Recent Developments in Quarkonium and Open Flavour Production Calculations

Recent Developments in Quarkonium and Open Flavour Production Calculations Mathias Butenschön (Hamburg University) XIV International Conference on Hadron Spectroscopy

Production and decay rates of Heavy Quarkonia Heavy Quarkonia: Bound states of heavy quark and antiquark. Charmonia (cc ) and Bottomonia (bb ) Top decays to fast for bound state. The classic approach: Color-singlet model Calculate cross section for heavy quark pair in physical color singlet (=color neutral) state. In case of J/ψ: cc [ 3 S [] ] Multiply by quarkonium wave function (or its derivative) at origin Mid 90 s: Strong disagreement with Tevatron data apparent Nonrelativistic QCD (NRQCD): Rigorous effective field theory: Bodwin, Braaten, Lepage (995) Based on factorization of soft and hard scales (Scale hierarchy: Mv 2, Mv << Λ QCD << M) Could explain hadroproduction at Tevatron M. Butenschön Recent developments in quarkonium and open flavour production calculations /20

J/ψ Production with NRQCD Factorization theorem: n: Every possible Fock state, including color-octet states. σ cc [n] : Production rate of cc [n], calculated in perturbative QCD <O J/ψ [n]>: Long distance matrix elements (LDMEs): describe cc [n] J/ψ, universal, extracted from experiment. Scaling rules: LDMEs scale with definite power of v (v 2 0.2): scaling v 3 v 7 v n 3 S [] S 0 [8], 3 S [8], 3 P J [8]... Double expansion in v and α s Leading term in v (n = 3 S [] ) equals color-singlet model. M. Butenschön Recent developments in quarkonium and open flavour production calculations 2/20

J/ψ Production with NRQCD: Knowledge until 2005 Hadroproduction at Tevatron: Photoproduction at HERA: γγ Scattering at LEP: 0 0-0 -2 0-3 BR(J/ψ μ + μ - ) dσ(pp _ J/ψ+X)/dp T (nb/gev) s =.8 TeV; η < 0.6 total colour-octet S 0 + 3 P J colour-octet 3 S LO colour-singlet colour-singlet frag. 5 0 5 20 p T (GeV) dσ(γ p J/ψ X)/dz (nb) 0 2 0 ZEUS (38 pb - ) H (80 pb - ) (scaled) H (80 pb - ) high W KZSZ (LO, CS+CO) KZSZ (NLO, CS) 0.7 < α s (M Z ) < 0.2.3 < m c <.6 GeV 50 < W < 80 GeV p T > GeV 0 0.2 0.4 0.6 0.8 z NRQCD 3 P [8] 3 J P [] J S [8] 0 0 dσ/dp T 2 (pb/gev 2 ) 0 - e + e e + e J/ψ X at LEP2 NRQCD DELPHI prelim. MRST98 fit CTEQ5 fit S = 97 GeV 2 < y J/ψ < 2 3 S [8] CSM 0-2 0 2 3 4 5 6 7 8 9 0 2 p T (GeV 2 ) CO LDMEs extracted from Born fit to Tevatron (one linear combination). Used for predictions at HERA and LEP. No NLO calculations for color-octet (CO) contributions yet! Universality of CO LDMEs open question. M. Butenschön Recent developments in quarkonium and open flavour production calculations 3/20

NLO Corrections to Color Octet Contributions Petrelli, Cacciari, Greco, Maltoni, Mangano (998): Photo- and hadroproduction (Only 2 processes) Klasen, Kniehl, Mihaila, Steinhauser (2005): γγ scattering at LEP (neglecting resolved photons) M.B., Kniehl (2009): Photoproduction at HERA (neglecting resolved photons) Zhang, Ma, Wang, Chao (2009): e + e scattering at B factories Ma, Wang, Chao (200): Hadroproduction (including feed-down contributions) M.B., Kniehl (200): Hadroproduction (combined HERA-Tevatron fit) Necessary: Only recently: A rigorous global data analysis! Fit CO LDMEs to 94 data points from 0 experiments. Test LDME universality. [M.B., Kniehl (20)] M. Butenschön Recent developments in quarkonium and open flavour production calculations 4/20

