Quantum Diaries

By now, I would imagine anyone tech savvy enough to be following this blog site has been exposed to the chilling stories, images, and videos of the events which took place last week at my university.

Not surprisingly, the actions of the university police, called for by the administration, have greatly enraged the students, alumni, staff, faculty, and friends of UC Davis.  A rally was held yesterday on the main quad to demonstrate, in overwhelming numbers, the disgust and shame felt by our community in light of these events.

In response to these events the undersigned faculty of the UC Davis Physics department have prepared a statement (original here):

Chancellor Linda Katehi                                     November 22, 2011

UC Davis

Dear Chancellor Katehi:

With a heavy heart and substantial deliberation, we the undersigned faculty of
the UC Davis physics department send you this letter expressing our lack of
confidence in your leadership and calling for your prompt resignation in the wake
of the outrageous, unnecessary, and brutal pepper spraying episode on campus
Friday, Nov. 18

The reasons for this are as follows.
•   The demonstrations were nonviolent, and the student encampments
posed no threat to the university community. The outcomes of sending in
police in Oakland, Berkeley, New York City, Portland, and Seattle should
have led you to exhaust all other options before resorting to police action.

•   Authorizing force after a single day of encampments constitutes a gross
violation of the UC Davis principles of community, especially the
commitment to civility: “We affirm the right of freedom of expression within
our community and affirm our commitment to the highest standards of
civility and decency towards all.”

•   Your response in the aftermath of these incidents has failed to restore
trust in your leadership in the university community.
We have appreciated your leadership during these difficult times on working to
maintain and enhance excellence at UC Davis. However, this incident and the
inadequacy of your response to it has already irreparably damaged the image of
UC Davis and caused the faculty, students, parents, and alumni of UC Davis to
lose confidence in your leadership. At this point we feel that the best thing that
you can do for this university is to take full responsibility and resign immediately.
Our campus community deserves a fresh start.

Sincerely,

Andreas Albrecht                Glen Erickson                   Lori Lubin
(chair)                         Chris Fassnacht                 Markus Luty
Marusa Bradac                   Daniel Ferenc                   Michael Mulhearn
Steve Carlip                    Ching Fong                      David Pellett
Hsin-Chia Cheng                 Giulia Galli                    Wendell Potter
Maxwell Chertok                 Nemanja Kaloper                 Sergey Savrasov
John Conway                     Joe Kiskis                      Richard Scalettar
Daniel Cox                      Lloyd Knox                      Robert Svoboda
James P. Crutchfield            Dick Lander                     John Terning
Mani Tripathi
David Webb
David Wittman
Dong Yu
Gergely Zimanyi

Myself, along with many graduate and undergraduate students, stand with our faculty, and appreciate their strong voice on our behalf.

In recent posts we’ve seen how the Higgs gives a mass to matter particles and force particles. While this is nice, it is hardly a requirement there must be a Higgs boson—maybe particles just happen to have mass and there’s no “deeper” origin of that mass. In fact, there’s a different reason why particle physicists are obsessed about finding the Higgs (or something like it)—that’s called electroweak symmetry breaking.

The statement that we’d like to understand is the following:

The Higgs boson breaks electroweak symmetry spontaneously.

That’s pretty heady stuff, but we’ll take it one piece at a time. Write it down and use it to impress your friends. Just be sure that you read the rest of this post so you can explain it to them afterward. (There’s a second part to the statement that we’ll examine in a follow up post.)

Electroweak symmetry

You might be familiar with the idea that electricity and magnetism are two manifestations of the same fundamental force. This is manifested in Maxwell’s equations and is often seen written on t-shirts worn by physics undergraduates. (If you happen to own such a t-shirt, I refer you to this article.) Electroweak symmetry is, in a sense, the next step in this progression, by which the electromagnetic force is unified with the weak force. This unification into an ‘electroweak’ theory and the theory’s subsequent ‘breaking’ into separate electromagnetic and weak forces led to the 1979 Nobel Prize in Physics.

