HEAVY QUARKS FROM PHOTOPRODUCTION (AND DIS)

Transcription

1 HEAVY QUARKS FROM PHOTOPRODUCTION (AND DIS) INT 20, Seattle EIC workshop Week 6, Oct. 22, 20 H. Spiesberger based on work in collaboration with A. Kadeer, B. Kniehl, G. Kramer, C. Pisano, I. Schienbein, J. Smith H. Spiesberger (Mainz) INT, / / 26

2 OUTLINE Theoretical framework: the General-Mass Variable-Flavor-Number Scheme for 1-particle inclusive heavy-meson production A discussion of (partially preliminary) results for D-meson production at HERA, LHeC, erhic: γp DX and ep edx, (D D ±, D 0, D ±, D ± s ) H. Spiesberger (Mainz) INT, / / 26

3 MASSIVE OR MASSLESS Massive or Massless Heavy Quarks? m 0 m = 0 correct threshold behavior no collinear divergences from c c + g but terms log(µ/m) with µ = Q, p T,... large corrections at large µ mass singularities (1/ǫ-poles instead of log m 2 -terms) absorbed in PDFs and FFs QCD prediction: DGLAP (RG) evolution resums large logarithms log(µ/m) more reliable at large µ not reliable at heavy quark threshold Goal: combine massive (low scale) and massless (high scale) calculations exploit freedom to choose an appropriate factorization scheme Collins 1998 H. Spiesberger (Mainz) INT, / / 26

4 GENERAL-MASS VARIABLE FLAVOR NUMBER SCHEME The problem: Conventionally, PDFs and FFs are defined in the MS scheme MS scheme is based on a massless calculation Massless and massive calculations contain different singularities Can not use MS PDFs and FFs in a massive calculation? The solution: Match massless and massive calculations: dσ sub = lim m 0 d σ(m) dˆσ MS The subtracted cross section (in a massive calculation) dˆσ(m) = d σ(m) dσ sub can be used with MS parton distribution and fragmentation functions The GM-VFNS (general-mass variable flavor number scheme) H. Spiesberger (Mainz) INT, / / 26

5 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, charm is a parton: f c 0 for 1-particle inclusive heavy-quark production: fragmentation functions not only for c D: Dc D (z, µ 2 F ), but every parton can fragment into the observed heavy hadron VFNS: PDF for charm, f c = 0 below, f c 0 above threshold; GM-VFNS with m 0 Fragmentation functions, with non-perturbative input and perturbative RG evolution large collinear logarithms ln µ2 m 2 resummed in evolved f c(x, µ 2 ) and D D c (x, µ 2 ) H. Spiesberger (Mainz) INT, / / 26

6 HARD SCATTERING COEFFICIENTS WITH HEAVY QUARK MASSES Mass terms contained in the hard scattering coefficients: dˆσ(µ F, µ F, α s(µ R ), m p T ) Two ways to derive the subtraction terms: (1) Compare massless limit of a massive fixed-order calculation with a massless MS calculation to determine subtraction terms dσ sub dσ = lim m 0 d σ(m) dˆσ MS OR (2) Perform mass factorization using partonic PDFs and FFs H. Spiesberger (Mainz) INT, / / 26

7 SUBTRACTION TERMS FOR THE GM-VFNS VIA MASS FACTORIZATION (1) Mass factorization Subtraction terms are associated to mass singularities: can be described by partonic PDFs and FFs for collinear splittings a b + X initial state: f (1) g Q (x, µ2 ) = αs(µ) 2π P(0) g q(x) ln µ2 m 2 f (1) Q Q (x, µ2 ) = αs(µ) 2π C ˆ 1+z 2 F 1 z f g g(x, (1) µ 2 ) = αs(µ) 1 2π 3 µ2 (ln m2 2 ln(1 z) 1) + µ2 ln m2 δ(1 x) final state: d (1) g Q (z, µ2 ) = αs(µ) 2π d (1) Q Q (z, µ2 α ) = C s(µ) F 2π P(0) g q(z) ln µ2 m 2 ˆ 1+z 2 1 z µ2 (ln m2 2 ln(1 z) 1) + Other partonic distribution functions are zero to order α s Mele, Nason; Kretzer, Schienbein; Melnikov, Mitov H. Spiesberger (Mainz) INT, / / 26

8 SUBTRACTION TERMS FOR THE GM-VFNS VIA MASS FACTORIZATION (2) g and light q( q) collinear emission from initial or final state x 1 z 1 photoproduction: (a) (b) (a) initial state dσ sub (γ a QX) = Z 1 0 dx 1 f (1) a i (x 1, µ 2 F ) dˆσ(0) (γ i QX)[x 1 k 1, k 2, p 1 ] f (1) a i (x 1) dˆσ (0) (γ i QX) (b) final state dσ sub (ab QX) = Z 1 0 dz dˆσ (0) (ab kx)[k 1, k 2, z 1 p 1 ] d (1) k Q (z, µ 2 F ) dˆσ (0) (ab kx) d (1) k Q (z) Kniehl, Kramer, Schienbein, HS, EPJC41(2005)199 for DIS: Kniehl, Kramer, Pisano, Schienbein, Smith, HS, in preparation H. Spiesberger (Mainz) INT, / / 26

