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Monique Werlen (LAPTH)

Quark and gluon fragmentation functions into hadrons and photons. Main sources of uncertainty. Monique Werlen (LAPTH). Thanks to. Patrick Aurenche, Zouina Belghobsi, Thomas Binoth, Luc Bourhis, Pierre Chiappetta, Michel Fontannaz, Mario Greco, Jean-Philippe Guillet,

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Monique Werlen (LAPTH)

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  1. Quark and gluon fragmentation functions into hadrons and photons Main sources of uncertainty Monique Werlen (LAPTH) Parton fragmentation workshop, ECT

  2. Thanks to Patrick Aurenche, Zouina Belghobsi, Thomas Binoth, Luc Bourhis, Pierre Chiappetta, Michel Fontannaz, Mario Greco, Jean-Philippe Guillet, Gudrun Heinrich, Bernd Kniehl, Eric Pilon, Simona Rolli, … And of course, all mistakes, due to a poor experimentalist’s interpretation even after years of collaboration, are mine! Parton fragmentation workshop, ECT

  3. Outline • Terminology • Major sources of uncertainties in inclusive hadron cross sections • NLO Fragmentation functions fits on e+e- and pp data: methodology (CGGRW, BFGW) • Theoretical and experimental sources of uncertainty in FF • Inclusive photon cross sections • Photon FF The PHOX Family Parton fragmentation workshop, ECT

  4. Fragmentation functions Dhi (z, t) gives the distribution of momentum fraction z for hadrons of type h in a jet initiated by a parton of type i, produced in a hard process at scale t. Like for parton distributions in a hadron, Fhi (x, t), these are factorizable quantities, in which infrared divergences of PT can be factorized out and replaced by experimentally measured factor that contains all long-distance effects. Parton fragmentation workshop, ECT

  5. A B Hadro-production of pions AB→π X Fragmentation function Dπc(z,M2F): density of π in parton c with fraction z of c momentum X π z c Dπc Hard sub-process d a b xb xa FBb (xb,M2) FAa(xa,M2) PDF or structure function: density of parton a(b) in hadron A(B) with fraction xa(xb) of A(B) momentum Parton fragmentation workshop, ECT

  6. Origin of fragmentation scale M2F This scale separates • short distance (calculated perturbatively) from • long distance (experimental measurement) similar to factorization scale M2 for structure function Parton fragmentation workshop, ECT

  7. Theoretical and experimental sources of uncertainties • data: • statistical error, • systematic, • normalization • z and Q2 range, sensitivity to quark, gluon FF • theory: • choice of functional form, z range of assumptions • choice of scales • order of theory (leading, NLO, resum) • further parameters (Structure Function, αs ) Parton fragmentation workshop, ECT

  8. PDF uncertainties: an old debate See Joel Feltesse introduction to the technical session on PDF uncertainties at PDF4LHC meeting (Feb.22-23, 2008) Many issues are similar (in particular the treatment of experimental systematic errors) but not yet so much debated for FF uncertainties Parton fragmentation workshop, ECT

  9. Importance of uncertainties on inclusive hadron cross sections • Do we care about the uncertainty in fragmentation function? • How does it compare to other uncertainties? Parton fragmentation workshop, ECT

  10. BFG: photon FF KKP: pion FF γ/π0 hep-ph/0311131 prepared for CERN YR-2004-009 Hard probes in heavy-ion collisions at LHC Parton fragmentation workshop, ECT

  11. Reducible ππ and γπ vs irreducible γ γ backgrounds to H→γ γ search Eur. Phys. J. C4,7 Binoth, Guillet,Pilon, M.W. Explore with DIPHOX the strong isolation cuts, uncertainties due to large z pion FF Parton fragmentation workshop, ECT

  12. EPJ C13,347 Parton fragmentation workshop, ECT

  13. Production of π0, E706 data vs NLO theory u(KKP)/u(BKK ) MF=3 GeV Gluon(KKP)/Gluon(BKK) Better fit with fragmentation functions KKP than BKK <z> 0.75-0.9 M=MF=μ=pT/3 Binoth,Guillet,Pilon,M.W. EPJC24,245 Parton fragmentation workshop, ECT

  14. Typical SF uncertainties in π0 production? Parton fragmentation workshop, ECT

  15. Uncertainties at RHIC energy due to fragmentation, factorization and renormalization scales Improved with ln(1-z) resummation of soft gluons ? Parton fragmentation workshop, ECT

