Quark recombination in high energy collisions for different energies

Steven RoseWorcester Polytechnic InstituteMentor: Dr. Rainer FriesTexas A&M University

Motivations

Understand the mechanisms that allow for particle creation in high energy collisions

Understand QCD (strong force interactions) at high temperatures and densities Quark-Gluon Plasma is such a system

Quarks/Partons

Quark- elementary particle that carries a color charge

There are three color charges and their opposites

Quarks also have one of six ‘flavors’ Strong interactions conserve color and flavor Gluons are the strong force carriers

Both quarks and gluons make up hadrons

Hadrons

Hadrons are particles constructed of quarks

(Anti)-Baryons have three (anti)-quarks

Mesons have a quark-anti-quark pair All hadrons are color

neutral due to confinement

Sea Quarks and Virtuality

Quantum Mechanics allows for qqbar pairs to be created by violating energy conservation for short periods of time

These pairs are always opposite in color and flavor Violation of CoE is an attribute of virtuality

tE222 mpE

The Collision – What Happens? Impact- Temperature and pressure are raised

and cause a phase transition. QGP- Hadrons “melt” as quarks become

relevant degrees of freedom System expands, reaches a thermal freeze

out and hadrons are recreated, but how?

The Collision – Characteristic Quanitities

Jets

Fragmentation

Partons may escape the QGP before freeze out, but confinement must hold true.

The ‘freed’ quark is virtual, but it loses it’s own energy to create many qqbar pairs that form hadrons.

Each qqbar pair brings the quarks collectively closer to the mass shell, until there is no virtuality.

Diagrams for Fragmentation

Feynman diagram modeldescribes fragmentation witha perturbative approach

The gluon-string model givesa better insight as to howconfinement plays a role

Recombination

Fragmentation built on the idea of a single quark in a vacuum, doesn’t consider many quarks

Recombination describes hadronization of many quarks Applicable in QGP

Recombination argues that only quarks close in phase space will be able to form hadrons

Hadron Ratio - Evidence

•P+P Collisions have nearly constant, and small ratios•Large nuclei exhibit a growth in the same ratio

Fragmentation and Recombination Fragmentation is dominant in p+p and electron-

positron annhilations for pt > 1 GeV/c Fails at intermediate pt (1..6 GeV/c) for heavy ions Fragmentation has to win for high pt Recombination wins at intermediate pt, if phase

space is densely populated

Methodology- Fragmentation

Perform perturbative calculations to create jet spectra for various collisions/energies/nuclei Many integrals, best speed with FORTRAN

Calculation is Leading Order, so fits the shape well, but not the size- scale by an appropriate “k-factor” Simple least squares fit, done easily with

Mathematica Used KKP fragmentation functions

Methodology- Nuclear Effects Experimental data has no control over impact

parameter, but generalizes ‘centrality bins’ This determines fireball geometry for

calculated jet path length With path length, we allow interactions to

drain energy from the jet, changing apparent momentum Gluons lose more energy than quarks!

Methodology- Recombination

We assume thermal quark spectra (fq = distribution) with temperature T and radial flow vt

Example: A meson in terms of recombination

23 )1()( xxqfxfqpd

dNE meson

Resulting pt spectraAu+Au 200 GeV

Au+Au 62.4 GeV Central

More pt spectraAu+Au 62.4 GeV Peripheral

Cu+Cu 22.5 GeV

Other Observables – P/Pi, RAA

Conclusions

In high energy, massive nuclei collisions, Recombination is a critical mechanism for hadron

production in the range of 1 – 6 GeV/c. Fragmentation is the dominant process for hadron

production above 6 Gev/c Recombination contributes less to smaller

collisions (low A, large b)

Always under construction

Need better fragmentation functions Experimental data on mid- to light-ion

collisions Systematic study of parameters and

comparison to hydrodynamics