Exchange Bosons of the Weak Interaction and the Higgs Boson
12.1 Real W and Z Bosons
Chapter 12
Exchange Bosons of the Weak Interaction
186 12 Exchange Bosons of the Weak Interaction and the Higgs Boson
W bosons can also be produced in eCereactions, but only in pairs:
eCCe ! WCCW:
Hence, significantly higher energies are necessary for their production: p s >
2MWc2.
In 1996 the beam energy at LEP was upgraded from 50 to 86 GeV and later even to 104.6 GeV. This made a precise measurement of the W-mass and of the decay products of the WCWpairs possible.
For many years the production of W˙ or Z0bosons was only possible with the help of quarks and antiquarks in the proton via the reactions
uCu!Z0; dCu!W; dCd!Z0; uCd!WC:
For these reactions, however, it is insufficient to collide two proton beams each with half the rest energy of the vector bosons. Rather, the quarks which participate have to carry enough centre-of-mass energyp
O
s to produce the bosons. In a fast moving system, quarks carry only a fractionxPpof the proton momentumPp (cf.
Sect.7.3). About half the total momentum is carried by gluons; the rest is distributed among several quarks, with the meanxfor valence quarks and sea quarks given by
hxvi 0:12 hxsi 0:04 : (12.1) One can produce a Z0boson in a head-on collision of two protons according to
uCu ! Z0:
But the proton beam energyEpmust be close toEp600GeV in order to satisfy MZc2 D p
Os p
hxuihxui s D 2p
0:120:04Ep: (12.2) Proton-antiproton collisions are more favourable, since the momentum distribu- tions of the u- and d-valence quarks in antiprotons are equal to those of the u- and d-valence quarks in protons. Consequently, only about half the energy is necessary.
Since a p and a p have opposite charges, it is also not necessary to build two separate accelerator rings; both beams can in fact be injected in opposite directions into the same ring. At the SPS (Super Proton Synchrotron) at CERN, which was renamed Sp¯pS (Super Proton Antiproton Storage ring) for this, protons and antiprotons of up to 318 GeV were stored; at the Tevatron (FNAL), 980 GeV beam energies were attained.
12.1 Real W and Z Bosons 187
Fig. 12.1 “Lego diagram” of one of the first events of the reaction qq!Z0!eCe, in which the Z0boson was detected at CERN. The transverse energies of the electron and positron detected in the calorimeter elements are plotted as a function of the polar and azimuthal angles [7]
φ θ
e2
e1
10 GeV
360° 270° 180° 90
° 0° 140°
90° 40
°
The bosons were detected for the first time in 1983 at CERN at the UA1 [6] and UA2 [5,8] experiments in the decays
Z0 eCCe; WCeCCe; Z0 CC; WCCC:
The Z0 boson has a very simple experimental signature. One observes a high- energy eCe orC pair with the lepton and antilepton flying off in opposite directions. Figure12.1shows a so-called “lego diagram” of one of the first events.
The figure shows the transverse energy measured in the calorimeter cells plotted against the polar and azimuthal angles of the leptons relative to the incoming proton beam. The height of the “lego bars” measures the energy of the leptons. The total energy of both leptons corresponds to the mass of the Z0.
The detection of the charged vector bosons is somewhat more complicated, since only the charged lepton leaves a trail in the detector and the neutrino is not seen.
The presence of the neutrino may be inferred from the momentum balance. When the transverse momenta (the momentum components perpendicular to the beam direction) of all the detected particles are added together the sum is found to be different from zero. Thismissing(transverse)momentumis ascribed to the neutrino.
Mass and width of the W boson The distribution of the transverse momenta of the charged leptons may also be used to find the mass of the W˙. Consider a WC produced at rest and then decaying into an eCand ae, as shown in Fig.12.2a. The transverse momentum of the positron is roughly given by
petC MWc
2 sin ; (12.3)
188 12 Exchange Bosons of the Weak Interaction and the Higgs Boson
Fig. 12.2 (a) Kinematics of the decay WC!eCCe. The maximum possible transverse momentumptof the eCisMWc=2.
(b) Distribution of the transverse momentumptof eCand ein the reaction q1Cq2!e˙C“nothing”, from the D0 experiment at the Tevatron (After [3])
where is the angle at which the positron is emitted with respect to the beam axis.