So what’s going on here? We know that the force particle for electromagnetism is the photon, and we know that the force particles for the weak force are the W+, W-, and Z bosons. Permit me to make the a priori bold claim that the “unified” set of particles are actually the following: three W bosons and something we’ll call a B boson.

What? Now there are three W particles? And what’s this funny B boson; we never drew any diagrams with that weirdo in our guide to Feynman diagrams! Don’t worry, we’ll see shortly that because of the Higgs, these particles all mix up into the usual gauge bosons that we know and love. This should at least be plausible, since there are four particles above which we know must give us the four electroweak particles that we know: the W+, W-, photon, and Z.

Note that this new “unified” batch of gauge bosons don’t really look very unified: The Ws look completely different from the B. This illustration reflects an actual physical difference: the Ws mediate one type of force while the B mediates a different force. In this sense, the “unified” electroweak symmetry isn’t actually so unified!

Electroweak symmetry  is broken

In everyday phenomena, we observe electricity and magnetism as distinct phenomena. The same thing happens for electromagnetism and the weak force: instead of seeing three massless Ws and a massless B, we see two massive charged weak bosons (W+ and W-), a massive neutral weak boson (Z) and a massless photon. We say that electroweak symmetry is broken down to electromagnetism.

Now that masses have come up you should suspect that the Higgs has something to do with this. Now is a good time to remember that there are, in fact, four Higgs bosons: three of which are “eaten” by the weak gauge bosons to allow them to become massive. It turns out that this “eating” does more that that: it combines the ‘unified’ electroweak bosons into their ‘not-unified’ combinations!

The first two are easy; the W1 and W2 combine into the W+ and W- by “eating” the charged Higgs bosons. (Technically we should now call them “Goldstone” bosons.)

We’ll say a bit more about why eating a Higgs/Goldstone can cause the W1 and W2 particles to combine into, say, a W+. For now, note that the number of “degrees of freedom” match. Recall that ‘degree of freedom’ roughly translates in to the number of distinct particle states. In the electroweak theory we have two massless gauge bosons (2 × 2 polarizations = 4 degrees of freedom) and two charged Higgses (2 degrees of freedom) for a total of six degrees of freedom. In the broken theory, we have two massive gauge bosons (2 × 3 polarizations) which again total to six degrees of freedom.

A similar story goes through for the W3, B, and H⁰ (recall that this is not the same as the Higgs boson, which we write with a lowercase h). The W3 and B combine and eat the neutral Higgs/Goldstone to form the massive Z boson. Meanwhile, the photon is the leftover combination of the W3 and B. There are no more Higgses to eat, so the photon remains massless.

It’s worth noting that the Ws didn’t combine into charged Ws until electroweak symmetry breaking. This is because [electric] charge isn’t even well-defined until the electroweak theory has broken to electromagnetic theory. It’s only after this breaking that we have a photon that mediates the force that defines electric charge.

Electroweak symmetry is broken spontaneously

Alright, we have some sense of what it means that “electroweak symmetry” is broken. What does it mean that it’s broken spontaneously, and what does this whole story have to do with the Higgs? Now we start getting into the thick of things.

The punchline is this: the Higgs vacuum expectation value (“vev” for short) is what breaks electroweak symmetry. You might want t quickly review this post where we first introduced the Higgs vev in the context of particle mass. For those who like hearing fancy physics-jargon, you can use the following line:

The Higgs vev is the order parameter for electroweak symmetry breaking.

First, let’s see why the Higgs obtains a vacuum expectation value at all. We can draw nice pictures since the vev is a classical quantity. The potential is a function that tells you the energy of a particular configuration. You might recall problems in high school physics where you had to find the minimum of an electric potential, or determine the gravitation potential energy of a rock being held at some height. This is pretty much the same thing: we would like to draw the potential of the Higgs field. (To be technically clear: this is the potential for the combined bunch of four Higgses.)

Let’s start with what a “normal” potential looks like. Here on the x and y axes we’ve plotted the real and imaginary parts of a field ϕ; all that’s important is that a point on the x-y plane corresponds to a particular field configuration. If the particle is sitting at the origin (in the middle) then it has no vacuum expectation value, otherwise, it does obtain a vacuum expectation value.

