Download Partial widths of the Z

Partial widths of the Z
The total width G of a resonance such as the Z is a measure of how fast it decays. It is related
to the mean lifetime t of the resonance by G.t =  (familiar energy-time uncertainty
relation). If there is more than one way that the resonance can decay then we can define
partial widths for each of the decay modes, Gk , which are the widths that the resonance
would have if it only decayed to mode k. The sum S Gk = G. It is plausible ( see Martin &
Shaw for details ) that the cross section for production of a resonance by colliding a pair of
the possible decay particles (e.g. e+e- ) is proportional to the partial width for that decay mode
Gee. In fact the Breit-Wigner formula for the Z resonance is
s(eeZ ff) = 12.p.mZ-2 . Gee. Gff / [ (E- mZ)2 + G2/4 ] .
The partial widths of the Z are predicted by the standard model to be
Gff = N.GF.mZ3/(24.p.sqrt(2)).[ 1 + ( 1 – 4.|Q|.sin2qW )2 ] where
N=1 for leptons and N=3.( 1 + as/p + O(as2) ) for quarks
( 3 colours + gluon radn.)
So measurement of the partial widths provide a test of the standard model because the
parameters on the r.h.s. are already measured with high precision in other experiments.
Z to electrons
Electron events are characterised by:
• The full beam energy is seen in just
two clusters in the ECAL.
• It is also seen in a track pointing to
each cluster.
• The tracks and clusters and beam all
lie in a common plane.
• There is no energy in the HCAL.
Z to muons
Muon events are characterised by
two tracks with:
• Energy close to the beam energy
• Little in ECAL and HCAL
• Signals in muon chambers
• Co-planar with beam
Z to taus
Tau events are characterised by:
• Low multiplicity of charged
tracks in two narrow jets: Divide
the event into hemispsheres.
• 1-5 tracks in each hemisphere
• Low hemisphere mass (mt =1.8
GeV)
• Some missing momentum in each
hemisphere.
• Harder cuts if both hemispheres
are identified as electrons, or both
as muons.
• If visible energy is very low, hard
cuts on acolinearity to remove twophoton events.
Z to quarks
• High multiplicity of tracks and
photons
• Most of the tracks are hadrons
• Most of the beam energy is visible
• Special cuts against the lepton
topologies
Quark flavour identification
A lot more can be got from the Z  qq events if we know which flavour of quarks they are.
The heavier the original quark, the easier it is to pick out from the mass of particles produced
in the hadronisation process.
approximate momentum ordering
Original quark is somewhere in
here.
lots of new quarks
and anti-quarks.
Mainly u and d (~3/7
each) , some s (~1/7),
very little c,b.
Original anti-quark is somewhere in
here
The double tagging method
In practice, only jets originating from b or c quarks can be identified (tagged) with
any confidence. The remainder are lumped together as “uds” or light flavour.
None of the tagging methods are highly efficient or free of background. Worse,
their e and b are always rather sensitive to details of hadronisation and resonance
decays which are not well known. Rather than rely on a Monte Carlo program to
simulate all the details correctly, there is another way: We know that Z always
decays to flavour anti-flavour pairs ( is this a valid assumption when we are testing the SM? ) so
we can use the flavour correlation between the two jets in each event to measure
the efficiency with the data. A simple example with b jets:
Select Zqq events. Divide each event into two jets. Tag the flavour of each jet
independently. fs is the fraction of jets tagged as being b jets. fd is the fraction of
events in which both jets were tagged as being b jets.
fs = Rb.eb + small background
2
fd = Rb.eb + very small background
Rb is the thing we want to
measure BR(Zbb)/BR(Zqq).
eb is the tag efficiency which can
now be calculated.
The backgrounds must still come
from Monte Carlo simulation.
Fragmentation pions
Pion distribution is very soft. Note gap where pions become impossible to distinguish from kaons by dE/dx measurement.
Fragmentation and decay of b
Unlike the fragmentation of light quarks,
a jet which originated from a b quark
often contains a b meson with a high
proportion of the jet energy.
High energy alone is not enough to tag a b
quark, but it makes things much easier.
We must also see some of the products of
b decay.
The b quark is heavy (~4.2 GeV) but its
decay is suppressed by the small value of
the CKM matrix element Vcb  0.04
Spectator
model
An aside on weak decay lifetimes
B quark decay is one more example of muon-like weak decay to three
much lighter particles via a virtual W.
Since the W coupling is equally strong to all the fermion doublets it is
only necessary to know one lifetime of this type and we can estimate
all the others.
1/tm= GF2 mm5/192p3 . So lifetime scales with mass to the 5th power. We also need to take account of the
number of different ways that the virtual W can decay,Nchan , which depends on the available energy. Also
remember that there is a CKM matrix element squared, which can be small at the l.h. vertex. So test= tm .
( m/mm )5 / fCKM . Nchan
particle
m
t
c
b
test (s)
tmeasured (s)
mass(MeV)
fCKM.Nchan
106
1×1
1777
1×5
3.3 × 10-13
2.9 × 10-13
1200
1×5
2.3 × 10-12
D0 0.4×10-12
D+ 1.0×10-12
1.8 ×
1.6 ×
4200
0.0016×8
2.2 × 10-6
10-12
10-12
Why is top decay
missing from this
table ?
What is this CKM matrix ?
Jenny has (or Stefan will) explain in detail :
•Why Cabibbo invented it when only the u,d and s quarks were known,
•How Kobayashi and Maskawa extended it,
•How it can describe quark mixing and CP violation,
•How the terms can be measured.
For us, the essential point is that the quark mass eigenstates are not the same as the weak
eigenstates. ( In the lepton sector the mass and weak eigenstates are the same – a W couples
a lepton with its own flavour of neutrino and no other ).
The weak (primed) eigenstates are related to the mass eigenstates by a mixing matrix which
conventionally applies to the –1/3 charge quarks:
Approximate values of magnitudes of CKM elements.
d’
Vud
Vus
Vub
d
s’ =
Vcd
Vcs
Vcb
s
b’
Vtd
Vts
Vtb
b
,
0.97
0.22
0.004
0.22
0.97
0.04
0.004
0.04
0.99
B tagging with leptons
We can identify (tag) jets originating from b quarks by looking for the electrons and muons
coming from b decay. Naively expect 1/8th of decays to each type of lepton. Reality is close ;
BR(be) = 10.9 % , BR(bm) = 10.9 % .
But there are other sources of leptons in jets, such as K+ m+n, p0  ge+e- and conversion of
photons to e+e- in the material of the detector.
We can cut out most of these other sources be requiring that the lepton has either a high
fraction of the jet energy and/or high momentum transverse to the direction of the remainder
of the jet.
P and pT of leptons in
jets.
shaded: uds,
cross hatched: c,
white: b.
The requirement of a lepton
in the jet has already
reduced the uds to a low
level. Asking for high p or
pT further enhances the
heavy flavours.