So let us jump to the money plot: the combined limit produced by ATLAS by putting together information from a dozen search channels, which employ from 1.0 to 2.3 inverse femtobarns of proton-proton collision data at 7 TeV centre-of-mass energy (the range is due to some analyses taking longer to be produced than others). The relevant figure is shown below.

And a blowup of the low-mass region is in the following figure:

As always, this "Brazil band" plot shows the upper limit in the Higgs boson production rate, obtained by observing that no signal stands out in the data, and thus placing a limit in the number of possible Higgs boson decay events may be still hidden there without being detected. The limit which is obtained is the black curve, and it should be compared to two different things: one is the horizontal line at 1.0, which represents the production rate that the Higgs boson should have in the Standard Model, given the particular mass hypothesized for it.

In other words, if I imagine that the Higgs exists and it has a mass of 200 GeV, then the Standard Model predicts that its production rate is X; if my analysis says that the production rate is instead observed to be less than Y, the black line will be located, for the horizontal tick mark at 200 GeV, at a value Y/X. The limit is thus plotted in units of "times the Standard Model predicted rate". By comparing the black curve with the horizontal line at 1.0, one can visually say where the data is incompatible with the existence of a Standard Model Higgs: when the black curve goes below 1.0 the respective mass value is "excluded", at the given confidence level (95%). Mass values for which the black curve is above 1.0 are instead ones which still are possible, given the data.

The other important feature of the figure is the Brazil band: this represent a range of possible values that the black limit curve could have taken. The width of the curve thus represents the possible outcomes of the experiment, given statistical fluctuations into account, if the Higgs boson does not exist (for each particular mass value). One can therefore gauge how much the data is in accord with the pre-data predictions of the experimental sensitivity (which are based on the details of the search procedures): if the actual limit curve is much above the Brazil band for some mass point, one can start to wonder whether the departure is due to the fact that a Higgs boson may indeed be contributing to the data in that mass range. If, however, the black curve goes significantly below the band, this only points in the direction of a badly overestimated background, such that there is an observed deficit of data for searches of the Higgs boson in that mass range.

Sorry for taking this long to explain the graph: there is indeed a tremendous amount of information in it. If you go back to it and check where the black line goes below 1.0, you see that ATLAS excludes Higgs boson masses above 145 GeV, and out to 466 GeV (apart from a couple of points in-between, which are however excluded by a previous CMS search if I'm not mistaken). You also see that the limit is two-sigma above the prediction (the edge of the upper yellow band) for Higgs masses in the 140-160 GeV range. But while the 160 GeV mass point is really excluded (the black curve is much below the line at 1.0), the 140 GeV point is not excluded.

A real Higgs boson of 140 GeV mass would indeed produce a visible upward fluctuation in the number of observed events, so the data is not totally incompatible with that hypothesis; however, one would see a larger effect. This is explained graphically in the following, very informative, graph.

On the x axis there still is the tentative Higgs mass; on the y axis there are two curves: one is the p-value of the compatibility of data and expected backgrounds (full black curve), the other is the median p-value that would be observed by the combined searches in ATLAS IF THE HIGGS BOSON WERE THERE (dashed curve). You can therefore check (but alas, only qualitatively, since ATLAS does not give 1-sigma width information to its dashed curve) how much the observed "deviation" at 140 GeV is compatible with the existence of a 140 GeV Higgs: one sees that if the Higgs has really a mass of 140 GeV, ATLAS has been very unlucky, since it was expecting to be able to find an excess with a significance of over three standard deviations, while they got only about two.

With two standard deviations you don't really go anywhere nowadays... So the opinion I stated just a month ago seems correct after all: back then, using half the data and combining information from CMS and ATLAS, many were claiming that the strength of the 140 GeV tentative signal was close to four sigma, but I was warning everybody that that conclusion was unsupported by the data, given some caveats and the look-elsewhere effect. Another fluke headed to the cemetery.

Mildly more interesting, in my opinion, is the "excess" at 125-130 GeV (see again the graph above), where the significance is really much lower, but it is really in the ballpark that ATLAS would expect to see if the Higgs were there: in other words the full black curve and the dashed one are almost coincident there. What to say -we'll see by the end of 2011 if this, too, is just a fluke !

## Comments

Doesn't the last graph also mean, assuming the Higgs was there at a little over 160 GeV, ATLAS would at best have a 4.5 sigma signal with the current data set?

