Physics Update Course Summer 2013

Discover the COSMOS particle physics activity

Lynne Long, Professor Peter Watkins and Dr John Wilson

University of Birmingham

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Z Mass with MINERVA talk

This is an activity you can do yourself and it is very similar to some of the analysis activities that take place at CERN. My year 13 students do the first part of the activity when they attend a particle physics masterclass.

Minerva Instructions

Identifying and Measuring Mass of Invisible Particles at the LHC

Starting MINERVA

MINERVA can be accessed by downloading the file at the following web address:

http://epweb2.ph.bham.ac.uk/user/mclaughlan/minerva/DtC/MINERVA.zip

Unzip the file (eg on Windows right click on MINERVA zip file and select extract all)

Run atlantis.jar (by double clicking on it)

This will start the MINERVA program on any operating system with a recent version of Java.

Basic Use of MINERVA

Once you have started MINERVA, two windows will appear. The left hand window displays the various projections of the ATLAS detector (the Canvas) and the right hand window displays the controls (the GUI).

The Canvas window, by default, is split into three different projections. The largest of these is the ‘side’ view (r-Z projection) along the bottom. The top left window shows a cross-section looking along the beam at ATLAS (X-Y projection). (Note that these two views must be used simultaneously to get the full overview of the event, as particles detected in the forward regions are only shown in the r-Z projection).

Identifying collisions where W or Z bosons are produced

You will be looking to identify collisions where:

• Z decays into e+ e- or mu+ mu-

• W decays into electron and neutrino or muon and neutrino

• Other events which we will consider as background which often include jets

Introductory Exercise (the easy bit)

The MINERVA session that you started contains a preloaded sample of 25 simulated collisions in the ATLAS detector.

The first five events are examples of W decay to electron and neutrino , W decay to muon and neutrino, Z decay to electron and positron, Z decay to muon and antimuon and a background event in that order.

After looking at these first five events to get familiar with the display and how to identify particles in the ATLAS detector, determine which of the other events should be classified as W decays to electrons or muons, Z decays to electrons or muons or other ‘background’ events. Record this information for each event on your tally sheet.

Characteristics of the different event types

image  image

Z àee (- 2 electrons with high pT)       Z àmm  (- 2 muons with high pT (>10GeV))

image   image

Upper left picture:    W à eu (- one electron with high pT) (- large missing ET (>10GeV))

Upper right picture:  W àmu  (- one muon with high pT) ( – large missing ET (>10

GeV))

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Background – mainly jets (particle bunch) – only occasionally an electron or muon

How to identify electrons, muons, jets and neutrinos

 

Identification of muons (m)

          track (orange line) in the muon detector (blue detector)

          corresponding track (orange line if the muon is in the central part, blue line if it’s in the forward region) in the tracking detector (black detector)

 

Identification of electrons (e)

          big energy deposit in electro-magnetic calorimeter (green)

          NO energy deposit in the hadronic calorimeter (red)

          track (blue line) in the tracking detector (black detector) in front of the calorimeter

 

Identification of jets

          big energy deposit in electro-magnetic calorimeter (green)

          energy deposit in the hadronic calorimeter (red)

          multiple tracks (blue lines) in the tracking detector (black detector) in front of the calorimeter.

 

Identification of neutrinos (n)

          done indirectly via missing “side-way” or transverse energy (Missing ET, dashed red line, thickness corresponds to the value, thick line: small – medium missing ET, thick line: high missing ET, no line: very small missing ET)

image

Questions to ask to classify our events into different types

 

How many muons or electrons are in the event?

          If there are two:

          è It’s a Z®ee or Z®mm event

          If there is one:

o   Is missing ET large?

§  If yes, is the muon/electron and missing ET back-to-back? In case muon/electron is in the forward region: is energy balanced?