We now consider the dependence of the cross-section onptor on cos. We have d
dpt
D d
d cos d cos dpt
; (12.4)
from which follows d dpt
D d
d cos 2pt
MWc 1
p.MWc=2/2pt2
: (12.5)
The cross-section should have a maximum at pt D MWc=2 (because of the transformation of variables, also called a Jacobian peak) and should then drop off rapidly. Since the W is not produced at rest and has a finite decay width the distribution is smeared out. In Fig.12.2b a recent high statistics measurement of the ptdistribution by the D0 experiment at the Tevatron/FNAL [3] is shown.1The data have been obtained in p-p collisions at a centre-of-mass energy ofN 1:96TeV. The most precise figures to date for the width and mass of the W are [19]
MWD80:385˙0:015 GeV/c2;
WD 2:085˙0:042 GeV: (12.6)
1Instead of the transverse momentum, one nowadays rather uses the transverse mass m2t D 2peCtc
pet
c .1cos.eC; e//, whereis the opening angle between the electron momentum and the reconstructed neutrino momentum [15].
12.1 Real W and Z Bosons 189 Mass and width of the Z boson Since the cross-section for creating Z-bosons in eCecollisions is much larger than the cross-section for creating W bosons, in either eCe or pp collisions, the mass and width of the Z0 boson have been much more precisely determined than their W boson counterparts. Furthermore, the energies of the eCand ebeams are known to an accuracy of a few MeV, which means that the measurements are very precise. The experimental values of the Z0 parameters and width are [19]
MZ D91:1876˙0:0021GeV/c2;
ZD 2:4952˙0:0023GeV: (12.7) Decays of the W boson When we dealt with the charged-current decays of hadrons and leptons we saw that the W boson only couples to left-handed fermions (maximum parity violation) and that the coupling is always the same (universality).
Only the Cabibbo rotation causes a small correction in the coupling to the quarks.
If this universality of the weak interaction holds, then all types of fermion- antifermion pairs should be equally likely to be produced in the decay of real W bosons. The colour charges mean that an extra factor of 3 is expected for quark- antiquark production. The production of a t-quark is impossible because of its larger mass. Thus, if we neglect the differences between the fermion masses, a ratio of 1 : 1 : 1 : 3 : 3 is expected for the production of the pairs eCe,C,C, ud0, and cs0, in the decay of the WCboson. Here, the states d0and s0are the Cabibbo-rotated eigenstates of the weak interaction.
Because of the process of hadronisation, it is not always possible in an exper- iment to unequivocally determine the type of quark-antiquark pair into which a W boson decays. Leptonic decay channels can be identified much more easily.
According to the above estimate, a decay fraction of 1/9 is expected for each lepton pair. The experimental results are [19]
W˙ ! e˙C./e 10:75˙0:13% ˙C./ 10:57˙0:15%
˙C./ 11:25˙0:20%; (12.8) in very good agreement with our prediction.
Decays of the Z boson If the Z boson mediates the weak interaction in the same way as the W boson does, it should also couple with the same strength to all lepton- antilepton pairs and to all quark-antiquark pairs. One therefore should expect a ratio of 1 : 1 : 1 : 1 : 1 : 1 : 3 : 3 : 3 : 3 : 3 for the six leptonic channels and the five hadronic channels which are energetically accessible; i.e., 1/21 for each lepton-antilepton pair, and 1/7 for each quark-antiquark pair.
190 12 Exchange Bosons of the Weak Interaction and the Higgs Boson To determine the branching ratios, the various pairs of charged leptons and hadronic decays must be distinguished with appropriate detectors. The differ- ent quark-antiquark channels cannot always be separated. Decays into neutrino- antineutrino pairs cannot be directly detected. In order to measure their contribution, the cross-sections for all other decays are measured, and compared to the total width of the Z0boson. Treating the spin dependencies correctly [18], we rewrite the Breit- Wigner formula (9.8) in the form
i!f.s/D12.„c/2 if
.sM2Zc4/2CMZ2c4tot2
: (12.9)
Here,iis the partial width of the initial channel (the partial width for the decay Z0 !eCe) andf is the partial width of the final channel. The total width of the Z0is the sum of the partial widths of all the possible decays into fermion-antifermion pairs:
tot.Z0/D X
all fermions f
.Z0!ff/ : (12.10)
Each final channel thus yields a resonance curve with a maximum atp
sDMZc2, and a total width of tot. Its height is proportional to the partial width f. The partial widthf can experimentally be determined from the ratio of the events of the corresponding channel to the total number of all Z0events.
Analyses of the experiments at LEP and SLC yield the following branching ratios [19]:
Z0 ! eCCe 3:363˙0:004% CC 3:366˙0:007% CC 3:370˙0:008% e;;Ce;; 20:00 ˙0:06 %
hadrons 69:91 ˙0:06 %: (12.11)
Thus, the probability for a decay into charged leptons is significantly different from the decay probability into neutrinos. The coupling of the Z0boson apparently depends on the electric charge. Hence the Z0 cannot simply be a “neutral W boson” coupling with the same strength to all fermions; rather it mediates a more complicated interaction.