Higgs 101

By John Conway | November 6, 2007 6:26 pm

The Higgs boson..the “God Particle” (ick…sorry Leon). The Holy Grail of particle physics. (Um, also there’s that dark matter stuff but who knows what it might be…)

Where to begin? The Higgs boson is one thing, or many, there, or not, waiting to be discovered, if we can. But what is it? Why is it? Does it exist at all?

We know a lot, now, after decades of experiments at the great accelerators. Working backwards: the Tevatron at Fermilab, LEP 1 and 2 at CERN, KEK-B at KEK in Japan, PEP2 at SLAC, CESR at Cornell, the SLC at SLAC, the SppS at CERN, HERA at DESY, Tristan at KEK, PEP at SLAC, PETRA at DESY. But it’s all coming down, sooner or later, to the Big One: the LHC at CERN. This machine will, in all likelihood, answer the question: what is the origin of electroweak symmetry breaking? That is, why do the carriers of the weak nuclear force, the W and Z bosons, have mass (and large mass at that) and the photon does not have mass at all? If we are really lucky we may start to get an answer to the question: why do fundamental particles have masses at all, and the rather peculiar masses they do have? And even if we know all this, so what? What then?

That was a lot of jargon and acronyms for one paragraph…so we’ll start there. Firstly, the word “electroweak”. We believe that all of the particles we know about interact “electroweakly” in the sense that they all partake of the weak nuclear force and, if they have electric charge, interact electromagnetically as well. We believe that the electromagnetic and weak nuclear forces are manifestations of a single underlying force of nature. The word “electromagnetic” should start to give you the flavor of the enterprise. Electricity=magnetism has been with us for nearly 150 years, first unified in the form of the “classical” electromagnetic relations of James Clerk Maxwell in 1861. This feat gave humanity its first taste of victory over matter, energy, space, and time, and propelled us headlong into the modern age. Surely one could unify electromagnetism with the other obvious force of nature, gravity, the universal nature of which was established in the late 1600’s by Isaac Newton.

But no. Gravity has stubbornly resisted unification to this day. Perhaps more on that later. Meanwhile, the late 1800’s and early 1900’s saw an incredible unfolding of unexpected events: the establishment of an apparently absolutely empty vacuum (no “ether” to serve as host to electromangetic waves), the undeniable ultimate universal speed limit namely that of light. Then in rather quick succession came the quantum, special relativity, the atom, the nucleus, and finally the dawning of the quantum mechanical description of our world.

By 1930 the quantum revolution was complete, and we could set about the usual human pattern of (intellectual) colonization, militarization, exploitation, and capitalization. All the modern technology we now enjoy derives principally on our ability to first understand and then technologize the quantum world.

We’d done it: unlocked the secrets of the atom! And we got the nucleus as a bonus! So much energy in so small a place…unbelievable. Could there be more? We humans never stop – we probe ever deeper, and in this case deeper means smaller, and smaller means more energy, and more energy means bigger, and more expensive. What government, what power, would want to miss out on this one, though? If you could build nuclear weapons maybe something even smaller was inside protons and neutrons and you could build an even bigger or better weapon? No question – the military drove this one. And in the US, with a nuclear-weapon economy much larger than the auto industry, the scientists had free rein in the 1950s and 1960s to pursue these questions: were there smaller things still inside the nucleons (the protons and neutrons?)

Yes. Lots. As the energies of accelerators grew ever larger, we produced more new and strange particles, never before seen. We already knew since the 1930’s, or at least believed we knew, that there exists antimatter in the world. Antimatter looks just like the regular stuff, but has opposite charge. The jargon is “quantum numbers”: for every particle with its known quantum numbers, there are antiparticles with all the same properties but the opposite quantum numbers. The electron has electric charge -1 and its antiparticle has the same mass and interactions but has electric charge +1. The antielectron does not have “anti-mass” in any sense, but looking at the equations you can sort of tilt your head, and if you hold you mouth just right, the antielectron looks like an electron with negative energy moving backward in time. But never mind that. Anti-electrons, or positrons, do indeed exist, they move forward in time, and they have positive energy. (Lost yet? Don’t worry…)

All the fundamental matter particles we know about have antiparticle cognates. But what are the fundamental particle/antiparticles? Which are fundamental in the sense of being truly indivisible, unexcitable, basic, utterly elementary?

A whole zoo of particles emerged in the 50’s, 60’s and 70s, but let’s cut to the chase: here is a picture of all the fundamental matter particles, and every bit of matter we know about (except dark matter; again more later on that) is made of these things:

periodic-particles2.gif

There are six quarks (and their antiquark mirror images), and six leptons. They are apparently arranged in three “families” or “generations” in order of increasing mass. Within each generation we find the same four apparently fundamental types: one neutrino, one charged lepton, and two quarks. The quarks interact strongly, that is, by the force that holds the nucleus itself together. All the particles interact weakly, that is, via the weak nuclear force. And all of them except the neutrinos interact electromagnetically – they carry electric charge.

