... SPS[*]
SPS - Super Proton Synchrotron, located at CERN 
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... (2D)[*]
we denote azimuthal angle by $ \zeta $ to reserve $ \phi$ and $ \psi$ for the wavelet functions 
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... ensembles[*]
... this is not the first DWT power spectrum analysis performed on experimental data in the physics of high energy hadron collisions - to my knowledge, the first one was performed on a couple of JACEE cosmic ray events in work [6]. The scarce event statistics left the feature eduction potential of the DWT power spectrum underutilized. Another difference from our case is that only a 1D pseudorapidity-bound DWT was used in that work. 
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...): [*]
With the normalization technique actually used, the accuracy of this estimate does not affect the accuracy of the normalized particle yields, and the estimate is given here for orientation only. 
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... observation[*]
The acceptance is narrow and not every event produces tracks in the spectrometer! 
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... pad[*]
$ \mu$ is defined for each pad in a sample of events. 
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... 1[*]
An estimate for orientation: for Poissonian distribution of hits, $ \mu=1$ means that probability of having 1 or more hits is $ 1-P(0)=1-exp(-1)\approx 0.63$, i.e. the detector, in fact, is merely semi-occupied. 
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...) [*]
Their peculiar ``banana'' shape in the $ p_T$ and $ y$ variables is due to the constraint, imposed on $ p_T$ and $ p_z$ by constancy of momentum $ p$ : $ {p_T}^2+{p_z}^2=p^2=const$, and, differentiating, from $ \,dp/\,dy = 0 $ one gets $ \,dp_T/\,dy=-p_z E/p_T < 0$. 
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... system[*]
With '94 and '95 data, H4 was not yet used in the offline analysis. 
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... section.[*]
By mid 1990s, after the long years of service, the scintillator's transparency became reduced by radiation damage to a level which severely undermined independence of the signal on the impact position along the face of the stack. I had to correct for that problem - more on this in section 4.4. 
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... pions[*]
In UCAL, 1-10 MeV neutrons from the nuclear break-ups in hadronic showers do not go unnoticed but induce fissions. These fissions contribute to the measured signal, thus rising it to a level typical for an electromagnetic cascade caused by decay products of a $ \pi^0$ of the same energy. 
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... channels[*]
due to zero suppression 
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... H4[*]
Before the Pb run, H1 was replaced by a pad chamber, but the nomenclature for the rest of the hodoscopes was not changed 
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... TIC[*]
this multichannel Threshold Image Cherenkov detector does not play any role in this analysis and I give no special description of it. Its design and operation are described in [37]. 
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... production[*]
The reason to choose this Lorentz-invariant combination of quantities is the fact that differential cross-section of an interaction of particles $ A$ and $ B$ with an arbitrary number of secondaries (indexed by $ f$) in the final state is given by  [39]

$\displaystyle \,d\sigma = ((2S_A+1)(2S_B+1)4j)^{-1} \times \sum_{S_i,S_f}\vert ... ..._f \frac{\,d{p_f}^3}{2E_f(2\pi)^3} \big) (2\pi)^4 \delta^4(p_A+p_B-\sum_f p_f) $

where $ j$ is an invariant flux, $ S_A$, $ S_B$, $ S_f$ are spin quantum numbers, and $ \vert M\vert^2$ is the squared modulus of the invariant amplitude of the process. Therefore Eq.  4.1 represents the $ \vert M\vert^2$ integrated over the phase space of the non-observed particles, with certain coefficients. 
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... range.[*]
This is supported by the existing data  [41] on the change of $ <p_T>$ with $ y$ for primary negative hadrons. As $ y$ goes from 3.4 to 3.9, $ <p_T>$ drops from $ \approx 0.382$ $ GeV/c$ to $ \approx 0.378$ $ GeV/c$, i.e. by $ \approx 1\%$. Such an effect will not be visible due to other larger error bars. 
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... factorized[*]
$ B(y)$ and $ T(m_T)$ are defined by Eq. 4.8 itself. Either one of them therefore can contain an arbitrary multiplier. For our goals, this ambiguity is irrelevant, as will be clear from the way $ B(y)$ and $ T(m_T)$ enter Eq. 4.13 and Eq. 4.14. 
