BS and SUSY

  The decay of a neutral Bs meson into a muon pair is a very rare process whose rate in principle could be severely affected by new physics beyond the standard model. We now know it is not: given the rate measured by the LHCb experiment, any new contribution to the decay amplitude has to be smaller than the standard model one. There's a medical discussion going on and on about the interpretation of this result in the context of supersymmetry.  Indeed,  the statements describing the LHCb result as "a blow to supersymmetry" or "putting SUSY into hospital" are silly (if you think it's the most spectacular  change of loyalties since Terminator 2, read on till the end ;-) But what is the true meaning of this result?

To answer this question at a quantitative level it pays to start with a model independent approach (and technical too, to filter the audience ;-)  B-meson decays are low-energy processes which are properly described within a low-energy theory with heavy particles, like W/Z bosons or new physics, integrated out. That is to say, one can think of the Bs→μμ decay as caused by effective 4-fermion operators with 1 b-quark, 1 s-quark, and 2 muons: 

Naively, integrating out a mediator with mass M generates a 4-fermion operator suppressed by M^2. In the standard model, only the first operator is generated  with ML,SM≈17 TeV, dominantly by the diagram with the Z-boson exchange pictured here. That scale is much bigger than the Z mass because the diagram is suppressed by a 1-loop factor, and furthermore it is proportional to the CKM matrix element V_ts whose value is 0.04. The remaining operators do not arise in the SM, in particular there are no scalars that could generate MS or MP (the Higgs boson couples to mass, thus by construction it has no flavor violating couplings to quarks). 

In terms of the coefficients of these operators, the Bs→μμ branching fraction relative to the SM one is given by

LHCb says that this ratio should not be larger than 2 or smaller than 1/3. This leads to model-independent constraints on the mass scales suppressing the 4-fermion operators. And so, the lower bound on ML and MR is about 30 TeV, that is similar in size of the standard model contribution. The bound on the scalar and pseudoscalar operators is much stronger: MS,MP≳150,200 TeV. \begin{digression} The reason is that the contribution of the vector operators to the Bs→μμ  decay is suppressed by the small ratio of muon and Bs masses, which goes under the name of helicity suppression. Bs is spin zero, and a vector particle mediating the decay always couples to 2 muons of the same chirality. In the limit mμ=0,  when chirality=helicity,  the muons spins add up, which forbids the decay by spin conservation \end{digression}.

Consequently, the LHCb result can be interpreted as a constraint  on new physics capable of generating the 4-fermion operators  listed above. For example,  a generic pseudoscalar with order 1 couplings and flavor violating couplings to quarks and leptons must be heavier than about 100 TeV. It may sound surprising that the LHC can probe physics above 100 TeV, even if indirectly. But this is in fact typical for B-physics: observables related to CP violation and mixing of B-mesons are sensitive to similar energy scales  (see e.g Table I of this paper). Notice however that 100 TeV is not a hard bound on new pseudoscalars. If the new physics has a built-in mechanism suppressing the flavor violating couplings then even weak scale masses may be allowed.      

Now, what happens in SUSY? The bitch always comes in package with an extended Higgs sector, and the exchange of the heavier cousins of the Higgs boson can generate the operators MS and MP. However, bounds on the heavy Higgs masses from Bs→μμ will always be much weaker than 100 TeV quoted above. Firstly, the Higgses couple to mass, thus the Yukawa couplings relevant for this decay are much smaller than one. Secondly, the Higgses have flavor conserving couplings at tree-level, and flavor violation is generated only at 1 loop. Finally, models of low-energy SUSY always assume some mechanism to suppress flavor violation (otherwise all hell breaks loose); in typical realizations flavor violating amplitudes will be suppressed by the CKM matrix elements, much as in the standard model.  All in all, SUSY appears less interesting in this context than other new physics models, and SUSY contributions to Bs→μμ are typically smaller than the standard model ones.

