Part II Particle Physics : Question 14

Shown below are a selection of events recorded by the OPAL detector at LEP. For each event try to answer the questions. The events are divided into two section. The first set, LEP 1 events, were recorded in 1994 when LEP operated with a centre-of-mass equal to the Z⁰ mass, i.e. 91.2 GeV. The second set, LEP 2 events, were recorded in 2000 when LEP operated at the highest ever e⁺e^- centre-of-mass energy, 206 GeV. Don't spend too much time on this question. However, if you manage to make it to the end you should have a good feel for the physics/measurements at LEP

LEP 1 EVENTS

EVENT 1

The basics and hints:

The BLUE lines emanating from the centre are tracks left by charged particles. The curvature of the track due to the magnetic field provides a measure of the particle momentum.
The YELLOW blocks represent energy deposits in the electromagnetic calorimeter (ECAL). The signal in the ECAL is proportional to the energy deposited.

The measurments:

Particle 1 : p = 46.0 ą 3.2 GeV, E = 44.7 ą 1.2 GeV
Particle 2 : p = 49.5 ą 3.5 GeV, E = 46.0 ą 1.2 GeV

The questions:

What is the event ?
The event is e⁺e^- -> Z⁰ -> e⁺e^-
Draw the Feynman diagram for the process.

EVENT 2

The basics and hints:

The MAGENTA blocks indicate energy deposits in the hadron calorimeter (HCAL)
The ARROWS indicate hits in the MUON chambers.
The small size of the YELLOW blocks indicate small energy deposits in the ECAL.

The measurments:

Particle 1 : p = 44.6 ą 2.6 GeV, E = 1.2 GeV
Particle 2 : p = 43.2 ą 2.4 GeV, E = 0.7 GeV

The questions:

What is the event ?
The event is e⁺e^- -> Z⁰ -> mu⁺mu^-
Draw the Feynman diagram for the dominant process.

EVENT 3

The basics and hints:

Note that in the zoomed view two of the tracks (tracks 2 and 4) form a vertex beyond the beam pipe.

The measurments:

Particle 1 : p = 4.1 GeV, E = 4.0 GeV
Track 2 : p = (-4.73, +6.09, -7.18) GeV
Track 3 : p = (-9.11, +12.98, -15.59) GeV
Track 4 : p = (-0.65, +0.98, -1.10) GeV

The questions:

What particle produces the two tracks which form the vertex displaced from the beam pipe ?
A photon converting to e⁺e^- in the material surrounding the tracking chamber.
What is the event ?
The event is e⁺e^- -> Z⁰ -> tau⁺tau^-. One tau decays to an electron and the other decays to a hadron (in this case it is tau -> rho nu_tau)

EVENT 4

The measurments:

TOTAL ECAL energy = 40.3 GeV
TOTAL TRACK momentum = 42.6 GeV
TOTAL HCAL energy = 27.8 GeV

The questions:

What is the event ?
The event is e⁺e^- -> Z⁰ -> q qbar.

EVENT 5

The questions:

What is the event ?
This 3-jet event is e⁺e^- -> Z⁰ -> q qbar gluon.
Draw the Feynman diagram.

EVENT 6

The questions:

What is the event ?
This is a 4-jet event e.g. e⁺e^- -> Z⁰ -> q qbar gluon gluon.
Draw two possible Feynman diagrams for this process.

LEP 2 EVENTS

EVENT 7

The measurments:

Particle 1 : E = 96.2 ą 2.8 GeV
Particle 2 : E = 100.6 ą 3.0 GeV

The questions:

What is the event ?
This is e⁺e^- -> gamma gamma.
Draw the Feynman diagram for the process.

EVENT 8

The measurments:

Particle 1 : p = 95.2 ą 13.3 GeV
Particle 2 : p = 100.0 ą 15.9 GeV

The questions:

What is the event ?
The event is e⁺e^- -> mu⁺mu^-
Draw 2 possible Feynman diagrams for the process.

EVENT 9

The measurments:

Particle 1 : p = 68.4 ą 16.1 GeV
Particle 2 : p = 39.7 ą 2.7 GeV
Mass (12) : M₁₂ = sqrt[(E₁+E₂)²-(p₁+p₂)²] = 81.3 +-9.6 GeV

The questions:

What is the event ?
The event is e⁺e^- -> gamma Z⁰ -> mu⁺mu^-. This process is called radiative return. The incoming electron/positron radiates a photon such that the invariant mass of the e⁺e^- equals M_Z. The cross section is enhanced due to the Z⁰ resonance.

Note that typically the photon is radiated in the direction of the incoming electron and positron and hence goes down the beam pipe and is not observed.
Draw the Feynman diagrams for the process.

