A new rightwing world waiting to complement the biased leftwing world we've been living in?
The detectors at the LHC have found hints of a \(W'\)boson at mass \(2.1\TeV\) or so, a \(2.9\TeV\) \(Z'\)boson or something like that, and another resonance at \(5.2\TeV\).
In the article about the \(2.9\TeV\) event, I discussed a leftrightsymmetric model that has made exactly this prediction in June. It's a leptophobic model – so that some of the bosons have vanishing interactions with the leptons (while nonzero ones with quarks). I decided to consider the possibility that all the three signals are real and the extension of the Standard Model and the interpretation of the bumps is "really simple", something that a playful kid could tell you.
What would you hear? Well, just like we have the ordinary three bosons with the increasing masses, we have three new ones. The table of the boson masses in the units of \(1\TeV\) would look like this:\[
\begin{array}{lccc}
\hline m/{\rm TeV} & W & Z & {\rm Higgs} \\
\hline {\rm left} & 0.0804 & 0.0912 & 0.1253 \\
\hline {\rm right} & 2.1 & 2.9 & 5.2 \\ \hline
\end{array}
\] Note that we have switched to a new era in which the main unit may become \(1\TeV\) rather than \(1\GeV\) so the masses of the \(W\)bosons, the \(Z\)boson, and the Higgs boson have been converted to \(\TeV\).
The heavier, righthanded cousins \(W',Z',H'\) have the increasing masses as well, namely \(2,3,5\TeV\). Isn't it cool and simple? We simply double the spectrum and add the righthanded sector where the boson masses are \(25\)\(40\) times higher.
I have previously discussed the leftrightsymmetric models and they're cool. The hypercharge is written as\[
\frac{Y}2 = I_{3R} + \frac{BL}{2}
\] (some people use the symbol \(Y\) for what I call \(Y/2\) here) so that the familiar electric charge has a nicer and more symmetric form\[
Q = I_{3L} + I_{3R} + \frac{BL} 2
\] constructed out of two analogous \(SU(2)_{L,R}\) groups as well as a \(U(1)\) group whose generator (charge) is simply \((BL)/2\) – which is \(+1/6\) for all quarks and \(1/2\) for all leptons (and opposite in sign for antiparticles), whether it's the lefthanded or righthanded components in them.
At some higher energy scale, ideally the multi\({\rm TeV}\) scale we are discussing in the three bumps, the \(U(1)_{BL} \times SU(2)_R\) group could be broken to the \(U(1)_Y\) hypercharge group while \(SU(3)_{c}\times SU(2)_L\) remain unbroken up to much lower energy scales.
The breaking of \(U(1)_{BL} \times SU(2)_R\) to \(U(1)_Y\) seems to be completely analogous to the electroweak breaking of \(U(1)_Y\times SU(2)_L\) to the electromagnetic \(U(1)_{Q}\) group. You have an \(SU(2)\times U(1)\) group to start at a higher energy scale and another \(U(1)\) energy at a lower scale.
The kid would probably choose a breaking by another Higgs doublet – a wouldbe rightwing counterpart of the our new beloved \(125\GeV\) Higgs boson which is also a part of a doublet. Because the situations at the two scales are so terribly analogous, we may choose some more suggestive terminology. I will use the term "hyperhypercharge" for \((BL)/2\). It's something that mixes with the third component of the soontobebroken \(SU(2)\) to produce the unbroken ordinary, lowerenergy charge – which is the electric charge in the electroweak case, and the hypercharge in the rightwing electroweak case.
You want the hypercharge to remain unbroken beneath the rightwing electroweak scale (several \({\rm TeV}\)) so the component of the rightwing Higgs with the nonzero vev has to have \(Y=0\), just like it did have \(Q=0\) in the ordinary electroweak case.
Due to these similarities, you may recycle the formulae from the electroweak theory such as\[
\frac{m_W}{m_Z} = \cos \theta_W
\] The ratio of the electroweak \(W\)boson and \(Z\)boson masses is equal to the cosine of the Weinberg angle. Similarly, you could expect\[
\frac{m_{W'}}{m_{Z'}} = \cos \theta_M
\] where I reflected the letter \(W\) to get the mirror image of Weinberg's first letter. Another explanation of the notation is that the Weinberg angle is relevant for the lefthanded fermions and the bosons coupled to them. Here, we need a rightwing counterpart of Weinberg – although it's a bigger heavyweight by a factor of \(25\)\(40\) – and I have volunteered. ;) But due to my extreme modesty, I will call it the Meinberg angle.
