22.4. The discovery of the W
± and Z
0 at the CERN p¯ p collider
397
is good, but there is a suggestion that the tree-level prediction is on the low
side. Indeed, loop corrections adjust (22.78) to a value M
th
⋍ 91.19 GeV,
Z
in excellent agreement with the current experimental value (Nakamura et al.
2010).
The total Z
0 width Γ Z is an interesting quantity. If we assume that, for
any fermion family additional to the three known ones, only the neutrinos are
significantly less massive than M Z /2, we have
Γ Z ⋍ (2.5 + 0.16ΔN ν ) GeV
(22.111)
from section 22.3, where ΔN ν is the number of additional light neutrinos
(i.e. beyond ν e , ν μ and ν τ ) which contribute to the width through the process
Z
0
→ νν ¯. Thus (22.111) can be used as an important measure of the number
of such neutrinos (i.e. generations) if Γ Z can be determined accurately enough.
The mass resolution of the ¯
was
as the total
pp experiments
of the same order
expected Z
0 width, so that (22.111) could not be used directly. The advent
of LEP provided precision checks on (22.111); at the cost of departing from
the historical development, we show data from DELPHI (Abreu et al. 1990,
Abe 1991) in figure 22.19, which established N ν = 3.
We turn now to the W
± . In this case an invariant mass plot is impossible, since we are looking for the eν (μν) mode, and cannot measure the ν’s.
+ −
However, it is clear that – as in the case of Z
0
→ e e decay – slow moving
massive W’s will emit isolated electrons with high transverse energy. Further,
such electrons should be produced in association with large missing transverse
energy (corresponding to the ν’s), which can be measured by calorimetry, and
which should balance the transverse energy of the electrons. Thus electrons of
high E T accompanied by balancing high missing E T (i.e. similar in magnitude
to that of the e
− but opposite in azimuth) were the signatures used for the
early event samples (UA1, Arnison et al. 1983a; UA2, Banner et al. 1983).
The determination of the mass of the W is not quite so straightforward as
that of the Z, since we cannot construct directly an invariant mass plot for the
eν pair: only the missing transverse momentum (or energy) can be attributed
to the ν, since some unidentified longitudinal momentum will always be lost
down the beam pipe. In fact, the distribution of events in p eT , the magnitude
of the transverse momentum of the e
− , should show a pronounced peaking
towards the maximum kinematically allowed value, which is p eT ≈
1 M W , as
2
may be seen from the following argument. Consider the decay of a W at rest
1
1
(figure 22.20). We have |p | = M W and |p eT | = M W sin θ ≡ p eT . Thus the
e
2
2
transverse momentum distribution is given by
(
) (
) −1/2
dσ
dσ
d cos θ
dσ
2p eT
1
2
=
=
M
2
,
W − p
(22.112)
dp eT
d cos θ
|
|
|
| dp eT
|
|
|
| d cos θ M W
4
eT
and the last (Jacobian) factor in (22.112) produces a strong peaking towards
1
p eT = M W . This peaking will be smeared by the width, and transverse
2
motion, of the W. Early determinations of M W used (22.112), but sensitivity
± and Z
0 at the CERN p¯ p collider
397
is good, but there is a suggestion that the tree-level prediction is on the low
side. Indeed, loop corrections adjust (22.78) to a value M
th
⋍ 91.19 GeV,
Z
in excellent agreement with the current experimental value (Nakamura et al.
2010).
The total Z
0 width Γ Z is an interesting quantity. If we assume that, for
any fermion family additional to the three known ones, only the neutrinos are
significantly less massive than M Z /2, we have
Γ Z ⋍ (2.5 + 0.16ΔN ν ) GeV
(22.111)
from section 22.3, where ΔN ν is the number of additional light neutrinos
(i.e. beyond ν e , ν μ and ν τ ) which contribute to the width through the process
Z
0
→ νν ¯. Thus (22.111) can be used as an important measure of the number
of such neutrinos (i.e. generations) if Γ Z can be determined accurately enough.
The mass resolution of the ¯
was
as the total
pp experiments
of the same order
expected Z
0 width, so that (22.111) could not be used directly. The advent
of LEP provided precision checks on (22.111); at the cost of departing from
the historical development, we show data from DELPHI (Abreu et al. 1990,
Abe 1991) in figure 22.19, which established N ν = 3.
We turn now to the W
± . In this case an invariant mass plot is impossible, since we are looking for the eν (μν) mode, and cannot measure the ν’s.
+ −
However, it is clear that – as in the case of Z
0
→ e e decay – slow moving
massive W’s will emit isolated electrons with high transverse energy. Further,
such electrons should be produced in association with large missing transverse
energy (corresponding to the ν’s), which can be measured by calorimetry, and
which should balance the transverse energy of the electrons. Thus electrons of
high E T accompanied by balancing high missing E T (i.e. similar in magnitude
to that of the e
− but opposite in azimuth) were the signatures used for the
early event samples (UA1, Arnison et al. 1983a; UA2, Banner et al. 1983).
The determination of the mass of the W is not quite so straightforward as
that of the Z, since we cannot construct directly an invariant mass plot for the
eν pair: only the missing transverse momentum (or energy) can be attributed
to the ν, since some unidentified longitudinal momentum will always be lost
down the beam pipe. In fact, the distribution of events in p eT , the magnitude
of the transverse momentum of the e
− , should show a pronounced peaking
towards the maximum kinematically allowed value, which is p eT ≈
1 M W , as
2
may be seen from the following argument. Consider the decay of a W at rest
1
1
(figure 22.20). We have |p | = M W and |p eT | = M W sin θ ≡ p eT . Thus the
e
2
2
transverse momentum distribution is given by
(
) (
) −1/2
dσ
dσ
d cos θ
dσ
2p eT
1
2
=
=
M
2
,
W − p
(22.112)
dp eT
d cos θ
|
|
|
| dp eT
|
|
|
| d cos θ M W
4
eT
and the last (Jacobian) factor in (22.112) produces a strong peaking towards
1
p eT = M W . This peaking will be smeared by the width, and transverse
2
motion, of the W. Early determinations of M W used (22.112), but sensitivity