Procedure for the Weak Mixing Angle Lab
H. Schellman and G. Zeller
Version 2.3 March 28, 2005
Many times in introductory physics classes you are asked to repeat experiments
that were performed centuries ago. This lab is very different. Here you will
be repeating a very recent measurement. You may have even heard about it
in the news.
The NuTeV experiment's Weak Mixing Angle results received quite a bit of
press when they were released in late 2001. Here is your chance to use REAL
neutrino data (data actually taken by the NuTeV experiment) and calculate
this fundamental parameter of the Standard Model of particle physics, the
Weak Mixing Angle. The parameter describes the relative frequency of the
two possible weak interactions, the charged current and the neutral current.
Click here for more information
This lab involves getting real neutrino data off the web
and analyzing it with Excel. Step-by-step instructions are provided below.
Please turn in answers to the following questions and any plots you are
asked to produce.
For ease it grading (and in issuing partial credit),
please show as much of your work as possible in performing the various
- First look at the page
This is a picture of an neutrino interaction which defines the
variables used in this lab.
- Next, go to
The files here represent
the first 50 or so neutrino interactions found on
a data tape written on Sept. 6, 1996. Before downloading the data into
a spreadsheet, let's first look over the events. In doing so, keep in
mind that there are two counters for every drift chamber,
so an event of LENGTH = PLACE-CEXIT+1 = 20 should show hits in roughly
10 drift chambers.
- (a) How many of the events are probably neutral current (NC)
How many are probably charged current (CC)
- (b) From (a) compute the ratio of NC/CC events. Also calculate
the statistical error
on this ratio.
- (c) Can you classify the events with PLACE=20? Hint: look at
- (d) Are most of the hadronic showers contained in LENGTH < 20?
Check this by looking at the
drift chamber and counter
information (for example, PLACE and SHEND) shown at the
top of the displays.
- (e) Which event is not a neutrino interaction? How can you
tell? Note: such events are
cosmic ray interactions
and will have to be removed
from our data sample.
- (f) Which event does not have its hadronic shower energy fully
contained in the detector? Note: we will have
to be careful
to remove events with poor energy containment from our
In real life, however, given the vast amount of data collected by high
energy physics experiments, it is not feasible to hand scan the many thousands
of events collected. It is common practise to develop "cuts" (or requirements)
to isolate events of interest. This is why you will be importing a large data
file into a spreadsheet for further analysis. Don't worry, you will not have
to look through all of these by eye!
- Download the neutrino data into an Excel
spreadsheet using the Import command (after saving the data
as a text file, use the command
Data/Get External Data/Import Text File). Split out the cosmic ray
data (beamoff=1) into a separate Excel worksheet and save.
- Use IF statements or the Sort command to select events
which are within the 'fiducial region', in other words, events which
are contained within the central portion of the detector in order to
avoid problems pointed out in #2. PLACE should
be several counters from the upstream end of the detector (counter 84)
and far enough away from counter 1 so that an interaction of length
greater than a LENGTH cut of 20 can be detected. Recall 2(c).
You also want to make certain that the hadronic
shower is well contained. Recall 2(f). Do this via a cut on VERTX and
VERTY. Hint. Note that some events have
so little energy that VERTX and VERTY could not be determined; their
values are 9999.9. Histogram the energy, EHADNC, for such events
with VERTX and/or VERTY = 9999.9 and then delete them from your
spreadsheet. The energy distribution should give you some indication
as to why these events did not have a VERTEX found.
- (a) Which PLACE and VERTX,Y cuts did you decide to use?
- Calculate a LENGTH for each event:
LENGTH = (PLACE-CEXIT+1).
Warning: you will need to make a special case of events with CEXIT=1.
Remember these are long events which pass all the way into the toroid
spectrometer. Using the IF command,
define all CEXIT=1 events as having some
large length, say LENGTH=99, by default. Using the histogramming facility in
Excel, plot the LENGTH of events with L<99 (otherwise, the L=99 CC toroid
events will swamp your plot). Histogram help.
Does a LENGTH cut at 20 seem reasonable for use in separating NC and CC events?
- Count the number of events which pass the selection cut and have
LENGTH > 20 and LENGTH 20. The short events will be your
neutral current (NC) candidates and the long ones your charged current (CC)
candidates. Report what you obtain for the ratio of short/long = NC/CC events
at this step prior to the corrections you will apply to these numbers in
Questions 7 and 8. (Note: don't forget to include the LENGTH=99 events in
your CC sample).
- Remember we are only interested in the ratio of
neutrino-induced NC (short) and CC (long) events.
We have already seen that our neutrino data
contains some small fraction of non-neutrino events; recall #2(e).
Therefore, the NC and CC events you found in your beamoff=0 sample
in #6 will contain some non-neutrino (cosmic ray) interactions
which you will want to remove. To correct your numbers for the
background (i.e. non-neutrino interactions), you will need
to subtract the cosmic ray background from your observed events to get
the true number of neutrino interactions. To make this easy, cosmic ray
events were collected during a special running period with the neutrino
beam turned off.
- (a) Count the number of events passing your fiducial cuts in the
cosmic ray gate (beamoff=1).
Remember these events are in the
separate spreadsheet you saved in step #3.
The cosmic ray data is taken for a longer time period than the neutrino
data, so you need to correct for this difference in times. For the data
in this lab, a clock counted away and was recorded for both beam
conditions. To compute this scaling factor, take the ratio of the
clock*live quantities for neutrino and cosmic ray events in
the neu.sum file. The ratio of these numbers
allows you to rescale the cosmic events to the same running time as
the neutrino beam data. This then tells you how many cosmic ray events
you should have expected to occur coincidentally during the neutrino
- (b) What is the cosmic ray scaling factor?
- (c) How many scaled cosmic ray events pass your fiducial cuts?
Correct the number found in 7(a) by 7(b).
- (d) Next, you need to subtract this number from your observed
number of events to get the true number of
interactions. Hint: you may want to plot the LENGTH for these
events to determine whether you
should subtract this
number from your short (NC) or long (CC) sample. Are the cosmic
ray events short or long?
- (e) Report what you calculate for the ratio of short/long =
NC/CC events after subtracting the non-neutrino
- You also need to correct for CC events that may have made it into
our short "NC" sample. Scan about 100 short "NC" events in the area:
- (a) What fraction of the short events are actually charged current
events where the muon leaves the detector?
Remember you are looking for an obvious (continuous) muon track in which
the muon has either exited out the side of the detector, ranged out in the
middle of the detector, or gone through the toroid. Correct the number of
neutral current and charged current events you found in question #9 for
this effect. Hint
- Calculate the ratio NC/CC from the short and long events you now
have in your final sample and extract the Weak Mixing Angle, :
- (a) Report what you obtain for the ratio short/long = NC/CC.
Also calculate the statistical
error on this ratio.
- (b) Does this number agree (within errors) with the ratio you
obtained from your visual scan in 2(b)?
- (c) Did the cosmic ray subtraction and short CC correction bring
your calculated ratio closer to or
farther from the
visual scan results? Which had a larger effect on your ratio:
the cosmic ray subtraction
or the short CC correction?
- (d) Using the NC/CC ratio you calculated in part 9(a), extract
a value for the Weak Mixing Angle, .
Hint. Assume r=1/2.
Given the statistical error on the NC/CC ratio computed in
part (a), calculate the statistical
error on the Weak
Mixing Angle. Hint
- (e) How does your Weak Mixing Angle measurement compare with the
theoretical expectation that = 0.22?
Does it agree
within the uncertainties of your measurement?