lecture 9 - istituto nazionale di fisica nucleare · 2018. 6. 20. · 6/20/2018 experimental...

Lecture 9

6/20/2018 Experimental Methods in High Energy Physics - An Introductory Course (L. Moroni) 2

Introduction to Particle Identification

• We have just learned how to measure the momentum of a HE charged particle

• Now, we have to measure its velocity, or , to obtain its mass and therefore to identify it completely

– In principle, we could equally measure the particle energy and extract its mass from , but this becomes unpractical already at few GeV• for a pion of 5 GeV/c momentum is 0.04%

• Recall we are dealing with the final-state particles produced by the process under investigation, once even the short lived particles have decayed

• We have then to distinguish among a limited number of stable or quasi-stable charged particles, and mainly

– e, , p , , k

• In this HE context, a particle is called quasi-stable when it is very likely that it can crosses the apparatus without decaying

• This is the case for and k mesons, which have a mean life of the order of 10-8 sec

22 pEm

ppE 22


Particle Identification

• Unfortunately, there isn’t a single method capable to measure the particle velocity over a wide range of

• Depending on the value, different techniques are used and can be summarized as follows

1. For low values we typically measure the time of flight between two fast counters

2. For 5 up to of the order of 100 we employ Cerenkov detectors

– Aerogel dets in the low range, threshold Cerenkov dets in the middle range and then differential Cerenkov dets

3. For larger values and up to 1000, we measure the relativistic rise of the particle dE/dx in gaseous detectors

– Multiple (100) dE/dx sampling is necessary to compensate for the huge fluctuations

4. For higher values (>1000), we use the transition radiation detectors


Time of Flight

• The method is very simple:• We measure the time-of-flight difference over a distance L for two equal

momentum particles of masses, m1 and m2

• That is, for p2>>m2

• Therefore, for a given time difference, L increases as p2

• Using a very good scintillator counter system with t 300 ps, /k separation at 4 t level would require a flight path, L, of 3m at 1 GeV/c and 12 m at 2 GeV/c

• In conclusion, given the time resolution of the present fastest detectors, e.g. 50 ps for spark chambers, this method would anyhow need very long flight paths and hence can be used only for very low values of

2

2

2

2

2

1

21

11p

m

p

m

c

L

c

L

c

Lt

2

2

2

2

1

2p

mm

c

Lt


Time of Flight Performance


Cerenkov Detectors: Physics Principles

• Let’s consider a particle of mass m and velocity v, which interacts with the medium of the detector via a photon of energy and momentum

• Energy and momentum conservation requires

• For “soft collisions”, i.e. and , we get

h kh

m

EE

p

m

khvkh

mc

hh

Recall22

122

2

2mch mvkh

kv


Just in case you need further explanations

• Momentum & Energy conservation

• Therefore

2

2 2 2 4 2 2 2 2

2 4 2 2 2 2 2 2 2 2 2 2 4 2 2 2

2 2 4 2 2 2 2 2 2 4 2

2

2 2

2

( ) ( )

2 2

2 2 (1 )2

(1 )2 2

out

out

in out

p mv k

E mc

E E m c mv k c mc

m c m v c k c m v kc m c mc

m c k c m v kc m c mcmc

kv k

m mc


Physics of the Cerenkov Effect

• Now, the behavior of a photon in a non-magnetic medium obeys the following dispersion relation

• where is the dielectric constant• Therefore, we obtain

• where n is refractive index of the medium

• This means that, if , the C angle is real and thus real

photons can be emitted

• This is know as Cerenkov effect and the velocity as Cerenkov threshold

nv

cC

11cos

022

2

ck

1v

c

n

ccv


Frequency Dependence of

• So far we have assumed real.• In practice, this is only true below the ionization

threshold of the medium • In fact, the general behavior of the dielectric constant

of a medium is that sketched in the following figure

•


The Optical and the Absorption regions

• At low frequencies real and >1: this is the optical region, where the medium is transparent and the refractive index n>1

– Since >1, even for <1 and thus Cerenkov

radiation can be emitted

– The emission of sub-threshold Cerenkov radiation in presence of discontinuities in the medium is also possible and is called “optical transition radiation” • This is not important for particle ID