            è It’s a W®en or W®mn event

          If there are zero:

è It’s a background event

 

W/Z Ratio in the ATLAS Expt. at the LHC

Please analyse collisions from file group_01.zip:

Event

Number

W e ν

 

W μ ν

Z e e

Z μ μ

H4l (l=e,μ)

Background

           1

 

 

 

 

 

 

2

 

 

 

 

 

 

3

 

 

 

 

 

 

4

 

 

 

 

 

 

5

 

 

 

 

 

 

6

 

 

 

 

 

 

7

 

 

 

 

 

 

8

 

 

 

 

 

 

9

 

 

 

 

 

 

10

 

 

 

 

 

 

11

 

 

 

 

 

 

12

 

 

 

 

 

 

13

 

 

 

 

 

 

14

 

 

 

 

 

 

15

 

 

 

 

 

 

16

 

 

 

 

 

 

17

 

 

 

 

 

 

18

 

 

 

 

 

 

19

 

 

 

 

 

 

20

 

 

 

 

 

 

TOTALS

 

 

 

 

 

 

Main measurement (the difficult bit)

For the main measurement you are going to focus on Z boson decays and try to measure the Z boson mass even though it decays before it travels a distance less than the size of a proton!.

We need to use just one crucial equation from relativity that relates the mass, momentum and energy of any particle. A particle with momentum p and mass m has an energy E given by:

              E^2 = m^2 c^4 + p^2c^2

where c is the speed of light.

The energy and momentum of the Z boson can be found from the scalar sum of energy (Sum E) and vector sum of momentum (Sum p) of its two decay products.

The earlier equation can be rearranged to give:

            (Mc^2)^2 = (Sum E)^2 – (Sum pc)^2

It is very convenient to define units for energy, momentum and mass that include the terms in c so that we don’t have to introduce the numerical value of c when using this equation.

We simply bundle the c terms in with the units, so the unit of mass becomes GeV/c^2, unit of momentum becomes GeV/c, and the energy in GeV as usual. In this experiment you should quote all of your results in these units. Note the mass of proton is close to 1 GeV/c^2.

As an example a proton (mass = 0.938 GeV/c^2 ) with energy 4 GeV will have a momentum given by p = sqrt( E^2 –  m^2)  = sqrt (42 – 0.9382) = 3:89 GeV/c.

This allows us to write the formula in the much simpler form :

M2 = (Sum E)^2 – (Sum p)^2

For a particle decaying into two particles the mass of the parent can therefore be written, where Ei and pi are the energy and momentum of the ith particle, as:

M^2 = (E1 + E2)^2 – [(p1x + p2x)^2 + (p1y + p2y)^2 + (p1z + p2z)^2]

You can obtain the values of px , py and pz by ‘picking’ on each of the two energetic decay tracks in MINERVA. The masses of the electron and muon are negligible compared to their high momenta and so the energy of each particle can be approximated as the magnitude of the momentum via

 E ~ p = sqrt (px^2 + py^2 + pz^2)

Take care when adding the components of momentum to include the sign of these components.

Adding the two energies is much easier as these are scalar quantities.

Main measurement – Measuring the mass of a Z boson

Download the file at the following URL.

http://epweb2.ph.bham.ac.uk/user/mclaughlan/minerva/lab/Zevents.zip

This is a file of 50 Z candidate events similar to those studied in the previous exercise.

Loading Extra Events into Minerva

To load a set of events other than the defaults, you will need to use the GUI menu bar at the top of the screen. Click ’File’, then ’Read Event Locally’, or the icon. Then navigate to the location of the events you wish to load, click the event (or a .zip file of the events) and click Open.

For this exercise you will need to identify the tracks from the two most energetic leptons in each event which will be an electron-positron pair or a muon-antimuon pair.  Record the three momentum components of each of these two leptons. Using the formulae given above calculate the mass of the Z boson for each event. You can do this using an Excel worksheet if you prefer.

There is another faster way to calculate the mass of the Z boson candidate in Minerva once you have understood how the method above works.