EVENT 10

The measurments:

Particle 1 : p = 97.1 ą 5.0 GeV, E = 103.2 ą 5.0 GeV
Particle 2 : p = 102.2 ą 7.4 GeV, E = 98.5 ą 5.4 GeV

The questions:

What is the event ?
The event is e⁺e^- -> e⁺e^-
Why are events of this type seen much frequently than events such as EVENT 8
In addition to the diagrams of EVENT 8 there is another possibility:

EVENT 11

Event 10 BORDER=5 HSPACE=5 VSPACE=5 height=400></a>
<img align=

The measurments:

The isolated ECAL cluster (large YELLOW block) : E = 74.1 GeV

The questions:

e⁺e^- -> gamma Z⁰ -> qq gamma. Radiative return again, but in this case the photon is observed.

The invariant mass of the Z⁰ may be reconstructed from the photon energy and knowledge of the beam energy.

Draw the Feynman diagram for the process.

Hint:

Express the invariant mass of the jet-jet system in terms of the centre-of-mass energy, 206 GeV, and the energy of the isolated ECAL cluster.

EVENT 12

Hint:

The arrow in this event indicates the direction of the missing momentum in the event, i.e. minus the summed momenta of the electron and jets. This is a clear signature for a neutrino.

The measurments:

Electron energy : 45.0 ą 2.1 GeV
Missing energy : 58.0 ą 10.5 GeV

The questions:

What is the event.
e⁺e^- -> W⁺W^- -> qq e nu_e.
Draw the possible Feynman diagrams

EVENT 13

The questions:

What is this event ?
e⁺e^- -> W⁺W^- -> e⁺ nu_e mu^- nubar_mu.
What is the approximate production rate compared to that for EVENT 12 ?
1/6 (2 q-qbar flavours ud and cs multiplied by 3 colours)

EVENT 14

Hint:

This is a clear 4 jet event. This event could comes from the process e⁺e^- -> X Y where both X and Y decay to a quark/anti-quark pair. In this case there are 3 possible associations of 4 jets to the two particles X and Y. To identify the process it is useful to reconstruct the masses of particles X and Y for each jet combination.

The measurments:

Jet pairing (12)(34) : M_X = 71.0 ą 1.7 GeV, M_Y = 70.1 ą 2.0 GeV.
Jet pairing (13)(24) : M_X = 79.1 ą 1.8 GeV, M_Y = 79.8 ą 1.9 GeV.
Jet pairing (14)(23) : M_X = 102.8 ą 5.9 GeV, M_Y = 101.5 ą 5.8 GeV.

The questions:

Suggest the possible origins of the event.
e⁺e^- -> W⁺W^- -> qqqq
e⁺e^- -> Z⁰Z⁰ -> qqqq
e⁺e^- -> Z⁰H⁰ -> qqqq
Based on M_X and M_Y what is the most likely explanation for the event ?
e⁺e^- -> W⁺W^- -> qqqq since jet pairing (13)(24) gives the W mass for both jet pairs

EVENT 15

The questions:

⁺

⁰

⁺

Draw the Feynman diagram.

EVENT 16

The measurments:

Jet pairing (12)(34) : M_X = 95.5 ą 2.2 GeV, M_Y = 77.1 ą 2.4 GeV.
Jet pairing (13)(24) : M_X = 78.7 ą 1.8 GeV, M_Y = 88.1 ą 2.3 GeV.
Jet pairing (14)(23) : M_X = 86.2 ą 2.2 GeV, M_Y = 90.5 ą 2.3 GeV.

The questions:

Suggest the possible origins of the event.
- e⁺e^- -> Z⁰H⁰ -> qqqq

Based on M_X and M_Y what is the most likely explanation for the event ?

e⁺e^- -> Z⁰Z⁰ -> qqqq since jet pairing (14)(23) gives the Z mass for both jet pairs (within errors)

EVENT 17

The questions:

The invariant mass of the two electrons in this event is consistent with the Z⁰ mass. What is the event ?
e⁺e^- -> Z⁰Z⁰ -> qq e⁺e^-
Compare the production rate for this process with that of EVENT 15.
1/40 (partial width for Z->qq is 20 times greater than Z->ee, plus two combinations qqee eeqq )

EVENT 18

Health warning:

A much harder question !

The measurments:

Energy of isolated ECAL cluster : E = 102.0 ą 3.0 GeV
Invariant mass of the tracks : M = 3.3 ą 0.4 GeV

The questions:

What are the two particles produced in this process ?
photon and two muons. The two muons are from the decay of a J/psi as can be seen from the invariant mass.
Draw the Feynman diagram.
Radiative return to the J/psi diagram similar to Q11 with the Z⁰ replaced by a photon and the qq replace with a the bound cc state J/psi

MAT, 14-Feb-2003

Part II Particle Physics : Question 14

LEP 1 EVENTS

EVENT 1

The event is e+e- -> Z0 -> e+e-

EVENT 2

The event is e+e- -> Z0 -> mu+mu-

EVENT 3

A photon converting to e+e- in the material surrounding the tracking chamber.