I believe that the greatest (and I mean THE greatest) discovery of the 20th century was to recognize that every symmetry in nature coresponds to some conserved physical quantity. It is a great sorrow that Emmy Noether did not win the Nobel Prize for this profound work. Symmetries are all around us – some are very simple, and some not so simple. For example, consider symmetry in time. The laws of physics are (we presume) the same now as they are at the time you finish reading this sentence, and will be the same 100 years from now. If you move (translate) in time, the rules stay the same. This symmetry in fact leads to conservation of energy. Likewise, if you move in space, the laws of physics are the same. This leads to conservation of momentum. If you rewrite the laws of physics in a frame of reference rotated 42.6 degrees from the one where you are writing them now, they are the same…conservation of angular momentum! Wow!

But it gets much better. We know, since the beginning of the last century, that you need to obey the rules of relativity. Fine. Also quantum mechanics. Okay…how? We write down wavefunctions that obey all the rules. Then we make them also obey all the symmetries we know about.

It turns out that wavefunctions are represented by complex numbers, which have real and imaginary parts. (By imaginary, we mean multiples of the square root of negative 1, not “eleventy-forty seven” which is perhaps another imaginary number.) Complex numbers are rich and fascinating, and the calculus of complex functions of complex numbers is great fun and beautiful. Most remarkably, this calculus describes the world perfectly when combined with quantum mechanics and relativity!

“Describes the world perfectly.”? Okay, well, it describes a broad swath of phenomena at the subatomic particle level really well…freakily well. We call it the Standard Model. I give it capital letters here because it has become so deeply established, and has such predictive power over such a broad range of phenomena that you have to give it a proper name. And I and most of my friends live for the day when we can destroy it and return it to lower case letters, the formerly standard model.

It’s only a model, after all. To build the Standard Model we assume that our wavefunctions obey certain peculiar symmetries, called gauge symmetries. The simplest to understand is called U(1). With complex wavefunctions, the probability for finding a particle at a certain place/time is calculated by finding modulus of the wavefunction, sort of its absolute value or magnitude. You square it, basically, in the complex space in which it lives. It turns out, though, that you get exactly the same answer for this probability if you square the wavefunction, or the wavefunction multiplied by a complex number of modulus 1 (e to the something imaginary). This something imaginary can in fact be a function of position in spacetime. It is, in fact, the same as a rotation of the wavefunciton in the complex plane…and that’s U(1) symmetry.

Here comes the miracle: if you impose upon our relativistic, complex, quantum-mechanical wavefunctions the requirement that they be invariant under these U(1) transformations, then you get electromagnetism. Conservation of electric charge. A massless photon. QED – quantum electrodynamics, in all its 12-digit precision glory. Electromagnetism is a simple consequence of the U(1) symmetry of any wavefunction.

When you have a hammer, especially one like this, everything starts to look like a nail. So in the 60’s and 70’s, the theorists starting banging away, and came up with the next level of symmetry, which (surprise) was called SU(2). If we impose SU(2) on our wave functions we get…well, a puzzle. Because whereas U(1) appears to be exactly obeyed, and though particles appear to obey SU(2), it’s only approximate. (Particle friends, please close your virtual ears/eyes here because I am guilty of oversimplification here.) It’s a “broken” symmetry. Maybe at very, very high energies it appears exact, but down here on cold hard Earth it’s broken, sort of badly.

Then, BREAKING NEWS, circa 1970s: It *does* appear that the strong nuclear force can be described by an exact SU(3) symmetry! But, alas, our ability to calculate anything in the quantum mechanics of SU(3) is stymied by the facts that a) the carrier of the strong force, the “gluon” (analogous to the photon) can interact directly with itself, and b) the strong force is damned strong and we cannot use our favorite quantum mechanical approximation trick, perturbation theory, to calculate much of anything that we can measure. A subculture of particle theorists and experimentalists is born, and continue to sport 70’s sideburns (not the women) well into the 90’s, when they mysteriously return to fashion. Quantum chromodynamics is what our theory of the strong force is called, “color charge” is what’s conserved, and it explains the strong interactions rather perfectly.

Meanwhile, a number of models with SU(2)-type symmetries are proposed, but one in particular wins out in the intense intellectual battle that ensues. This one, the creation of Sheldon Glashow, Abdus Salam, and Stephen Weinberg, combines SU(2)xU(1) with the then-little-known Higgs mechanism to produce a theory that conserves “weak hypercharge”, and accounts for both the weak interactions and the photon (electromagnetism). Awesome in its sweeping scope and power, this theory predicts the existence of two heavy “weak vector bosons”, the particles that transmit the weak nuclear force: the W and Z bosons. The weak nuclear force is weak, and short range, because the W and Z are very heavy: 80 and 91 GeV, respectively, nearly two orders of magnitude times the mass of the proton.

The W and Z are then discovered at CERN in 1983 in the debris of collisions of protons and antiprotons. Weinberg/Salam/Glashow had already won the Nobel prize in 1979 for their work, and Carlo Rubbia and Simon van der Meer won it for their discovery (along with hundreds of colleagues on the UA1 and UA2 experiments at CERN) the next year, 1984. A new field, high energy hadron collider physics, is firmly established. The hunt is on for the Higgs boson!