M.B., Kniehl (20): Global Fit of CO LDMEs dσ(ee J/ψ ee+x)/dp 2 T [pb/gev 2 ] DELPHI data 0 0 - y < 2 0-2 W < 35 GeV θ el < 32 mrad s = 97 GeV 0-3 2 3 4 5 6 7 8 9 0 p 2 T [GeV 2 ] dσ(ep J/ψ+X)/dp 2 T [nb/gev 2 ] 60 GeV < W < 240 GeV 0.3 < z < 0.9 Q 2 < GeV 2 s 0 - = 34 GeV 0-2 0-3 0-4 H data: HERA 0-5 0 p 2 T [GeV 2 ] dσ(ep J/ψ+X)/dW [nb/gev] s = 34 GeV, Q 2 < GeV 2 H data: HERA 0 2 0.3 < z < 0.9 pt 2 > GeV 2 0-2 0 0-3 s = 34 GeV Q 2 < GeV 2 p 2 T > GeV 2 H data: HERA 60 GeV < W < 240 GeV 60 80 00 20 40 60 80 200 220 240 0.3 0.4 0.5 0.6 0.7 0.8 0.9 W [GeV] z dσ(ep J/ψ+X)/dz [nb] dσ(ep J/ψ+X)/dp 2 T [nb/gev 2 ] 60 GeV < W < 240 GeV 0.3 < z < 0.9 Q 2 < 2.5 GeV 2 0 - s = 39 GeV 0-2 0-3 0-4 0-5 dσ(ep J/ψ+X)/dW [nb/gev] s = 39 GeV, Q 2 < 2.5 GeV 2 0 2 0.3 < z < 0.9 pt 2 > GeV 2 0-2 0 0-3 H data: HERA2 H data: HERA2 60 GeV < W < 240 GeV 0-6 0 0 2 60 80 00 20 40 60 80 200 220 240 0.3 0.4 0.5 0.6 0.7 0.8 0.9 p 2 T [GeV 2 ] W [GeV] z dσ(ep J/ψ+X)/dz [nb] H data: HERA2 s = 39 GeV Q 2 < 2.5 GeV 2 p 2 T > GeV 2 σ(e + e - J/ψ+X) [pb] 2.5 2.5 0.5 0 BELLE data: s = 0.6 GeV σ = (0.43±0.3) pb (J/ψ+cc contribution subtracted) : σ = 0 : σ = (0.24 +0.20-0.09) pb : σ = 0.23 pb : σ = (0.70 +0.35-0.7) pb dσ(ep J/ψ+X)/dp 2 T [nb/gev 2 ] 0-0 -2 0-3 0-4 50 GeV < W < 80 GeV 0.4 < z < 0.9 Q 2 < GeV 2 s = 300 GeV ZEUS data 5 0 5 20 25 30 pt 2 [GeV 2 ] dσ(ep J/ψ+X)/dW [nb/gev] s = 300 GeV, Q 2 < GeV 2 0.4 < z < 0.9 pt 2 > GeV 2 0-2 0-3 ZEUS data 60 80 00 20 40 60 80 W [GeV] dσ(ep J/ψ+X)/dz [nb] 0 2 ZEUS data 0 s = 300 GeV Q 2 < GeV 2 pt 2 > GeV 2 50 GeV < W < 80 GeV 0-0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 z dσ/dp T (pp J/ψ+X) B(J/ψ ee) [nb/gev] 0 2 PHENIX data 0-0 0-2 0-3 s = 200 GeV 0-4 y < 0.35 3 4 5 6 7 8 9 0 dσ/dp T (pp J/ψ+X) B(J/ψ μμ) [nb/gev] 0 2 CDF data: Run 0 0-0 -2 0-3 s =.8 TeV 0-4 y < 0.6 6 8 0 2 4 6 8 20 dσ/dp T (pp J/ψ+X) B(J/ψ μμ) [nb/gev] CDF data: Run 2 0 2 0 0-0 -2 0-3 s =.96 TeV 0-4 y < 0.6 4 6 8 0 2 4 6 8 20 ALICE data 0 3 0 2 0 0-0 -2 2.5 < y < 4 3 4 5 6 7 8 9 0 0 3 ATLAS data 0 2 0 0-0 -2 0-3 y < 0.75 4 6 8 0 2 4 6 8 20 0 3 ATLAS data 0 2 0 0-0 -2 0-3 0.75 < y <.5 4 6 8 0 2 4 6 8 20 0 3 ATLAS data 0 2 0 0-0 -2 0-3.5 < y < 2.25 4 6 8 0 2 4 6 8 20 0 3 CMS data 0 2 0 0-0 -2 0-3 y <.2 4 6 8 0 2 4 6 8 20 0 3 CMS data 0 2 0 0-0 -2 0-3.2 < y <.6 0-4 4 6 8 0 2 4 6 8 20 0 3 CMS data 0 2 0 0-0 -2 0-3.6 < y < 2.4 0-4 4 6 8 0 2 4 6 8 20 LHCb data 0 2 0 0-0 -2 0-3 2 < y < 2.5 4 6 8 0 2 4 LHCb data 0 2 0 0-0 -2 0-3 2.5 < y < 3 4 6 8 0 2 4 LHCb data 0 2 0 0-0 -2 0-3 3 < y < 3.5 0-4 4 6 8 0 2 4 LHCb data 0 2 0 0-0 -2 0-3 3.5 < y < 4 0-4 4 6 8 0 2 4 LHCb data 0 2 0 0-0 -2 0-3 4 < y < 4.5 0-4 4 6 8 0 2 4 <O[ S 0 [8] ]> = (4.97 ± 0.44) 0-2 GeV 3 <O[ 3 S [8] ]> = (2.24 ± 0.59) 0-3 GeV 3 <O[ 3 P 0 [8] ]> = (-.6 ± 0.20) 0-2 GeV 5 M. Butenschön Recent developments in quarkonium and open flavour production calculations 5/20

