# Particle physics plots

I'm having a hard time understanding what some of the plots that are presented by ATLAS/CMS actually show. See for example: http://resonaances.blogspot.com/2011/07/higgs-wont-come-out-of-closet.html What is the y-axis? How would the plot look like if a Higgs was in the given mass range?

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Hi Jim: if you search through some of the older posts of this blog you'll find many lucid and pedagogical explanations of particle physics graphs: blog.vixra.org – qftme Aug 4 '11 at 13:55

These plots (sometimes called "brazil-band" plots) show the 95% exclusion limit on the production rate ($\sigma\times BR$, i.e. productino cross section times branching fraction) of the Higgs boson as a function of its mass. This is usually normalized to the $\sigma\times BR$ of the standard model Higgs.

So let's take the ATLAS plot

At very low masses the ATLAS experiment can state with 95% confidence "If a Higgs boson exists and has mass 120GeV it is not produced at a rate 5 times larger than what the standard model would predict" (this is the peak at the leftmost part of the plot)

Now this isn't very conclusive, since this doesn't rule out the existence of a higgs at that mass. After all we weren't expecting that the Higgs is produced at five times the rate. If the SM Higgs exists it will be produced with exactly the rate the SM predicts (i.e one times the rate).

This is why the really interesting parts are the ones where the line drops below one. Then the experiments can state with 95% confidence "Between 300 and 450 GeV, the Higgs boson, if it exists, is not produced at the rate the SM predicts, thus we can rule out its existence in those mass ranges". Now there might be other particles in this mass range, but there surely is no Higgs boson that behaves (BR, crosssections, coupling) like the one prdicted by the SM.

So in conclusion the way to read this plots is to look for the places where the line drops below 1.

How would the plot look like when there would be a higgs? Well at that mass point, the experiemnt shouldn't be able to exclude it. Higgs observation would then be another analysis and another set of plots (like looking for resonances).

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I love the productino typo. Please don't fix that :) – Marek Aug 4 '11 at 9:24
Thank you very much for your answer. Just to make it absolutely clear: "If a Higgs boson exists and has mass 120GeV it is not produced at or above a rate 5 times larger than what the standard model would predict". What does the "expected" line stand for? A theory prediction does not seem to make sense (then the colored band should lie above the dashed line at 1). – Jim Aug 5 '11 at 16:36
@Jim: There are presumably known reasons (background, detector response, etc) that mean that there is a threshold production rate of Higgs below which the detector will not detect it even if produced. So the places where the theoretical graph rises above 1 shows you that the detector is not sensitive enough to detect the standard model Higgs, if it had a mass in those ranges. – Shanth Sep 17 '11 at 19:04

The plots in the y axis are representing confidence levels for the value of the ratio of measured_cross_section/standard_model. The Vixra blog has the plots better labeled.

The cut off line is y=1. If below the line, it means that the cross section is below that of the standard model within the confidence levels. The expected line has all the detector, and decay mode choices ( these plots are composite of many decay modes) taken into account. What is below 1 is exclude within 2sigma, so the plot leaves a window below 150GeV where the Higgs may be hiding and another around 280. The 280 is excluded by the CMS plot. Over 450 it is open season.

I interpret the plot on the lines that if what exists is only the standard model Higgs then with increasing statistics the "expected" lines should converge to 1, since the standard model in the denominator and, for "expected the numerator too, must have been evaluated for the corresponding Higgs mass.

Why are expectations plotted instead of mass distributions with predictions of SM? Because each individual channel studied has very few events, of the order of five or ten, whose statistical significance ( let alone systematic error estimates) leads to no exclusions or detection. Combining many channels in this format allows the imagination to play the "Can the Higgs be hiding here" game with confidence levels.

2 sigma, which are these plots, do not make for a detection, 5 sigma is gold plated detection though a 4 sigma deviation from the standard model would get everybody excited.

Edit : In order to have a first hand impression of the scarcity of data, yet, and of why the summary plots sound so esoteric have a look at a summary talk. On page 32 there is an enlightening 4lepton plot for various channels, showing from 3 to 6 events over an expanse in mass of 400 GeV/c^2. Like medieval maps that marked "here there be tigers" one can look and say : probably there is no 350GeV/c^2 Higgs there since not even one event falls in its theoretical width.

The composite plots under discussion are a summation of various channels in the hope that summing the exclusions will extract some new physics knowledge. The method they found, that of dividing with the standard model predictions (shown as solid line in the linked plot, for a specific higgs mass), allows a summary and combination of the exclusion regions from such plots, thus increasing the significance over all. One has to keep in mind though that the information is tortured out of very few events.

Edit 2 to clarify "expected" and "observed".

Expected hides behind it a ratio of two Monte Carlo event simulation runs. The numerator run has the statistics of the samples under consideration, i.e. it simulates the data sample also in the number of events. The denominator is a high statistics monte carlo simulation so that the errors in the denominator are irrelevant. If the numerator and denominator came from the same large statistics monte carlo simulations, the "expected" would sit on 1.

The smaller statistics the real data ( "observed") has, the more possible undulation will appear in this ratio plots, both expected and observed. The reason is as I explained in the first edit: it is a composite plot and the kinematics of the various channels differ; as the statistics are few events in each channel, as seen in the links of the first edit, there will be statistical fluctuations in the overall shape.

"observed" is the ratio of the number of events observed at that specific Higgs mass, over the number of events the Standard model would give at that specific Higgs mass. The one sigma and 2 sigma curves from the "expected" line, gives a window of statistically allowed deviations. Only in the regions where the "observed" is higher than 1 and higher statistically than expected, can a Higgs signal be hiding.

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ViXra blog may have nicer labels on y-axis but Phil Gibbs of viXra blog himself is, let's say, a little bit sloppy exactly about the meaning of the y-axis, thinking that the value on the y-axis is some kind of confidence level. – Luboš Motl Aug 4 '11 at 11:10
Well the line is marked "Observed CLs" where CL stands for Confidence Level, but a more detailed explanation is required. – Philip Gibbs - inactive Aug 4 '11 at 12:14
And for a real good laugh on a rainy afternoon, peruse the preprints uploaded to the vixra site in the various categories. In the "religions" section you find papers directly dictated by Jesus Christ, it appears :) – Lagerbaer Aug 4 '11 at 14:53
@Lagerbaer all that proves is that vixra is an open archive. Can you debunk all 2000+ papers there? Even arxiv has some dodgy material and they try to filter it out. – Philip Gibbs - inactive Aug 4 '11 at 15:11
Yes, arxiv also has some dodgy material. But I'm not sure if it is that good for a laugh. Note that my statement is not a broad dismissal of everything ever put on viXra. But it should be obvious that a completely open archive attracts a lot of crackpots. – Lagerbaer Aug 4 '11 at 16:07