SUSY and Higgs: romance or drama?

At the beginning of 2012, particle physicists are in such a confusing state of mind: Higgs has been practically discovered but we're not allowed to celebrate yet. It's like when your football team is on top of the league, playing in the last round against a relegated team and winning 2:0 after the first half; nothing is decided yet, anything may happen, but... come on... So, to stay sane, most of us act as if the 125 GeV Higgs were a fact and work out the consequences.

In that vein, this post is about a complicated relationship between the 125 GeV Higgs and supersymmetry. There is this lore that SUSY predicts the Higgs mass below 130 GeV, and you might have heard people saying that the recent almost-discovery of the Higgs is an incredible success of supersymmetry. Well, strictly speaking, the number 130 GeV is taken out of my ass. Instead, with some degree of rigor, one can make the following 3 statements:

1. Minimal SUSY without fine-tuning predicts the Higgs mass close to the Z boson mass, that is about 90 GeV.
2. Minimal SUSY ignoring fine-tuning predicts the Higgs boson lighter than 160 GeV.
3. Non-minimal SUSY in general makes no predictions about the Higgs mass.

The last point is pretty obvious: once you agree to extend the minimal supersymmetric model (MSSM) then options become infinite. Even straightforward extensions of the MSSM, such as the NMSSM with one additional singlet field in the Higgs sector, allow one to cover the entire Higgs mass range up to almost a TeV. (You might be confused if you heard that the NMSSM predicts the Higgs mass below 140 GeV. That however is the case when the Higgs self-coupling is required to stay perturbative all the way up to the GUT scale, a strong and not particularly motivated assumption.)

The statement #1 on my list boils down to the fact that in the MSSM the quartic term in the Higgs potential (which fixes the Higgs mass, given its vacuum expectation value) is not a free parameter. Instead, supersymmetry ties the quartic coupling to the electroweak gauge couplings.
Up to 1-loop precision the Higgs mass is given by the formula:
(for vanishing A-terms, a large tanβ, and universal stop masses, and setting yt=1). In the first approximation one gets the famous bound m_Higgs ≤ m_Z. Thus, if the MSSM were for real, the Higgs should have been seen at LEP.

Only when supersymmetry is badly broken, that is when the top mass is much smaller than the mass of its scalar partner the stop, the one-loop logarithmic term can be large enough to raise the Higgs mass considerably above the Z boson mass. In particular, for the 125 GeV Higgs the tree-level and loop contributions must be, amusingly, almost exactly equal. The price for making the stop mass large goes under the name of fine-tuning. Since vacuum equations in the MSSM generically marry the SUSY scale to the weak scale, m_stop ~ m_Z , as soon m_stop >> m_top one needs to carefully tune the parameters of the theory so as to cancel various excessive contributions to the Z boson mass. This goes against the original motivation for supersymmetry which was precisely to exorcise fine-tuning.

This brings us the statement #2 on my list. When the fine-tuning issue is ignored, the scenario known as split supersymmetry (SS), the Higgs mass in the MSSM can be much larger than the Z boson mass. In the plot on the right (from this paper), you can see that the Higgs mass can reach 155 GeV for scalar SUSY partner masses at the GUT scale. From the same plot, one finds that the 125 GeV mass correspond to roughly 10 TeV squark masses. Thus, the almost-discovery of the 125 GeV Higgs at the LHC clearly points to Somewhat Split Supersymmetry (SSS) ;-)

All in all, the story of Higgs and SUSY is getting less like a Hollywood romance and more like a Ken Loach movie of hardship and misery. Of course, it is well known that 10 TeV squark masses are not an inevitable consequence of the MSSM and 125 GeV Higgs. Playing with another SUSY breaking parameter, the so-called A-term, the Higgs mass can be dialed to any desired value. When the A-term is judiciously chosen, the scalar top partners could even be at a few hundred GeV, well within the reach of last year's LHC run. See the violet band in the plot on the right. Thus a happy ending cannot be completely excluded at this point. However, more and more theorists are beginning to prepare an exit strategy, like ...nobody said SUSY had to show up at the LHC, maybe fine-tuning 1:1000 is not so bad, maybe SUSY is really at 10 TeV, etc... In a sense, this is right: from the theory point of view there is no fundamental difference between 1 in 100 and 1 in 1000 fine-tuning. Only a practical one, for LHC experimentalists :-)