Hold the m key on the keyboard and pick each of the two decay tracks with the pick cursor.

The mass that is displayed after the second track is the approximate mass of the two tracks and can be used in the histogram for the events.

You will need to produce a histogram of the Z boson masses from the events that you measure. To do this visit the following webpage:

http://epweb2.ph.bham.ac.uk/user/mclaughlan/minerva/lab/plot.html

Input each of your masses into the plotting tool and it will automatically create a histogram. Once you have enough data (ten events or more) , use the Fit button to fit a Breit-Wigner curve to the histogram. This has a similar shape to a Gaussian but gives a more precise description of the resonant peak for a short-lived particle. The central value of the fitted curve corresponds to your measured Z boson mass with its associated uncertainty.

Note that as you will probably only have time to calculate the mass for a small number of events the plot package has the option to add extra events automatically to the histogram so that you can see the effect of higher statistics on the fitted parameters.

The fitted width of the resonant peak distribution is also calculated and this contains information about the lifetime of Z boson. The Heisenberg Uncertainty Principle states that in simultaneous measurements the product of the uncertainty on energy and uncertainty on time cannot be less than Planck’s constant. As the Z boson decays in such a short time the uncertainty on time is very small and this forces the uncertainty in energy (or mass) to be large. This means that even in an experiment with no experimental uncertainties the Z mass measurements will always produce a range of values which is summarised in the width measurement.

Minerva Features

Open Minerva:

–        Double click on the atlantis.jar icon in the Minerva folder. (If the folder is zipped, right click and select extract all before you do this).

What you see in the Atlantis canvas:

–        in the upper left plot you see the end-on view of the ATLAS detector (x-y-projection). In this view you ONLY see particles in the central region

–        in the upper right plot you see the calorimeter deposits in the electromagnetic part in green and in the hadronic part in red. An electron should only have electromagnetic energy deposits and no hadronic ones

–        In the lower plot you see the side view (R-z projection) of the detector. Here you see what particles were produced in the barrel as well as in the forward region. You ALWAYS have to check this view to ensure you don’t ‘miss’ something important

Read events (sets of LHC events can be downloaded from the Minerva Toolbox on the Discover the Cosmos portal, from http://www.discoverthecosmos.eu ) :

–        in the upper right corner click on ‘File’

–        select ‘Read Event locally’ from the menu

–        select the file you want

–        click on this file and then ‘open’

Read next event:

–        click on ‘Next’ on top of  the Atlantis GUI

Read previous event:

–        in case you were clicking too fast or have 2nd thoughts you can go back one event by clicking on ‘Previous’

Find out about the track transverse momentum (pT):

–        click on the ‘hand’ in the Atlantis GUI

–        move the pointer over the track for which you want to know its pT

–        click on the track

–        in the lower part of the Atlantis GUI the track parameters are displayed and you have to find the pT (Advice: you might want to increase the display window a bit by moving the separator between the upper and lower part of the window)

Find out about the energy deposited in the calorimeter (ET):

–        click on ‘Pick’ in the Atlantis GUI

–        in the Atlantis canvas click on the purple square situated behind the calorimeter

–        in the lower part of the Atlantis GUI the jet parameters are displayed and you have to find the ET value (Tip: you might want to increase the display window a bit)

–        Hint: if you click on the purple square it turns grey in all 3 views of the ATLAS detector. This makes it easy to identify the particle in the different projections.

Find out about the missing ET in the event:

–        The value of missing ET is given by the thickness of the missing ET vector.

–        The value is plotted in the upper right corner of the upper right plot.

–        If the value is very small, no missing ET will be visualised

Reset the setup:

– if you have been playing around with too many other Atlantis options, you can reset them by clicking the ‘Reset’ button in the top part of the Atlantis GUI

 Spreadsheet Minerva Z mass calculator

Result sheet 20 (If you want to cheat)

 

 

 

 

 

 

 

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