And so at last we come to the Higgs boson. The electroweak theory posits a “Higgs field” permeating all spacetime. You just paste it into the “Lagrangian”, the equation that tells you how all possible wavefunctions behave in the presence of the U(1), SU(2), and SU(3) symmetries that we believe must be obeyed. The Higgs field has a certain potential energy form that leads to the SU(2) symmetry being broken, and only imperfectly obeyed, at low energies (that is, our world). I you wrote out the full electroweak Lagrangian, this is what you get (oops, there is a missing parenthesis…can you spot it?):

sm-lagrangian1.gif

The Standard Model is not pretty, but it does work. As we said before, it’s only a model. Does the Higgs field exist? Well, if it does, and if it’s broken the way we think it is, then a massless photon exists and so do massive W and Z bosons. Since these do exist, and behave in precisely the predicted manner, then can we but conclude that the Higgs must exist as well?

If so, we should try to find it, and as I have said in Cosmic Variance before, I have been searching for it for about twenty years, with no success yet. Should I or my hundreds of colleagues in this quest be discouraged? No, because if it does exist we don’t really think we should have been quite able to see it yet.

Why not? The basic reason is that all our best data indicate it should have a mass of about 120 GeV, give or take, and the Higgs boson is very feebly interacting. Therefore it’s hard to make lots of Higgs bosons.

Nevertheless, at the LEP 1 and LEP 2 accelerators we had a real chance to produce and detect Higgs bosons, because in addition to interacting with our matter particles (the quarks and leptons) the Higgs interacts with the W and Z bosons. At the LEP accelerator, electrons and positrons collided at very high energies, equivalent to the mass of the Z boson at LEP 1 and up to more than twice that energy at LEP 2. When you produce a Z boson, it can occasionally give you a Higgs boson and a “virtual” Z that almost immediately decay. The LEP experiments all looked feverishly for the Higgs in the 1990s, but in the end there was no evidence for a Higgs boson with mass less than 114.4 GeV. This was a major accomplishment, and if the Higgs boson did exist with a mass less than this value, I am certain LEP would have found it. There were some tantalizing collision events at the very end, but not enough to say “this is it”.

In the mean time we refined what we know about the Standard Model, and discovered the top quark at the Tevatron in 1995. This was an important key to unlocking the Higgs boson, because the Higgs boson mass can be calculated, somewhat roughly, if we know the mass of the top quark, the W boson, and how the Z behaves in its production and decays. The answer that we get is that the Higgs boson should have a mass which is probably less than the limit we’ve set! I say probably because the uncertainties in this calculation allow some possibility that the Higgs boson mass could be larger than the present limit, say, 120 GeV, without causing too much difficulty with the other existing measurements.

In the end, then, the Higgs boson of the Standard Model could be just out of range of the LEP accelerator, which was decommissioned at the end of 2000 to make way for the Large Hadron Collider, the LHC at CERN, which will begin operating next year if all goes well. Meanwhile, the Tevatron proton-antiproton collider at Fermilab in Illinois has had an opportunity to observe the Higgs boson before the LHC turns on.

The Tevatron began operating in 1985 and has been the highest energy proton-antiproton collider in the world ever since. In the early 1990s plans were underway to construct the gargantuan SSC, the Superconducting Supercollider, in Texas, to begin operating in about 1999. Miles of tunnel underground were excavated, and the SSC laboratory was taking shape when, in late 1993, the US Congress de-funded the project in the wake of a ballooning cost estimate. The cancellation of the SSC meant that the next big accelerator would be the LHC at CERN, but it was going to take over a decade to complete it. This meant that by the mid-1990s the only place to look for the Higgs was the Tevatron. The CDF and D0 experiments were ready, flush with the victory of the top quark discovery and eager to join the hunt, underway at LEP, for the Higgs.

As we mentioned above, though, the Higgs interacts rather feebly with quarks, leptons, and the W and Z bosons. The “coupling” to fermions like quarks and leptons is in fact proportional to their mass, and so the Higgs boson favors the heaviest ones: the top quark, the bottom quark, the tau lepton, and the charm quark. If you produce a Higgs boson, it will decay to the heaviest quark or lepton paris (for example a bottom quark and antiquark) that it can. If it can decay to pairs of W or Z bosons, though, it prefers to do that. The Higgs boson is produced at the Tevatron in an analogous fashion to how it produced at LEP. At the Tevatron, quarks in the protons collide with antiquarks in the antiproton, and make virtual W or Z bosons, which in turn can give a real W or Z plus a Higgs boson. We call this the VH process, because the W and Z are vector bosons (meaning they have spin 1).

At the Tevatron, though, the challenge was to get a high enough proton-antiproton collision rate to make the Higgs, and so the whole Fermilab complex underwent a major upgrade in the late 1990s, adding a new Main Injector to get more beam into the Tevatron, and numerous improvements to the rest of the machines. By 2001 new data started to roll in and the hunt resumed, having ended the year before at LEP.

The Tevatron luminosity (the number of collisions per second), steadily grew until the machine hit its stride in the past few years. If the Higgs boson is there, then we should have been able to produce thousands of Higgs boson events. But at the Tevatron, one is also producing billions of non-Higgs events! This gives you a very difficult, nearly overwhelming “background” of events at the Tevatron that look just like Higgs events but aren’t. The detectors, furthermore, have imperfect energy resolution for the Higgs decay products, and so it’s hard to get a nice sharp mass peak right at the Higgs mass.