In Detail: Hadroproduction (LHC, Tevatron) dσ/dp T (pp J/ψ+X) B(J/ψ μμ) [nb/gev] 0 2 0 0-0 -2 0-3 2.5 < y < 3 LHCb data dσ/dp T (pp J/ψ+X) B(J/ψ μμ) [nb/gev] 0 2 0 0-0 -2 0-3 0-4 s =.96 TeV y < 0.6 CDF data: Run 2 dσ/dp T (pp J/ψ+X) B(J/ψ μμ) [nb/gev] 0 2 0 0-0 -2 0-3 0-4 s =.96 TeV y < 0.6 CDF data 3 S [] S [8] 3 0 S [8], NLO, NLO, NLO 3 P [8] J, NLO - 3 P [8] J, NLO Total, NLO 4 6 8 0 2 4 p T [GeV] 4 6 8 0 2 4 6 8 20 p T [GeV] 4 6 8 0 2 4 6 8 20 p T [GeV] Color singlet model not enough to describe data (although increase from Born to NLO) CS+CO can describe data. 3 P J [8] short distance cross section negative at p T > 7 GeV. But: Short distance cross sections and LDMEs unphysical No problem! M. Butenschön Recent developments in quarkonium and open flavour production calculations 6/20

In Detail: Photoproduction (HERA) dσ(ep J/ψ+X)/dp 2 T [nb/gev 2 ] 0-0 -2 0-3 0-4 50 GeV < W < 80 GeV 0.4 < z < 0.9 Q 2 < GeV 2 p 2 T [GeV 2 ] s = 300 GeV ZEUS data 5 0 5 20 25 30 dσ(ep J/ψ+X)/dW [nb/gev] 0-2 0-3 s = 300 GeV, Q 2 < GeV 2 0.4 < z < 0.9 pt 2 > GeV 2 ZEUS data 60 80 00 20 40 60 80 W [GeV] dσ(ep J/ψ+X)/dz [nb] 0 2 0 ZEUS data s = 300 GeV Q 2 < GeV 2 pt 2 > GeV 2 50 GeV < W < 80 GeV 0-0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 z dσ(ep J/ψ+X)/dz [nb] 0 2 0 ZEUS data Direct, NLO Resolved, NLO Total, NLO s = 300 GeV Q 2 < GeV 2 pt 2 > GeV 2 50 GeV < W < 80 GeV 0-0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 z dσ(ep J/ψ+X)/dp 2 T [nb/gev 2 ] 0-0 -2 0-3 0-4 50 GeV < W < 80 GeV 0.4 < z < 0.9 Q 2 < GeV 2 p 2 T [GeV 2 ] s = 300 GeV ZEUS data 5 0 5 20 25 30 dσ(ep J/ψ+X)/dW [nb/gev] 0-0 -2 0-3 ZEUS data 3 S [], NLO S [8] 0, NLO 3 S [8], NLO - 3 P [8] J, NLO Total, NLO s = 300 GeV, Q 2 < GeV 2 W [GeV] 0.4 < z < 0.9 p 2 T > GeV 2 60 80 00 20 40 60 80 dσ(ep J/ψ+X)/dz [nb] 0 2 0 ZEUS data 3 S [], NLO S [8] 0, NLO 3 S [8], NLO - 3 P [8] J, NLO Total, NLO s = 300 GeV Q 2 < GeV 2 pt 2 > GeV 2 50 GeV < W < 80 GeV 0-0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 z Photoproduction = Photon-proton scattering in ep collider Distributions: Transverse momentum (p T ), photon-proton c.m. energy (W), and z = Fraction of photon energy going to J/ψ. Again: Color singlet alone below the data, CS+CO describes data well. Calculation includes resolved photon contributions: Important at low z. M. Butenschön Recent developments in quarkonium and open flavour production calculations 7/20

