Energy loss in cold nuclear matter and suppression of forward hadron production.

Energy loss in cold nuclear matter and suppression of forward hadron production. 2, François Arleo, Stephane Peigné 2 LAPTh Annecy & LLR Palaiseau 2 SUBATECH, Nantes 3 rd NeD/TURIC Workshop, 94.VI.24, Hersonissos, Crete

Outline Motivations Hadron suppression data in pa collisions E-loss interpretation of forward hadron suppression Motivations Forward hadron suppression in p A collisions Energy loss interpretation of suppression data Scaling properties of medium induced radiation Asymptotic parton Parton produced in medium The induced radiation spectrum Phenomenology References F. Arleo, S. Peigné JHEP 33 (23) 22 [22.434] F. Arleo, RK, S. Peigné, M. Rustamova JHEP 35(23)55 [34.9] S. Peigné, F. Arleo, RK arxiv:[42.67] S. Peigné, RK arxiv:[45.424]

A tool to study hot and dense matter Hadron suppression data in pa collisions E-loss interpretation of forward hadron suppression Study of hadron spectra w.r.t. scaled pp and Central/Peripheral ratios R AA/pA (y, p t ) = d 2 σ AA/pA dydp t N coll d 2 σ dydp t AA/pA ; R CP = N coll P d 2 σ dydp t AA/pA, C N coll C dσ dydp t AA/pA, P Suppression already seen in p(d)a data Quarkonia production (starting from SPS energies) Forward light hadron production at RHIC Dihadron correlations The proper interpretation is important Baseline for hot matter eect studies Initial state of fast nucleus and production mechanisms

Examples of suppression in RHIC dau data Hadron suppression data in pa collisions E-loss interpretation of forward hadron suppression Pions J/Ψ.8 R dau/pp (y).6.4.2 PHENIX s = 2 GeV -3-2 - 2 3 y Small-x part of parton distribution is probed from the target side

Examples of suppression in RHIC dau data Hadron suppression data in pa collisions E-loss interpretation of forward hadron suppression Two-pion correlations at forward rapidity, coincidence probability Small-x part of parton distribution is probed from the target side

Hadron suppression data in pa collisions E-loss interpretation of forward hadron suppression Interpretation of forward hadron suppression So far two reasonable interpretations exist: Saturation of gluon densities in nuclear target Smaller target parton densities at low x suppression [ Jalilian-Marian'4 ] Momentum transfer from target partons k t Q s few GeV dissociation of quarkonia [ Fujii Gelis Venugopalan'6 ] forward dijet decorrelation [ T.Lappi, H.Mantysaari'2 ]. Parton energy loss interpretation Due to induced gluon radiation projectile parton distribution has to be taken at higher x values where it is depleted Only qualitative explanations in some cases.

GavinMilana model of J/ψ suppression Hadron suppression data in pa collisions E-loss interpretation of forward hadron suppression First attempt to describe J/ψ suppression via E -loss [ Gavin Milana'92 ] Energy loss via the induced initial and nal state radiation and scaling (the average) as E E L M 2 allows for description of both Drell-Yan and J/ψ suppression at high x F in E866 ( s = 38.7 GeV) J/ψ {}}{ 2 2 ω di dω + }{{} Drell-Yan

Hadron suppression data in pa collisions E-loss interpretation of forward hadron suppression Forward di-jet suppression from energy loss [ Strikman, Vogelsang' ] Target rest frame: Back-to-back (peak) Uncorrelated (pedestal) Back2back fwd jets come from splitting of a parton with x Extra rescatterings in nuclear target lead to induced radiation higher x proj needed to produce a dijet with same kinematics Suppression is less for uncorrelated contribution (both nucleons can contribute in dau, smaller shift in x proj ) Qualitative explanation relying on importance of energy loss

Hadron suppression data in pa collisions E-loss interpretation of forward hadron suppression Forward di-jet suppression from energy loss [ Strikman, Vogelsang' ] Target rest frame: Back-to-back (peak) Uncorrelated (pedestal) Back-to-back with extra gluon Back2back fwd jets come from splitting of a parton with x Extra rescatterings in nuclear target lead to induced radiation higher x proj needed to produce a dijet with same kinematics Suppression is less for uncorrelated contribution (both nucleons can contribute in dau, smaller shift in x proj ) Qualitative explanation relying on importance of energy loss

