Suppression of Heavy Quarkonium Production in pa Collisions

Transcription

1 Suppression of Heavy Quarkonium Production in pa Collisions Jianwei Qiu Brookhaven National Laboratory Based on works done with Z.-B. Kang, G. Sterman, P. Sun, J.P. Vary, B.W. Xiao, F. Yuan, X.F. Zhang, INT Program (INT-14-3) Focused workshop on Heavy Flavor and Electromagnetic Probes in Heavy Ion Collisions Institute for Nuclear Theory, University of Washington, Seattle, WA 9/15-10/10, 2014

2 Outline q Introduction heavy quarkonium production q Suppression of heavy quarkonium production in p+a: ² Total production rate ² pt spectrum ² xf (or y) distribution q Heavy quarkonium production in polarized p+a collisions ² Transverse single spin asymmetry (or phenomenon) ² New and complimentary probe of small-x physics q Summary

3 Introduction q Hadronic heavy quarkonium production: A(P 1 )+B(P 2 ) H(P )[J/ψ, ψ,...]+x q Partonic picture: q Momentum exchange: >m c 3.1 GeV q J/ is unlikely to be formed at: r H 1 2m c 1 15 fm Production of a heavy quark pair is likely to be perturbative!

4 Basic production mechanism q QCD factorization is likely to be valid for producing the pairs: ² Momentum exchange is much larger than 1/fm ² Spectators from colliding beams are frozen during the hard collision A B Perturbative Non-perturbative 1 Δr m 2 Q σ AB J/ψ (P J/ψ ) n Models & Debates Quarkonium Coherent soft interaction q Approximation: on-shell pair + hadronization dq 2 σ AB [Q Q](n) (q 2 ) F [Q Q(n)] J/ψ (P J/ψ,q 2 ) F [Q Q(n)] J/ψ (P J/ψ,q 2 ) ó Different assumptions/treatments on how the heavy quark pair becomes a quarkonium?

5 A long history for the production q Color singlet model: 1975 Only the pair with right quantum numbers Effectively No free parameter! q Color evaporation model: 1977 All pairs with mass less than open flavor heavy meson threshold One parameter per quarkonium state q NRQCD model: 1986 All pairs with various probabilities NRQCD matrix elements Infinite parameters organized in powers of v and s q QCD factorization approach: 2005 P T >> M H : M H /P T power expansion + s expansion Unknown, but universal, fragmentation functions evolution q Soft-Collinear Effective Theory + NRQCD: 2012 See my talk last week Einhorn, Ellis (1975), Chang (1980), Berger and Jone (1981), Fritsch (1977), Halzen (1977), Caswell, Lapage (1986) Bodwin, Braaten, Lepage (1995) QWG review: 2004, 2010 Nayak, Qiu, Sterman (2005), Kang, Qiu, Sterman (2010), Fleming, Leibovich, Mehen,

6 Transition from the pair to a quarkonium q Large phase space available for gluon radiation: Q 2! 4M C 2! 4M D 2! 4M C 2! 6 GeV 2 q Larger heavy quark velocity in production than decay: v decay v prod q c m c 4M 2 J/ψ 4m2 c 4m 2 c 4m 2 D 4m2 c 4m 2 c >v decay Direct impact the approximation of production models

7 Color evaporation model (CEM) q Transition distribution: ² vanishes above the open charm threshold ² independent of pair s mass and color, and ² is a constant F ( CC!J/! q 2 ) q 2 0 4m 2 D 4m 2 c 4m 2 σab J/ψ CEM (P D 4m2 c J/ψ) F c c J/ψ 0 dq 2 σ AB c c (q 2 ) ² One transition constant for each heavy quarkonium state ² Heavy quark mass Is only another adjustable parameter

