Editing Ring-imaging Cherenkov detector (section)

=== Particle Identification ===

Given the known momentum of the emitting particle and the refractive index of the radiator, the expected Cherenkov angle for each particle type can be predicted, and its difference from the observed mean Cherenkov angle calculated.  Dividing this difference by  <math> \sigma_m </math> then gives a measure of the 'number of sigma' deviation of the hypothesis from the observation, which can be used in computing a probability or likelihood for each possible hypothesis.  The following Fig.4 shows the 'number of sigma' deviation of the kaon hypothesis from a true pion ring image (''π not k'') and of the pion hypothesis from a true kaon ring image (''k not π''), as a function of momentum, for a RICH with <math>n</math> = 1.0005, <math>N_c</math> = 25, <math> \sigma </math> = 0.64 [[milliradian]]s;

[[File:Pion-kaon separation Nsigma.jpg|thumb|upright=1.5|top|Fig.4: Pion-kaon separation Nsigma]]

Also shown are the average number of detected photons from pions(''Ngπ'') or from kaons(''Ngk''). One can see that the RICH's ability to separate the two particle types exceeds 4-sigma everywhere between threshold and 80 GeV/c, finally dropping below 3-sigma at about 100 GeV.

It is important to note that '''this result is for an 'ideal' detector''', with homogeneous acceptance and efficiency, normal error distributions and zero background.  No such detector exists, of course, and in a real experiment much more sophisticated procedures are actually used to account for those effects; position dependent acceptance and efficiency; non-Gaussian error distributions; non negligible and variable event-dependent backgrounds, where the signal from any track is a background to the rest.<ref name="Adinolfi">{{cite journal |last1=Adinolfi |first1=M. |display-authors=etal |title=Performance of the LHCb RICH detector at the LHC |journal=The European Physical Journal C |date=2013 |volume=73 |issue=5 |page=2431 |arxiv = 1211.6759 |bibcode = 2013EPJC...73.2431A |doi=10.1140/epjc/s10052-013-2431-9|pmid=25814859 |pmc=4371097 }}</ref><ref>{{cite journal |last1=Wilkinson |first1=G. |title=In search of the rings: Approaches to Cherenkov ring finding and reconstruction in high energy physics |journal=Nuclear Instruments and Methods in Physics Research Section A |date=2008 |volume=595 |issue=1 |pages=228–232 |doi=10.1016/j.nima.2008.07.066|bibcode=2008NIMPA.595..228W }}</ref>

In practice, for the multi-particle final states produced in a typical [[collider]] experiment, separation of kaons from other final state [[hadrons]], mainly pions, is the most important purpose of the RICH.  In that context the two most vital RICH functions, which maximise signal and minimise combinatorial backgrounds, are its ability to ''correctly identify a kaon as a kaon'' and its ability ''not to misidentify a pion as a kaon''. The related probabilities, which are the usual measures of signal detection and background rejection in real data,  are plotted in Fig.5 below to show their variation with momentum (simulation with 10% random background);

[[File:Kaon identification plot.jpg|thumb|upright=1.5|left|Fig.5: Kaon identification plot]]

Note that the ~30% ''π → k'' misidentification rate at 100 GeV is, for the most part, due to the presence of 10% background hits (faking photons) in the simulated detector; the 3-sigma separation in the mean Cherenkov angle (shown in Fig.4 above) would, by itself, only account for about 6% misidentification. More detailed analyses of the above type, for operational RICH detectors, can be found in the published literature.

For example, the [[LHCb]] experiment at the CERN LHC studies, amongst other ''[[B-meson]]'' decays, the particular process ''B<sup>0</sup> → π<sup>+</sup>π<sup>−</sup>''. The following Fig.6 shows, on the left, the ''π<sup>+</sup>π<sup>−</sup>'' mass distribution without RICH identification, where all particles are assumed to be ''π''; the ''B<sup>0</sup> → π<sup>+</sup>π<sup>−</sup>'' signal of interest is the turquoise-dotted line and is completely swamped by background due to ''B'' and  ''Λ'' decays involving kaons and protons, and combinatorial background from particles not associated with the ''B<sup>0</sup>'' decay.<ref name="Adinolfi"/>

[[File:LHCb RICH Btoππ.jpg|thumb|upright=2.5|Fig.6: LHCb RICH Btoππ]]

On the right are the same data with RICH identification used to select only pions and reject kaons and protons; the ''B<sup>0</sup> → π<sup>+</sup>π<sup>−</sup>'' signal is preserved but all kaon- and proton-related backgrounds are greatly reduced, so that the overall ''B<sup>0</sup>'' signal/background has improved by a factor ~ 6, allowing much more precise measurement of the decay process.