Energy loss of asymptotic parton Asymptotic parton Parton born in medium Radiation formation time: t f = ω/k 2 t Small ω, t f < λ, L/λ Independent radiation at each scattering ω di dω = L L λ ω di dω L single λ α s Larger ω, λ t f L λµ 2 ω ω c µ2 L 2 λ t f = ω k 2(t t f ) = ω = λω t f /λµ 2 µ 2 Medium acts as eective scatt. centers, ω di dω L L t f (ω) ω di ωc dω single ω α s

Energy loss of asymptotic parton Asymptotic parton Parton born in medium Even larger ω ω c (Small medium L < λe/µ 2 ω c < E ) t f L Comes from interference of initial- and nal-state emissions Medium acts as a single scatt. center kt 2 L λ µ2, similar to Gunion-Bertch Dominant contribution to the E -loss E α s E ln k t 2 (L) Λ 2

Parton born in medium Asymptotic parton Parton born in medium Dierent setup: instantly produced parton radiates w/o medium ω di = ω di dω dω ω di L dω ω < ω c t f < L ω > ω c ind same as for asympt. charge t f L cancels out in the induced spectrum Left with radiation of kt 2 ω/l ω di dω α s ω E αω c α s µ 2 L 2 λ L=

Coherent vs incoherent E -loss Asymptotic parton Parton born in medium Initial/nal state energy loss Interference btw. initial and nal state emissions can be neglected prompt photons, Drell-Yan, weak bosons jets and hadrons produced at large angles Coherent energy loss (asymptotic parton) Comes from interference between IS and FS emission amplitudes Long formation times of induced radiation Color charge must be resolved in hard process Medium modications to E due to extra rescatterings induced radiation also scale as E [ Arleo, Peigné, Sami 2 ]

, the setup Working in target rest frame tag on nal energetic compact color object with Mt 2 ˆqL energetic parent parton suers single hard exchange qt 2 ˆqL multiple semihard l 2 t ˆqL qt 2 ω di dω derived in the opacity expansion [ Gyulassy,Levai,Vitev 2 ] Focus on the part of the induced spectrum which gives E E Implies induced radiation with t f L Purely Initial State and Final State radiation are aected by the medium only for t f L negligible Only interference terms contribute at t f L

, the setup Compact color object in a nal state: Same color representation for incoming and outgoing object Elastic scattering of a color charge (q or g ) tagged with q t ˆqL in the nal state g q q, 3 3 = 8 Dierent color representations Production of a dijet: q qg, 3 8 = 3 6 5 g gg, 8 8 = 8 a 8 s 27

Lowest order in opacity, same color representation q q and g g(q q) case: di x = α s dzd 2 l dxd 2 V (l) k t C R λ R π 2 x ω g /E energy fraction carried by the soft gluon. q t (or M t ) dependence enters via the nal state gluon emission vertex. The answer: q(g) q(g): g q q: x di dx = (2C R N c ) α ) s L ln ( + µ2 π λ g x 2 q 2 ) x di dx = N α s L c ln ( + µ2 π λ g x 2 Mt 2

All orders in opacity [ Peigné, Arleo, RK 42.67 ]

All orders in opacity For L λ q(g) q(g): g q q: x di dx = (2C R N c ) α s x di dx = N α s c π ln ) ( π ln + µ2 L λ g ln L λ g x 2 q 2 ) ( + µ2 L λ g ln L λ g x 2 M 2 t [ Peigné, Arleo, RK 42.67 ]

Lowest order in opacity, change of color representation q qg case. Model for a 2-jet production q t q t k t>> qt The production amplitude squared: + + + 2Re{ + + }

Lowest order in opacity, change of color representation q qg case. Model for a 2-jet production q t q t k t>> qt The production amplitude squared: + + + 2Re{ + + } st order in opacity: additional soft gluon additional soft scattering 2 possible arrangements, but LOTS of simplications

Lowest order in opacity, change of color representation q qg case. + + + 2Re{ + + } Focus on radiation with long formation times, t f t hard soft g emission in the amplitude from incoming q line and in the conjugate from outgoing q or g line q t l t rescattering couples to soft gluon in the amplitude

Lowest order in opacity, change of color representation q qg case. + + + 2Re{ + + } Focus on radiation with long formation times, t f t hard soft g emission in the amplitude from incoming q line and in the conjugate from outgoing g line q t l t rescattering couples to soft gluon in the amplitude Take N c non-planar graphs are suppressed ( N 2 ) c