But then SUSY has many knobs and buttons.  The one called tanβ -- the ratio of the vacuum values of the two Higgs fields -- is useful here because the Yukawa couplings of the heavy Higgses to down-type quarks and leptons happen to be proportional to tanβ. Some SUSY contributions to the branching fraction are proportional to the 6th power of  tanβ. It is then possible to pump up tanβ such that the SUSY contribution to Bs→μμ exceeds the standard model one and becomes observable.  For  this reason, Bs→μμ  was hailed as a probe of SUSY. But, at the end of the day, the bound from Bs→μμ on the heavy Higgs masses  is relevant only in the specific corner of the parameter space (large tanβ), and even then the SUSY contribution crucially depends on other tunable parameters:  Higgsino and gaugino masses, mass splittings in the squark sector, the size of the A-terms, etc.   This is illustrated by the plot on the right where the bounds (red) change significantly for different assumptions about the μ-term and the sign of the A-term. Thus, the bound may be an issue in some (artificially) constrained SUSY scenarios like mSUGRA, but it can be easily dodged in more the general case.   

To conclude, you should interpret the LHCb measurement of the Bs→μμ branching fraction as a strong bound on theories on new physics coupled to leptons and,  in a flavor violating way, to quarks. In the context of SUSY, however, there are far better reasons to believe her dead (flavor and CP, little hierarchy problem, direct searches). So one should not view Bs→μμ as the SUSY killer,  but as just another handful of earth upon the coffin ;-)

Some pictures borrowed from Mathieu Perrin-Terrin's talk. 

Higgs: what's new

I know, there's already a dozen of nice summaries on blogs (for example here, here, and here) so why do you need another one? Anyway... the new release of LHC Higgs results is the clue of this year's HCP conference (HCP is the acronym for  Human CentiPede). The game is completely different than a few months ago: there's no doubt that a 126 GeV Higgs-like particle is there in the data,  and nobody gives a rat's ass whether the signal significance is 5 or 11 sigma. The relevant question now is whether the observed properties of the new particle match those of the standard model Higgs.  From that point of view, today's update brought some new developments, all of them depressing.

The money plots from ATLAS and CMS summarize it all:

We're seeing the Higgs in more and more channels, and the observed rates are driven, as if by magic, to  the vertical line denoting the standard model rate. 

It came to a point where the most exciting thing about the new Higgs release was what wasn't there :-) It is difficult not to notice that the easy Higgs search channels, h→γγ and ATLAS h→ZZ→4l,    were not updated.  In ATLAS, the reason was the discrepancy between the Higgs masses measured in  those 2 channels: the best fit mass came out 123.5 GeV in the  h→ZZ→4l, and 126.5 GeV in the  h→γγ channel. The difference is larger than the estimated mass resolution, therefore ATLAS decided to postpone the update in order to carefully investigate the problem.  On the other hand in CMS, after unblinding the new analysis in the h→γγ channel, the signal strength went down by more than they were comfortable with; in particular the new results are not very consistent with what was presented on the 4th of July. Most likely, all these analyses will be released before the end of the year, after more cross-checking is done.

Among the things that were there, the biggest news is the h→ττ decay. Last summer there were some hints that the ττ  channel might be suppressed, as the CMS exclusion limit was reaching the standard model rate. It seems that the bug in the code has been corrected:  CMS, and also ATLAS, now observe an excess of events over the non-Higgs backgrounds consistent with what we expect from the standard model Higgs.  The excess is not enough to claim observation of this particular decay, but enough to suppress the hopes that some interesting physics is lurking here. 

Another important update concerns the h→bb decay, for the Higgs produced together with a  W or Z boson. Here, in contrast, earlier  hints from the Tevatron suggested that the rate might be enhanced by a factor of 2 or so. The LHC experiments are now at the point of surpassing the Tevatron sensitivity in that channel, and they don't see any enhancement: CMS observes the rate slightly above the standard model one (though again, the excess is not enough to claim observation), while ATLAS sees a large negative fluctuation. Also, the Tevatron has revised downward the reported signal strength, now that they know it should be smaller.  So, again, it's "move on folks, nothing to see here"...

