INCLUSIVE D- AND B-MESON PRODUCTION

Transcription

1 INCLUSIVE D- AND B-MESON PRODUCTION AT THE LHC Seminar Universitaet Muenster, May 7, 22 G. Kramer based on work in collaboration with B. Kniehl, I. Schienbein, H. Spiesberger G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 / 37

2 OUTLINE Theoretical framework: the General-Mass Variable-Flavor-Number Scheme for -particle inclusive heavy-meson production measure p T and η of observed heavy meson Numerical results for D- and B-meson production: p + p D + X, (D = D ±, D, D ±, D ± s ), p + p B + X, (B = B ±, B, B s ) for comparison with LHC data from ATLAS, ALICE, LHCb, CMS At the LHC: expect higher statistics, higher transverse momentum more reliable test of QCD, better understanding of background for new physics searches G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 2 / 37

3 MASSIVE OR MASSLESS Massive or Massless Heavy Quarks? -particle inclusive heavy-meson production: two scales, m and p T m m = correct threshold behavior no collinear divergences from Q Q + g (Q = charm, bottom) but terms log (p T /m) large corrections at large µ mass singularities (/ɛ-poles instead of log m 2 -terms) absorbed in PDFs and FFs QCD prediction: DGLAP (RG) evolution resums large logarithms log (p T /m) more reliable at large p T not reliable at heavy quark threshold G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 3 / 37

4 HEAVY FLAVOUR SCHEMES Two basic approaches: Fixed Order Perturbation Theory (FFNS) Parton Model (ZM-VFNS) (FFNS: Fixed Flavour Number Scheme, VFNS: Variable Flavour Number Scheme, ZM: Zero Mass) Fixed-Flavor-Number Scheme (FFNS): only light partons in the initial state heavy quark produced in the final state available at fixed order: O(α s) Zero-Mass Variable Flavor-Number Scheme (ZM-VFNS): heavy quark is a parton: PDFs, FFs resum large logarithms (DGLAP, RG) heavy quark treated as massless Interpolating scheme: Parton Model with quark masses: GM-VFNS tailored for DIS (F c 2, F c L ): ACOT, S-ACOT χ G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 4 / 37

5 GENERAL-MASS VARIABLE FLAVOR NUMBER SCHEME General-Mass Variable Flavor-Number Scheme (GM-VFNS): Combine massive (low scale) and massless (high scale) calculations: exploit freedom to choose an appropriate factorization scheme (Collins 998) Conventionally, PDFs and FFs are defined in the MS scheme and MS scheme is based on a massless calculation (massless and massive calculations contain different singularities) Match massless and massive calculations: sub = lim m d σ(m) d ˆσ MS The subtracted cross section (in a massive calculation) d ˆσ(m) = d σ(m) sub can be used with universal MS parton distribution and fragmentation functions G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 / 37

6 MASSIVE VFNS (GM-VFNS) Collinear logs: log(p 2 T /m 2 ) = log(p 2 T /µ 2 ) + log(µ 2 /m 2 ), terms with log(µ 2 /m 2 ): subtracted from hard part and absorbed in parton distribution and fragmentation functions resummed by DGLAP evolution equations Parton distribution functions for g, u, d, s, and c, (and b), heavy quark is a parton: f Q for -particle inclusive heavy-quark production: fragmentation functions Not only for Q H, H = D, B: DQ(z, H µ 2 F ), but every parton can fragment into the observed heavy hadron VFNS: PDF for heavy quark, f Q = below, f Q above threshold; GM-VFNS with m Fragmentation functions, with non-perturbative input and perturbative RG evolution Large collinear logarithms ln(µ 2 /m 2 ) resummed in evolved f c(x, µ 2 ) and D D Q(x, µ 2 ) (set µ = p T, eventually) G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 6 / 37

7 SUBPROCESSES Subprocesses at LO: g + g Q + Q, q + q Q + Q (hadroproduction, for photoproduction, DIS: γ + g c + c) at NLO: -loop diagrams, gluon bremsstrahlung g + g Q + Q + g also g + q Q + Q + q and heavy-quark-initiated processes: e.g., g + Q g + Q (treated as a massless parton) Every parton can fragment to the heavy meson: fragmentation functions for c D, g D, q D and b B, g B, q B, including c B G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 7 / 37