As you know have been following the raw data rather than the Brazil plots, because I believe the latter can actually be misleading. I have been integrating over the Higgs resolution at the most likely mass, and on this data I am just about ready to rule out a SM Higgs! The main accumulation of new data from ATLAS has been in the ZZ-4l (golden) channel 2fb-1, and WW-ll channel 1.7fb-1. So Ill comment on those.

In the WW channel (without jets) one would have expected a 4sig signal at 140GeV if the trend in the 1fb-1 data continued, instead the signal has gone down. The ATLAS plots show 75/122/95 events, expected background/expected background+SM Higgs/observed, respectively. That is almost 3sig too few events! And at the most likely mass of 140GeV for this set of data. For a 120-130GeV its even worse in this channel. There is still a 2sig excess above expected background in this window, but this is reflected outside the window as well.

In the ZZ-4l (golden channel) its even worse. There are 2fb-1 in this channel, and in the 130-150Gev range there is 1.8/5.8/3. Moreover the three events (which were also present in the first 1fb-1) are typical of the raised background throughout the channel.

So there is almost all hope gone.

I think you are running way too much. The first 1/fb gave, true, some hints. But the uncertainty on the possible yield was large, and so is the uncertainty in the predicted additional yield that a signal would give. The same goes for the other channels.

I think that the plots above, however not easy to interpret correctly, are the best possible summary of the situation, as far as statistics goes. This, if one knows some additional details, such as the typical resolutions of the various channels contributing at the different masses, and the relative sensitivities, of course. But still, your conclusions do not hold. A 120-140 GeV Higgs may appear in O(10 fb). Nothing in the Atlas plots rules out this possibility.

Cheers,

T.

Hi tommaso, i am not an expert at all but this Higgs is really an interesting beast. What if the LHC will not find a strong support for the Higgs? What if the deviations from the SM predictions will remains the same even after the LHC will reach its maximum power?

Cheers,

T.

I will answer the last question from my perspective as a theoretical physicist. If theres no SM Higgs it means we can go and rip out two chapters out of almost every book on quantum field theory and particle physics that I have, almost 50 books. The Higgs mechanism is the only one presented for breaking EW symmetry, because everything else one could think of (such as technocolor) was beset with even more problems. It also means there is a real Nobel prize in the offing, for whoever can come up with the right solution. It also means that some of the more exotic theories into which so much effort was poured over the last 30 years, such as superstring and supersymmetry were a bit of an indulgence given we did not even get the essence of the standard model right.

I understand that if no Higgs is found that would be a breaking news. On the other hand, do you think that it is possible that the LHC will never give us a definitive answer about the Higgs? From all the discussions made on this and other blogs, i understand that there are one or more ranges where the Higgs can hide himself. But the findings are still not evidence because of low standard deviations. It is possible that this standard deviations will remain too low even after the LHC will reach its maximum power (but would be still deviations from SM)? What to do in that case?

A worst case SM Higgs at 115GeV would require 17/fb of data from the LHC to discover at a five sigma confidence level. The sum of Atlas and CMS data is currently a bit less than 5/fb and should pass 40/fb by the end of next year. The original plan calls for the LHC to collect 3000/fb in total.

IIRC, the worst case for the lightest MSSM Higgs would require something like 300/fb to discover. I tried to google for a similar figure for NMSSM, but I think it's never been calculated.

The Higgs or something like it is required to fix some processes (WW scattering) where the Standard Model fails to be unitary; the probabilities don't add up to one. And in the real world, you can't have a 50% chance of heads and 60% of tails. I'm not sure if 3000/fb at 14TeV will be enough to observe any and all possible mechanisms to fix this problem but it's quite plausible.

Disclaimer; I'm not a physicist. Feel free to correct any misconceptions I have.

"It also means that some of the more exotic theories into which so much effort was poured over the last 30 years, such as superstring and supersymmetry were a bit of an indulgence given we did not even get the essence of the standard model right."

no shit sherlock.

Time to give Cristoph Schiller a look Tommaso? He predicted this back in 2009.

WAT? are you also a proponent of the boring universe? you must think something else must be find then? Otherwise what's the point of working on the acclerator?

Like Brian Greene then for example? But perhaps you don't consider him to be a physicist. I think Tommaso hopes for something else to be found instead of the Higgs, i just want to find out what that is.

I also remember seeing a talk made by Martinus J Veltmann a couple of years back where he showed a plot that apparently indicated that the higgs didn't exist. i would love to see that again now. Anyone else who've seen this?

usually the reason why a more massive particle is harder to detect, at a hadron collider, is that there are fewer collisions that have enough energy to turn into the mass of the body. This is due to the parton distribution functions, which yield probabilities of finding partons with large fraction of the parent momentum going quickly to zero.