To wrap up this inflammatory post: the point I was trying to make is that 125 GeV Higgs is not a successful prediction but rather a serious setback from the point of view of SUSY. In non-minimal SUSY any Higgs mass is possible. Minimal SUSY can accommodate any mass up to almost 160 GeV, depending on how much fine-tuning you're willing to accept; 125 GeV Higgs points to 10 TeV squarks, outside the LHC reach.

Five

So, here's another candle on my cake. Resonaances has been hanging around the blogosphere for exactly 5 years now, gaining reputation for spreading unfounded rumors, for trying (in vain) to sound funny, and for (successfully) annoying everybody around. Traditionally, the New Year time is a lazy moment when bloggers take a pause and, rather than chasing news stories, post various summaries and wishlists. From me, as a birthday present, here's a list of 5 important questions in particle physics that likely will be answered by the end of 2012.

• Is there a Higgs boson and why at 125 GeV?
  Particle physicists are divided into those who think that Higgs is as good as discovered and those who think one should not say it loud. In any case, 2012 will go down in history books as the discovery year. Moreover, we will start learning something the Higgs couplings, thus kicking off with Higgs precision physics - the subject that will probably dominate particle physics for the next 2 decades.
• Is there anomalous top quark forward-backward asymmetry?
  There is this persistent anomaly at the Tevatron: the direction of motion of top quarks is statistically more forward than that of antitop quarks (where forward/backward is the direction of the proton/antiproton beam); the asymmetry is 10-15% larger than predicted by the state-of-art Standard Model calculations. This year we'll get more insight into this phenomenon thanks to analyses of the full Tevatron dataset. Moreover, the LHC will narrow down on the related observable called the charge asymmetry of top pair production, and see whether any discrepancy with the Standard Model appears. If it does, it's gonna be a beautiful year. On the other hand, if nothing unusual is seen by the end of this year, that will be a big blow to our hopes that new physics is lurking there.
• Is there anomalous CP violation in the B meson sector?
  Back in 2010 the D0 experiment found in their data the di-muon charge anomaly: a 1% excess of events with 2 negatively charged muons over those with 2 positively charged muons. The most appealing interpretation of that asymmetry was anomalous CP violation in B meson mixing, that is anti-B mesons turning into B-mesons more often than the other way around. However that interpretation is now under serious strain, because no CP violation has been observed by LHCb in the Bs meson decay to J/Ψ ϕ and to J/Ψ f0, and simultaneously no CP violation in the Bd meson sector has been seen in B-factories. This year LHCb should weigh in with another measurement of the difference of Bd and Bs meson CP asymmetries. That should sweep the floor once and for all, or, hopefully, open Pandora's box.
• What went wrong in OPERA?
  Most physicists, including those working for the OPERA collaboration, don't think that neutrinos are superluminal (because of theoretical and indirect experimental arguments). It seems likely that the bug explaining the 60 nanosecond shift of the arrival time of neutrinos sent from CERN to Gran Sasso will be found already this year. The talk in town is that more experimental work will be done soon, with Gran Sasso's experiments ICARUS and Borexino joining in the game with independent measurements of the neutrino speed. Is it the GPS? The clock? A delay in electronics? Or is it the magic mountain?
• Is there supersymmetry below the TeV scale?
  SPOILER ALERT: No. Well, so far we know for sure it's not there in its most popular incarnation, with gluino and squarks decaying via short cascades to much lighter stable neutralinos, thus producing a lot of missing energy. This year the net will be made much tighter, thanks to more data, the collision energy (likely) increased to 8 TeV, and many new analyses targeting more stealthy SUSY scenarios. By the end of this year surviving scenarios with squarks and gluinos below TeV will become collector's items, cherished for their rarity rather than beauty.

As a bonus, one more question that will be answered by the end of the year, and that is probably more pressing for a larger audience:

• Will there be an Armageddon on December 21?
  Not sure about it, but definitely the LHC should not be running on that day. So that, if the world ends, they won't blame us.

