Recent Developments in Quarkonium and Open Flavour Production Calculations

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

2 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

3 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

4 J/ψ Production with NRQCD: Knowledge until 2005 Hadroproduction at Tevatron: Photoproduction at HERA: γγ Scattering at LEP: BR(J/ψ μ + μ - ) dσ(pp _ J/ψ+X)/dp T (nb/gev) s =.8 TeV; η < 0.6 total colour-octet S P J colour-octet 3 S LO colour-singlet colour-singlet frag p T (GeV) dσ(γ p J/ψ X)/dz (nb) 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 ) < < m c <.6 GeV 50 < W < 80 GeV p T > GeV 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 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

5 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

6 M.B., Kniehl (20): Global Fit of CO LDMEs dσ(ee J/ψ ee+x)/dp 2 T [pb/gev 2 ] DELPHI data y < W < 35 GeV θ el < 32 mrad s = 97 GeV 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 H data: HERA p 2 T [GeV 2 ] dσ(ep J/ψ+X)/dW [nb/gev] s = 34 GeV, Q 2 < GeV 2 H data: HERA < z < 0.9 pt 2 > GeV s = 34 GeV Q 2 < GeV 2 p 2 T > GeV 2 H data: HERA 60 GeV < W < 240 GeV 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 s = 39 GeV dσ(ep J/ψ+X)/dW [nb/gev] s = 39 GeV, Q 2 < 2.5 GeV < z < 0.9 pt 2 > GeV H data: HERA2 H data: HERA2 60 GeV < W < 240 GeV 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] BELLE data: s = 0.6 GeV σ = (0.43±0.3) pb (J/ψ+cc contribution subtracted) : σ = 0 : σ = ( ) pb : σ = 0.23 pb : σ = ( ) pb dσ(ep J/ψ+X)/dp 2 T [nb/gev 2 ] GeV < W < 80 GeV 0.4 < z < 0.9 Q 2 < GeV 2 s = 300 GeV ZEUS data pt 2 [GeV 2 ] dσ(ep J/ψ+X)/dW [nb/gev] s = 300 GeV, Q 2 < GeV < z < 0.9 pt 2 > GeV ZEUS data 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 z dσ/dp T (pp J/ψ+X) B(J/ψ ee) [nb/gev] 0 2 PHENIX data s = 200 GeV 0-4 y < dσ/dp T (pp J/ψ+X) B(J/ψ μμ) [nb/gev] 0 2 CDF data: Run s =.8 TeV 0-4 y < dσ/dp T (pp J/ψ+X) B(J/ψ μμ) [nb/gev] CDF data: Run s =.96 TeV 0-4 y < ALICE data < y < ATLAS data y < ATLAS data < y < ATLAS data < y < CMS data y < CMS data < y < CMS data < y < LHCb data < y < LHCb data < y < LHCb data < y < LHCb data < y < LHCb data < y < <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

7 In Detail: Hadroproduction (LHC, Tevatron) dσ/dp T (pp J/ψ+X) B(J/ψ μμ) [nb/gev] < y < 3 LHCb data dσ/dp T (pp J/ψ+X) B(J/ψ μμ) [nb/gev] s =.96 TeV y < 0.6 CDF data: Run 2 dσ/dp T (pp J/ψ+X) B(J/ψ μμ) [nb/gev] 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 p T [GeV] p T [GeV] 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

8 In Detail: Photoproduction (HERA) dσ(ep J/ψ+X)/dp 2 T [nb/gev 2 ] GeV < W < 80 GeV 0.4 < z < 0.9 Q 2 < GeV 2 p 2 T [GeV 2 ] s = 300 GeV ZEUS data dσ(ep J/ψ+X)/dW [nb/gev] s = 300 GeV, Q 2 < GeV < z < 0.9 pt 2 > GeV 2 ZEUS data W [GeV] dσ(ep J/ψ+X)/dz [nb] ZEUS data s = 300 GeV Q 2 < GeV 2 pt 2 > GeV 2 50 GeV < W < 80 GeV z dσ(ep J/ψ+X)/dz [nb] ZEUS data Direct, NLO Resolved, NLO Total, NLO s = 300 GeV Q 2 < GeV 2 pt 2 > GeV 2 50 GeV < W < 80 GeV z dσ(ep J/ψ+X)/dp 2 T [nb/gev 2 ] GeV < W < 80 GeV 0.4 < z < 0.9 Q 2 < GeV 2 p 2 T [GeV 2 ] s = 300 GeV ZEUS data dσ(ep J/ψ+X)/dW [nb/gev] 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 dσ(ep J/ψ+X)/dz [nb] 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 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

9 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] BELLE data: σ = (0.43±0.3) pb (J/ψ+cc contribution subtracted) : σ = 0 : σ = ( ) pb : σ = 0.23 pb : σ = ( ) pb s = 0.6 GeV dσ(ee J/ψ ee+x)/dp 2 T [pb/gev 2 ] DELPHI data y < W < 35 GeV θ el < 32 mrad s = 97 GeV 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

NNLO*: Consider only tree level pp QQ + 3 Jets and impose IR cutoffs.

10 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

11 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 (a) CDF Data NRQCD k T -factorization p T (GeV/c) λ ZEUS 468 pb - LO CS NLO CS LO k T (JB) LO k T (dgvr) LO CS+CO p T (GeV) [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 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

12 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

13 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) M. Butenschön Recent developments in quarkonium and open flavour production calculations 2 / 20

14 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) 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 qg QX 9 qg QX q q QX M. Butenschön Recent developments in quarkonium and open flavour production calculations 3 / 20

15 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

16 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

17 FITTING THE FRAGMENTATION FUNCTIONS (KKKSC) dσ/dx p (e + e - D + ) (nb) /σ tot dσ/dx(e + e - D + ) BELLE CLEO x p OPAL total b-tagged 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

18 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 y y y p T (GeV) p T (GeV) 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) [2] Acosta et al., PRL9(2003)24804 M. Butenschön Recent developments in quarkonium and open flavour production calculations 7 / 20

19 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 pp, 0 - D K π + - s = 7 TeV,.4 nb µb/gev/c 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 stat. unc. syst. unc. FONLL GM-VFNS PWG3-Preliminary GeV/c p t 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

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

21 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

INCLUSIVE D- AND B-MESON PRODUCTION

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)