8 Non-Relativistic QCD (NRQCD) model q Transition distribution ² Narrowly peaked distribution at q 2 m 2 c ² Velocity expansion is a good approximation v q /m c ² Perturbatively defined color singlet and octet states m c Λ QCD σ AB [Q Q](n) (q 2 ) q 2 m m d m! dq 2 σ AB [Q Q](n)(q 2 = 0) m m d σ AB [Q Q](n)(q 2 = 0) F ( CC!J/! q 2 ) q 2 σ AB J/ψ (P J/ψ ) n,m O dq 2 q dq 2 2 m F m! [Q Q(n)] J/ψ (q 2 ) σ AB O (q 2 = 0)O J/ψ q Velocity expansion might have large corrections: v prod ~0.88 for m c =1.4GeV

9 Role of semihard gluon radiation Q 2 Q 2 q Over 6 GeV 2 phase space for gluon radiation q Pair with large q 2 has a vanishing chance to become J/ψ in NRQCD Model q Radiation pays a penalty in coupling But, gains a lot on wave function a s (Q 2 ) ln(q 2 /4M c2 ) F(4M c2 ) Threshold behavior for the transition distribution! Q 2 Q 2

10 Heavy quarkonium in p(d)-a collisions q Proton (deuteron) Nucleus Collisions: P A ² NO QGP (m Q >> T)! Cold nuclear effect for the production ² Necessary calibration for AA collisions ² Hard probe (m Q >> 1/fm) quark-gluon structure of nucleus! Nucleus is not a simple superposition of nucleons!

11 q Production of QQ: A B Production in pa collisions Perturbative Non-perturbative 1 Δr m 2 Q Coherent soft interaction Quarkonium Same wave function Nuclear PDFs Almost Not affected Multiple scattering q Various factorizations: A B Coherent soft interaction Quarkonium Production vs destruction

12 Production in pa collisions q Incoherent multiple scattering on a gluon : See Arleo s talk on Friday ² Leads to a shift in y and p T Suppression in forward y Broadening in p T Without including shadowing, this leads to the same production rate if integrating over y and p T q Multiple scattering resolves the quark and antiquark: A B Coherent soft interaction If Q s m Q v Quarkonium Multiple scattering could change production rate!!

13 Production in pa collisions q If J/ were produced at the collision point: ² Nuclear effect in PDFs ² Medium dependence from J/ -nucleon absorption q Glauber model: σ AB ABσ NN e J/ ψ 0 abs LAB ρσ AB q Expect a straight line on a semi-log plot q Need a much too larger abs L AB

14 Suppression in total production rate q Anomalous suppression: Not a straight line on the semi-log plots additional suppression!

15 Suppression in total production rate q Multiple scattering in A: q Final-state: Increases the relative momentum of the pair Q 2 > Q 2 q 2! q 2 +!L AB Suppression of J/ ε ˆq q 2 T q Threshold effect leads to different effective abs Curved line for R pa q Different suppression for

16 Suppression in total production rate Qiu, Vary, Zhang, PRL 2002 Single parameter: ε ˆq ² Exact shape of transition distribtions? ² Transverse momentum broadening

17 Quarkonium pt distribution q Quarkonium production is dominated in low p T region q Both quarkonium and Drell-Yan low p T distributions at collider energies are determined by the gluon shower of incoming partons (initial-state effect) Qiu, Zhang, PRL, 2001 q Because of heavy quark mass, final-state interactions suppress the formation of J/, but should not be an important factor for low p T spectrum Area Width ² Similar p T broadening, but, different magnitude ² Extra overall suppression for J/ Shadowing Guo, Qiu, Zhang, PRL, PRD, 2000

18 Quarkonium pt distribution q PT spectrum is not completely perturbative: Guo, Qiu, Zhang, PRD 2002 E772 CFS I) Intrinsic II) Shower Sudakov III) Perturbative tail

19 Quarkonium pt distribution q Y-spectrum is almost perturbative: Berger, Qiu, Wang, PRD 2005 A prediction I) Intrinsic II) Shower Sudakov III) Perturbative tail Dominated by perturbative small-b contribution in its Fourier conjugate space all order resummation of soft gluon shower

