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Section 11: Beyond the Standard Model: New Forces of Nature?

The experiments at the LHC will help extend the reach of our knowledge by being sensitive to new particles around and somewhat above the weak scale. If Nature is kind to us, the collider will reveal physics beyond the Standard Model—information about the underlying structure of the theory. Since the Standard Model requires the Higgs to have a mass below 1,000 GeV, physicists expect that the Higgs will appear at the LHC. Since the LHC will represent a significant jump in collider energy, one might naturally expect that new physics will reveal itself, in addition to the Higgs, as often occurs when experimental sensitivity increases. However, beyond typical expectations, there are compelling theoretical motivations to believe that there are new phenomena lurking just around the corner.

One motivation for physics beyond the Standard Model stems from the quantum effects on the Higgs field. While the Higgs mechanism gives masses to Standard Model particles, the actual calculated value of those masses is dramatically affected by quantum corrections, or Feynman diagrams with loops. When one computes these diagrams, they contribute infinity to the physical value of the mass of the Higgs (and W, Z). So one assumes right away that the Standard Model isn't the whole story. The infinity comes from the fact that a rule for computing these diagrams is to sum up all possible momenta in the loop, up to infinity. A solution to this type of issue in quantum field theory is to assume something significant happens at an energy (say, at energy M), in such a way that you only have to sum up to M. If you do this, the quantum correction to the Higgs mass from diagrams with one loop gives a result around M, suggesting that the mass of the Higgs should be around M, and thus new physics should be discovered at the same energy scale at the Higgs.

Canceling loops in supersymmetry.

Figure 38: Canceling loops in supersymmetry.

Source: © David Kaplan. More info

One example of new physics that could get rid of the infinity in the Higgs mass is to have new particles appear at a mass around the mass of the Higgs such that the additional Feynman diagrams required in the complete calculations cancel the infinities. Such a perfect cancellation would imply a symmetry of couplings. A leading possibility for that symmetry is called "supersymmetry." In supersymmetric field theories, there is a symmetry between particles of different spin—specifically between fermions and bosons. Making the Standard Model supersymmetric would give every particle a "superpartner" with the same mass and couplings, but with a spin that differs by half of a unit. For example, the electron would have a partner with the same mass and charge but zero spin. Supersymmetry cannot be a perfect symmetry of Nature; if it were, we would have discovered both particles and superpartners. But what if the symmetry is "softly" broken, so the superpartners have heavier masses while their couplings still match those of the Standard Model? The soft breaking of supersymmetry would be the source of the mass of the Higgs boson and the energy scale of the Higgs mechanism. Such a model would then predict the discovery of superpartners at the LHC.

This Feynman diagram representing a composite Higgs and top quark is a part of the Higgs mass calculation in a supersymmetric model.

Figure 39: This Feynman diagram representing a composite Higgs and top quark is a part of the Higgs mass calculation in a supersymmetric model.

Source: © David Kaplan. More info

As discussed in the previous section, the supersymmetric version of the Standard Model predicts the unification of couplings. That is because the superpartners have an effect on the coupling strengths at short distances. An additional motivation for supersymmetry comes from the fact that most versions of the theory predict the existence of a stable, uncharged, weakly interacting particle. Using known and inferred information about the evolution of the universe, one can predict the abundance of these stable particles in our galaxy and beyond. Such estimates seem to predict amounts consistent with the amount of dark matter in the universe, which will be explored in Unit 10.

Another possibility is that the Higgs boson is a composite particle. If a new strong force existed at the 1 TeV scale, the Higgs could naturally have a mass of 100 GeV—and the loop diagrams would no longer be fundamental, and by their rules, would not require summing momenta up to infinity. The electroweak scale would then be populated with hadrons of the new force and its associated quarks. In the extreme limit of this model (and the original version from the late 1970s), the confinement of the new strong color force itself breaks the electroweak symmetry, or causes the condensation that gives mass to the W, Z, and the rest of the fermions, and no Higgs exists. Such a model is disfavored by precision data on the Z boson due to corrections from the new physics. The original name for this type of model is "technicolor."

An extra dimension can curl up in a manner that is nearly impossible to discern for an inhabitant of the larger, uncurled dimensions.

Figure 40: An extra dimension can curl up in a manner that is nearly impossible to discern for an inhabitant of the larger, uncurled dimensions.

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A more exotic-sounding possibility for new physics is extra dimensions. We experience particle physics (and life) entirely in four dimensions—three space and one time—up to energy scales of around 1,000 GeV, which correspond to length scales of about 0.00000000000000002 centimeters, or 2 x 10-17 centimeters. However, because gravity is so weak, physicists have not tested it at distances shorter than 100 microns. Why is this important? Extra dimensions could be finite in size and curled up, like the circular direction on a cylinder. Thus, one or more extra dimensions could exist within which gravity operates, but the Standard Model particles and the other fundamental forces, while remaining four-dimensional, live only on the boundary. Such extra dimensions could thus be as large as 100 microns. Tests of gravity at this scale are discussed in Unit 3. The extra dimensions would dilute gravity in such a way that experiments at the LHC could directly test quantum gravity, as described in Unit 4.

The Standard Model particles could be confined to the surface of a membrane, while gravity is free to leak into other dimensions.

Figure 41: The Standard Model particles could be confined to the surface of a membrane, while gravity is free to leak into other dimensions.

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Theorists have also imagined an extra dimension that is warped. The warping would allow four dimensional gravity to be weak while the total of five dimensions produces a quantum gravity theory at 1 TeV of energy. In this type of case, the LHC will probe a strongly coupled theory that is not four dimensional gravity. This can be understood by a revolutionary speculation, made by Argentine theorist Juan Maldacena in 1997, that certain four dimensional quantum field theories without gravity are equivalent to string theories with gravity in a larger number of dimensions. We will come to this remarkable conjecture in Unit 4. It implies future discoveries at the LHC similar to those of a new strong force.

Where we are now, with the near completion of the Standard Model, is simply a step along the way. Physicists hope that the LHC will shed light on the next step, or on the deeper principles at play not immediately visible with current data. But what we learn at the energy frontier will not simply teach us more information about matter and the vacuum—it will better guide us towards the questions we should be asking.