Nevertheless, lots of extremely talented people are working very hard to analyze the data we’ve collected and perform the search for the Standard Model Higgs boson. I’ve been working on the CDF experiment since 1993, and have done quite a bit o this work myself…it is extremely challenging, and takes the collaboration of dozens of people to succeed. The Tevatron experiments are inching closer to being able to extend the limit set by LEP (if the Higgs is not there) and maybe, just maybe, get a glimpse of the Higgs before the LHC turns on and acquires enough data to do the trick.

Can the Tevatron do it? I say “maybe” above and that’s always the right thing to say because it’s true. My own bet is that with about four times the present data sample, and with new ideas and methods, we can surely extend the LEP limit and get a glimpse if it is there at a mass less than about 125 GeV, or (oddly) has a mass close to 160 GeV, where it decays predominantly to WW. Can the Tevatron get four times more data? Yes, if all goes well, and the Tevatron runs through 2010. Is that too late? Maybe… The LHC could turn on in 2008, but will probably not produce enough collisions to see the SM Higgs. What about 2009? It is much more likely that this would be the first year that the LHC could conceivably discover the Higgs, if the detectors are well-understood, the LHC machine works very well, and the Higgs has a favorable mass, around 120 GeV. It actually could happen earlier if the Higgs mass is larger and its ZZ decays become significant, but as we noted above, the theoretically favored mass for an SM Higgs is not much larger than the present limit, 114.4 GeV.

Should the Tevatron run in 2010 or not? This question is beginning to be addressed by the community and the government. It would cost about $30 million to run the machine in 2010, according to what I have heard, and would require a staff of accelerator people and people from the experiments to operate the detectors and analyze the data. Considering the huge investment the US and countries around the world have made in this beautifully running machine and well-understood and efficient experiments, it’s a bargain.

There are good physics reasons to do this. If the LHC does see an SM Higgs signal it will be in a very rare decay mode at first: its decays to pairs of gamma rays. This distinct signal occurs in one of every 500 Higgs boson decays, and will give a sharp peak at the mass of the Higgs in the ATLAS And CMS detectors, once about a year’s worth of collisions is analyzed. The Tevatron, by contrast, would see a Higgs boson via its decays to b quark pairs; the LHC will not be able to do this for several years due to the overwhelming backgrounds. Seeing both decay modes is an important test of whether in fact it is a Higgs boson we are seeing at all, and a good cross check of its mass and other parameters.

The Tevatron can also continue to refine the knowledge of the top quark mass and the mass of the W boson, so that when a Higgs is observed we can test whether its mass agrees with the theory – another important test.

Perhaps more importantly is the fact that it might not be a Standard Model Higgs boson at all that we seek. There are very good reasons to believe that, theoretically, the Standard Model Higgs cannot be the only fundamental particle remaining to be discovered. Theoretically, the calculations of its mass suffer from corrections that grow dramatically with the mass of any new heavy fermion that might exist, and in fact the Higgs receives corrections to its mass from itself that are unstable and need to somehow be finely tuned to cancel to many orders of magnitude. It is, as the thoerists say, “unnatural” to expect nature to have done this.

Solutions to this problem have been sought, and found, for decades now. If the universe obeys a symmetry called “supersymmetry” which relates bosons (integer spin particles) to fermions (half-integer spin particles) then there must exist a supersymmetric partner for every particle we know about. Supersymmetry is clearly not perfect; it must be broken if it is there, otherwise we would know about all the supersymmetric particles, which would have the same masses as their ordinary particle partners. The presence of these particles cancels off the instability in the Higgs mass in a neat way, greatly reducing the unnaturalness of the situation. The cost, though, is to add many many new particles and parameters to the theory…Occam would perhaps not be impressed.

And, though we’ve looked for supersymmetry for decades, we have not found any evidence of any supersymmetric particles…nevertheless some theorists are convinced it must be there, and we continue that hunt as well. If supersymmetry does exist, the Higgs boson gets more interesting. There are not one but at least two Higgs fields permeating spacetime, one giving mass to the up type quarks, and the other giving mass to the down-type quarks and the leptons. There would be not one but three neutral Higgs boson states to look for, plus a charged Higgs boson. The lightest neutral Higgs boson could have properties very similar to those of the Standard Model Higgs boson, and therefore if we do see a Standard-Model-like Higgs boson we need to measure it carefully to see if it is the one from supersymmetry or not.

Even better, if supersymmetry exists then the Higgs bosons it predicts could be produced at a rate greatly enhanced compared with the rate for the Standard Model one. This means that the Tevatron, and the LHC, can produce more massive Higgs bosons more rapidly. For the Tevatron this could be the way that it could discover the Higgs boson and get evidence for supersymmetry before the LHC turns on.

This was the subject of m previous “Bump Hunting” series of posts at CV, and the latest results are that there is no evidence for production of supersymmetric Higgs bosons at an enhanced rate. This null result allows us to rule out regions of possible supersymmetry parameters. There are numerous variants of the supersymmetry, however, with even more complicated Higgs boson families. It’s fair to say we ave not looked for all of them, and even fairer to say that we have not explored all possible supersymmetric Higgs phenomena theoretically.