9 SUBPROCESSES Subprocesses LO: γ + g c + c (photoproduction, DIS) or g + g c + c (hadroproduction) at NLO: 1-loop diagrams, gluon bremsstrahlung γ (g) + g c + c + g also γ (g) + q c + c + q and charm-initiated: γ (g) + c g + c (treated as a massless parton) for photoproduction (Q 2 = 0): resolved photon, need all hadronic subprocesses: g + g c + c(+g), g + q g + q(+g), q + q q + q (+g) etc. with photon-pdfs every parton can fragment to the heavy meson: fragmentation functions for c D, g D, q D H. Spiesberger (Mainz) INT, / / 26

10 FRAGMENTATION FUNCTIONS 1/σ tot dσ/dx(e + e - D + ) dσ/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 2008 analysis based on GM-VFNS µ 0 = m Bowler parametrization global fit: data from ALEPH, OPAL, BELLE, CLEO also available: BELLE/CLEO fit KKKS: Kneesch, Kramer, Kniehl, Schienbein, NPB799 (2008) tension between low and high energy data sets speculations about nonperturbative (power-suppressed) terms H. Spiesberger (Mainz) INT, /22 20 / 26

11 APPLICATIONS Applications available for γ + γ D ± + X direct and resolved contributions γ + p D ± + X photoproduction for HERA and LHeC p + p (D 0, 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 work in progress for e + p D + X EPJC22, EPJC28 EPJC38, EPJC62, PLB679 PRD71, PRL96, PRD79 PRD77 H. Spiesberger (Mainz) INT, / / 26

12 MASS EFFECTS AT LO (DIS) mass effects from kinematics and from matrix element: 0.1 dσ [nb GeV 3 ] dq 2 dp T 3 dσ [nb GeV 3 ] dq 2 dp T Q 2 = GeV 2 6 Q 2 = 0 GeV p T[GeV] p T[GeV] Correct treatment of mass in kinematic definitions is essential Mass-dependent terms in the matrix elements less important Mass-dependent terms do not decrease at large Q 2 H. Spiesberger (Mainz) INT, / / 26

13 FRAGMENTATION: DEFINITION OF z-scaling (DIS) Different definitions of the scaling variable z in the fragmentation functiond Q H (z): not restricted by theory dσ dp T [nb/gev] η < < y e < GeV 2 < Q 2 < 50 GeV 2 scaling: p Q p H = zp Q : (a): z = p H p Q (b): z = E H+ p H E Q + p Q (c): z = E H E Q with E 2 H = p 2 H + m 2 H unavoidable (and large) uncertainties at small p T p T [GeV] H. Spiesberger (Mainz) INT, / / 26

14 DIS: SUBTRACTION TERMS FOR THE GM-VFNS FROM MASSLESS LIMIT (1) for DIS: work in progress Massive calculations in the Fixed Flavor Number Scheme FFNS need limit lim m 0 d σ(m) to obtain subtraction terms Inclusive heavy quark production in DIS E. Laenen, S. Riemersma, J. Smith, W. L. van Neerven Nucl. Phys. B 392 (1993) 162, 229 Fully exclusive version: HVQDIS B. W. Harris, J. Smith Nucl. Phys. B452 (1995) 9 and Phys. Rev. D 57, 2806 (1998) Tabulated matrix elements, for F c 2 : S. Riemersma, J. Smith, W. L. van Neerven Phys. Lett. B 347 (1995) 143 H. Spiesberger (Mainz) INT, / / 26

15 DIS: SUBTRACTION TERMS FOR THE GM-VFNS FROM MASSLESS LIMIT (2) Massless MS calculation: dˆσ MS taken from ZM-VFNS (Zero-Mass Variable Flavor Number Scheme): Inclusive hadron production in DIS TIMBA A. Daleo, D. de Florian, R. Sassot Phys. Rev. D 71, (2005) Also available: calculations / programs by P. Aurenche et al.; G. Kramer et al., in particular program by C. Sandoval performed various tests (photoproduction limit, comparison with previous results in the literature, subtraction terms from mass factorization); find necessary modifications in Daleo s code to obtain perfect agreement preliminary results H. Spiesberger (Mainz) INT, / / 26

16 TEST: GMVFNS VERSUS FFNS AND ZM-VFNS PRELIMINARY dσ dq 2 dp T Q 2 = 50 GeV 2 5 [nb GeV 3 ] 15 p T[GeV] (1) subtraction terms (2) massive calculation (HVQDIS) (3) subtracted massive calculation (HVQDIS - dσ sub ) (4) GMVFNS: HVQDIS subtraction terms + incoming charm (not included: F L and quark-initiated processes) H. Spiesberger (Mainz) INT, / / 26