What does this all mean for new physics? If one goes beyond the standard model, the Higgs couplings to matter can take in principle arbitrary values, and the LHC measurements can be interpreted as constraints on these coupling. As it is difficult to plot a multi-dimensional parameter space, for presentation purposes one makes simplifying assumptions.  One common ansatz is to assume that all tree-level Higgs couplings to gauge bosons get rescaled by a factor cV, and all couplings to fermions get rescaled by an independent factor cf.  The standard model corresponds to the point cf=cV=1. Every Higgs measurement selects a preferred region in the  cV-cf parameter space, and measurements in different channels constrain different combinations of cV and cf.  The plot on the right shows 1-sigma bands corresponding to individual decay channels, and the 68%CL and 99%CL preferred regions after combining all LHC Higgs measurements. At the end of the day,  the standard model agrees well with the data. There is however a lower χ2 minimum in the region of the parameter space where the relative sign between the Higgs couplings to gauge bosons and to fermions  is flipped. The sign does not matter for most of the measurements, except in the h→γγ channel. The reason is that h→γγ is dominated by two  1-loop processes, one with the W boson and one with the top quark in the loop. Flipping the sign changes the interference between these two processes from destructive to constructive, the latter leading to an enhancement of the h→γγ rate in agreement with observations. On the down side, I'm not aware of any model where the flipped sign would come out naturally (and anyway the h→γγ will  go down after CMS updates h→γγ, probably erasing the preference for the non-SM minimum).

Finally,  we learned at the HCP that the LHC is taking precision Higgs measurements to a new level, probing not only the production rates but also more intricate properties of the Higgs signal. In particular,  CMS presented an analysis of the data in the h→ZZ→4l channel that discriminates between a scalar and a pseudoscalar particle. What this really means is that they discriminate between 2 operators allowing a decay of  the Higgs into Z bosons: 

The first operator occurs in the standard model at tree level, and leads to a preference for decays into  longitudinally polarized Z bosons. The other is the lowest order coupling possible for a pseudoscalar, and leads to decays into transversely polarized Z bosons only. By looking at the angular distributions of the leptons from Z decays (a transverse Z prefers to emit leptons along the direction of motion, while a longitudinal Z - perpendicularly to the direction of motion) one can determine the relative amount of transverse and longitudinal Z bosons in the Higgs sample, and thus discriminate between the two operators.  CMS observes a slight 2.5 sigma preference for the standard model operator, which is of course not surprising (it'd be hard to understand why the  h→ZZ rate is so close to the standard model one if the other operator was responsible for the decay). With more data we will obtain more meaningful constraints on the higher dimensional couplings of the Higgs.

To summarize,  many particle theorists were placing their bets that Higgs physics is the most likely place where new physics may show up. Unfortunately, the simplest and most boring version of the Higgs predicted by the standard model is emerging from the LHC data. It may be the right  time to start scanning job ads in condensed matter or neuroscience ;-)

All Higgs parallel session talks are here (the password is given in the dialog box).

Fermi on the Fermi line

The 130 GeV monochromatic gamma-ray emission from the galactic center detected by the Fermi satellite may be a signal of dark matter. Until last week the claim was based on freelance analyses by theorists using publicly available Fermi data. At the symposium last week the Fermi collaboration made the first public statement on the tentative line signal.  Obviously, a word from the collaboration has a larger weight, as they know better the nuts and bolts of the detector. Besides, the latest analysis from Fermi uses reprocessed data with the corrected energy scale and more fancy fitting algorithms, which in principle should give them a better sensitivity to the signal. The outcome is that you can see the glass as half-full or half-empty. On one hand, Fermi confirms the presence of a narrow bump in the gamma-ray spectrum near 130 GeV. On the other hand, certain aspects of the data cast doubt on the dark matter origin of the bump. Here are the most important things that have been said.  

