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Hadronization at high pT: Recombination and Scaling Rudolph C. Hwa University of Oregon Heavy-Ion Collisions McGill, June 24-28, 2003 Outline High pT in AA collisions: p/p anomaly Fragmentation versus Recombination Scaling in centrality and energy Hadron production at high pT Fractional energy loss Conclusion 2 Hadronization in heavy-ion collision rare dominant dominant rare before after p,n p,n A A q, g q, g hard collision calculable in pQCD 3 Quark fragmentation q In vacuum e+ e- q q p phenomenological fragmentation function D p /q(z) not calculable momentum fraction z<1 In medium q p fragmentation function energy loss modified XNWang, XFGuo, NPA696, 788 (2001) 4 If hadronization in nuclear medium is by quark fragmentation, then the p/p ratio R p/p = ( q p ) / ( q p ) in AA should be about the same as R p/p in pp, since • nuclear effects on quarks cancel in the ratio • fragmentation into p vs p has to do with the masses and the quark contents of the hadrons, so • one would expect R p/p to be small in both cases. But that is not the case: R p/p ~ 1 at pT ~ 3-4 GeV/c in Au-Au at RHIC 5 PHENIX PRL 88, 24301(2002) central peripheral 6 The black box of fragmentation q 1 p z A QCD process from quark to pion, not calculable in pQCD Momentum fraction z < 1 Dp/q Phenomenological fragmentation function z 1 7 Let’s look inside the black box of fragmentation. q 1 p z fragmentation gluon radiation quark pair creation Although not calculable in pQCD (especially when Q2 gets low), gluon radiation and quark-pair creation and subsequent hadronization nevertheless take place to form pions and other hadrons. 8 Drawing a smaller circle Let’s look inside the black box of fragmentation q x1 x2 p 1 z recombination z = x1 +x2 , x1,2 < z < In AA collision 1 q x1 x2 p p X X X p One can adopt the view that all hadrons are formed by recombination. 9 Coalescence Dover,Heinz,Schnedermann,Zimanyi, PRC44,1636(1991) Nuclear physics at intermediate energy or higher (AGS) p + n d at low relative momentum n + , S + S, L + L H dibaryons Input: thermal distribution Output: yields, no momentum distributions Recombination Das,Hwa, PL68B,459(1977); Hwa, PRD22,1593(1980). Particle physics at high energy in p + p p + anything u + d p+ , d + s K-, … Input: parton distributions in proton Output: meson distributions at large pL (or large xF) Now, both models generalized to particle production at high pT in AA collisions at RHIC energies. 10 In recombination/coalescence approaches Fries,Meuller,Nonaka,Bass PRL 90,202303 (2003) Greco, Ko, Levai, PRL 90, 202302 (2003) Inputs: soft + hard components Soft: F(pT ) exp( - b pT ) Hard: F(pT ) ( 1 + pT /p0 ) -n It is claimed that h+h recombination is not important h+h: p1T -n p2T -n ~ (pT/2)-n (pT/2)-n ~ pT-2n « pT-n s+s: exp[- b (p1T+p2T )] ~ exp( - b pT ) Quark fragmentation is still important at very high pT q(p1T ) h(z p1T) : (p1T )-n (z p1T)-n ~ p1T -n Frag > Recom at high pT Assumption: piT ~ pT/2 p1T Pion recombination function allows pT p2T p1T » p2T p1T then the result may be viewed as quark fragmentation pT p2T 11 Crucial issue in recombination model: Input Quark Distributions Soft: thermal distr. (hydrodynam) Quark Distr. Hadron Distr. Hard: pQCD (energy loss) hadronization evolution Our approach (tests Recomb only, w/o free parameters) p q, q qqq p Hwa, CBYang, PRC67,034902(2003) 12 [HY-I] It is easy to get p/p ~ 1 in the recombination model Fq Fq x2 x1 x2 x3 x1 pion proton quark momenta add 13 The results (2): Central p0 SPS RHIC 130 RHIC 200 • Slow increase of power- law slopes with sqrt(s) 14 The results (3): pp vs AuAu (peripheral & central) p0 from PHENIX pp @ 200 GeV • Peripheral: (Hisa Torii's talk) • Central: 70-80% PERIPHERAL 0-10% CENTRAL Ncoll =12.3 ±4.0 Ncoll =975±94 • Consistent with Large suppression (increasing with pT) Ncoll scaling above pT~1 GeV/c compared15 to scaled pp. The results (1): High-pT p0 spectra • Spectra up to pT~10 GeV/c • 30 Million events analyzed. “ min. bias” trigger, |z_vtx| < 30 cm 16 Min. bias, most central & periph. Scaling (in centrality and energy) Npart N pT z scale change K (s, N) 1 dNp (z) A(N) 2p pT dpT A(N) normalization d K(s, N) K(s,N) change dN (z) pT dpT d peripheral central pT z 17 Scaling distribution for all centralities and all energies Hwa, CBYang, PRL 90, 212301 (2003) [HY-II] 18 K(s,N) is normalized to 1GeV at s=200GeV, N=350. Ncoll = 0.44N1.33 19 KNO scaling of multiplicity distribution variable rescaling normalization rescaling 20 KNO scaling of nch in e+e- annihilation 5 GeV 34 GeV 21 Lepton-proton scattering p np np 22 Actually, (z) is only analogous to KNO scaling function. The KNO-type scaling function is Y(u). z pT u z pT HY-II 23 To have a universal curve raises a question: QGP is supposed to give a different nuclear suppression effect from that of the normal nucleus. Peripheral (small Npart) cold, uncompressed Central (large Npart) hot, dense (perhaps QGP) A universal scaling curve (z) suggests that there does not exist a drastic change of suppression effect ---- at energies up to s = 200 GeV Implications: either (1): no QGP yet or (2): no drastic change of suppression effect i.e., large pT is not a good region to look for the signature of QGP. 24 Is there a universality in fragments in intermediate energy nuclear collisions? 25 Outline High pT in AA collisions: p/p anomaly Fragmentation versus Recombination Scaling in centrality and energy Hadron production at high pT Fractional energy loss Conclusion 26 Outline High pT in AA collisions: p/p anomaly -- goal Fragmentation versus Recombination -- vehicle Scaling in centrality and energy -- avenue Hadron production at high pT Fractional energy loss Conclusion 27 Outline High pT in AA collisions: p/p anomaly -- goal Fragmentation versus Recombination -- vehicle Scaling in centrality and energy -- avenue Hadron production at high pT -- DRIVE ON Fractional energy loss Conclusion 28 Recombination model d 3 Np 3 3 d p1 d p2 E 3 F ( p1 , p2 )Rp (p1, p2 , p) Hwa(II) (1980) d p E1 E2 Apply now to high transverse momentum Integrate out y (at midrapidity) and f (collinear) and change to scaling variable z HY-I(03) dN p dz1 dz2 z1 z 2 F(z1 , z 2 )Rp (z1, z2 , z) zdz Parton distributions Recombination function Should be for partons just before Should depend on the recombination, thus after hydro- wave function of the expansion and Q2 evolution. pion in terms of the constituent quarks 29 Recombination model d 3 Np 3 3 d p1 d p2 E 3 F ( p1 , p2 )Rp (p1, p2 , p) Hwa(II) (1980) d p E1 E2 Apply now to high transverse momentum Integrate out y (at midrapidity) and f (collinear) and change to scaling variable z HY-I(03) dN p dz1 dz2 z1 z 2 F(z1 , z 2 )Rp (z1, z2 , z) zdz Since q and q are copious in AA collisions, Recombination assume function F(z , z ) F (z )F (z ) 1 2 q 1 q 2 Further, since / p ~ 0.7const, assume p 1 (z1 + z 2 z) z Fq (z) (0.7)1/ 3 Fq (z) 30 Recombination function Rp(z1, z2,z) The wave function of hadrons in terms of momentum fractions can best be determined in the