Mu2E: Exploring Lepton Flavour Violation At Fermilab
    By Tommaso Dorigo | December 3rd 2012 08:55 AM | 13 comments | Print | E-mail | Track Comments
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    I am an experimental particle physicist working with the CMS experiment at CERN. In my spare time I play chess, abuse the piano, and aim my dobson...

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    The conceptual design report of the Mu2E experiment at Fermilab is out in the arxiv for you to browse. Mind you - it is a rather thick document, 562 pages in all, so if all you have is 15' of lunch break you have better try something lighter.

    The experiment aims at searching for muon decays to electrons in the field of heavy nuclei (tungsten or aluminum, as far as I understand from a quick browsing). Leaving aside the nucleus, I would bet that if you have a basic knowledge of the standard model of fundamental interactions, gathered by reading standard undergraduate books such as the Perkins or the Burcham-Jobes, you might be tempted to say that muon conversions to electrons are a very exotic kind of non-standard physics to search for. In fact, they entail the violation of the rule of lepton number conservation, which has been one of the best-verified rules of fundamental physics in the XXth century.

    In reality, we know that lepton flavour violation must occur: this bit of knowledge came from the groundbreaking results of the Super-Kamiokande experiment in Japan, which in 1998 proved the neutrino oscillation phenomenon. Both cosmic-ray neutrinos and neutrinos from the sun were observed to change flavour, solving an astrophysical puzzle which had lasted for over twenty years (the solar neutrino deficit problem).

    When neutrinos change flavour, they violate lepton flavour conservation all right. This of course need not be a proof that charged leptons (the electron, the muon, and the tau) also turn one into another: flavour violation could well be a mechanism specific of neutrinos. However, Occam's razor -a principle usually preventing the construction of unnecessary hypotheses, and as such a great tool for the sceptical mind- can be used this time to support the notion that there is nothing special with charged leptons: being electrically charged is arguably a less fundamental property of being a lepton. So if neutrinos do it, why not electrons and muons ?

    If lepton flavour is violated also by charged leptons, we may expect decays such as the one of a muon to an electron plus a photon, or even direct conversion of a muon into an electron in the field of a nucleus; in both cases, no neutrinos are emitted, so energy conservation can be checked with precision if one is capable of detecting and measuring the final state bodies. Given the ease of producing intense beams of muons at today's accelerator facilities, and the rather striking signature of the mentioned decays, it is not surprising to learn that the rate of muon decays to electrons has been already constrained to be smaller than 2.4 x 10^-12 (two point four trillionths), e.g. by the mu-e-gamma experiment, or down to 7x10^-13 (seven tenths of a trillionth) by the SINDRUM II experiment.

    While the electron plus photon decay used by MEG exploits the back-to-back, energy-balancing decay into a photon and an electron (see figure, right), Mu2E like SINDRUM II searches for an electron with energy almost exactly equal to the muon rest mass (the heavy nucleus taking off only a very small fraction of the released energy, to conserve momentum!). The expected single-event sensitivity, given the total statistics envisioned in the report, corresponds to 5x10^-17, probing four orders of magnitude deeper into extremely rare decays. This is quite a lot of unexplored land, where many new physics scenarios could pitch in, turning on the searched reaction.

    In the graph on the left you can see the kind of signal expected by SINDRUM II: a tiny peak of muon conversions to electrons at the energy corresponding to the muon rest mass. The three histograms with different shades of grey show the data at different levels of selection. The darker one is after the removal of the nasty cosmic-ray background: a signal corresponding to some decays per trillion muons is shown by the white dots.

    The Mu2E experiment will cost about 250 million dollars, and is planning to operate in year 2020 at Fermilab. A sketch of the experimental area is shown in the graph on the right, where you can see on the left the interaction point where pions are copiously produced; muons produced from the decay of pions are then directed to the detector on the right, where decay electrons can be accurately measured. The figure does not include the cosmic ray shield, which is a must in this kind of experiments.