20 A-dependence of the pt distribution q Multiple scattering in medium: J/ψ, ² Each scattering is too soft to calculate perturbatively ² Resummation + multiple scattering (small-x limit) q Moment of P T -distribution: ² more inclusive calculable ² based on observed particles only ² less sensitive to hadronization q Broadening: ² Sensitive to the medium properties ² Perturbatively calculable

21 A-dependence of the P T distribution q Ratio of x-sections: Guo, Qiu, Zhang, PRL, PRD 2002 Similar formula for J/ q Spectrum and ratio:

22 Broadening of heavy quarkonia q Initial-state only: Kang, Qiu, PRD77(2008) q Experimental data from d+a: Clear A 1/3 dependence But, wrong normalization! Final-state effect octet channel dominated! J.C.Peng, hep-ph/ Only depend on observed quarkonia Johnson,et al, 2007

23 Final-state multiple scattering q Heavy quarkonium is unlikely to be formed when the heavy quark pair was produced Kang, Qiu, PRD77(2008) ² If the formation length: no A-enhancement from final-state interaction ² If the formation length: additional A 1/3 -type enhancement from the final-state interaction q Final-state effect depends on how quarkonium is formed NRQCD model, color evaporation model,

24 Color evaporation model q Double scattering A 1/3 dependence: q Multiparton correlation: q Broadening twice of initial-state effect: if gluon-gluon dominates, and if r F > R A

25 NRQCD model q Cross section: q Broadening: Hard parts: Only color octet channel contributes q Leading features:

26 Broadening of heavy quarkonia in p(d)+a q Final-state effect is important: Kang, Qiu, PRD77(2008) in both CEM and NRQCD q Mass independence, not very sensitive to the feeddown

27 Broadening of heavy quarkonia in A+A q If no hot medium was formed: Superposition of pa q If hot medium is formed: Slow expanding hot & dense medium at RHIC and the LHC! could be less than 0! final-state energy loss, initial-state thermal medium?

28 P(d)+A collision at forward rapidity q Puzzling rapidity dependence: ² x F scaling (not x 2 -scaling) in low energy data ² Less suppression from LHC data (early CGC calculation does not work)

29 Multiple scattering in DIS q Consequence of OPE for inclusive DIS: σ = ˆ σ [1 + C α + C α +...] T ( x) h i (1, 2) (2, 2 ) 2 i/ h phys 2 s s 2 i ˆ σ Q (1, 4) (2, 4) 2 i/ h [1 C αs C αs...] T4 ( x) i ˆ σ 6 (1, 6) (2, 6 ) 2 i/ h + [1 + C α...] 4 s + C αs + T6 ( x) Q +... Power corrections Leading twist q Predictive power: v Coefficient functions are IR safe v Distributions/correlations/matrix elements are universal q Distributions are defined to remove all collinear divergences of the partonic scattering

30 Size of power corrections q Coherent multiple scattering ( S) ( D) dσ dσ + dσ +... Naïve power counting: 2D lightcone dynamics q Medium parton density: q For a hard probe: q Nuclear size enhancement: dσ dσ ( D) ( S) : F α QR A 1 Q αs 2 R F + α + α s = /3 x ϕ q Small x enhancement: ( x) 6 2 F F + α + α A 1/3

31 Tree-level power corrections to DIS q At small x, the hard probe covers several nucleons, coherent multiple scattering could be equally important at low Q + + q To take care of the coherence, we need to sum over all cuts for a given forward scattering amplitude Scatterings Cuts Summing over all cuts is also necessary for IR cancellation

32 Multi-parton correlation functions q Parton momentum convolution: Cuts ( y ) i + ixi p yi + dy e P F P i A i i All coordinate space integrals are localized if x is large q Leading-pole approximation for dx i integrals : ² dx i integrals are fixed by the poles (no pinched poles) ² x i =0 removes the exponentials ² dy integrals can be extended to the size of nuclear matter Leading-pole leads to highest powers in medium length, a much smaller number of diagrams to worry about A

33 Multiple coherent scattering to DIS q LO contribution to DIS cross section: q NLO contribution: q Nth order contribution: Infrared safe!

