# 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 calculations.

1. First look at the page key.html. This is a picture of an neutrino interaction which defines the variables used in this lab.

2. Next, go to http://www-e815.fnal.gov/wma-lab-web/pix.html. 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) interactions?
How many are probably charged current (CC) interactions?

(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 event 05467-00455.

(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 data sample.

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!

3. 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. Hint

4. 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). Hint

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. Histogram help.

(a) Which PLACE and VERTX,Y cuts did you decide to use?

5. 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? Hint

6. 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).

7. 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 cosmic ray 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 data taking.

(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
neutrino 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
cosmic ray interactions.

8. 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:

http://www-e815.fnal.gov/wma-lab-web/shortpix.html

(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

9. 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?