High energy particle physics experimentalist/phenomenologist Dr Tommaso Dorigo has published a history of the 1970s discovery of weak neutral currents in his post:

http://dorigo.wordpress.com/2008/07/20/on-the-supremacy-of-us-over-europe-in-hep/

‘To search for neutral current interactions one could look for neutrino collisions with atomic nuclei. In a charged current interaction, the neutrino would change into a charged lepton -typically a muon, given the composition of neutrino beams saw the predominance of muon neutrinos. In a neutral current, instead, one would not observe any lepton downstream, but just the remnants of the nucleus and other light hadrons. These events were studied with the Gargamelle bubble chamber at CERN, which used a neutrino beam obtained from a 26-GeV proton beam. The typical signal, the appearance of a star of hadronic tracks, could be mocked by neutrons produced upstream, and the difficulty in calculating the rate of those events made the discovery of true neutral current events hard.’

Here’s my comment:

Thanks for the interesting history of neutral currents. Maybe you might take the space to explain what neutral currents actually are physically, e.g., the exchange of neutral weak gauge bosons (Z0) between quarks or leptons? The motion of a charged weak boson (W+ or W-) constitutes an electric current in Maxwell’s equations, so a deflection or scattering of the particle implies a modification to the symmetry of the electric current, which changes it’s energy implying a gauge interaction with an exchange of of field quanta by Noether’s theorem.

The 1967 theory predicting weak currents was just a new modification of the interpretation of the Yang-Mills SU(2) theory. Glashow’s Nobel Lecture of 8 December 1979 states:

‘Schwinger, as early as 1956, believed that the weak and electromagnetic interactions should be combined into a gauge theory. The charged massive vector intermediary and the massless photon were to be the gauge mesons. As his student, I accepted his faith. … We used the original SU(2) gauge interaction of Yang and Mills. Things had to be arranged so that the charged current, but not the neutral (electromagnetic) current, would violate parity and strangeness. Such a theory is technically possible to construct, but it is both ugly and experimentally false [H. Georgi and S. L. Glashow, Physical Review Letters, 28, 1494 (1972)]. We know now that neutral currents do exist and that the electroweak gauge group must be larger than SU(2).’

So the Schwinger and Glashow 50s work used SU(2) with its two charged vector bosons mediating charged weak interactions, and the neutral vector boson mediated electromagnetism. So they were trying to use SU(2) in place of what is now U(1) x SU(2). The essential problem was that they omitted the neutral weak gauge bosons, believing that only one kind of neutral gauge bosons existed, the photons of electromagnetism.

However, when you look at U(1) x SU(2) in today’s standard model, it’s not a neat theory in which U(1) is electromagnetism and SU(2) is the weak force. The photon doesn’t directly from U(1) and the Z0 doesn’t come directly from SU(2). Instead, there is an epicycle-type fiddle called the Weinberg mixing angle, which mixes up the properties of the B gauge boson from U(1) with those of the W0 gauge boson from SU(2) to give the electromagnetic photon and the weak neutral gauge boson W0.

I was disappointed to discover this. As a kid I read Fenyman’s book QED, where in Chapter 4 he describes the U(1), SU(2) and SU(3) gauge theories as being separate, not mixed up! E.g., on page 141 he states that the Z0 is a particle ‘which we could think of as a neutral W’, and he repeats this error in figures 87-88. In Figure 88, he suggests that because the coupling for the Z0 is similar to that for the photon, they ‘may be different aspects of the same thing’.

This completely ignores the Weinberg mixing angle which exactly how the two neutral gauge bosons are related in the standard model, they’re products of a mixture.

What’s really a mess here is that you have to mix up the neutral gauge bosons of two separate symmetry groups, U(1) and SU(2), to get two mixture products which fit observations. There is no reason why this is, and most popular expositions cover up this ad hoc fiddle.