For the LHC this is not an issue, since there is energy aplenty. What matters, instead, is the signal to noise ratio. At low mass, the Higgs decays preferentially to bottom-antibottom quark pairs, which are unfortunately also produced by very un-exotic strong interaction processes at a rate a million time higher. At high mass, the Higgs decays to pairs of bosons (WW and ZZ), and in this case backgrounds are quite manageable. That's, in a nutshell, the reason.

One can of course discuss the various search channels that are favourable at low and high mass, and compare the sensitivities. I will try to do that soon in another post.

Cheers,

T.

Hi, nice to see how well the LHC works and the recorded data is rapidly increasing!

But there is something I never understood: Why do these "brasilian band plots" not include error bars for the "observed" curve??? I think it is meaningless to speculate about possible bumps without considering the errors. But maybe I just havent understood these plots well enough... (Or maybe there is no error methods in this root class for making these plots :-) )

For the case that there really would be e.g. a 120GeV SM Higgs, what would we see then here? Both the black and the dotted line at 1 for M_H=120 as a peak and below 1 for all the other M_H values?

Thanks for answering my questions.

the way 95% upper level limits are constructed, there is little meaning in plotting the "error bar" on the location of the limit on the vertical scale. That is because the limit already includes the consideration of errors (in the calculation of backgrounds, in the selection efficiencies, etcetera). To help you visualize the matter, think of a Gaussian function representing the probability density function of the Higgs boson production rate, given the data. The curve includes everything we know about the uncertainties on the various inputs. Say the curve has a mean of 15 whatchamacallits and a sigma of 2 whatchamacallits. You integrate the curve from 19 whatchamacallits to infinity, and find that the integral contains 5% of the total area of the curve. You thus say that the Higgs production rate, given the data, is smaller than 19 whatchamacallits, at 95% confidence level.

Cheers,

T.

A few late comments based on more recent developments - since this is apparently the main place on a blog where Brazil plots are explained...

First, is 'sigma' the *production* cross-section - not some composite of decay cross-sections? And is there some assumption about the decay channels that goes into the measured 'sigma' value - i.e. assume no decays into channels that we don't search for? Or is such an assumption not needed?

Second, could discovery be claimed for a new particle - say, a slightly non-Standard Higgs - that had (say) sigma/sigma_SM = 0.8? And could discovery be claimed for a mass that was in the 'SM excluded region'?

If one collected a few dozen events from such a particle it would be highly significant above background, but at the same time one would be able to set a 95% upper limit, at the particle's mass, which could easily be at a value below sigma_SM. In fact the more events you gather the more confidently you can rule out both background and a Higgs with sigma=sigma_SM. So you could claim a discovery even though the mass is in the 'excluded region' and the cross-section is below the expected one?

good questions, useful to be answered.

1) sigma is the symbol for the production cross section, but usually this is used liberally, including in it the branching ratio for the searched decay mode. Once that is understood, one considers the product of σB and forgets about potential issues.

1b) When we search for the SM Higgs, for any mass we have a prediction of the various branching fractions. Then, if we look in one decay mode, the relevant BR is used to define "μ".

2) Certainly yes. In fact at 160 GeV now CMS and ATLAS could discover a particle which had a observable rate (say in WW) three or four times as low as the SM prediction. It is not as if we do not look there any more. If we found something in the excluded regions, this would not be a SM Higgs.

Cheers,

T.

Thanks Tommaso. So, coming back to point 1, when considering all SM decay modes together, as you do for global search results, you would put a 95% limit on the *sum* of sigma x B over all SM modes, where sigma is the true production xsection?

Would there be a problem with this if the values of B were separately quite different from the SM but their sum was similar to the SM value?

Also, it looks like the p-value is actually calculated separately for different decay modes (based on their individual sigma x B values) and then combined for a global p-value. Again, in the scenario where several modes contribute and some have larger or smaller B than expected in the SM, doesn't this mean a 'global' Brazil plot based on the total decay rate over SM modes would not indicate the correct combined p-value?

yes, the combination assumes SM branching fractions. However, individual searches set limits on the sigmaxB of the various final states independently. So if a particle had different mix of BR's, you should not look at the combination.

So if you are looking for modified scenarios, the combinations are not what you want to spend your time on.

Cheers,

T.

## Comments