Heavy-quarkonium suppression in p A collisions from induced gluon radiation Fran¸ cois Arleo LAPTH, Annecy Workshop pA@LHC CERN – June 2012 Fran¸ cois Arleo (LAPTH) Quarkonia suppression from gluon radiation Workshop pA@LHC 1 / 18
Outline Motivations J /ψ suppression data in p A collisions Revisiting energy loss New scaling properties from medium-induced coherent radiation Phenomenology Model for J /ψ and Υ suppression in p A collisions Comparison with data and LHC predictions References FA, S. Peign´ e, T. Sami, 1006.0818 FA, S. Peign´ e, 1204.4609 + in preparation Fran¸ cois Arleo (LAPTH) Quarkonia suppression from gluon radiation Workshop pA@LHC 2 / 18
J /ψ suppression in p A collisions at forward rapidities E866 √ s = 38 . 7 GeV PHENIX √ s = 200 GeV 1 1 0.8 0.8 R W/Be (x F ) R dAu/pp (y) 0.6 0.6 0.4 0.4 0.2 0.2 E866 J/ ψ √ s = 38.7 GeV PHENIX √ s = 200 GeV 0 0 0 0.25 0.5 0.75 -3 -2 -1 0 1 2 3 x F y Strong J /ψ suppression reported at large x F and y Weaker suppression in the Drell-Yan process Observed at various √ s Fran¸ cois Arleo (LAPTH) Quarkonia suppression from gluon radiation Workshop pA@LHC 3 / 18
J /ψ suppression in p A collisions Many explanations suggested. . . yet none of them fully satisfactory Nuclear absorption requires unrealistically large cross section nPDF effects and saturation constrained by Drell-Yan Intrinsic charm assuming a large amount of charm in the proton Parton energy loss requires ∆ E ∝ E . . . supposedly ruled out Fran¸ cois Arleo (LAPTH) Quarkonia suppression from gluon radiation Workshop pA@LHC 4 / 18
J /ψ suppression in p A collisions Many explanations suggested. . . yet none of them fully satisfactory Nuclear absorption requires unrealistically large cross section nPDF effects and saturation constrained by Drell-Yan Intrinsic charm assuming a large amount of charm in the proton Parton energy loss requires ∆ E ∝ E . . . supposedly ruled out This talk: revisiting energy loss processes Fran¸ cois Arleo (LAPTH) Quarkonia suppression from gluon radiation Workshop pA@LHC 4 / 18
Gavin–Milana model Simple model assuming (mean) energy loss scaling like parton energy [ Gavin Milana 1992 ] ∆ E ∝ E L M − 2 for both Drell-Yan and J /ψ (though larger due to final-state energy loss) Caveats Ad hoc assumption regarding E , L , and M dependence of parton energy loss, no link with induced gluon radiation Failure to describe Υ suppression ∆ E ∝ E claimed to be incorrect in the high energy limit due to uncertainty principle — so-called Brodsky-Hoyer bound Fran¸ cois Arleo (LAPTH) Quarkonia suppression from gluon radiation Workshop pA@LHC 5 / 18
A bound on energy loss ? Induced gluon radiation needs to resolve the medium [ Brodsky Hoyer 93 ] t f ∼ ω ω � k 2 q L 2 � L ⊥ L ∼ ˆ k 2 ⊥ Bound independent of the parton energy Energy loss cannot be arbitrarily large in a finite medium Apparently rules out energy loss models as a possible explanation However Not necessarily true in QCD [ FA Peign´ e Sami 10 ] Fran¸ cois Arleo (LAPTH) Quarkonia suppression from gluon radiation Workshop pA@LHC 6 / 18
Revisiting energy loss scaling properties Two cases whether gluon radiation is coherent or incoherent (i) Incoherent radiation in the initial/final state Radiation of gluons with large formation times cancels out in the induced gluon spectrum, leading to t f ∼ L qL 2 ∆ E ∝ ˆ Hadron production in nuclear DIS and Drell-Yan in p A collisions Jets and hadrons produced in hadronic collisions at large angle Fran¸ cois Arleo (LAPTH) Quarkonia suppression from gluon radiation Workshop pA@LHC 7 / 18
Revisiting energy loss scaling properties Two cases whether gluon radiation is coherent or incoherent (ii) Coherent radiation (interference) in the initial/final state Induced gluon spectrum dominated by large formation times √ ˆ qL ∆ E ∝ E M Production of light and open heavy-flavour hadrons at forward rapidities in the medium rest frame (nuclear matter or QGP) Production of heavy-quarkonium if color neutralisation occurs on long time-scales t octet ≫ t hard Fran¸ cois Arleo (LAPTH) Quarkonia suppression from gluon radiation Workshop pA@LHC 7 / 18
