Perturbative origin of azimuthal anisotropy in nuclear collisions Amir H. Rezaeian Uiversidad Tecnica Federico Santa Maria, Valparaiso Sixth International Conference on Perspectives in Hadronic Physics ICTP 8 Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 1 / 3
Non-centeral heavy-ion collisions and elliptic flow Observables will become azimuthally dependent if they are sensitive to the density and size of system A good test of many features of QGP Z Y X Y φ ψ X b E d3 N i = 1 ( d N i d 3 π d dy 1 + n=1 v n i cos(n(φ ψ))) v = cos((φ ψ)) φ = tan 1 p y /p x Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 / 3
Outstanding questions yet at RHIC: Which microscopic interaction mechanism is responsible for the large observed elliptic flow? 1: What is the origin of Fast thermalization. : Why Hydrodynamics with η =. 3: Initial conditions for Hydro (τ, T, s) are yet to be understood. 4: Elliptic flow at non-zero rapidity and for more prepherial need to be described. Hydrodynamics breakdown for more prepherial collisions. Do longitudinal boost invariance and local thermal equilibrium breakdown away from midrapidity? 5: What is the fate of elliptic flow at high. 6: Need to understand scaling properites of azimuthal anisotropy: mass ordering, eccentricity scaling, valence quark number scaling (where are gluons?)... 7: v for direct photon. Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 3 / 3
Azimuthal asymmetry and color dipole orientation f 1 ( s, r) qq 1 α r α s s f 1 ( s, r) > f ( s, r) qq qq f ( s, r) qq 1 α r α The main idea: An azimuthal asymmetry appears due to dependence of the interaction of a dipole on its orientation. Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 4 / 3
Azimuthal asymmetry and dipole orientation A toy model: two-gluon exchange An azimuthal asymmetry appears due to dependence of the interaction of a dipole on its orientation. Imf q qq ( s, r) = d q d q α s (q )α s (q ) 9π (q + µ )(q + µ ) [e i q ( s+ r/) e i q ( s r/)] [ e i q ( s+ r/) ] i q ( s r/) e ( = 8α s [K µ 9 s + r ) ( K µ s r )] This expression explicitly exposes a correlation between r and s: the amplitude vanishes when s r =. Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 5 / 3
Color dipole orientation Kopeliovich, Pirner, A.H.R., Schmidt, PRD 77, 3411 (8) Imf N qq( s, r, β) = 1 d q d q 1π q q α s F(x, q, q )e i s ( q q ) (e i q rβ e i q r(1 β)) ( ) e i q rβ e i q r(1 β) where α s = α s (q )α s (q ) q q β 1 β r(1 β) rβ F(x, q) = F(x, q, q = q ). σq q N (r) = d s Imfq q N ( s, r) = 4π d q 3 q 4 (1 e i q. r )α s (q )F(x, q). (1) Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 6 / 3 r
Color dipole orientation The forward slope of the differential cross section of dipole-nucleon scattering, B ( qq)n el (r) = 1 d s s Imf N qq ( s, r). () σn qq (r) The slope for small-dipole-proton elastic scattering was measured in diffractive electroproduction of ρ-mesons at high Q at HERA. The measured slope, B ( qq)n el (r) 5 GeV, agrees with the expected value B ( qq)n el (r) B pp el /. 18 B el (GeV - ) 16 14 1 1 1 1 3 s (GeV) Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 7 / 3
