Mass Production Requires Precision Engineering

This talk is in two parts both entitled mass production requires precision engineering. The first is about the dynamical generation of mass for matter particles in gauge theories. I will explain how the details of this depend on a precision knowledge of the interactions. The second is about tests of the mechanism of chiral symmetry breaking in QCD that the precision engineering of high luminosity colliders and particle detectors will shortly make possible. Since the latter topic has been described in Ref. 1, here I will just discuss the first: the production of mass from nothing. 1 The problem of mass production The Standard Model of the strong, weak and electromagnetic interactions is highly successful at collating and correlating a vast amount of experimental information in terms of a relatively simple Lagrangian. However, this involves a large number of free parameters — parameters that have to be fixed from experiment — the masses of the quarks and leptons and the CKM matrix elements that relate the mass eigenstates to those seen by the charged weak current. In the Standard Model, these are fixed by the couplings to the Higgs. So if we observe the Higgs boson at the LHC, we can measure its couplings to each fermion-antifermion pair and check that these agree with the Standard Model. However, even if these do agree, this won’t explain why they have the couplings they do. This is determined by dynamics beyond the Standard Model, by some interactions we have not yet discovered. This naturally leads us to ask the question when can masses be generated dynamically in a gauge theory? This was asked by Miransky et al. , Maskawa and Nakijima and many others 3 some time ago, building on the even earlier classic papers of Johnson, Baker and Willey . The discussion of this can be made sufficiently straightforward that one can readily answer this question. 1 We ask when can it be that, though the bare masses in the Lagrangian of a gauge interaction are zero, non-zero physical masses are generated? This must be a strong physics problem. It is well-known that if the bare mass is zero, then it remains zero at each order in perturbation theory. Consequently, mass generation must be non-perturbative. The lattice is often claimed to be the way to solve such problems. However, though the lattice nicely regulates the ultra-violet behaviour of the interactions, it is not possible to put massless particles on a finite size lattice. Consequently, lattice calculations have to be performed for a series of non-zero bare masses and then as well as taking the lattice spacing to zero we must extrapolate to zero mass. Whether a dynamical mass results is all in this extrapolation, which can really only be done if one already knows the answer. This makes the continuum the natural place to study such a strong physics problem.