Details Behind Last Week’s Supersymmetry Story

Last week, I promised you I’d fill in the details of my statement that the recent measurement (of the rare process in which a B_s meson decays to a muon and an anti-muon — read here for the physics behind this process) by the LHCb experiment at the Large Hadron Collider [LHC] had virtually no effect on the constraints on any speculative theories, including supersymmetry, contrary to the statements in the press and by a certain LHCb member. Today I’m providing you with some sources for this statement.

A number of my colleagues have tasked themselves with keeping track of how measurements at the Large Hadron Collider and elsewhere are affecting certain subclasses of variants of the supersymmetry. They call themselves the “Mastercode Project”; here’s their website. They’re not the only ones looking at this, but among them is Professor Gino Isidori, whom I was talking to last week, so I’ve gotten this information from him. I quote from the MasterCode website regarding last week’s result from LHCb: “The new measurement provides a valuable new constraint on the supersymmetric parameter space, but the observation of a Standard Model-like branching fraction for the B_s→μ⁺μ^– decay is quite consistent with supersymmetry. In fact, a Standard Model-like branching fraction of this decay was expected in constrained supersymmetric models like the CMSSM or NUHM1 (see, e.g., the recent MasterCode results for further details). As a result, the favoured regions in the parameter space of these models do not change significantly after the inclusion of the new constraint. ”

Now before I explain what this means, it’s important to have some terminology, running from most general to most specific.

• Supersymmetry: the general theory that space and time are more subtle than they appear to be, and as a result, for every known particle in nature there is a corresponding superpartner particle with the property that either the particle is a boson and its superpartner a fermion, or vice versa. (Read more about supersymmetry here, and more about fermions and bosons here and here.)
• TeV-Scale Supersymmetry: the masses of each particle and its superpartner do not differ by more than 1 TeV/c² (recall that the proton-proton collisions at the LHC have energy of 8 TeV in 2012, and the mass of the new Higgs-like particle is about 125 GeV/c² = 0.125 TeV/c².) In this case, signs of supersymmetry should be discovered by the Large Hadron Collider [LHC]; you can read here about how LHC experimentalists usually try to do this (and about the limitations of their simplest methods, which they are beginning to go beyond).
• MSSM — Minimal supersymmetric Standard Model: a subclass of supersymmetric theories in which the only particles in nature are the known particles and their superpartners, along with a total of 5 Higgs particles and their superpatners.
• CMSSM (Constrained MSSM): a much smaller subclass of variants of the MSSM in which the masses of the superpartners are assumed to be related to each other in particular ways (the details are technical and not essential, so I’ll skip them.)
• NUHM1 (Non-Uniform Higgs Mass variant of the MSSM): another small subclass of the MSSM variants, slightly more general than the CMSSM.

Keep in mind that

• ruling out the CMSSM or NUHM1 does not mean that the MSSM is ruled out;
• ruling out the MSSM does not mean that supersymmetry at the TeV scale is ruled out;
• ruling out supersymmetry at the TeV scale does not mean that supersymmetry is ruled out.

Among the many goals of the LHC is to find or rule out supersymmetry at the TeV scale. (It cannot hope to rule out supersymmetry altogether; that would presumably require a vastly more powerful collider that won’t likely be built for centuries, if ever.) It’s not enough to rule out the CMSSM, or the NUMH1, or even the MSSM. Similar statements apply for other speculative ideas that propose as yet unknown particles and forces; it’s not enough for the LHC to rule out just the simplest variants of these ideas.

Now if it turns out that supersymmetry is part of nature, rather few of my colleagues expect the variant we find to be contained within the CMSSM or NUHM1; and personally (though I’m probably in the minority) I have long doubted that it would be contained within the MSSM. Nevertheless, it is instructive to look at how LHC data is impacting the CMSSM and the NUHM1 subclasses of supersymmetry variants.   One just must be careful not to over-interpret; the exclusion of most variants in the CMSSM is not an indication that most variants of TeV-scale supersymmetry as a whole are excluded.