And to finish the party, here's the song that David Bowie wrote especially for today's anniversary of Resonaances:

2011 Recap

What a year it was! It started with an earthquake, followed by rising tension. In the previous years I had to think hard to make up a decent blogging subject, this year it was enough to just sit and wait for the next breaking news. Here's a pick of the most important events in the particle world in the year 2011.

January: CDF finds new physics in tops
Measurements of the forward-backward asymmetry of the top pair production at the Tevatron have been showing interesting hints of new physics for a long time. CDF found that this asymmetry displays a very steep dependence of the energy of the colliding partons (that is on the invariant mass of the top pair) which represents a 3.4σ departure from the Standard Model predictions. Unfortunately, later on D0 did not confirm the steep mass dependence, and we need to wait more for the matter to be clarified.

April: CDF gives us goosebumps
CDF studied the invariant mass spectrum of jet pairs produced in association with a W boson, and found a bump near the 150 GeV dijet mass. After the subsequent update, the significance of the bump exceeded 4σ. It would be a clear evidence of new physics if not for the evil D0 who did not find any bump in their data. The origin of the bump will probably remain a mystery forever, much like the Roswell incident, because the Tevatron management is not very determined to resolve it.

April: Xenon100 does not find dark matter
Dark matter searches gain sensitivity at an impressive pace. Xenon100, currently the most sensitive detector for the vanilla dark matter particles, published the results based on the first 100 days of running. No luck so far. As a consolation, for each experiment that does not find dark matter there is one that does; this year CRESST joined the latter club, while CoGeNT announced an annual modulation of its detection rate. In any case, the hunt continues, it will take several more years before we may conclude we're looking in the wrong place.

April: Red Higgs Alarm
It was the first Higgs alarm this year: an internal ATLAS memo leaked to a blog was claiming a 4σ evidence for a 115 GeV Higgs in the γγ channel. The second time the alarm buzzed was after the EPS conference, when the unpublished combination of ATLAS and CMS was showing nearly 4σ evidence for a Higgs around 145 GeV. In both cases the evidence was quickly washed away by more data from the LHC. One positive thing we learned is that in the digital era collaboration secrecy is moot :-)

Summer: LHC bites deep into new territory
Around the EPS and Lepton-Photon conferences the LHC presented a number of new physics searches based on 1 inverse femtobarn of data. Alas, nothing exciting was found. SUSY, at least in its simplest incarnations, is being pushed above 1 TeV. And so are extra dimensions, technicolor, Z primes, dijet resonances, and any broader scenario that is not stealthy by design. Cold sweat is running down the backs of particle theorists...

September: OPERA goes superluminal
The OPERA collaboration stunned the world announcing that neutrinos produced at CERN arrive to their detector in Gran Sasso about 60 nanoseconds earlier than expected if they traveled at the speed of light. However the physics community remains unconvinced. There is indeed a number of very strong phenomenological and theoretical arguments that the OPERA result cannot be right. What do I think? At first I thought the pulse shape was the culprit, but that criticism was subsequently addressed by repeating the measurement with 3 nanosecond pulses. Now I think they should patent their set-up as a GPS synchronization tool :-)

September: US pulls the plug on Tevatron
It was like seeing an old dog put to death: you know it's for the better, but still it feels so sad. Of course, the Tevatron has not said the final word yet; we're still waiting for the collaborations to analyze the full data set. But the number of searches where the Tevatron can compete with the LHC is shrinking rapidly...
November: LHCb finds CP violation in charm
LHCb found that decays of D mesons into π+π- and K+K- violate the CP symmetry (at least one of them). We have seen CP violation in the K and B meson sectors, but the LHCb result was a big surprise: there was a lore that discovering CP violation in the charm meson sector at the 1% level would be a clear sign of new physics (although that is no longer so clear). Whatever it is, we learned something new about the world...

December: LHC glimpses Higgs
Higgs has been finally cornered and we think we're seeing the tip of his hat. Both ATLAS and CMS observe an excess of events in the γγ, ZZ and WW channels consistent with a Higgs boson of mass around 125 GeV. To be continued and ultimately resolved in 2012.

