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.

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, Δm2H, is zero. This result leaves the Higgs mass lower than the Planck mass.

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 λf. When a Higgs boson couples with an up-quark, λf = +1/2; when it couples with a down-quark, λf = -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.

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 μHuHd, 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.