On the z axis we draw the potential V(ϕ). The particle wants to roll to the minimum of the potential, so in the cartoon above—the “normal” case—the particle obtains no vacuum expectation value. I’ll mention in passing that concave of the potential is related to the particle’s mass.

Now let’s examine what the Higgs potential looks like. Physicists refer to this as the “Mexican hat” potential (These images are based on an illustration that is often used in physics talks. Unfortunately I am unable to find the original source of this graphic and ended up re-drawing it.):

What we observe is that the origin is no longer a minimum of the potential. In other words, the Higgs wants to roll down the hill where it can have lower potential energy. I’m not telling you why the potential is shaped this way (there are a few plausible guesses), and within the Standard Model this is an assumption about the Higgs.

So the Higgs must roll off of its hill into the ravine of minimum potential energy. This happens at every point in spacetime, meaning that the Higgs vev is “on” everywhere and matter particles can bounce off it to obtain mass. There’s something even more important though: this vev breaks electroweak symmetry.

In the cartoons above, there’s something special about the origin. If the particle sits at the origin, you can do a rotation about the x-y plane and the configuration doesn’t change. On the other hand, if the particle is off of the origin, then doing a rotation will send the particle around along a circular trajectory (shown as a solid green line). In other words, the rotational symmetry is broken because the physical configuration changes.

The case of electroweak symmetry is the same, though it requires more dimensions than we can comfortably draw. The point is that there are originally four Higgses which are all parts of a single “Higgs.” In the unified theory where electroweak symmetry is unbroken, these four Higgses can be rotated into one another and the physics doesn’t change. However, when we include the Mexican hat potential, the system rolls into the bottom of the Mexican hat: one of the Higgses obtains a vev while the others do not. Performing a “rotation” then moves the vev from one Higgs to the others and the symmetry is broken—the four Higgses are no longer being treated equally.

Now to whet your appetite for my next post: you can see that once electroweak symmetry is broken, there is a “flat direction” in the potential (the green circle). Remember when I said that the concave of the potential has to do with the particle’s mass? The fact that there is a flat direction means that there are massless particles. In fact, for the Higgs, there are three flat directions that correspond to—you guessed it—the three massless Higgs/Goldstone particles which are eaten by the weak gauge bosons: the H+, H-, and H⁰. The fourth Higgs—the particle that we usually call the Higgs—corresponds to an excitation in the radial direction where there is a concave, so the Higgs boson has mass.

Do we really need a Higgs?

Okay, so if you’ve followed so far, you have an idea of how electroweak symmetry breaking explains how the massless W and B bosons combine with the Higgses to form the usual W+, W-, Z, and photon. We’ve also reviewed how matter particles get mass (by bumping into the resulting vev) and how some of those gauge bosons got mass (by eating some of the Higgses). But was all of this necessary, or did we just cook it all up because we liked the idea of electroweak unification?

We will see in one of my follow up posts that in fact, electroweak symmetry breaking is almost necessary for our theory to make sense. (I’ll quantify the “almost” when we get there, but the technical phrase will be “perturbative unitarity.”) Note that I said that electroweak symmetry breaking is the important thing. Throughout this entire post you could have replaced the Higgs boson with “something like it.” There are plenty of theories out there with multiple Higgs bosons, no Higgs bosons, or generically Higgsy-things-but-not-quite-the-Higgs. That’s fine—in all of these theories, the “Higgsy-thing” always breaks electroweak symmetry. In doing so, you always end up with Goldstone bosons that are eaten by the W+, W-, and Z. And you always end up with some kind of particle like the Higgs that we expect to find at the LHC.

One last request: vote to support this blog

Hi everyone, if you liked this post (or any of my other posts, e.g. the Feynman diagram series) I’d like to ask you to vote for me (Philip Tanedo) for the 2011 Blogging Scholarship. The voting goes on for about another week and you can vote once per day. If you re-blog any of my posts, it would mean a lot if you could encourage your readers/friends/Facebook friends, etc. to also vote for me. For the past two years I’ve been able to blog due to support from the National Science Foundation and the Paul and Daisy Soros foundation, but without additional support like the Blogging Scholarship for next year I would be unable to continue with US LHC / Quantum Diaries.