•  Recall that Fermi's previous line search in 2-years data didn't report any signal.  Actually, neither does the new 4-years one, if Fermi's a-priori optimized search regions are used. In particular, the significance of the bump near 130 GeV in the 12x10 degree box around the galactic center is merely 2.2 sigma.  There is no outright contradiction with the theorist's analyses, as th e latter employ different, more complicated search regions. In fact, if Fermi instead focuses on a smaller 4x4 degree box around the galactic center, they see a signal with  3.35 sigma  local significance (after reprocessing data, the significance would be 4 sigma without reprocessing). This is the first time the Fermi collaboration admits seeing a feature that could possibly be a signal of dark matter annihilation.  
• Another news is that the 130 GeV line has been upgraded to a 135 GeV line: it turns out that reprocessing the data shifted the position of the bump. That should make little difference to dark matter models explaining the line signal, but in any case you should expect another round of theory papers fitting   the new number ;-) 
• Unfortunately, Fermi also confirms the presence of a 3 sigma line near 130 GeV in the Earth limb data (where there should be none). Fermi assigns the effect to a 30% dip in detection efficiency in the bins above and below 130 GeV. This dip cannot by itself explain the 135 GeV signal from the galactic center. However, it may be that the line is an unlucky fluctuation on top of the instrumental effect due to the dip.  
• Fermi points out a few other details that may be worrisome. They say there's some indication that the 135 GeV feature is not as smooth as expected if it were due to dark matter. They find bumps of similar significance at other energies and other places in the sky. Also,  the significance of the 135 GeV signal drops when reprocessed data and more advanced line-fitting techniques are used, while one would expect the opposite if the signal is of physical origin. 
• A fun fact for dessert. The strongest line signal that Fermi finds is near 5 GeV and has 3.7 sigma local significance (below 3  sigma with the look-elsewhere effect taken into account). 5 GeV dark matter could fit the DAMA and CoGeNT direct detection, if you ignore the limits from the Xenon and CDMS experiments.  Will the 5 GeV line prove as popular with theorists as the 130 GeV one?

So, the line is sitting there in the data, and potential consequences are mind blowing.  However,  after the symposium there are more reasons to be skeptical about the dark matter interpretation. More data and more work from Fermi should clarify the situation. There's also a chance that the HESS telescope (Earth-based gamma-ray observatory) will confirm or refute the signal some time next spring.  

Higgs: New Deal

The new round of Higgs data will be presented on the 15th of November at a conference in Kyoto, and on blogs a few days earlier. The amount of data will increase by about 2/3 compared to what was available last summer.  This means the errors should naively drop by 30%, or a bit more in the likely case of some improvements in the analyses. Here's a short guide to the hottest Higgs questions that may be answered.

