Rationale for UV-filtered clover fermions

We study the contributions Sigma_0 and Sigma_1, proportional to a^0 and a^1, to the fermion self-energy in Wilson's formulation of lattice QCD with UV-filtering in the fermion action. We derive results for m_{crit} and the renormalization factors Z_S, Z_P, Z_V, Z_A to 1-loop order in perturbation theory for several filtering recipes (APE, HYP, EXP, HEX), both with and without a clover term. The perturbative series is much better behaved with filtering, in particular tadpole resummation proves irrelevant. Our non-perturbative data for m_{crit} and Z_A/(Z_m*Z_P) show that the combination of filtering and clover improvement efficiently reduces the amount of chiral symmetry breaking -- we find residual masses am_{res}=O(10^{-2}).Comment: 25 pages, 4 figures; v2: typo in eqn. (37) fixed [agrees with published version

Quasi-exactly solvable quartic potential

A new two-parameter family of quasi-exactly solvable quartic polynomial potentials $V(x)=-x^4+2iax^3+(a^2-2b)x^2+2i(ab-J)x$ is introduced. Until now, it was believed that the lowest-degree one-dimensional quasi-exactly solvable polynomial potential is sextic. This belief is based on the assumption that the Hamiltonian must be Hermitian. However, it has recently been discovered that there are huge classes of non-Hermitian, ${\cal PT}$-symmetric Hamiltonians whose spectra are real, discrete, and bounded below [physics/9712001]. Replacing Hermiticity by the weaker condition of ${\cal PT}$ symmetry allows for new kinds of quasi-exactly solvable theories. The spectra of this family of quartic potentials discussed here are also real, discrete, and bounded below, and the quasi-exact portion of the spectra consists of the lowest $J$ eigenvalues. These eigenvalues are the roots of a $J$th-degree polynomial.Comment: 3 Pages, RevTex, 1 Figure, encapsulated postscrip

Pseudosmooth Tribrid Inflation

We explore a new class of supersymmetric models of inflation where the inflaton is realised as a combination of a Higgs field and (gauge non-singlet) matter fields, using a "tribrid" structure of the superpotential. Inflation is associated with a phase transition around GUT scale energies. The inflationary trajectory already preselects the later vacuum after inflation, which has the advantage of automatically avoiding the production of dangerous topological defects at the end of inflation. While at first sight the models look similar to smooth inflation, they feature a waterfall and are therefore only pseudosmooth. The new class of models offers novel possibilities for realising inflation in close contact with particle physics, for instance with supersymmetric GUTs or with supersymmetric flavour models based on family symmetries.Comment: 16 pages, 5 figures. v2 matches publication in JCA

On non-gaussianities in single-field inflation

We study the impact of higher dimension operators in the inflaton Lagrangian on the non-gaussianity of the scalar spectrum. These terms can strongly enhance the effect without spoiling slow-roll, though it is difficult to exceed f_NL ~ 1, because the scale which suppresses the operators cannot be too low, if we want the effective field theory description to make sense. In particular we explicitly calculate the 3-point function given by an higher derivative interaction of the form (\nabla\phi)^4, which is expected to give the most important contribution. The angular dependence of the result turns out to be quite different from the minimal case without higher dimension operators.Comment: 10 page

The effects of aging of scientists on their publication and citation patterns

The average age at which U.S. researchers get their first grant from NIH has increased from 34.3 in 1970, to 41.7 in 2004. These data raise the crucial question of the effects of aging on the scientific creativity and productivity of researchers. Those who worry about the aging of scientists usually believe that the younger they are the more creative and productive they will be. Using a large population of 13,680 university professors in Quebec, we show that, while scientific productivity rises sharply between 28 and 40, it increases at a slower pace between 41 and 50 and stabilizes afterward until retirement for the most active researchers. The average scientific impact per paper decreases linearly until 50-55 years old, but the average number of papers in highly cited journals and among highly cited papers rises continuously until retirement. Our results clearly show for the first time the natural history of the scientific productivity of scientists over their entire career and bring to light the fact that researchers over 55 still contribute significantly to the scientific community by producing high impact papers.Comment: 12 pages, 4 figure