Inconstant

The funniest April Fools prank was definitely the one about time variation of $\pi$. That idea is of course absurd because the Bible unambiguously sets the value of $\pi$ to be equal three. But the physical constants like the QCD scale or the Fermi constant are not mentioned in the Bible which suggests that they might not be constants. Recently, Harald Fritzsch put on ArXiv a neat status report of various theoretical and experimental pursuits of varying fundamental constants.

For almost a century the idea of varying fundamental constants has been attracting most brilliant minds and complete crackpots alike. At the theoretical level the mechanism is easy to imagine: the physical constants can be set by a vacuum expectation value of a scalar field that evolves on cosmological timescales. In high-energy theory we already have one evolving scalar field for inflation and sometimes another one for quintessence, so that introducing yet another one for varying constants is not that difficult to swallow.

At the beginning of this century the idea has received renewed attention due to some experimental claims that the electromagnetic constant $\alpha$ may vary in time. A group of astrophysicists studying absorption spectra of very distant quasars concluded that 10 billion years ago $\alpha$ was smaller than today by $\Delta \alpha/\alpha \sim 10^{-5}$, corresponding to a time variation of order $10^{-15}$ per year. This claim is very controversial because of various assumptions involved in the determination $\alpha$ and, most of all, because other groups did not confirm this result. A more recent claim that the proton-to-electron mass ratio was different 10 billion years ago also remains highly controversial.

Yet another reason why the above claims are taken with a huge grain of salt is that the so-called Oklo bounds imply a slower variation of $\alpha$. 2 billion years ago, when the Earth was young and beautiful, the uranium-235 isotope was five times more abundant than today. Thanks to that fact and some other lucky coincidences, near the river Oklo in today's Gabon nature could create a fully organic nuclear reactor which operated for 100 million years. The uranium fission produced many rare isotopes, and the particular ratio of Samarium-149 to Samarium-147 can be used to constrain variation of the fundamental constants. The point is that the cross-section for the neutron capture on Samarium 149 is accidentally enhanced by a presence of resonance just 0.1 eV above the threshold. From the fact that the position of this resonance could not migrate by more than 0.1 eV one can set the bound $\Delta \alpha/\alpha \sim 10^{-7}$ (assuming that only the electromagnetic constant is varied) corresponding to a time variation $10^{-16}$ per year. If $\alpha$ was changing faster than that (as suggested by some astrophysical results) it had to stabilize at least two billion years ago.

In the neat future there is hope for more progress from precision measurements in a controlled laboratory environment. Experiments in quantum optics have recently reached a similar sensitivity to varying constants as the astrophysical observations. In particular, Theodor Haensch's group in Munich is running an experiment that studies time variation of the frequency of the 1s-2s transition in atom hydrogen (review here). The measurements from different years are related to the hyperfine transitions of Cesium-133 and to another precision measurement of quadrupole transitions in Mercury, which allows them to constrain the variation of both the electromagnetic constant and the QCD scale. The results published several years ago constrain the variation of both at the level of few times $10^{-15}$ per year.

Actually, Harald Fritzsch is spreading wild rumors that the most recent results from Munich imply the time variation of the QCD scale at the level of $3 \cdot 10^{-15}$ per year. Well, I'd rather bet that at the end of the day the constants will once more turn out to be constants. But who knows...in the end the Hubble constant has changed since the nucleosynthesis by some 17 orders of magnitude.

Dark Matter more like Baryons

April Fools is over; I'm staying dead serious for the rest of the year. The most serious things in the months before the first LHC results are dark matter searches high and low. Here is another idea what they might find.

The most popular scenario for dark matter assumes that it consists of weakly interacting massive particles (WIMPs) who were once in thermal equilibrium. In the early hot and dense universe such a particle can efficiently annihilate into familiar particles like photon or electrons, and in this way dark matter is kept in equilibrium with the the rest of the cosmic plasma. The equilibrium ceases to hold when the temperature T of the universe falls below the dark matter particle mass M. In that regime, the number of dark matter particle very quickly decreases - as an exponential $e^{-M/T}$ - and at some point dark matter freezes out: there isn't enough dark matter particles around that they could find each other and annihilate. The surviving particles float around in the universe playing hide and seek with astronomers and physicists alike.

