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What is the Higgs Boson Particle? Part 2

Find out what all the hubbub is over the Higgs boson, why you should care about it, and the crucial role that statistics played in its discovery.

By
Jason Marshall, PhD,
Episode #113

To quickly recap where we left things last time: After decades of looking for something called a Higgs boson, it appears that physicists at CERN (the European Organization for Nuclear Research) and their collaborators have finally found it. Understandably, these physicists are (to put it mildly) super excited, and the good news for us is that math played a major role in all of this. But what exactly was that role? And why is it more important to your daily life than you might think? After a quick review of the details of last week’s big findings, those are precisely the questions we’ll dive into today..

Recap: Higgs Boson Primer

In last week’s article, What is the Higgs Boson Particle? Part 1, we talked about the physics behind the discovery of the Higgs boson. So if you’re not sure what a Higgs particle is and why it’s important, you may want to check out that article before continuing on with this one.

The quick and dirty summary of the story so far is that particle physicists have spent nearly 50 years searching for something called a Higgs particle (which they’ve done as part of a quest to verify the existence of a more fundamental thing called the Higgs field), and it looks like they’ve finally found it. We aren’t going to worry about understanding exactly what the Higgs field is, but it is interesting to understand what it does. In particular, it’s interesting to know that the Higgs field plays a major role in your life because up until this discovery of the Higgs boson, physicists couldn’t actually say why matter has mass. Just to be clear, by matter I’m talking about everything from tiny particles like electrons, protons, and neutrons up to much bigger things like you, me, and panda bears. Which means that in a very real but also very particular sense, this discovery explains why you exist!

What is Statistical Significance?

It’s important to realize that not only has a Higgs particle been found, its existence has been confirmed to a remarkably high level of confidence. More precisely, physicists can now say with 99.9999% confidence that a Higgs-like particle has been detected. This high level of confidence means that this result is what’s called “statistically significant” because it’s extremely unlikely that it could be due to pure chance. It’s good to remember that “extremely unlikely” does not mean “impossible,” but the 99.9999% confidence level means that the odds of this result being due to a cruel and unusual act by the universe intended to confuse us and throw us off its trail are only something like one in several million.

So we know this thing is real, but where did this 99.9999% confidence level come from? To answer that, we need to know a bit more about how the experiment to find the Higgs particle was carried out, and we also need to know a bit more about statistics. Since everybody loves statistics, let’s start with that.

Physicists can say with 99.9999% confidence that a Higgs-like particle has been detected.

Tossing Coins to the Higgs Boson

Imagine putting 10 normal coins in a box, covering it, shaking the whole thing up, and then taking the lid off and counting the number of heads. How many do we expect? Well, assuming these are fair coins—meaning they have an equal probability of landing heads or tails—on average we’d expect that half of them will end up heads. Which means we expect to see 5 heads. Of course, that doesn’t mean we will see exactly 5 heads every time—we could see 0, 1, 2, or all the way up to 10 heads—it only means that on average we expect to see 5 heads. Here’s what that means: Let’s say we do this experiment and get 4 heads, then we do it again and get 7 heads, and we do it a third time and get 6 heads. So we’ve gotten an average of (4 + 7 + 6) / 3 = 5.7 heads—which is fairly close to the expected value of 5. But if we then do the experiment 10, 100, 1,000 times and even more, the average value we get should continually get closer and closer to the expected value…as long as the coins are 50-50 fair.

But what if the coins aren’t fair? What if the probability of tossing heads is a little higher—say 51%—and the probability of tossing tails is therefore only 49%? What would you see if you tossed these loaded coins? Well, if you only toss a few, you won’t notice any difference at all since the results will be too similar to tell apart. But imagine you toss the coins thousands, millions, billions, or even more times. If you were to do that, you’d notice real differences between the number of heads you get with the fair versus the loaded coins. And the more times you tossed the coins, the more confident you’d be of this difference. For example, if you tossed the coins 100 times, the 1% difference means you’d only expect to see an average of 1 more heads with the loaded coins. But if you tossed them 1,000,000 times, you’d expect to see an average of 10,000 more heads—which is certainly something you’d notice! And that’s going to be a very key idea in just a minute.

How Statistics Found the Higgs Boson

So what does this all have to do with finding the Higgs boson? Well, as we discussed in Part 1 of this series, there are many things happening inside the particle accelerator used to discover the Higgs that produce the same types of signals as actual Higgs particles. We’ll call all this stuff the background noise. The goal of the Higgs experiment is basically to figure out if we live in a world in which the signal from the particle accelerator is caused solely by this background noise (which would be a world in which the Higgs boson does not exist) or a world in which the signal from the particle accelerator is the sum of this background noise and the signal from actual Higgs bosons.

To see how this works, notice that the world in which the Higgs particle does not exist is analogous to the world in which we tossed fair coins. In that world, no matter how many times we tossed our coins, we never expected the results to deviate much from the 50-50 split of heads and tails. Similarly, no matter how much data we collect from a particle accelerator in this world, nothing we see will suggest the presence of anything but the humdrum background noise. On the other hand, the world in which the Higgs particle does exist is analogous to the world in which we tossed loaded coins. In that world, after tossing enough coins, we were able to detect the presence of an anomalous number of heads. Similarly, after accumulating tons and tons of data from the particle accelerator in this world—which it turns out is our actual world—physicists have discovered an anomalous bit of extra signal. After crunching the numbers, statistics says with 99.9999% confidence that this extra signal is very real…and that it looks an awful lot like the long sought Higgs boson.

And that’s the story of how math—and in particular statistics—helped find the Higgs boson!

Wrap Up

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Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

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