Ridges, Jets and Recombination in Heavy-ion Collisions Rudolph C. Hwa University of Oregon Shandong University, Jinan, China October, 2012

Outline Introduction Ridges Minijets Particle spectra and correlations Azimuthal anisotropy Large Hadron Collider Conclusion

---- which can be tuned to reproduce data. The conventional method to treat heavy-ion collisions is relativistic hydrodynamics ---- which can be tuned to reproduce data. There is no proof that it is the only way (necessary) ---- can only demonstrate that it is a possible way (sufficient). We propose another possible way Yang Chunbin (Wuhan) Zhu Lilin (Sichuan) Charles Chiu (U. Texas) ---- minijets and recombination. An area of focus is about Ridges which is an interesting phenomenon in its own right.

Ridge

Collision geometry pseudorapidity azimuthal angle transverse momentum 5

p1 p2  

Correlation on the near side    J+R ridge R Jet J R J Ridgeology Putschke, QM06 STAR trigger Properties of Ridge Yield Dependences on Npart, pT,trig, pT,assoc, trigger 

on pT,trig 2. 1. Dependence on Npart R Ridge yield as Npart pt,assoc. > 2 GeV STAR preliminary 1. Dependence on Npart participants Jet+Ridge () Jet () Jet) Putschke, QM06 Ridges observed at any pT,trig R Ridge yield as Npart  depends on medium Ridge is correlated to jet production. Surface bias of jet  ridge is due to medium effect near the surface Medium effect near surface

3. Dependence on pT,assoc Ridge is exponential in pT,assoc slope independent of pT,trig Putschke, QM06 STAR Ridge Exponential behavior implies thermal source. Yet Ridge is correlated to jet production; thermal does not mean no correlation. Ridge is from thermal source enhanced by energy loss by semi-hard partons traversing the medium.

4. Dependence of jet and ridge yields on trigger s Feng, QM08 4. Dependence of jet and      ridge yields on trigger s STAR jet part, near-side ridge part, near-side 20-60% jet part, near-side ridge part, near-side top 5% In-plane Out-of-plane 1 4 3 2 5 6 s 3<pTtrig<4, 1.5<pTassoc<2.0 GeV/c Different s dependencies for different centralities --- important clues on the properties of correlation and geometry

Effect of Ridge on two-particle correlation without trigger STAR, PRC 73, 064907 (2006) Auto-correlation between p1 and p2 0.15<pt<2.0 GeV/c, ||<1.3, at 130 GeV Ridges are present with or without triggers.

From the data on ridge, we learn that Ridge is correlated to jets (detected or undetected). Ridge is due to medium effect near the surface. Ridge is from the thermal source enhanced by energy loss by semihard partons traversing the medium. Geometry affects the ridge yield. On the basis of these phenomenological properties we build a theoretical treatment of the ridge. But first we outline the theoretical framework that describes the formation of hadrons from quarks.

Theoretical treatment Usual domains in pT at RHIC low ReCo intermediate high pT 2 6 Hydro pQCD GeV/c TT TS SS Hadronization Cooper-Frye Fragmentation kT > pT k1+k2=pT lower ki higher density

Proton formation: uud distribution Pion formation: distribution thermal shower soft component soft semi-hard components usual fragmentation (by means of recombination) Proton formation: uud distribution

In high pT jets it is necessary to determine the In high pT jets it is necessary to determine the shower parton distributions. Once the shower parton distributions are known, they can be applied to heavy-ion collisions. The recombination of thermal partons with shower partons becomes conceptually unavoidable. D(z) h fragmentation S q A

In high pT jets it is necessary to determine the In high pT jets it is necessary to determine the shower parton distributions. Once the shower parton distributions are known, they can be applied to heavy-ion collisions. The recombination of thermal partons with shower partons becomes conceptually unavoidable. h Now, a new component

TT TS SS soft thermal Pion distribution (log scale) hard fragmentation Transverse momentum

 production by TT, TS and SS recombination thermal fragmentation Hwa & CB Yang, PRC70, 024905 (2004)

Now, back to Ridge. How do we relate ridge to TT, TS, SS recombination? Recall what we have learned from the ridge data: Ridge is correlated to jets (detected or undetected). Ridge is due to medium effect near the surface. Ridge is from the thermal source enhanced by energy loss by semihard partons traversing the medium. Geometry affects the ridge yield.

