## Thursday, March 17, 2011

### Neutel 11 Update

One could be forgiven for finding the news from Neutel 11 a little disappointing, with many inconclusive results being announced, but it is still early days for precision neutrino physics and this has to be one of the most exciting conferences of the year.

Yesterday's blog updates include this short exchange between Carlo Rubbia and the neutrino physicist Altarelli. Altarelli is of course thinking about CPT violation, and Carlo Rubbia is understandably reluctant to introduce something so ugly into apparently local physics. Hello there, people! As we keep trying to explain, you can quantitatively account for the MINOS results without invoking an ugly CPT violation. It's simple. You just have to give up the idea that an antineutrino is the antiparticle of a neutrino. It's really a mirror neutrino.

1. Big news, I wonder why I've not seen it before now. CPT violation in top quark mass vs anti-top quark: http://arxiv.org/abs/1103.2782

2. Cool, Carl. I'll check it out.

3. "As we keep trying to explain"

Isn't part of the problem that you don't have a working field theory limit of your ideas? You have this argument, involving matrices and braids, that new particles with certain quantum numbers (including mass) exist. OK. But can you write down a field theory showing explicitly how these new particles interact with the old ones? Can you indicate how such a field theory limit arises from whatever your fundamental framework is? Do we have to throw out part of conventional field theory, even in accessible experimental regimes, in favor of a new formalism (Carl's?), in order to describe these interactions?

4. Mitchell, the whole point of this research program is that the SM must be rewritten in a non local language, using operad cohomology to replace the twistor scattering language. There is no need to get bogged down in 'Lagrangians' (ie. your precious 'field theory') if we can exactly reproduce experimental results without one. Moreover, I never set out to work this whole damned thing out myself. Of course we are throwing out part of the conventional theory. Why else would I be listing anomaly after anomaly, along with a few quantitative BSM predictions? Just for a laugh? So, the 'field theory limit' you are after would be a construction of the motivic expressions for QCD using higher dimensional operad polytopes and their associated braids. No need for any effective Lagrangians. If you want effective Lagrangians, then by all means continue to work on string theory until the dust falls off your bones.

5. While it's very useful to have this new increment of information about the big picture (your remarks about how to get the field theory limit from the operad cohomology), it doesn't clarify what I was really getting at.

Suppose I'm an experimental particle physicist, like Tommaso, or the people who work on MINOS. I may be quite agnostic about the ultimate nature of physics, I might be prepared to believe that fundamentally it's all "operads". But what I work with to understand my data, right now, are field theory and effective Lagrangians.

Now you are telling me that I can understand the MINOS data if I posit the existence of some new particles, "mirror particles", which are doing stuff that I thought antiparticles were responsible for. You can even tell me their masses; great. So what I want to know, first, is this: I have my standard field-theoretical ways of representing "particle with mass X". I can add a Majorana spinor-field kinetic term to my usual Lagrangian, give it this mass, and give it some interactions. Is it a valid interpretation of your ideas to do this - in which case, I can start computing scattering amplitudes, lifetimes, and all the other practical details that field theory is used for? Or do I have to wait until the twistorial (or post-twistorial?!) reformulation of field theory is more advanced, before I can compute anything at all?

6. No, it is not valid to discuss non local physics in terms of Lagrangians. Mitchell, at some point one has to start doing new physics with new techniques. Where would QM be without matrices? Or GR without Riemannian geometry? And yet these techniques were thought to be irrelevant to physics before they became essential. Now, you are welcome to prove me wrong by attempting to calculate quantities using effective Lagrangians, but it just doesn't make any sense to me.

7. The definition of 'anti-neutrino' and 'mirror neutrino' you are proposing is still not quite clear to me. I hope you'll indulge me in some questions to try to sort it out...

You want to interpret the MINOS results as demonstrating different mass splittings in the neutrino and *mirror* neutrino sectors, so that CPT isn't violated (i.e. the real anti-neutrinos have the same mass splittings as the neutrinos). Right?

I think you have said that you want to interpret the invisible particle in beta-decay as a 'mirror neutrino'; is that right? So we have an interaction W- -> e- + mnu_e, where mnu stands for mirror neutrino and the subscript tells us it partners the electron in such interactions.

My understanding of MINOS is the following (mostly gleaned from 0711.0769; note I will ignore the irrelevant issue of electron neutrino content of the beam). They smash protons into a target to produce a shower of hadrons. Such showers are packed full of pi+ and pi- mesons, which decay predominantly to muons: in the standard picture, I would say

pi+ -> mu+ + nu_mu
pi- -> mu- + nubar_mu

where nubar means an anti-neutrino. All charged stuff is then stripped out, leaving a(n) (anti-)neutrino beam. The detectors then measure these (anti-)neutrinos via charged current interactions with nuclei:

nu_mu + nucleus -> mu- + different nucleus
nubar_mu + nucleus -> mu+ + different nucleus

These occur via W exchange i.e. the interaction nu_mu -> W+ + mu- and nubar_mu -> W- + mu+. The extent to which the flux changes between the near and far detectors tells us about the oscillation parameters, including mass splittings.

Your suggestion (as I understand it) implies that we actually have

pi+ -> mu+ + nu_mu
pi- -> mu- + mnu_mu

where the second comes from W- -> mu- + mnu_mu, the muon version of the beta decay interaction. But in the detector, we have nu_mu -> mu- + W+. In QFT, the equality of these two interactions implies that mnu_mu and nu_mu are anti-particles, but in your framework it does not.

Is the above a fair summary of this part of your theory?

8. Rhys, as you can see, we are still thinking about the mirror structure of mesons and nuclei, but there is no real mystery about the proposed mirror neutrino states. We are simply taking all possible three strand ribbon braids, and these correspond to precisely what is observed, no more nor less. Yes, we are saying that $\nu$ and mirror $\nu$ are NOT antiparticles, as MINOS observes, and remember that the weak states are not the same as the mass states! Strictly speaking, it is only the mass states that one should consider when talking about particle annihilation. Now the mass states of the neutrinos and mirror neutrinos ARE closely related via the mixing and Koide matrices, so there is still a sense in which the weak states 'pair up' nicely as per usual.

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