Research on Axion Discovered by P L Jain & G Singh from UB SUNY

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The Jan. 2007 issue of the British Journal of Physics G: Nuclear and Particle Physics is publishing the research of P L Jain and G Singh from the University at Buffalo, The State University of New York.

http://www.iop.org/EJ/abstract/0954-3899/34/1/009
Read it for free before they make you pay for it!

Frank Wilczek is claimed to have once said something like:
Discovering the axion will be one of the greatest triumphs for theoretical physics.
 
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What did the bartender say to the axion?

No charge :)

You can read about what the axion is:
http://physicsweb.org/articles/news/8/11/13/1

(Note that this is MUCH older article dating from 2004 so it does NOT mention the discovery.)
 
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I am not very impressed with the paper. Looking at their figures it is very difficult to see how they can see any statistically significant peaks at all. for example, fig 4b looks like it has peaks all over the place, indicating that the statistical significance is bad. Unfortunately they don't give any quantification of the statistical significance (or indeed account for systematic errors).

Doing a naive statistical analysis myself, there are 1163 events so there are roughly 116 events in the 7MeV 'peak'. Statistically (and naively) we might expect this to have an error of \sqrt{116} = 10.75. The fit looks to be about 6% at this value, which is about 70 events, so this looks like a 4.2 standard deviation effect.

Normally one needs 5 standard deviations for a discovery, and my estimate was very rough and excluded systematic errors.

Also, what is their justification for attributing these 'escesses' with axions?
 
There is one aspect to this question that I find very confusing. Axions are considered by some to be a candidate for dark matter, which requires them to be stable. However the experiment is about particles with extremely short half lives. Something is wrong!
 
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I'm following this paper by Kitaev on SL(2,R) representations and I'm having a problem in the normalization of the continuous eigenfunctions (eqs. (67)-(70)), which satisfy \langle f_s | f_{s'} \rangle = \int_{0}^{1} \frac{2}{(1-u)^2} f_s(u)^* f_{s'}(u) \, du. \tag{67} The singular contribution of the integral arises at the endpoint u=1 of the integral, and in the limit u \to 1, the function f_s(u) takes on the form f_s(u) \approx a_s (1-u)^{1/2 + i s} + a_s^* (1-u)^{1/2 - i s}. \tag{70}...

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