17 TEST: GMVFNS VERSUS FFNS AND ZM-VFNS PRELIMINARY dσ dq 2 dp T [nb GeV 3 ] (1) massless calculation (Daleo) (2) massless calculation corrected (3) GMVFNS: HVQDIS subtraction terms + incoming charm Q 2 = 50 GeV p T[GeV] (not included: F L and quark-initiated processes) more work to do H. Spiesberger (Mainz) INT, / / 26

18 t PHOTOPRODUCTION: COMPARISON WITH H1 PRELIMINARY DATA D* in Photoproduction [nb/gev] dσ(ep ed*x)/dp 2 1 H1 Preliminary HERA II H1 data (prel.) FFNS (CTEQ5F3) < 1.7 GeV 1.3 < m c < µ / m 2 c +p < 2 r,f t GMVFNS (CTEQ6.5) Q < 2 GeV 0 < W γ P < 285 GeV p (D*) > 1.8 GeV t η(d*) < p (D*)[GeV] H1prelim t H. Spiesberger (Mainz) INT, / / 26

19 PHOTOPRODUCTION: COMPARISON WITH H1 PRELIMINARY DATA dσ(ep ed*x)/dη[nb] H1 Preliminary HERA II D* in Photoproduction H1 data (prel.) FFNS (CTEQ5F3) < 1.7 GeV 1.3 < m c < µ / m 2 c +p < 2 r,f t GMVFNS (CTEQ6.5) η(d*) H1prelim dominated by low-p T H. Spiesberger (Mainz) INT, / / 26

20 LHEC Photoproduction at the LHeC Q 2 < 1 GeV 2 inelasticity y = E γ/e e: 0.1 < y < 0.9 resolved photon: γ-pdf of AFG (Aurenche, Fontannaz, Guillet) proton PDF: CTEQ6.5 fragmentation functions: KKKS 2008, fit based on combined Belle+CLEO data charm mass: m = 1.5 GeV, α s at NLO with Λ MS N f =4 = GeV, i.e. α s(m 2 Z) = kinematic range: 5 < p T < 20 or 20 < p T < 0 GeV and η < 2.5 Reference: HERA with E p = 920 GeV, E e = 27.6 GeV LHeC: E p = 7 TeV, E e = 50, 0, 150 GeV H. Spiesberger (Mainz) INT, / / 26

21 LHEC dσ/dp T (nb/gev) GM-VFNS e p e D * X E e = , 0, 150 GeV E p = 920, 7000, 7000, 7000 GeV 1 dσ/dp T (pb/gev) GM-VFNS e p e D * X E e = , 0, 150 GeV E p = 920, 7000, 7000, 7000 GeV -2.5 y y p T (GeV) much higher cross section, much higher p T,... H. Spiesberger (Mainz) INT, / / 26

22 LHEC dσ/dη (nb) GM-VFNS e p e D * X E e = 27.6, 50, 0, 150 GeV E p = 0.92, 7, 7, 7 TeV 5.0 p T dσ/dη (nb) GM-VFNS e p e D * X E e = 27.6, 50, 0, 150 GeV E p = 0.92, 7, 7, 7 TeV 20 p T 0 GeV η η... and extended reach in rapidity H. Spiesberger (Mainz) INT, / / 26

23 INTRINSIC CHARM Intrinsic charm: c(x, µ 0 ) 0 at initial scale µ 0 = m c Models implemented in CTEQ 6.5C (PRD75, 2007) global fit allows average momentum x c+ c or order 1 % 1 Light-cone Fock-space picture (Brodsky et al.), concentrated at large x x c+ c = 0.57, 2.0% 2 Meson-cloud model (Navarra et al.) x c+ c = 0.96, 1.8% 3 Phenomenological model: sea-like charm, broad in x x c+ c = 1.1, 2.4% H. Spiesberger (Mainz) INT, / / 26

24 INTRINSIC CHARM: TEVATRON AND RHIC Tevatron CTEC6.5cx/CTEC6.5c0 p p D 0 X RHIC CTEC6.5cx/CTEC6.5c0 p p D 0 X GM-VFNS S = 200 GeV -1 y p T (GeV) p T (GeV) PRD79, 2009 H. Spiesberger (Mainz) INT, / / 26

25 INTRINSIC CHARM: ERHIC 0 1 dσ/dp T [nb/gev] γp D ± X erhic dσ/dp T [ratios] γp D ± X , y < , y < 1 erhic(5 325, y < 1) p T [GeV] p T [GeV] large cross sections, but limited reach in p T reduced sensitivity to charm PDF more work needed H. Spiesberger (Mainz) INT, / / 26

26 HEAVY MESON PRODUCTION The General-Mass Variable-Flavor-Number Scheme: theoretical framework for one-particle inclusive heavy quark production resummed large logarithms in universal PDFs and FFs mass terms fully kept at O(α s) To be done Finalize implementation for deep inelastic scattering Work out more detailed predictions for ep, photoproduction for EIC H. Spiesberger (Mainz) INT, / / 26