Medium-induced gluon spectrum Gluon spectrum dI / d ω ∼ Bethe-Heitler spectrum of massive (color) charge � � �� E 2 Λ 2 1 + E 2 ∆ q 2 � � � ω dI = N c α s � ⊥ QCD ln − ln 1 + � d ω π ω 2 M 2 ω 2 M 2 � ind ⊥ ⊥ � ∆ q 2 � ⊥ − Λ QCD � d ω ω dI � ∆ E = = N c α s E � d ω M ⊥ � ind ∆ E ∝ E neither initial nor final state effect nor ‘parton’ energy loss: arises from coherent radiation Physical origin: broad t f interval : L , t hard ≪ t f ≪ t octet for medium-induced radiation Fran¸ cois Arleo (LAPTH) Quarkonia suppression from gluon radiation Workshop pA@LHC 8 / 18
Model for heavy-quarkonium suppression [ FA Peign´ e 1204.4609 ] d σ ψ � ǫ max d ǫ P ( ǫ ) d σ ψ x F , √ s pA pp � � = ( x F + δ x F ( ǫ )) dx F dx F 0 pp cross section fitted from experimental data d σ ψ ∝ (1 − x ′ ) n ( √ s ) / x ′ � x ′ ≡ pp x 2 F + 4 M 2 ⊥ / s dx F Shift given by δ x F ( ǫ ) ≃ ǫ/ E beam ω = √ ˆ P ( ǫ ): quenching weight, scaling function of ˆ qL / M ⊥ × E Length L given by L = 3 / 2 r 0 A 1 / 3 Fran¸ cois Arleo (LAPTH) Quarkonia suppression from gluon radiation Workshop pA@LHC 9 / 18
Quenching weight Poisson approximation assuming independent emission [ BDMS 2001 ] ∞ � n � � n � 1 � dI ( ω i ) � � � P ( ǫ ) ∝ d ω i δ ǫ − ω i n ! d ω n =0 i =1 i =1 � ∆ q 2 However, radiating ω i takes time t f ( ω i ) ∼ ω i ⊥ ≫ L For ω i ∼ ω j ⇒ emissions i and j are not independent For self-consistency, constrain ω 1 ≪ ω 2 ≪ . . . ≪ ω n � ∞ P ( ǫ ) ≃ dI ( ǫ ) � � d ω dI exp − d ω d ω ǫ Fran¸ cois Arleo (LAPTH) Quarkonia suppression from gluon radiation Workshop pA@LHC 10 / 18
Transport coefficient q related to gluon distribution in a proton ˆ [ BDMPS 1997 ] q ( x ) = 4 π 2 α s C R ˆ c − 1 ρ xG ( x , ˆ qL ) N 2 Typical value for x x = x 0 ≃ ( m N L ) − 1 for t hard � L ⇒ ˆ q ( x ) = constant q ( x ) ∝ x − 0 . 3 x ≃ x 2 for t hard > L ⇒ ˆ For simplicity we assume � 0 . 3 � 10 − 2 ˆ q ( x ) = ˆ q 0 x = min( x 0 , x 2 ) x q 0 only free parameter of the model ˆ Fran¸ cois Arleo (LAPTH) Quarkonia suppression from gluon radiation Workshop pA@LHC 11 / 18
Procedure Fit ˆ q 0 from J /ψ suppression E866 data in p W collisions 1 Predict J /ψ and Υ suppression for all nuclei and c.m. energies 2 Fran¸ cois Arleo (LAPTH) Quarkonia suppression from gluon radiation Workshop pA@LHC 12 / 18
Procedure Fit ˆ q 0 from J /ψ suppression E866 data in p W collisions 1 Predict J /ψ and Υ suppression for all nuclei and c.m. energies 2 ∧ ∧ q 0 = 0.09 GeV 2 /fm q 0 = 0.05 GeV 2 /fm + sat. 1 1 0.8 0.8 R W/Be (x F ) R Fe/Be (x F ) q 0 = 0 . 09 GeV 2 / fm ˆ 0.6 0.6 0.4 0.4 0.2 0.2 E866 √ s = 38.7 GeV (fit) E866 √ s = 38.7 GeV 0 0 -0.2 0 0.2 0.4 0.6 0.8 -0.2 0 0.2 0.4 0.6 0.8 1 x F x F Fe/Be ratio well described, supporting the L dependence of the model Fran¸ cois Arleo (LAPTH) Quarkonia suppression from gluon radiation Workshop pA@LHC 12 / 18
Procedure Fit ˆ q 0 from J /ψ suppression E866 data in p W collisions 1 Predict J /ψ and Υ suppression for all nuclei and c.m. energies 2 ∧ ∧ q 0 = 0.09 GeV 2 /fm q 0 = 0.05 GeV 2 /fm + sat. 1 1 0.8 0.8 R W/Be (x F ) R Fe/Be (x F ) q 0 = 0 . 09 GeV 2 / fm ˆ 0.6 0.6 0.4 0.4 0.2 0.2 E866 √ s = 38.7 GeV (fit) E866 √ s = 38.7 GeV 0 0 -0.2 0 0.2 0.4 0.6 0.8 -0.2 0 0.2 0.4 0.6 0.8 1 x F x F Fe/Be ratio well described, supporting the L dependence of the model Let’s investigate J /ψ suppression at other energies Fran¸ cois Arleo (LAPTH) Quarkonia suppression from gluon radiation Workshop pA@LHC 12 / 18
Extrapolating to other energies Two competing mechanisms might alter heavy-quarkonium suppression Nuclear absorption if hadron formation occurs inside the medium t form = γ τ form � L Low √ s and/or negative x F Indicated later assuming τ form = 0 . 3 fm Fran¸ cois Arleo (LAPTH) Quarkonia suppression from gluon radiation Workshop pA@LHC 13 / 18
Extrapolating to other energies Two competing mechanisms might alter heavy-quarkonium suppression saturation effects when Q 2 s ∼ m 2 � nPDF c R pA = R E . loss q ) × S sat A ( Q s ) / S sat (ˆ p ( Q s ) pA S sat A ( Q s ) parametrized as [ Fujii Gelis Venugopalan 2006 ] � 0 . 417 � 2 . 65 S sat A ( Q s ) = s [GeV 2 ] 2 . 65 + Q 2 No additional parameter: Q 2 s ( x , L ) = ˆ q ( x ) L [ Mueller 1999 ] q 0 = 0 . 05 GeV 2 / fm Reduces fitted transport coefficient: ˆ s ( x = 10 − 2 ) = 0 . 08 – 0 . 15 GeV 2 consistent with fits to DIS data Q 2 [ Albacete et al AAMQS 2011 ] Fran¸ cois Arleo (LAPTH) Quarkonia suppression from gluon radiation Workshop pA@LHC 13 / 18
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