So raise your glasses, this one's over. According to the Mayans, the year 2o12 will be a bit shorter, but it shouldn't be less eventful ;-)

Sleeping with the Higgs

All my life the Higgs was sort of a legend. Something like a unicorn: you know well how it's supposed to look like but you don't seriously expect to see it. Since last week it feels different. Of course, everybody from the CERN DG to common bloggers justly calls for caution and not jumping to conclusions. Of course, we've seen much larger excesses go away. Of course, there is statistics, likelihoods, look-elsewhere effects, and other attributes of civilization. But there's also the good old hunch. The latter, after digesting the totality of ATLAS and CMS findings, tells me there's about a 90% chance that the Higgs exists in the mass range 124-126 GeV. This high estimate follows from the remarkable consistency of the signal between ATLAS and CMS, and between different search channels. Moreover, that mass neatly fits into the ballpark suggested by electroweak precision fits. Last not least, most of the remaining Higgs mass range is either excluded or disfavored, except maybe around 119 GeV. In other words, I don't care much about the look-elsewhere correction because there isn't any elsewhere to speak of.

Thus, I'm slowly getting used to the idea of the Higgs becoming flesh and bones. On one hand this gives me thrills, as one of the greatest mystery of the universe is being solved in front of our eyes. At the same time I can see dark clouds at the horizon. There has been a well-founded hope that the Higgs would show some unexpected properties, thus opening us the doors to new physics. In the end, it would not make sense if a theoretical concept put forward 40+ years ago showed up in Nature in precisely the predicted form, would it? Yet what ATLAS and CMS are seeing looks dangerously close to the Standard Model Higgs: the signal is showing up everywhere it should, and with roughly the size it should. Of course (now this is a serious of course) we're in no position yet to make any quantitative statements about the properties of the Higgs. Indeed, measuring the couplings of the Higgs to matter will be the clue of the experimental particle physics program for the next 20 years. The more precisely we'll measure these couplings, the bigger chance there is to catch a glimpse of new physics. Still, it is getting more likely than ever that the Standard Model is the correct description of physics at the TeV energies. This is dubbed the nightmare scenario; in the first place a nightmare for particle theorists who become expendable, but in a 30 years perspective also a nightmare for the entire particle physics program. Before the start of the LHC I was giving the nightmare scenario a 50% chance. It's more than that now. Once the Higgs is formally discovered and it fits the Standard Model one... I'm getting cold shivers just thinking about it...

PS. Regardless, isn't it a beauty ;-)

Visual on Higgs

Today CERN presented the latest Higgs search results. But, first things first. The live podcast of the seminar was stalling, choking, or breaking down completely. Well into the 21st century a huge international lab doing cutting edge science (and boasting of inventing the world wide web) is unable to provide a smooth transmission of its most important public presentation of the year. One may call it ironic, or repeat Didier Drogba's famous words after the 2009 Champions League semi-finals.

OK, after venting my anger I can talk some physics.

• The main news, correctly rumored on blogs before, is that there is a significant excess of Higgs-like events corresponding to the Higgs mass of ~125 GeV. More precisely, the local significance of the ATLAS excess is 3.6σ, or 2.5σ sigma when the "look-elsewhere effect" in the 110-146 GeV mass range is taken into account. For the CMS the significance is somewhat smaller: 2.6/1.9 with/without the look-elsewhere effect. Separately, these excesses would be shrugged off; combined, they are very suggestive that we're seeing the real thing at last.
  
  
  
  
  
  
  
  
  
  
  
  
  
• In ATLAS, only the H→γγ and H→ZZ*→2l+2l- channel have been updated with the full 2011 dataset. Those are the ones where statistics is limited due to the small Higgs branching fractions. However, in these final states the 4-momentum of the Higgs can be fully reconstructed to a good precision, offering a very good mass resolution of order 2 GeV. CMS updated all main channels, also those that do not provide a lot of mileage near 125 GeV at this point.
• The excess is seen by both experiments and in each of these channels. The excess in H→γγ peaks around 124 GeV it CMS, and around 126 GeV in ATLAS, which I guess is perfectly consistent within resolution. In the 4-lepton channel, ATLAS has 3 events just below 125 GeV, while CMS has 2 events just above 125 GeV. On top of that there's the long-standing excess in the H→WW*→l+l-2ν channel, which however is not the driving force anymore. It's is precisely this overall consistency that makes the signal so tantalizing.
  