• Will the γγ rate remain high? 
  Last summer the Higgs boson showed up quite like predicted by the standard model. The most  intriguing  discrepancy was that both ATLAS and CMS saw too many Higgs decays to photon pairs, exceeding by 80% and 60% respectively the standard model expectation.  Statistically speaking, the excess in both experiments is below 2 sigma, so at this point all the observed rates are in a decent agreement with the standard model. But that doesn't stop of us from dreaming and crossing our fingers. If the excess is a statistical fluke we would expect that the central value of the measured H→γγ  rate will decrease, and that the significance of the excess will remain moderate. But if,  purely hypothetically,  the central value remains high and the  significance of the excess grows then.... well, then  it's gonna get hot.  
• Will the ττ rate remain low?
  Another puzzling piece of Higgs data from last summer was that CMS failed to see any excess in the H→τ+τ- channel, despite their expected sensitivity being close to the predicted standard model rate. In fact, they came close to excluding the 125 GeV standard model Higgs in that channel! This discrepancy carries less weight than the diphoton excess because it is reported by only one experiment (ATLAS did not update the ττ channel with 8 TeV data last summer) and because the strong limit seems to be driven by a large negative background fluctuation in one of the search categories.  Nevertheless, it is conceivable that something interesting is cooking here. In 3 weeks  both experiments should speak up with a clearer voice, and the statistics should be high enough to get a feeling what's going on.
• Is the Vh → bb rate enhanced? 
  The LHC has proven that Higgs couples to bosons: gluons, photons, W and Z, however it has not pinpointed the couplings to fermions yet (except indirectly, since the effective coupling to gluons is likely mediated by virtual top quarks). As mentioned above, no sign of Higgs decays to tau lepton pairs has been detected so far. Also, the LHC has not seen any clear signs of Higgs decays to b-quarks (even though it is probably the most frequent decay mode). On the other hand, the Tevatron experiments in their dying breath have reported a 3 sigma evidence for the h → bb decays, with the Higgs produced in association with the W or Z boson. The intriguing (or maybe suspicious) aspect of the Tevatron result was that the observed rate was twice that predicted by the standard model. In 3 weeks the sensitivity of the LHC in the b-bbar channel should exceed that of the Tevatron. It is unlikely that  we'll get a clear evidence for h→bb decays then, but at least we should learn whether the Tevatron hints of enhanced Vh → bb can be true.
• Will they see h→Zγ?
  Another possible channel to observe the Higgs boson is via its decay to 1 photon and 1 Z boson, where Z subsequently decays to a pair of charged leptons. Much like in the well-studied h→ZZ→4l and h→γγ channel, the kinematics of the    h→Zγ→γ2l decay can be cleanly reconstructed and offers a good  Higgs mass resolution.  The problem is the low rate: the Higgs decay to Zγ is even more rare than that to γγ, plus one needs to pay the penalty of the low branching fraction for the Z→l+l- decay. According to the estimates I'm aware of, the LHC is not yet sensitive to the  h→Zγ produced with the standard model rate. However, if we assume it's new physics that's boosting the  h→γγ rate, it is very likely that the h→Zγ rate is also boosted by a similar or a larger factor. Thus, it interesting to observe what limits can the LHC deliver in the  h→Zγ channel, as they may provide non-trivial constraints on new physics.  
• Does Higgs have spin zero?
  Obviously, this question carries a similar potential for surprise as a football game between Brazil and Tonga. Indeed, spin-1 is disfavored on theoretical grounds (an on-shell spin-1 particle cannot decay to two photons), while a spin-2 particle cannot by itself ensure the consistency of electroweak symmetry breaking as the Higgs boson does. Besides, we already know the 125 GeV particle couples to the W and Z bosons, gluons and photons with roughly the strength of  the standard model Higgs boson. It would be an incredible coincidence if a particle with another spin or parity than the Higgs would reproduce the event rates observed at the LHC, given the tensor structure of the couplings are completely different for other spins. Nevertheless, a clear experimental preference for spin-0 would be useful to satisfy some pedantic minds or some Nobel committees. In particular, one needs to demonstrate that the Higgs boson is produced isotropically (without a preferred direction) in the center-of-mass frame of the collision. With the present statistics it should already be possible to discriminate between spin-0 and alternative hypotheses.  

So, keep your ear to the ground, the data are being unblinded as we speak, and the first numbers are already being bandied about in cafeterias and on facebook. Intriguingly, this blog post clearly hints there is a lot to rumor about in the new data ;-) Is it the high γγ rate? The low ττ rate? Something else? Well, there's still 3 weeks left and the numbers may shift a bit, so let's not spoil the fun just yet... In any case, if you have an experimentalist friend now it's the best time to invite her to a drink or to dances ;-)

A problem with bees

This one is not about the colony collapse disorder but about particle bees, also known as b-quarks. Older readers who still remember the LEP collider may also remember a long-standing anomaly in one of the LEP precision measurement. The observable in question is the forward-backward asymmetry of the b-quark production in electron-positron collisions. In the events with a pair of b-jets in the final state one counts the number of b-quarks (as opposed to b-anti-quarks) going in the forward and backward directions (defined by the electron and positron beam directions), and then defines the asymmetry as:

The observable is analogous to the top forward-backward asymmetry, widely discussed in the context of the anomalous Tevatron measurements, although the origin of the 2 anomalies is unlikely to be directly related. At LEP, the b-quark pair production is mediated mostly by a photon or a Z-boson in the s-channel. The latter has chiral couplings to matter, that is to say, it couples differently to left- and right-handed particles. Thanks to that, a significant b-quark asymmetry of order 10% is predicted in the standard model. However, the asymmetry observed at LEP was slightly smaller than predicted. The anomaly, sitting in the 3 sigma ballpark, has attracted some attention but has never been viewed as a smoking-gun of new physics. Indeed, it was just one anomaly in the sea of LEP observables that perfectly matched the standard model predictions. In particular, another b-quark precision observable measured at LEP  - the production rate of b-quark pairs,  the so-called Rb - seemed to be in perfect agreement with the standard model.  New physics models explaining the data involved a certain level of conspiracy: one had to arrange things such that the asymmetry but not the overall rate was affected. 