Color dipole orientation Generalized unintegrated gluon density: α s F(x, q, q ) = 3σ 16π q q R (x)e 1 8 R (x)(q +q ) e 1 R N( q q ), σ = 3.3 mb, R (x) =.4 fm (x/x ).144 with x = 3.4 1 4 Assumption: The Pomeron-proton form factor F p IP (k T ) = exp( k T R N /), so the slope of the pp elastic differential cross section is B pp el = RN + α IP ln(s/s ). Imf N qq( s, r, x, β) = { σ exp [ 8πB el [ exp r R ] [ s + r(1 β)] + exp [ B el ]} [ s + (1/ β) r] B el, ] ( s rβ) B el where we defined B el = R N + R (x)/8. Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 8 / 3
Color dipole orientation α r q γ α = (β = 1/) s = s = fm 1 α Im f N qq 1 g 3 r [fm] 4 - δ 1.5 4-6 6 q q β 1 β r r (1 β) β β=1/( α) r α α = 1 (β = 1) 3.69 3.69 3.688 3.686 3.684 4 6 s =..1-4 s = fm - 6 Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 9 / 3
The transverse momentum distribution of photon bremsstrahlung from interaction of quark with a target t( nucleon: t=n, nucleus t=a) Kopeliovich, A.H.R., Schmidt, arxiv:71.89, to appear in NPA dσ qt γx (b, p, α) d(lnα)d d b = 1 (π) in,f d r 1 d r e i.( r 1 r ) φ γq (α, r 1)φ γq (α, r )F t ( b, α r 1, α r, x), where α = p γ + /p q + and F t ( b, α r 1, α r, x) which is a linear combination of qq dipole partial amplitudes on a target t at impact parameter b, with F t ( b, α r 1, α r, x) = Imf t q q ( b, α r 1, x) + Imf t q q ( b, α r, x) Imfq q(b, r) A = 1 exp[ σq q(r) N = Imf t q q ( b, α( r 1 r ), x), d s Imf N q q( s, r)t A ( b + s)] d b Imf N q q ( b, r) Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 1 / 3
Dilepton spectrum in 8 GeV pp Kopeliovich, A.H.R, Pirner, Schmidt, PLB 653, 1 (7) Ed 3 σ/d 3 P [pb/gev ] 1 1-1 1-1 -3 x F =.63, M=5.7 GeV E866 Data GBW GBW-DGLAP GBW-DGLAP-Primordial Ed 3 σ/d 3 P [pb/gev ] 1 1-1 1 - x F =.63, M=4.8 GeV E866 Data GBW GBW-DGLAP GBW-DGLAP-Primordial 1-4 1 3 4 5 (GeV) 1-3 1 3 4 5 (GeV) constant primordial momentum k =.4GeV is incorporated within the GBW-DGLAP dipole model (solid line) Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 11 / 3
Direct photon productions at RHIC and Tevatron for pp Ed 3 σ/d 3 P [pb/gev ] 1 4 1 3 1 1 1 1 RHIC data GBW GBW-DGLAP d σ/d dη [pb/gev] 1 4 1 3 1 1 1 1 CDF data GBW GBW-DGLAP 1-1 1-4 6 8 1 1 14 16 18 4 (GeV) 1-1 1-4 6 8 1 1 (GeV) Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 1 / 3
Direct photon productions at RHIC and LHC AHR et al. arxiv: 77.4 Ed 3 σ/d 3 P [pb/gev ] 1 4 1 3 1 1 1 1 1-1 PHENIX, s = GeV s = GeV d σ/d dη [pb/gev] 1 5 1 4 1 3 1 1 1 1 1-1 CDF, s = 1.8 TeV s = 1.8 TeV s = 5.5 TeV s = 14 TeV 1-4 6 8 1 1 14 16 18 4 (GeV) 1-4 6 8 1 1 14 16 18 (GeV) Neither K-factor, nor higher twist corrections, no quark-to-photon fragmentation function are to be added. Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 13 / 3