It is also possible that there isn’t a Standard Model Higgs boson or a supersymmetric one. A number of theories have been proposed recently (an not so recently) that would explain electroweak symmetry breaking as a byproduct of the existence of some new force, even stronger than the strong nuclear force, which comes into play at a high energy scale, possibly even with new particles.

Other theories propose to solve the naturalness problem by the addition of a minimal set of new particles and/or extra spatial dimensions. Typically one still gets a Higgs or Higgs-like boson, but at a possibly higher mass than we’ve been sensitive to so far.

In short, if you’ve slogged your way through to this point, you might get the idea we don’t really know what we are looking for at all! There is some truth to that. It is important to keep our minds open to new ideas and to be ready to look for as-yet-un-thought-of predictions that come from them. And we do try to do that…yet…

It is hard to look at the beautiful agreement between indirect determinations of the Higgs mass and the prediction from the measurement of the top quark mass and W mass, made in the context of the idea of the Higgs field, and think that this is all just an accident, an random approximation of something else entirely. My own gut feeling is that there really is an excellent chance that in a few years here, at the LHC and/or the LHC, we will see something that looks like a Higgs boson, quite likely at a mass of 120 GeV or thereabouts.

If we don’t see a Higgs boson (SM-like or supersymmetric) with mass less than about 130 GeV, things will get very interesting – it’s almost a certainty then that some other model is the correct explanation. That would be amazing, too, and may be very difficult to unravel at the LHC, with such large background rates.

This whole post barely scratches the surface of the present state of affairs in the search for the Higgs boson and the explanation of electroweak symmetry breaking. I shall leave to a future post the larger question: If we do discover a Higgs boson, of what use might it be, as J.J. Thomson wondered about his great discovery, that of the electron, 110 years ago?

CATEGORIZED UNDER: Science
  • graviton383

    Wow! Great posting John!!

  • CanuckRob

    Great post John, this is one of many reasons I lenjoy well written scienceblogs and popular sicence books, they make complex ideas graspable by my layman’s mind. If it ever strikes your fantasy I would love to read a precis of the alternate (but not crackpot) theories that don’t require a Higgs boson. Thank you.

  • Jack

    “Electromagnetism is a simple consequence of the U(1) symmetry of any wavefunction.”

    This is the classic example of that amazing phenomenon in physics: the way wrong ideas can be much more fruitful than right ones! [When you analyse this statement as mathematics, it comes down to “given a principal U(1) bundle, the existence of connections on that bundle is a consequence of the existence of the bundle.” Whether that counts as a tautologous statement or a meaningless one I leave to the reader’s taste….] I’m sure it’s true that the people who believe such fantasies end up contributing much more than the people who don’t. I wonder why.

  • http://blogs.discovermagazine.com/cosmicvariance/john John

    Jack, I am puzzled… I think that it’s fair to say that the fact that, in relativistc quantum field theory, one gets EM from imposing U(1) symmetry is not the same as claiming that this is the only possible way that EM could come about. There are probably many, many other mathematical formalisms which also give EM, and from which we can make all the wonderful predictions at which QED succeeds so well…do you know of any?

    As scientists we are open to new ideas. But why do you say this one is “wrong” ?

    I think I miss your point. The bundle thing doesn’t parse for me…

  • Moshe

    I think Jack means that the U(1) global symmetry does not have to be necessarily gauged, and electromagnetism is a consequence of gauge symmetry (and Lorentz invariance), not simply of the U(1) symmetry alone. Seems like a semantic difference to me..

    Maybe a quick chance to mention my pet peeve, quickly as to not detract from this wonderful piece: there is a common confusion between wavefunctions and classical fields, but in reality quantum mechanics never enters the argument. Electrodynamics is perfectly fine as a classical field theory, and neutral particles have perfectly consistent quantum mechanics. The phase rotation one gauges is not that of of the wavefunction, it is that of a classical field. In that context gauge invariance and Lorentz invariance indeed imply electrodynamics.

  • lt.milo

    this is exactly why i love CV

  • manyoso

    I’m more interested in your next piece. What are the consequences if we just discover the last predicted particle from the Standard Model and …. nothing else.

    Where does that leave unification with gravity… string theory…. supersymmetry… the origin of the fine structure constant and all the other fine tuning…

    Can you imagine the letdown if the LHC just reinforces the Standard Model and provides zero hints in the ‘Beyone the Standard Model’ tale??

    That would suck.

  • manyoso

    Also, if evidence of supersymmetry is also not found or ruled out by the experiments at LHC where is that going to leave the search for the neutralino and dark matter?

  • mattk

    Thank you for a great post! I left particle physics at the undergraduate level, and I never quite followed the excitement in looking for the Higgs. This explained it very well for me.

    OK, back to the lurking for me :)

  • Tumbledried

    A very thoughtful, well written summary of the current state of particle physics. I really enjoyed reading it, thankyou!

  • Nonnormalizable

    Brilliant! As I slog through the calculations in my graduate QFT course, it’s great to be hear again about the big picture (in a comparatively easy to understand way). This sort of thing reminds me of why I got into physics and makes me even more glad I’ve chosen particle physics.

