# Ring-imaging Cherenkov detector

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The ring-imaging Cherenkov, or RICH, detector is a device for identifying the type of an electrically charged subatomic particle of known momentum, that traverses a transparent refractive medium, by measurement of the presence and characteristics of the Cherenkov radiation emitted during that traversal. RICH detectors were first developed in the 1980s and are used in high energy elementary particle- , nuclear- and astro-physics experiments.

In the physical sciences, subatomic particles are particles much smaller than atoms. The two types of subatomic particles are: elementary particles, which according to current theories are not made of other particles; and composite particles. Particle physics and nuclear physics study these particles and how they interact. The idea of a particle underwent serious rethinking when experiments showed that light could behave like a stream of particles as well as exhibiting wave-like properties. This led to the new concept of wave–particle duality to reflect that quantum-scale "particles" behave like both particles and waves. Another new concept, the uncertainty principle, states that some of their properties taken together, such as their simultaneous position and momentum, cannot be measured exactly. In more recent times, wave–particle duality has been shown to apply not only to photons but to increasingly massive particles as well.

In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction in three-dimensional space. If m is an object's mass and v is the velocity, then the momentum is

In the field of optics, transparency is the physical property of allowing light to pass through the material without being scattered. On a macroscopic scale, the photons can be said to follow Snell's Law. Translucency is a superset of transparency: it allows light to pass through, but does not necessarily follow Snell's law; the photons can be scattered at either of the two interfaces, or internally, where there is a change in index of refraction. In other words, a translucent medium allows the transport of light while a transparent medium not only allows the transport of light but allows for image formation. Transparent materials appear clear, with the overall appearance of one color, or any combination leading up to a brilliant spectrum of every color. The opposite property of translucency is opacity.

## Contents

This article outlines the origins and principles of the RICH detector, with brief examples of its different forms in modern physics experiments.

## Ring-imaging Cherenkov (RICH) detector

### Origins

The ring-imaging detection technique was first proposed by Jacques Séguinot and Tom Ypsilantis, working at CERN in 1977. [1] Their research and development, of high precision single-photon detectors and related optics, lay the foundations for the design [2] [3] and construction of the first large-scale Particle Physics RICH detectors, at CERN's OMEGA facility [4] [5] and LEP (Large Electron–Positron Collider) DELPHI experiment. [6]

The European Organization for Nuclear Research, known as CERN, is a European research organization that operates the largest particle physics laboratory in the world. Established in 1954, the organization is based in a northwest suburb of Geneva on the Franco–Swiss border and has 23 member states. Israel is the only non-European country granted full membership. CERN is an official United Nations Observer.

The Large Electron–Positron Collider (LEP) was one of the largest particle accelerators ever constructed.

DELPHI was one of the four main detectors of the Large Electron–Positron Collider (LEP) at CERN, one of the largest particle accelerators ever made. Like the other three detectors, it recorded and analyzed the result of the collision between LEP's colliding particle beams.

### 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 ${\displaystyle n}$ > 1. The identification is achieved by measurement of the angle of emission, ${\displaystyle \theta _{c}}$, of the Cherenkov radiation, which is related to the charged particle's velocity ${\displaystyle v}$ by

Cherenkov radiation is an electromagnetic radiation emitted when a charged particle passes through a dielectric medium at a speed greater than the phase velocity of light in that medium. The characteristic blue glow of an underwater nuclear reactor is due to Cherenkov radiation.

In optics, the refractive index or index of refraction of a material is a dimensionless number that describes how fast light propagates through the material. It is defined as

${\displaystyle \cos \theta _{c}={\frac {c}{nv}}}$

where ${\displaystyle c}$ is the speed of light.

Knowledge of the particle's momentum and direction (normally available from an associated momentum-spectrometer) allows a predicted ${\displaystyle v}$ for each hypothesis of the particles type; using the known ${\displaystyle n}$ of the RICH radiator gives a corresponding prediction of ${\displaystyle \theta _{c}}$ that can be compared to the ${\displaystyle \theta _{c}}$ of the detected Cherenkov photons, thus indicating the particle's identity (usually as a probability per particle type). A typical (simulated) distribution of ${\displaystyle \theta _{c}}$ 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 figure:

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 ${\displaystyle \theta _{c}}$ than does a single photon, 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 ${\displaystyle \theta _{c}}$ can be determined.

A polar plot of the Cherenkov angles of photons associated with a 22 GeV/c particle in a radiator with ${\displaystyle n}$=1.0005 is shown below; both pion and kaon are illustrated; protons are below Cherenkov threshold, ${\displaystyle c/nv>1}$, 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−12 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 ${\displaystyle N_{c}}$ ~ 25 (see below). The distribution in azimuth is random between 0 and 360 degrees; the distribution in ${\displaystyle \theta _{c}}$ is spread with RMS angular resolution ~ 0.6 milliradians.

In particle physics, a pion is any of three subatomic particles:
π0
,
π+
, and
π
. Each pion consists of a quark and an antiquark and is therefore a meson. Pions are the lightest mesons and, more generally, the lightest hadrons. They are unstable, with the charged pions
π+
and
π
decaying with a mean lifetime of 26.033 nanoseconds, and the neutral pion
π0
decaying with a much shorter lifetime of 84 attoseconds. Charged pions most often decay into muons and muon neutrinos, while neutral pions generally decay into gamma rays.

In particle physics, a kaon, also called a K meson and denoted
K
, is any of a group of four mesons distinguished by a quantum number called strangeness. In the quark model they are understood to be bound states of a strange quark and an up or down antiquark.

