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The formation of hadrons inside the deconfined matter at RHIC & LHC
Rene BellwiedWayne State University
Christina MarkertUniversity of Texas at Austin
Phys. Lett. B669, 92 (2008) = arXiv:0807.1509(w. Ivan Vitev)
Phys. Lett. B691, 208 (2010) = arXiv:1005.5416
The fundamental questions How do hadrons form ?
◦ Fragmentation or recombination◦ An early color neutral object (pre-hadron) or a long-
lived colored object (constituent quark) When do hadrons form ?
◦ Inside the deconfined medium or in the vacuum ?
Not addressed by HEPbecause it is non-perturbative
and can not be calculated
The ‘purposefully ignorant’Formation time is largely ignored in heavy ion
collisions.Based on the simple Lorentz boost argument,
which is insufficient for in-medium fragmentation, it was concluded early on that only colored partons will traverse the system and only fragment outside the medium i.e. in vacuum. This makes the energy loss calculation much easier.
All energy loss models (ASW, AMY, GLV) are based on purely partonic energy loss, either collisional or radiative energy loss.
Greiner, Gallmeister, Cassing (Phys. Rev. C67, 044905 (2003)) suggested early hadronization and hadronic energy loss.
The principle: a question of timeThere is per-se no reason to believe that a
process such as fragmentation, which does not thermalize with the system (i.e. the surrounding medium), would take more or less time in-medium than in vacuum. (Almost true, see below).
One could use in-vacuum formation time.Two aspects in-medium:
◦ Lorentz boost: the higher the energy the longer the formation time
◦ Energy conservation: the higher the fractional momentum the shorter the formation time (since partons lose energy through bremsstrahlung in medium).
◦ But the early formed hadron can not have a fully developed wave function because of the uncertainty principle = pre-hadron (quark content fixed but not all properties fixed)
The concept of formation time
In string fragmentation as well as general QM considerations (e.g. Heisenberg’s uncertainty principle) the formation time of a hadron is given by:
This leads to the principle known as ‘inside-outside cascade’ (Bjorken (1976))
Modeling of hadronization
Lund String Model:
Breaking the color string from the struck parton to the target remnant (constituent length)
Eq = struck quark energystr = string tension
Energy conservation Lorentz boost
Kopeliovich: the Lorentz boost in formation is offset by energy conservation in fragmentation. A high z particle has to form early otherwise the initial parton loses too much energy (outside-inside cascade).
Combining inside-out and outside-in Combining inside-out and outside-in in light cone variablesin light cone variables
Inside-outside cascade (boost)
o ~ 1 fm/c : proper formation time in hadron rest frame
E : energy of hadron
m: mass of hadron E/m = high energy particles are produced laterheavy mass particles are produced earlier
Outside-inside Cascade (pre-hadron formation)
large z (=ph / pq)
= resonance is leading particle in jet
shortens formation time
C. Markert, RB, I. Vitev(PLB 669, 92 (2008))
Statistical evolution of relativistic heavy ion collisions
Model: lQCD SHM BlastwaveEffect: hadronization chemical f.o. kinetic f.o.
Freeze-out surface: Tcrit Tch Tkin() Tkin(,k,p)Temperature (MeV): 190 165 160 80 Expansion velocity: =0.45 =0.6
time: ~4 fm/c ~4 fm/c (nucl-ex/0604019)
Hydro condition ?
Fast equilibration measurements: Fast equilibration measurements: strangeness enhancement & v2 strangeness enhancement & v2
Analytic approach to proper times
What is the proper 0 ?◦ 0 requires thermalization which is an open issue at RHIC and
LHC. Simple collision time c ~ 2RA/ is definitely too short.◦ General approach 0 ~ 1/<pT>◦ Leads to 0(RHIC)=0.44 fm/c and 0(LHC)=0.23 fm/c
(with <pT> = 450 and 850 MeV/c respectively)
What is the proper QGP lifetime ?◦ Upper limit based on longitudinal Bjorken expansion◦ QGP = 0 (T0/Tc)3 with
T0(0,RHIC)= 435 MeV and T0(0, LHC)= 713 MeV and Tc = 180 MeV(see pre-print for more detail)
◦ QGP (RHIC) = 6.2 fm/c , QGP (LHC) = 14 fm/c◦ RHIC result slightly higher than data driven partonic lifetime
estimate based on HBT and resonances (QGP (RHIC) ~ 5 fm/c)
Formation Time of Hadrons in RHIC / LHC QGP(C. Markert, RB, I. Vitev, 0807.1509)
Two questions of increasing complexity – (1)
What sets the scale in our light cone variable approach ?
The mass. Which mass ? Final hadron mass
Brodsky and Mueller (1988) First time distinction between p (production time) and f
(formation time). Production time determines production of co-moving constituent quarks.
Since all quark configurations are possible the order parameter becomes the mass difference between all possible states of the same quark configuration.
Kopeliovich: approximate by the mass difference between the ground state and the 1st excited state (resonant state), e.g. for the pion this time is considerably shorter than the time when taking the final hadron mass.
RB & CM: taking the final hadron mass can approximate the formation time of the final hadron wavefunction.
