Minerva Lab Experiment

L.A.Lewis

12th September 2009

Abstract

This experiment consists of a general introduction of the ATLAS experiment at the LHC at CERN. Students will be using MINERVA to visualise collisions from the proton-proton beam. Intially, students will be asked to identify specific events such as Z and W decays, leading onto more difficult decays from tt̄. Using the information gathered from MINERVA the mass and lifetime of the particles can be determined. Using the values of the mass and width of the Z the number of neutrinos that exist can be investigated. As an extension students can try looking further into the tt̄ decays.

1 Introduction

In this experiment you will be visualizing events similar to those that will be seen in ATLAS [?], which is a particle physics experiment at the Large Hadron Collider at CERN. The ATLAS detector will search for new discoveries in the head-on collisions of protons of extraordinarily high energy. ATLAS will search for new particles and learn about the basic forces that have shaped our Universe since the beginning of time and that will determine its fate. Among the possible unknowns that will be probed are the origin of mass, extra dimensions of space, microscopic black holes, and evidence for dark matter candidates in the Universe.

MINERVA is a software package that visualizes the information recorded by ATLAS after each collision. The same package is used by physicists working on the experiment. You will need to familiarize yourself with using MINERVA; the primary goals of the program are the visual investigation and the understanding of the physics of single collisions (events)[?]. You will be learning how measurements of different types of particles are made; and investigate how the mass and lifetime of short-lived particles are determined.

2 MINERVA

See Separate sheet. Quick Guide to MINERVA for labs.

3 Identifying Events

The W and Z bosons were discovered in 1983 at CERN. Their properties are very well known, so why are you being asked to learn how to detect them? Investigating W and Z events at the LHC will provide additional tests of the standard model of particle physics. Another reason to study these particles is the search for the Higgs boson. Physicists have theorized a Higgs field that is made of Higgs bosons. Particles acquire mass by interacting with this field. The Higgs boson may be discovered by its decay into WW or ZZ. The Z boson is also a common background process for other searches for new particles and must be understood well.

The Z boson is a massive, neutral particle that decays into any lepton-anti-lepton pair or a quark antiquark pair. If at rest the decay products are produced back-to-back to conserve momentum.

The W boson is a massive, charged particle that decays into a lepton and neutrino or a quark antiquark pair (u-d or s-c). The presence of the neutrino can be deduced by using momentum conservation. The branching ratio is the fraction of particles that decay by individual decay paths. Write down all the different decay paths of the W boson, remembering that quarks each have 3 colours. Hence, calculate the branching ratios for the W boson.

The events from W and Z decays chosen for this experiment will not include those decaying to quarks. It is more difficult to study quarks as they are detected as a collection of hadrons travelling close together, called a jet. There are many jets produced in proton-proton collisions.

Exercise 1 Read the Quick Guide to MINERVA. Open five of the sample sets, this will give you 100 events from proton-proton collisions. Determine which events are W decays, Z decays or Di-jet. Record how many of each type of event there are. Measure the W/Z ratio. Comment on your result.

(If continuing onto exercise 2 record for each Z event the momentum components of the two decay leptons).

If continuing onto exercise 3 record for each W event the transverse momentum components(Px and Py) of the charged lepton track and missing energy.

4 Determining Rest Mass of Z and W Bosons

The invariant mass, M is the same as the rest mass of a particle.

M^{2} = (∑ E)^{2} − (∑ p̄)^{2}

∑ E is the sum of all the energies of the decay particles. ∑ p̄ is the vector sum of the momenta of the decay particles (including both magnitude and direction of the momenta).

For electrons and muons you can assume that the magnitude of momentum is equal to the energy of the particle since the mass is negligible for energetic particles.

Exercise 2 Ask your demonstrator for the file containing only Z events. Read the Guide to create histograms using MS excel^{1}. Plot a graph of the invariant mass of the Z boson.

What can the shape of the graph can tell you about the properties of the particle?

Exercise 3 For the W boson, only the transverse momentum can be measured because of the undetectable neutrino. Transverse momentum is the momentum of a particle in the x-y plane. Only the transverse component of the missing momentum (neutrino momentum) can be measured because other particles may escape along the beam pipe (zdirection), therefore, the measurement of missing momentum along the z direction would be inaccurate.

Using the transverse momentum of the lepton and transverse missing energy, find the transverse invariant mass of the W events. Plot this as a histogram; can you explain the shape of the plot?