  
  
  
  
  
  
  
  
  
  
  
• ATLAS observes slightly more events than expected from the Standard Model Higgs at that mass. In ATLAS the best fit to the Higgs cross section corresponds to roughly 1.5 the Standard Model value. Thus, one way or another, the 125 GeV thing is a fluke. It may have been good luck if these events are due to Higgs, or bad luck if they are due to other Standard Model backgrounds...
  
  
  
  
  
  
  
  
  
  
  
• CMS now excludes Higgs down to 127 GeV. The ATLAS limits slightly worse around 130 GeV, but thanks to lucky background fluctuations they happened to exclude the low mass region between 112.7 and 115.5 GeV. The latter is a spectacular confirmation that what the ALEPH experiment saw back in 2001 was a genuine fundon (fundons are elementary particles produced in high-energy collider near the end of the budgetary cycle).

So much for now. The ATLAS and CMS combination notes are already out.

Tinker Taylor Soldier Higgs

Tomorrow the ATLAS and CMS experiments will reveal new results of the Higgs search based on the full 2011 dataset. The date of the presentation was not chosen accidentally: December 13 is the anniversary of the capture of Saddam Hussein. Is this suggesting that tomorrow we'll see another notorious fugitive dragged out of its hole?

Two things are 100% certain because they appeared in an official statement from CERN:

1. Neither experiment will announce the discovery of the Higgs, in the sense of a signal with a significance of 5 sigma.
2. Neither experiment will exclude the Standard Model Higgs over the whole low-mass range.

The rest of the story can be to a good approximation reconstructed from blogs, facebook status updates, whispers in the corridors and coffee rooms, drafts mistakenly left on printers, microfilms smuggled in diplomatic mail, etc. The story that emerges can be summarized as follows:

• The Standard Model Higgs boson is excluded down to approximately 130 GeV, but not below.
• As already reported widely on blogs, both experiments have an excess of events consistent with the Higgs particle of mass around 125 GeV.
• The excess is larger at ATLAS, where it is driven by the H→γγ channel, and supported by 3 events reconstructed in the H→ZZ*→4l channel at that mass. The combined significance is around 3 sigma, the precise number depending on statistical methods used, in particular on how one includes the look-elsewhere-effect.
• CMS has a smaller excess at 125 GeV, mainly in the H→γγ channel. They have 3 events in H→4l as well, but they are oddly shifted to somewhat lower masses of order 119 GeV. All in all, the significance at 125 GeV in CMS is only around 2 sigma.
• With some good faith, one could cherish other 2-sigmish bumps in the γγ channel, notably around 140 GeV. Those definitely cannot be the signal of the Standard Model Higgs, but could well be due to Higgs-like particles in various extensions of the Standard Model.

Stay tuned, in about 24 hours we'll know everything there is to know. More in-depth interpretations of the ATLAS and CMS findings depend on the quantitative details of the results, in particular, to what extent the signals in various channels are consistent between the 2 experiments and with the predictions based on the Standard Model Higgs. There is a good chance we're finally looking at the real thing, I'd say 50% based on the data alone and 80% adding our sincere convictions that Higgs must really be in that mass range. However, one should not forget that last summer the combination of ATLAS and CMS 1 fb-1 results was showing an excess corresponding to a ~145 GeV Higgs with the significance as large as 4 sigma, which was blown away when more data arrived.

You're of course welcome to fill in more details or paste an excerpt of the ATLAS or CMS draft into the comment section ;-)

Update on CP violation in charm

This post came out a bit cryptic. Don't even start if you're not a huge fan of flavor physics.

