## Theoretical Particle Physics

### Michael Vaughn

Emeritus Professor

PhD Purdue University, 1960

(617)373-2954

m.vaughn@neu.edu

### Research Summary:

Most recently, Professor Vaughn has written a graduate-level text/reference work entitled “Introduction to Mathematical Physics”, published by Wiley-VCH. The important new feature of this book is the introduction of differential forms and other geometrical concepts early on. There are also introductions to nonlinear problems, and to group theory, and a reduced emphasis on the special functions that arise in the solution of Laplace’s equation and its relatives.

In the late 1990s, Prof. Vaughn worked with Prof. Robert Markiewicz in studying the role of higher symmetries in condensed matter physics, especially in the theory of the cuprate high Tc superconductors and other quasi-two-dimensional condensed matter systems. Earlier, he worked with several collaborators, notably Steve Martin (an NU post-doc at the time) and Marie Machacek (NU Professor Emerita), on deriving two-loop beta-functions for the Yukawa and scalar quartic couplings in gauge field theories of elementary particles.

Analysis based on the renormalization group (RG) has played an important role in the development of quantum chromodynamics and grand unified gauge theories, in addition to finding useful applications in the theory of critical phenomena and phase transitions. My own interest is mainly in the application of RG methods to the phenomenology of unified gauge theories and their supersymmetric extensions. Data from LEP suggestsed that if there is ultimately a unified theory of all elementary particle interactions, supersymmetry will be an essential feature of this theory. With the imminent startup of the LHC, we eagerly await new experimental data that will provide critical tests for the presence of supersymmetry.

In any case, it will be necessary to rely heavily on renormalization group methods to extrapolate from present experimental energy scales in the range 100 GeV to 1 TeV, and up to a few TeV at the LHC, to the superheavy scales in the range 10^{14} to 10^{19} GeV at which unification is expected to occur.

### Selected Publications:

Michael T Vaughn, “Introduction to Mathematical Physics”, Wiley – VCH (2007).

R. S. Markiewicz, M. T. Vaughn, “Stripe Disordering Transition”, (cond-mat/9903422); R.S. Markiewicz, C. Kusko, and M.T. Vaughn, “SO(6)-Generalized Pseudogap Model of the Cuprates”, (cond-mat/9903421), (U. of Miami Conference on High Temperature Superconductivity, Miami, FL, Jan. 7-13, 1999 — HTS99; R.S. Markiewicz and M. T. Vaughn, “Stripes, pseudogaps, and SO(6) in the cuprate superconductors”, J. Phys. Chem. Sol. 59, 1737 (1998) (cond-mat/9709137).

R. S. Markiewicz and M. T. Vaughn, “Higher Symmetries in Condensed Matter Physics”, in Particles, Strings and Cosmology — PASCOS98, P. Nath (ed.) , World Scientific (Singapore, 1999) (cond-mat/9809119).

S. P. Martin and M. T. Vaughn, “Two-Loop Renormalization Group Equations for Soft Supersymmetry-Breaking Couplings”, Phys. Rev. D50, 3537 (1994); “Regularization Dependence of Running Couplings in Softly Broken Supersymmetry”, Phys. Lett. B318, 331 (1993).

M. E. Machacek and M. T. Vaughn, “Two-Loop Renormalization Group Equations in a General Quantum Field Theory I. Wave Function Renormalization”, Nucl. Phys. B222, 83 (1983); “… II. Yukawa Couplings”, *ibid.* B236, 221 (1984); “… III. Scalar Quartic Couplings”, *ibid.* B249, 83 (1985).