The transverse invariant mass does not take into account any momentum in the beam direction. Since the W and Z bosons have similar mass, it may be possible to find the actual invariant mass by calculating a mass correction factor. Investigate this; find the Z transverse mass, using the transverse momentum of the electrons and muons and find the ratio Z mass/ Z transverse mass . Apply this correction factor to the W transverse mass results and compare the W ’corrected’ mass result with the known mass from the Particle Data Group [?].

1If continuing onto exercise 4 you may save time by using a different program than excel.

5 Z Lifetime

For particles with extremely short lifetimes, there will be a significant uncertainty of the measured energy due to Heisenberg Uncertainty Principle,

ΔEΔt ≥ \frac{ℏ}{2}

In the figure below gamma is the full width half maximum (FWHM). Gamma relates to the lifetime of the particle by

ΔE = \frac{Γ}{2} = \frac{ℏ}{2τ}

Insert pic of z width*

Exercise 4 Use the same Z events from exercise 2. For this exercise you will need to use a program that can fit gaussian curves to a histogram eg SCIDAVis (freeware) [?]. Plot a histogram of the invariant masses the mass and lifetime of the Z boson can be determined. Use the Quick Guide to SCIDAVis create a histogram of the Z invariant mass and fit a Gaussian curve to the plot. Find the width and peak position of the fitted Gaussian curve. What is the lifetime of the Z boson?

6 Z Line Shape

Experiments at the large electron=positron collider (LEP)used the result from the precisely measured Z mass distribution to show that there are only three types of neutrino that the Z can decay into. The total width of the Z boson is made up of partial widths of different decay modes. The Z can decay into any lepton -antilepton or quark -antiquark pair, excluding tt̄, which is forbidden due to energy restrictions.

The decay width is

Γ_{Z} = Γ(z → qq) + Γ(z → ee) + Γ(z → μμ) + Γ(z → ττ) + N_{ν}Γ(z → νν)

whereN_{ν}is the number of neutrinos.

Optional It is possible to calculate this yourself using the partial Z decay widths Γ_{f} which are given by

Γ_{f} = \frac{G_{f}M_{Z}^{3}}{6π\sqrt{2}} N_{c} [(C_{V}^{f})^{2} + (C_{A}^{f})^{2}]

Where Nc is number of colours (1 for leptons, 3 for quarks). C_{V}^{f} and C_{A}^{f} are the Z couplings to fermions shown in the table below.

C_{V}^{f}  C_{A}^{f}
ν_{l} \frac{1}{2} \frac{1}{2}
eμτ -\frac{1}{2} + 2sin^{2}θ_{w} −\frac{1}{2}
uct \frac{1}{2} − \frac{4}{3}sin^{2}θ_{w} \frac{1}{2}
dsb -\frac{1}{2} + \frac{2}{3}sin^{2}θ_{w} −\frac{1}{2}

sin^{2}θ_{w} = 0.230

\frac{G_{f}}{(ℏc)^{3}} = 1.6637 × 10^{−5}GeV^{−2}

7 Top Quark Mass

In ATLAS a top quark and top antiquark pair are expected to be frequently produced. The top quark is twice as heavy as the W and Z bosons, and always decays into a high energy b quark and W boson. The W can be detected as seen in the previous exercises or as two jets, whereas, the b quark produces a jet including a B hadron which decays slightly away from the collision point. The possible decay modes of the tt̄ pair are:

tt̄→ bb̄qq̄′q̄q′ F ully Hadronic, 6 jets.

tt̄→ bb̄qq̄′l^{−}ν̄_{l} or tt̄→ bb̄l^{+}ν_{l}q̄q′ Semi Leptonic, 4 jets.

tt̄→ bb̄l^{+}ν_{l}l^{−}ν̄_{l} F ully Leptonic, 2 jets.

Using the W branching ratios, (1/9 for each lepton type and 2/3 for quark antiquark decays )calculate the branching ratios of the tt̄ decay being fully hadronic, semi leptonic or fully leptonic.

Exercise 5 Open the file containing the tt̄ events. For each event identify the lepton and the jets with the highest transverse momentum. The top quark mass can be determined from finding the invariant mass of the three jets comprising two quark jets and the b jet. Use the three jets with the largest vector sum of transverse momentum for this calculation.

Plot a histogram of the top quark’s invariant mass and compare your results with the value of the top quark mass in the Particle Data Group (PDG).