Fun with Fonts: Algorithmic Typography

Over the past decade, we have designed six typefaces based on mathematical theorems and open problems, specifically computational geometry. These typefaces expose the general public in a unique way to intriguing results and hard problems in hinged dissections, geometric tours, origami design, computer-aided glass design, physical simulation, and protein folding. In particular, most of these typefaces include puzzle fonts, where reading the intended message requires solving a series of puzzles which illustrate the challenge of the underlying algorithmic problem.Comment: 14 pages, 12 figures. Revised paper with new glass cane font. Original version in Proceedings of the 7th International Conference on Fun with Algorithm

Renormalization-Group Improvement of Effective Actions Beyond Summation of Leading Logarithms

Invariance of the effective action under changes of the renormalization scale $\mu$ leads to relations between those (presumably calculated) terms independent of $\mu$ at a given order of perturbation theory and those higher order terms dependent on logarithms of $\mu$. This relationship leads to differential equations for a sequence of functions, the solutions of which give closed form expressions for the sum of all leading logs, next to leading logs and subsequent subleading logarithmic contributions to the effective action. The renormalization group is thus shown to provide information about a model beyond the scale dependence of the model's couplings and masses. This procedure is illustrated using the $\phi_6^3$ model and Yang-Mills theory. In the latter instance, it is also shown by using a modified summation procedure that the $\mu$ dependence of the effective action resides solely in a multiplicative factor of $g^2 (\mu)$ (the running coupling). This approach is also shown to lead to a novel expansion for the running coupling in terms of the one-loop coupling that does not require an order-by-order redefinition of the scale factor $\Lambda_{QCD}$. Finally, logarithmic contributions of the instanton size to the effective action of an SU(2) gauge theory are summed, allowing a determination of the asymptotic dependence on the instanton size $\rho$ as $\rho$ goes to infinity to all orders in the SU(2) coupling constant.Comment: latex2e, 30 pages, 2 eps figures embedded in mansucript. v2 corrects several minor errors in equation

Experimental Probes of Localized Gravity: On and Off the Wall

The phenomenology of the Randall-Sundrum model of localized gravity is analyzed in detail for the two scenarios where the Standard Model (SM) gauge and matter fields are either confined to a TeV scale 3-brane or may propagate in a slice of five dimensional anti-deSitter space. In the latter instance, we derive the interactions of the graviton, gauge, and fermion Kaluza-Klein (KK) states. The resulting phenomenological signatures are shown to be highly dependent on the value of the 5-dimensional fermion mass and differ substantially from the case where the SM fields lie on the TeV-brane. In both scenarios, we examine the collider signatures for direct production of the graviton and gauge KK towers as well as their induced contributions to precision electroweak observables. These direct and indirect signatures are found to play a complementary role in the exploration of the model parameter space. In the case where the SM field content resides on the TeV-brane, we show that the LHC can probe the full parameter space and hence will either discover or exclude this model if the scale of electroweak physics on the 3-brane is less than 10 TeV. We also show that spontaneous electroweak symmetry breaking of the SM must take place on the TeV-brane.Comment: 62 pages, Latex, 22 figure

Black Hole Chromosphere at the LHC

If the scale of quantum gravity is near a TeV, black holes will be copiously produced at the LHC. In this work we study the main properties of the light descendants of these black holes. We show that the emitted partons are closely spaced outside the horizon, and hence they do not fragment into hadrons in vacuum but more likely into a kind of quark-gluon plasma. Consequently, the thermal emission occurs far from the horizon, at a temperature characteristic of the QCD scale. We analyze the energy spectrum of the particles emerging from the "chromosphere", and find that the hard hadronic jets are almost entirely suppressed. They are replaced by an isotropic distribution of soft photons and hadrons, with hundreds of particles in the GeV range. This provides a new distinctive signature for black hole events at LHC.Comment: Incorporates changes made for the version to be published in Phys. Rev. D. Additional details provided on the effect of the chromosphere in cosmic ray shower

