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Recombination and Fragmentation of Hadrons from a Dense Parton Phase

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Recombination and Fragmentation of Hadrons from a Dense Parton Phase

Rainer J. Fries

University of Minnesota

Talk at the RIKEN Workshop on Flow and Collective Phenomena

BNL, November 19, 2003

- R.J. Fries, C. Nonaka, B. Müller & S.A. Bass, PRL 90, 202303 (2003)
- R.J. Fries, C. Nonaka, B. Müller & S.A. Bass, nucl-th/0305079, JPG t.a.
- R.J. Fries, C. Nonaka, B. Müller & S.A. Bass, PRC 68, 044902 (2003)
- C. Nonaka, R.J. Fries & S.A. Bass, nucl-th/0308051, submitted to PLB

Rainer J. Fries

- Motivation: hadron spectra, ratios and flow at RHIC
- The recombination idea
- Calculations using recombination + fragmentation
- v2 scaling

Rainer J. Fries

Central Au+Aucollisions: suppression of pions by a factor ~5

Suppression of hard (pQCD) hadron production

Rainer J. Fries

- For pt>2 GeV, protons are as abundant as pions and kaons!
- hadron production via fragmentation yields p/π ratio of ~0.1

- where does the large proton over pion ratio at high pt come from?
- Why do mesons differ from hadrons?

Rainer J. Fries

- hyperon v2 saturates later and higher than kaon v2.
- same effect observed for protons and pions.
- what drives the different pT scales for KS and Λ v2?
- novel mechanism of baryon formation?

Sorensen SQM 2003

Rainer J. Fries

A possible solution to the puzzle:

- parton recombination

Where is pQCD?

Rainer J. Fries

Fragmentation:

- for exponential parton spectrum, recombination is more effective than fragmentation
- baryons are shifted to higher pt than mesons, for same quark distribution
- understand behavior of protons!

fragmenting parton:

ph = z p, z<1

recombining partons:

p1+p2=ph

Rainer J. Fries

basic assumptions:

- at low pt, quarks and antiquarks recombine into hadrons on a hadronization hypersurface:
- hadron momentum P is much larger than masses and momentum scales of the wave function of the hadron;
- features of the parton spectrum are shifted to higher pt in the hadron spectrum

- parton spectrum has thermal part (effective quarks) and a power law tail (quarks and gluons) from pQCD.

Rainer J. Fries

High Energy Physics Phenomenology:

- K.P. Das & R.C. Hwa, Phys. Lett. B68, 459 (1977)
Quark-Antiquark Recombination in the Fragmentation Region

- description of leading particle effect (field of recent activity!)
Heavy-Ion Phenomenology:

- T. S. Biro, P. Levai & J. Zimanyi, Phys. Lett. B347, 6 (1995)
ALCOR: a dynamical model for hadronization

- yields and ratios via counting of constituent quarks
- R.C. Hwa & C.B. Yang, PRC66, 025205 (2002)
- R. Fries, B. Mueller, C. Nonaka & S.A. Bass, Phys. Rev. Lett. 90
- V. Greco, C.M. Ko and P. Levai, Phys. Rev. Lett. 90
Anisotropic flow:

- S. Voloshin, QM2002, nucl-ex/020014
- Z.W. Lin & C.M. Ko, Phys. Rev. Lett 89, 202302 (2002)
- D. Molnar & S. Voloshin, nucl-th/0302014

Rainer J. Fries

Express number of mesons by the quark density matrix .

Introduce 2-quark and meson Wigner functions W, .

Rainer J. Fries

choose a hypersurface Σ for hadronization

use local light cone coordinates (hadron defining the + axis)

wa(r,p):single particle distribution functions for quarks at hadronization

ФM & ФB:light-cone wave-functions for the meson & baryon respectively

x, x’ & (1-x): momentum fractions carried by the quarks

integrating out transverse degrees of freedom yields:

Rainer J. Fries

- important features: ph = Σ pq
d3N/dp3h (wq)n (with n=2,3)

- for an exponential distribution:

- product of all distribution functions only depends on hadron momentum!
- results are insensitive to the model used for recombination
- Baryon/Meson ratio is independent of momentum, e.g.

(Cp, Cπ : degeneracy factors)

Rainer J. Fries

Fragmentation…

…nevercompetes with recombination for a thermal (exponential) spectrum:

… but it wins out at large pT, when the spectrum is a power law ~ (pT)-b :

Rainer J. Fries

- Fragmentation of perturbative partons dominates at high pt.
- Recombination kicks in at 4-6 GeV at RHIC energies.
- Our description of recombination fails when /PT and m/PT corrections become large (from 1-2 GeV on at RHIC).
- But: recombination will still be the dominant hadronization mechanism. Take into account binding energies, mass effects.