  • Adam

    Even if we didn’t find anything past the standard model, that would still be quite a puzzle, as isn’t a consistent theory up to very high energies. Something different needs to happen, or we need to figure out some other formalism.

  • Thomas Larsson

    I recently learned something curious here. The two best indirect estimates for the Higgs mass are 31 GeV and 420 GeV, and you only get the celebrated 120 GeV by averaging over these mutually incompatible values.

  • http://countiblis.blogspot.com Count Iblis

    Why can’t we extract the properties of the Higgs from the radiative corrections it causes to the things we have already measured?

  • Low Math, Meekly Interacting

    It’s this level of expositional excellence that keeps me coming back to CV. It’s easy to lose sight, when there’s so much attention paid in the popular science press to speculative details of wormholes in so-called theories of quantum gravity or somesuch, of the fact that the firmer foundation, the stuff it all depends on, is an incredibly challenging and rich array of subjects that we should all at least make the effort to grasp (as much our individual ability allows, of course). Without someone out there willing to take the time to address that need, it’s hard to put things in perspective. Thank you and all the CV expositors for doing so.

  • gonamar

    Great post!

  • Jason dick

    manyoso,

    Well, yes, it would suck if the Standard Model seemed to be exact. But this seems obscenely unlikely to be the case, given the way science has progressed. What would be really neat would be if we managed to find something completely unexpected, that doesn’t obey supersymmetry, but describes some entirely different mathematics that we just hadn’t yet thought of.

    As for dark matter, other experiments are probing entirely different regions of parameter space by looking for dark matter particles from cosmological sources. These, too, are only just beginning to probe the interesting region of parameter space for dark matter, and, if the dark matter is only visible in one or the other, gives us a greater chance of finding it. If it’s visible in both, well, then that’ll make the two types of experiment excellent corroborations of one another.

  • tyler

    Thank you for an excellent post on one of the most interesting and important questions of our time.

    I have never read “The God Particle,” because the title just annoys the crap out of me. I don’t want to be seen carrying a book with that title, it is just so freaking dumb ;o)

    However, I’m obviously interested in the subject matter. So, those of you expert enough to judge – title aside, does the book have merit, enough to be worth reading for those of us on the amateur, well-read-physics-fanboy side of the fence?

    If not, is there an accessible alternative? Doesn’t have to be *too* accessible, like “New Scientist” accessible (i.e. in the limit where “accessible” actually means “laughably inaccurate”). I’m willing to read over my head if I can get the gist of it…lord knows Penrose gives me enough of that these days…

    thanks!

  • Low Math, Meekly Interacting

    Dr. Lederman’s book is, to me, alternately one of the most enjoyable and irritating reads I’ve found on the subject. That he’s a true mensch seems to leap off the page, it’s loaded not only with good science popularization, but also loads of good humor and more-or-less true anecdotes about the giants of 20th century physics who Lederman rubbed elbows with.

    Then again, it’s got more than its fair share of the Creator waving Her (perhaps metaphorical) magic wand over the whole affair, enough well-meaning-but-heavy-handed left-wing idealizing to make me wince, and some downright sappy moralizing on the hubris of Mankind’s pursuits in the face of The Infinite. Skim or skip these weak passages, and the rest is definitely worth your time, IMO.

  • http://msm.grumpybumpers.com Coin

    So, a question:

    My understanding is that if the Higgs exists, it is the source of the rest mass of ALL particles– that anything with rest mass (i.e. everything but photons, gluons and gravitons), it is so because of its interactions with the Higgs field. Is this correct?

    However, when you listen to physicists talk about the Higgs and why it’s important, they’re not really interested in all those other particles– they only seem interested in electroweak symmetry breaking, which I take to mean only the mechanism by which that broken SU(2) gauge symmetry comes to be broken. Sometimes I’ll see where physicists are proposing models without Higgs fields (like this Technicolor thing); writings about these models seem exclusively concerned with EWSB and never seem to bring up the subject of what mechanism provides rest mass to all other particles. Apparently the Higgs interacting with a fermion is just boring.

    The thing is, as far as I know all that “electroweak symmetry is broken” means is that the three WZ bosons are supposed to be symmetrical, but since they have different masses, they’re not. So it seems like if we’re only interested in the Higgs for its role in EWSB, then we’re only really interested in the Higgs because of the special mass value it gives to the Z boson. The Higgs determines mass for ALL particles, but only in one case do we seem to care!

    This just seems very strange. What am I missing here? What is it about the asymmetrical masses of the W and Z bosons that makes EWSB so incredibly important and interesting to physicists, to the more or less exclusion of caring about the Higgs interacting with anything else?

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Coin, the Higgs is responsible for the masses of all the elementary particles in the Standard Model. Composite particles, like protons and neutrons, get the large majority of their mass from QCD, completely independently of the Higgs.

    “Electroweak symmetry breaking” and “the Higgs” are used interchangeably in the context of giving mass to elementary particles, because it’s the Higgs that breaks the electroweak symmetry. If the symmetry were unbroken, it would forbid masses for the fermions, as well as for the W/Z bosons. Any theory that hopes to replace the Higgs mechanism with something else (like technicolor) has to figure out how the fermions get masses, and that’s been a longstanding problem with technicolor theories. It’s not impossible, but it’s messy, and specific models tend to run into trouble with constraints from precision measurements.