  16. Uncertainties at LHC energy due to fragmentation, factorization and renormalization scales Rem. scales frozen below M0=2GeV, Mf0=sqrt(2) GeV Parton fragmentation workshop, ECT

  17. Typical fragmentation function and scale uncertainties in charged hadron production at RHIC energy uncertainties from scale > uncertainties from FF Parton fragmentation workshop, ECT

  18. Importance of uncertainties on inclusive hadron cross sections • Do we care about the uncertainty in hadron fragmentation function? • How does it compare to other uncertainties? At RHIC energy, uncertainties from: • scales are important: +-50% at pt= 8 GeV/c as well as from • different FF sets(Kretzer set reduces sizably the cross section compared to KKP and BFGW sets) At LHC energy, uncertainties from • scales are of order of: +-20% for pt> 10 GeV/c while • differences from FF sets are dominant Parton fragmentation workshop, ECT

  19. Production of π0, E706 data vs NLO and NLL theory Vogelsang + de Florian PR D71 (2005) 114004 much reduced scale dependence with threshold resummmation (NLL) ( rem: NLO with small scale pt/3 to pt/2 rough approximation) Parton fragmentation workshop, ECT

  20. Fragmentation functions: methodology • Parametrize FF z dependence at a given scale (MF=2GeV) • Fit inclusive cross section data (pp and/or e+e-) with NLO theory • Further uncertainties from: • structure functions, • factorization scale M (evol. SF) • fragmentation scale MF (evol. FF) • renormalization scale μ (evol. αs ) • running coupling constant αs • Complementarities pp and e+e-: • pp data more sensitive to gluon FF • e+e- data more sensitive to quark FF • z range : LEP most statistics z<0.7 Neutral pions: Chiappetta, Greco, Guillet, Rolli, M.W. Nucl. Phys. B412,3 (1994) (first attempt to get NLL πo FF) Charged hadrons: Bourhis, Fontannaz, Guillet, M.W. Eur. Phys. C19,89 (2001) Parton fragmentation workshop, ECT

  21. minimize NLO QCD fits for fragmentation Get the parton i to hadron h fragmentation function Di(z,MF2) by fitting the inclusive cross section data in e+e- →h X and pp →h Xwith NLO QCD theory assume shape at MF2=MF20 evolution fromMF20toMF2data DGLAP: Calculate NLL cross section at scale MF2 for all data points: get parameters with errors and correlation (covariance matrix) get Parton fragmentation workshop, ECT

  22. minimize NLO QCD fits for fragmentation “theoretical” systematic uncertainties from functional shape at MF2=MF20 choice of scales,running coupling αs in evolution fromMF20toMF2data DGLAP: Calculate NLL cross section at scale MF2 for all data points: choice of scales in SF evolution (pp) and αs get Parton fragmentation workshop, ECT

  23. Inclusive π0 production in NLO approximation AB = pp or e+e- Parton fragmentation workshop, ECT

  24. Fragmentation function: evolution inside the parton i carrying a fraction z of the parton impulsion at fragmentation scale Mf density of Petronzio, Furmansky Phys. Lett. B97,437 (1980) code from P.NASON Parton fragmentation workshop, ECT

  25. Fragmentation function: parameterization 9 parameters For valencequark, sea quark , and gluon fragmentation Dv(z)=Nv(1-z)βvzαv Ds(z)=Ns(1-z)βszαs Dg(z)=Ng(1-z)βgzαg set I fix av=as=ag=0 Parton fragmentation workshop, ECT

  26. NLO fits to e+e- dataquark fragmentation NLO theory Altarelli, Ellis, Martinelli, Pi Nucl. Phys. B160,301 (1979) Parton fragmentation workshop, ECT

  27. NLO fits to pp data gluon fragmentation NLO theory Ellis, Sexton: matrix elements Nucl. Phys. B269,445 (1986) Aversa,Chiappetta,Greco,Guillet Nucl. Phys. B327,105 (1989) Order αs2 Order αs3 Parton fragmentation workshop, ECT

  28. NLO fits to pp data gluon fragmentation Data at √s=23,31,63,540,630 GeV • WA70 Z.Phys. C38,371 (1988) • E706 Phys. Rev.D45,3899 (1992) • R806 Z.Phys. C5,104 (1980) • UA2 Z. Phys C27,329 (1985) Phys. Lett. B176,239 (1986) pp->g pp->u+d Parton fragmentation workshop, ECT