    I believe that the price tag of the experiment, given that it is one which puts all the eggs in one basket, being as it is a very focused search on a narrow hypothesis, is rather steep. However, what I think is nice about this project is that if we found some kind of Supersymmetry at the LHC we would benefit a lot from measuring the rate of muon decays to electrons with Mu2E. In the graph below, also taken from the conceptual report, you can see that much of the parameter space accessible to LHC could in principle allow coherent muon decays to electrons at rates measurable by Mu2E. So the complementarity of this experiment to others is certainly there.  Also worth mentioning is the complementarity of the physics responsible for coherent muon-to-electron decays with the one investigated by experiments searching for the muon-to-electron-gamma decay: there are two different parts of an extended Lagrangian which enable the two processes, so one really needs to study both processes. More on this topic in Section 3.2 of the report.

    In the figure you can see as red and green crosses the predicted conversion rates of muons into electrons as a function of the universal mass M_1/2, for two distinct scenarios of supersymmetry, and at tan(β)=10. The points "illuminate" the parameter space allegedly accessible to the LHC. I am not sure what assumptions are used to constrain the space accessible to the LHC, but the report cites a very thick paper written by LHC theorists and experimentalists, so it is probably okay.


    You write "When neutrinos change flavour, they violate lepton flavour conservation all right. This of course need not be a proof that charged leptons (the electron, the muon, and the tau) also turn one into another: flavour violation could well be a mechanism specific of neutrinos."

    Once you have mixing in the neutrino sector, even if the charged sector starts out with no mixing in the classical lagrangian, wouldn't you generically expect a flavor mixing matrix to show up due to renormalization from bubble diagrams lepton -> W nu -> W other-nu -> lepton? So that the absence of mixing would be a fine tuning and also would not be preserved by the RG? There's no symmetry to protect off-diagonal zeros.

    Or, for the experiment in question, wouldn't you get the decay mu->e gamma by a penguin diagram with a neutrino flavor mixing matrix insertion and no other non-SM physics?

    Dear Tommaso,

    I am the Mu2e co-spokesperson and appreciate your writing about our experiment! A couple of technical points. Mu-e conversion can be mediated both through the photonic processes that MEG can see, and in that case our experiment will probe just a little better than their proposed upgrades, essentially the same to x2. In the "direct" processes (heavy neutrinos, compositeness, leptoquarks,...) we have reach but MEG does not. This is good -- it makes the experiments complementary and gives them constructive interference. If we both see something it pins down models in parameter space, if we do and they don't it tells you it's the direct process, etc. So quoting rates for MEG and SINDRUM-II in the same sentence isn't quite right, since in the photonic term we're suppressed by alpha/pi, and then of course we're sensitive to different combination of processes, as I said.

    The excellent question above has a simple but surprising answer. Yes, one does get mu-e conversion from neutrino oscillations in loops, but it is suppressed by a sum over neutrino species ~((dm2/M_W^2))^2 and when you put in all the numbers the rate for mu->e gamma is 10^{-54} and about that for us too. So there's effectively no SM background.

    Finally, you have to be careful about the cost. The cost in DOE numbers includes all sorts of things that are not counted in Japan or at CERN. We include a lot of salaries, overhead, etc. It's neither bad not good but makes us look very expensive compared to how a physicist would cost it.

    Hello Robert,

    thank you for taking part in this thread! Yes, I have slightly exaggerated my feelings about the cost of the project - I like to give a polemic tone to some of what I write, to stimulate thought and replies ;-)

    Thanks also for the explanation of direct and indirect processes. Good luck!

    out of pure curiosity, what's the reason for the S-shaped tube between the production and detection solenoids?

