Tag Archives: particle physics

Third step in the Triplet Model is up.

Advanced particle physics today:

Today I’m continuing the reader-requested explanation of the “triplet model,”  (a classic and simple variation on the Standard Model of particle physics, in which the W boson mass can be raised slightly relative to Standard Model predictions without affecting other current experiments.) The math required is pre-university level, just algebra this time.

The third webpage, showing how to combine knowledge from the first page and second page of the series into a more complete cartoon of the triplet model, is ready. It illustrates, in rough form, how a small modification of the Higgs mechanism of the Standard Model can shift a “W” particle’s mass upward.

Future pages will seek to explain why the triplet model resembles this cartoon closely, and also to explore the implications for the Higgs boson. 

Please send your comments and suggestions!

Triplet Model: Second Webpage Complete

Advanced particle physics today:

I’m continuing the reader-requested explanation of the “triplet model,” a classic and simple variation on the Standard Model of particle physics, in which the W boson mass can be raised slightly relative to Standard Model predictions without affecting other current experiments.

The math required is pre-university level, mostly algebra and graphing.

The second webpage, describing what particles are in field theory, and how the particles of one field can obtain mass from a second field, is ready now. In other words, the so-called “Higgs mechanism” for mass generation is sketched on the new page.

Meanwhile the first page (describing what the vacuum of a field theory is and how to find it in simple examples) is here. 

Please send your comments and suggestions, as I will continue to revise the pages in order to improve their clarity.

Triplet Model: First Webpage Complete

Advanced particle physics today:

Based on readers’ requests, I have started the process of explaining the “triplet model,” a classic variation on the Standard Model of particle physics, in which the W boson mass can be raised slightly relative to Standard Model predictions without affecting other current experiments.

The math required is pre-university level, so it should be broadly accessible to those who are interested.

My guess is that I’ll structure the explanation as four or five webpages, and will put up about one a week. The first one, describing what the vacuum of a field theory is and how to find it in simple examples, is here. Please send your comments and suggestions, as I will continue to revise the pages in order to improve their clarity.

The Simplest Way to Shift the W Boson Mass?

Some technical details on particle physics today…

Papers are pouring out of particle theorists’ offices regarding the latest significant challenge to the Standard Model, namely the W boson mass coming in about 0.1% higher than expected in a measurement carried out by the Tevatron experiment CDF. (See here and here for earlier posts on the topic.) Let’s assume today that the measurement is correct, though possibly a little over-stated. Is there any reasonable extension to the Standard Model that could lead to such a shift without coming into conflict with previous experiments? Or does explaining the experiment require convoluted ideas in which various effects have to cancel in order to be acceptable with existing experiments?

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A Few Remarks on the W Boson Mass Measurement

Based on some questions I received about yesterday’s post, I thought I’d add some additional comments this morning.

A natural and persistent question has been: “How likely do you think it is that this W boson mass result is wrong?” Obviously I can’t put a number on it, but I’d say the chance that it’s wrong is substantial. Why? This measurement, which took several many years of work, is probably among the most difficult ever performed in particle physics. Only first-rate physicists with complete dedication to the task could attempt it, carry it out, convince their many colleagues on the CDF experiment that they’d done it right, and get it through external peer review into Science magazine. But even first-rate physicists can get a measurement like this one wrong. The tiniest of subtle mistakes will undo it.

And that mistake, if there is one, might not even be their own, in a sense. Any measurement like this has to rely on other measurements, on simulation software, and on calculations involving other processes, and even though they’ve all been checked, perhaps they need to be rechecked.

Another question about the new measurement is that it seems inconsistent not only with the Standard Model but also with previous, less precise measurements by other experiments, which were closer to the Standard Model’s result. (It is even inconsistent with CDF’s own previous measurement.) That’s true, and you can see some evidence in the plot in yesterday’s post. But

  • it could be that one or more of the previous measurements has an error;
  • there is a known risk of unconscious experimental bias that tends to push results toward the Standard Model (i.e. if the result doesn’t match your expectation, you check everything again and tweak it and then stop when it better matches your expectation. Performing double-blinded experiments, as this one was, helps mitigate this risk, but it doesn’t entirely eliminate it.);
  • CDF has revised their old measurement slightly upward to account for things they learned while performing this new one, so their internal inconsistency is less than it appears, and
  • even if the truth lies between this new measurement and the old ones, that would still leave a big discrepancy with the Standard Model, and the implication for science would be much the same.

