The time’s come for me to return home to the United States. It is almost impossible to convey the intensity of the last few weeks. I’m excited, exhilarated and exhausted.

Even in more normal times, a visit to the CERN laboratory that built and operates the Large Hadron Collider [LHC] always wipes me out. When I’m there, several times a day I run into physicists I know who work on the LHC experiments, and so I’m constantly getting into impromptu conversations, both about the most recent scientific results and about planning how to investigate the data in future. And then there are lots of theoretical physicists of all stripes to talk to and learn from, including not only CERN faculty but also many, many visitors from all around the world.

This visit, of course, was unique. Not only did was there the historic presentation July 4th that convinced the particle physics community that a new particle, most likely a type of Higgs particle, has been found, it was followed (as was anticipated) by days and days of incessant discussions about interpreting the data that demonstrated the particle’s presence, and about future strategies to learn more about it. Then there was a five-day workshop at CERN (over a weekend!) concerning not only the Higgs search but also all of the other new results (of which there are many, though not as newsworthy) that the LHC experiments have produced. *[For that workshop, I was asked to put together a presentation on a subject on which I don’t feel entirely an expert, which was an interesting but rather stressful experience.]* And finally there was a three-day Higgs Hunting Workshop on the outskirts of Paris, entirely focused on the Higgs, where we saw some new Higgs data presented by the ATLAS experiment, a full review of all the previously presented Higgs data from all the relevant experiments, lots of theoretical talks about how to calculate the properties of the simplest type of Higgs particle with very high precision, discussions of the implications of the current data for whether the new particle might be a Higgs of a more complicated type, and also presentations reviewing the history of the Higgs search and looking forward into the near-term and long-term future. All Higgs All The Time! *[Yet again, I had to prepare a presentation that I found very stressful, and struggled with until almost the last moment. Between my departure from Geneva Tuesday afternoon until the Higgs Hunting Workshop ended late Friday afternoon, I don’t think I took a break except for meals.]*

So I think you can understand why I’ve been a little slow to post and why I’m a little slow to answer your questions and comments just now. I expect to be ready to start answering questions and putting more pedagogical stuff up on the site over the coming week. *In fact, for those of you who’ve had a bit of a freshman physics course, I’ve figured out how to explain how the Higgs field does its thing, namely, how it gives mass to other particles. Maybe as I put that explanation together I’ll figure out how to explain it even for those of you who haven’t had freshman physics, though that will be a lot trickier.
*

But right now I’m still winding down, and trying to clear my brain. Much work lies ahead of us in particle physics — for the LHC is still in its early stages, and we need many years of study of the new particle before it will teach us what we need to know about the Higgs field(s).

Dear Professor,

Would you mind mentioning some physics and math subjects, useful to our discussions, that a college grad in science could brush up on? While I appreciate how well you keep math out of these pictures, sometimes I’m willing to take a running jump at some of it. Presently I’m reviewing my college calculus to work up to my first understanding of Maxwell’s equations. I can see that Einstein’s are a few degrees of difficulty beyond that.

If you could name a few key concepts, a little beyond calculus and linear algebra, as intermediate goals, I might educate myself in a more organized fashion. Or perhaps I should get some statistics under my belt?

Hmm… You really don’t need more than beginning multivariable calculus to understand Maxwell’s equations. This seems like a sufficiently difficult goal that I wouldn’t put more on your plate.

I’m afraid there’s a reason it takes six years of full-time work to really understand modern physics. What are your real goals?

I agree that 21st century physics is beyond this retired scientist. But I find myself fascinated by 19th century stuff, that set the stage for quantum physics. Multivariable calculus is about where I am now.

However, if I look at Einstein, it seems at least two levels up from Maxwell.

My real goal is just to satisfy my curiosity. Or perhaps discover that, as with classical piano, the opportunity for me to be serious has already passed by? Yet I find I can still learn much more about music. Perhaps physics and math also?

There are several paths you could follow. From Maxwell you can indeed go to Einstein’s special relativity (confusing but not hard) and from there to general relativity (confusing and very hard, typically requiring advanced multivariable calculus). Alternatively you can go from Maxwell to Einstein’s theory of light quanta and certain aspects of quantum mechanics. Or from there to electrons and atoms and other aspects of quantum mechanics. Quantum mechanics also uses multivariable calculus and linear algebra. And then you can combine Maxwell with quantum mechanics to reach quantum field theory, which uses math you don’t learn in math class. Each of these steps involves two or three levels of complication and subtlety. You really should decide whether it is relativity or quantum theory that you want to understand over the first years. There are on-line lectures on these subjects by now, I’m sure.

