Saturday 28 February 2009

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.

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.

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.

Monday 23 February 2009

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.

Saturday 14 February 2009

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.

Tuesday 3 February 2009


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.