I’ve heard some cynicism: “Is this just an old experiment trying to make a name for itself and get headlines?” Don’t be absurd. No one seeking publicity would go through the hell of working on one project for several years, running down every loose end multiple times and checking it twice and cross-checking it three times, spending every living hour asking oneself “what did I forget to check?”, all while knowing that in the end one’s reputation will be at stake when the final result hits the international press. There would be far easier ways to grab headlines if that were the goal.

Someone wisely asked about the Z boson mass; can one study it as well? This is a great question, because it goes to the heart of how the Standard Model is checked for consistency. The answer is “no.” Really, when we say that “the W mass is too large,” what we mean (roughly) is that “the ratio of the W mass to the Z mass is too large.” One way to view it (not exactly right) is that certain extremely precise measurements have to be taken as inputs to the Standard Model, and once that is done, the Standard Model can be used to make predictions of other precise measurements. Because of the precision with which the Z boson mass can be measured (to 2 MeV, two parts in 100,000), it is effectively taken as an input to the Standard Model, and so we can’t then compare it against a prediction. (The Z boson mass measurement is much easier, because a Z boson can decay (for example) to an electron and a positron, which can both be observed directly. Meanwhile a W boson can only decay (for example) to an electron and a neutrino, but a neutrino can only be inferred indirectly, making determination of its energy and momentum much less precise.)

In fact, one of the ways that the experimenters at CDF who carried out this measurement checked their methods is that they remeasured the Z boson mass too, and it came out to agree with other, even more precise measurements. They’d never have convinced themselves, or any of us, that they could get the W boson mass right if the Z boson mass measurement was off. So we can even interpret the CDF result as a measurement of the ratio of the W boson mass to the Z boson mass.

One last thing for today: once you have measured the Z boson mass and a few other things precisely, it is the consistency of the top quark mass, the Higgs boson mass and the W boson mass that provide one of the key tests of the Standard Model. Because of this, my headline from yesterday (“The W Boson isn’t Behaving”) is somewhat misleading. The cause of the discrepancy may not involve the W boson at all. The issue might turn out to be a new effect on the Z boson, for instance, or perhaps even the top quark. Working that out is the purview of theoretical physicists, who have to understand the complex interplay between the various precise measurements of masses and interactions of the Standard Model’s particles, and the many direct (and so far futile) searches for unknown types of particles that could potentially shift those masses and interactions. This isn’t easy, and there are lots of possibilities to consider, so there’s a lot of work yet to be done.

The W Boson Isn’t Behaving

The mass of the W boson, one of the fundamental particles within the Standard Model of particle physics, is apparently not what the Higgs boson, top quark, and the rest of the Standard Model say it should be.  Such is the claim from the CDF experiment, from the long-ago-closed but not forgotten Tevatron.  Analysis of their old data, carried out with extreme care, and including both more data and improved techniques, calibrations, and modeling, has led to the conclusion that the W boson mass is off by 1/10 of one percent (by about 80 MeV/c2 out of about 80,400 MeV/c2).  That may not sound like much, but it’s seven times larger than what is believed to be the accuracy of the theoretical calculation.

  • New CDF Result: 80,443.5 ± 9.4 MeV/c2
  • SM Calculation: 80,357± 4 [inputs]± 4[theory] MeV/c2
The new measurement of the W mass and its uncertainty (bottom point) versus previous ones, and the current Standard Model prediction (grey band.)

What could cause this discrepancy of 7 standard deviations (7 “sigma”), far above the criteria for a discovery?  Unfortunately we must always consider the possibility of an error.  But let’s set that aside for today.  (And we should expect the experiments at the Large Hadron Collider to weigh in over time with their own better measurements, not quite as good as this one but still good enough to test its plausibility.) 