The real question is whether you can be brought to a point of satisfying your curiosity without understanding all the technical details, and instead focusing just on some of them. I don’t know of books that are aimed at people with such a goal, unfortunately; there may indeed be a need for such things.

If you want advice on how to learn about general relativity, I would check to see what my more expert colleagues at Cosmic Variance have to say.

Mike: find a used copy of Bjorken and Drell vol One (1) and work through it line by line. You know enough math. It doesn’t cover the Standard Model but you’ll then be able to see the wood for the trees in the more up-to-date books with Ryder’s QFT a great first choice. And check out Leslie Howard playing Abschied on Youtube.

Dear Matt,

That all sounds like an amazing time – thanks for describing it for us, it’s great to get a sense of the atmosphere at CERN. One little niggling detail I am curious about in the Higgs detection: when the proton beams collide, I imagine a Higgs, if one is produced, will fly off at quite a speed before decaying (I know it decays very quickly, but I imagine it is also moving very quickly). How far does it tend to travel between being created in the collision and decaying into parts that you can detect? And is its direction essentially random, depending on details of how the protons collide?

Thanks so much for this window into a really exciting world.

The lifetime of the Higgs (which is the average survival time of a Higgs particle in its own frame of reference) is about 10

^{-21}seconds. Typically it is moving at a speed which is a significant fraction of the speed of light (maybe half as fast) so it travels a distance which is smaller than the distance across an atom but a hundred or thousand times further than the distance across a proton.Its direction of motion tends to be roughly along the direction in which the beams are traveling, but with some velocity sideways as well. And it’s random, collision to collision, but with a distribution that can be predicted using quantum field theory.

Is there a proper distinction between a process that involves scattering via virtual Higgs exchange and a process which sees the same final state products coming from the decay of a real, but unstable Higgs?

This is a general question, not specific to the Higgs. Let’s consider the W particle.

At the Tevatron and LHC, one can produce the process quark + anti-quark –> electron + anti-neutrino via a W particle. The question is: how can you tell the difference between a real W and a virtual W, when they both lead to the same final state?

The answer is clear, but the difference is not sharp; there is a cross-over region between the two. The longer is the lifetime of the particle, the sharper is the distinction and the smaller is the cross-over region.

Exactly the same issue arises for any resonant system, like a ball on a spring. A spring has (a) a resonant frequency (how the spring vibrates on its own), (b) a damping time (how long it takes for vibrations to die out). In particle physics these correspond, in precise mathematical analogy, to (a) the mass-energy [E=mc^2 energy] of a particle, and (b) the lifetime of the particle.

If the damping time is infinite (a perfect oscillator) then if you push on the system in a periodic way, you will either get a huge response from the spring, if you push with the resonance frequency, or a very limited response, if you push with any other frequency. The further away you are from the resonance frequency, the more muted the response. This corresponds, in precise mathematical analogy, to the statement that for a particle like an electron with an infinite lifetime, you either have a real electron or a virtual one; there is a sharp distinction. And highly virtual electrons are harder to make than slightly virtual ones.

If the damping time is finite (a more realistic oscillator), then a strong response by the spring will occur as long as you are pushing quite close to the resonant frequency, but not necessarily on top of it; the difference of the pushing (“driving”) frequency and the resonant frequency should be smaller than the inverse of the damping time. If it isn’t, you’ll get a weak response. This corresponds, in precise mathematical analogy, to the statement that if you smash a quark and anti-quark together — trying to push the universe at a particular frequency in order to make W particles — you will have a very decent chance of making a W as long as the energy of the quark and anti-quark differs from the mass-energy of the real W by something less than the inverse of the W’s lifetime times Planck’s constant. But if the collision energy differs very greatly from the mass-energy of the W, you will instead get a very weak response from the universe, and thus will produce the electron and anti-neutrino with a greatly suppressed probability. The first regime involves a real but unstable particle; the second involves a virtual particle; and there is a cross-over between the two regimes.

For the Higgs, whose lifetime is very long compared to Planck’s constant divided by the Higgs mass-energy, the distinction between the two regimes is very sharp, not as sharp as for an electron but much sharper than for the W.

OK, if I calculate a cross-section, I get a peak at s=m^2 from the pole in the propagator, which I’ve just been happy to interpret as scattering via a real unstable particle, and scattering at other energies as virtual particle exchange. Is this OK?