Direct photon productions and scaling ( s ) n d σ/d dη 1 18 1 15 1 1 RHIC: s = GeV CDF: s = 1.8 TeV LHC: s = 5.5 TeV LHC: s = 14 TeV 1 9.5.1.15..5 / s d σ/d dη (s/s ) n/ F (x T ), prediction: n=3. Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 14 / 3
Direct photon v for qn collisions.4.3. b =.6 fm b = 1 fm Solid: s = GeV Dashed: s = 5.5 TeV v qn.1 -.1 -. b =.4 fm b =. fm.5 1 1.5.5 3 (GeV) Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 15 / 3
Direct photon v for qa collisions Imf A q q (b, r) = 1 exp[ d s Imf N q q ( s, r)t A( b + s)]. Sources of azimuthal anisotropy: rescatterings and shape of the system T(b) T (b) 1,5 T (b) 1,5 -,5 1 3 4 5 6 7 8 9 1 11 b[fm] Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 16 / 3
Prompt photon v for qa collisions at RHIC.1.8 Solid: WS Profile Dashed: HS Profile v qa.4 -.4 b = 6 fm b = 7 fm b = 8 fm -.8 b = 7 fm -.1.5 1 1.5.5 3 3.5 4 (GeV) Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 17 / 3
Prompt photon v for qa collisions at RHIC: the uncertainty of nuclear profile.15.1 HS Profile WS Profile v qa.5 -.5 b = 7 fm b = 5 fm -.1.5 1 1.5.5 3 3.5 4 (GeV) Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 18 / 3
Kopeliovich, A.H.R., Schmidt, arxiv:71.89, to appear in NPA v qn.4.3..1 -.1 -. b =.6 fm b =.4 fm b =. fm b = 1 fm Solid: s = GeV Dashed: s = 5.5 TeV v qa.1.8.4 -.4 -.8 b = 6 fm b = 7 fm b = 8 fm Solid: WS Profile Dashed: HS Profile b = 7 fm v pa.4 -.4.5 1 1.5.5 3 (GeV) b = 6 fm b = 7 fm v AA -.1.5 1 1.5.5 (GeV) 3 3.5 4.1.5 -.5 -.1 B = 9.4 fm B = 7 fm -.8 -.1 b = 8 fm -.15 -. -.5.5 1 1.5.5 3 3.5.5 1 1.5.5 3 3.5 Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 19 / 3 B = 13 fm
On the sign of v v qn.4.3..1 -.1 -. b =.6 fm b =.4 fm b =. fm β=1/( α) b = 1 fm Solid: s = GeV Dashed: s = 5.5 TeV v qn.5..15.1.5 b =.6 fm b =.4 fm b =. fm b = 1 fm β=1/ Solid: s = GeV Dashed: s = 5.5 TeV.1.8.4.5 1 1.5.5 3 (GeV) Solid: WS Profile Dashed: HS Profile..4.6.8 1 1. 1.4 1.6 (GeV).8.7.6.5 b = 7 fm Solid: WS Profile Dashed: HS Profile v qa -.4 -.8 b = 6 fm b = 7 fm b = 8 fm b = 7 fm v qa.4.3..1 b = 8 fm b = 7 fm -.1.5 1 1.5.5 3 3.5 4 (GeV) b = 6 fm.5 1 1.5.5 3 3.5 (GeV) Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 / 3
Direct photon v at RHIC Prompt Photons bremsstrahlung Thermal Photons T v γ Turbide et al, PRL 96, 333 (6).8 N-N + jet-frag. direct γ.6 direct γ (no E-loss).4. -. -.4 3 4 5 6 7 8 - % -4 % 4-6 % 3 4 5 6 7 8 3 4 5 6 7 8 (GeV/c) v AA Kopeliovich, AHR, Schmidt, arxiv:71.89.1 B = 9.4 fm.5 -.5 -.1 -.15 -. -.5 B = 13 fm B = 7 fm.5 1 1.5.5 3 3.5 (GeV).4 3%-- 4% Au+Au @ s 1/ = GeV NN. 4%-- 5% Jet Photons conv T Chatterjee et al, PRL 96, 3 (6) v. -. -.4 jet-photon conv total -.6 initial production jet fragment -.8 4 6 8 1 (GeV/c) 6 8 1 (GeV/c) Liu and Fries, arxiv:81.453 Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 1 / 3
Direct photon Elliptic flow at RHIC: published data R v (inclusive γ) - v (b.g.), v (inclusive γ), v (b.g.).5 -%..15.1.5 -.5.5..15.1.5 -.5 4-6% -4% Au+Au GeV -9% v (b.g.) v (inclusive γ) R v (inclusive γ) - v (b.g.) 4 6 4 6 (GeV/c) PHENIX collaboration, PRL. 96 (6) 33 Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 / 3