  • http://msm.grumpybumpers.com Coin

    Sean, thanks, that helps a lot!

    I’m still a little confused though– is there some explanation you could give for why unbroken electroweak would forbid fermion masses, or is this just one of those “it’s complicated, you have to go work through the math” sort of things?

    And would it be the case that– when you say that unbroken electroweak would “forbid masses for the fermions”– you only mean the elementary fermions? I mean, if composite particles can get rest mass through QCD interactions, then surely they could continue to do this even if EW symmetry were unbroken?

    …And I guess overall the thing about composite particles acquiring rest mass through QCD confuses me a lot, because if that’s the case then I guess I didn’t/don’t know what “rest mass” even means. It kind of sounds like the “rest mass” of a thing just refers to the total energy of that thing’s field interactions. If that’s the case, then the reason why the rest mass of an elementary particle is due only to the Higgs would seem to be because the Higgs is the only interaction that the particle can take part in when there aren’t any other particles around to interact with; systems of particles, on the other hand, can interact internally, and the energy of those interactions gives the system rest mass. Is this right? But if that’s the case, does then a system gain rest mass due to energy contained in other kinds of interactions also, besides just the higgs and qcd? Like, what about electromagnetic interactions? Weak interactions? Gravitational interactions? Also, if systems containing strong interactions acquire rest mass thereby, then shouldn’t a single gluon have rest mass, since gluons can self-interact?

    Sorry if these questions are kind of elementary…

  • Tilahun (Til) Eneyew

    If the Higgs ( the Standard or Supersymmetric version) exists, it must contribute to the Cosmological Constant since it permeates spacetime. I think it may also contribute to dark energy. Can Sean enlighten us on this issue?

  • Tim

    Wow! That was awesome. I feel like I’ve taken a brain vitamin.

    Tks

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  • http://blogs.discovermagazine.com/cosmicvariance/john John

    Thanks to all for the kind words…

    Til (#22): excellent question. I like to say that “the universe would never have expanded to be larger than a grapefruit” if there is just a SM-type single Higgs field, given its vacuum energy. Actually, it could be orders of magnitude larger or smaller than that, I just don’t know. But it would not be this big…would it? Could dark energy be counteracting the Higgs field vacuum energy? Or something else? I am quite ignorant here of the deeper cosmological thinking on this question.

    Even if the presence of the Higgs field is why the fundamental fermions have mass, we don’t have a clue as to why they have different masses, or for that matter why there are three generations, or any of that. Really the SM scenario tells us only why the photon is massless and the W/Z are not, and leaves open many other questions.

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  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    The funny thing about the electroweak symmetry is that it acts only on “left-handed” versions of fermions, not on the right-handed ones. If particles move at the speed of light, they can’t ever switch from left to right; but massive particles, which move slower than light, can interchange back and forth. So an unbroken symmetry that treats left and right-handed particles differently wouldn’t allow for any massive fermions.

    About the vacuum energy: well, that’s a big mystery. According to conventional wisdom, the Higgs gives a huge contribution to the vacuum energy. So does QCD, which is well understood. So do the zero-point fluctuations of every field in the universe. Any one of those contributions is individually much larger than what we observe in nature. So either they miraculously cancel out against each other, or something more subtle is going on that we don’t understand.

  • Crudely Wrott

    I’ve read “The God Particle” and a number of other contemporary books dealing with the state of knowledge concerning physics and cosmology. Used to have quite a respectable library on the subjects. Every now and again, while reading, I would catch that elusive glimpse that has no concise explanation yet speaks to me of a limitless potential for understanding. Like an old idea and a new one merging in a flash of clarity. I felt like the alchemist who first found that sodium and water released light and heat, copiously. Surely knowledge of transcendent power! What would he have made of say, Lexan, or aluminum foil?

    Mind you, my library is gone and I’ve been off my studies for a while. None the less, an idea has always tickled the back of my brain:

    What if it’s just particles all the way down? Not only farther than we can see now, but farther down, no matter how closely (or at what energies) we can look?

  • http://freiddy.blogspot.com/ Freiddie

    Great post.

  • http://www.geocities.com/CapeCanaveral/Hall/2638/ lfmorgan

    By every means available to you or me, I have found the Higgs Particle—somewhere in your locked-limited Box, you wrote: The Higgs particle comes as a result of the changes needed to make the theory explain the weak field and the electric field.

    Which it does – in spades. The problem is that in spite a great deal of effort, no one has ever found the Higgs particle. Which brings into question the whole wonderful edifice.

    So the question is, are we looking in the wrong place, or do we need to figure out the error in the theoretical underpinnings…” well said now….

    please visit my website with an open mind and find what you say you are looking for —but I do not think your ego will let you see it! Better still, go first to http://www.geocities.com/CapeCanaveral/Hall/2638/1MrMorganNewPhysics.doc

  • Changcho

    Great post, thank you, answers a lot of my questions. Hopefully the LHC will clarify things when it starts production runs.

  • http://blogs.discovermagazine.com/cosmicvariance/john John

    Crudely Wrott (#29): It is entirely possible it’s particles all the way down, as you say… Certainly every time we have banged things together we’ve found smaller things inside. Why should that pattern ever cease?

