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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.

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reader Peter F. said...

I'm almost ashamed to admit it but this article evokes in me an always present but usually kept under the carpet hunger for new scientific sources of extraordinary philosophical titillation. %}


reader Dilaton said...

Thanks for this nice update Lumo, I`m still curious about what is going on with the stops, if there is something going on ... :-)
As I draw the Feynman diagram described in the last blue box of this article, I do not see how it contributes to the forward-backward asymmetry for the top / antitop either ...:-/ ?

(Now I urgently need a "sealed" and an "innocent" smiley ... :-P)


reader Luboš Motl said...

Dear Dilaton, sorry, DISQUS has no plans to add picture-based smileys and similar modifications in the DISQUS iframe are explicitly made impossible by their system.


The diagram obviously contributes to the asymmetry because the top quark's velocity in the diagram is correlated with the initial down-quark's velocity, and therefore the proton's velocity, while the anti-top-quark tends to move in the opposite direction.


reader Luboš Motl said...

Thanks for amusing while humbling titillating words, Peter.


reader Peter F. said...

Thanks for being how you are "in my optics" (as you sometimes say it)! :)


reader Dilaton said...

Dear Lumo,
about the smileys I`m rather joking than complaining ;-)
... should probably stop it then ...


reader Shannon said...

Peter, me too ! Yesterday as I was driving, I came to the conclusion that TRF is nietzschean... it was a great "titillation". (and I didn't even ran a red light). Still, I'm still on the previous article (scale-invariant theories)... I'm still in an invariant state... however, I feel I do understand better what renormalization is now. I love big pictures.


reader Shannon said...

I suggest we all learn these smileys-like abbreviations : http://www.mob1le.com/sms.html


reader Luboš Motl said...

Wow, that's a lot of learning, Shannon. Have you mastered all of them? ;-)


reader Dilaton said...

... yeah, I did never want to say that anybody should do anything about the smileys ... ;-).
Thanks for the link Shannon, I`ve bookmarked it :-)

Of course I did see that the top quarks are more likely to move to the right and the anti tops to the left in the blue boxed example; but for some reason I did not recognize that this already is THE famous asymmetry ... :-(

I feel very embarassed now, maybe I should suspend myself for a while and just shut up and read here, silently lurking in the background ... :-/


reader Luboš Motl said...

Dear Dilaton, please don't pour too many ashes on your head because you could violate the entropy bounds! ;-)


reader Shannon said...

Ooh I knew you'd say that :-7


reader Shannon said...

Please Dilaton, do NEVER shut up.


reader Shannon said...

...Lubos is doing the calculations for us anyway :-)


reader Peter F. said...

I like ONE big picture (or map of What Is was and will be going on) with enough (for me) plotted terrain on it. Our common "mate" (meant the Australian way), Lubos Motl, has - aside from provided me with much fun - helped me to fill in parts of such a picture - parts that I would most likely not have been able to perceive without him.


reader Shannon said...

Peter, why do you use the past form ? :-\


reader Benjamin Allanach said...

Actually, Depuis et al have *exactly the same* model as in our paper. I just screwed up the labels in the figure of the Feynman diagram: yes, the top and anti-top labels should be swapped in the diagram, so the top should couple to the down quark and the anti-top to the anti-down. All the calculations in the paper were correct, it's just these labels that were wrong in the figure. Thanks a lot for pointing this out: I'll certainly fix the typo!


reader Luboš Motl said...

Thanks, Prof Allanach! It's great if the error is localized to the labels in the figure although it seems a bit counterintuitive why the resulting asymmetry is positive in that case.


reader Benjamin Allanach said...

Erm, I mean the down should couple to anti-top and anti-down to the top...


reader Benjamin Allanach said...

I couldn't agree more - that's why we provide whatever LHC tests we can for the hypothesis in our article. Also, related to this, you may like to see mine and Ben Gripaios' article http://inspirehep.net/record/1091074
about RPV natural SUSY: we have light gluinos and stops decaying by baryon number violation. We point out that same sign di-leptons are a generic signature of RPV natural SUSY then, although Raman's paper takes the light gluinos out of the equation (but then finding SUSY is much harder).


reader Dilaton said...

Oh thanks for the kind words Shannon and Lumo ;-)
You and many other people here are very nice :-)


reader Synchronize said...

http://www.sciencewatch.com/ana/st/super/12junSTSuperHamed/
A new Nima interview!


reader Peter F. said...

:-)) Great pointing Shannon!
Would it be to much if a stepped up on my soapbox and horribly loudly hollered out my total confidence in that I am afflicted by a tiny tinge of defensive-aggressive arrogance and hubris?? ;>>
%DD
P.S. Please pray with me for Smileys!


reader Benjamin Allanach said...

About the physical intuition: I'm not sure it's so easy. Sridhar and I will check over the next week or so, but it may be that the interference term with QCD is important in the asymmetry and so one can't use simple physical reasoning. I also noticed that in some areas of parameter space one can achieve *different signs* of the contribution to A_FB. I hadn't really thought about the physical intuition before - we just tried RPV and it worked, so thanks for bringing it up - I'd like to understand it. My impression was that if one had a vectorlike coupling (a vectorlike Z'), then the pure new physics contribution to A_FB would be zero (although again - like in the SM - the interference with QCD might give you a non-zero contribution). If this is the case, the simple "down quark from a proton imparting momentum to the antitop" type reasoning doesn't work. Hmmmm....


reader Luboš Motl said...

Thanks, Benjamin, exactly, if your result is right, there has to be some negative interference. So instead of my naive intuition, "antitop likely to move in the proton's direction", there is actually just a "large probability amplitude for antitop to move in the proton's direction". However, this large amplitude has mostly the opposite sign/phase than some other contributions, to it actually diminishes the overall cross section.


If one computes the cross section, there are various subterms that don't really interfere with each other because they have different dependences of the amplitudes on the color indices etc. So one has to carefully study intermediate color sextets or color triples or color octets and separately in the s-channel and t/u-channel etc. When one realizes the diversity of the possible algebraic structure, a full calculation is probably preferred over *any* incomplete intuition. ;-)


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