The WIMP scenario is nice and robust but it sheds little light on the surprising fact that the present abundanceof dark matter $\Omega_{DM}$ is very close to that of the ordinary matter who is today dominated by the baryon (proton and neutrons) abundance $\Omega_{B}$. After WMAP data we are confident that the ratio $\Omega_{DM}/\Omega_B$ is roughly five. Of course, one can always cook up the parameters of the WIMP model such that this constraint is satisfied, but nevertheless the proximity of $\Omega_B$ and $\Omega_{DM}$ is intriguing. It may suggests that baryons and dark matter have a common origin. But baryons are definitely NOT a cold relic!

In fact, we don't know for sure what is the origin of baryons in our universe but we have a bunch of ideas that go under the name of baryogenesis. The general idea is that the very early universe contains an equal number of baryons and antibaryons, but at some point in its evolution the fundamental interactions in the plasma produce a tiny $10^{-10}$ asymmetry between matter and antimatter. Once the temperature falls below the baryon mass most of the baryons and anti-baryons annihilate with each other and turn into the sea of photons, leaving only the small unpaired $10^{-10}$ fraction of baryons. These are the protons and neutrons that make galaxies and stars today.

Is it conceivable that dark matter originates in a similar fashion? That is to say, the early universe contains dark matter and anti dark matter particles which almost completely annihilate away leaving only the small asymmetric fraction? Can the dark asymmetry and the baryon asymmetry have the common origin? The answer to these questions is yes, and the first practical realization I'm aware of is due to David B. Kaplan in early nineties. In that model, the dark matter particle carries a charge under an additional U(1) global symmetry who, much as the U(1) baryon symmetry, has a mixed anomaly with the electroweak SU(2) gauge symmetry. Because of the anomalies, non-perturbative electroweak interactions that are effective in the early universe violate both the baryon number and the dark matter number. Then, if some conditions are satisfied, the electroweak phase transition generates the baryon and the dark asymmetries roughly of the same order. At the end of the day on obtains the relation $\Omega_{DM}/\Omega_B \sim m_{DM}/m_{proton}$ and the experimentally measured ratio is recovered if the dark matter particle's mass is around 5 GeV.

Kaplan's original model is long gone for several reasons, but the idea is still floating in the backchannels of model building. The most recent approach in the context of supersymmetry was made by David E. Kaplan et al (David E. Kaplan is a more recent version of David B. Kaplan with more features). In that model, there's no new quantum number invented especially for the dark matter particle; instead, it carries the lepton (or baryon in another version) quantum number. Furthermore, the model does not rely on electroweak baryogenesis but rather it assumes that the the B - L asymmetry is generated at high energies (for example by leptogenesis). That asymmetry is later redistributed between baryons and dark matter by higher-dimensional interactions. When these interactions fall out of equilibrium, dark matter asymmetry is frozen in and one again ends up with $\Omega_{DM}/\Omega_B \sim m_{DM}/ m_{proton}$. All that remains is to find 5-15 GeV dark matter in the sky, or in colliders or by direct detection...

April Fools'09: No Higgs particle after all?

While the LHC, after initial difficulties, is on the straight path for first collisions the particle physics community has been given yet another bitter pill to swallow. Yesterday at CERN Peter Higgs gave a seminar whose message was really shocking. No more no less, Higgs demonstrated that the famous particle that carries his name cannot exist! He pointed out a mistake in his original '64 paper which did not take into account the topological anomalies of the symmetry group of the Standard Model. He also presented a concise and elegant proof that the existence of the Higgs particle would lead to an instability of the vacuum.

In reply to angry voices from the audience, Higgs said:

Yes i got it wrong back then. I mean, i got it right at first, but then the referee confused me and I added the particle to get the paper published quickly.

Why did Higgs wait more than 40 years to correct his mistake? He explained:

You know, I was flattered - not everybody has his own particle. I thought that sooner or later someone else would point out the mistake anyway. But now there's so much talking of that particle at the LHC that I had to come out to prevent greater disappointment.

Cern theorist John Ellis commented:

This seems unbelievable, but the math is there on the blackboard... I'm afraid Higgs is right this time. The whole story demonstrates how important is to independently verify scientific results rather than to follow fashion. We have learned our lesson.