    Nima Arkani-Hamed was at UC Davis a couple weeks ago and gave a talk where he said that if this were the outcome, that would be the “ordinary” outcome, the
    easy solution to the problem. Not that we wouldn’t be excited to explore the new forces/particles we find! But finding a Higgs scalar, indicating this Higgs field permeating all spacetime, would be the “extraordinary” outcome, a truly new thing for this field o physics.

    There are days when I think that these “compositeness” models might be right after all. And they are not at all out of fashion thee days…

    Ultimately it’s an experimental question, and we ma know the answer soon.

  • Crudely Wrott

    Thanks, John (#33) for the reply.

    I fully agree that a Higgs discovery would be useful and wonderful. In the same manner that the discovery of the electron, proton and neutron were. On each occasion much was made of the idea that a complete understanding of the nature of, well, nature, was at hand. Alas, closer inspection, based upon the new knowledge that emerged, only served to show a more subtle and counter-intuitive view.

    Having barely enough knowledge to be marginally dangerous, I find a kind of Zen in the idea that all particles are infinitely divisible. OK, there may certainly be a practical, fundamental limit and that is not for me to say. But the idea that there is one ultimate particle strikes me with the same inner discomfort as the idea that there is one ultimate creator or one particular definition of the question to which the answer is 41.99999 . . . . I would sure hate to have to tell everyone that the show is over and pack up the tent in the rain to set off to the next gig not only without a map but without even the possibility of a map existing.

    Funny how our individual perceptions and biases color our definitions yet, without actual observation, how can we otherwise define anything practical or fundamental? Ah! The joy of science, mankind’s only legitimate child.

    Others have said that it is all not only stranger than we imagine it is; it is stranger than we can possibly imagine (given present knowledge and the tools at hand).

    I am anticipating the advent of the LHC. Certainly both our knowledge and our tools will be changed. And then we will be able to draw the map to the next gig.

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  • http://zhogin.narod.ru Ivan

    All the elementary particles known from experiments for today
    have some spin (1/2, or 1, ..). Maybe this is the exact rule of nature
    that spin zero elem.particles do not exist (at all; and i’m
    almost inclined to bet on
    ..):).

    However, new vector bosons possessing higgs-like functionality
    (ie, interconversion of left and right fermions) could still exist
    (even if no condensate is present); these bosons are also
    well suitable for hunting:-).

  • Jugalator

    Thanks for the post! Even someone like me can digest a lot of this, and it’s all very interesting science. :) This is exactly the kind of stuff I come here to this blog, hoping to find.

  • http://valatan.blogspot.com bittergradstudent

    And there are a bunch of other scenarios where something like the Higgs mechanism is what’s going on, but it is not the Glashow, Salam and Weinberg model at all, right?

    Things like where the underlying group is SU(2)xSU(2) instead of SU(2)xU(1), and the missing two gauge bosons have a mass in excess of 150 GeV, or where there is no Higgs boson, but instead a cooper pair of two fermions looks like a Higgs, or something like that, ya?

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  • Dumbo

    Is the Higgs boson a gauge boson? If not, why not? What is a gauge boson anyway? What about the graviton? When is a boson not a gauge boson? Are there gauge fermions?

  • http://valatan.blogspot.com bittergradstudent

    Dumbo–

    the Higgs boson is a scalar particle. It is defined, classically, by a single function

    Gauge bosons are particles that exhibit a gauge symmetry–namely, they are written down using a certain number of functions, but the actual physics they describe involves a smaller number of functions. Therefore, in describing the actual physics involved with the gauge boson, we are free to set an arbitrary relationship between the various functions that we have written down, before we even begin to solve the problem. The most common example of this is the four dimensional vector potential function in Electricity and magnetism–we are free to add the gradient of an arbitrary function to the vector potential, and we will not change the electric or magnetic fields described by this potential.

    In this sense, the graviton is certainly a gauge boson–in order to write down the gravitational field, we need ten functions. Careful analysis, however, reveals that there are only two physically meaningful local degrees of freedom to the gravitational field. Of course, we can’t write down a consistent quantum mechanical description of the graviton, so perhaps this description is wrong.

    This leaves us with the vector particles, which are bosons of spin one, that are classically described by four dimensional vectors. We have a perfectly good quantum mechanical theory of vector particles. So, typically, when particle physicists talk of ‘gauge bosons’, the things that they are describing are vector particles.

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  • http://zhogin.narod.ru Ivan

    Yea, to draw gage symmetry by one hand that to break it by the
    other, this looks much the same strange as those deferents
    broken by epicycles.
    (Unbroken gage symmetry is way better.)

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  • collin237

    I think I remember reading something about discovering the Higgs many years ago. Did that turn out to be wrong?

  • Rahul Ghosh

    Its really very exiting, I want to know more about it.

  • http://blogs.discovermagazine.com/cosmicvariance Arsen D

    You won’t find it!!!!!!!!!!!!!!!!!!!

  • Domann

    Even thou you may not have the time to read new theories, I think that it will take you not more than a few minutes to read the abstract and the conclusions of a completely new approach to theoretical physics.

    Please have a look at http://www.odomann.com/

    O. Domann

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