effects of minijet degradation on hadron observables in heavy-ion collisions lilin zhu sichuan...
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Effects of minijet degradation on hadron
observables in heavy-ion collisions
Lilin Zhu
Sichuan University
QPT2013, Chengdu
QPT2013, Chengdu
Outline
Introduction
Physics ideas of the recombination model
New property of minijet distribution
Hadronic spectra
Conclusion
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Lilin Zhu QPT2013, Chengdu 3
Transverse momentum spectra
pT2 6
low intermediate
high
pQCDhydro
no rigorous theoretical framework
At intermediate pT recombination model has been successful.
That is where abundant experimental data exist.
Lilin Zhu CPOD2011, Wuhan 4
ReCo models
Duke group: I. 6-dimensional phase spaceII. using Wigner function from density matrix
Texas A&M/BudapestI. Monte Carlo implementationII. Soft and hard partonsIII. Soft-hard coalescence is allowed
Oregon group:I. one-dimensional momentum spaceII. using phenomenological recombination function
PRL90,202301(03), PRC68,044902(03),ArXiv:1102.5723.
PRL90,202302(03), PRC68,034904(03).
PRC67,034902(03), PRC70,024905(04).Hwa, QGP4, p.267.
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Oregon recombination model
pT distributions of and p Recombination functions
Hwa, Phys. Rev. D (1980).
S : shower parton
T : thermal parton = T T + T S + SS
==T T T T T T + + T T S T T S + + T SS T SS + + SSSSSS
fragmentation
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Parton distributions before recombination
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Parton distributions
Thermal partons:
Shower distribution
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SPD, Obtained from FF, Hwa-Yang (04)
T is the inverse slope parameter, not the hydro temperature
let’s see how to take parton momentum degradation into account
hard and semihard parton distributions at the medium surface. Integrated over all initial creation points.
Lilin Zhu
p2dynamical path length
Fries, et al PRC(03)
The process of momentum degradation
parton distribution at creation point
Calculation in pQCD is not reliable at intermediate q and difficult to account for the nuclear complications at various c and
The degradation of momentum from k to q can be written as a simple exponential Hwa-Yang(10)
Nuclear complicatioin is in the determination of
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Lilin Zhu QPT2013, Chengdu 8
The probability of having at and c in the medium
Since depends on the nuclear medium and the azimuthal angle, so we could express in terms of angle and centrality c.
That is contained in the probability function in relating to
Mean dynamical path length
As the system expands, the density D decreases but t1 increases, so is not very sensitive to the expansion dynamics.
probability of production of a (semi)hard parton at creation point x0 and y0
The dynamical effect of energy loss per unit length i=g, q.
Whereas depends on , c implicitly, the mean depends on them explicitly.
determined by fitting nuclear modification factor
The geometrical path length is weighted by the local density along the trajectory marked by t.
not time
Hwa-Yang(10)
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Mean dynamical path length
Points determined from calculation that account for nuclear complications.
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For calculating the pT spectra of any hadron produced later, we make averaged over
No momentum degradation
More suppression for gluons than for quarks throughout the whole region.
Minijet distribution at RHIC
minijet distribution, averaged over , initial creation points.
Minijet Degradation Factor
QPT2013, ChengduLilin Zhu
Increase is rapid at low q.
Rg is roughly half of Rq, but q and c dependencies are similar in shape.
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It is analogous to the nuclear modification factor RAA for , but for minijets.
parametrization for
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Tsallis distribution could fit the minijet distribution very well
Tt=0.32 is universal;
ni depends on parton type.
pion production
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The formalism for recombination of thermal and shower partons has been developed previously. Hwa-Yang, PRC(04)
Hwa-Zhu, PRC(11)Now we generalize to non-central collisioins, especially show the contributions from various species of semihard partons
Zhu-Hwa , 1307.3328
The two shower partons are from the same minijet with momentum q
TT
TS
SS
proton production
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TTT
TTS
SSS
TSS
pion at central collision
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The inverse slope is adjusted to fit the low pT behavior.
T=0.283 GeV.
It’s the same value for all hadrons at low pT.
The pT of TS and SS are fixed by minijets, whose magnitudes depend on .
TTTS
SS
QPT2013, ChengduLilin Zhu
Zhu-Hwa, 1307.3328
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pion
Only vary C(Npart) for the thermal partons. No parameters are adjusted for the shape of the pT distribution at intermediate and high pT region at all centralities.
proton
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It is our prediction for proton pT>5 for c > 20%.
Quark minijets are more influential than gluons in the proton distribution at high pT.
Kaon
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Good fit out to 9 GeV/c for all centralities.
p/pi at RHIC
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For 0-10% the ratio is very well reproduced. For 20-40% not as well around the peak.
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Lilin Zhu QPT2013, Chengdu 21
at LHC
pion
Hwa-Zhu, PRC (11)
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Pb-Pb collisions at 2.76 TeV
At LHC minijets are pervasive and their effects dominate the spectra at the low and intermediate pT range.
TS>TT at pT>0.5 GeV/c.
RHIC
TT
TS
SS
Zhu-Hwa, 1307.3328
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K/p/Λ spectra (0-5% Central)
T=0.38 for thermal partons is higher than 0.283 at RHIC.
For p and Λ, TTS>TTT
0-5%0-5%
0-5%
Hwa-Zhu, PRC(11)
Lilin Zhu QPT2013, Chengdu
effect of minijets at LHC
T=0.38 GeV at LHC
T=0.283 GeV at RHIC
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Due to the abundant production of minijet,TS is elevated going from RHIC to LHC
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Summary & outlook
new features of momentum degradation of minijets produced at intermediate q before hadronization.
pT and c dependencies of hadronic observables are well
reproduced-- by the minijet approach in the framework of the recombination model
Extension of the study to hyperons production, such as: Omega.
Hadron production at LHC.
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Thank you!
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QPT2013, Chengdu
backup
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Hwa-Zhu, (12)
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The good fits support our minijet approach to the treatment of azimuthal anisotropy.
Lilin Zhu CPOD2011, Wuhan 29
Determining RFs
R p was determined from CTEQ From the parton distributions in proton a=b=1.755, c=1.05 at Q2=1GeV2
R was determined from Drell-Yan processes a=b=0 See Phys. Rev. C 66, 025204
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Recombination functions
Given by the valon distribution of the hadrons
1 2
1 2 3
, ,...1 2 1 2 1 2
, ,...1 2 3 1 2 3 1 2 3
( , ) ( , )
( , , ) ( , , )
KQ Q
p nQ Q Q
R y y y y G y y
R y y y y y y G y y y
1 2
1 2 3
1 2 1 2 1 2
1 2 3 1 2 3 1 2 3
( , ) ( 1)
( , , ) ( 1)
a bQ Q
a b cQ Q Q
G y y y y y y
G y y y y y y y y y
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Recombination model for fragmentation
Fragmentation function known from fitting e+e- annihilation data S V G S K G K
Biennewies, Kniehl, KramerKniehl, Kramer, Pötter
Recombination function known in the recombination model
Hwa, Phys. Rev. D (1980).
Shower parton distributions
K, L, G, Ls, Gs
Hwa and Yang, PRC70,024904(2004)