The real solution is quite different. If you look at SU(2), you see that it actually has three massless gauge bosons, which acquire mass at low energy by a separate unobserved mass-giving (Higgs) field.

Instead of adding on U(1) for electromagnetism and having all the problems of electroweak symmetry breaking and the ad hoc Weinberg mixing angle of neutral gauge bosons from the two gauge groups, why not replace the ad hoc Higgs field model with something more predictive and falsifiable, so that at low energy mass is only given to a portion of the gauge bosons of SU(2). This would mean that at low energy, some of the three gauge bosons of SU(2) would remain massless, and would the generate infinite-range electromagnetic and gravitational interactions. The two massless charged gauge bosons could be able to propagate as exchange radiations (in two opposite directions along each path between charges as they are exchanged) because when passing both ways along a path the magnetic field curl of each propagating massless charged component cancels out that of the other, thus overcoming the usual problem with the propagation of charged massless radiation (i.e. magnetic self-inductance). These massless charged gauge bosons respectively produce positive and negative electric fields, and where those fields move relative to an observer you see magnetic fields appear (because the cancellation is then imperfect). The neutral massless gauge boson is not the electromagnetic field quanta, but rather the graviton. I’ve compiled evidence that the idea that gravity is a massless version of the weak neutral current does lead to a lot of falsifiable predictions, some of which have already been confirmed over the last decade.

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The evidence is linked to from posts such as

http://nige.wordpress.com/professor-johnsons-insistence-on-calculations-to-back-up-ideas/,

http://nige.wordpress.com/2008/01/30/book/,

http://nige.wordpress.com/comment-to-blog-of-andrew-thomas/,

and

http://nige.wordpress.com/comment-to-blog-of-andrew-thomas/

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Tommaso was good enough to reply:

‘As for generating the observed pattern of the Standard Model with something else than a mixing between U(1) and SU(2), I have my doubts that anything different from the Standard Model -i.e. something that does not incorporate it as a low-energy limit or in some other way- can produce the level of agreement with data that we have seen since the seventies.’

My response:

Hi Tommaso, thanks, but the reason for the excellent agreement is between the electroweak portion of the Standard Model and empirical facts is precisely due to the ability to fine tune the Weinberg mixing angle so that it works.

The only reason why the Standard Model’s electroweak theory works well is because the Weinberg mixing angle is 26 degrees (i.e. sin^2 theta = 0.2).

If U(1) described electromagnetism and SU(2) described the weak interaction, then the Weinberg mixing angle would be precisely zero. This seems to the basis for Feynman’s misleading claim that the Standard Model is three separate field theories.

There is no theoretical reason or prediction that the Weinberg mixing angle is 26 degrees. It’s just a fudge factor in the Standard Model that makes it work. It’s not a rigorous theory, but an empirical model containing a mixing of gauge bosons to ensure that couplings and interaction rates match those of observations.

The mixing angle 26 degrees is the difference in vector contributions of the Z0 and the W0. If they were the same thing (as Feynman claimed) then the Z0 would be the W0. It isn’t. Both the observed photon and the observed weak neutral Z0 can only be produced in the Standard Model by mixing together the unobserved B predicted by U(1) with the unobserved W0 predicted by SU(2).

Because there is no physical or theoretical reason for this mixing other than forcing the Standard Model to agree with experimental data, I disagree with your claim that it would be hard for another theory to be as successful as the Standard Model. If you’re allowed ad hoc adjustment factors such as mixing angles to mix up the gauge bosons predicted from different symmetry groups, then it’s easy to model things. In any case, all I’m suggesting is a simplification of the Standard Model. get rid of U(1) and replace the unobserved Higgs field model that currently gives 100% of the weak gauge bosons mass at low energy with one that gives only half of them mass (i.e.g, only the left-handed spinor interactors, modelling for the left-handedness of weak interactions), then the massless SU(2) gauge bosons remaining present at low energy will generate two long range interactions, electromagnetism and gravity. Easy.

