Scintillation counters Scintillation counters
Magnetic field B
Muon detector
Lead glass counter Wire chamber
Vertex detector
Supraconductive coil Iron yoke
}
e− e+
Fig. 9.3 Sketch of a4-detector, as used in eCecollision experiments. The detector is inside the coil of a solenoid, which typically produces a magnetic field of around1T along the beam direction. Charged particles are detected in a vertex detector, mostly composed of silicon microstrip counters, and in wire chambers. The vertex detector is used to locate the interaction point. The curvature of the tracks in the magnetic field tell us the momenta. Photons and electrons are detected as shower formations in electromagnetic calorimeters (of, e.g., lead glass). Muons pass through the iron yoke with little energy loss. They are then seen in the exterior scintillation counters
9.1 Lepton Pair Production
Before we turn to the creation of heavy quarks, we want to initially consider the leptons. Leptons are elementary spin-1=2 particles which feel the weak and, if they are charged, the electromagnetic interaction – but not, however, the strong interaction.
Muons The lightest particles which can be produced in electron-positron collisions are muon pairs:
eCCe!CC:
The muon and its antiparticle1theCboth have a mass of only105:7MeV=c2 and they are produced in all usual eCe storage ring experiments. They penetrate matter very easily,2 whereas electrons because of their small mass and hadrons because of the strong interaction have much smaller ranges. After that of the
1Antiparticles are generally symbolised by a bar (e.g.,e). This symbol is generally skipped over for charged leptons since knowledge of the charge alone tells us whether we have a particle or an antiparticle. We thus write eC,C,C.
2Muons from cosmic radiation can still be detected in underground mines!
126 9 Particle Production in eCeCollisions neutron, theirs is the longest lifetime (2s) of any unstable particle. This means that experimentally they may easily be identified. Therefore the process of muon pair production is often used as a reference point for other eCereactions.
Tau leptons If the centre-of-mass energy in an eCe reaction suffices, a further lepton pair, the andC, may be produced. Their lifetime,31013s, is much shorter. They may weakly decay into muons or electrons as will be discussed in Sect.10.1f.
The tau was discovered at the SPEAR eCe storage ring at SLAC when oppositely charged electron-muon pairs were observed whose energy was much smaller than the available centre-of-mass energy [16].
These events were interpreted as the creation and subsequent decay of a heavy lepton-antilepton pair:
eCCe !CC
j j!CC or eCeC
jj!eCCeC or CCC:
The neutrinos which are created are not detected.
The threshold forC-pair production, and hence the mass of the-lepton, may be read off from the increase of the cross-section of the eCe reaction with the centre-of-mass energy. One should use as many leptonic and hadronic decay channels as possible to provide a good signature for-production (Fig.9.4). The experimental threshold atp
sD2mc2implies that the tau mass is1:777GeV=c2.
0.15
0.10
0 0.05
4 5 6 7
Charm threshold
σ (e+e-- e + --+-- + X + Y) +--+--σ (ee μμ)
s [GeV]
√⎯s [GeV]
√⎯
Fig. 9.4 Ratio of the cross-sections for the production of two particles with opposite charges in the reaction eCCe!e˙CXCY, to the cross-sections for the production ofCpairs [5,6]. Here Xdenotes a charged lepton or meson and Y symbolises the unobserved, neutral particles. The sharp increase atp
s 3:55GeV is a result of -pair production, which here becomes energetically possible. The threshold for the creation of mesons containing a charmed quark (arrow) is only a little above that for-lepton production. Both particles have similar decay modes which makes it more difficult to detect-leptons
9.1 Lepton Pair Production 127 Cross-section The creation of charged lepton pairs may, to a good approximation, be viewed as a purely electromagnetic process (exchange). The exchange of Z0 bosons, and interference between photon and Z0exchange, may be neglected if the energy is small compared to the mass of the Z0. The cross-section may then be found relatively easily. The most complicated case is the elastic process eCe !eCe, Bhabha scattering. Here two processes must be taken into account: the annihilation of the electron and positron into a virtual photon with subsequent eCe-pair creation (Fig.9.5(left)) and secondly the scattering of the electron and positron off each other (Fig.9.5 (right)). These processes lead to the same final state and so their amplitudes must be added in order to obtain the cross-section.
Muon pair creation is more easily calculated. Other eCereactions are therefore usually normalised with respect to it. The differential cross-section for this reac- tion is:
d d˝ D ˛2
4s.„c/2
1Ccos2
: (9.4)
Integrating over the solid angle˝yields the total cross-section:
D 4˛2
3s .„c/2; (9.5)
and one finds
.eCe!C/D21:7 nbarn
.E2=GeV2/: (9.6) The formal derivation of (9.4) may be found in many standard text books [10,14, 15], we will merely try to make it plausible: The photon couples to two elementary charges. Hence the matrix element contains two powers ofeand the cross-section, which is proportional to the square of the matrix element, is proportional toe4or˛2.
e+
γ
e−
e+ e−
e+
γ
e− e+ e−
+
Fig. 9.5 The two processes contributing to Bhabha scattering
128 9 Particle Production in eCeCollisions
12 16 20 24 28 32 36 40 44 48 52 CELLO
JADE e+e− μ+μ−
τ+ τ−
10-2 10-1 1
σ [nb]
s [GeV]
√⎯
Fig. 9.6 Cross-sections of the reactions eCe !C and eCe !Cas functions of the centre-of-mass energyp
s(From [7] and [8]). Thesolid lineshows the cross-section (9.6) predicted by quantum electrodynamics
The length scale is proportional to„c, which enters twice over since cross-sections have the dimension of area. We must further divide by a quantity with dimensions of [energy2]. Since the masses of the electron and the muon are very small compared tos, this last is the only reasonable choice. The cross-section then falls off with the square of the storage ring’s energy. The.1Ccos2/ angular dependence is typical for the production of two spin-1=2particles such as muons. Note that (9.4) is, up to this angular dependence, completely analogous to the equation for Mott scattering (5.39) once we recognise thatQ2c2DsD4E2D4E02holds here.
Figure9.6 shows the cross-section for eCe ! C and the prediction of quantum electrodynamics. One sees an excellent agreement between theory and experiment. The cross-section for eCe ! C is also shown in the figure. If the centre-of-mass energyp
sis large enough that the difference in theand rest masses can be neglected, then the cross-sections forC andC production are identical. One speaks oflepton universality, which means that the electron, the muon and the tau behave, apart from their masses and associated effects, identically in all reactions. The muon and the tau may to a certain extent be viewed as being heavier copies of the electron.
Since (9.6) describes the experimental cross-section so well, the form factors of the and are unity – which according to Table 5.1 means they are point-like particles. No spatial extension of the leptons has yet been seen. The upper limit for the electron is1018m. Since the hunt for excited leptons so far has also been unsuccessful, it is currently believed that leptons are indeed elementary, point-like particles.