Direct photon Elliptic flow at RHIC: preliminary data Direct photon v.5.4.3..1 - -.1 -. -.3 centrality - % s NN =GeV Au+Au collisions -.4 PHENIX preliminary -.5 1 3 4 5 6 7 8 9 1 [GeV/c] Direct photon v.5.4.3..1 - -.1 -. -.3 centrality - 4 % s NN =GeV Au+Au collisions -.4 PHENIX preliminary -.5 1 3 4 5 6 7 8 9 1 [GeV/c] Direct photon v.5.4.3..1 - -.1 -. -.3 centrality 4-6 % s NN =GeV Au+Au collisions Direct photon v -. -.3 -.4 -.4 PHENIX preliminary PHENIX preliminary -.5 1 3 4 5 6 7 p 8 T [GeV/c] 9 1 -.5 1 3 4 5 6 7 p 8 T [GeV/c] 9 1 Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 3 / 3.5.4.3..1 - -.1 centrality - 9 % s NN =GeV Au+Au collisions
Direct photon at RHIC: Cronin effect and suppression R da ( ) R da ( ) 3.5 1.5 1.5 Isospin + Cronin (Au) d+au Cronin+Shadowing d+au Cronin+Shadowing+ΔE(IS) Isospin + Cronin (Cu) d+cu Cronin+Shadowing d+cu Cronin+Shadowing+ΔE(IS) d+au preliminary, Min.bias 5 1 15 [GeV] 3 Cold nuclear Isospin + Cronin (Au).5 matter d+au Cronin+Shadowing 1.5 1.5 Cold nuclear matter Minimum bias s 1/ = GeV Minimum bias s 1/ = 6.4 GeV d+au Cronin+Shadowing+ΔE(IS) Isospin + Cronin (Cu) d+cu Cronin+Shadowing d+cu Cronin+Shadowing+ΔE(IS) 5 1 15 [GeV] R AA ( ) R AA ( ) 3.5 1.5 1.5 Au+Au Cronin+Shadowing Au+Au Cronin+Shadowing+ΔE(IS) Cu+Cu Cronin+Shadowing Cu+Cu Cronin+Shadowing+ΔE(IS) R AA -1% preliminary Au R AA -1% preliminary Au (fit) 5 1 15 [GeV] 3.5 s 1/ = 6.4 GeV Au+Au Cronin+Shadowing dn g /dy = 8 (Au) Au+Au Cronin+Shadowing+ΔE(IS) 55 (Cu) Cu+Cu Cronin+Shadowing 1.5 1.5 s 1/ = GeV dn g /dy = 115 (Au) 37 (Cu) Cu+Cu Cronin+Shadowing+ΔE(IS) R CP -1%/3-6% preliminary Au 5 1 15 [GeV] The contribution of the final-state photon production at < 5 GeV is limited to 35%, and at high transverse momenta, the modification of the direct photon cross section is dominated by initial-state cold nuclear matter effects. Vitev, et al., arxiv:84.385 Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 4 / 3
Pion v at RHIC in d+au collision dσ h pa d = K i,j,k,l F i/p F j/a d ˆσ dˆt (ij kl) Dh k ( F i/p = f i/p xi, Q ) () dn i ( d (x i, b) and F j/a = T A (b) f j/p xj, Q ) dnj k it d (x j, b). k jt q A G G q A Johnson, Kopeliovich and Tarasov, PRC 63 (1) 353 dn i d = 1 [ k it (π) d r 1 d r e i k T ( r 1 r ) k T σ N qq( r 1 r, x) T A (b) π e 1 (r 1 +r ) k T ] [ e 1 σn qq ( r1 r,x) T A(b) ] d s Imf N q q( s, r 1 r, x)t A ( b + s) Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 5 / 3
Hadron production from SPS to RHIC energies Ed 3 σ/d 3 P [mb/gev ] 1 1-4 s = GeV, π Data, p+p Data, d+au min bias EKS <k T > = 3 GeV Ed 3 σ/d 3 P [mb/gev ] 1 1-4 1-8 pp π + X Data E lab = 8 GeV Data E lab = 4 GeV Data E lab = 3 GeV <k T > = 3 GeV 1-8 5 1 15 (GeV) 4 6 8 1 [GeV] Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 6 / 3