But is it not too late? If the Higgs particle is not out there, does this make the 5 billion worth LHC accelarator a useless toy? CERN director general Rolf Heuer carefully chooses his words:

One can never predict the course of scientific developments . Important discoveries may arise as side effects of the LHC program, as it happened before with the World Wide Web.

But even in these grim circumstances there are some who see the glass half-full. As someone from the audience pointed out:

At least the Tevatron won't have it either...

Happy April Fools everyone :-)

Dr Jekyll and Mr Higgs

There has been recently a lot of excitement around the world concerning the race for the Higgs. Fermilab now claims that they have 50-50 chance to get a 3 sigma Higgs signal before the LHC, thus providing a modern reenactment of Aesop's The tortoise and the hare. As for me, the prospective discovery itself, although eagerly awaited, is not actually that thrilling. There are compelling theoretical arguments that Higgs does exist (he was recently spotted in Edinburgh opera). Moreover, experiment directly constrains the Higgs mass to be larger than 115 GeV and, indirectly, smaller than some 150 GeV. This leaves a narrow ballpark making the situation somewhat similar to the top-quark discovery. The more exciting question is *which* Higgs will we find. Yes, the God particle has numerous incarnations that answer different prayers of theorists. Here is a brief summary of the most popular Higgs avatars.

Standard Higgs

A perfect guy, to the point of being boring. He does everything he is supposed to do, and perfectly matches all experimental results so far (apart from the small tension with electroweak precision tests). We know everything about him except for the mass. It is believed, however, that left alone and unprotected he would acquire a large mass. This purely theoretical argument prompts most of what follows.

Susy Higgs

The marriage of Susy and Higgs has lasted for more than 30 years. Susy provides stabilization to Higgs, keeping its mass small enough. Sadly enough, bad tongues and the LEP experiment have left deep scars on this relationship. The problem is that the minimal supersymmetric model ties the Higgs boson mass to the Z boson mass. The failure to discover Higgs LEP implies that the parameters of the minimal model must be finely-tuned in order to accommodate the higher mass, thus spoiling the naturalness of the whole construction.

Composite Higgs

Higgs does not have to be that elementary - it is natural to imagine that Higgs is a bound state like many other particles we have observed. For example, it could be a meson made of new quarks glued together by new strong interactions. The problem with this idea is that a simple back-of-a-napkin estimate suggests that the Higgs mass should not be much different from the scale of the new strong interactions. Since we have seen nothing like that up to a few hundreds of GeV, the mass of the composite Higgs would have to be larger, contrary to what electroweak precision tests seem to tell us. Or there must be some more structure that keeps the mass light enough...

Pseudo-Goldstone Higgs

Susy does not have exclusive rights on controlling quantum corrections to the Higgs mass. Particle's masses can also be protected by spontaneously broken global symmetries. A similar mechanism operates in real life and was awarded a Nobel prize last year: thanks to that mechanism the QCD pions remain lighter than the QCD scale. The Higgs boson could also arise as a pseudo-Goldstone boson when a new strong dynamics spontaneously breaks its own global symmetries. But at the end of the day this simple idea does not work as well as it is supposed to. First, the name is unattractive and difficult to pronounciate (worse still, around Chicago it becomes a pseudo-Nambu-Goldstone-boson-Higgs monster). Besides, the new strong interactions meddle with electroweak precision observables, and at the end of the day the fine-tuning is only slightly better than in minimal supersymmetry.

Little Higgs

Little Higgs is a variation on the theme of the pseudo-Goldstone Higgs. The new strong interactions are pushed to higher scales, around 10 TeV, while an additional structure - the so-called collective symmetry breaking - protects that scale separation. While this idea can be made completely realistic and the fine-tuning of parameters can be acceptably small, fully realistic constructions are situated somewhere between late baroque and early racoco.

Fat Higgs

Not that he's very pretty, but he has a cool name. This one combines the ideas of composite Higgs and supersymmetry. A strongly coupled Susy gauge theory sits in the conformal window all the way down till the TeV scale. At that point, due to the fact that some of the flavors have TeV scale masses, the theory drops out of the window and confines. The challenge is make all the numbers work and get rid of all the excess bagagge that comes along.

