### Research — Dynamical electroweak symmetry breaking and the origin of mass

While the energy of strong QCD interactions is responsible for the vast majority of the mass of composite particles, a small fraction comes from the masses of elementary particles themselves. The elementary particles, such as the quarks and electrons highlighted in the picture below, are those objects that do not yet exhibit any signs of substructure. So far as our best experiments can determine, elementary particles are points of zero size. Many of them possess nonzero masses, however, the origin of which is a longstanding mystery in particle physics.

More than 50 years ago, physicists realized that a fundamental symmetry of nature (the electroweak unification of electromagnetism and the weak nuclear force) appeared to be incompatible with the existence of massive elementary particles. This difficulty was overcome in the 1960s with the discovery that the electroweak symmetry can be hidden (or "spontaneously broken"), a process popularly known as the Higgs mechanism. While the generic picture of electroweak symmetry breaking (EWSB) has been strongly supported by experiments since the 1970s, the physics underlying this process remains unknown. Understanding EWSB is a central challenge in particle physics today, and is the main goal of the Large Hadron Collider at CERN, the European Organization for Nuclear Research.

A theoretically-elegant explanation of electroweak symmetry breaking relies on the existence of some new force (call it "technicolor") that becomes strongly-interacting at distance scales some 1000 times smaller than characteristic scale of QCD. That is, if we imagine pulling apart two hypothetical technifermions that feel this force, we would need 10 tons of force to separate them by as little as an attometer (10^{-18} m), compared to the femtometer scale of QCD mentioned in the first paragraph on this page.

As you can guess from the discussion above, theories of electroweak symmetry breaking through new strong dynamics are analytically intractable due to their reliance on strong interactions. As a result, although these theories were introduced in the 1970s, we do not yet know whether they can successfully explain the origin of mass. Using numerical lattice field theory to study new strong dynamics may seem intuitively obvious. However, lattice studies relevant to EWSB are more computationally demanding than the corresponding lattice QCD investigations, and have only started to become practical in the last few years.

My work in this field so far has been carried out as a member of both the Lattice Strong Dynamics (LSD) Collaboration and the US BSM Collaboration of USQCD. With the LSD Collaboration, I have explored how the behavior of strongly-interacting theories changes depending on how many types of light fermions feel the corresponding force [arXiv:0910.2224, arXiv:1002.3777]. Only two light quarks (the up and down quarks) feel the strong nuclear force, a very small number. As more fermions feel a force, the low-energy (long-distance) behavior of the corresponding interaction changes dramatically.

A particularly important observable to investigate this way is known as the *S* parameter [arXiv:1009.5967]. In the absence of direct evidence revealing the physics responsible for electroweak symmetry breaking (which the Large Hadron Collider may discover), decades of effort have been dedicated to using precise measurements of electroweak observables to constrain possible theories of EWSB. *S* parameterizes this information, and provides the tightest constraints on theories of new strong dynamics.

However, because physicists were previously unable to perform quantitatively-reliable non-perturbative calculations of strongly-interacting theories, they often studied theories of new strong dynamics by assuming that these theories closely resemble QCD, and therefore can be related to experimental measurements of the strong nuclear force. Because of how the behavior of strongly-interacting theories changes depending on how many types of light fermions feel the corresponding force, this approach is only applicable to a subset of possible models.

Experimentally, the *S* parameter is small and negative, *S ≈ -0.15 ± 0.10*. If QCD were used to model new strong dynamics, as discussed above, it would imply *S > 0.3*, in considerable disagreement with experiment. This corresponds to the red points in the plot below, which I calculated using lattice QCD and published in arXiv:1009.5967. The blue points come from calculations of new strong dynamics with three times as many light fermions as QCD. For this model, we find that *S* can be significantly smaller than for QCD, much closer to the experimental value.

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Last modified 6 September 2015