Stop squark rumors and R-parity violation

At the beginning of this year, Murray Gell-Mann as well as the rest of us were exposed to gossip about stop squarks seen at the LHC. In the four months that followed, no discovery was announced, some observations that could have made the discovery were published and they didn't make it, and no new comprehensible leaks were added.

However, I've been watching various phenomenology papers for suggestions that some people could know more about these things than others; and for possible proposed models for which the assumed validity of the gossip was a key pillar although the authors obviously didn't admit it. (I don't claim that the authors of any particular paper mentioned below know some detailed gossip!)

It's been getting increasingly likely from my perspective that if the gossip is true, the processes in which the stop squarks appeared were probably processes requiring R-parity-violating supersymmetry.




Just to remind you, the R-parity is a quantity that may be equal either to \(+1\) or \(-1\). In fact, it is equal to \(+1\) for all the known particles of the Standard Model and \(-1\) for all of their superpartners. One may calculate the R-party by an explicit formula\[

P_R = (-1)^{2J+3B+L}.

\] Well, any odd coefficient such as \(\pm 3\) in front of \(L\) would do the same job and it could be more natural in particular models. You may check that the quantity above is positive (even) for all known particles: the fermions have an odd \(2J\) but they also have an odd \(3B+L\) because they're either quarks carrying a baryon number or leptons carrying a lepton number. And odd plus odd equals even. In the same way, all particles with an even \(2J\), namely bosons, carry vanishing lepton and baryon numbers so all the terms in the exponents are even.

The superpartner of a given particle has the same \(B,L\) but its \(2J\) differs by one so it is obvious that all superpartners of the Standard Model particles have a negative (odd) R-parity.

Related, Frank Wilczek: The Nobel-winning co-father of QCD just wrote a newly updated guest blog for PBS where he explains the Higgs phenomena, says that God deserves the full credit or blame for them, and explains why he will be heartbroken if the LHC won't discovery supersymmetry (Nature would turn out to have a very different taste than Frank Wilczek haha), among other things. ;-)

It's been often assumed that the R-parity is conserved. If it were so, the lightest particle with \(P_R=-1\) i.e. the lightest superpartner (LSP) would be stable because the conservation law for energy and for R-parity prevents it from all decays: there aren't any lighter particles with the same value of \(P_R\) and the same value is required. The light LSP could be a gravitino or neutralino (either closer to a bino or to a neutral wino).

Such a particle (LSP) could therefore constitute the bulk of the dark matter! For the neutralino, the R-parity conservation is rather critical if it wants to be employed as a dark matter particle.

However, the R-parity is likely to be broken, at least a little bit. After all, the numbers \(B,L\) or their combinations aren't exactly conserved quantum numbers. Evaporating black holes (and probably lighter objects as well) must be able to change their values (the conservation laws can't be exact because there would have to be new long-range forces analogous to electromagnetism if the symmetries were exact but there aren't any because they would destroy the tests of the equivalence principle). So the exponential is rather likely to be un-conserved, too. Now, the question is whether the R-parity violation is strong or weak.

Again, people typically assume – or derive from a deeper starting point (but I don't understand any of these derivations myself) – that the R-parity violation must be so weak that it can't be seen by the present accelerators. For example, that's a proposition behind the models by Gordon Kane, Bobby Acharya, and others. The conservation of R-parity makes it easier to preserve the longevity of the proton. While the baryon and lepton number conservation laws are allowed to be violated, the R-parity still bans some "intermediate steps" involving virtual R-parity-odd particles and makes the decay harder.

However, if one allows R-parity to be strongly violated, one should better only allow R-parity-violating terms that also violate the baryon number but that preserve the lepton number; or only terms that also violate the lepton number but that preserve the baryon number. If both lepton number and baryon number were violated, the proton decay would almost certainly be rapid, in a flagrant contradiction with the observations.

It's my impression that the baryon-number-violating R-parity-violating (BNV RPV) models have been gaining an upper hand in recent months. A cool feature is that the stop squarks' virtual activity could explain not only the stop squark gossip but also the Tevatron forward-backward asymmetry: a squark-like particle in a \(t\)-channel has always been the favorite explanation of mine for this only recent "new physics" claim by the Tevatron that wasn't self-evidently nonsensical.

Now, let me scare you with six recent 2012 papers about related issues:

April: Arnold et al.
April: Perez
May: Dreiner et al.
May: Allanach et al.
June: Dupuis et al.
June: Brust et al.

Left-wing readers will appreciate that the recent 3 months were treated in a nice, egalitarian way; all the other months were put down in a gas chamber.

In particular, Allanach et al. and Dupuis et al. analyzed models with intermediate stop and sbottom squarks in the \(t\)-channel and they concluded that these effects could explain the large Tevatron forward-backward top-antitop asymmetry while preserving peace with the negative results of all other searches! Dupuis et al. was published after Allanach et al. but they claim to be better because they also consider the atomic parity violation constraint.

Brust et al. love the RPV BNV SUSY models – one of the few viable incarnations of weak-scale SUSY preserving naturalness, if we use their words. Note that R-parity violation explains the negative result in all the searches that rely on missing energy: there's not much missing energy in these decays because the LSP (missing energy) doesn't have to be emitted (the only reason why it has to be emitted otherwise is to conserve R-parity).

Also, several TRF articles such as this one discuss some 2-sigma bumps supporting the idea that the R-parity-violating supersymmetry exists in Nature.

One more reason leads me to believe that the gossip makes more sense with the R-parity violation. It was rather strong and specific – it almost looked like the folks could measure the mass of the stop although we weren't told what it was. This is only possible if the energies can be measured rather accurately i.e. if a big part of the stop energy isn't wasted for the LSP. But that's only possible if the stop squark violates the R-parity during its decay. So it's plausible that they just observe e.g. 2-top or 4-top events without missing energy in which the tops together with some other well-defined jets may be added up to sharply determine the stop mass.

At any rate, the basic model that e.g. Allanach et al. use to explain the forward-backward asymmetry is very simple. They rely on one R-parity-violating, baryon-number-violating term in the superpotential only,\[

W = \frac{\lambda''_{313}}{2}\bar T_R \bar D_R \bar B_R

\] This terms is able to induce various detailed interactions between the quarks and their superpartners. However, the only one that matters for the forward-backward asymmetry are two identical vertices in the following story:

A right-handed down-quark moves to the right (inside a proton), its antiparticle moves to the left (in the Tevatron antiproton). Using the cubic vertex above, the down-quark changes to a right-handed top-quark moving roughly in the same direction – this transformation is accompanied by the emission of a right-handed sbottom antisquark (yes, it violates both \(P_R\) as well as \(B\), by one). This sbottom antisquark is absorbed by the right-handed down anti-quark for it to morph into a right-handed top anti-quark. So the top-quark tends to fly in the same direction as the down-quark (and therefore the proton); and similarly for the antiquarks (and antiproton).

So it's just the exchange of a sbottom squark in the \(t\)-channel. What I am puzzled by is why the down-quark changes to a top-quark. Shouldn't the vertex change it to a top-antiquark? Just look at it carefully. This would produce the negative sign of the asymmetry! I just sent a question and/or correction to Ben Allanach.

Such a mistake would surely make the model less appealing (it sort of looks like that Dupuis et al. don't have this bug and they claim to achieve similar results) but from a broader perspective, these models have many appealing features. However, if they were true, theorists would have to return to the drawing board when it comes to the explanation of the dark matter. All the hints in the direct searches and the gamma-ray lines would have to go away. At most long-lived gravitinos would remain somewhat viable dark matter candidates.