A proton is a subatomic particle, symbol
p
or
p+
, with a positive electric charge of +1e elementary charge and a mass slightly less than that of a neutron. Protons and neutrons, each with masses of approximately one atomic mass unit, are collectively referred to as "nucleons".

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 fill a light-cone in space.

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, the radius of which gives a measure of the Cherenkov emission angle ${\displaystyle \theta _{c}}$. The resolving power of this method is illustrated by comparing the Cherenkov angle per photon, see the first plot above, with the mean Cherenkov angle per particle (averaged over all photons emitted by that particle) obtained by ring-imaging, shown below; the greatly enhanced separation between particle types is very clear:

This ability of a RICH system to successfully resolve different hypotheses for the particle type depends on two principal factors, which in turn depend upon the listed sub-factors;

• The effective angular resolution per photon, ${\displaystyle \sigma }$
• Chromatic dispersion in the radiator (${\displaystyle n}$ varies with photon frequency)
• Aberrations in the optical system
• Position resolution of the photon detector
• The maximum number of detected photons in the ring-image, ${\displaystyle N_{c}}$
• The length of radiator through which the particle travels
• Photon transmission through the radiator material
• Photon transmission through the optical system
• Quantum efficiency of the photon detectors

${\displaystyle \sigma }$ is a measure of the intrinsic optical precision of the RICH detector. ${\displaystyle N_{c}}$ is a measure of the optical response of the RICH; it can be thought of as the limiting case of the number of actually detected photons produced by a particle who's velocity approaches that of light, averaged over all relevant particle trajectories in the RICH detector. The average number of Cherenkov photons detected, for a slower particle, of charge ${\displaystyle q}$ (normally ±1), emitting photons at angle ${\displaystyle \theta _{c}}$ is then

${\displaystyle N={\dfrac {N_{c}q^{2}\sin ^{2}(\theta _{c})}{1-{\dfrac {1}{n^{2}}}}}}$

and the precision with which the mean Cherenkov angle can be determined with these photons is approximately

${\displaystyle \sigma _{m}={\frac {\sigma }{\sqrt {N}}}}$

to which the angular precision of the emitting particle's measured direction must be added in quadrature, if it is not negligible compared to ${\displaystyle \sigma _{m}}$.

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 ${\displaystyle \sigma _{m}}$ 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 figure 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 ${\displaystyle n}$ = 1.0005, ${\displaystyle N_{c}}$ = 25, ${\displaystyle \sigma }$ = 0.64 milliradians;

A milliradian, often called a mil or mrad, is an SI derived unit for angular measurement which is defined as a thousandth of a radian. Mils are used in adjustment of firearm sights by adjusting the angle of the sight compared to the barrel. Mils are also used for comparing shot groupings, or to compare the difficulty of hitting different sized shooting targets at different distances. When using a scope with both mil adjustment and a reticle with mil markings, the shooter can use the reticle as a "ruler" to count the number of mils a shot was off target which directly translates to the sight adjustment needed to hit the target with a follow up shot. Optics with mil markings in the reticle can also be used to make a range estimation of a known size target, or vice versa to determine a target size if the distance is known, a practice called "milling".

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. [7] [8]

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 below to show their variation with momentum (simulation with 10% random background);

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 the 4th plot 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 B0 → π+π. The following figure shows, on the left, the π+π mass distribution without RICH identification, where all particles are assumed to be π ; the B0 → π+π 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 B0 decay. [7]

On the right are the same data with RICH identification used to select only pions and reject kaons and protons; the B0 → π+π signal is preserved but all kaon- and proton-related backgrounds are greatly reduced, so that the overall B0 signal/background has improved by a factor ~ 6, allowing much more precise measurement of the decay process.

### RICH Types

Both focusing and proximity-focusing detectors are in use. In a focusing RICH detector, the photons are collected by a spherical mirror with focal length ${\displaystyle f}$ and focused onto the photon detector placed at the focal plane. The result is a circle with a radius ${\displaystyle r=f\theta _{c}}$, independent of the emission point along the particle's track (${\displaystyle \theta _{c}\ll 1}$). This scheme is suitable for low refractive index radiators (i.e., gases) with their larger radiator length needed to create enough photons.

In the more compact proximity-focusing design a thin radiator volume emits a cone of Cherenkov light which traverses a small distance, the proximity gap, and is detected on the photon detector plane. The image is a ring of light the radius of which is defined by the Cherenkov emission angle and the proximity gap. The ring thickness is mainly determined by the thickness of the radiator. An example of a proximity gap RICH detector is the High Momentum Particle Identification (HMPID), one of the detectors of ALICE (A Large Ion Collider Experiment), which is one of the five experiments at the LHC (Large Hadron Collider) at CERN.

In a DIRC (Detection of Internally Reflected Cherenkov light), another design of a RICH detector, light that is captured by total internal reflection inside the solid radiator reaches the light sensors at the detector perimeter, the precise rectangular cross section of the radiator preserving the angular information of the Cherenkov light cone. One example is the DIRC of the BaBar experiment at SLAC.

The LHCb experiment on the Large Hadron Collider uses two RICH detectors for differentiating between pions and kaons. [9] The first (RICH-1) is located immediately after the Vertex Locator (VELO) around the interaction point and is optimised for low-momentum particles and the second (RICH-2) is located after the magnet and particle-tracker layers and optimised for higher-momentum particles. [7]

The Alpha Magnetic Spectrometer device AMS-02, recently mounted on the International Space Station uses a RICH detector in combination with other devices to analyze cosmic rays.

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