Lowest order in opacity, change of color representation q qg case. + + + 2Re{ + + } Focus on radiation with long formation times, t f t hard soft g emission in the amplitude from incoming q line and in the conjugate from outgoing g line q t l t rescattering couples to soft gluon in the amplitude Take N c non-planar graphs are suppressed ( N 2 ) c 2Re{ + + + + } +2Re{ + + }

The spectrum [ Peigné, RK 45:424 ] Lowest order: di () x = [ + ( x h) 2 K 2 ] Nc α s dx (K x h q) 2 π q qg L λ g log ( µ 2 x 2 K 2 )

The spectrum [ Peigné, RK 45:424 ] All orders: x di dx = q qg x n= di (n) dx κ q qg ( ) N c α s q 2 = κ q qg log (L) π x 2 K 2 q qg (K x h q) 2 (K x h q) 2 + ( x h ) 2 K 2.

The spectrum [ Peigné, RK 45:424 ] All orders: x di dx = q qg x n= di (n) dx κ q qg ( ) N c α s q 2 = κ q qg log (L) π x 2 K 2 q qg (K x h q) 2 (K x h q) 2 + ( x h ) 2 K 2. For x h = /2 the spectrum coinsides with the result obtained in the saturation formalism (κ q qg = 4/5) [ Liou, Mueller 42.647 ] A conjecture guided by the outlined spectra [ ] x di ( ) α s q 2 dx = P R (C R + C R C t ) n π log (L) x 2 R K 2 Prefactor 5/3 for g gg case (checked by an explicit calculation, coincides with saturation result [ Mueller, private comm. ])

Model for heavy-quarkonium suppression Physical picture and assumptions Color neutralization happens on long time scales: t octet t hard Hadronization happens outside of the nucleus: t ψ L c c pair produced by gluon fusion Medium rescattering do not resolve the octet c c pair

Model for heavy-quarkonium suppression Energy shift [ Arleo Peigné 22.434 ] dσ ψ pa ( ) εmax E, s = A de dε P(ε, E q 2 ) dσψ pp de pp cross section tted from experimental data ( E + ε, s ) E dσψ pp de = dσψ pp dy ( 2M cosh y) n( s) s P(ɛ): quenching weight, scaling function of ˆω = ˆqL/M E Eective length L e is given by Glauber model, L pp =.5 fm ( ) part ˆq(L e L pp ) = N part A σbroad ψ µ 2 NA = ˆq ψ σ inel σ inel ρ

Procedure Motivations Fit ˆq from J/ψ E866 data in p W collisions: ˆq =.75 GeV 2 /fm 2 Predict J/ψ and Υ suppression for all nuclei and c.m. energies

Procedure Motivations Fit ˆq from J/ψ E866 data in p W collisions: ˆq =.75 GeV 2 /fm 2 Predict J/ψ and Υ suppression for all nuclei and c.m. energies.8.8 R W/Be (x F ).6 R Fe/Be (x F ).6.4.4.2 q =.75 GeV 2 /fm (fit).2 q =.75 GeV 2 /fm E866 s = 38.7 GeV E866 s = 38.7 GeV -.2.2.4.6.8 x F -.2.2.4.6.8 x F Fe/Be ratio well described, supporting the L dependence of the model

SPS Motivations.2 q =.75 GeV 2 /fm.2 R Pt/p (x F ).8.6.4.8.6.4 R Pt/p (x F ).2 NA3 s = 9.4 GeV NA3 s = 6.7 GeV (π - beam).2 R Pt/p (x F ).8.6.4.8.6.4 R Pt/p (x F ).2 NA3 s = 9.4 GeV (π - beam).2.4.6 x F NA3 s = 22.9 GeV (π - beam).2.4.6.8 x F Agreement when x F > x min (and even below) F Natural explanation of the dierent suppression in p A vs π A from n πp =.4 vs. n πp = 4.3.2

RHIC Motivations R dau (y).4.2 ˆq =.75 GeV 2 /fm d-au J/ψ s =.2 TeV.8.6.4.2 E. loss E. loss + EPS9 PHENIX -3-2 - 2 3 y Good agreement at all rapidity npdf eects may improve the agreement Smaller experimental uncertainties would help

Comparison with preliminary ALICE data R pa (y): good agreement despite large uncertainty on normalization

Summary Outlook An honest pqcd calculation of the induced spectrum. Neither initial nor nal state eect di /d ω and E have specic parametric dependence Heavy-quarkonium suppression predicted for wide range of s Good agreement with all existing data for J/ψ including rapidity (x F, p and centrality dependence Model in good agreement with LHC p Pb preliminary data The coherent energy loss taken alone underestimates suppression of ψ at the LHC. Application to forward light hadron production is foreseen.

