J/Ψ-Production in γγ-collisions at NLO. Michael Klasen LPSC Grenoble April 19, 2005
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1 J/Ψ-Production in γγ-collisions at NLO Michael Klasen LPSC Grenoble April 19, 2005
2 CERN / Fréjus LPSC ILL ESRF April 19, 2005 Michael Klasen, LPSC Grenoble 2
3 Research at LPSC Grenoble Astroparticles: Particles: Hadrons: Reactors: Medicine: AMS, Planck D0, ATLAS G0, ILL/PSI Cadarache GEANT 4, SPIRAL-II Theory: Few-body systems (J.-M. Richard) Lattice QCD (J. Carbonell + N.N.) Phenomenology (M.K. + N.N.) April 19, 2005 Michael Klasen, LPSC Grenoble 3
4 Publications With B.A. Kniehl, L. Mihaila, M. Steinhauser NPB 609 (2001) 518: γγ J/Ψ+2 jets (ILC) PRL 89 (2002) : γγ LO (LEP) PRD 68 (2003) : pp LO (RHIC) NPB 713 (2005) 487: γγ NLO (ILC) PRD 71 (2005) : γγ NLO (ILC) April 19, 2005 Michael Klasen, LPSC Grenoble 4
5 Motivation The two sides of QCD: Quarks and gluons: Asymptotically free, carry color Hadrons: Color-singlets, non-perturbative, confinement Simplest laboratory: Quarkonia Rich spectroscopy Charmonia: η c (2S), X(3872) (?) Bottomonia: Υ(1D) Experimental data: C-/B-factories: BES, CLEO, Babar, Belle Fixed target: HERA-B, E866 Colliders: LEP, HERA, Tevatron Review: N. Brambilla et al.: CERN Yellow Report, hep-ph/ April 19, 2005 Michael Klasen, LPSC Grenoble 5
6 Color singlet state: Color Singlet Model Preserved from hard QQ-pair production Strong selection rules: J/Ψ wave function _ Theoretical problems: Uncanceled infrared divergences, e.g. in P-wave decays Phenomenological problems: p T -distribution of J/Ψ, Ψ and χ c,j at the Tevatron z-distribution of J/Ψ in photoproduction at HERA Einhorn, Ellis; Berger, Jones; Baier, Rückl (1975-) April 19, 2005 Michael Klasen, LPSC Grenoble 6
7 Color singlet state: Color Evaporation Model Created by soft gluon exchange with underlying event Open heavy quark production: Universal factors F H, Phenomenological problems: J/Ψ prompt hadroproduction and from χ c,j -decay in B-decays Ratio of χ c,1 and χ c,2 hadroproduction cross sections not 3/5 Polarization in e + e - -annihilation at B-factories not zero Fritzsch; Halzen; Glück, Owens, Reya (1977-) April 19, 2005 Michael Klasen, LPSC Grenoble 7
8 Hard Comover Scattering Model Color singlet state: Created by hard gluon exchange with classical color field Rescattering kernel: Isotropic field Γ: Generated by bremsstrahlung of initial state partons Phenomenological successes: Explains ratio of χ c,1 and χ c,2 hadroproduction cross sections Explains non-polarization of hadroproduced J/Ψ and Ψ Hoyer, Marchal, Peigné (1997-) April 19, 2005 Michael Klasen, LPSC Grenoble 8
9 Color singlet state: NRQCD (1) Created by soft gluon exchange with underlying event Separation of mass scales: (v c 2 = 0.3, v b 2 = 0.1) m c = 1.5 GeV (annihilation and production threshold) m c v c = 0.9 GeV (size of bound state) m c v c2 = 0.5 GeV (splitting of resonances) Double expansion in α s and v (pertur. and relat. corrections) Lagrangian: ψ and χ are two-component heavy (anti-)quark spinors δl reproduces L QCD :, Gauge completion: [Nayak, Qiu and Sterman, PLB 613 (2005) 45] April 19, 2005 Michael Klasen, LPSC Grenoble 9
10 NRQCD (2) Cross section factorization: Sum over all spin, angular momentum and color states Proven for decays, related to production by vac. saturation Operator matrix elements: Non-perturbative: Lattice-QCD; experimental fits Velocity scaling rules for Fock states and operators Caswell, Lepage; Bodwin, Braaten, Lepage (1986-) April 19, 2005 Michael Klasen, LPSC Grenoble 10