Now in this context, let’s see how the new measurement that was announced last week affects the CMSSM and the NUHM1. In Figure 1 is a plot showing the allowed variants of the CMSSM and the NUMH1, as a function of two quantities: on the horizontal axis, M_A, which if large is (approximately but essentially) the mass of four of the five Higgs particles in the MSSM, and on the vertical axis, tan β, the ratio of the values of the two non-zero Higgs fields that are required in the MSSM. In solid red and solid blue are the one-standard-deviation and two-standard-deviation allowed regions after the new LHCb measurement is accounted for; any variant of the theory not sitting inside the blue region is excluded by the data. The dashed bands show the same thing before the new LHCb measurement. Since the dashed and solid blue bands are right on top of each other, you see there’s almost no effect at all. That’s what was behind my claim last Friday.

But please, don’t misinterpret what I’m saying (or my colleagues) as suggesting that the LHC’s data has had no impact on the list of possible variants of supersymmetry! Far from it! Many variants are excluded, and many popular (but not necessarily more likely) subclasses of variants of supersymmetry have been pushed into regions that many would consider corners. The only statement in Figure 1 is that the new LHCb measurement didn’t make these corners smaller.  But to see how things have changed since before the LHC began, look at Figure 2, which shows how the LHC as a whole — all the measurements from LHCb, ATLAS and CMS taken together — have affected the CMSSM and NUMH1 since 2009. (The CMSSM and NUHM1 also make assumptions about where dark matter comes from, so even effects of the dark matter measurements from the XENON100 experiment are included here.)

Figure 2 is a similar plot to Figure 1 — but this time, solid blue and red indicate the impact of LHC data as of summer 2011, and the dashed blue and red indicate the situation before the LHC started. Now compare the dashed blue line in Figure 2 (before the LHC) with the solid blue line in Figure 1 (now); note the scale on the horizontal axis is different!. You’ll see that in the CMSSM it was possible before the LHC to have M_A as low as 350 GeV/c², but now it has to be over 900 GeV/c², which many would consider a rather high value. In the NUHM1 there’s been a similar shift from 150 to about 300 GeV/c², not yet so high but still a significant increase. And meanwhile, while almost any value of tan β from 2 up to 60 was allowed before the LHC, this number is now limited to a smaller range. For example, if M_A were below 900 GeV/c², then the CMSSM would be excluded and the NUHM1 would be allowed only for tan β < 30 or so.  This upper limit on tan β is mainly caused by the similar LHCb measurement presented back in March (and mentioned by me on Friday), and by similar ones from the CMS, CDF and ATLAS experiments.

But clearly there are plenty of variants within the NUHM1 that remain viable.  And the NUHM1 is not representative of the full range of possibilities within the MSSM, so even if the NUHM1 were excluded, we’d still have a long way to go to exclude the MSSM, much less all of TeV-scale supersymmetry. In short, it’s neither all nor nothing. Yes, a lot of progress has been made; LHC data (and data from other sources) have ruled out a lot of variants of TeV-scale supersymmetry.  But no, we’re not yet close to ruling out the full range of variants.

Please note that I’m not telling you this because I’m some devotee of supersymmetry who believes deeply in his heart that we’ll someday find it, and is trying to persuade you not to give up. I’m just laying out for you the facts on the ground. Do you imagine that I’m happy that a long, painful slog lies ahead, during which particle physicists — theorists and experimentalists — will painstakingly cover all the possible variants of supersymmetry, and slowly but surely determine whether or not supersymmetry is absent at the TeV scale? Don’t you think my life and that of my colleagues would be a lot easier if we could snap our fingers and with one or two quick measurements settle the question of whether supersymmetry is a fact of nature or not? Unfortunately, things don’t work that way.  You should simply ignore the irresponsible grand statements you will see in the press and on various blogs; indeed, sweeping remarks are a sign of careless thinking, and you should beware. The truth is that only through very hard work — by the experts who make the measurements, by those who advise them on which measurements to make, and by those who do the calculations that are the ingredients for studies like the MasterCode Project — can we hope to settle profound questions about nature.