Valon Model. Hwa(I) PRD22,759(80) Proton: use parton distributions from HY, PRC66,025204(02) deep inelastic scattering CTEQ4LQ, http://zebu.uoregon.edu~parton p u U u U D Pion: use Drell-Yan production data in pp collision Sutton,Martin,Roberts,Stirling,PRD45,2349(1992) U p D GD/p(x) e+ U e- p x U 0 1 31 D Valon distributions are independent of the virtuality Q HY (02) 32 Recombination function (time reversal of valon distribution) 1 1 Rp (z1 , z 2 , z ) 2 Gp (x1 , x2 ) 2 (x1 + x2 1) z z 1 xi z i / z (z1 + z 2 z) z It is as likely for x1 >> x2 as for x1 ~ x2 . Recall dN p dz1 dz2 z1 z 2 Fq (z1 )Fq (z 2 )Rp (z1 , z 2 , z) zdz From the observed pion distribution, Fq(z) can be determined without assumptions about their origin. Fq (z) 15(z 2 + 0.47z + 0.72) 4.25 33 Quark distribution (just before hadronization) ~ exponential HY-III(03) Power-law: ~z-8.5 34 This quark distribution Fq(z) can then be used to calculate qqq recombination to form proton dN p dz1dz 2 dz 3z1 z 2 z3 F(z1, z2 , z 3 )Rp (z1, z2 , z 3 , z) zdz F(z1, z 2, z3 ) Fu (z1 )Fu (z2 )Fd (z 3 ) Proton recombination function valon distribution of proton HY(02) Rp (z1, z2 ,z3 ,z) R0 z 2 Gp (x1 ,x 2 , x3 ) Gp (x1 ,x 2 ,x3 ) g(x1x2 ) x3 b (x1 + x2 + x3 1) 1.755, b 1.05 35 In the invariant form for dN p there is no dependence on zdz the proton mass: the formalism is valid only for pT values where the mass effect is insignificant. We take it to correspond to z 2 To extend the calculation to z<2, one would have to consider recombination in the rest frame by Lorentz boost, assuming some form of the wave function of the proton. Using the relativistic formalism we now can calculate the p/p ratio. dN p / zdz Rp / p (z) 36 HY-I(03) PHENIX (preliminary) pT in GeV/c 37 String fragmentation cannot explain the large p/p ratio. Baryon junction was suggested. (There are basic questions about strings for AA collisions.) In the recombination picture, no exotic mechanism is needed. Just add the quark momenta to form proton. 38 Color strings e+e- annihilation e+ e- pp collision p p AA collision A A 39 Energy loss Centrality dependence of quark distribution Fq Fq(x,N) Fq(z) scaling Fq Suppression F(x,N) < F(x,2) Shift F(x-X,N) = F(x,2) N=2 N x-X x · In pQCD, calculate quench factor: medium effect vs vacuum (N=2) X x Baier,Dokshitzer,Mueller,Schiff, JHEP 0109 (2001) 033 40 Pion distribution in AA collision dN p (z) Y(u) x pT / p0 xdx 10 GeV/c Normalized probability P(x,N) P(x,N) (dNp / xdx)/ dxxdNp / xdx Shift X: P(x-X,N) = P(x,2) Using the scaling distribution (z), one can solve for X. Get: X(x,N) = x0(N) + f(N) x HY-IV(03) Fractional energy loss small X/x ~ f(N) ~ f N, f5.3104, (at N=350, X/x ~ 0.17) Quark distribution behaves similarly, due to scaling. Data disagree with pQCD’s prediction: f ~ 1/pT 41 Origin of Scaling For DN = , there is a corresponding Dx = . x Dx DN x- N If , x N N+ then F(x,N) F(z) scaling, with z = x / K(N), requires N K(N) ~ N except for N very small 0 We re-examined scaling and found HY (very recently) Implication 13.4 x N 42 new scaling K(N) N 0.07 46 - 43 CONCLUSION Hadron production at high pT in AA collisions • Recombination is the mechanism (can’t ignore the low-pT soft partons) • No anomaly in the p/p ratio • Scaling in centrality and energy • Fractional energy loss is independent of pT and increases linearly with Npart (or fractional increase of N) pQCD not reliable at pT < 10 GeV for RHIC experiments. Centrality scaling : where are the effects of QGP? 44

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