Minimal Supersymmetric Standard Model

The hunt for supersymmetry: Reviewing the first run – 2

I’d linked to a preprint paper [PDF] on arXiv a couple days ago that had summarized the search for Supersymmetry (Susy) from the first run of the Large Hadron Collider (LHC). I’d written to one of the paper’s authors, Pascal Pralavorio at CERN, seeking some insights into his summary, but unfortunately he couldn’t reply by the time I’d published the post. He replied this morning and I’ve summed them up.

Pascal says physicists trained their detectors for “the simplest extension of the Standard Model” using supersymmetric principles called the Minimal Supersymmetric Standard Model (MSSM), formulated in the early 1980s. This meant they were looking for a total of 35 particles. In the first run, the LHC operated at two different energies: first at 7 TeV (at a luminosity of 5 fb^-1), then at 8 TeV (at 20 fb^-1; explainer here). The data was garnered from both the ATLAS and CMS detectors.

In all, they found nothing. As a result, as Pascal says, “When you find nothing, you don’t know if you are close or far from it!”

His paper has an interesting chart that summarized the results for the search for Susy from Run 1. It is actually a superimposition of two charts. One shows the different Standard Model processes (particle productions, particle decays, etc.) at different energies (200-1,600 GeV). The second shows the Susy processes that are thought to occur at these energies.

Cross sections of several SUSY production channels, superimposed with Standard Model process at s = 8 TeV. The right-handed axis indicates the number of events for 20/fb.

The cross-section of the chart is the probability of an event-type to appear during a proton-proton collision. What you can see from this plot is the ratio of probabilities. For example, stop-stop* (the top quark’s Susy partner particle and anti-particle, respectively) production with a mass of 400 GeV is 10¹⁰ (10 billion) less probable than inclusive di-jet events (a Standard Model process). “In other words,” Pascal says, it is “very hard to find” a Susy process while Standard Model processes are on, but it is “possible for highly trained particle physics” to get there.

Of course, none of this means physicists aren’t open to the possibility of there being a theory (and corresponding particles out there) that even Susy mightn’t be able to explain. The most popular among such theories is “the presence of a “possible extra special dimension” on top of the three that we already know. “We will of course continue to look for it and for supersymmetry in the second run.”

On the shoulders of the Higgs

On July 4, 2012, when CERN announced that a particle that looked a lot like the Higgs boson had been spotted, the excitement was palpable. A multibillion-dollar search for an immensely tiny particle had paid off, and results were starting to come in.

On March 6, 2013, when CERN announced through a conference in Italy that the particle was indeed the Higgs boson and that there were only trivial indications as to otherwise, there was closure. Textbook-writers and philosophers alike could take the existence of the Higgs boson for granted. People could move on.

The story should’ve ended there.

It would’ve, too, but for a theory in particle physics that many physicists aren’t quite fond of, called the Standard Model.

For particle physicists, everything in the universe is made up of extremely tiny particles. Even the protons, neutrons and electrons that make up atoms are made up of tinier particles even though we don’t encounter them or their effects in our daily lives.

And those tiny particles, of tinier particles, until particle physicists are satisfied they’ve hit upon the “stuff” of the universe, as it were.

This “stuff”, physicists have found, comes in three types: Leptons, bosons and quarks. They are the ingredients of the universe and everything within it.

Leptons are the lightest of the lot. One example of the lepton is a neutrino, whose mass is so low that it has no problems travelling at very near to the speed of light.

Bosons are the force-carriers. When two particles exert a force on each other, particle physicists imagine that they’re simple exchanging bosons. What kind of boson is being exchanged throws light on the nature of the acting force. Examples include the massless photon, the W and Z bosons, and gluons.

Quarks are the proverbial building blocks of matter. They come in six types, each called a flavour. Unlike leptons and bosons, quarks can be stuck together using gluons to form heavier composite particles. For example, two up-flavoured quarks and one down-flavoured quark together make up the proton.

In the universe as a cauldron, these ingredients come together to make up different phenomena we perceive around us. While each particle sticks to its properties while mixing with others, its behavior is continuously modified by other particles around it. If there are too many particles in the fray, which is natural, matters can get complex for physicists studying them. But after studying them over long periods of time, they found that there are patterns and a few rules that aren’t ever broken.

The set of all these patterns and rules is called the Standard Model. In fact, the Higgs boson was the last remaining piece of this framework, and now that it’s been found, the Model is good as true.

So far, so good.

Where the Model really flounders is when physicists asked why it was the way it was. Why are there six quarks and not five or seven, why are there three kinds of leptons – electron, muon, tau – and now two or four, why can one quark only always be found in the company of another quark and never alone… such questions were just the beginning.

These are the real questions that physicists want the answers to – the ultimate “why” is the goal of all scientific studies.

Many pinned their hopes on CERN’s Large Hadron Collider (LHC), which led the search for the Higgs boson by smashing protons together and open at high energies to see if a Higgs boson popped out. Based on preliminary calculations and simulations, they speculated that something more significant would pop out with the Higgs boson.