The event is e+e- -> Z0 -> tau+tau-. One tau decays to an electron and the other decays to a hadron (in this case it is tau -> rho nutau)

EVENT 4

The event is e+e- -> Z0 -> q qbar.

EVENT 5

This 3-jet event is e+e- -> Z0 -> q qbar gluon.

EVENT 6

This is a 4-jet event e.g. e+e- -> Z0 -> q qbar gluon gluon.

LEP 2 EVENTS

EVENT 7

This is e+e- -> gamma gamma.

EVENT 8

The event is e+e- -> mu+mu-

EVENT 9

The event is e+e- -> gamma Z0 -> mu+mu-. This process is called radiative return. The incoming electron/positron radiates a photon such that the invariant mass of the e+e- equals MZ. The cross section is enhanced due to the Z0 resonance.

Note that typically the photon is radiated in the direction of the incoming electron and positron and hence goes down the beam pipe and is not observed.

EVENT 10

The event is e+e- -> e+e-

In addition to the diagrams of EVENT 8 there is another possibility:

EVENT 11

e+e- -> gamma Z0 -> qq gamma. Radiative return again, but in this case the photon is observed.

The invariant mass of the Z0 may be reconstructed from the photon energy and knowledge of the beam energy.

EVENT 12

e+e- -> W+W- -> qq e nue.

EVENT 13

e+e- -> W+W- -> e+ nue mu- nubarmu.

1/6 (2 q-qbar flavours ud and cs multiplied by 3 colours)

EVENT 14

e+e- -> W+W- -> qqqq e+e- -> Z0Z0 -> qqqq e+e- -> Z0H0 -> qqqq

e+e- -> W+W- -> qqqq since jet pairing (13)(24) gives the W mass for both jet pairs

EVENT 15

EVENT 16

e+e- -> W+W- -> qqqq e+e- -> Z0Z0 -> qqqq

e+e- -> Z0Z0 -> qqqq since jet pairing (14)(23) gives the Z mass for both jet pairs (within errors)

EVENT 17

e+e- -> Z0Z0 -> qq e+e-

1/40 (partial width for Z->qq is 20 times greater than Z->ee, plus two combinations qqee eeqq )

EVENT 18

photon and two muons. The two muons are from the decay of a J/psi as can be seen from the invariant mass.

Radiative return to the J/psi diagram similar to Q11 with the Z0 replaced by a photon and the qq replace with a the bound cc state J/psi

The event is e⁺e^- -> Z⁰ -> e⁺e^-

The event is e⁺e^- -> Z⁰ -> mu⁺mu^-

A photon converting to e⁺e^- in the material surrounding the tracking chamber.

The event is e⁺e^- -> Z⁰ -> tau⁺tau^-. One tau decays to an electron and the other decays to a hadron (in this case it is tau -> rho nu_tau)

The event is e⁺e^- -> Z⁰ -> q qbar.

This 3-jet event is e⁺e^- -> Z⁰ -> q qbar gluon.

This is a 4-jet event e.g. e⁺e^- -> Z⁰ -> q qbar gluon gluon.

This is e⁺e^- -> gamma gamma.

The event is e⁺e^- -> mu⁺mu^-

The event is e⁺e^- -> gamma Z⁰ -> mu⁺mu^-. This process is called radiative return. The incoming electron/positron radiates a photon such that the invariant mass of the e⁺e^- equals M_Z. The cross section is enhanced due to the Z⁰ resonance.

The event is e⁺e^- -> e⁺e^-

e⁺e^- -> gamma Z⁰ -> qq gamma. Radiative return again, but in this case the photon is observed.

The invariant mass of the Z⁰ may be reconstructed from the photon energy and knowledge of the beam energy.

e⁺e^- -> W⁺W^- -> qq e nu_e.

e⁺e^- -> W⁺W^- -> e⁺ nu_e mu^- nubar_mu.

e⁺e^- -> W⁺W^- -> qqqq
e⁺e^- -> Z⁰Z⁰ -> qqqq
e⁺e^- -> Z⁰H⁰ -> qqqq

e⁺e^- -> W⁺W^- -> qqqq since jet pairing (13)(24) gives the W mass for both jet pairs

e⁺e^- -> W⁺W^- -> qqqq
e⁺e^- -> Z⁰Z⁰ -> qqqq
e⁺e^- -> Z⁰H⁰ -> qqqq

e⁺e^- -> Z⁰Z⁰ -> qqqq since jet pairing (14)(23) gives the Z mass for both jet pairs (within errors)

e⁺e^- -> Z⁰Z⁰ -> qq e⁺e^-

Radiative return to the J/psi diagram similar to Q11 with the Z⁰ replaced by a photon and the qq replace with a the bound cc state J/psi