If you embed the hypercharge \(Y\) to the minimum \(SU(5)\) GUT – and the embedding may be further embedded to \(SO(10)\) – you may notice the nonstandard normalization of the hypercharge by the factor of \(\sqrt{3/5}\). Because of that, the natural GUT prediction for the Weinberg angle says\[
\sin^2 \theta_W = \frac{3}{8}
\] at the GUT scale. The denominator eight is computed as three plus five. Because of a simple calculation of \({\rm Tr}_{\bf 16} [(BL)^2] \) that I did, I believe that in the rightwing electroweak case, the corresponding normalization factor for \((BL)/2\), the hyperhypercharge, becomes \(\sqrt{2/3}\) which should mean that\[
\sin^2 \theta_M = \frac{2}{5}
\] at the GUT scale and \[
\frac{m_{W'}}{m_{Z'}} = \sqrt{ \frac{3}{5} } \approx 0.775
\] This is just the zerothorder treelevel prediction but it is not too far from the ratio of the masses extracted from the two bumps,\[
\frac{2.1\TeV}{2.9\TeV} \approx 0.724.
\] Update: When I was rechecking the algebra, I decided that I inverted the interpretation of \(\sqrt{2/3}\). The correct figure should have effectively been \(\sqrt{3/2}\) which would mean that \(\sin^2\theta_M=3/5\) at the GUT scale and \(m_{W'}/m_{Z'}\) is on the contrary predicted to be \(\sqrt{2/5}\approx 0.63\), a bit further from the observed ratio.
Finally, most ambitiously, the \(5.2\TeV\) particle seen in four events is the new Higgs boson. That one decayed to two (or three) jets (no lepton evidence) but that's pretty normal because the Higgs couplings may be negligible for leptons and only the strongly coupled quarks matter. I am highly tempted to find an explanation for the flavorviolating \(h\to \mu^\pm\tau^\mp\) decay of the light Higgs. TwoHiggs models are enough for such processes and we have two Higgses here.
The ordinary electroweak Higgs vev is about\[
\langle h_L \rangle = v_L \approx 246\GeV
\] and I believe that the righthanded Higgs could have something like\[
\langle h_R \rangle = v_R \approx 7.7\TeV.
\] There is some quartic coupling and if Nature calculates the second derivative around the maximum of the potential, She gets those \(m_{h_R} \approx 5.2\TeV\) suggested by those events.
The \(SO(10)\) grand unified model building is a lot of fun but maybe if the LHC forces us to study things from the bottom, we will find simpler ways to calculate things, including the fermion masses. The big GUT symmetries generally imply that there are just a few independent Yukawa couplings. But maybe if we look at all those things hierarchically, in terms of the electroweak scale a factor of 30 beneath the rightwing electroweak scale, we will become able to relate the quark and lepton masses to each other in some more natural hierarchic way.
I think that almost no one had expected issues of the grand unification to be studied at the LHC soon. But given the character of these bumps, it may very well happen, and happen before we discover supersymmetry. I don't have to tell you how stunning it would be. If all the three bumps are there, the LHC may make as important discoveries within months as the discoveries of elementary particles done in the 1980s (the gauge bosons) and the early 2010s (the Higgs boson).
Now, the LHC could simply see a whole new complementary rightwing world with the heavy siblings of these three particles. The leftright symmetry is broken in Nature but one must be totally ready for the possibility that it's broken spontaneously, not explicitly. Well, in quantum gravity, there is a lore – supported both by formal general arguments as well as specific stringy constructions etc. – that all symmetries have to be local. Maybe even approximate symmetries have to be local, and therefore spontaneously broken. The rightwing guys are heavyweights in comparison with their leftwing counterparts.
If we were forced to extend the Standard Model into this leftrightsymmetric structure, we could also gain a different perspective on the hierarchy problem. I increasingly believe that it's "right" to view the Standard Model – or its extension – as some "modification" of a classically scaleinvariant theory. The Higgs Yukawa coupling could always be the same classically – and the same for the leftwing and rightwing Higgs above. But the negative quadratic terms that are responsible for the symmetry breaking could be generated dynamically, from some even smaller effect involving either instantons or some heavier particles. I still think that SUSY is needed to stabilize those scales against the loop corrections but there will be a rich explanation on how these scales are actually generated from the much higher GUT and Planck scales.
Happy Halloween from…the discrete Wigner function?

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