    There are many reasons. The three magnets are solenoids. When you have a curved solenoid you get an effective dipole field (see Jackson) which pushes negative muons one way and positives the other. The center of the S has an asymmetric collimator that sign-selects negatives and blocks positives. The second half of the S brings the negatives back on-axis. We want negatives since the experiment works by capturing negative muons in Al in a 1s state and letting them convert into electrons by interacting with the nucleus. Why we choose Al over Ti or other materials is a whole lecture. Go to arXiv:0904:0957 for theory, or a nice paper at hep-ph/0512039. The choice of materials now is dictated by experimental needs, but this is the wrong forum for details. Tune in for Mu2e upgrades at Project X.

    Be careful with the impurities in Aluminum!

    Hi Tommaso,

    Some of this answer is very sketchy and I'm obviously compressing and leaving out details.

    On the isotopic and other impurities in Aluminum, that is a potential issue if you aren't careful because of the decay-in-orbit background. Decay-in-orbit is normal (Michel) muon decay while the muon is in the 1s state. The spectrum is distorted for us from the normal Michel spectrum because the outgoing electron can exchange a photon with the nucleus, and the endpoint, up to neutrino mass(!) is the the conversion energy. See Czarnecki et al., arXiv:1111:4237 for the best calculation of the spectrum. More or less, the spectrum near the endpoint goes as (E_endpoint - E)^5, just the three body Sargent rule. The fraction of the distorted spectrum near the endpoint gives us about 0.23 bkg events with all resolution effects for the 6e-17 90% CL limit.

    The physics is that the DIO endpoint is the muon mass minus binding energy minus a nuclear recoil term, so low Z is less binding, the endpoint goes up, and the rapidly falling spectrum moves up and turns on with the fifth power. The higher-Z materials are not such a problem because the endpoint of the decay-in-orbit background spectrum is shifted to lower energy and out of the signal region. If you want I can send you my Mathematica notebook of endpoint vs. Z. Isotopes can give the same general category of problem because the change in mass of the nucleus also shifts the endpoint. See Czarnecki et al. again for the formulae.

    So we have studied that and will get special high purity Al, make support structures out of appropriate materials, take care about oxidation, etc. We have memos on the amount of impurities we can tolerate and impurities don't look like a problem if we take care.

    I feel like I'm answering a question at a seminar, so I will give the standard closing: does that satisfy your concern and answer any questions? This is not a good forum to answer subtle questions but I'm doing my best.

    --best, Bob

    Hi Bob,

    you sure have answered quite extensively!

    I remember doing a simple muon lifetime measurement twenty years ago, and having to
    deal with boron and carbon impurities was even for such a simple measurement not trivial
    at all. I do appreciate the problems you mention above, but luckily it is possible to have
    enough purity for the material.

    562 pages in all
    Chicken feed — compared to the 2000 pages of the report produced by the recent Leveson Inquiry into the culture, practices and ethics of the British press.
    you might be tempted to say that muon conversions to electrons are a very exotic kind of non-standard physics to search for.   In fact, they entail the violation of the rule of lepton number conservation,
    I’m a bit puzzled here.  According to that fons sapientiae omnis, Wikipedia:
    Together with the electron, the tau, and the three neutrinos, the muon is classified as a lepton.

    "The poor King looked puzzled and unhappy". Illustration by Peter Newell to "Through the Looking-Glass and What Alice Found There", chapter "Looking-Glass House".

    Robert H. Olley / Quondam Physics Department / University of Reading / England
    Hi Robert, the point is that the SM predicts *individual* lepton flavor numbers to be conserved (modulo 10^{-54} effects), i.e., the electron number (number of electrons minus number of positrons) cannot change and the muon number (number of muons minus number of antimuons) cannot change.
    A mu->e conversion would violate both, although the general lepton number would still be conserved.

    Robert H. Olley

    also on wikipedia:



    Thanks for the link.  I find it most informative.
    Robert H. Olley / Quondam Physics Department / University of Reading / England

    I am not a scientist yet I wish I was. I have been trying to grasp that which I can and learn from direct fascination from all work considered in this huge task. As I personally watch on the nieve side of your experiments I am humbeled by what you do and why