Looking forward to your explanation of how the Higgs field does its thing after you take a little R&R!

Hi Matt, as you will get over your desynchronosis, we shall wait patiently for your explanation on how Higgs field gave mass to some particles.

Speaking – unofficially of course, for participating group in this blog and undoubtedly a bunch of great future physicists, I am reminded of Abdus Salam Nobel acceptance speech, when he said: “This, in effect, is the faith of all physicists; the deeper we seek, the more is our wonder excited, the more is the dazzlement for our gaze”..

Matt

You made a point of saying you will try to explain how the Higg’s field gives mass to “other” particles. Can you also explain how the Higg’s particle obtains its mass?

Thank you for your dedication to helping us understand the wonder of it all.

I will explain it — to the extent we understand it. There is certainly an unknown sitting there.

To Mike Anthis,

I believe you could learn a lot by reading B.F.Schutz’s “Introduction to General Relativity”. This is an excellent book which will definitely allow you to understand Einstein’s field equations, as this seems to be what you’re looking for.

I second the recommendation about Schutz, I found it a great intro to the subject. You’d need a more basic primer on special relativity though, since Schutz assumes you’re competent with it already, and just reviews the important points quickly in the first chapter.

Schutz is good. I remember using Faber’s “Differential Geometry and Relativity Theory” which starts with 2 dimensional surfaces as a warmup. Has anyone else had experience with this book?

I wonder if you could also explain the higgs “interaction” between two particles also. What I mean by this is that if there are two opposite electric charges that are at rest close to each other they will exchange “virtual” photons. These longitudinal and scalar photons are the Coulomb interaction. Is there an analogous Higgs interaction if two particles that couple to the Higgs are placed next to each other? Since the Higgs has zero spin, the interaction would seem to be always attractive then. And also, shouldn’t this then be considered as the fifth “fundamental” interaction (i guess a matter of semantics)? Or is the Higgs interaction a matter of the particles both zagging at the same time (in some popular descriptions of the Higgs mechanism, the Higgs field causes a particle to zig-zag thru spacetime thus generating mass). I apologize for the run-on questions.

Yes, there is a Higgs force, due to the Higgs field, just as there is an electric force due to the electric field (which is just what virtual photons are in this context); yes, because the Higgs has spin-zero, the force is always attractive. But it is very short range, a bit shorter than the weak nuclear force (because the Higgs is a bit heavier than the W and Z). Also, for ordinary matter, it is much, much weaker than the weak nuclear force — ordinary matter is made from very lightweight particles, which are lightweight precisely because their interaction with the Higgs field is very small — though for top quarks the effect is quite significant and may someday be observed, with a precision measurement.

It is indeed a fifth fundamental interaction. But it’s also different from the other four in certain ways (each of the other four has something to do with a conservation law, while the Higgs interaction does not.)

Don’t make too much of the “zig-zag” picture. There is no change in direction when a particle interacts with the Higgs field. I’ve explained this somewhat more accurately in https://profmattstrassler.com/articles-and-posts/particle-physics-basics/the-known-apparently-elementary-particles/the-known-particles-if-the-higgs-field-were-zero/

A more complete physical description of how the Higgs field induces mass for other particles will appear on this site soon (a couple of weeks if all goes well.)

Thanks for the answer Prof.

Prof, I have another distantly related question..What is the weak isospin of th Higgs boson (3rd component of weak isospin)? I see a different answers to this (0 or 1/2). Based on vector fusion production, it would seem to me that it is 0. I’m confused. Thanks again.

Once the Higgs field becomes non-zero, weak-isospin quantum numbers are not conserved [at least not apparently so, because they can be absorbed by the Higgs field.] So the question doesn’t make sense, and that’s why you’re getting confusing answers.

Before the Higgs field is non-zero, the Higgs is a doublet and has a +1/2 and -1/2 component. By convention the -1/2 component is usually taken to be the one with a non-zero value.

The W+ W- H interaction appearing in vector boson fusion, in fact,

does not existif the H field is zero. The vertex would only be W+ W- H0* H0, which does conserve isospin. Only once H0 has a non-zero value v in the vacuum does it become v W+ W- H0. Indeed, this is why the existence of vector boson fusion is a direct test of the Higgs mechanism for mass generation. The same is true for q qbar –> W + H. We’re all looking forward to convincing evidence that these processes do occur.