• At intermediate frequencies, becomes complex and its imaginary part is responsible for the absorption of the virtual photons, which give rise to the ionization of the medium– The correspondent ionization loss of the particle is given

by Bethe-Bloch expression for dE/dx

11


The x-ray Region

• The residual absorptive part of is still responsible of small contributions to the tail of the dE/dx distribution, but at frequencies above its K-edge the medium becomes again nearly transparent – is nearly real, but, since its value is <1, the

Cerenkov threshold velocity is greater than c

– Nevertheless, the emission of sub-threshold Cerenkov radiation in presence of discontinuities in the medium may still occur; this is known as X-ray Transition Radiation and it is exploited for particle ID by the Transition Radiation Detectors as we will see in the next


An Explicit Example: Argon Gas


Transition Radiation

• To introduce the physics principles at the basis of the transition radiation we will use the following heuristic argument due to Frank, who in 1944 together with Ginzburg predicted this phenomenon.

Transition Radiation and The Cerenkov Effect: I.M.Frank, Sov. Phys. Usp. 4 740, 1962



• As already anticipated, when a relativistic particle traverse an inhomogeneous medium characterized by a sudden discontinuity of the dielectric properties, such as the interface between two materials, transition radiation can be emitted

• We are particularly interested in the X-ray TR, since it depends on the factor of the particle, thus allowing for an identification of the particles in a very high energy region (>1000) where other methods fail

• Let’s study the main properties of this radiation as illustrated on the PDG

•


How to exploit TR in a Detector

• As we have just learned, we should stack many thin foils together in order to increase the amount of emitted radiation and thus facilitate the detection

• Doing this we should care of the interference effects and therefore find the right periodicity to obtain coherence

• To this extent, we have to recall that the expressions we just studied are valid for a single foil in vacuum; when several foils are placed in a gas, as in the usual detectors, also the formation zone in the gas play an important role

• In this case, it can be shown that the optimal configuration for coherence features stacks of a formation zone thick foils and, analogously, a formation zone thick gaps between foils, keeping in mind that the formation zone of the foils differs from that of the gas because of the different p

• This is substantially the philosophy at the basis of the TR detectors as we will describe later

• In addition we will see that particular care should be paid to minimize the absorption of the radiation in the next foils of the stack


Cerenkov Threshold Counters

• These counters represent the simplest application of Cerenkov detectors for particle identification

• Their operation is based on the fact that, for a certain value of momentum, a particle of mass m1 emits Cerenkov radiation, whereas another one with m2>m1 does not

• In general, the amount of Cerenkov radiated energy per unit of length is

• This tells us that

•

• and, therefore, the spectrum of emitted Cerenkov photons is flat in any frequency range where the refraction index, n, can be assumed constant .

• In particular, the number of visible photons emitted on a length L is

• i.e. 500 sin2C photons per cm for unit charge, z=1, particle• If we extend the detection into the UV region we can increase this yield by a factor of 2-3

dnc

hz

ds

dE

n

1

22

2 11

2

C

nm

nm

C LzdLzN

22

700

400

2

22 sin500

sin2

222

2

22

2 11

211

2

n

z

dsd

dN

nc

z

dsd

dN

or


Cerenkov Threshold Counters: Principle of Operation

• The counter typically consists of radiator volume, whose length is set by the desired amount of Cerenkov photons

• The radiated Cerenkov photons are collected by a mirror at the end of the radiator tank and focused on an external PMT


Radiator Length to Distinguish m1 from m2

• Let’s now calculate the radiator length L needed to distinguish two particles of mass m1 and m2 respectively (m1<m2) at a certain momentum p

• We would choose for a radiator with a refractive index n such that heavier particle with mass m2 be below threshold or just below threshold, or equivalently

• Thus the amount of Cerenkov light from the particle of mass m1 is proportional to

• which for >>1 becomes

• In a radiator of length L, detecting visible photons with a QE of 20%, the number of photoelectrons is