Pre-hadron formation: A. Accardi, 0808.0656
dressed parton has inelastic cross section comparable to hadronic one = pre-hadron (h*).
undressed quark lifetime (tP), color neutralization time (tcn)
sometimes to simplify tP = tcn, hadron formation time (th)
parton pre-hadron hadron
The difference in our approach
Using the final hadron mass will increase the formation time since thefinal mass is smaller than the difference between the ground and excited states.
Is the in-medium state colored or color neutral ?Kopeliovich, Accardi: color neutral DOFCassing et al.: colored DOF
A colored object will continue to interact and not develop a hadronic wave function early on (constituent quark)
A color-neutral object will have a reduced size and interaction cross section (color transparency) and develop wave function properties early
Only a color neutral state can exhibit hadronic features (e.g. can pre-resonance decay prior to pion hadronization ?)
Two questions of increasing complexity – (II)
Alternate: Cassing et al., 0808.0022
Partons dress up throughout the partonic phase (PHSD = parton-hadron string dynamics)
At hadronization very massive pre-hadronic resonances form through recombination of dressed (constituent) quarks = quasi-particles (DQPM = dynamic quasi-particle model)
Resonances subsequently decay into ground state mesons and octet baryons.
Does this make sense near the QCD phase transition ?
A re-interpretation of the Polyakov Loop calculation in lattice QCD
Color transparency (P. Jain et al., Phys. Rep. 271, 67 (1996))P. Jain et al., Phys. Rep. 271, 67 (1996))
An important concept in our paper, since it reduces (or eliminates) the interaction probability between color-neutral and colored objects.
In the strictest sense only applicable to point-like configurations, i.e. directly produced color-neutral states from higher twist diagrams (Brodsky, Sickles).
Kopeliovich showed that early produced objects (i.e. coalescing constituent quarks) also have reduced interaction cross section.
Reduction in pT broadening due to color transparency in medium
Reduction in energy loss due to color transparency in medium of color-neutral pre-hadrons
Medium modification of early produced resonances due to chiral restoration
pT broadening as signature in DIS
Difference in <pt> between nuclearand elementary collisions
pT broadening occurs when partons interact, pre-hadron would have little interaction cross section, thus no pT broadening
If pre-hadron is formedin nucleus:
(exponent = 0.5 from HERMES analysisbut also close to LUND model prediction)
If quark fragments outside thenthere is no dependence on z or
similar toCronin effect
HERMES results on <pT> broadening
Two distinctly different hadronization processes Two distinctly different hadronization processes (both postulated in 1977)(both postulated in 1977)
More likely in vacuum ?
More likely in medium ?
B/M ratio in AA can be attributed to recombination or to color transparency
(Sickles & Brodsky, PLB 668 (2008))
A directly (or early) produced proton (color-neutral) will undergo almost no rescattering, thus its high pT yield is
enhanced relative to later formed mesons.
Nuclear suppression patterns in HI collisions become more
complexSurprising particle dependence in RAA (hadro-chemistry or flavor change) ? This is not simple partonic energy loss.
Early hadronization or enhanced species dependent gluon-splitting factors (Sapeta & Wiedemann)
S&W use a parameter in their splitting probability that depends on the final hadron mass (ad-hoc parametrization)
Our predictions for energy loss
Additional measurement in nDIS
Nh = hadron multiplicity in (,Q2) binNe = inclusively scattered lepton in same bin
withz = hadron fractional energy = virtual photon energypt
2 = hadron transverse momentumQ2 = lepton four-momentum squared
In dense partonic medium
either Short production time
hadronization ( > 0)
or Long lived quarks with
lose energy and fragment
outside the medium ( < 0)
Resonances: measure vacuum and medium hadronization in same
See arXiv: 0807.1509:
in medium-modification inside/outside jets (either jet cone or quadrant analysis)
Example: Hadron – (1020) correlation in Cu+Cu
Hadron trigger pT > 3 GeV (2.5M) (1020) asso pT =1-2 GeV
Not corrected for v2
First bin in delta phi
No evidence for mass shifts andwidth broadenings on the away-side
Need higher pT resonances
Width:6.0±0.7 MeVWidth:6.0±0.7 MeV
Width:7.2±0.9 MeVWidth:7.2±0.9 MeV
M(K+ K-) GeV/c2
M(K+ K-) GeV/c2
For the LHCIn quadrants or inside/outside jets at sufficiently high fractional momentum
(pT = 3-10 GeV/c):
baryon / meson ratios rare particle species
(s,c,b) resonancespT broadening
Can all already be done in pp (underlying event analysis). Need statistics at high pT in pp and AA.
Summary The question of hadronization in QCD is highly relevant for the evolution of
the initial deconfined and chirally symmetric QCD phase. Studies of pT, width, mass broadening, nuclear suppression, yields and ratios
of identified particles and resonances in the fragmentation/recombination region of their spectrum gives us a unique tool to answer these many decade old questions:◦ Is there local parton-hadron duality ?
◦ Is hadronization due to recombination or fragmentation ?
◦ Do color neutral objects form early and are they less likely to interact with the colored medium ?
◦ When does the hadronic wave function (or mass) form ? In the ALICE year-1, studies of high multiplicity proton proton collisions will
give additional important clues.