Cronin effect at RHIC AHR, et al.(preliminary results) R dau 1.8 1.6 1.4 1. 1 s = GeV, dau π X RHIC Data (min bias) EKS HKM HIJING-b <k T > = 3 GeV R dau 1.8 1.6 1.4 1. 1 s = GeV, dau π X RHIC Data (min bias) σ gg = 9/4 σ qq σ gg = σ qq <k T > = 3 GeV, EKS R dau 1.8 1.6 1.4 1. 1 s = GeV, dau RHIC Data (min bias) <k T > = 3 GeV <k T > = GeV EKS π X.8.8.8.6.6.6.4 4 6 8 1 [GeV].4 4 6 8 1 [GeV].4 4 6 8 1 [GeV] Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 7 / 3
pion v for d + Au collision v..1 b = 7 fm s = GeV, dau π X <k T > = 3 GeV, EKS b = 8 fm v.4.3. s = GeV, dau π X HKM, <k T > = 3 GeV HIJING-b, <k T > = 3 GeV EKS, <k T > = 3 GeV EKS, <k T > = GeV EKS, <k T > = GeV b = 6 fm b = 9 fm.1 1.5.5 3 3.5 4 4.5 5 5.5 [GeV] 3 4 5 [GeV] The bigger the cronin effect, the bigger v for dau collisions Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 8 / 3
Summary and outlook We introduced dipole orientation which satisfies all the imposed boundary consitions. The developed theoretical tools can be applied to the calculation of the azimuthal asymmetry in DIS and in Drell-Yan reactions on a proton, as well as to the production of direct photons and Drell-Yan pairs in proton-nucleus and heavy ion collisions. We have computed the azimuthal asymmetry of direct photon originates from primary hard scatterings between partons. This can be accounted for by the color dipole orientation which is sensitive to the rapid change of the nuclear profile. We show that the direct photon elliptic anisotropy v coming from this mechanism changes sign and becomes negative for peripheral collisions, albeit it is quite small for nuclear collisions at the RHIC energy. Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 9 / 3
Dipole parametrizations Golec-Biernat, Wusthoft (GBW) 1999: σ q q (x, r) = σ (1 e r /R ), it does not match with QCD evolution DGLAP at large value of Q. This failure can be clearly seen in the energy dependence of σ γ p tot for Q > GeV, where the the model predictions are below the data. GBW couple to DGLAP, Bartels et al : ( σ q q (x, r) = σ (1 exp π r α s (µ )xg(x, µ )) ), 3σ where the scale µ is related to the dipole size by xg(x, µ ) ln µ = α s(µ ) π µ = C r + µ. 1 x dzp gg (z) x z g(x z, µ ). Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 3 / 3
Direct photon v for AA collisions v A 1 A (B, ) = «R R dφ d b cos(φ) cos(θ 1 ) dσγ (pa 1 γx ) dx F d d T b A ( b ) + cos(θ ) dσγ (pa γx ) 1 dx F d d T b A1 ( b 1 ) «, R R dφ d dσ γ (pa1 γx ) b dx F d d T b A ( b ) + dσγ (pa γx ) 1 dx F d d T b A1 ( b 1 ) Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 31 / 3
puzzel #, high problem Direct photon cross-section (pp γx) η <.9, s = 1.8 TeV conversions CES-CPR NLO QCD CTEQ5M, µ= statistical errors only We find that the shape of the cross section as a function of is poorly described by next-to-leading-order QCD predictions, but agrees with previous CDF measurements...cdf collaboration, PRD 7 (4) 748 Amir H. Rezaeian (USM) Perturbative origin of azimuthal anisotropy ICTP 8 3 / 3