8 APPLICATIONS Applications available for γ + γ D ± + X direct and resolved contributions γ + p D ± + X photoproduction for HERA and LHeC p + p (D, D ±, D ±, D ± s, Λ ± c ) + X good description of Tevatron data intrinsic charm p + p B + X works for Tevatron data at large p T for the LHC (this talk): p + p B + X p + p D + X EPJC22, EPJC28 EPJC38, EPJC62, PLB679 PRD7, PRL96, PRD79 PRD77 PRD84 arxiv: G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 8 / 37

9 SET-UP Input PFD from CTEQ6.6 FF from fits to e + e data: for D, D ±, D : Kneesch, Kniehl, Kramer, Schienbein, 28 for D s, Λ c: Kniehl, Kramer, 26 for B-mesons: Kniehl, Kramer, Schienbein, Spiesberger, 28 Results always for average with charge-conjugated states Kinematic range following measurements of the LHC collaborations Scale parameters for factorization: initial-state, PDF: µ I, final-state, FF: µ F, and renormalization: µ R µ i = ξ i qm 2 + p 2 T varied by factors 2 up and down Charm mass m c =. GeV, bottom mass m b = 4. GeV G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 9 / 37

10 B-MESON PRODUCTION p + p B + X with B = B ±, B, B s Phys. Rev. D84 (2) 9426 G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 / 37

11 FRAGMENTATION FUNCTIONS FOR B MESONS / had d /dx(e + e - B) / had d /dx(e + e - B).6 ALEPH, OPAL, SLD x.6 ALEPH, OPAL, SLD x FF for b B from fitting to e + e data (ALEPH, OPAL, SLD, µ = M Z ) very poor fit from Peterson: D(x, µ 2 ) = N x( x)2 [( x) 2 +ɛx] 2 use Kartvelishvili-Likhoded: D(x, µ 2 ) = Nx α ( x) β starting scale µ = m b = 4. GeV same shape for all B, B +, B s valid for average of B + + B etc. Kniehl, G. K., Schienbein, Spiesberger PRD77 G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 / 37

12 B AT THE TEVATRON CDF data open symbols: J/Ψ CDF 2 solid symbols: J/ΨK + CDF 27 FFN (old input): obsolete PDFs, α s too low p T m b : GM-VFNS merges with ZM-FVNS, FFN breaks down G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 2 / 37

13 B + AT THE LHC 4 /dp T [nb/gev] pp B + + X GM-VFNS S = 7 TeV y 2.4 /dp T [nb/gev] pp B + + X GM-VFNS S = 7 TeV y p T [GeV] p T [GeV] LHC at s = 7 TeV reach to larger p T with much larger cross sections and reduced scale uncertainties (red: central values, blue: scale variation by factors 2 up and down) G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 3 / 37

14 B + AT CMS /dp T [nb/gev] pp B + + X GM-VFNS S = 7 TeV y 2.4 CMS data 3 4 /d y [nb] GM-VFNS p T GeV pp B + + X S = 7 TeV CMS data p T [GeV]. 2 y present data from CMS for (B + + B )/2 p T up to 3 GeV dotted line: ξ I = ξ F =.7 G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 4 / 37

15 B AT CMS /dp T [nb/gev] pp B + X GM-VFNS S = 7 TeV y 2.2 CMS data 3 4 /d y [nb] GM-VFNS p T GeV pp B + X S = 7 TeV CMS data p T [GeV]. 2 y present data from CMS for (B + B )/2 p T up to 4 GeV dotted line: ξ I = ξ F =.7 G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 / 37

16 B s AT CMS 3. B /dp T [nb/gev] pp B s + X GM-VFNS S = 7 TeV y 2.4 CMS data 3 2. B /d y [nb] pp B s + X GM-VFNS S = 7 TeV p T 8 GeV CMS data p T [GeV]. 2 y... and for (B s + B s)/2: p T up to GeV with good agreement between data and theory G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 6 / 37

17 D-MESON PRODUCTION p + p D + X with D = D, D ±, D ±, D s arxiv: G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 7 / 37

18 FRAGMENTATION FUNCTIONS FOR CHARMED MESONS / tot d /dx(e + e - D + ) d /dx p (e + e - D + ) (nb) OPAL total b-tagged x BELLE CLEO x p FF for c D + from fitting to e + e data 28 analysis based on GM-VFNS µ = m =. GeV Bowler parametrization global fit: data from ALEPH, OPAL, BELLE, CLEO also available: BELLE/CLEO fit KKKS: Kneesch, Kramer, Kniehl, Schienbein, NPB799 (28) tension between low and high energy data sets speculations about nonperturbative (power-suppressed) terms G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 8 / 37

