5 sigma result proof for particle discovery Source: Carrolls : "Particle at The End of The Universe" P. 177

I am just checking my understanding of Carroll's point about "a 5 sigma result being the gold standard" of experimental proof.  Carroll uses the example of flipping a coin 100 times and the expected deviations resulting from that to give an analogy regarding the proof involved in finding the Higgs Boson.
My question is: is my assumption, that because of the probabilistic nature of particle interactions, to get a binomial curve as in the picture above, is what you would expect to find for a "natural" event. It therefore supports the discovery of any new particle, not just Higgs related particles or decay products?
By way of constrast, if we had obtained, for example  a dirac delta distribution, basically just a vertical straight line in the limit, would probably have been viewed as an artifact. Apologies for any loose terminology here.
Hopefully my question is clearly put, I would be happy to clarify further if required. 
 A: If the accuracy of the experimental measurements is smaller than the width of the gaussian  then the shape describes the probability distribution one should get for any decay in particle physics. If the experimental accuracy is larger than the width of the decay then one gets a gaussian from the randomness of the experimental error .
Example J/psi in fermilab

The true width of the J/psi is of order of keV
The Higgs plot,  where the theoretical width is expected to be of the order of MeV,  has errors of order of  GeV, which is the experimental error width. 

The Standard prediction
  For a Higgs mass of ~125 GeV, the Standard Model predicts a Higgs width of ~4 MeV. Quite a low width, especially when compared to its compatriots, the W and Z bosons (with ~2 GeV and ~ 2.5 GeV widths, respectively). Before this new result, the best limit on Higgs width had it under 3.4 GeV, based on direct measurements.

..............

In 2012, theorists demonstrated that, with fewer assumptions and using events with pairs of Z particles, the high invariant mass tail can be used to constrain the Higgs width. Using this technique, the CMS collaboration was able to produce the impressive new result.

Even if  the J/psi ( or the Higgs) were a delta function, still the plot would be the same due to the limits of the experiments.
In other words in particle physics at high energies the errors involved in the measurements will give gaussian distributions due to the randomness of the experimental errors.There is a lot more work involved in measuring the real width coming from the quantum mechanical nature of the decay. 
In low energy resonances in particle physics the Breit Wigner distribution is expected to be fitted to the data, and has been used extensively where the errors are smaller than the real width of the resonance. This is a probability based distribution coming from quantum mechanical calculations.
Now to address the 5 sigma part:
Let us take the discovery of the HIggs for Higgs to gamma gamma


Combined diphoton mass spectrum illustrating the significance of the observed excess, where events are weighted by the expected signal-to-background ratio. The corresponding background-subtracted distribution is shown in the lower panel.

Each experimental  bin in the plot has a statistical error given by the square root of the number of hits for that bin. The background for that bin is at the level of the dashed line under the curve. The background is calculated by using the theory of the standard model in a generator in a monte carlo program that has all the detector errors and behavior incorporated. A large number of monte carlo events are generated to create the solid-dashed curve. The significance is estimated by the difference in the number of events from the dashed line to the curve. 
The sum of the events over the background (dashed) curve  has to be equal or  larger than five sigma for the particle physics community to consider it gold plated.
When I was a student more than fifty years ago, four sigma was considered a good solid discovery. Until it was discovered that other factors enter the statistical error, like the look elsewhere effect, that could give a false security of a gold plated discovery. I was in an experiment where we found a four sigma pimu resonance with four sigma on the curve statistically, which  was not confirmed by any other experiment. This we discovered was due to the great number of cuts done in order to reach the plot that contained the four sigma signal. So even though the signal is still there, someplace in the archives, it is not a secure discovery. The goal posts were moved to five sigma.
The possibility of unknown factors entering an analysis of experimental data is also the reason why there are two similar experiments in the LHC, looking at the same physics with different analysis, instruments, people. Overlooked systematic errors are always a danger in the most carefully done analysis.
A: The curve you show is not a Gaussian. It is a binomial distribution with $n=100$ and $p=0.5$ (if it is an unweighted coin). This arises from processes where there are two outcomes. It approximates a Gaussian/Normal distribution when $n$ is large. 
This distribution has little to do with particle detection other than perhaps as a means of explaining what is meant by 5-sigma.
In a particle detection experiment you generally expect the detection peak to have a Gaussian with a width equal to the energy resolution of the detector. This is because the intrinsic energy of the particle (depending on its lifetime) will usually be much narrower than the instrumental resolution. However, I do not think that is what you are asking about.
Usually the number of counts detected in a random decay process follows the Poisson distribution. This also approximates to a normal distribution in the case where a large number of counts are expected.
The detection of a blip/peak amounts to rejecting the null hypothesis that the peak could have been caused by random chance given a number of expected background events. A 5 sigma detection (should) mean that the excessive number of counts detected would be expected in no more than 1 in about 3.5 million independent randomised trials of the exxperiment, given the level of background expected. However, in the case of detecting a particle of unknown energy, life is more complicated. If the peak is allowed to occur at any energy, then essentially each independent energy resolution element of your instrument must be included as a random trial. i.e. If there are 20 energy resolution elements (and I am looking at the Higgs plot in AnnaV's answer) then that 1 in 3.5 million reduces to 1 in 175 thousand, because the peak could occur in any one of 20 independent energies. I believe this is what is referred to by AnnaV as the "look elsewhere effect". See also this from the CMD website or page 4 of this, which applies the look elsewhere effect to this very Higgs problem and concludes that it is hard to pin down what the look elsewhere factor should be.
A further complication is that the background level may not be known exactly and this has to be factored in.  
A bottom line would be - if someone says they have a 5-sigma detection, check the small print for what exactly they mean by that.