A conjecture Motivations BACKUP

A conjecture Motivations Motivation for a conjecture: [ ] x di ( ) α s q 2 dx = P R (C R + C R C t ) n π log (L) x 2 R K 2 Color factors for radiation accompanying elastic R R 2T a R T a R = (T a R )2 + (T a R )2 + (T a R T a R )2 = C R + C R C t Logarithmic integration in k t : Compact object k t x K Constrained by the broadening k t ˆqL

LHC predictions BACKUP

LHC predictions R ppb (y).4.2 Υ and J/ψ suppression with error bands p-pb J/ψ s = 5 TeV R ppb (y).4.2 p-pb Υ s = 5 TeV.8.8.6.6.4 E. loss.4 E. loss.2 E. loss + EPS9.2 E. loss + EPS9-5 -4-3 -2-2 3 4 5 y -5-4 -3-2 - 2 3 4 5 y Weaker suppression for Υ as a consequence of the coherent E -loss scaling properties E M

LHC predictions.5 y = E. loss E. loss + saturation.5.5 y = 2.5 E. loss E. loss + saturation.5 R RpPb/pp (p T ).5.5 R RpPb/pp (p T ) R RpPb/pp (p T ).5.5 R RpPb/pp (p T ) Centrality class Centrality class 2 Centrality class Centrality class 2 R RpPb/pp (p T ).5.5 R RpPb/pp (p T ) R RpPb/pp (p T ).5.5 R RpPb/pp (p T ) Centrality class 3 5 p T (GeV) Centrality class 4 5 5 p T (GeV) Centrality class 3 5 p T (GeV) Centrality class 4 5 5 p T (GeV) Suppression expected up to p 34 GeV Possible enhancement in most central collisions

LHC predictions 2.5 ϒ LHC s = 5 TeV y= Centrality class 2 ϒ LHC s = 5 TeV y=2.5 Centrality class.5 R ppb/pp (p T ) R ppb/pp (p T ).5 E. loss E. loss + saturation 5 5 2 p T (GeV).5 E. loss E. loss + saturation 5 5 2 p T (GeV) Weaker suppression in the Υ channel, which however extend to slightly larger p

Comparison with preliminary ALICE data No pp data at 5 TeV needed smaller uncertainty Predictions with only npdf underestimate the suppression

Comparison with preliminary ALICE data R FB (p ): good agreement, better agreement with energy loss supplemented by shadowing

Υ suppression at 7 TeV R ppb (y).4.2 p-pb s = 5 TeV.8.6.4.2 E. loss J/ψ E. loss Υ -5-4 -3-2 - 2 3 4 5 y Weaker suppression for Υ as a consequence of the coherent E -loss scaling properties E M

Comparison with preliminary ALICE data No pp data at 5 TeV needed smaller uncertainty Predictions with only npdf underestimate the suppression

E866 p t dependence R pfe/pbe (p T ) R pfe/pbe (p T ) E866 s = 38.7 GeV E. loss + broad. Broad. only.4.4.2.8.6.4.2.2.8.6.4.2 Fe / Be x F =.38 Fe / Be x F =.48 2 4 p T (GeV) W / Be x F =.38 W / Be x F =.48 2 4 6 p T (GeV) Good description of R pa/pb for p t 3 GeV Possible reasons for discrepancy at p t > 3 GeV: Model calculations at xed x F rather than averaging p t dependence from t to E789 pp data at x F =..2.8.6.4.2.2.8.6.4.2 R pw/pbe (p T ) R pw/pbe (p T )

Backup - HERA-B.4.2 R W/C (x F ).8.6.4.2 q =.75 GeV 2 /fm HERA-B s = 4.5 GeV -.4 -.3 -.2 -...2 x F Also good agreement in the nuclear fragmentation region (x F < ) Enhancement predicted at very negative x F

Backup L e Motivations vs centrality class Np min ; Np max Glauber, RHIC P(class) P(N ) N c L Au class Np min ; Np max Glauber, LHC P(class) P(N ) N c L Pb A ; 97.28 5.9 2.87 2; 28.246 4.8 3.46 B 8; 2.24.9 9.62 2 9; 2.25.5 9.55 C 5; 8.23 7. 7.7 3 5; 8.25 6.5 6.29 D 2; 4.29 3.6 3.84 4 ; 5.428 2.4 3.39

