Discovery of the Higgs Boson rumoured to be at 3.5 sigma.

http://www.math.columbia.edu/~woit/wordpress/?p=4212

by jsmcgd • 15 years ago

76 47 15 years ago

math.columbia.edu

sarbogast• 15 years ago

OK, now thanks to Wikipedia, I have a vague idea of what a higgs boson is and why it is important. But could someone explain to me what those sigma's are (in non Sheldon Cooper terms)? Is it a measure of the degree of certainty of the particle actually being there?

jerf4• 15 years ago

Yes. See http://en.wikipedia.org/wiki/Standard_deviation . In that first graphical plot, the little σ after the number is lowercase Greek sigma. (The upper case sigma, which may be more recognizable, is Σ, which you may recognize as being used for summation.) Per the chart about halfway down the page, a 5 sigma result means that there is a 1 / 1,744,278 probability that it has come from pure chance.

tomjen3• 15 years ago

Buy that same table at 3 sigma there is still 99% chance that they have found the damn thing.

Isn't it usually accepted that it is statistically significant when p goes above 0.95? If so, why aren't they happy with a 20 times better result?

neutronicus3• 15 years ago

To expand on what was already a good answer, the Higgs Boson itself is not long-lived enough to interact with any of the ATLAS detectors. It decays into several other particles, which also decay until you're left with a bunch of less exotic particles.

Since a whole bunch of things are happening at once, all shooting particles at your detectors, you get a whole mess of particles all at once, and it's kind of a pain to separate which bunches of particles go together. So what they're saying is that the detectors have been seeing bunches of particles that look like they might have come from decaying Higgs Bosons, but there's still some chance that some other bunch of particles could have have been decaying in just the right places to look like decaying Higgs Bosons.

prawn• 15 years ago

This is Hacker News - do we really need "god particle" added to the headline? It's not present in the article.

jsmcgd• 15 years ago

Sorry prawn, on reflection I think you're probably right. It's unnecessary.

windsurfer• 15 years ago

I thought you were being rude but prawn really is his name.

akg• 15 years ago

I was always curious how they measured these things. Does anyone have a good reference that doesn't involve years of particle physics study?

bmuon• 15 years ago

It's a long way down the rabbit hole. There's a series of steps for measuring in a particle accelerator and each itself is a big area of knowledge: - Detectors - Hardware triggers - Software triggers - Data storage - Statistical analysis

I guess Wikipedia can give you an idea: http://en.wikipedia.org/wiki/ATLAS_experiment A common statistical method used in particle physics is the Monte Carlo method: http://en.wikipedia.org/wiki/Monte_Carlo_method

orijing3• 15 years ago

Well, if we take the 3.5 sigma at face value and bound it using Chebychev's inequality [1], it seems that the discovery of the Higgs Boson is bounded by 1/3.5^2, which is 8%. In fact, the standard inequality is two-tailed. If we're measuring just from one tail, we can use the single-sided inequality to yield 7.5%. Remember, we can't always assume a distribution is normal, a mistake that even respected researchers often make.

[1] http://en.wikipedia.org/wiki/Chebyshevs_inequality

sbayless• 15 years ago

Hmm, I don't actually think chebyshev applies (in a meaningful way) in this context. 3.5 sigmas refers to the probability of the observation being significant, not the average mass of the higgs. Or did I misunderstand what you meant?

As an aside, there is a typo in the parent's link: http://en.wikipedia.org/wiki/Chebyshev_inequality

tel• 15 years ago

3.5 sigmas refers to the probability of some statistic being as severe as they're observing under a model where the Higgs does not exist. Regardless of the distribution, Chebyshev applies solely by assumption that sigma is a meaningful unit. It may be overly conservative though.

orijing3• 15 years ago

Thanks for the correction. That link worked when I checked...

Well, Chebyshev inequality always applies. It just might not be the tightest bound possible. Unless we know the distribution better, this is the best estimate (tightest bound that's provably correct given the single assumption about standard deviation)

orijing3• 15 years ago

I wonder if they can combine the experimental results from the 2.5 sigma and the 3.5 sigma experiments. If two independent experiments confirmed some hypothesis at 2.5 and 3.5 sigma, the combined evidence is surely much larger than 3.5. Does anyone know what the right way of combining experimental results is, to yield a more accurate answer?

carbocation3• 15 years ago

Really depends on the experimental approach, but there are certainly techniques for combining independent results. For example, in genetics, inverse-variance weighted meta analysis is common. Studies are essentially combined with their effect weighted by the degree to which their results are tightly clustered around that study's mean result.

I would be interested to learn about common procedures from physics as well.

elwin• 15 years ago

Assuming the errors are random and uncorrelated, the total significance is the square root of the sum of the squares. In this case, that's only 4.3 sigma.

nknight• 15 years ago

> only 4.3 sigma

I generally treat particle physics as a black box from which magic appears, but my understanding was that 3 is where things start getting interesting, and 5 is where it's considered pretty conclusive, so wouldn't going from 3.5 to 4.3 be a significant jump?

eberfreitas• 15 years ago

Honest question: what are they gonna do once they find it?

jerf4• 15 years ago

First, a big celebration.

Then after the party, everybody has the hangover that may never end, because finding the Higgs right where we expected it is potentially the worst case scenario: http://www.sciencemag.org/content/315/5819/1657.full

umarmung• 15 years ago

Informative, but strange circular arguments in that article, especially from a scientific process perspective.

There are a ton of questions that Higgs cannot answer already and yet if we find Higgs precisely, research comes to a stop?

It almost feels like there's a split between theoretical physcists and everyone else, with theoreticians saying if you take away our broken toy, you better replace it with something we can play with!

Given Nature already trumped Einstein, his contemporaries, and all since, I think we can be fairly secure that we will ALWAYS having find something new to learn or discover from practical science.

After all, that's how we used to almost exclusively learn before scientists went a bit crazy with maths. These days there seem to be many more models out there than there is good science behind it - at least to a layperson like me. :)

DaniFong3• 15 years ago

Sure, it's 3.5 sigma in this particular energy band, but is it 3.5 sigma in every energy band?

It might be like expressing amazement that someone in the world won the lottery. There's a difference between someone in particular winning the lottery, and anyone winning the lottery.

Xkcd says it better than me. (hat tip to starwed)

http://xkcd.com/882/

bdonlan2• 15 years ago

They don't expect it to show up in every energy band - the whole point is that they expect to see a lot of Higgs boson formation at a specific energy level, and anything higher or lower drops to a background level. The sigma value is basically a measure of how many standard deviations off from the background event count the event count for this particular energy level is.

DaniFong3• 15 years ago

I'm sorry but I don't see how this addresses my point? If they are checking 20 bands for results with p < 0.05, the likelihood is that one will show up, just from fluctuations from background.

Discovery of the Higgs Boson rumoured to be at 3.5 sigma.

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