19 ALICE s = 7 GEV 4 3 dp T [nb/gev] pp D X s = 7 GeV y 4 3 dp T [nb/gev] pp D ± X s = 7 GeV y 4 3 dp T [nb/gev] pp D ± X s = 7 GeV y ALICE data ALICE data ALICE data p T [GeV] p T [GeV] p T [GeV] D, D ±, D : ALICE data with good agreement between data and theory G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 9 / 37

20 ALICE s = 7 GEV, ξ =.8 AND MSTW28-NLO... (ratios) dp T pp D ± X dp (ratios) T pp D X dp (ratios) T pp D X s = 7 GeV y s = 7 GeV y s = 7 GeV y 2 pt [GeV] 2 pt [GeV] 2 pt [GeV] Choose proper value for scale parameters: ξ I = ξ F =.8, ξ R = and MSTW28-NLO: value of m c =. GeV consistent with FF and PDF histogram and data normalized to predictions with ξ I = ξ F = ξ R = G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 2 / 37

21 ALICE s = 7 GEV, PDF UNCERTAINTY.. dp (ratios) T pp D ± X. dp T (ratios) pp D X s = 7 GeV y s = 7 GeV y dp (ratios) T pp D X s = 7 GeV y 2 pt [GeV] 2 pt [GeV] 2 pt [GeV] (all results normalized to prediction with ξ I = ξ F =.7, ξ R =, CTEQ6.6) dashed: PDFs from CT, HERAPDF. (NLO), MSTW8-NLO, NNPDF 2. G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 2 / 37

22 ALICE s = 7 GEV, CHARM MASS. ξ i = Uncertainties due to the value of the charm mass? m c =..4 GeV small increase at low p T ξ i =.7 dp (ratios) T pp D X s = 7 GeV y (MSTW28-NLO) 2 p T [GeV] G. Kramer (Universitaet Hamburg) Muenster, May 7, / 37

23 ALICE s = 2.76 GEV 4 3 [nb/gev] dp T pp D X s = 2.76 GeV y 4 3 [nb/gev] dp T pp D ± X s = 2.76 GeV y 4 3 [nb/gev] dp T pp D ± X s = 2.76 GeV y p T [GeV] p T [GeV] p T [GeV] CERN-PH-EP-ALICE used to determine suppression in Pb-Pb collisions G. Kramer (Universitaet Hamburg) Muenster, May 7, / 37

24 ALICE FFNS 6 4 dp T [nb/gev] pp D X s = 7 GeV y FFNS: describes turnover at low p T, but too high at high p T GM-VFNS: reduced scale uncertainty due to resummed large logs 3 2 FFNS GM-VFNS for FFNS: no FF, BR(c D ) = p T [GeV] 3 G. Kramer (Universitaet Hamburg) Muenster, May 7, / 37

25 ALICE FFNS X) [nb/gev] 6 4 (p p D T (D + D )/2 S=7 TeV CTEQ6.6 - < y < BR(c D )=.62 FFNS: no FF m c =. GeV µ=m T X) [nb/gev] (p p D d /dp 2 FFNS GM-VFNS T (D + D )/2 S=7 TeV CTEQ6.6 - < y < BR(c D )=.62 c =.2 m c =. GeV µ=m T 3 d /dp 2 FFN GM-VFN p [GeV] T no evolved fragmentation function p [GeV] T Peterson FF: FFNS closer to GM-VFNS, but still too steep G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 2 / 37

26 D-MESONS AT ATLAS 4 dp T [nb/gev] pp D X s = 7 GeV y dy [nb] pp D X s = 7 GeV 3. p T 4 GeV p T [GeV]. 2 y D, similar for D ±, D : to be compared with ATLAS data good agreement between data and theory G. Kramer (Universitaet Hamburg) Muenster, May 7, / 37

27 D-MESONS AT LHCB d /dp T (nb/gev) p p D X GM-VFNS S = 7 TeV 2. y y y y y y d /dp T (nb/gev) p p D + X GM-VFNS S = 7 TeV 2. y y y y y y. D, D ±, D, D s, p T (GeV) p T (GeV) for a comparison with data LHCb data: d /dp T (nb/gev) p p D * X GM-VFNS S = 7 TeV 2. y y y y y y. d /dp T (nb/gev) p p D s + X GM-VFNS S = 7 TeV 2. y y y y y y. LHCb-CONF-2-3 good agreement p T (GeV) p T (GeV) G. Kramer (Universitaet Hamburg) Muenster, May 7, / 37