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... [*]
This is the $ \sigma$ of the pion distribution according to RQMD and also the $ \sigma$ of the NA49's $ h^-$  [41] distribution. My attempts to determine this parameter from our own pion data led me to conclude that this can only be done with accuracy as poor as 50% because of narrowness of our coverage in $ y$. The result however is consistent with NA49 and RQMD. This remark applies to the kaons too. 
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.... [*]
As in RQMD. 
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... procedure[*]
due to Michael Murray 
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... extrapolating[*]
here the artificial mass assignment is equivalent to changing the integration variable within the integral and does not change the result 
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... area.[*]
The resulting $ y$ ranges are listed in Table 5.2. 
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... be[*]
assuming that the dependence of the apparent inverse slope $ T$ on the width is smooth enough so that it can be inter- and extrapolated by the two points. 
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... 1.4.[*]
The somewhat arbitrarily chosen number here is 99.7%. 
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... side[*]
that is, the side of the detector, free of $ \delta $-electrons due to the deflecting effect of the dipole magnetic field. 
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... DST[*]
DST - the Data Summary Tape. 
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... path.[*]
In the subsequent event texture analysis, I extracted the $ \,dN/\,d\eta$ shape from the Si data. It was not different from that of RQMD or HIJING. 
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... beam[*]
for the definition, see Subsection 3.4.1 
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...sird_figure. [*]
A caveat: the above described correction method is not rigorous because the simulation of effect is reduced to sampling from the distributions of observed $ NTOTAL$ and $ NFAKE$. In the procedure, $ NTOTAL$ and $ NFAKE$ are being sampled independently of each other. Useful pairs of $ NTOTAL$ and $ NFAKE$ are only those where $ NTOTAL \ge NFAKE$. This means that the distribution of ``useful'' $ NTOTAL$ and $ NFAKE$, which will enter the correction procedure, will differ from the observable ones. However, in practice, for a central trigger run, in most cases $ NTOTAL \gg NFAKE$. The result of this is that in case of the central runs, the bias coming from the condition $ NTOTAL \ge NFAKE$ is negligible. 
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... hit[*]
read out by Gasplex 
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... scintillator.[*]
as discussed in detail in Appendix A 
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... deterioration[*]
An increase in the the sum/ $ \sqrt{\mbox{product}}$ means that the attenuation length decreases, see Appendix A. 
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... threshold[*]
This was not seen until I calibrated out the position dependence of the UCAL signal, significant due to the radiation damage in the scintillator (see Subsection 4.4.2). 
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...$ \pi $[*]
We neglect $ e^+(e^-)$ for the reasons outlined in Subsection 4.4.3. 
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... correction[*]
Particles of different mass and life time have different acceptance corrections, and they are calculated separately. By ``pionic'' one I mean the one calculated for pions. 
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... spectrometer,[*]
data on momentum acceptance is found in Table  3.2 
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... counter[*]
see section  3.4.1 for description 
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...H3. [*]
see section  3.4.1 for description 
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...counting [*]
To emphasize: we do not have to identify, but merely have to count the rejected kaons for this task. 
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... potential[*]
parameter of statistical models needed to account for the fact that the total baryon number in the system is fixed (conserved). 
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... $ \mu/T \sim 6-7$[*]
too high for the SPS freeze-out conditions, but the authors of that early work [20] considered lab energies up to $ E/A \approx 4 GeV$ 
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... Preliminary[*]
To the best of my knowledge as of July 2001, these NA49 data have not yet been published in the refereed press 
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... midrapidity[*]
from -0.5 to 0.5 in the CMS 
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... triggered[*]
we normally call it ``central trigger'', but in the field-off situation this name is hardly justifiable, as seen from the context 
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... fits.[*]
This is not surprising for at least two reasons: 1) a sample of events in a run is not a sample of a constant total multiplicity - the multiplicity varies event by event. Thus varies the mean multiplicity $ \mu$. A sum of multiple Poissonians of different $ \mu$ and arbitrary weights is not expected to be a Poissonian. 2) When the total multiplicity is fixed, the dominant reason for the deviation will be correlations between particles (e.g. the Bose-Einstein ones). In our case, however, the dominant reason is (1). 
