Methods of Studying Net Charge Fluctuations
in Nucleus-Nucleus Collisions
Henrik Tydesjö
Evert Stenlund
Joakim Nystrand
Event-by-event fluctuations of the net charge in
local regions of phase space have been proposed
as a probe of the multiplicity of resonances
(mainly ρ and ω) in a hadron gas, and may –
according to some models – be sensitive to a
quark-gluon plasma phase transition.
A lot of variables for measuring the fluctuations
have been proposed. Two of them are addressed
here. The net charge, Q, and charge ratio, R, are
defined by
Q  n  n
n
R
n
Consider a scenario, where each particle is
assigned a random charge of +1 or –1 with equal
probability. With a fixed number of charged
particles within the acceptance, the variance of Q
is V(Q) = <Q2> - <Q>2 = nch. The variance of R
approaches the value 4/nch. It is therefore useful
to define normalized variances. They are
V (Q)
v(Q) 
nch
where n+ and n- are the numbers of reconstructed
positive and negative particles in the event.
v( R)  V ( R)  nch
In a hadron gas the values of v(Q) and v(R) are
expected to be near 1 and 4 respectively.
SCENARIO 1
Random emission with charge symmetry
In a quark-gluon plasma, where the quarks carry
± 2/3 and ± 1/3 unit charges, the corresponding
value for v(Q) is 5/18. So if the charge distribution
in the plasma survives the transition to ordinary
matter, a 72% reduction of the fluctuations would
be seen.
In a real experiment there are also a lot of other
factors influencing the values of v(Q) and v(R).
The effects of such factors are simulated in
different scenarios below. The behavior of v(Q)
and v(R) is studied as a function of detector
acceptance. A detector with 4π coverage is used
(except for scenario 7) and the acceptance is varied
by cuts in the azimuth (p = Δφ/2п). 1.000.000
events with 1.000 charged particles each were
generated for each scenario.
SCENARIO 2
Random emission with charge asymmetry
SCENARIO 3
Random emission with charge symmetry and
global charge conservation
As expected, v(Q) = 1 and v(R) approaches 4 asymptotically. v(R)
rises for low values of p, because events with n+ = 0 or n- = 0 have
to be excluded.
SCENARIO 4
Random emission with charge symmetry,
global charge conservation and less than 100%
detection efficiency
With a charge asymmetry defined by
ε
 n    n 
 n    n  
v(Q) = 1 – ε2 and v(R) = 4 + 16 ε + O(ε2) asymptotically. In the
figure above ε = 0.1 is used and the influence on v(R) is huge.
SCENARIO 5
Random emission with charge symmetry,
global charge conservation and a nonnegligible background
With global charge conservation the fluctuations seen in scenario 1
are reduced by a factor (1-p). With an acceptance of 1 there are of
course no fluctuations.
SCENARIO 6
Random emission of (π+π-)-resonances
In this scenario resonances with random azimuthal angle φ are
decaying into a π+ and a π-. The azimuthal angles of the pions are
φ+dφ and φ-dφ, where dφ is randomly chosen from a Gaussian
with width σφ. In the figures below σφ = π/3, π/6 and π/18. There
is a stronger reduction of the fluctuations with smaller opening
angles of the pions.
In this simulation the detection efficiency, E, is 80%. The
fluctuations from scenario 1 are reduced by a factor (1- pE).
SCENARIO 7
Random emission of (π+π-)-resonances at two
detectors separated in azimuth
This sample includes a background, b = 20%, of uncorrelated
particles. The fluctuations from scenario 1 are reduced by a factor
(1- p(1-b)). If scenario 4 and scenario 5 are combined the general
expression of the reduction is 1-p(1-b)E.
SCENARIO 8
Random emission of pions from a quarkgluon plasma
Here two detectors are used, each covering 25% of the acceptance
and placed opposite to each other. When trying to combine the
information from both detectors, this strange behavior is seen. The
separation between the detectors is greatly influencing the shapes
seen in scenario 6. In this simulation an opening angle between the
pions with width σφ = π/6 was used.
A simple model of the hadronization of the quark-gluon plasma is
used. The combinations
dd , ud , uu , du
hadronize with the same probability and create 2 pions in 60% of
the cases and 3 pions in 40% of the cases. In this simulation the
opening angle between the pions has σφ = π/18.