In Detail: e + e and γγ Collisions Electron-Positron Collisions at BELLE: CS: Large overlap with data, CS+CO: Small overlap. Experimentally measurement of total cross section difficult, discrepancies between BELLE and BABAR. For e + e color singlet, NNLO terms been calculated, increasing cross section. Not part of the global fit. [Ma, Zhang, Chao (2009); Gong, Wang (2009)] σ(e + e - J/ψ+X) [pb] 2.5 2.5 0.5 0 BELLE data: σ = (0.43±0.3) pb (J/ψ+cc contribution subtracted) : σ = 0 : σ = (0.24 +0.20-0.09) pb : σ = 0.23 pb : σ = (0.70 +0.35-0.7) pb s = 0.6 GeV dσ(ee J/ψ ee+x)/dp 2 T [pb/gev 2 ] 0 0 - DELPHI data y < 2 0-2 W < 35 GeV θ el < 32 mrad s = 97 GeV 0-3 2 3 4 5 6 7 8 9 0 p 2 T [GeV 2 ] Two Photon scattering at DELPHI (LEP): Includes direct, single and double resolved photons. CS below data, but also CS+CO prediction too low. Possible explanations: Uncertainties in the measurement (Just 6 events involved!) Hint at problems with LDME universality. M. Butenschön Recent developments in quarkonium and open flavour production calculations 8/20

Improve the Color Singlet Model: NNLO* Idea: At large p T gluon fragmentation channels dominate, but in CSM is NNLO process. Try to estimate these and similar contributions without performing full NNLO calculation. NNLO*: Consider only tree level pp QQ + 3 Jets and impose IR cutoffs. Result: For bottomonium ϒ(S) and charmonium ψ(2s), color singlet contributions might be enough to describe data [Artoisenet, Campbell, Lansberg, Maltoni, Tramontano (2008); Lansberg (2009)]: ψ(2s) M. Butenschön Recent developments in quarkonium and open flavour production calculations 9/20

Status for J/ψ Polarization Available calculations for photo- and hadroproduction: NLO color singlet model predictions [Gong, Wang (2008); Artoisenet, Campbell, Maltoni, Tramontano (2009); Chang, Li, Wang (2009)] k T factorization predictions [Baranov (2002); Baranov (2008)] Color octet contributions so far only at leading order. α 0.8 0.6 0.4 0.2 0-0.2-0.4-0.6-0.8 - (a) CDF Data NRQCD k T -factorization 5 0 5 20 25 30 p T (GeV/c) λ.5 0.5 0-0.5 - -.5 ZEUS 468 pb - LO CS NLO CS LO k T (JB) LO k T (dgvr) LO CS+CO 2 3 4 5 6 7 8 9 0 p T (GeV) 2 4 6 8 0 [GeV] α or λ = - (+): Fully longitudinally (transversely) polarized J/ψ. Still large theoretical and experimental uncertainties. LHC data awaited. Will be crucial observable to distinguish production mechanisms. α 2 0 - Data (γp) Baranov - CSM k T fact. (Set A0) Baranov - CSM coll. fact. (LO) Artoisenet et al. - CSM (NLO) P T, ψ H M. Butenschön Recent developments in quarkonium and open flavour production calculations 0/20