• Demanding for a minimum of 10 PE, we get

• Therefore, also in this case, the needed radiator length, L, scales as p2

22

1

2 11sin

nC

2

2

1

2

2100p

mmLNPE

2

2

1

2

2

2

2

2

2

1

2

2

2

2

2

1

2

2

22

2

2

1

2

2

1

2

22 11sinp

mm

mp

mm

E

EE

pE

EpC

)(10 2

1

2

2

2

mm

pL

2

2

2 1 n

)1( 2

2

2

2

2 n


Some Useful Formula for n close to 1• Since the refractive index, n, is really close to 1, it is interesting to write it as

n=1+, where <<1• Since,

• and

• recalling

• we obtain

• This expression can be written in two ways,

• The first, which follows from , giving the Cerenkov threshold condition, the second the mass of the particle as a function of the Cerenkov angle

2

22 2

p

mC

21cos

21

2

2

2

22

CC

p

m

mp

p

E

p

2

2

2

2 21

)2

1)(1(

11

p

m

p

mn

nC

1cos

222 CTr pmmppC

02 C


/k Separation at High Momentum

• Now we want to study how efficiently we can distinguish from k at high momentum using a Cerenkov threshold counter

• To this extent, we will choose as radiator the gas with the lowest refractive index, the Helium

• At atmospheric pressure and room temperature, its refractive index is such that =3510-6

• Now, from

• we obtain

• Therefore, we can achieve a full /k separation from 17 to 59 GeV/c• Now, assuming 5 m radiator length and 20% QE, we get

• The corresponding inefficiency (Poisson)

• tells us that we would confuse a pion with a kaon in the 3.4% of cases

2mpCTr

GeV/c5910352

494.0GeV/c17

10352

140.0

66

k

TrTr CCpp

4.3)2(5005002.0 22 pmNPE

%4.3ecyInefficien -3.4


Combinations of Cerenkov Threshold Counters

• For practical purposes, as for HE experiments, the particle ID, and in primisthe /k/p separation, is accomplished employing suitable combinations of different threshold counters

• It follows that the identification will be complete in a certain ranges of momentum, ambiguous in other ranges and even total confused in other ones

• The following table describe the main parameters of the FOCUS Cerenkov threshold system

• I leave you as an exercise to determine the resulting ID efficiencies as a function of momentum

Cerenkov Cone Radius

at image plane for =1


Differential Cerenkov Counters

• You might have wondered why, instead of complicating our life with Cerenkov threshold counters and their puzzling truth tables, we shouldn’t directly measure the Cerenkov angle and then extract the particle mass from the equation

• Well, this is possible and can be accomplished using a special class of detectors called “Differential Cerenkov counters”

• But, as usual in practical life, these advantages do not come for free

• Typically, these detectors are very sophisticated, expensive and such to require an army of physicists to keep them calibrated and efficient in a HE experiment

• Therefore, despite the clear advantages in terms of particle ID efficiency , we would choose for them only on the basis of a proven gain in Physics

• Now, let’s see how these Differential Cerenkov counters works

22 Cpm


Differential Cerenkov Counters: Principles of Operation

• In a differential counter, the Cerenkov light produced by a particle traversing the radiator gas is focused into a tight ring on a plane.

• The optics is illustrated below for a particle radiating a Cerenkov photon at a distance Z from a parabolic mirror of focal length f– Recall that all Cerenkov photons are radiated in a cone of half angle C

• The position yl of the reflected ray on a plane at an arbitrary distance l from the mirror can be computed in the small angle approximation as follows

• where ym is the distance between the intersection of the ray at the mirror plane and the optical axis

C

m

Cm

m

C

mCmy

f

y

yy

ff

Z

f

y

1

101

recall

my

c c'PP Z

l

ly


Differential Cerenkov Counters: Principles of Operation

• Now, recalling from the previous equation, we obtain

• This means that yl will in general depend on Z, the position at which the photon was radiated, but, if we choose the image plane (l=f), yl will be independent of Z

• Thus, all photons become focused on a tight ring independent of where they are radiated– This is the crucial requirement for a differential Cerenkov system since the total

number of radiated photons is generally very low and hence, if they are not well focused, the radius of their ring would be impossible to be measured

• The ring radius becomes

• and, therefore, recalling , we finally obtain

( ) ( ) (1 )Cl C C C C C C

Z ly Z l Z l l Z

f f

Cf fyR

22 Cpm

2

2

2f

Rpm


The DISC and the RICH

• DISC counters– The optical structure we have just discussed works in principle only for particles

which radiate exactly along the axis of the mirror – This optics is indeed used for the DISC counters, which provide particle ID for a

well collimated particle beam of a definite momentum, coming around a definite axis.