Invisible Higgs

Could it be that Higgs was at LEP but we missed it? Actually, in models with additional singlet fields it is common that Higgs decays into exotic particles that escape from the detector without being seen. Such a cheap trick would not fool LEP, however, and invisible Higgs is just as well constrained as the standard one. Nevertheless, one can devise more complicated models where Higgs is partly invisible and hides from LEP analyses even though his mass is below 115 GeV.

Unhiggs

Every kid has to go through a negation phase at some point. It may be that Higgs is neither a god nor a particle after all. Instead, it could be a fuzzy continuum of excitations and still perfectly fulfill its role.

Higgsless

Finally one should mention that Higgs might not exist. This athehigsm has some scientific support. Electroweak symmetry can be broken by a condensate in a strongly interacting theory, much as it happens to chiral symmetries in QCD. In that case Higgs is expandable, and his role is played by new resonances whose spin is one rather than zero. That is not as bad as it seems since these new resonances must have masses within the LHC reach to make the picture consistent. Higgsless theories are disfavored by electroweak precision and flavor tests, but the ultimate answer will be given by the LHC. Unless reality is Unhiggsless.

WHO IS GOING TO WIN THE RACE? WILL IT BE HIGGS-THE-PERFECT-BORING-GUY? OR HIGGS' LOVE FOR SUSY WILL OVERCOME THE OBSTACLES? OR MAYBE SOMEONE ELSE WILL MEDDLE IN THE RACE? STAY TUNED FOR THE NEXT EPISODES. To definitely nail down the nature of Higgs we'll probably need to wait for future linear colliders, but some partial answers should be provided in two years from now, if all goes well.

What's up at Susy's?

Remember Sunset Boulevard? An aging star (Susy) who fell from grace (after the LHC) ponders on her past glory, forgotten in a vast mansion (MSSM), attended only by her ex-lover (John Ellis)... Well, we are not exactly at that stage yet -- Susy is still found attractive and is being actively pursued by many. Actually, decadence fosters art: the subject of low energy supersymmetry has recently seen several interesting theoretical developments. I'd like to point out here the latest take on gauge mediated supersymmetry breaking.

Susy predicts tons of new particles whose masses should not be larger than TeV. Although colliders have not yet probed the TeV scale directly, certain precise measurements at lower energies are in principle sensitive to the TeV scale. This is especially true for flavor violating processes, that is the ones that do not conserve generation quantum numbers such as (S)trangenes or (B)eauty. In the Standard Model, the amplitudes for all such processes can be predicted in terms of a few elements of the CKM matrix. Precise studies of the kaon mixing as well as the recent flood of experimental results from the B-factories have confirmed the Standard Model predictions leaving little room for new physics. New particles required by Susy generically violate the flavor symmetries of the Standard Model leading to new large contributions to flavor violating processes. The reason is that, in principle, the mass terms for squarks and slepton masses do not have to respect the approximate flavor symmetries of the Standard Model. In the half-empty approach that is very unfortunate and leads to the conclusion that there can be no Susy at the TeV scale. In the half-full approach that is fortunate as it gives us a clue as to how the supersymmetric particles are organized. The flavor problem strongly hints that something like gauge mediated supersymmetry breaking is at work.

Gauge mediated supersymmetry breaking, proposed back in the early eighties, is a scheme designed to overcome the Susy flavor problem. It assumes that the masses of squarks and sleptons are produced in 3 steps. First, there is a dark sector somewhere out there, in which supersymmetry is broken, perhaps dynamically. Second, there exists a set of fields, called the messengers, who communicate between the dark sector and the MSSM. The messengers couple to the dark sector and directly experience the supersymmetry breaking, so that the masses of the messenger fermions and scalars are different. At the same time, the messengers also couple to the MSSM gauginos and gauge bosons, because they are charged under the Standard Model color and electroweak group. Thanks to that, in the last step supersymmetry breaking masses for the squarks and the sleptons are generated via loop diagrams involving the messenger fields. Because gauge interactions are flavor blind - gauge bosons couple in the same way to all three generation - the squark and slepton masses end up being approximately diagonal in the generation space. A diagonal matrix does not break any symmetries - approximate flavor symmetries of the Standard Model are protected. The world is saved again.