Ridge is from enhanced thermal source caused by semi-hard scattering. Recombination of partons in the ridge Medium effect near surface associated particles SS trigger ST peak (J) TT ridge (R) These wings are useful to identify the Ridge   At 0 it is mainly the  distribution that is of interest.

Hard parton directed at s , loses energy along the way, and enhances thermal partons in the vicinity of the path. s The medium expands during the successive soft emission process, and carries the enhanced thermal partons along the flow.  Flow direction  normal to the surface Reinforcement of emission effect leads to a cone that forms the ridge around the flow direction . But parton direction s and flow direction  are not necessarily the same. s  If not, then the effect of soft emission is spread out over a range of surface area, thus the ridge formation is weakened. Correlation between s and 

Correlated emission model (CEM) Chiu-Hwa, PRC 79, 034901 (09) STAR Feng QM08 3<pTtrig <4 1.5 <pTassoc <2 GeV/c s 

Single-particle distribution at low pT (<2 GeV/c) That was Ridge associated with a trigger Single-particle distribution at low pT (<2 GeV/c) Region where hydro claims relevance --- requires rapid thermalization 0 = 0.6 fm/c Something else happens even more rapidly Semi-hard scattering 1<kT<3 GeV/c Copiously produced, but not reliably calculated in pQCD t < 0.1 fm/c 1. If they occur deep in the interior, they get absorbed and become a part of the bulk. 2. If they occur near the surface, they can get out. --- and they are pervasive.

? Ridge can be associated with a semihard parton without a trigger. Ridge, dependent on , hadrons formed by TT reco Base is the background, independent of  How is this untriggered ridge related to the triggered ridge on the near side of correlation measurement? Correlated part of two-particle distribution on the near side trigger assoc part JET RIDGE

Ridge is present whether or not 1 leads to a trigger. 2 Two events: parton 1 is undetected thermal partons 2 lead to detected hadrons with the same 2 Ridge is present whether or not 1 leads to a trigger. Semihard partons drive the azimuthal asymmetry with a  dependence that can be calculated from geometry. (next slide) If events are selected by trigger (e.g. Putschke QM06, Feng QM08), the ridge yield is integrated over all associated particles 2. untriggered ridge triggered ridge yield

Geometrical consideration for untriggered Ridge Hwa-Zhu, PRC 81, 034904 (2010) Geometrical consideration for untriggered Ridge b normalized to RA Top view: segment narrower at higher b Side view: ellipse (larger b) flatter than circle (b=0) around =0. For every hadron normal to the surface there is a limited line segment on the surface around 2 through which the semihard parton 1 can be emitted. 2   elliptical integral of the second kind Ridge due to enhanced thermal partons near the surface R(pT,,b)  S(,b) nuclear density D(b)

Asymmetry of S(,b)  =0 =/2 =0 =/2 S(,b) converts the spatial elliptical anisotropy to momentum anisotropy --- key step in calculating v2 without free parameters.

Momentum asymmetry Conventional hydro approach px py Conventional hydro approach x y higher pressure gradient Good support for hydro at pT<2 GeV/c Assumption: rapid thermalization Elliptic flow Inputs: initial conditions, EOS, viscosity, freeze-out T, etc.

