CGC effects on J/ψ production

Transcription

1 CGC effects on J/ψ production Kirill Tuchin based on work with D. Kharzeev, G. Levin and M. Nardi 6th Winter Workshop on Nuclear Dynamics Jan.-9 Ocho Rios, Jamaica

2 Introduction I Inclusive light hadron and open charm production at s= GeV dau.5! = + h +h -.5! = + h +h -.5! =. - h.5! = 3. - h R CP R CP R CP R CP.5.5 -%/6-8% 3-5%/6-8% p T [GeV/c] p T [GeV/c] p T [GeV/c] p T [GeV/c] R AA Au+Au s NN = 3 GeV central -% (h + +h - )/ π α+α CERN-ISR π Pb+Pb(Au) CERN-SPS Conclusion: at y= there are no cold nuclear matter effects that produce suppression in inclusive q and G production. binary scaling BUT: This is true only if there is a factorization between the nuclei! 4 p T (GeV/c)

3 dσ pa d k dy = [ ] [ Theoretical support: an approximate kt - factorization holds in G and light q production. ] [ ] [ C F α s π (π) 3 k d B d b d z z n G (z, b B, ) e ik z z N G (z, b, ). d k k dσ pa MV d k dy = A approximation. d k k dσ pp MV d k dy Kovchegov, KT, proton One can trace the origin of the (approximate) factorization in that there is no restriction on the quantum numbers of the product (Spin, Color etc.) nucleus 3

4 Production of the q-anti-q pair: pa Fujii, Gelis, Venugopalan kt-factorization is broken down 4

5 Introduction II Inclusive J/ψ production at s= GeV Conclusion: at y= the cold nuclear matter effects are insufficient to produce the observed suppression in J/ψ inclusive production WRONG! Because factorization is badly broken in J/ψ production in pa and AA collisions 5

6 #$%!%&&%'()*%!+,-./().!'/.--!-%'().-!&/.!&)(-!.&!3+.+4-!'+5'65+().- " #$)-!)-!!"#!+!+((%(!(.!%D(/+'(! F!#$)-!)-! G6-(!+!+/+%(%/)H+().!.&!($%!=+(+!($+(! )-!)=%%=%(!+(!%+'$!/+)=)(EC Stolen from T. Frawley #$%!/%=!.)(-!+/%!($%!+*%/+B%-!+(! E!I!JKCL!+=!>KCLC!! 6

7 What breaks factorization? Coherence. q q k l c = k + (q k) q k k x = k p l c = Mx ) lc>>ra coherent scattering: all nucleons participate in scattering simultaneously. ) lc<<ra incoherent scattering: every nucleon acts as independent scattering center.

8 Coherence in E&M Landau-Lifshitz, II 8: Scattering of waves with large frequencies q~/λ Coherent scattering: If λ>>r qr<< Exp(i q r)= All scattering centers equally contribute. Incoherent scattering: If λ<<r qr>> Exp[i q (ra-rb)]= when ra=rb, otherwise ; i.e. different scattering centers are independent. QED analogy: coherent vs Raman (combinational) light scattering 8

9 Glauber-Gribov model Glauber: assume projectile-nucleon amplitudes are not correlated. QCD: if α sa /3 Quasi-classical approximation Gribov: hadrons do not diagonalize the scattering matrix => diffraction UR particle travels along the straight lines in external field Scattering matrix S is diagonal in the transverse coordinate space. 9

10 Beyond Factorization Relevant variables: transverse coordinates of charges. E.g. for q and anti-q: x and y or r=x-y and B=(x+y)/ r B ba Write the scattering amplitude in terms of transverse coordinates of all excitations `dipole model. σ q qa tot (s; r) = d b N A (r, b, Y ) = d b ( e ) qn σq tot (s;r) ρ T A(b) Glauber-Mueller formula In the Born approximation: σ q qn tot (s; r) = α s N c π r xg(x, /r )

11 Production of the q-anti-q pair: pa { } { } Heavy quark approximation (valence quark doesn t interact): dσ tot (pa) dy d k d b = x [ G(x, m c) d r e i k r d r e i k r Φ G (l, r, r, z = /) { exp[ σ(x, r ) ρ R A ] exp[ σ(x, r ) ρ R A ] + exp[ σ(x, ( r r ) ) ρ R A ] }. λ,s,s [ r r ] rr K (rm c ) K (r m c ) + K (rm c ) K (r m c ), KT, 4

12 Production of the q-anti-q pair P A z z Inelastic processes: dσ in (pa) dy d k d b = x G(x, m c) RA n= d r d r Φ G (m c, r, r, z = /) e i (r r) k ρ ˆσ in (x, r, r ) dz e [σ(x,r )+σ(x,r )] ρ R A RA z d z... RA RA dz n z n z n dz n ρ n ˆσ n in(x, r, r ) (α sa /3 ) n ˆσ in (x, r, r ) σ(x, r ) + σ(x, r ) σ(x, (r r ) ). o distinguish the dipole cross section defined in (.6) from ( )

