Motivation:
A key question of the heavy ion program at RHIC is to understand whether the hot matter produced in the midst of heavy ion collisions undergoes a transition to and from a quark gluon plasma phase before it hadronizes. Fluctuations measurements in heavy ion collisions gives a clear signal of QGP formation and these fluctuations depend on the properties of the system. It has been predicted that near a critical point fluctuations will be strongly enhanced. Fluctuations of conserved quantities have been suggested as the definite probes for providing information on the quark-hadron phase transition. Recently it has been possible to perform detailed lattice calculations to obtain quantitative number for various types of fluctuations. The main fluctuations variables are multiplicity, energy, charge, mean pT fluctuations & hypercharge fluctuations etc. In the lattice framework one calculates the susceptibilities which are variances and covariances of various quantum numbers. These susceptibilities provide valuable information on the degrees of freedom in the hot phase of QCD. Hypercharge fluctuations probes the transitions from hadronic matter to a deconfined QGP
Experiments like RHIC can study the fluctuations in conserved quantities in heavy ion collisions in different rapidity windows. With proper particle identification, one can measure in the experiments both absolutely conserved quantities like baryon number (B), electric charge (Q), as well as quantities which are conserved in the strong interaction, such as the third components on Isospin (I3), strangeness (S) and the hypercharge (Y). These observations can be used to extract fluctuations in the numbers of these quantities.
In particle
physics, the hypercharge (represented by Y)
is the sum of the baryon
number B and the flavor charges:
strangeness
S, charm
C, bottomness Ḃ and
topness
T, although the last one can be omitted given the extremely
short life of the top quark (it decays to other quarks before
strong-interacting with other quarks).
Strong
interactions, actions between elementary
particles mediated, or carried, by gluons. They
are responsible for the binding of protons and neutrons in the
nucleus
and interactions between quarks. Quantum
field theory applied to the understanding of
these strong interactions is called quantum
chromodynamics (QCD). Strong interactions are
one of four fundamental interactions in nature, the others being
gravitation,
electromagnetism, and the weak
interactions.
The Gell-Mann/Nishijima
Law relates hypercharge with isospin
and electric
charge:
2.
Q = Iz + 1/2 Y
where Iz is the third component of isospin and Q is the particle's charge. This allow us to express the hypercharge in terms of isospin and charge:
3. Y = 2( Q - Iz)
Isospin creates multiplets of particles whose average charge is related to the hypercharge by:
4.
Y = 2Q
which is easily derived from (3), since the hypercharge is the same for all members of a multiplet, and the average of the Iz values is 0.
Examples:
The nucleon group (proton plus neutron) have an average charge of 1 + 0 = +1/2, so they both have hypercharge Y = 1 (baryon number B = +1, flavor charges set to 0). From Gell-Mann / Nishima Law we know that proton has isospin +1 - 1/2 = +1/2, while neutron is the 0 − 1/2 = −1/2.
This also works for quarks: for the up quark, with a charge of +2/3, and an Iz of +1/2, we deduce a hypercharge of 1/3, due to its baryon number (since you need 3 quarks to make a baryon, a quark has baryon number of ±1/3).
For a strange
quark, with charge −1/3, a baryon number of 1/3 and strangeness
of −1 we get a hypercharge Y = −1/3, so we deduce an Iz
= 0. That means that a strange quark makes a singlet of its
own (same happens with charm, bottom and top
quarks),
while up and down constitute an isospin doublet.
Following are steps which are followed:
Part A
Part B
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