Fast forward to the year 2012. The Gfitter group posted an update of the standard model fits to the electroweak precision observables. One good reason to look at the update is that, as of this year, the standard model has no longer any free parameters that haven't been directly measured: the Higgs mass, on which several precision observables depend via loop effects, has been pinpointed by ATLAS and CMS to better than 1%.  But there's more than that. One notices that, although most precision observables perfectly fit the standard model, there are two measurements that stand out above 2 sigma. Wait, two measurements?  Right, according to the latest fits not only the b-quark asymmetry but also the b-quark production rate at LEP deviates from  the standard model prediction at the level of 2.5 sigma.   

The data hasn't changed of course. Also, the new discrepancy is not due to including the Higgs mass measurement, as that lies very close to the previous indirect determinations via electroweak fits. What happened is that the theory prediction has migrated.  More precisely, 2-loop electroweak corrections to Rb computed recently turned out to be significant and moved the theoretical prediction down. Thus, the value  of Rb measured at LEP is, according to the current interpretation, larger than predicted by the standard model. The overall goodness of the standard model fit has decreased, with the current p-value around 7%. 

Can this be a hint of new physics?  Actually, it's trivial to  explain the anomalies in a model-independent way. It is enough to  assume that the coupling of the Z-boson to b-quarks deviates from the standard model value:

In the standard model gLb ≈ -0.4, and gRb ≈ 0.08, and  δgLb = δgRb = 0. Given two additional parameters δgLb and δgRb we have enough freedom to account for both the b-quark anomalies.  The fit from this paper shows that one needs an upward shift of the right-handed coupling by 10-30%, possibly but not necessarily accompanied by a tiny (less than 1%) shift of the left-handed coupling. This sort of  modification is easy to get in some concrete scenarios beyond the standard model, for example in the Randall-Sundrum-type models with the right-handed b-quark localized near the IR brane.

So, maybe, LEP has seen a hint of compositeness of right-handed b-quarks? Well, one more 2.5 sigma anomaly does not make a summer; overall the standard model is still in a good shape.  However it's intriguing that both b-quark-related LEP precision observables do not quite agree with the standard model. Technically, modifying both AFB and Rb is much  more natural from the point of view of new physics interpretations. So I guess it may be worth,  without too much excitement but with some polite interest, to follow the  news on  B' searches at the LHC.


Important update: Unfortunately, the calculation of Rb referred to in this post later turned out to be erroneous. After correcting the bug, Rb is less than 1 sigma away from the standard model prediction.

Swedes playing Russian Roulette

No particle physicist received a phone call from Stockholm today. There had been some expectations for an award honoring the Higgs discovery. Well, it was maybe naive but not completely unrealistic to think that the Nobel committee might want to reestablish some connection with the original Nobel's will (which, anecdotally, awarded prizes for discoveries made during the preceding year). To ease my disappointment, let me write about a purely probabilistic but potentially gruesome aspect of today's decision. Warning: the discussion below is a really bad taste; don't even start reading unless Borat is among your favorite movies!

Peter Higgs is 83, and François Englert is almost 80.  Taking the US data on lifetime expectancy as the reference, they have respectively 9% and 6% probability to pass away within a year from now.  Thus, the probability of at least one of them being gone by the time of the next announcement is approximately 14%! To give an everyday analogy, it's only a tad safer than playing Russian Roulette with 1 bullet in a 6-shot colt revolver. The probability grows to stunning 27% if one includes Philip Anderson among the potential recipients (nearly 89, 15%). Obviously, the probability curve is steeply rising as a function of t, and approaches 100% for the typical Nobel recognition time lag.     

