Relation of observables to experimental techniques

Every probe in the search for the QGP in relativistic heavy ion collisions tends to have a different experimental technique associated with it. In all cases the multiplicities in nuclear collisions are so large that all the detectors used are very highly segmented. For measuring the charged multiplicity or dn/dy,a segmented multiplicity detector, usually an array of proportional tubes with pad readout, or a silicon pad array were used in early experiments, while Time Projection drift Chambers (TPC) have become popular more recently. For measuring transverse energy flow, dET/dy, a hadron calorimeter is used. Some groups use an electromagnetic shower counter for this purpose. This has the advantage of being smaller, cheaper and higher in resolution than a full hadron calorimeter; but it has the disadvantage of being biased, since only π0 and η0 mesons are detected (via their two photon decay). Nuclear fragmentation products are detected by calorimeters in the projectile direction and by E, dE/dx scintillator arrays in the target fragmentation region. The particle composition and transverse momentum distributions are measured using magnetic spectrometers with particle identification. Typically, time-of-flight, gas and aerogel Cerenkov counters, and dE/dx are used to separate pions from kaons, protons, deuterons, etc. Drift chambers are generally utilized for charged particle tracking, although streamer chambers and TPCs are also in use. Lepton pair detectors are very specialized, and usually combine magnetic spectrometers with lepton identification (muons by penetration, and electrons by “gas” and “glass”).

The CCRS experiment at the CERN-ISR

A very interesting thing happened in the second round of ISR experiments, two first round experiments decided to combine their detectors and join forces. The Saclay–Strasbourg experiment (R102) had proposed a second spectrometer arm (Arm 2) to study what was produced opposite in azimuth to balance the transverse momentum of the high pT hadrons [281]. Then, together with the CCR experiment (R103), it was proposed [282] to add the CCR lead glass counters (PbGl) behind the Arm 2 to enable improved detection of single electrons and gamma rays at high pT as well as to continue the search for e+e- pairs. This became R105, the CERN–Columbia–Rockefeller–Saclay experiment, CCRS (Figure 7.1). This detector turned out to be very powerful and was rewarded with one major discovery, one near-miss and several excellent measurements.

The key features of this detector were the following:

1. (i)≥105 charged hadron rejection from electron identification in the Cerenkov counter combined with matching the momentum and energy of an electron candidate in the magnetic spectrometer and the PbGl;

2. (ii) minimum of material in the aperture to avoid external conversions;

3. (iii) zero magnetic field on the axis to avoid de-correlating conversion pairs;

4. (iv) rejection of conversions in the vacuum pipe (and small opening angle internal conversions) by requiring single ionization in a hodoscope of scintillation counters H′ close to the vacuum pipe, preceded by a thin track chamber to avoid conversions in the H′ counters;

5. (v) precision measurement of π0 and η, the predominant background source;

6. (vi) precision background determination in the direct single e± signal channel by adding an external converter, to distinguish direct single e± from e± from photon conversion.

The late 1960s were very exciting for experimental high energy physicists. Two new accelerators, the CERN-ISR, in Europe [240], and the National Accelerator Laboratory (NAL, now Fermilab), in the USA [241,242], were under construction. The call for proposals went out in January 1969 for the CERN-ISR [243], with eventual first collisions in January 1971. For NAL, proposals were requested in March 1970 [244] with first operation in March 1972. Everybody who was anybody in experimental high energy physics at that time was involved in proposals at one or both laboratories.

Fermilab's accelerator was a traditional fixed target machine which provided 200 to 400 GeV primary proton beams and a large variety of secondary beams, while the CERN-ISR was the first proton–proton collider. The size and scope of the machines was quite different although both were destined to make important contributions to high pT physics, a subject that did not exist before these machines operated. Also, Fermilab was a brand new laboratory totally dedicated to the new accelerator while CERN had been in existence since 1954 with several operating accelerators [248].

The Fermilab program, circa 1970

Fermilab had held summer studies in 1968 and 1969 for users to help design and specify the various beams and facilities at the new laboratory. The layout of the accelerator [249] together with a more expanded view of the initial (circa 1973–1975) beam lines and facilities [250] is shown in Figure 6.1. Note the 1 km radius of the main accelerator.

The maximum likelihood method and least squares fits

The likelihood function L is defined as the a priori probability of a given outcome. Since Gaussian probability distributions are common (as a consequence of the central limit theorem) and since there is also an important theorem regarding likelihood ratios for composite hypotheses, it is convenient to use the logarithm of the likelihood, W = -2 ln L.

There are generally two types of fits used for data from experiments. (i) The standard maximum likelihood method is to fit a function to n independent trials of the same distribution, for example the muon lifetime measured from the decay times ti of individual decays. (ii) The method of least squares is also an extremum method which performs Gaussian least squares fits for binned data from histograms to predictions of the expectation values at each data point, which may be functions of parameters to be determined. This will be discussed following a review of the standard maximum likelihood method and the likelihood ratio test.

Maximum likelihood fit to a Gaussian, an instructive example

A nice example of the standard maximum likelihood method is a fit to a Gaussian with mean μ and variance σ2 from the observation of n independent trials with values xi from this distribution, in other words a sample of n trials from this population.

Commissioning of the Large Hadron Collider (LHC) in late summer 2009 opened a new, long awaited, era of high energy particle physics. The scientific quest of the LHC is the completion of the Standard Model (SM) of particles and forces and the search for novel phenomena beyond the SM. Exciting physics questions such as the existence of the Higgs boson, the missing link of the SM, supersymmetric particles, extra dimensions and many others are expected to be answered at the LHC. Another experimental effort follows the direction of exploration of hot and dense nuclear matter created in ultra-relativistic nuclear collisions. It is believed that such excited nuclear medium forms a soup of deconfined quarks and gluons known as a Quark Gluon Plasma (QGP) [1] and provides an ideal laboratory to study the many-body aspects of Quantum ChromoDynamics (QCD).

HighpT particle production played a key role in the foundation of QCD as a theory of the strong interaction. Shortly after the discovery of point-like constituents inside the proton in Deeply Inelastic Scattering (DIS) experiments at the Stanford Linear Accelerator Center (SLAC) [2] and the observation of particle production at large transverse momenta in p + p collisions at the Intersecting Storage Rings (ISR) at CERN [3], QCD emerged as a mathematically consistent theory [4].

Why were some people studying “high pT” physics in the 1960s?

The quick answer is that they were looking for a “left handed” intermediate boson W±, the proposed carrier of the weak interaction [35]. Although the possibility of Fermi's point-like weak interaction of β decay [18,19] being transmitted by a boson field was originally discussed by Yukawa [222] and other authors, the modern concept of the parity-violating intermediate vector bosons W± as the quanta that transmit the weak interaction was introduced by Lee and Yang in the year 1960 [35, 36] to avoid a breakdown of unitarity in neutrino scattering at high energies if the weak interaction remained point-like [35]; and experiments were proposed to detect the intermediate bosons with high energy neutrinos [37, 38]. Neutrino beams at the new BNL-AGS and CERN-PS accelerators provided the first opportunity to study weak interactions at high energy, whereas previously weak interactions had only been studied via radioactive decay.

The first high energy neutrino experiment at the BNL-AGS [39] set a limit on the mass of the intermediate boson of roughly less than the mass of the proton MW ≲ Mp. However, much more importantly, this experiment discovered that the neutrinos from charged pion decay produced only muons.