11 NRQCD (3) Lattice determination of operator matrix elements: Only possible for decay matrix elements Related to production by vac. saturation (directly for CS) Velocity scaling should be the same Lattice action: Lepage et al., PRD 46 (1992) 4052 Improved tadpoles: Lepage, Mackenzie, PRD 48 (1993) 2250 Quenched results on lattice: [Bodwin, Lee, Sinclair, hep-ph/ ] April 19, 2005 Michael Klasen, LPSC Grenoble 11
12 Amplitude factorization: NRQCD (4) Spin and color projectors:,, For non-integer D 4 not only S=0,1, but infinite set of states No spin flip for m ; sufficiently low order in v for finite m At least O(ε) at higher orders in v, no soft/collinear poles Angular momentum projectors:, April 19, 2005 Michael Klasen, LPSC Grenoble 12
13 Color singlet state: k T -Factorization Any of the previous models Cross section factorization: Unintegrated parton densities: Factorized form: Normalization: Gaussian k T -distribution:, fit BFKL equation (log 1/x): Sridhar, Martin, Stirling; Yuan, Chao; Lipatov (1998-) April 19, 2005 Michael Klasen, LPSC Grenoble 13
14 J/Ψ-Cross Section at the Tevatron (1) [Braaten (1995); Cho, Leibovich (1996)] Similar situation for Ψ and χ c, see M. Krämer, Prog. Part. Nucl. Phys. 47 (2001) 141 April 19, 2005 Michael Klasen, LPSC Grenoble 14
15 J/Ψ-Cross Section at the Tevatron (2) Hägler et al., PRD 63 (2001) Bodwin, Braaten, Lee, hep-ph/ April 19, 2005 Michael Klasen, LPSC Grenoble 15
16 J/Ψ- and Υ-Polarization at the Tevatron Braaten, Kniehl, Lee, PRD 62 (2000) Braaten, Lee, PRD 63 (2001) April 19, 2005 Michael Klasen, LPSC Grenoble 16
17 J/Ψ-Cross Section at HERA and LEP Cacciari, Krämer, PRL 76 (1996) 4128 MK et al., PRL 89 (2002) April 19, 2005 Michael Klasen, LPSC Grenoble 17
18 NLO Quarkonium Production Color-singlet model: γp J/Ψ+jet Krämer, Zunft, Steegborn, Zerwas, PLB 348 (1995) 657 Krämer, NPB 459 (1996) 3 Full NRQCD: pp/γp Quarkonium Petrelli et al., NPB 514 (1998) 245 Maltoni, Mangano, Petrelli, NPB 519 (1998) 361 April 19, 2005 Michael Klasen, LPSC Grenoble 18
19 J/Ψ-Production in γγ-collisions at LO Photon-photon scattering at e + e - -colliders: Direct and resolved processes: High p T : ILC Low p T : LEP/HERA Suppressed: TeV/LHC Large theoretical uncertainties: Coupling constant/operator renormalization Parton densities/fragmentation functions April 19, 2005 Michael Klasen, LPSC Grenoble 19
20 Direct J/Ψ+jet Production at LO Feynman diagrams: Cross sections: April 19, 2005 Michael Klasen, LPSC Grenoble 20
21 Virtual Corrections Typical Feynman diagrams: Cross section: Light box contribution: April 19, 2005 Michael Klasen, LPSC Grenoble 21
22 Computational Details Large number and size of amplitudes: High degree of automatization Two completely independent calculations Diagram generation: FeynArts/Qgraf Dirac and color trace evaluation: FeynCalc/Form Loop integrals: FeynCalc/LoopTools Numerical evaluation: Two subprocess libraries/monte Carlo integration programs April 19, 2005 Michael Klasen, LPSC Grenoble 22
23 Regularization Dimensional regularization: D = 4 2ε Reduction of tensor integrals: Passarino-Veltman scheme Non-trivial for 5-point functions and P-waves Singularities: UV: Self-energies, vertex corrections IR: Vertex corrections, box diagrams Coulomb:Longitudinal gluon exchange April 19, 2005 Michael Klasen, LPSC Grenoble 23