Rainer J. Fries

Results & Comparison to Data

- hadron spectra
- hadron ratios
- RAA

Rainer J. Fries

Input for the model is the momentum distributions of constituent quarks and anti-quarks at the time of hadronization

- the quark distribution is assumed to have a low pt thermalcomponent and a high pt pQCD mini-jet component
- the thermal component is parameterized as:
with a flavor dependent fugacity ga, temperature T,

rapidity width Δ and transverse distribution f(ρ,ф).

- the pQCD component is parameterized as:
with parameters C, B and β taken from a lo pQCD calculation

Rainer J. Fries

Use hypersurface with t2-z2=2; = 5 fm/c.

Fix T=175 MeV

Determine:

- Radial flow =0.55 c
- Emission volume
- Energy loss parameter
- Fugacities

Rainer J. Fries

Rainer J. Fries

Rainer J. Fries

Rainer J. Fries

anisotropic or “elliptic” flow is sensitive to initial geometry

low pt domain:

high pt domain:

more flow in collision plane than perpendicular to it

less absorption in collision plane than perpendicular to it

total elliptic flow is the sum of both contributions:

r(pt): relative weight of the recombination contribution in spectra

Rainer J. Fries

azimuthal anisotropy of parton spectra is determined by elliptic flow:

(Фp: azimuthal angle in p-space)

with Blastwave parametrization for parton spectra:

azimuthal anisotropy is parameterized in coordinate space and is damped as a function of pt:

Rainer J. Fries

in the recombination regime, meson and baryon v2 can be obtained from the parton v2 in the following way:

- neglecting quadratic and cubic terms, one finds a simple scaling law:

Rainer J. Fries

Results & Comparison to Data

- elliptic flow

Rainer J. Fries

parton elliptic flow:

relative weight of recombination:

grey area: region of uncertainty for limiting behavior of R & F

hadron v2 calcuated separately for R and F and superimposed via:

Rainer J. Fries

- Recombination describes measured flavor-dependence!

Rainer J. Fries

- high pt: v2 for all hadrons merge, since v2 from energy-loss is flavor blind
- charged hadron v2 for high pt shows universal & limiting fragmentation v2
- quark number scaling breaks down in the fragmentation domain

Rainer J. Fries

- smoking gun for recombination
- measurement of partonic v2 !

- New PHENIX Run-2 result on v2 of 0’s:
- New STAR Run-2 result on v2 for ’s:
- ALL hadrons measured to date obey quark recombination systematics

PHENIX Preliminary

p0

X

STAR Preliminary

Rainer J. Fries

- Another test: the meson. Do we see a mass effect or the valence quark structure of hadrons?
- Reco differs from hydro!
- The deuteron and the pentaquark should have tremendous v2.
- STAR: deuteron v2 follows the scaling law!

Rainer J. Fries

The + will be measured at RHIC. Will v2 scale with n=5?

What about other resonances? Influence of the hadronic stage?

Rainer J. Fries

The Recombination + Fragmentation Model:

- provides a natural solution to the baryon puzzle at RHIC
- describes the intermediate and high pt range of
- hadron ratios & spectra
- jet-quenching phenomena
- elliptic flow
- provides a microscopic basis for the Statistical Model
- One universal parametrization of the parton phase can explain the data!
- v2: proof of collectivity in the parton phase
issues to be addressed in the future:

- entropy & energy
- resonances and influence of the hadronic phase
- need improved data of identified hadrons at high pt

Rainer J. Fries

The End

Rainer J. Fries

R+F model applicable over full range of centrality

deviations from SM as soon as fragmentation sets in

low pt deviations due to neglected const. quark mass

Rainer J. Fries

R+F model describes different RAA behavior of protons and pions

Lambda’s already exhibit drop into the fragmentation region

in the fragmentation region all hadron flavors exhibit jet-quenching

Rainer J. Fries

azimuthal anisotropy is driven by parton energy/momentum loss Δpt

L: average thickness of the medium

the unquenched parton pt distribution is shifted by Δpt.

- v2 is then calculated via:

Rainer J. Fries

double parton scattering scales:

meson

A

A

single parton scattering and fragmentation scales:

T. Ochiai, Prog. Theor. Phys. 75 (1986) 1184

Rainer J. Fries

Can we distinguish production scenarios for the pentaquark?

5q recombination

K+N recombination & coalescence,

K+N fragmentation & coalescence

K+N fragmentation & coalescene in a jet cone (= 5q fragmentation)

Even obtain information about the structure?

Rainer J. Fries