34 Resummed contribution to structure functions q Transverse structure function: Qiu and Vitev, PRL (2004) +Δx Single parameter for the power correction, and is proportional to the same characteristic scale q Similar result for longitudinal structure function

35 Neglect LT shadowing upper limit of ξ ξ : GeV

36 Rapidity dependence in p+a q Resummed multiple scattering: σ PA (p T,x F ) a,b ξ 2 g x d dx fa/p (x F + x)f b/a (x) x=x 2 (x F,Q) In the forward region, d dx fa/p (x F + x) d x=x 2 (x F,Q) dx x 1 = x F + x 2 x 2 = 1 2 fb/a (x) x=x 2 (x F,Q) x 2F +4Q2 /s x F

37 Heavy quarkonium p T distribution in pa q QCD factorization for A 1/3 enhanced contribution: Time dilation factor: Condition for multiple scattering not to interfere with hadronization q Heavy quarkonium production in pa collisions: ² Kang et al.: NRQCD, CEM, P T ~ Q s >> M, small-x evolution + CGC multiple scattering No numerical prediction yet ² Qiu et al.: NRQCD, CEM, P T ~ Q s << M Coherent multiple scatteing + Sudakov resummation

38 Polarized p+a collisions Excellent probe for distinguishing various contributions to SSA Excellent probe for studying small-x Physics SSA increases as x F (or y) increases

39 Polarized proton and A N q Definition: Kang, Yuan, Difference of x-sections! q A N proportional to the k T slop of TMD:

40 q Polarized p+a: A unique opportunity

41 Saturation scale depenence q Nuclear TMD is broadened: Smaller slop in kt Smaller contribution to AN q Expectation:

42 Sources of contribution to AN

43 q polarized p+p: Separation of various sources Jet, photon, vs single hadron - Sivers vs Collins q polarized p+a: Kang et al. Magnitude + peak location Interesting test: 0 Kovchegov et al.

44 A N of heavy quarkonium F. Yuan Low pt: A N (P h ) P h Q 2 s e δ 2 P 2 h (Q 2 s )2 High pt:

45 Summary q Heavy quarkonium production has been a powerful tool to test and challenge our understanding of strong interaction and QCD q Both initial-state and final-state multiple scattering are relevant for nuclear dependence of Quarkonium production could redistribute the p T - & y-dependence q Final-state multiple scattering could be an effective source of J/ suppression because of the shape threshold behavior q Polarized p+a at RHIC is a new and exciting opportunity q More discussion and work on QCD factorization is needed for p+a collision. A weaker factorization is likely true to pa s A-dependence, but, not for AA collisions Thank you!

46 Backup slides

47 Melting a quarkonium in QGP q Start with a J/ψ ² This works with other charmonium states as well ² The J/ is easiest to observe q Put it in a sea of color charges q The color lines attach themselves to other quarks This forms a pair of charmed mesons q These charmed mesons wander off from each other q When the system cools, the charmed particles are too far apart to recombine Essentially, the J/ has melted Matsui & Satz (1986)

48 Multiple scattering in cold nuclear matter Dominguez, Kharzeev, Levin, Mueller, and Tuchin, 2011 PHENIX: y=0, s=200 GeV ALICE: y=3.25, s=2.76 TeV PHENIX: y=1.7, s=200 GeV bcgc Model for dipole scattering OK for pa, but, far off for AA J/ melting in QGP (MS 1986)?

49 How collinear factorization generates SSA? q Collinear factorization beyond leading power: p, s k σ(q, s) t 1/Q 2 Expansion Too large to compete! Three-parton correlation q Single transverse spin asymmetry: Efremov, Teryaev, 82; Qiu, Sterman, 91, etc. σ(s T ) T (3) (x, x) ˆσ T D(z)+δq(x) ˆσ D D (3) (z,z)+... T (3) (x, x) D (3) (z,z) T (3σ) (x, x) Qiu, Sterman, 1991, Kang, Yuan, Zhou, 2010 Kanazawa, Koike, 2000 Integrated information on parton s transverse motion!