– In this case, a annular diaphragm is placed on the image plan to let go through only photon of a particular Cerenkov angle and thus coming from a particular kind of particles present in the beam

– Behind the diaphragm, a suitable matrix of photo-detectors is located to detect the photon and thus to signal the presence of the preselected particle

• RICH counters (the acronym of Ring Imaging Cherencov)– A variant of this optics is required when the differential Cerenkov counter is

used for an experiment– In this case, in fact, the incoming particles come roughly from a single point, the

interaction region, but have wildly different directions– The axis of the mirror should then be degenerate in order to match all the rays

coming from the interaction point– The most natural solution would then be to employ a spherical mirror as shown

in the figure on the following page


Principle of RICH Counters

• Since the focal length of the mirror is RM/2, the Cerenkov light emitted along the particle path is focused onto a ring on the detector sphere

• Because the radius of the ring is CRM/2, its opening angle as seen from the IP or target is again C

RICH Schematic for FT-like Experiment


Expected Particle ID Performance

Cherenkov angle vs P

Gas

• Magnification of the gas detector characteristics


BaBar Detector for Internally Reflected Cherenkov light


The BaBar DIRC


The DIRC Pictorial View


The BaBar DIRC


Transition Radiation Detectors: Choice of the Radiator

• Here , as anticipated, the problem is to minimize the absorption of the TR X-rays in the stack of thin foils– Indeed, many coherent foils are requested in order to

get an efficient detector

• This would then ask for a low Z material for the radiators, since the X-ray absorption goes as Z3.5

• On the other hand, the amount of radiated energy is proportional to the square root of the electron density or the radiator

• Hence, the best compromise is a material with high electron density and low Z

• The most used material are typically Lithium, Carbon, CH2 (polyethylene) or C5H4O2 (Mylar)


Transition Radiation Detectors

• Actual TR counters consist of a radiator-foil stack followed by a proportional gas chamber filled with Xenon (Z=54) for the detection of the emitted X-rays


X-ray Detection in TDR

• The main problem to this extent is to distinguish the ionization due to the passage of the charged particle from that due to the absorption of the associated TR X-rays, since they practically overlap in the detector– TR1/

• The simplest way to separate them is to exploit the different amount of ionization released by the two processes, as shown in figure

• A direct threshold discrimination of the collected signal will then work, or even better a discrimination based on ionization cluster counting– In the latter method, indeed, one can reduce the overlap due to the

long Landau tail, since the number of clusters is Poisson distributed


TDR Performance

• In this case, an electron efficiency of 90% was reached with a pion contamination lower than 10-3 at 15 GeV/c– 3104 for the electron

• These excellent figures were obtained for a particular cluster threshold energy of 4 KeV

• On the side are shown the advantages of the cluster counting method


TDR Performance

• Here, a kaon rejection of 10-2

was achieved for a 90% piondetection efficiency at 140 GeV/c– 103 for the pion

• Again, cluster counting improves the performance by about a factor of 10

• For further details see the caption below


Particle ID Through dE/dx

• There is a region of between 100 and 1000 where none of the methods we have studied is applicable for particle ID– Cerenkov counters, indeed, can be operated up to 100, whereas TDR work for >1000

• In this region, the only way to gather some information on the particle velocity is to exploit the relativistic rise (1.5) of the ionization loss in the gases– This to avoid the density effect, which, for higher

density materials, would reduce the amount of dE/dx rise


From CERN Academic Training Lectures

lecture 9 - istituto nazionale di fisica nucleare · 2018. 6. 20. · 6/20/2018 experimental...

Documents