24 Renormalization of Hard Coefficients Heavy quark mass: Wave functions: Strong coupling constant: April 19, 2005 Michael Klasen, LPSC Grenoble 24
25 Renormalization of Operators NRQCD Feynman diagrams: Unrenormalized result at one-loop: Renormalized result: Generates Coulomb and IR counterterms April 19, 2005 Michael Klasen, LPSC Grenoble 25
26 Scale Dependence of Operators Renormalization group equation: Identify µ = λ Integrate over λ Scale dependence of operators: One- and two-loop coefficients of QCD β-functions: April 19, 2005 Michael Klasen, LPSC Grenoble 26
27 Real Corrections Gluon emission: Light quark emission: April 19, 2005 Michael Klasen, LPSC Grenoble 27
28 Soft/Collinear Singularities Two possible methods: Dipole subtraction method Phase space slicing method Hard/non-collinear region: No singularities Numerical integration Soft/collinear regions: FS collinear singularities: IS collinear singularities: Renormalization of PDF s: Factorization scheme: MS: DIS γ : April 19, 2005 Michael Klasen, LPSC Grenoble 28
29 Cross section: Finite NLO Cross Section Singularity cancellation: April 19, 2005 Michael Klasen, LPSC Grenoble 29
30 e + e - -collider: Numerical Input ILC with s = 500 GeV Superposition of bremsstrahlung and beamstrahlung Parameters: m c = 1.5 GeV, α = 1/ , n f = 3, Λ 1/2-loop = 204/299 MeV Operator matrix elements: Take O LO = O NLO (λ=m) Braaten, Kniehl, Lee, PRD 62 (2000) Photon densities: Glück, Reya, Schienbein, PRD 60 (1999) April 19, 2005 Michael Klasen, LPSC Grenoble 30
31 Cut-off Dependence April 19, 2005 Michael Klasen, LPSC Grenoble 31
32 Renormalization Scale Dependence April 19, 2005 Michael Klasen, LPSC Grenoble 32
33 Factorization Scale Dependence April 19, 2005 Michael Klasen, LPSC Grenoble 33
34 Transverse Momentum Dependence April 19, 2005 Michael Klasen, LPSC Grenoble 34
35 Direct J/Ψ+γ Production at NLO Leading order: Electromagnetic color singlet process No renormalization scale dependence Unrenormalized operator at one-loop: Singularity cancellation: April 19, 2005 Michael Klasen, LPSC Grenoble 35
36 Renormalization Scale Dependence April 19, 2005 Michael Klasen, LPSC Grenoble 36
37 Inclusive J/Ψ Production at RHIC April 19, 2005 Michael Klasen, LPSC Grenoble 37
38 Towards J/Ψ Hadroproduction at NLO Our aim: Full NRQCD calculation Next steps: J/Ψ+dijets in γp and pp Matrix elements calculated Summation Numerical integration Check Krämer, Petrelli INT workshop: Find some time New ideas? [A. Petrelli, Nucl. Phys. Proc.Suppl. 86 (2000) 533] April 19, 2005 Michael Klasen, LPSC Grenoble 38
39 Conclusion Quarkonia: Simplest bound states, study hadronization Color singlet model: Very predictive, but incomplete NRQCD: Effective field theory, but needs factorization proof Existing NLO calculations for production: Inclusive color singlet photoproduction Exclusive NRQCD photo-/hadroproduction Recent progress: Gauge completion: Fragmentation at NNLO Lattice determination: Verification of scaling rules Our program: Inclusive NRQCD photo-/hadroproduction Completed for direct γγ J/Ψ+jet and γγ J/Ψ+γ processes Now putting γp J/Ψ+2 jets and pp J/Ψ+2 jets together April 19, 2005 Michael Klasen, LPSC Grenoble 39
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