It’s now just a matter of formalizing the theory by finding the lagrangian, which should be possible by correcting the lagrangian of the Standard Model, in particular the Higgs sector.

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Update (23 July 2008): Here’s my response to various helpful ideas raised over there to that:

Guess Who, comment 8: I don’t think it’s that hard to do. :) The SU(2) weak isospin lagrangian is known. Delete the Higgs field which gives SU(2) bosons mass at low energy, and then set up a suitable path integral formulation for the massless SU(2) bosons. The half that do get mass are the left-handed interacting weak gauge bosons, and the other half that don’t acquire mass are the long-range bosons for gravity and electromagnetism. Massless neutral currents are graviton exchanges.

Kea, comment 10: people haven’t tried to find a lagrangian for massless SU(2) gauge bosons interactions where the massless neutral current is quantum gravity and the massless charged currents mediate electromagnetic interactions. The nearest thing was the 1957 incorrect Schwinger-Glashow theory in which the massless neutral current of SU(2) was used to replace U(1) for electromagnetism, and the two charged field quanta of SU(2) were used for weak interactions. This is not what I’m arguing which is that the two charged massless field quanta of SU(2) are electromagnetic field quanta (the extra polarizations of the virtual photon are electric charge) and the massless neutral field quantum is the graviton.

If there is a way of using noncommutative geometry to deal with Feynman diagrams in place of a path integral involving an amplitude containing an action which is an integral of a lagrangian equation for the gauge theory, then please let me know. I’m interested in path integrals because for low-energy approximations (representing the Newtonian and Coulomb laws), the only significant contribution to the interaction histories summation is for the simplest Feynman diagram, i.e., a simple exchange of a photon between charges. All of the loop diagrams can be ignored at low energy for the classical approximations. So the only summing of histories in the path integral is for that single simple type of interaction integrated over all possible paths in spacetime, each with an equal contribution but a different phase vector that determines interference. The first priority is to check how this theory works for low-energy physics.

Tony Smith, comment 13: thanks for that information that you have the Weinberg mixing angle calculated from your model, pages 82-86 in http://www.tony5m17h.net/E8physicsbook.pdf Your physics writings are always fascinating. Your calculation of the Weinberg mixing angle on page 85, namely Sin(theta_w)^2 = 1 – (M_W+/- / M_Z0)^2 = 1 – ( 6452.2663 / 8438.6270 ) = 0.235, is impressive. I don’t however physically understand how the B gauge boson of U(1) gets mixed with that of the neutral W_0 boson of SU(2) to produce the observed photon and the observed weak boson Z_0. Mixing of gauge bosons would physically make more sense to me if it was between massless and massive versions of gauge bosons within the same symmetry group such as SU(2), i.e., mixing of massive and massless versions of the SU(2) gauge bosons might occur with a physical mechanism in terms of how the Higgs-type field gives mass to SU(2) gauge bosons as a function of handedness and energy.

Eric, comment 14: ‘Quantum mechanically, two U(1)’s generically are going to mix together whether you like it or not.’ The mixing is between the gauge boson of one U(1) and the neutral gauge boson of SU(2). It’s not the U(1) weak hypercharge gauge boson B and the U(1) electromagnetic photon which are being mixed together to produce the W_0 and the Z_0. It’s instead the weak hypercharge U(1) unobserved gauge boson, ‘B’, and the SU(2) unobserved W_0 get mixed up to produce the two observables, the photon and the Z_0.

‘In the SM, the Weinberg angle may seem ad hoc in the sense that it is a free parameter. However, the value of the Weinberg angle comes out automatically when one goes to SUSY GUTs.’

Thanks for this news, which is a competitor with Tony Smith’s calculation, but SU(5) GUTs, whether SUSY or not, don’t include gravity. Gravity and electromagnetism have similarities in both being long range interactions, needs to be incorporated into a symmetry group.

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