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Physics

This picture of hadronization is inspired by Van Hove's scenario [87] of a first order phase transition via droplet fragmentation of a QGP fluid. QGP droplets are dynamic spatial texture phenomena. However, we measure texture in the two dimensional space of directions, spanned by polar and azimuthal angles. The mechanism that makes us sensitive to the spatial texture is longitudinal flow; the concept of boost-invariant longitudinal expansion was introduced by Bjorken [82]. Two droplets, separated along the longitudinal coordinate, will be separated in $y$ and $\eta$. As long as there is longitudinal expansion, a spatial texture will be manifested as (pseudo)rapidity texture. In the multifireball event generator, we generate the pseudorapidity texture explicitly, omitting the spatial formulation of the problem. The total $p_T$ of each fireball is 0; its total $p_Z$ is chosen to reproduce the observed $\,dN/\,dy$ of charged particles by Lorentz-boosting the fireballs along the $Z$ direction, keeping the total $\vec{p}$ of an event at 0 in the rest frame of the colliding primaries. The fireballs hadronize independently into charged and neutral pions and kaons mixed in a realistic proportion. By varying number of particles $N_p$ per fireball, one varies ``grain coarseness'' of the event texture in $\eta$.

Figure: $\,dN/\,dy$ distribution of charged particles in the multifireball event generator in four individual events with different number of fireballs: $\triangle$ - 2 fireballs, $\Box$ - 4 fireballs, $\Diamond$ - 8 fireballs, $\bigcirc$ - 16 fireballs. One can see how the texture becomes smoother as the number of fireballs increases. We remind the reader that the detector's active area covers $2\pi$ azimuthally and pseudorapidity 1.5 to 3.3. In general, acceptance limitations make it more difficult to detect dynamic textures.

To illustrate the discussion, Fig.7.3 presents examples of $\,dN/\,dy$ distributions in four events with different number of fireballs. The dynamic textures seen on the figures are peculiar to these particular events and are gone after $\,dN/\,dy$ of many events are added.

• Particle production:
  • creates only kaons (charged and neutral) and pions (charged and neutral) in a proportion realistic for the SPS PbPb data.
  • Glauber model of the dependence of the number of participants on the impact parameter (done as a Monte Carlo generator of a random number of participants $N_{part}$ for a given impact parameter)
  • The total multiplicity of mesons in an event scales as $N_{part}$, with a fixed coefficient.
• Kinematics:
  • a Gaussian distribution of $p_X$, $p_Y$, $p_Z$ with adjustable sigma, same for the three directions (isotropy) is simulated for an individual fireball. The data on $\,dN/\,dy$ exclude $pT/pZ$ isotropy - an isotropic fireball with $<p_T>$ about 0.35 GeV/c has $\,dN/\,dy$ with RMS 0.7 - much narrower than seen in the data; therefore, the longitudinal flow needs to be simulated.
  • The longitudinal flow is simulated by randomly (but conserving total $p_Z$ ) boosting individual fireballs along the $Z$ direction.

    $$\frac{\,dN}{\,dp_Z} = \frac{\,dN}{\,dy}\frac{\,dy}{\,dp_Z} = \frac{\,dN}{\,dy} \frac{1}{E},$$ (95)

    
    
    In this formula, $N$, $y$, $p_Z$, $E$ refer to fireballs, rather than particles; the fireballs do not move transversely. In this formula, I take Gaussian $\,dN/\,dy$ with an adjustable parameter $\sigma_{\mbox{long}}$. $\sigma_{\mbox{long}}$ of a fireball is adjusted by comparing the final $\,dN/\,dy$ (fireballs + the longitudinal flow) with the data. Fig. 7.4 illustrates the result of the adjustment: despite the different event-by-event dynamics, the ensemble observable $\,dN/\,dy$ for negative hadrons looks very similar! (These results were obtained with $\sigma_{\mbox{long}}$ =1.6)

  Figure: $\,dN/\,dy$ from negative hadrons obtained in 5% most central events of the multifireball event generator with different clustering parameter $N_{ch}$/fireball.

  

• Fireball multiplicity:

  This is a variable parameter. The fireball multiplicity is Gaussian with variable mean and sigma , subject to the constraint of fixing the total event multiplicity in a given event (Subsection 7.2.2 describes the mathematical technique).