There has been nothing so far, i.e. the frustratingly familiar Standard Model is all we have.

But physicists took heart. “The Model is all we have… for now,” they said. Every time a new ingredient of the universe was hoped for and there was none, physicists only believed the hypothetical particle didn’t exist at the energy they were combing through.

Like this, with only negative results to show over hundreds of trials across a swath of energies, physicists have put together a stack of upper and lower limits between which new particles, crucial to the future of particle physics, can be spotted.

A good place to start was that the conditions for these “new” ingredients all were tied in with the conditions in which the Higgs boson could show itself. So, the converse must also be true: the conditions in which the Higgs boson showed itself could contain traces of the conditions for “new physics” to show itself. All physicists would have to do is ask the right questions.

One example is an instance of the fermiophobic Higgs. Because it’s so heavy and energetic, the Higgs boson quickly breaks down into lighter particles like photons, W and Z bosons, leptons and quarks. Of them, leptons and quarks are collectively titled fermions. True to its name, a fermiophobic Higgs doesn’t decay into fermions.

As a result, it will have to decay into the other kinds of particles more often. While they had the resources, physicists were able to determine that a fermiophobic Higgs didn’t exist in the energy range 110-124.5 GeV, 127-147.5 GeV, and 155-180 GeV with 99 per cent confidence.

Another example, this one more favoured in the scientific community, is called suppersymmetry, SUSY for short. Its adherents posit that for every fermion, there is a heavier partnering boson that we haven’t found yet, and vice versa, too. Thus, the Higgs boson has a hypothetical partnering fermion, tentatively called the Higgsino.

When physicists tried to incorporate the rules of SUSY into the Standard Model, they saw that five Higgs bosons would be necessary to explain away some problems. Of these, three would be neutral, and collectively denoted as Φ, and two would be charged, denoted H+ and H-. Moreover, the Φ Higgs would have to decay into two particular kinds of quarks a whopping 90 per cent of the time.

While running experiments to verify this decay rate, tragedy struck: the Standard Model stood in the way. It predicts that the Higgs will decay into the two quarks only 56.1 per cent of the time… And the results swore by it.

The never-say-die faith persisted: Now, physicists wait for 2015, when the LHC will reawaken with doubled energy, possibly bringing them closer to the very high energies at which SUSY might be thriving.

There are other models like these, such as one that suggests there are hidden fermions we haven’t found yet and one that suggests that the Higgs boson decays to lighter, undetected versions of itself before coming into a form we can study. But until 2015, they will be the stuff of science fiction, the Standard Model will rule as a tolerable tyrant, and we will be no closer to understanding the stuff of the universe.

What’s allowed and disallowed in the name of SUSY

The International Conference on High Energy Physics (ICHEP) is due to begin on July 7 in Melbourne. This is the 26th episode of the most prestigious scientific conference on particle physics. In keeping with its stature, scientists from the ATLAS and CMS collaborations at the LHC plan to announce the results of preliminary tests conducted to look for the Higgs boson on July 4. Although speculations still will run rife within the high-energy and particle physics communities, they will be subdued; after all, nobody wants to be involved in another OPERAtic fiasco.

Earlier this year, CERN announced that the beam energy at the LHC would be increased from 3.5 TeV/beam to 4 TeV/beam. This means the collision energy will see a jump from 7 TeV to 8 TeV, increasing the chances of recreating the elusive Higgs boson, the “God particle”, and confirming if the Standard Model is able to explain the mechanism of mass formation in this universe. While this was the stated goal when the LHC was being constructed, another particle physics hypothesis was taking shape that lent itself to the LHC’s purpose.

In 1981, Howard Georgi and Savas Dimopoulos proposed a correction to the Standard Model to solve for what is called the hierarchy problem. Specifically, the question is why the weak force (mediated by the W± and Z bosons) is 10³² times stronger than gravity. Both forces are mediated by natural constants: Fermi’s constant for the weak force and for gravity, Newton’s constant. However, when operations of the Standard Model are used to quantum-correct for Fermi’s constant (a process that involves correcting for errors), its value starts to deviate from closer to Newton’s constant to something much, much higher.

Desktop1 — Savas Dimopoulos (L) and Howard Georgi

Even by the late 1960s, the propositions of the Standard Model were cemented strongly enough into the psyche of mathematicians and scientists the world over: it had predicted with remarkable accuracy most naturally occurring processes and had predicted the existence of other particles, too, discovered later at detectors such as the Tevatron, ATLAS, CMS, and ZEUS. In other words, it was inviolable. At the same time, there were no provisions to correct for the deviation, indicating that there could be certain entities – particles and forces – that were yet to be discovered and that could solve the hierarchy problem, and perhaps explain the nature of dark matter, too.

So, the 1981 Georgi-Dimopoulos solution was called the Minimal Supersymmetric Standard Model (MSSM), a special formulation of supersymmetry, first proposed in 1966 by Hironari Miyazawa, that paired particles of half-integer spin with those of integer spin and vice versa. (The spin of a particle is the quantum mechanical equivalent of its orbital angular momentum, although one has never been representative of the other. Expressed in multiples of the reduced Planck’s constant, particle spin is denoted in natural units as simply an integer or half-integer.)

