Monday evening, I posted a diary mentioning that the most important particle physics conference in 30 years was beginning at the end of the week, and that we would almost certainly learn something about the greatest mystery of the Standard Model of particle physics: the Higgs boson. I was stunned and gratified by the response--the diary shot up to the top of the rec list and stayed there all evening. A physics diary!! As one commenter noted: can you imagine this happening on redstate?

Well, the preliminary results were announced a couple of hours ago, and I'm writing this diary to update the earlier one. If you are not familiar with the Higgs boson, and did not read the earlier diary, please do so now (I'm no longer commenting on it) or you will have trouble understanding this.

Let me remind you of the situation before today's announcement. In the Standard Model, the Higgs mass can be anywhere between 50 GeV and 500 GeV (the proton mass is a little less than 1 GeV). Experiments at the Tevatron (at Fermilab, in Illinois) and in Geneva have narrowed the possibilities.

They haveFor reasons I will discuss later, the vast majority of particle physicists believe that the Higgs will not be above 150 GeV, and thus the lower range, 114 GeV - 158 GeV is the most likely.excludedthe possibility of Higgs masses below 114 GeV and masses between 158 GeV and 176 GeV. Thus, the remaining possibilities are 114 - 158 and 176 - 500

In order to properly discuss the new results, I have to be specific about what is meant by "excluded", and that requires a brief statistics lesson. If you know what "95% confidence level" and "statistical fluctuations" mean, you can skip this.

Suppose you have a fair coin, and you flip it many times. Now suppose someone proposed a hypothesis "If Markos concentrates, he can make the coin come up heads 53% of the time". How do you test this? First, you get Markos to agree to concentrate, and then you flip the coin. If you flip it 100 times, and get 53 heads and 47 tails, that does **not** mean that the hypothesis is correct, since if you flip a coin without Markos around you will occasionally get 53 heads. Statisticians (this is taught in undergraduate stats classes) can tell you the following:

Here is how you read this table. If you flip a coin 100 times, then 95% of the time you will get between 40 and 60 heads (try it, if you are patient). If you flip it 1000 times, then 95% of the time, you will get between 470 and 530, and if you flip it 10000 times, then 95% of the time you will get between 4900 and 5100. In the right column is what you expect if the Markos hypothesis is correct. You can see that 100 flips per trial is useless---a fair coin would quite likely to give you 53 (or more) heads. 10000 flips per trial is more than enough to test the hypothesis, since the chance of a fair coin getting 5300 is very, very small. 1000 flips per trial is right on the edge. If you got 500, then you could say that the Markos hypothesis is

Number flips Range of 95% Expectation if Markos

per trial of the trials hypothesis is correct

100 40 - 60 53

1000 470 - 530 530

10000 4900 - 5100 5300

**"excluded with a 95% confidence level"**. Of course, you might get unlucky and get 520 heads, in which case it would be impossible to make such a strong statement. So you need a lot of data, and a little luck (hoping that the fair coin doesn't have an upward fluctuation). Bottom line--the exclusion plots always give 95% confidence level that the Higgs is not in the exclusion region. It is not certainty that it isn't there---getting to 99% takes about twice as much data--but is the typical standard in the field.

So, what are the results? There are two detectors at the LHC--- ATLAS and CMS. They analyze their data independently and do not combine them (that can be done later); this provides a good check. They didn't quite analyze all of the data collected, but only about 80% of it. With luck, as noted in the previous diary, they could exclude the entire region from about 135 GeV to about 400 GeV. However, since they are only analyzing 80% of the data, it is unlikely they could exclude that entire region. The results were just announced.

**Results:** Neither ATLAS nor CMS can rule out the entire region, because they see an **excess of events over the expected background** in two places, although in only one is the excess fairly substantial. The strongest one is at around 130-140 GeV, the other is (weaker) around 250 GeV. Of course, either of these (or both) could just be bad luck, like flipping 1000 coins and getting 525 (you couldn't then rule out the Markos hypothesis). Or one (or both) could be a Higgs.

In fact, if a Higgs were in either place, this is what you would expect to see. For ATLAS, the signal at 120-140 is (technical term: 2.8 sigma) much stronger than the one at 250 (technical term: 1.8 sigma or so). For CMS, the signal at 130 or so is stronger as well (technically: it looks like 1-2 sigma, but the graph isn't out yet), and the one at 250 is much weaker. In fact, if one used 90% confidence level instead of 95%, CMS would exclude 145 GeV - 480 GeV.

Here are the more precise results:

ATLAS excludes Higgs between 155-190 GeV and between 295-450 GeV. They see a small excess around 250, and a bigger excess between 120 and 140.

CMS excludes Higgs between 149 - 206 GeV and between 300-440 GeV. They also exclude much of the region in 200-300, and using 90% confidence instead of 95% would rule out 149 - 480 GeV. They see very little excess around 250, and a bigger excess between 130 and 150.

Now the one problem with a Higgs at 250 GeV. In the last diary, I said that the Standard Model gave very precise predictions to a part per thousand. But in that third decimal place, there is a dependence on the Higgs mass. If the Higgs is above about 150 GeV, then the Standard Model predictions are off. Thus most physicists expect it to be lighter.

Here are the possibilities for the 250 GeV bump:

1. It is just bad luck, and will disappear after the next round of data (we will know if this is the case within two months).My personal guess is that #1 is 80% likely, #2 is 5% likely, #3 is 15% likely. We will know within a few months.

2. It is a Higgs, but the Standard Model has other particles that we haven't included in the precision calculations, so 230 GeV is ok.

3. The theory actually has two neutral Higgs, and the 230 GeV one is the heavier of the two (the other could be at 145 or lower). This is not crazy. Virtually every extension of the Standard Model has two Higgs particles (and tens of thousands of papers with two Higgs have been written).

For the 130-140 GeV bump, the possibilities are:

1. It is just bad luck, and will disappear after the next round of data (we will know within two months).My personal guess is that #1 is 30% likely, #2 is 30% likely, #3 is 40% likely.

2. It is the Standard Model Higgs.

3. It is a Higgs of a model with more Higgs bosons.

The next big conference is August 22nd in Mumbai. There will be a lot more data then.

The new era in particle physics has begun.

UPDATE: Nice general review at http://www.nature.com/...