At long last, here it is! From the Hadron Collider Physics conference in Paris, and as documented by the CMS and ATLAS collaborations, the plot you have all been waiting for:

As we last saw, CMS and ATLAS had each set limits on the rate of production of standard-model Higgs bosons at the Lepton-Photon conference in August. Now, for the first time ever, the two collaborations have combined their results. Each experiment has recorded about the same amount of data, so to first approximation, this combination allows us to double the number of collisions that are analyzed, and thus to set more stringent limits on Higgs mass (or possibly to discover a Higgs).

Since one of my colleagues took me to task just this morning for these plots being impenetrable, let’s review what is being measured and what the plot shows. First, remember that pretty much everything in particle physics is a counting experiment. You record so much data, and then count the number of times you observe a given phenomenon in the data. On the basis of this, you can essentially say, “given that I’ve seen this happen X times, surely if I were to do this experiment over and over, it would be very unlikely for me to see this happen more than N > X times.” N is then the “upper limit” on the number of events that we would expect to observe. (I’m sure my statistical friends will forgive me for this hand-waving description). We can convert that upper limit on event counts into an upper limit on the cross section for the process; the cross section is essentially the probability for a process to occur, which is obtained after normalizing out how much data has been recorded. The vertical axis of this plot gives the upper limit on the cross section for Higgs production, normalized to the expected cross section that we calculate from the quantum mechanics of the standard model.

The points show the upper limits that are obtained as a function of putative Higgs mass. It is a different upper limit for each Higgs mass because as the mass changes, you have different Higgs production and decay rates and different sensitivity to those decays; depending on the Higgs mass, it can be easier or harder to observe. As can be observed, the points fall below y = 1 over a wide range of Higgs masses. This indicates that we are observing fewer putative Higgs events than we would expect from the standard model prediction, and thus we claim to “exclude” that prediction, and thus the possibility of a standard-model Higgs at those particular mass values.

One should also pay attention to the dotted line and the colored bands. The dotted line represents what limit we would be able to set if there were no Higgs boson at all, and all there were to observe were background processes that look similar to the Higgs but aren’t. The bands represent the one and two standard deviation uncertainties on that expected limit. In general, the limits set are about as good as those we expected to set. There are some excursions from expectations, but they are generally no worse than two standard deviations, which is not impossible. This gives us some confidence that the observed limits aren’t anything crazy.

By combining the results of the two experiments, a very wide range of possible Higgs masses is excluded. Neither experiment alone could produce a result this strong, and hence the great interest in the combined result, which took many months and much coordination between the two experiments. Each group of experimenters had to understand the others’ measurement in detail to be able to do the combination correctly. It’s a lot of work, but the improvement in the bottom-line result is worth it.

And what do we learn from this? It appears that if there is a standard-model Higgs boson, it must have a very large mass (which is disfavored by other measurements), or a mass between 114 and 141 GeV. Optimists will note that in that region, more candidate events are observed than would be expected from a no-Higgs scenario, although not with any statistical significance worth talking about. If one believes everything about a standard-model Higgs, then ATLAS and CMS are currently putting quite a squeeze on its properties.

Of course, that’s a big “if.” The contrarian in me likes to keep two things in mind. First, all of this statistical stuff is just a convention we’ve adopted to communicate with each other. (We’ll see if my statistical friends forgive me for saying that!) The definition of excluded is, in my opinion, rather arbitrary, and you could imagine doing things differently and coming up with a different range of excluded Higgs mass values. If we are are to claim a discovery of a Higgs boson someday, I would assert that the evidence will have to be even clearer than what can be obtained from such statistical analyses.

Second, why should we believe any of the predictions? They are cooked up from many ingredients, each of which have their own uncertainties with them. It is hard to believe that the predictions are to be wildly off, but how the physics really works might not be what the standard model says it is, and thus we have to keep an open mind.

