MINERvA muon neutrino measurement 2019



First things: online tools

Each computer should have robust internet access (preferred) or the DVD version of the masterclass loaded. Two students should work together at each computer to complete a 50 events dataset.


  • Students must have access to the event display program ARACHNE Simple using an up-to-date browser.
  • Students must have access to the online spreadsheet. These will be linked from the videoconference Indico pages, to be found in the Videocon section.
  • Students should have access to the MINERvA Masterclass website prior to the masterclass day.

Download versions:

See documentation, below.


Grab the data:

See Data Analysis, below.


Familiarize yourself:

Share these with students when appropriate!



Students arrive

This should occupy the first 30-60 min

  • Registration: please have students sign in on a registration sheet with name, school, and teacher.
  • Gateway experience: have a cloud chamber, e/m apparatus, or something similar to whet interest
  • Ice-breaker activity: students in small inhomogeneous groups create 1-2 good questions about particle physics, neutrinos, MINERvA, and/or DUNE.



Shift training

Get students ready for their data analysis shift! This will take about 3 hours, though parts of it can be moved to other times of the day.

Mentor presentation, 30-60 min:

  • keep it interactive - ask questions about prior experience, shows of hands, wild guesses, etc.
  • give students something to touch, e.g. a wave-shifting fiber
  • connect to classroom prep
  • touch on standard model
  • talk about your research
  • Focus on theme of MINERvA masterclass: using a neutrino beam from Fermilab to probe the atomic nucleas and better undersand weak scattering in preparation for DUNE.


Tour, 30-60 min:

  • adds much to the day - often most popular part
  • if you have an accelerator to show, great!
  • if not: any interesting labs, even if not particle physics, are still great
  • have enthusiastic grad students around to chat and explain

Analysis Prep (30-60 min):

  • Have a teacher lead this if practical.
  • Use/adapt the data analysis slides.
  • Important: go through "masterclass-samples" in ARACHNE Simple on the projector with the students:
    • Show students how to navigate to a data file.
    • Discuss how to use the tools in ARACHNE.
    • Discuss each event in terms of:
      • Signal vs. (vertex or recoil) background
      • Where the neutrino goes, where the vertex is, muon and proton tracks
      • Copying kinematic data to the spreadsheet.
    • What we plan to do with the recorded data.

Lunch with a Physicist (30-60 min):

  • This is also very popular and a great way for students to interact and get comfortable with scientists.



Data Analysis

This is the heart of the masterclass and takes about 60 min. There should be 2 students at each computer, cooperating to get their data measured. Mentors, tutors, and teachers should circulate to help the students analyze the events and work out any problems they have. Don't give them answers. Help them figure things out and learn to see data as scientist does. 

  • Instructional screencast
  • Data and event display
  • Cheat sheet

Here are the current links to Arachne Simple and the Data:

  1. mergedTuple_1.root
  2. mergedTuple_2.root
  3. mergedTuple_3.root
  4. mergedTuple_4.root
  5. mergedTuple_5.root
  6. mergedTuple_6.root



Sharing Results

This takes a little over one hour. Both parts are important.

Discussion (30-45 min):

  • Mentor leads, students interact.
  • Look at combined mass plots for your institute in spreadsheet.
  • Help students analyze histograms to find:
    • Neutrino beam momentum and energy
    • Uncertainty in px and py
    • Estimate of carbon nucleus radius using Uncertainty Principle and Fermi Gas approximation
    • See box below.
  • Discuss meaning of result for understanding nucleus and weak scattering.


Analysis of MINERvA Masterclass results



A muon neutrino encounters a carbon nucleus in the targer area of MINERvA. It interacts with a neutron in the nucleus by emitting a W+ boson. As it emits the W+, the neutrino transforms into a muon. The W+ is absorbed by a down quark in the neutron, changing it to an up quark and transforming the neutron into proton. Both the muon and the proton carry the original momentum of the neutrino and thus move rapidly away from the carbon nucleus into the detector modules.


Beam momentum and energy:

The defined z-axis of the detector system is aligned to the direction of the Fermilab neutrino beam. The histogram of values of pz should make a normal distribution with the peak at the central value of the neutrino momentum in MeV/c. Since the masses of the neutrinos are extremely small and the momenta are quite high, the same number in MeV is the beam energy.


Momentum in x- and y-directions:

Since the momenta of the neutrinos are in the z-direction by definition, the net momenta they give to the outgoing protons and muons must be zero. If the neutrons are initally rest before the interaction, then the histograms of net px and net py must peak at zero and be quite narrow. If there is a wide distribution, then the momenta in x and y must be random and mostly non-zero, producing a fairly wide normal distribution centerd on zero.

The uncertainty in the distribution of px or py can be estimated as half of the Full Width Half Maximum (FWHM/2). To find this, find the level halfway below the peak and measure the width of the distribution at that point. Divide by 2.

Radius of Carbon Nucleus:

The radius of an atomic nucleus in Fermi (fm; 1 fm = 10-15m) is extimated using the equation 

R = (1.25 fm)A1/3,

where A is the atomic mass number. For carbon, A = 12 and therefore

R = (1.25 fm)(121/3) = 2.7 fm.

If the neutrons in carbon have their own momenta then they are constrained in their movement by the radius of the nucleus. If we understand the process of the neutron-neutrino interaction and resulting ejection of the proton and muon well enough, our x- and y-momentum data analysis should yield a reasonable estimate of this distance-of-travel constraint, that is, 2.7 fm, as the uncertainty in position of the neutron.


Calculation of Δx or Δy:

We shall examine Δx only as the analysis of Δy is identical. 

The Heisenburg Uncertainty Principle states that the uncertainties in position and momentum form a complimentary pair, the products of which are no smaller than Planck's constant divided by 4π, or

ΔpxΔx ≥ h/4π.

Using momentum in MeV/c and distance in fm, it turns out that h/4π is about 150 MeV-fm/c. However, this assumes that the neutron is completely free to move. It is not as it is bound to quantized energy states in the nucleus and no two of them can occupy the same state due to the Pauli Exclusion Principle. A collection of particles that behaves this way is called a Fermi Gas; the Fermi Gas approximation of the behavior of the neutrons just about doubles the constant in the Uncertainty Principle to 300 MeV-/fm. Then the uncertainty in x is estimated as

Δx = (300 MeV-fm/c) / Δpx.

If this number is significantly less that the carbon nuclear radius of about 2.7 fm, then there is more physics needed to fully understand the interaction. Getting the interaction right is one of the main purposes of MINERvA and is needed to make precision measurments of neutrinos in DUNE.


Videoconference (30-45 min):

Connecting to videoconferences:

Course of a videoconference:

  • Connect to videoconference link or Indico page (see above).
  • Someone should log into the videoconference 15 min early to be sure the connection is established. See the Schedules page.
  • Follow the agenda on Indico:
    • Introductions and warm-up
    • Institute results
    • Combined results
    • Discussion, Q&A, and wrap-up
  • It is good to have a student spokesperson but try to arrange so it is not too hard for another student to make a comment or ask a question.

After this, we have post-discussion and closeout.

Before you go home:

Please report your attendance numbers on our Attendance Form!

Have a great day!



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