Particles of half-integer spin are called fermions and include leptons and quarks. Particles with integer spin are called bosons and comprise photons, the W± and Z bosons, eight gluons, and the hypothetical, scalar boson named after co-postulator Peter Higgs. The principle of supersymmetry (SUSY) states that for each fermion, there is a corresponding boson, and for each boson, there is a corresponding fermion. Also, if SUSY is assumed to possess an unbroken symmetry, then a particle and its superpartner will have the same mass. The superpartners are yet to be discovered, and if anyone has a chance of finding them, it has to be at the LHC.

MSSM solved for the hierarchy problem, which could be restated as the mass of the Higgs boson being much lower than the mass at which new physics appears (Planck mass), by exploiting the effects of what is called the spin-statistics theorem (SST). SST implies that the quantum corrections to the Higgs-mass-squared will be positive if from a boson, and negative if from a fermion. Along with MSSM, however, because of the existence of a superpartner to every particle, the contribution to the correction, Δm²_H, is zero. This result leaves the Higgs mass lower than the Planck mass.

extra_dimension — The existence of extra dimensions has been proposed to explain the hierarchy problem. However, the law of parsimony, insofar as SUSY seems validatable, prevents physicists from turning so radical.

MSSM didn’t just stabilize the weak scale: in turn, it necessitated the existence of more than one Higgs field for mass-coupling since the Higgs boson would have a superpartner, the fermionic Higgsino. For all other particles, though, particulate doubling didn’t involve an invocation of special fields or extrinsic parameters and was fairly simple. The presence of a single Higgsino in the existing Higgs field would supply an extra degree of freedom (DoF), leaving the Higgs mechanism theoretically inconsistent. However, the presence of two Higgsinos instead of one doesn’t lead to this anomaly (called the gauge anomaly).

The necessity of a second Higgs field was reinforced by another aspect of the Higgs mechanism: mass-coupling. The Higgs boson binds stronger to the heavier particle, which means that there must be a coupling constant to describe the proportionality. This was named after Hideki Yukawa, a Japanese theoretical physicist, and termed λ_f. When a Higgs boson couples with an up-quark, λ_f = +1/2; when it couples with a down-quark, λ_f = -1/2. SUSY, however, prohibits this switch to the value’s complex conjugate (a mass-reducing move), and necessitates a second Higgs field to describe the interactions.

higgs2 — A “quasi-political” explanation of the Higgs mechanism surfaced in 1993 and likened the process to a political leader entering a room full of party members. As she moved through the room, the members moved out of their evenly spaced “slots” and towards her, forming a cluster around her. The speed of the leader was then restricted because there were always a knot of people around her, and she became slowed (like a heavy particle). Finally, as she moved away, the members returned to their original positions in the room.

The MSSM-predicted superpartners are thought to have masses 100- to 1,000-times that of the proton, and require extremely large energies to be recreated in a hadronic collision. The sole, unambiguous way to validate the MSSM theory is to spot the particles in a laboratory experiment (such as those conducted at CERN, not in a high-school chemistry lab). Even as the LHC prepares for that, however, there are certain aspects of MSSM that aren’t understood even theoretically.

The first is the mu problem (that arises in describing the superpotential, or mass, of the Higgsino). Mu appears in the term μH_uH_d, and in order to perfectly describe the quantum vacuum expectation value of the Higgsino after electroweak symmetry breaking (again, the Higgsino’s mass), mu’s value must be of that order of magnitude close to the electroweak scale (As an analog of electroweak symmetry breaking, MSSM also introduces a soft SUSY-breaking, the terms of which must also be of the order of magnitude of the electroweak scale). The question is whence these large differences in magnitudes, whether they are natural, and if they are, then how.

The second is the problem of flavour mixing. Neutrinos and quarks exhibit a property called flavours, which they seem to change through a mechanism called flavour-mixing. Since no instances of this phenomenon have been observed outside the ambit of the Standard Model, the new terms introduced by MSSM must not interfere with it. In other words, MSSM must be flavour-invariant, and, by an extension of the same logic, CP-invariant.

Because of its involvement in determining which particle has how much mass, MSSM plays a central role in clarifying our understanding of gravity as well as, it has been theorized, in unifying gravity with special relativity. Even though it exists only in the theoretical realm, even though physicists are attracted to it because its consequences seem like favourable solutions, the mathematics of MSSM does explain many of the anomalies that threaten the Standard Model. To wit, dark matter is hypothesized to be the superpartner of the graviton, the particle that mediates the gravitational force, and is given the name gravitino (Here’s a paper from 2007 that attempts to explain the thermal production of gravitinos in the early universe).

While the beam energies were increased in pursuit of the Higgs boson after CERN’s landmark December 13, 2011 announcement, let’s hope that the folks at ATLAS, CMS, ALICE, and other detectors have something to say about opening the next big chapter in particle physics, the next big chapter that will bring humankind one giant leap closer to understanding the universe and the stuff that we’re made of.