron (µR=µF=µ): [Mangano: hep-ph/9711337] FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  20. Q Q Q Q • it is important to match the PDFs with the order of the calculation. • e.g. one must avoid double counting: • at LO: • at NTLO: “intrinsic flavour” “flavour excitation” FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  21. Heavy Flavour in p/p-A FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  22. Nuclear shadowing antishadowing shadowing SPS RHIC LHC • PDFs in the nucleus different from PDFs in free proton • R = ratio of nuclear to nucleon PDFs • from Deep Inelastic Scattering (e-+p; e-+A), Drell-Yan (p+p, p+A -> l +l -+X) e.g.: R for gluons vs gluon momentum fraction x from EKS parametrization [Eskola et al.: EPJ C9 (1999) 61] • typical x for cc production (y 0) • x  10-1 @ SPS • x  10-2 @ RHIC • x  a few 10-4 @ LHC FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  23. Nuclear dependence • From pQCD one expects the cross section for production off nuclei to increase like number of nucleon-nucleon collisions (“binary collision scaling”) • proportional to number of nucleons (for min. bias collisions): • modulo shadowing effects, expected to be small • Experimentally: not far... e.g. WA82: • D production in p-+W/Si at SPS (340 GeV beam momentum) • (relatively) central production with a =1 “Feynman’s x” FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  24. Caveats... with • i) a = 1 does not work down to pp! • e.g.: MacDermott & Reucroft [PLB 184 (1987) 108] compare pA results with earlier hydrogen data from NA27, good agreement using: • note: similar situation for light flavours! systematic study by Barton et al. [PRD 27 (1983) 2580], for various reactions at 100 GeV FT e.g.: central for production of p, K, p from p on nuclear targets: FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  25. ii) lower a at large xF? • early beam dump experiments, sensitive at large xF (max acceptance for xF 0.5) (in tracking experiments, typically max. acceptance for xF 0.2) e.g. WA78 [Cobbaert et al.: PLB 191 (1987) 456] a for muons escaping dump (p-A at 320 GeV FT ): • note: a is known to decrease with xF for light hadrons [Barton et al.: PRD 27 (1983) 2580] FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  26. Heavy Flavour Fragmentation FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  27. Fragmentation • String fragmentation model: (e.g. [PYTHIA hep-ph/0308153]) • as coloured quarks fly away, energy is stored in the field: • above a certain distance it is cheaper to break the string by creating a new qq pair than to keep increasing the distance • the string snaps, e.g.: the heavy quark ends up “hadronising” together with a light antiquark • the newly created quarks are of course light • estimated ratios: u : d : s : c  1 : 1 : 0.3 : 10-11 • no heavy flavour production in string breaking! k 1 GeV/fm FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  28. Fragmentation function Peterson (e = 0.015) Colangelo-Nason (a = 0.9, b=6.4) • c  D, D takes fraction z of c momentum • fragmentation function: DD/c(z) • depends only on fraction z • e.g.: Peterson Colangelo-Nason e.g.: (parameters from fits to charm production at LEP) FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  29. Q Q e- Z0 e+ • How to measure the fragmentation function? • we don’t measure the original Q momentum ... • but in e+e- we do know the Q momentum (by energy conservation!) • e.g.: • fragmentation functions are usually extracted from e+e- measurements and then used for other collisions FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  30. e.g.: fits to charm x = 2E/s distributions in e+e-: [Cacciari & Greco: PRD55 (1997) 7134] • very similar parameters at the two energies (as expected) Peterson fragmentation s = 10.6 GeV (ARGUS) s = 91.2 GeV (OPAL) e = 0.015 (OPAL) e = 0.019 (ARGUS) FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  31. Q Q • like for the PDFs, the fragmentation function has to be matched to order of pQCD calculation • e.g. at NTLO a Q can radiate: • so final energy before non-perturbative part of fragmentation lower than at LO • harder fragmentation at NTLO • at NTLO: e 0.015 • at LO: e 0.06 (e.g.: [Cacciari & Greco: PRD55 (1997) 7134]) Peterson fragmentation e = 0.015 (NTLO) e = 0.06 (LO) FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  32. D* decays, D0(cu) / D+(cd) ratio FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  33. D* decays • Most of the D mesons (from spin counting, ~ 75%) are not directly produced at hadronization, but in D* decays • D±, D0 J=0 • D*±, D*0 J=1 • Due to fine tuning of the values of the masses: • m(D±) + m(p0) < m(D*±) • m(D0) + m(p±) < m(D*±) • m(D0) + m(p0) < m(D*0) but... • m(D±) + m(p±) > m(D*0) • ... the light quark content of charged D is preserved also in case of resonance decays: • a D0(cu) can originate from either D*0(cu) or D*+(cd) • a D+(cd) can only originate from a D*+(cd) FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  34. D0/D+ ratio at LEP • D*0 and D*+ both decay strongly into D’s, but: • D*+ can decay to both D0 and D+ • D*0 can only decay to D0 • From spin degeneracy one expects: D0 : D+ : D*0 : D*+ = 1 : 1 : 3 : 3 • ... and therefore a large D0/D+ ratio • using the experimental branching ratios: • but experimentally, at LEP: [ALEPH: EPJ C16 (2000) 597] FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  35. Heavy Flavour at Tevatron FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  36. Beauty at Tevatron • Discrepancy between pQCD and data seems to have disappeared... • from... a factor 5.5 (but only 1.6 s ...) • to... Run 0 [CDF: PRL 68 (1992) 3403] Spectrum of J/y from secondary B decays Run II [Cacciari et al: JHEP 0407 (2004)] FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  37. From run I on, important improvements in accuracy: • experiment (vertex detectors, high statistics) • prediction (post-HERA PDF sets) • Levels of stability over time: • no large room for new physics any more... • for more see, e.g.: [Cacciari et al: JHEP 0407 (2004) 033, Cacciari: hep-ph/0407187, Mangano: hep-ph/0411020] Data Predictions from [Cacciari et al: JHEP 0407 (2004) 033] FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  38. What about charm? • Nice data from CDF run II • roughly in agreement with full pQCD calculation (though prediction somewhat low) [CDF: Phys.Rev.Lett. 91 (2003) 241804] • A curiosity (?): good agreement between data and prediction for bare quark [Vogt: talk at SQM 2004] FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  39. Parte seconda : heavy flavour in collisioninucleo-nucleo FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  40. Charm and beauty: ideal probes • study medium with probes of known colour charge and mass • e.g.: energy loss by gluon radiation expected to be: • parton-specific: stronger for gluons than quarks (colour charge) • flavour-specific: stronger for lighter than for heavier quarks (dead-cone effect) • study effect of medium on fragmentation (no extra production of c, b at hadronization) • independent string fragmentation vs recombination • e.g.: D+s/D+ • + measurement important for quarkonium physics • open QQ production natural normalization for quarkonium studies • B meson decays non negligible source of non-prompt J/y FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  41. Heavy flavour production in AA • binary scaling: can be broken by: • initial state effects (modified PDFs) • shadowing • kT broadening • gluon saturation (colour glass) (concentrated at lower pT) • final state effects (modified fragmentation) • parton energy loss • violations of independent fragmentation (e.g. quark recombination) (at higher pT) FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  42. What do we know from the SPS? centralcollisions M (GeV/c2) • Intermediate mass dimuon excess in central Pb-Pb at SPS (NA50) • Main known sources in that region: Drell-Yan and charm pairs FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  43. Study of the I.M. excess in NA60 H.Woehri and C.Lourenco, Phys.Rep. 433 (2006) 127-180 NA60 6500 A, 2match < 3 • Fit weighted impact parameter distribution • prompt from J/ψ dimuons, charm from PYTHIA • requires > 2 x expected D-Y to fit data • sensitivity to assumption on cc pT, Δφ • extracted value of cc cross section ~ 2 – 3 larger than extrap. • but compatible with extrapolation from NA50 p-A FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  44. Heavy Flavour @ RHIC: experimental techniques FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  45. Non-photonic electrons • Identified electron spectra • STAR: dE/dx in TPC + TOF at low pT, EMC at high pT • PHENIX: combined RICH and E/p (with E from EM cal) • Rejection of non-heavy-flavour electrons • Main source of electrons: “photonic” • g e+e- conversions • Dalitz decays p0 e+e-g • Dalitz decays h e+e-g • STAR: • rejected by full invariant mass analysis of e+e- combinations • PHENIX: • estimated by simulation and subtracted (“cocktail method”) • measured by “converter method” and subtracted • Other sources of non-charm electrons: • w, r, j, K decays • estimated by sim. and subtracted (in both STAR and PHENIX) (“internal conversions”) FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  46. Reconstructed decays (STAR) • D0 K-p+ • tracks from TPC • K, p identification from dE/dx • no separation of D decay vertex • large combinatiorial background evaluated by event mixing and subtracted • residual background, subtracted with linear fit FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  47. Low pT muons (STAR) [C Zhang (STAR) QM06] • m/p in TPC (dE/dx) • m/p in TOF • fit to impact parameter distribution • charm m should ~ point to primary... FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  48. Experimental status FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

  49. PHENIX pp D0 • Excess wrt FONLL: • Similar situation also in CDF: Ratio: 1.72  0.02 (stat)  0.19 (sys) (0.3 < pT < 9.0 GeV/c) [A. Adare et al. (PHENIX) Phys.Rev.Lett. 97 (2006) 252002] FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009 [D. Acosta et al. (CDF) PRL 91 (2003) 241804]

  50. STAR v PHENIX pp hep-ex/0609010 • ~ a factor 2 discrepancy [J. Lajoie (PHENIX) QM06] FA - Quark Matter Italia - Roma Sanità - 24 aprile 2009

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