Well, the Nobel for the Higgs discovery will be awarded sooner or later. Even if one of the crucial actors does not make it, the prestige of the physics Nobel prize won't be hurt too much (it has  survived far more serious embarrassments). But, that would be just sad and unjust, even more so than the Cabibbo story. So why not make it rather sooner than later?    

Here's is more on the dangers of playing Russian Roulette:

What's the deal with vacuum stability?

This year we learned that the Higgs mass is 125.5 GeV, give or take 1 GeV.  As a consequence, we learned that God plays not only dice but also russian roulette. In other words, that life is futile because everything we cherish and hold dear will decay.  In other words, that the vacuum of the standard model is not stable.

Before we continue, keep in mind the important disclaimer:

All this discussion is valid assuming the standard model is the correct theory all the way up to the Planck scale, which is unlikely. 

Indeed, while it's very likely that the standard model is an adequate description of physics at the energies probed by the LHC, we have no compelling reasons to assume it works at, say, 100 TeV. On the contrary, we know there should be some new particles somewhere, at least to account for dark matter and the baryon asymmetry in the universe, and those degrees of freedom may well affect the discussion of vacuum stability. But for the time being let's assume there's no new particles beyond the standard model with a significant coupling to the Higgs field.      

The stability of our vacuum depends on the sign of the quartic coupling in the λ |H|^4 term in the Higgs potential: for negative λ the potential is unbounded from below and therefore unstable. We know exactly the value of  λ at the weak scale: from the Higgs mass 125 GeV and the expectation value 246 GeV it follows that λ = 0.13, positive of course.  But panta rhei and λ is no exception. At  large values of |H|, the Higgs potential in the standard model is, to a good approximation,  given by   λ(|H|) |H|^4 where λ(|H|) is the running coupling evaluated at the scale |H|.  If Higgs were decoupled from the rest of matter then  λ would grow with the energy scale and would eventually explode into a Landau pole. However, the Yukawa couplings of the Higgs boson to fermions provide another contribution to the evolution equations that works toward decreasing λ at large energies. In the standard  model the top Yukawa coupling is large, of order 1, while the Higgs self-coupling is moderate, so Yukawa wins.

In the plot showing the evolution of  λ  in the standard model  (borrowed from the latest state-of-the-art paper) one can see that at the scale of about 10 million TeV the Higgs self-coupling becomes negative. That sounds like a catastrophe as it naively means that the Higgs potential is unbounded from below. However, we can reliably use quantum field theory only up to the Planck scale, and one can assume that some unspecified physics near the Planck scale (for example, |H|^6 and higher terms in the potential) restore the boundedness of the Higgs potential. Still, between 10^10 and 10^19 GeV the potential is negative and therefore it has a global minimum at large |H| that is much deeper than the vacuum we live in. As a consequence, the path integral will receive contributions from the field configurations interpolating between the two vacua, leading to a non-zero probability of tunneling into the other vacuum.

Fortunately for us, the tunneling probability is proportional to Exp[-1/λ], and  λ gets only slightly negative in the standard model. Thus,  no reason to panic, our vacuum is meta-stable, meaning its average lifetime extends beyond December 2012. Nevertheless, there is something intriguing here. We happen to occupy a very special patch of the standard model parameter space. First of all there's the good old hierarchy problem: the mass term of the Higgs field takes a very special (fine-tuned?) value such that we live extremely close to the boundary between the broken (v > 0) and the unbroken (v=0) phases. Now we realized the potential is even more special: the quartic coupling is such that two vacua coexist, one at low |H| of order TeV and the other at large |H| of order the Planck scale. Moreover, not only λ but also it's beta functions is nearly zero near the Planck scale, meaning that λ evolves very slowly at high scales. Who sets these boundary conditions? Is that yet another remarkable coincidence, or is there a physical reason?  Something to do with quantum gravity? Something to do with inflation? I think it's fair to say that so far nobody has presented a compelling proposal explaining these boundary conditions satisfied by λ.    

Ah, and don't forget the disclaimer:

All this discussion is valid assuming the standard model is the correct theory all the way up to the Planck scale, which is unlikely.