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 on plots for τ form =.3 fm ( ) npdf / saturation eects when Q 2 s m 2 c Use npdf's or parameterized suppression from CGC calculation [ Fujii Gelis Venugopalan 26 ] R pa = R E.loss pa (ˆq) G npdf A (x 2,M ) G p(x 2,M ) or R pa = R E.loss pa (ˆq) Ssat A Sp sat (Qs) (Qs) No additional parameter: Q 2 s (x, L) = ˆq(x)L [ Mueller 999 ] Q 2 s (x = 2 ) =..4 GeV 2 consistent with ts to DIS data [ Albacete et al AAMQS 2 ]

Quenching weight, P(ɛ q 2 ) Radiation with t f (ω i ) ω i / q 2 L Self-consistency constraint ω ω 2... ω { n di (ɛ) } P(ɛ) dω exp dω di dω Broadening. q 2 = ˆqL ˆq related to gluon distribution in a target nucleon [ BDMPS 997 ] ˆq(x) = 4π2 α s C R N 2 c ρ xg(x, ˆqL) ˆq ( 2 /x ɛ ).3 Typical value for x depends on t hard E M M /(m px 2 ): t hard L x = x (m N L) ; ˆq(x) constant t hard > L x x 2 ; ˆq(x) x 2 G(x 2 ) ˆq only free parameter of the model

p dependence Most general case. The p t broadening: p = ˆqL e dσ ψ pa = A de d 2 p ε ϕ P(ε, E) dσ ψ pp de d 2 p (E+ε, p p ) Parametrization consistent with pp experimental data dσ ψ ( ) pp p 2 m ( n dy d 2 p p 2 2M +p2 s cosh y) N µ(p ) ν(y, p ) For P(ε, E) peaked at small ε R ψ pa (y, p ) R loss pa (y, p ) R broad pa (p )

p dependence Most general case. The p t broadening: p = ˆqL e dσ ψ pa = A de d 2 p ε ϕ P(ε, E) dσ ψ pp de d 2 p (E+ε, p p ) R ψ pa (y, p ) R loss pa (y, p ) R broad pa (y, p ) Overall depletion due to parton energy loss Possible Cronin peak due to momentum broadening RpA broad (y, p ) µ( p p ) ν(e, p p ) ; ϕ µ(p ) ν(e,p ) [ ] E ν(e+ε,p P(ε, E) ) E+ε ε ν(e,p ) R loss pa (y, p )

Centrality Motivations Centrality dependence is given by L e Experimental situation [ PHENIX 8, ALICE 2 ] Centrality selection via multiplicity in target fragmentation region NA ch NA ch part is strongly correlated with NA The model L e = L pp + N part A ψ σ inel ρ Glauber model estimates of N part A ψ with constraints on N part A [ Arleo, RK, Peigné, Rustamova 34.9 ]

RHIC: p t and centrality dependence 2 y=[-2.2;-.2] E. loss E. loss + saturation 2 R dau/pp (p T ).5.5.5.5 R dau/pp (p T ) Centrality -2% Centrality 2-4%.5.5 R dau/pp (p T ).5.5 R dau/pp (p T ) Centrality 4-6% 2 4 6 p T (GeV) Centrality 6-88% 2 4 6 8 p T (GeV) Good description of p and centrality dependence at y =.7

RHIC: p t and centrality dependence 2 y=[-.35;.35] E. loss E. loss + saturation 2 R dau/pp (p T ).5.5.5.5 R dau/pp (p T ) Centrality -2% Centrality 2-4%.5.5 R dau/pp (p T ).5.5 R dau/pp (p T ) Centrality 4-6% 2 4 6 p T (GeV) Centrality 6-88% 2 4 6 8 p T (GeV) Good description of p and centrality dependence at y =

RHIC: p t and centrality dependence 2 y=[.2;2.2] E. loss E. loss + saturation 2 R dau/pp (p T ).5.5.5.5 R dau/pp (p T ) Centrality -2% Centrality 2-4%.5.5 R dau/pp (p T ).5.5 R dau/pp (p T ) Centrality 4-6% 2 4 6 p T (GeV) Centrality 6-88% 2 4 6 8 p T (GeV) Good description of p and centrality dependence at y =.7