There's been some new developments since 2 weeks ago when LHCb came out with the evidence of CP violation in the charm meson sector. Recall that LHCb studied the D-meson decay to π+π- and K+K- meson pairs. The observable of interest was the asymmetry of D- and anti-D-meson decay rates to these final states, A(π+π-) and A(K+K-). A non-zero value of any of these two asymmetries signals CP violation (particle and anti-particle decay rates to the same CP eigenstate being different). LHCb found that the difference ΔA = A(K+K-) - A(π+π-) is (-0.82±0.24)%, which means that, with large confidence, at least one of these asymmetries is non-zero.

The most pressing question is whether the LHCb result implies new physics? Experts emphatically agree that the answer is definitely maybe. From the existing literature one can learn that "...CP violation from new physics must be playing a role if an asymmetry is observed with present experimental sensitivities O(1%)", and "...observation of CP violation in the decay of D mesons will not necessarily be a signal of new physics...". Now, a paper from last week makes a reassessment of the Standard Model predictions and clarifies the LHCb result may or may not signal new physics.

The problem is that we are lacking reliable methods to compute processes involving D mesons. Normally, when dealing with heavy flavored mesons, one employs an effective theory where the heavy Standard Model and possibly new physics particles have been integrated out, leaving effective 4-quark interactions. This allows one to compute observables at the leading order in the expansion in powers of (1 GeV/m_quark), the former being the typical scale for QCD effects, and the latter the suppression scale of higher-dimensional operators. That is a decent expansion parameter for bottom quarks, but not so much for charm quarks. Now, ignoring that convergence issue and taking the leading order predictions at face value one arrives at the estimate ΔA∼0.1%, well below the value measured by LHCb. The new paper by Brod et al. attempts to estimate the contribution of the higher order operators to the asymmetry, using some guidance from other experimental data on D-mesons. For example, one finds that the branching fraction for D0 → K0 K0bar, which receives contributions only at next-to-leading order in 1/mc, is about five times smaller than the branching fraction of D0 → K+ K-, which received leading order contributions. That means that the respective amplitudes differ only by a factor of two, which in turn proves that the higher order 1/mc contributions can be significant. Taking that into account, the paper concludes that the Standard Model can account for |ΔA| as large as 0.4%, uncomfortably close to the LHCb measurement.

Another last week paper takes a less pessimistic approach. It simply assumes that the asymmetry measured by LHCb is dominated by new physics and attempts to understand constraints on the underlying model. In the language of effective theory, to explain the LHCb result one needs to include a ΔC =1 four-quark operator (with 1 charm and 3 light quarks, [sbar Γ c][ubar Γ s]). There are many possibilities differing by the structure of Lorentz and color indices that lead to the same observable asymmetry. The scale suppressing this higher dimensional operator should be of order 10 TeV to match to the LHCb result. This is actually a very small suppression. From non-observation of CP violation in D meson mixing we know that the scale suppressing generic ΔC=2 4-quark operators (with 2 charm and 2 light quarks) must be close to 10 000 TeV. On the other hand, once a ΔC=1 operator is present, ΔC=2 ones will necessarily be generated by loop corrections. This means that a random new physics model explaining the LHCb result will be in conflict with the data on D-meson mixing. However, the paper by Isidori et al. concludes that a subset of the ΔC=1 operators explaining the LHCb asymmetry is consistent with all other experimental data. In particular, the ΔC=1 operators involving only right-handed quarks are not excluded by the data on D-meson mixing and on direct CP violation in kaon decays (ε'/ε in the flavor jargon).

Finally, a small experimental update. CDF posted on arXiv a new paper that is similar to the earlier public note but contains one bonus track. The known result is the separate CP asymmetries D-meson decays to pions and kaons:

A(K+K-) = -0.24 ± 0.24 A(π+π-) = 0.22 ± 0.26

The bonus is that they did the subtraction and also present the difference of the asymmetries:

ΔA = -0.46 ± 0.33

which can be directly compared to the LHCb result. The CDF asymmetry difference is perfectly consistent with the LHCb one, and it's also consistent with zero. This is a hint that the true asymmetry difference is probably at a lower end of the range suggested by the LHCb measurement, and therefore closer to the Standard Model prediction. One more point for the Standard Model, but the game is not over yet.