Partial widths of the Z

The total width of a resonance such as the Z is a measure of how fast it decays. It is related to the mean lifetime of the resonance by (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, k , which are the widths that the resonance would have if it only decayed to mode k. The sum k = 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 ee. In fact the Breit-Wigner formula for the Z resonance is

eeZ ff) = 12.mZ-2 . ee. ff / [ (E- mZ)2 + 2/4 ] .

The partial widths of the Z are predicted by the standard model to be

ff = N.GF.mZ3/(24.sqrt(2)).[ 1 + ( 1 – 4.|Q|.sin2W )2 ] where

N=1 for leptons and N=3.( 1 + s/+ O(s2) ) 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 electronsElectron 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 muonsMuon 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 tausTau 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 (m =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 two-photon 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.

Original quark is somewhere in here.

Original anti-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.

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The double tagging methodIn 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 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 Zqq 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.b + small background

fd = Rb.b2 + very small background

Rb is the thing we want to measure BR(Zbb)/BR(Zqq).

b 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 lifetimesB 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.

106 1×1 2.2 × 10-6

1777 1×5 3.3 × 10-13 2.9 × 10-13

c 1200 1×5 2.3 × 10-12 D0 0.4×10-12

D+ 1.0×10-12

b 4200 0.0016×8 1.8 × 10-12 1.6 × 10-12

1/GF2m

5/1923 . 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 est= m/m5 / fCKM . Nchan

particle mass(MeV) fCKM.Nchan est (s)measured (s)

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:

d’ Vud Vus Vub d 0.97 0.22 0.004

s’ = Vcd Vcs Vcb s , 0.22 0.97 0.04

b’ Vtd Vts Vtb b 0.004 0.04 0.99

Approximate values of magnitudes of CKM elements.

B tagging with leptonsWe 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(be) = 10.9 % , BR(b) = 10.9 % .

But there are other sources of leptons in jets, such as K+ 0 e+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 pof 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 pfurther enhances the heavy flavours.