Minijet approach If minijets are created within 1 fm from the surface, they get out before the medium is equilibrated. More in the x direction than in the y direction Their effects on hadronization have azimuthal anisotropy  asymmetry can be expanded in harmonics: We can show agreement with v2 data in this approach also --- with no more parameters used than in hydro and without assumption about rapid thermalization

Azimuthal anisotropy base ridge factorizable b pT T0 to be determined base ridge Enhancement factor factorizable b pT T0 is the only parameter to adjust to fit the v2 data Hwa-Zhu (12)

Npart dependence is independent of pT STAR Npart dependence is independent of pT Agrees with <cos2>S for Npart>100 No free parameters used for Npart dependence

T’ determines pT dependence of v2 as well as the ridge magnitude (T=T-T0) T0 = 0.245 GeV One-parameter fit of pT dependence (Npart dependence already reproduced). hydrodynamical elliptic flow ridge generated by minijets without hydro

When TS recombination is also taken into account, When TS recombination is also taken into account, we get better agreement with data R.Hwa - L. Zhu, Phys. Rev. C 86, 024901 (2012)

v2 and ridge are intimately related pT dependence of Ridge v2 and ridge are intimately related Inclusive T=0.283 GeV Base Ridge (inclusive) Inclusive ridge Base T0=0.245 GeV enhancement of thermal partons by minijets Ridge TR=0.32 GeV  dependence due to initial parton momenta

At pT>2GeV/c, we must further include SS recombination. Minijet Bridge B ridge TS recombination RHIC At pT>2GeV/c, we must further include SS recombination.

Large Hadron Collider (LHC) ALICE Using the same recombination model applied to Pb-Pb collisions at 2.76 TeV, we get T=0.38 GeV and good fits of all identified particle spectra.

R.H.-L.Zhu, PRC84,064914(2011)

We learn about the dependence of T and S on collision energy. pions quarks The pT range is too low for reliable pQCD, too high for hydrodynamics. Shower partons due to minijets are crucial in understanding the nature of hadronic spectra. TS and TTS recombination provides a smooth transition from low to high pT --- from exponential to power-law behavior.

Conclusion Minijets at LHC cannot be ignored --- even at low pT. Study of Ridge and Minijets gives us insight into the dynamical process of hadronization: Ridge in TT reco with enhanced T due to minijets Azimuthal anisotropy (v2) can be well reproduced without hydrodynamics. As is increased from RHIC to LHC, S is significantly higher. Spectra of all species of hadrons are well explained by TT, TTT, TS, TTS, TSS, SS, SSS recombination. Minijets at LHC cannot be ignored --- even at low pT.

At LHC the Higgs boson may have been found. But in Pb-Pb collisions, nothing so spectacular has been discovered. Most observables seem to be smooth extrapolations from RHIC in ways that have been foreseen. Can we think of anything that is really extraordinary? --- unachievable at lower energies e.g., a strange nugget? solid evidence against something?

The End Thank you

Backup slides

Hadron production by parton recombination Pion Recombination function q and qbar momenta, k1, k2, add to give pion pT Proton At low pT thermal partons are most important TT same T for partons, , p phase space factor in RF for proton formation TTT empirical evidence

PHENIX, PRC 69, 034909 (04) p Same T for , K, p --- in support of recombination. T=0.283 GeV Hwa-Zhu, PRC 86, 024901 (2012) Proton production from recombination Slight dependence on centrality

TS+SS recombination only adjustable parameter  Path length  hadronization q b  geometrical factors due to medium k probability of hard parton creation with momentum k degradation only adjustable parameter  is calculable from geometry Path length

Geometrical considerations Nuclear medium that hard parton traverses  x0,y0 k Geometrical path length D(x(t),y(t)) density (Glauber) Dynamical path length  to be determined Average dynamical path length Probability of hard parton creation at x0,y0

Higher harmonics Conventional approach: fluctuations of initial configuration Minijet approach: hadronization of minijets themselves outside the medium --- plays the same role as fluctuations of initial state S R J  T J stays close to the semihard parton, whose  angle is erratic; thus additional contribution to azimuthal anisotropy. pT dependence of TS component is known Hwa-Yang PRC(04),(10) =

a2=0.6, a3=1.6, a4=1.4 v2 arises mainly from v3, v4 come only from Hwa-Zhu a2=0.6, a3=1.6, a4=1.4 v2 arises mainly from v3, v4 come only from