Editing Ring-imaging Cherenkov detector (section)

=== Principles ===

A ring-imaging Cherenkov (RICH) detector allows the identification of electrically charged [[subatomic particle]] types through the detection of the [[Cherenkov radiation]]  emitted (as [[photons]]) by the particle in traversing a medium with [[refractive index]]  <math> n </math> > 1.  The identification is achieved by measurement of the angle of emission, <math> \theta_c </math>, of the [[Cherenkov radiation]], which is related to the charged particle's velocity <math> v </math> by
:<math>\cos \theta_c = \frac{c}{nv}</math>
where <math>c</math> is the speed of light.

Knowledge of the particle's [[momentum]] and direction (normally available from an associated momentum-[[spectrometer]]) allows a predicted <math> v </math> for each hypothesis of the particles type; using the known <math> n </math> of the RICH radiator gives a corresponding prediction of <math> \theta_c </math> that can be compared to the <math> \theta_c </math> of the detected Cherenkov photons, thus indicating the particle's identity (usually as a probability per particle type).  A typical (simulated) distribution of <math> \theta_c </math> vs momentum of the source particle, for single Cherenkov photons, produced in a gaseous radiator (n~1.0005, angular resolution~0.6mrad) is shown in the following Fig.1: [[File:Cherenlov angle plot.jpg|thumb|upright=1.6|left|Fig.1: Cherenkov angle vs Momentum]]

The different particle types follow distinct contours of constant mass, smeared by the effective angular resolution of the RICH detector; at higher momenta each particle emits a number of Cherenkov photons which, taken together, give a more precise measure of the average <math> \theta_c </math> than does a single photon (see Fig.3 below), allowing effective particle separation to extend beyond 100 GeV in this example.
This particle identification is essential for the detailed understanding of the intrinsic physics of the structure and interactions of elementary particles.  The essence of the ring-imaging method is to devise an optical system with single-photon detectors, that can isolate the Cherenkov photons that each particle emits, to form a single "ring image" from which an accurate <math> \theta_c </math> can be determined.

[[File:Polar plot of Chrenkov photons emission angles.jpg|thumb|upright=1.8|top|Fig.2: Cherenkov photons emitted by a 22 GeV/c pion or kaon]]
A polar plot of the Cherenkov angles of photons associated with a 22 GeV/c particle in a radiator with <math>n</math>=1.0005 is shown in Fig.2; both [[pion]] and [[kaon]] are illustrated; [[proton]]s are below Cherenkov threshold,
<math> c/nv > 1 </math>, producing no radiation in this case (which would also be a very clear signal of particle type = proton, since fluctuations in the number of photons follow [[Poisson statistics]] about the expected mean, so that the probability of e.g. a 22 GeV/c kaon producing zero photons when ~12 were expected is very small; ''e<sup>−12</sup>'' or 1 in 162755). The number of detected photons shown for each particle type is, for illustration purposes, the average for that type in a RICH having <math>N_c</math> ~ 25 (see below). The distribution in azimuth is random between 0 and 360 degrees; the distribution in <math> \theta_c </math> is spread with RMS angular resolution  ~ 0.6 [[milliradian]]s.

Note that, because the points of emission of the photons can be at any place on the (normally straight line) trajectory of the particle through the radiator, the emerging photons occupy a light-cone in space.

[[File:Mean Cherenkov angle vs momentum2.jpg|thumb|upright=1.6|left|Fig.3: Mean Cherenkov angle per particle vs momentum]]
In a RICH detector the photons within this light-cone pass through an optical system and impinge upon a position sensitive photon detector. With a suitably focusing optical system this allows reconstruction of a ring, similar to that above in Fig.2, the radius of which gives a measure of the Cherenkov emission angle <math> \theta_c </math>.

The resolving power of this method is illustrated by comparing the Cherenkov angle ''per photon'', see the first plot, Fig.1 above, with the mean Cherenkov angle ''per  particle'' (averaged over all photons emitted by that particle) obtained by ring-imaging, shown in Fig.3; the greatly enhanced separation between particle types is very clear.