Thus, even if we reach the point where we can exclude all reasonable values of the Higgs boson mass — a point that we might reach soon, given that the experiments have recorded at least twice as much data has have been included for this combined result — and we actually do exclude those values, the search will not be over! Even if the standard model is not correct and there is no Higgs as such, the signatures of Higgs production and decay are still interesting, and could still be an indication of some kind of new physics. Higgs or no Higgs, we have a very interesting few months ahead of us.

This week, the LHCb experiment reported an anomaly they have just observed in the decays of charmed mesons. Could this be the tip of the iceberg for new physics?

As I reported before, the main goal of the LHCb experiment is to use heavy quarks (called beauty and charm quarks) to make precise measurements in the hope of detecting small deviations from the Standard Model, the theoretical framework that has been guiding particle physicists for a few decades. But it has a few known shortcomings that make us think new physics should be discovered soon.

This is a great model that allows theorists to make very accurate predictions. So far, every single one of them has proven to be true but if we were to find a flaw, it would be like discovering the secret passage guiding us further into our investigation of how matter works.

The results presented this week by the LHCb experiment hint in this direction, although as usual, further checks are needed. The scientists involved were looking at decays of charmed mesons denoted D⁰, particles made of one charm quark c (with electric charge +2/3) and one antiquark u (-2/3).  The D⁰ is therefore electrically neutral and can decay into a pair of kaons, K⁺K^– (mesons containing an s quark) or pions π⁺π^–(mesons made of light quarks, u or d).

But one could also make a charmed antimeson with one antiquark c (-2/3) and one quark u (+2/3). This is the meson antimatter. These antimesons also decay into pairs of kaons or pions, K⁺K^– and π⁺π^–.

How can one know if he or she is dealing with a charmed meson or antimeson since both decay to the same final products? One way is to “tag” the charmed mesons when they are created. For this measurement, the LHCb team selected excited charmed mesons D*⁺ and D*^–, which decayed to a positively charged pion and a D⁰ charmed meson, or into a negative pion when charmed antimesons are created. The pion charge gives it away.

What LHCb measured is the difference between how often charmed mesons and how often charmed antimesons decay into K⁺K^–. The same measurement was repeated with D⁰ Þ π⁺π^– as final decay products. The idea is to see if there is a difference in the behavior of matter (the mesons) and antimatter (the antimesons), what we call charge-parity (or CP) violation.

Then they looked at the difference of the difference between the K⁺K^– and π⁺π^– channels. The advantage is that many potential experimental biases cancel out, while a true signal would remain, as the CP violation need not be the same in the two channels.

Our Standard Model of particle physics predicts that this difference should be very small, of the order of 0.01% to 0.1% (the theoretical uncertainly is fairly large here). LHCb measures −0.82 ± 0.21 (statistical uncertainty) ± 0.11 (systematic uncertainty)%, a 3.5 standard deviation away from zero. In other words, if every source of experimental uncertainty has been properly accounted for, there is only a 0.05% chance this is due to chance. Other experiments had detected a hint of this effect before, but with much less precision, so this in itself is an accomplishment.

Does this mean the Standard Model has been proven wrong? Not yet. We need to see if this effect will remains once the group has a chance to analyze all of the 2011 data, which should be completed by March next year. Only 60% were used for this analysis.

As Mat Charles, one of the four physicists directly involved in this analysis told me: “This could be the hint that something interesting is going on. Very much worth pursuing”. They plan to add a different channel, tagging the D⁰ mesons and antimesons using B mesons, those containing the beauty quark, instead of D*, just to be sure this is true. Let’s hope they’ll be lucky. Such a discovery would be a great step forward.

Pauline Gagnon

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Cette semaine, la collaboration LHCb a annoncé l’observation d’une anomalie dans les désintégrations de mésons charmés. Serait-ce la partie visible de l’iceberg précurseur de nouvelles découvertes?

Comme je l’avais rapporté cet été, l’expérience LHCb utilise des quarks lourds (charme et beauté) afin d’obtenir des mesures de hautes précisions dans l’espoir de détecter la moindre déviation du modèle standard, l’outil théorique qui guide les physiciennes et physiciens des particules depuis plusieurs décennies. Mais ce modèle a quelques lacunes qui laissent présagées qu’une « nouvelle physique » devrait bientôt être découverte.