OPEN FLAVOUR PRODUCTION Open flavour production: (D, B, Λ,...) Hadrons with one heavy quark (c, b) and one or two light quarks (u, d, s) Production through fragmentation of outgoing QCD partons. Two traditional methods: (Example: Heavy quark c) Fixed-Flavour-Number-Scheme (FFNS): Incoming quarks: u, d, s (m = 0). Outgoing: u, d, s (m = 0), c (m = m c) Reliable only at mc 2 pt 2, because of log(pt 2 /mc) 2 terms. Zero-Mass-Variable-Flavour-Number scheme (ZM-VFNS): Incoming quarks: u, d, s, c (m = 0). Outgoing: u, d, s, c (m = 0) Reliable only at mc 2 pt 2, because of missing mass terms. Interpolating schemes: Combining FFNS and ZM-VFNS: General-Mass-Variable-Flavour-Number-Scheme (GM-VFNS) Fixed-Order NLL scheme (FONLL) M. Butenschön Recent developments in quarkonium and open flavour production calculations / 20

S-ACOT: THEORETICAL BASIS FOR THE GM-VFNS Factorization Formula: [] dσ(p p DX) = X i,j,k Z dx dx 2 dz f i/p (x, µ F ) f j/ p (x 2, µ F ) dˆσ ij kx µ F, µ F, α s(µ R ), mc p T D D k (z, µ F ) dˆσ ij kx µ F, µ F, α s(µ R ), mc p T : Hard scattering cross sections. Heavy quark mass m c kept. PDFs f i/p (x, µ F ), f j/ p (x 2, µ F ): i, j = g, u, d, s, c FFs D D k (z, µ F ): k = g, u, d, s, c Factorization and PDF/FF DGLAP evolution like in zero-mass case. [] = Need short distance coefficients including heavy quark masses. [] J. Collins, Hard-scattering factorization with heavy quarks: A general treatment, PRD58(998)094002 M. Butenschön Recent developments in quarkonium and open flavour production calculations 2 / 20

GM-VFNS: LIST OF SUBPROCESSES Only light lines gg qx 2 gg gx 3 qg gx 4 qg qx 5 q q gx 6 q q qx 7 qg qx 8 qg q X 9 qg q X 0 qq gx qq qx 2 q q q X 3 q q gx 4 q q qx 5 qq gx 6 qq qx charge conjugated processes Heavy quark initiated (m Q = 0) - 2-3 Qg gx 4 Qg QX 5 Q Q gx 6 Q Q QX 7 Qg QX 8 Qg qx 9 Qg qx 0 QQ gx QQ QX 2 Q Q qx 3 Q q gx, q Q gx 4 Q q QX, q Q qx 5 Qq gx, qq gx 6 Qq QX, qq qx Mass effects: m Q 0 gg QX 2-3 - 4-5 - 6-7 - 8 qg QX 9 qg QX 0 - - 2 q q QX 3-4 - 5-6 - M. Butenschön Recent developments in quarkonium and open flavour production calculations 3 / 20

GM-VFNS: HEAVY QUARK MASS TERMS Mass terms contained in the hard scattering coefficients: dˆσ(µ F, µ F, α s(µ R ), m Q p T ) Two ways to derive them: OR: Compare massless limit of a massive fixed-order calculation with a massless MS calculation to determine subtraction terms [Kniehl, Kramer, Schienbein, Spiesberger, PRD7(2005)0408] 2 Perform mass factorization using partonic (perturbative) PDFs and FFs [Kniehl, Kramer, Schienbein, Spiesberger, EPJC4(2005)99] M. Butenschön Recent developments in quarkonium and open flavour production calculations 4 / 20

GM-VFNS: APPLICATIONS Applications available for γ + γ D ± + X direct and resolved contributions γ + p D ± + X photoproduction p + p (D 0, D ±, D ±, D ± s, Λ ± c ) + X good description of Tevatron and new LHC data p + p B + X works for Tevatron data at large p T work in progress for e + p D + X EPJC22, EPJC28 EPJC38, EPJC62 PRD7, PRL96, PRD79 PRD77 M. Butenschön Recent developments in quarkonium and open flavour production calculations 5 / 20