A shift in the W boson mass could occur through a wide variety of possible effects.  If you add new fields (and their particles) to the Standard Model, the interactions between the Standard Model particles and the new fields will induce small indirect effects, including tiny shifts in the various masses.  That, in turn, will cause the relation between the W boson mass, top quark mass, and Higgs boson mass to come into conflict with what the Standard Model predicts. So there are lots of possibilities. Many of these possible new particles would have been seen already at the Large Hadron Collider, or affected other experiments, and so are ruled out. But this is clearly not true in all cases, especially if one is conservative in interpreting the new result. Theorists will be busy even now trying to figure out which possibilities are still allowed.

It will be quite some time before the experimental and theoretical dust settles.  The implications are not yet obvious and they depend on the degree to which we trust the details.  Even if this discrepancy is real, it still might be quite a bit smaller than CDF’s result implies, due to statistical flukes or small errors.  [After all, if someone tells you they find a 7 sigma deviation from expectation, that would be statistically compatible with the truth being only a 4 or 5 sigma deviation.] I expect many papers over the coming days and weeks trying to make sense of not only this deviation but one or more of the other ones that are hanging about (such as this one.)

Clearly this will require follow-up posts.

Note added: To give you a sense of just how difficult this measurement is, please see this discussion by someone who knows much more about the nitty-gritty than a theorist like me ever could.

A Prediction from String Theory

(An advanced particle physics topic today…)

There have been various intellectual wars over string theory since before I was a graduate student. (Many people in my generation got caught in the crossfire.) But I’ve always taken the point of view that string theory is first and foremost a tool for understanding the universe, and it should be applied just like any other tool: as best as one can, to the widest variety of situations in which it is applicable. 

And it is a powerful tool, one that most certainly makes experimental predictions… even ones for the Large Hadron Collider (LHC).

These predictions have nothing to do with whether string theory will someday turn out to be the “theory of everything.” (That’s a grandiose term that means something far less grand, namely a “complete set of equations that captures the behavior of spacetime and all its types of particles and fields,” or something like that; it’s certainly not a theory of biology or economics, or even of semiconductors or proteins.)  Such a theory would, presumably, resolve the conceptual divide between quantum physics and general relativity, Einstein’s theory of gravity, and explain a number of other features of the world. But to focus only on this possible application of string theory is to take an unjustifiably narrow view of its value and role.

The issue for today involves the behavior of particles in an unfamiliar context, one which might someday show up (or may already have shown up and been missed) at the LHC or elsewhere. It’s a context that, until 1998 or so, no one had ever thought to ask about, and even if someone had, they’d have been stymied because traditional methods are useless. But then string theory drew our attention to this regime, and showed us that it has unusual features. There are entirely unexpected phenomena that occur there, ones that we can look for in experiments.

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Has a New Force of Nature Been Discovered?

There have been dramatic articles in the news media suggesting that a Nobel Prize has essentially already been awarded for the amazing discovery of a “fifth force.” I thought I’d better throw some cold water on that fire; it’s fine for it to smoulder, but we shouldn’t let it overheat.

There could certainly be as-yet unknown forces waiting to be discovered — dozens of them, perhaps.   So far, there are four well-studied forces: gravity, electricity/magnetism, the strong nuclear force, and the weak nuclear force.  Moreover, scientists are already fully confident there is a fifth force, predicted but not yet measured, that is generated by the Higgs field. So the current story would really be about a sixth force.

Roughly speaking, any new force comes with at least one new particle.  That’s because

  • every force arises from a type of field (for instance, the electric force comes from the electromagnetic field, and the predicted Higgs force comes from the Higgs field)
  • and ripples in that type of field are a type of particle (for instance, a minimal ripple in the electromagnetic field is a photon — a particle of light — and a minimal ripple in the Higgs field is the particle known as the Higgs boson.)

The current excitement, such as it is, arises because someone claims to have evidence for a new particle, whose properties would imply a previously unknown force exists in nature.  The force itself has not been looked for, much less discovered.

The new particle, if it really exists, would have a rest mass about 34 times larger than that of an electron — about 1/50th of a proton’s rest mass. In technical terms that means its E=mc² energy is about 17 million electron volts (MeV), and that’s why physicists are referring to it as the X17.  But the question is whether the two experiments that find evidence for it are correct. Continue reading