  29. Correlation Nglue-Nsea Complementarities of e+e- and pp data for the Ng and Ns determination ISR pp data very sensitive to Ng … but have a scale dependence illustrative only Parton fragmentation workshop, ECT

  30. Theoretical and experimental sources of uncertainties • data: • statistical error, • systematic, • normalization • z and Q2 range, sensitivity to quark, gluon FF • matching theory and data (binning, cuts, defs,..) • theory: • choice of functional form, z range of assumptions • choice of scales • order of theory (leading, NLO,…) • further parameters (Structure Function, αs ) Parton fragmentation workshop, ECT

  31. Systematic uncertainties from data Normalization free parameter allowed to vary within 3σ of normalization uncertainty quoted by expt Fitted normalization Point to point independent systematics sometime added in quadrature to statistical uncertainties . Parton fragmentation workshop, ECT

  32. Typical z range of LEP data sets (for BFGW fits) Parton fragmentation workshop, ECT

  33. z range of pp→πoX at 31 GeV (E706, ISR) Parton fragmentation workshop, ECT

  34. z range at ISR (63 GeV) Parton fragmentation workshop, ECT

  35. z range at LHC (version 16 TeV) Parton fragmentation workshop, ECT

  36. FF BFGW/BKK Parton fragmentation workshop, ECT

  37. ln (1-z) resummation of soft gluons in FF Resummation Cacciari Catani NPB617,253(2001) • Resummation reduces dependence on renormalization and fragmentation scale for e+e- • “optimized scales” in BFGW fit to e+e- (μ/Q≈ 0.2 at large x) was a rough approximation • (for a new approach, see AKK, arXiv 0711.1086) Parton fragmentation workshop, ECT

  38. Uncertainties on gluon fragmentation BFGW low and high Ng/BFGW Parton fragmentation workshop, ECT

  39. Fragmentation to charged hadron Parton fragmentation workshop, ECT

  40. Parton to hadron fragmentation at LO pt balance between hadron and jet at RHIC energy using JETPHOX direct access to fragmentation function may help discriminate sets at large z with Belghobsi, Fontannaz, Guillet, Heinrich, Pilon preliminary CTEQ6M, M=Mf=μ=pt(h)/2 pt(h)>25GeV pt(jet)>30GeV Parton fragmentation workshop, ECT

  41. Photons: Direct and Fragmentation Parton fragmentation workshop, ECT

  42. O(ααs) O(αs2α(1/αs+g)) Important at high √s and low pt (NLO ACFGP NPB399,34) O(ααs2) Parton fragmentation workshop, ECT

  43. Direct photon production O(ααs) “Direct” γ O(ααs2) Fragmentation Only the sum σ(D) + σ(F) is a physical observable Parton fragmentation workshop, ECT

  44. Direct photon production Guillet, DIS04 Parton fragmentation workshop, ECT

  45. The PHOX Family NLO event generators (parton level) for large ptPHOton (hadron or jet) X-sections http://www.lapp.in2p3.fr/lapth/PHOX_FAMILY/main.html P.Aurenche, T.Binot, M.Fontannaz, J.Ph.Guillet, G.Heindrich, E.Pilon, M.W. DIPHOX: h1 h2→γγ+X h1 h2→γh3+X h1 h2→h3 h4+X Parton fragmentation workshop, ECT

  46. Data vs NLO QCD 23 GeV≤√s≤1.96TeV Aurenche, Fontannaz, Guillet, Pilon, M.W. Phys. Rev. D73, 094007 (2006) Parton fragmentation workshop, ECT

  47. Data vs NLO QCD 23 GeV≤√s≤1.96TeV Aurenche, Fontannaz, Guillet, Pilon, M.W. Phys. Rev. D73, 094007 (2006) Phenix and D0 data clarify the data/theory puzzle Parton fragmentation workshop, ECT

  48. Importance of uncertainties on inclusive photon cross sections • Do we care about the uncertainty in photon fragmentation function? • Most of collider data obtained with isolation cuts • How does it compare to other uncertainties? Parton fragmentation workshop, ECT

  49. Parton to Photon fragmentation Bourhis, Fontannaz, Guillet Eur. Phys. C2,529 (1998) BFG set I and II gluon fragmentation set II set I Parton fragmentation workshop, ECT

  50. Theoretical uncertainties at RHIC energy Fragmentation BFGI/BFGII Scales uncertainty Uncertainties from scales > from fragmentation Parton fragmentation workshop, ECT

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