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Neutrinos in the Leaving Cert 2020

Updated: Mar 15

As somebody who has put more than one or two physics questions out into the world that subsequently turned out to have flaws, I have some sympathy with anybody tasked with the setting of state exam papers. There are just so many different ways in which a question can go wrong: you forget to supply all the relevant data or you supply flawed data, you either overcomplicate - or oversimplify - the phrasing, you fail to spot a possible misreading - or several possible mis-readings....the list goes on.


Mistakes in the Leaving Cert are mercifully rare, but an interesting argument/discussion ensued after the 2020 Leaving cert paper about question 10 (a) (iii)*, which asked students to: 'List the three types of neutrino in order of increasing mass.' Older sets of tables make the question seem straightforward, but more recent reprints make it seem unanswerable. Ultimately the issue was dealt with by awarding full makes to any student who listed the three neutrinos, and the issue of their mass was ignored. But like all good mistakes., this is something from which we can learn, and after asking many people for some guidance or explanation about this, I came across (via the IoP) this explanation of the situation from Professor Brian Dolan of Maynooth University - which I am reprinting here below with his permission.....


I am circulating this note to advise secondary school physics teachers that there was an error in last year’s Leaving Certificate Examination 2020, Physics Higher-Level paper. Question 10 a iii) asks the students to ”List the three types of neutrino in order of increasing mass”.
This cannot be answered with our current state of knowledge of neutrino masses, the neutrino masses are not known, we only have upper bounds on their masses. Neutrinos come in three types, or flavours: electron neutrinos, muon neutrinos and tau neutrinos. It is observed in experiments that these three flavours can change into one another over time, though the total number of neutrinos appears to be conserved. Electron neutrinos produced in the Sun, for example, can oscillate into muon neutrinos before they reach the Earth and even oscillate back into electron neutrinos. It would be very hard to account for these oscillations if neutrino were truly massless and by far the most likely explanation is that neutrinos have mass and the oscillation parameters give us some information, in particular they put bounds on the masses.
In fact the physics is rather subtle because these bounds come from rather indirect information, not from direct measurements. Ignoring its position and spin the state of a neutrino is actually described by a vector in a 3-dimensional vector space and these oscillations tell us that a neutrino with a definite mass is actually a linear combination of an electron, a muon and a tau neutrino — it does not have a specific flavour. Conversely a specific flavour does not have a definite mass.**
I have contacted the State Examination Commission (SEC) about the error and have been told that they were aware of the error and any student that attempted to answer Q10 a, part iii) was given full marks for this part of the question, by default. However my understanding is that the SEC will not contact teachers to inform them of the error and there is an obvious risk that teachers may use this question from last year’s paper to train students for future examinations, hence the reason I am circulating this note.
There is a history to this. I noticed in 2010 that SEC “Formulae and Tables” booklet listed masses for the neutrinos and I contacted the SEC to point out the error. They said that the error would be corrected in a future update of the booklet, and indeed it was corrected in the 2014 edition. It seems whoever set last years Leaving Certificate paper may have been using an old edition of the Formulae and Tables. There is a good website with the most up-to-date information on the current state of knowledge about the physical characteristics of fundamental particle, in particular their masses, at: https://pdg.lbl.gov/2020/tables/contents−tables.html.
I would recommend anyone who is involved in teaching particle physics to use this website rather than the Formulae and Tables, it is comprehensive and fully up to date and is not difficult to navigate.

Prof Brian Dolan Department of Theoretical Physics, Maynooth University



* and what a joy it is to see questions broken down so thoroughly into named or numbered parts.


** This is quantum mechanics: it’s a (complex) 3-dimensional Hilbert space and the quantum state of a neutrino is a vector in this space. Mass is a 3 × 3 matrix and flavour is a 3 × 3 matrix and these matrices do not commute. Eigenstates of flavour are not eigenstates of mass.

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