Many of you might be familiar with the minimal gauge mediation model. That model introduces very few free parameters: the scale of gauge mediation and the number of messengers (and some more parameters in the Higgs sector) and for this reason it makes sharp predictions. The most spectacular prediction is that the gravitino is the lightest supersymmetric particle to which all other superparticles ultimately decay. On top of that, minimal gauge mediation predicts specific mass relations among gauginos, squarks, and sleptons.

Minimal models are extremely important from the sociological point of view because they facilitate plotting exclusion limits, which has been the main activity in particle physics in the last 30 years.
At the cognitive level, however, it is interesting to know if gauge mediation makes general predictions that are independent of the particular model of messengers. That's quite relevant for the LHC who should be prepared for all sensible scenarios. There are also theoretical reasons to go beyond the minimal model, as some of its mass relations are troublesome. In particular, the fact that the stop squark is heavier than the lightest slepton by almost a factor of 10 leads to a large fine-tuning undermining the very motivation for supersymmetry.

There has been of course a lot on non-minimal models proposed in the last decades. But only one year ago the paper entitled General Gauge Mediation made an attempt to systematize all consistent realizations of that scheme. It turns out, perhaps unsurprisingly, that the mass relations between superparticles can be completely altered in general gauge mediation. There are however two sum rules for superparticle masses that remain true independently of all detail and, ultimately, these sum rules should allow us to distinguish gauge mediation from other models of supersymmetry breaking. Phenomenological consequences of general gauge mediation are just beginning to be explored, see here for example. The general formulation can be extended to the supersymmetry breaking parameters in the Higgs sector.

Theorists vs multi-muons

There has not been much talking recently about the CDF multi-muon anomaly. Unlike the PAMELA/ATIC cosmic-ray anomaly, the CDF one did not trigger a lot of theoretical activity. There is more than one reason for this shroud of silence. On one hand, even though it is possible to write an ad-hoc particle models that describe various characteristics of the multi-muon signal, it seems hopeless to fit that in a bigger picture. On the other hand, multiple members of the CDF collaboration refer to the multi-muon publication as "that crap" (when being polite), while those who signed it admit the fact with certain embarrassment. Besides, the main author of the analysis is, hmm, a controversial figure, which does not help either (to understand the context, see Tommaso's account of the superjets saga).

Nevertheless, there is always a possibility that the multi-muon anomaly signals genuine new physics rather than mice in the detector, and few theorists try their luck. Today there was a paper on arXiv that sheds some light on the possible production mechanism of the mysterious ghost particles. As explained earlier, the multi-muon signal can be a result of a pair of "ghost" scalar particles with the mass around 15 GeV cascade-decaying into four tau leptons each. But the question how these ghosts particles are produced in the first place was not addressed in the original publications. It turns out that a vialable possibility is to couple the ghost field $\phi$ to the Standard Model quarks q via higher-dimensional operators. The non-renormalizable dimension-5 operator:
$\frac{1}{\Lambda} (\bar q q) \phi^2$
provides a pretty good fit to the invariant mass distribution of the ghost muons, see the plot.
Dimension-six operators involving the ghost fields coupled to quarks or gluons are disfavored.

One can think of this dimension-5 operator as an effective interaction left after integrating out a heavier particle with renormalizable interactions (in analogy to the Fermi theory of weak interactions after integrating out the W boson). For example, what would do here is a heavy doublet field $H_q$ (but not the Higgs!) interacting with the quarks via $Q u H_q$ and with the ghost pair via $H \phi^2$. But there is a tension here. The cross-section for the ghost pair production is required to be very large for the particle physics standard: 200 picobarns or so. To match that, the scale $\Lambda$ suppressing the dimension-5 operator has to be as low as 200 GeV. In consequence, the integrated-out particle cannot be too heavy and there is a danger that it violates some of the known experimental bounds. In particular, it could generate other higher-dimension effective operators, like the four-quark operator $(q q)^2/\Lambda^2$ that would affect dijet distributions at the Tevatron. Surprisingly, unlike four-lepton operators that were extremely well constrained by LEP, there is no strong bounds in the literature on four-quark effective operators (except for the bound on $(Q \gamma_\mu Q)^2/2\Lambda^2$ which is $\Lambda > 700$ GeV, but that's not directly applicable here). Improving the bounds on four-quark operators could clarify the situation and, in fact, would be extremely interesting for many other applications.