13 Production of J/ψ: pp vs pa Ψ G (l ; r, z) Ψ V (r) Ψ G (l ; r, z) Ψ V (r) l, x l, x l, x l, x l 3, x A) B) z z hadron hadron collisions hadron nucleus collisions α 3 sa /3 = α s (α sa /3 ) α s α 4 sa /3 = (α sa /3 ) This mechanism is dominant only for central enough collisions Ψ G (m c, r, z) Ψ V (r, z) = 3 Γ J/Ψ e + e M J/Ψ m 3 c r 48 π α em 4 K (m c r) 3

14 Production of J/ψ: relevant time scales A pre-hadron cc pair is produced over time τ P = l c /c = 7 e y fm J/ψ wave function is formed over time τ F = M ψ M ψ M ψ l c = 4 e y fm Hierarchy of scales required for the dipole model: τf>>τp>>τint 4

15 At y> cc is produced coherently over entire nucleus and J/ψ is formed outside of it. d A At -<y< cc is produced coherently over a few nucleons. J/ψ is formed outside the nucleus. Note additional enhancement by N part Additional assumptions: J/ψ is non-relativistic. Relativistic correction depends on m but not on energy - included in prefactor. Parametrically small corrections due to the real part and offdiagonal matrix elements are neglected. 5

16 Propagation of c-anti-c through nucleus J/Ψ z z z Exponentiation works only at large Nc dσ in (pa) dy d b Only even number of inelastic interactions with the nucleus are allowed. RA = C F x G(x, m c) ρ ˆσ in (x, r, r ) d z ( e (σ(x,r ) + σ(x,r )) ρ R A RA n= z d z d r Ψ G (l, r, z = /) Ψ V (r) RA z dz... RA z n dz n+ ρ n+ ˆσ n+ in (x, r, r ) d r Ψ G (l, r, z = /) Ψ V (r ) ) { exp ( σ ( x, (r r ) ) ) ) ) ρ R A +exp ( (σ(x, r)+σ(x, r )+ˆσ in (x, r, r )) ρ R A exp ( (σ(x }, r)+σ(x, r )) ρ R A 6

17 Our model vs PHENIX data.4. y = -.7. Kharzeev, Levin, Nardi KT, 9 -. R DAu y = R DAu y = N coll y 7

18 Breakdown of x F -scaling Kharzeev, KT, 5! σ pa =A α σ pp α=/3 plateau: black disk regime dashed-dotted : "s = 5.5 TeV dotted : "s = GeV solid : "s = 38 GeV dashed : "s = 9 GeV x F 8

19 Production of J/ψ: AA Kharzeev, Levin, Nardi, KT z z z 3 A A We have to sum over all odd number of interactions with both nuclei {... } = RA n RA RA ( 8 Q s,a RA ) ( 8 Q s,a ) RA z z z { (r r ) dz dz exp } 8 (r + r ) (Q s,a + Q s,a ) ( ) k 8 Q s,a r r d z dz... dz k ρ k k= z z z k RA RA RA ( ) n k d z dz... dz n k ρ n k n= z z z n k 8 Q s,a r r g the following { mathematical identity ( ) n ( ) n = (n )! 8 (Q s,a + Q s,a ) r r (n )! 8 Q s,a r r n= ( ) } n (n )! 8 Q s,a r r ( ) ( ) ( ) = sinh 8 (Q s,a + Q s,a ) r r sinh 8 Q s,a r r sinh 8 Q s,a r r 9

20 dσ(aa) S A dy d b = C F 4π α s { ( r r exp 8 (r r ) (Q s,a + Q s,a ) exp ( 8 (r r ) Q s,a 8 ) (r + r ) Q s,a exp ( 8 (r r ) Q s,a 8 ) (r + r ) Q s,a d r Ψ G (l, r, z = /) Ψ V (r) d r Ψ G(l, r, z = /) Ψ V (r ) ) ( exp ) 8 (r + r ) (Q s,a + Q s,a ) + exp ( 8 (r + r ) Q s,a 8 ) (r + r ) Q s,a + exp ( 8 (r + r ) Q s,a 8 )} (r + r ) Q s,a, Approximately (for r>>r ): dn AA (Y, b) dy = C dn pp (Y ) dy dζ ζ 9 K (ζ) exp ( d s T A (s) T A (b s) ( Q s,a (x, s) + Q s,a (x, b s) ) ( ζ ( ( Q s,a (x, s) + Q s,a (x, b ) s) )). 8m c m c Fitted to Phenix DAu data x = m J/Ψ,t e Y, x = m J/Ψ,t e Y s s being the transverse momentum of the J/Ψ.

21 % dn/dy x ^6 5-4% 4-6% 5 6-9% y Unknown constant C is fixed from DAu data.rapidity dependence is reproduced well.. The width of the distribution decreases with Npart

22 Cold J/ψ suppression.4. R AA y=. y= N part Mechanism of suppression: large relative momentum between c and anti-c makes the J/ψ formation less probable.

23 Outlook. Better description of peripheral data: need to calculate a contribution of A+A J/ψ+g mechanism. Prediction for higher energies and for χ s 3

24 Summary I discussed hadron production in nuclear collisions at high energies: Generally, traditional factorization schemes are broken, although sometimes they approximately hold. I showed that J/ψ production mechanism in pp and pa/aa collisions is different due to strong coherence effects. Factorization is strongly violated. We are convinced, that most of J/ψ suppression in AA is a cold nuclear matter effect. 4