Ce modèle surprend par la précision de ses prédictions. Jusqu’à présent, on ne l’a jamais pris en défaut. Mais si cela devait se produire, ce serait comme découvrir un passage secret nous guidant plus loin dans nos recherches sur les lois intrinsèques de la matière.

Le résultat présenté cette semaine par LHCb fournit un indice dans cette direction, bien que comme toujours, la prudence est de mise et des vérifications plus poussées sont nécessaires. Les chercheurs impliqués étudiaient les désintégrations de mésons charmés, représentés par

D⁰, des particules faites d’un quark charmé ou c (charge électrique +2/3) et un antiquark u (-2/3).  Le D⁰ est donc électriquement neutre et peut se désintégrer en une paire de kaons, K⁺K^– (mésons contenant le quark s) ou en pions, π⁺π^–(mésons faits des quarks les plus légers, u et d).

Mais il existe aussi  des antimésons charmés formés d’un antiquark c (-2/3) et d’un quark u (+2/3). C’est l’antimatière des mésons. Ces antimésons peuvent eux aussi donner des paires de kaons ou pions, K⁺K^– et π⁺π^–.

Comment savoir si on a affaire à un méson ou à un antiméson charmé puisque les deux se désintègrent exactement de la même manière? On peut, par exemple, identifier les mésons et antimésons dès qu’ils sont formés. Pour la mesure qui nous intéresse, l’équipe du LHCb a d’abord sélectionné des mésons charmés excités, D*⁺ et D*^–, qui eux se désintègrent en produisant des pions positifs quand ils viennent avec des mésons charmés D⁰, ou des pions négatifs lorsqu’ils se désintègrent en antimésons charmés. La charge du pion révèle l’identité du méson.

LHCb a mesuré la différence entre la fréquence des désintégrations des mésons charmés en kaons, D⁰ ÞK⁺K^–, comparée à la même fréquence pour les antimésons. Cette mesure fut ensuite répétée avec les pions comme produit final, soit D⁰ Þπ⁺π^–. L’idée est de vérifier si la matière (les mésons) et l’antimatière (les antimésons) se comportent de la même façon. C’est ce qu’on appelle la « violation de charge et parité » ou simplement violation de CP.

Ils ont ensuite regardé la différence entre la différence des fréquences entre K⁺K^– et π⁺π^–. Grâce à cette soustraction, plusieurs biais expérimentaux s’annulent, tandis qu’un véritable signal émerge puisque le taux de violation de CP n’est pas nécessairement le même pour les pions et les kaons.

Le modèle standard de la physique des particule prédit que ce taux devrait être très petit, de l’ordre de 0.1% à 0.01% (avec une assez grande marge d’erreur ici). LHCb mesure −0.82% ± 0.21% (incertitude statistique) ± 0.11% (incertitude systématique), soit 3.5 déviations standards par rapport à zéro. En d’autres mots, si toutes les sources d’incertitude expérimentale ont bien été prises en compte, il y aurait seulement 0.05% de chances que ce résultat soit dû au hasard. D’autres groupes expérimentaux avaient aussi détecté une petite anomalie mais avec une précision bien moindre que le résultat présent, une réussite en soi.

Est-ce que cela signifie qu’on a prouvé pour la première fois que le modèle standard est incorrect? Pas encore. Il faut d’abord s’assurer que cet effet persistera une fois que toutes les données accumulées en 2011 auront été analysées, ce qui devrait être fait pour mars 2012. Seulement 60% des données ont été incluses pour cette analyse.

Comme me l’a dit Mat Charles, un des quatre physiciens impliqués dans cette mesure: “Ce pourrait être le premier indice que quelque chose d’intéressant se passe. Ça vaut donc vraiment le coup de pousser plus loin”. Ils ont l’intention d’essayer une méthode différente pour identifier mésons et antimésons charmés en partant de désintégrations de mésons plus lourds, des mésons B, ceux contenant le quark b ou beauté, juste pour être certains. Espérons qu’ils seront chanceux. Une telle découverte serait un immense pas en avant.

Pauline Gagnon

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