FITTING THE FRAGMENTATION FUNCTIONS (KKKSC) dσ/dx p (e + e - D + ) (nb) /σ tot dσ/dx(e + e - D + ).6.4.2 0.8 0.6 0.4 0.2 0.45 0.05 BELLE CLEO 0 0 0. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 x p 0.4 0.35 0.3 0.25 0.2 0.5 0. OPAL total b-tagged 0 0. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 x FFs for c D from fitting to e + e data 2008 analysis based on GM-VFNS µ 0 = m c Global fit: Data from ALEPH, OPAL, BELLE, CLEO [Kneesch, Kramer, Kniehl, Schienbein NPB799 (2008)] Tension between low and high energy data sets Speculations about nonperturbative (power-suppressed) terms M. Butenschön Recent developments in quarkonium and open flavour production calculations 6 / 20

HADROPRODUCTION OF D 0, D +, D +, D + s AT TEVATRON GM-VFNS results using KKKSc FFs []: 0 4 dσ/dp T (nb/gev) p p D 0 X GM-VFNS 0 4 dσ/dp T (nb/gev) p p D + X GM-VFNS 0 4 dσ/dp T (nb/gev) p p D *+ X GM-VFNS S =.96 TeV S =.96 TeV S =.96 TeV 0 3 - y 0 3 - y 0 3 - y 0 2 0 2 0 2 0 0 0 5 7.5 0 2.5 5 7.5 20 22.5 25 p T (GeV) 5 7.5 0 2.5 5 7.5 20 22.5 25 p T (GeV) 5 7.5 0 2.5 5 7.5 20 22.5 25 p T (GeV) dσ/dp T [nb/gev] y, prompt charm (b D subtracted) q Uncertainty band: /2 µ R /m T, µ F /m T 2 (m T = pt 2 + m2 c) CDF data from run II [2] GM-VFNS describes data within errors. [] Kniehl, Kramer, Schienbein, Spiesberger, PRD79(2009)094009 [2] Acosta et al., PRL9(2003)24804 M. Butenschön Recent developments in quarkonium and open flavour production calculations 7 / 20

t t ALICE: D 0 AND D + CROSS SECTIONS Prelim. results presented by A. Dainese at LHC Physics Day, 3. Dec. 200: µb/gev/c 3 0 2 0 pp, 0 - D K π + - s = 7 TeV,.4 nb µb/gev/c 3 0 2 0 + - D K π + π + - pp, s = 7 TeV,.4 nb dσ / dp y <0.5 0 ALICE Preliminary dσ / dp y <0.5 0 ALICE Preliminary - 0 stat. unc. syst. unc. FONLL GM-VFNS PWG3-Preliminary-024-0 stat. unc. syst. unc. FONLL GM-VFNS PWG3-Preliminary-025 0 2 4 6 8 0 2 4 GeV/c p t 0 2 4 6 8 0 2 4 GeV/c p t Both FONLL and GM-VFNS predictions compatible with data. M. Butenschön Recent developments in quarkonium and open flavour production calculations 8 / 20

LHCB: D + CROSS SECTION (TALK BY P. URQUIJO AT LPCC, DEC. 200) Prelim. results for D + K π + π +. Data: 4 % correlated error not shown. BAK et al.= GM-VFNS: Kniehl, Kramer, Schienbein, Spiesberger MC et al.= FONLL: Cacciari, Frixione, Mangano, Nason, Ridolfi M. Butenschön Recent developments in quarkonium and open flavour production calculations 9 / 20

THE SUMMARY Production of heavy quarkonia: NRQCD provides rigorous factorization theorem for production of quarkonia. But: Necessary to proof LDME universality. Recent global NLO analysis: All inclusive J/ψ production data except γγ can be described by NRQCD with unique CO LDME set. Color singlet alone falls short of data everywhere except in e + e. LHC results coming in for J/ψ polarization, higher charmonia and bottomonia. Open flavour production: Two schemes interpolating between FFNS (low p T ) and ZM-VFNS (high p T ): FONLL and GM-VFNS. Both schemes can describe D, B and Λ photo- and hadroproduction data well. FONLL also applicable for p T < 2m Q region. Factorization theorem of GM-VFNS on more solid theoretical ground. M. Butenschön Recent developments in quarkonium and open flavour production calculations 20 / 20