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... [*]
In this Chapter, I denote azimuthal angle by $ \zeta $ to reserve $ \phi$ and $ \psi$ for the wavelet functions 
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..., [*]
This value is $ ((\eta_{max}-\eta_{min})/16/5$, i.e. 1/5 of the pad's rapidity span. 
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... 0.01125.[*]
This value is 1/10 of the pad's rapidity span. 
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... cross-talk[*]
that is, the cross-talk between the given stimulated channel and all other channels of the chip 
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... negative[*]
that is, the induction has the opposite sign with respect to the stimulating signal 
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... theme[*]
In the Discrete Wavelet Transformation approach, a very similar problem - that of the varying mean density $ \bar{\rho}$ - is solved by virtue of the orthogonality of the basis, as will be explained in section 6.6. 
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... [*]
remember that $ i$ and $ j$ belong to the same half-ring and are therefore close in $ \eta $ 
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... amplitudes[*]
I am talking about calibrated amplitudes, where 0 corresponds to the pedestal - hence ``positive'' and ``negative''. 
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... positive.[*]
Incidentally, this is a good insight into the ``general theory'' of correlation measures - a two point correlation approach does not tell the whole story; one really needs a scale-differentiated texture study ! 
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... midrapidity,[*]
or, more accurately, towards pion midrapidity - $ \eta $ can approximate $ y$ well for $ m/p \ll 1$ 
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.... [*]
$ L^2({\mathbb{R}})$ is the space of functions whose second power is integrable: $ \int_{-\infty}^{+\infty}\vert f(x)\vert^2\,dx < \infty$. 
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... function[*]
Some authors call it ``mother function''. 
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... function.[*]
Some authors call it ``father function''. 
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... event.[*]
In our notation, a scalar product of $ f$ and $ g$ in the $ L^2({\mathbb{R}}^2)$ space is denoted as $ \langle f,g \rangle$: $ \langle f,g \rangle = \int \int f(x,y) g(x,y) \,dx \,dy$. Repeated indices are being summed over, even if the summation symbol is not written explicitly. 
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... bin.[*]
The binning was done in the total ionization amplitude; then charged multiplicity was assigned to those bins by dividing total ionization by mean ionization of a pion with $ p_T=0.4$ GeV/c. 
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... data.[*]
Specifically, the following are probabilities for a simulated particle to assume a particular identity: $ \pi^+$ - 0.260; $ \pi^-$ - 0.279; $ \pi^0$ - 0.270; $ K^+$ - 0.0635; $ K^-$ - 0.0317; $ K^0$ - 0.0952. 
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... Gaussian[*]
Not the most realistic one, it is chosen because it enables fast and simple momentum-conserving generation of random momenta. 
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.... [*]
In this approach, one obtains particles with a Gaussian $ \,dN/\,dy$ from a superposition of multiple isotropic fireballs in a single event. A single isotropic fireball can not produce a realistic combination of $ y$ and $ pT$ distributions. 
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... sigma[*]
Section 7.3 describes what they are 
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... observables[*]
We include flow observables in the event-by-event class 
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... problem.[*]
The NA49 $ \Phi_{p_T}$ measurement[12] addressed the issue and potentially could have revealed deviations from the local thermal equilibrium. It had, however, no potential of proving the equilibrium due to the logical structure of the Central Limit Theorem upon which it rests[107]: zero of the measure follows from the conditions interpretable as consistent with equilibrium - but not other way round. 
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... compression[*]
The DWT transformation in itself is not yet a compression since the number of expansion coefficients necessary to reconstruct the original image equals the number of original pixels. The common DWT compression techniques are based on suppressing the small expansion coefficients. The power spectrum (used in this work) is based on a summation of squared expansion coefficients and thus, effectively suppresses the impact of the small coefficients by squaring everything, and at the same time reduces the amount of data by the summation. 
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... channel[*]
in a dedicated run where natural radioactivity of U is measured by the scintillator 
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... calibrate.[*]
if not for the light attenuation, it would have been sufficient. 
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... bins.[*]
$ \xi_{min}$ and $ \xi_{max}$ depend on $ x$ and on the choice of binning. 
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