Quirks

Back in the old days life was so easy. Everybody knew that the right theory at the TeV scale was the MSSM who in turn was a compactification of the heterotic string theory. One could lead a quite life picking colors for the mSUGRA parameter space. This perfect world began to crumble at the turn of century. At first, the alternative models had the same objective as supersymmetry in mind: to solve the hierarchy problem and explain the lightness of the Higgs boson. But soon the rules got relaxed and everything became allowed. Recently, there has been a lot theoretical activity related to models motivated not by naturalness of electroweak symmetry breaking but rather by exotic collider signatures that are not covered by standard experimental searches. I guess the first example of such unmotivated model was split supersymmetry; unparticles and hidden valleys are more recent examples of this trend. Quirks, advertised in this paper by Junhai Kang and Markus Luty, is the latest addition in that list.

Imagine there is a hidden sector in the form of an SU(N) gauge theory. In addition, the hidden sector contains a quark (vector-like fermion in the fundamental representation of SU(N)) with mass m. Another mass parameter characterizing the gauge theory is the confinement scale $\Lambda$ - the analog of the QCD scale $\Lambda_{QCD}$ - where the hidden gluons and quarks become confined into glueballs, mesons and baryons. So far it looks standard. What distinguishes quirks from the familiar QCD-like dynamics is that the quark mass is much larger than the condensation scale:

$m \gg \Lambda$

and there are no other quarks that are lighter.

Models with such a heavy quark have pretty weird, quirky properties. To understand why, recall what happens in the usual QCD when a quark-antiquark pair is produced. The two quarks would like to fly apart from the collision point but, because of the nature of strong interactions, there is a color flux tube forming between them. This flux tube can be thought of as a string connecting the two quarks - that's what they call confinement. The energy stored in the string is proportional to the distance between the quarks, and to the string tension which is of the order of the QCD confinement scale $\Lambda_{QCD}$. In QCD, the string energy per unit length is large enough to produce a new quark-antiquark pair out of the vacuum. In consequence, the QCD string snaps. The end result is a lot of hadronic junk flying along the directions of the initial quarks that materialize as jets in a detector.

In the case of quirks, the energy of the string per unit length is far too small to rip a pair of new quirks out of the vacuum. Thus, the quirky string does not break. Furthermore, quirks cannot decay to the glueballs, even though the latter are much lighter, because of conserved quantum numbers. Once produced, two quirks are chained together by the string and oscillate back and forth. The typical length of the string is given $m/\Lambda^2$. Plugging in $m = 1$ TeV (so that we can produce quirks at the LHC) and $\Lambda$ between 100 GeV and 100 eV (why not), the length of the string varies from $10^{-17}$m (microscopic) to 10m (detector size!). That's why the experimenters at the LHC wear protective helmets: one may get hit anytime by the loose end of the string.

In order to produce quirks at the LHC, the quirks must be coupled to the Standard Model somehow. The simplest thing to assume is to give quirks the usual electric or color charge, although there are other possibilities. The search strategy also depends on the model assumptions. One phenomenologically important factor is the typical length of the string connecting the quirks.If the string is macroscopic, that is larger than a millimeter (corresponding to $\Lambda <10 a="" and="" annihilates="" annihilation="" antiquirk="" are="" argue="" back="" be="" because="" bound="" br="" brings="" broad.="" brown="" but="" by="" can="" cannot="" case="" collider="" completely="" context="" control="" could="" curvature="" decay="" details="" detector.="" difference="" different="" discovery.="" distribution="" easy="" employed="" event="" exerted="" exotic="" field="" for="" force="" if="" in="" invariant="" is="" kev="" less="" long-lived="" magnetic="" mass="" may="" mean="" microscopic="" millimeter="" muck="" not="" observe="" of="" one="" ordinary="" original="" pair="" particles.="" process="" products="" quirk-antiquirk="" quirk="" quirks="" quite="" rate="" resolve="" search="" separate="" shorter="" signatures="" similar="" so="" spectacular.="" spectacular="" state="" strategy="" string="" strings="" suppressed.="" surrounding="" than="" that="" the="" them="" then="" theoretically="" these="" this="" thus="" to="" together.="" tracks="" two="" ultimately="" varies="" very="" which="" would="">
More details in the paper. See also slides from a recent talk at CERN.