28 INTRINSIC CHARM Intrinsic charm: c(x, µ ) at initial scale µ = m c Models implemented in CTEQ 6.C (PRD7, 27) global fit allows average momentum x c+ c or order % Light-cone Fock-space picture (Brodsky et al.), concentrated at large x x c+ c = 7, 2. % 2 Meson-cloud model (Navarra et al.) x c+ c =.96,.8 % 3 Phenomenological model: sea-like charm, broad in x x c+ c =., 2.4 % G. Kramer (Universitaet Hamburg) Muenster, May 7, / 37

29 INTRINSIC CHARM: TEVATRON AND RHIC Tevatron CTEC6.cx/CTEC6.c p p D X RHIC CTEC6.cx/CTEC6.c p p D X GM-VFNS S = 2 GeV - y p T (GeV) p T (GeV) PRD79, 29 G. Kramer (Universitaet Hamburg) Muenster, May 7, / 37

30 INTRINSIC CHARM: LHCB 7 6 CTEQ6.6c/CTEQ6.6 p p D 2. y 2. X 2. y 3. GM-VFNS 3. y 3. S = 7 TeV 3. y y y CTEQ6.6c3/CTEQ6.6 p p D X 2. y y 3. GM-VFNS 3. y 3. S = 7 TeV 3. y y y p T (GeV) CTEQ6.6 updated: BHPS, 3. % (c + c) at µ =.3 GeV p T (GeV) high-strength sea-like charm large effects expected at large rapidities G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 3 / 37

31 SUMMARY The General-Mass Variable-Flavor-Number Scheme: Rigorous theoretical framework for one-particle inclusive heavy quark production Framework for global analysis including full mass dependence including resummed large logarithms in universal PDFs and FFs no ad-hoc weight functions Many new numerical results for pp D + X pp B + X Predictions for D- and B-meson production in good agreement, First comparisons with LHC data are promising Mass effects moderate From future LHC data expect tight constraints for D and B FFs G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 3 / 37

32 Backup Slides G. Kramer (Universitaet Hamburg) Muenster, May 7, / 37

33 ALICE s = 7 GEV, PDF UNCERTAINTY, ξ =... dp (ratios) T pp D X dp (ratios) T pp D ± X dp (ratios) T pp D X s = 7 GeV y s = 7 GeV y s = 7 GeV y 2 pt [GeV] 2 pt [GeV] 2 pt [GeV] (all results normalized to default prediction with ξ I = ξ F =, ξ R =, CTEQ6.6) dashed: PDFs from CT, HERAPDF. (NLO), MSTW8-NLO, NNPDF 2. G. Kramer (Universitaet Hamburg) Muenster, May 7, / 37

34 ALICE s = 7 GEV, ξ =.7 Choose proper value for scale parameters: ξ I = ξ F =.7, ξ R = dp T (ratios) pp D X s = 7 GeV y p T [GeV] (histogram and data normalized to default prediction with ξ I = ξ F = ξ R = ) G. Kramer (Universitaet Hamburg) Muenster, May 7, / 37

35 LHCB: Λ c d /dp T (nb/gev) p p c X GM-VFNS S = 7 TeV 2. y y y y y y. Λ c: to be compared with LHCb p T (GeV) G. Kramer (Universitaet Hamburg) Muenster, May 7, 22 3 / 37

36 LHCB: SCALE UNCERTAINTIES 4 dp T [nb/gev] pp D X s = 7 GeV 2. y 2. 4 dp T [nb/gev] pp D X s = 7 GeV 2. y 3. 4 dp T [nb/gev] pp D X s = 7 GeV 3. y pt [GeV] 2 pt [GeV] 2 pt [GeV] 4 3 dp T [nb/gev] pp D X s = 7 GeV 3. y dp T [nb/gev] pp D X s = 7 GeV 4. y dp T [nb/gev] pp D X s = 7 GeV 4. y pt [GeV] 2 pt [GeV]. 2 pt [GeV] G. Kramer (Universitaet Hamburg) Muenster, May 7, / 37

37 B AT THE TEVATRON 3 GM-VFN µ = m 2 b + ξp2 T dp T [nb/gev] p p B + X s =.96 TeV y evaluate b-quark initiated part at LO to match subtraction terms evaluate subtraction terms including m b dependence impose threshold condition ŝ > 4m 2 b choose µ 2 F = m 2 b + ξp 2 T so that µ F m b for p T m b = 4. GeV black: ξ = /4, red: ξ = /2, / p T [GeV] G. Kramer (Universitaet Hamburg) Muenster, May 7, / 37