Phenomenology of Randall-Sundrum Black Holes

We explore the phenomenology of microscopic black holes in the $S^1/Z_2$ Randall-Sundrum (RS) model. We consider the canonical framework in which both gauge and matter fields are confined to the brane and only gravity spills into the extra dimension. The model is characterized by two parameters, the mass of the first massive graviton $(m_1)$, and the curvature $1/\ell$ of the RS anti-de Sitter space. We compute the sensitivity of present and future cosmic ray experiments to various regions of $\ell$ and $m_1,$ and compare with that of Runs I and II at the Tevatron. As part of our phenomenological analysis, we examine constraints placed on $\ell$ by AdS/CFT considerations.Comment: Version to appear in Physical Review D; contains additional analysis on sensitivity of OW

Detecting Microscopic Black Holes with Neutrino Telescopes

If spacetime has more than four dimensions, ultra-high energy cosmic rays may create microscopic black holes. Black holes created by cosmic neutrinos in the Earth will evaporate, and the resulting hadronic showers, muons, and taus may be detected in neutrino telescopes below the Earth's surface. We simulate such events in detail and consider black hole cross sections with and without an exponential suppression factor. We find observable rates in both cases: for conservative cosmogenic neutrino fluxes, several black hole events per year are observable at the IceCube detector; for fluxes at the Waxman-Bahcall bound, tens of events per year are possible. We also present zenith angle and energy distributions for all three channels. The ability of neutrino telescopes to differentiate hadrons, muons, and possibly taus, and to measure these distributions provides a unique opportunity to identify black holes, to experimentally constrain the form of black hole production cross sections, and to study Hawking evaporation.Comment: 20 pages, 9 figure

The fully differential single-top-quark cross section in next-to-leading order QCD

We present a new next-to-leading order calculation for fully differential single-top-quark final states. The calculation is performed using phase space slicing and dipole subtraction methods. The results of the methods are found to be in agreement. The dipole subtraction method calculation retains the full spin dependence of the final state particles. We show a few numerical results to illustrate the utility and consistency of the resulting computer implementations.Comment: 37 pages, latex, 2 ps figure

Nuclear transparency from quasielastic A(e,e'p) reactions uo to Q^2=8.1 (GeV/c)^2

The quasielastic (e,e$^\prime$p) reaction was studied on targets of deuterium, carbon, and iron up to a value of momentum transfer $Q^2$ of 8.1 (GeV/c)$^2$. A nuclear transparency was determined by comparing the data to calculations in the Plane-Wave Impulse Approximation. The dependence of the nuclear transparency on $Q^2$ and the mass number $A$ was investigated in a search for the onset of the Color Transparency phenomenon. We find no evidence for the onset of Color Transparency within our range of $Q^2$. A fit to the world's nuclear transparency data reflects the energy dependence of the free proton-nucleon cross section.Comment: 11 pages, 6 figure

Dark Energy and Gravity

I review the problem of dark energy focusing on the cosmological constant as the candidate and discuss its implications for the nature of gravity. Part 1 briefly overviews the currently popular `concordance cosmology' and summarises the evidence for dark energy. It also provides the observational and theoretical arguments in favour of the cosmological constant as the candidate and emphasises why no other approach really solves the conceptual problems usually attributed to the cosmological constant. Part 2 describes some of the approaches to understand the nature of the cosmological constant and attempts to extract the key ingredients which must be present in any viable solution. I argue that (i)the cosmological constant problem cannot be satisfactorily solved until gravitational action is made invariant under the shift of the matter lagrangian by a constant and (ii) this cannot happen if the metric is the dynamical variable. Hence the cosmological constant problem essentially has to do with our (mis)understanding of the nature of gravity. Part 3 discusses an alternative perspective on gravity in which the action is explicitly invariant under the above transformation. Extremizing this action leads to an equation determining the background geometry which gives Einstein's theory at the lowest order with Lanczos-Lovelock type corrections. (Condensed abstract).Comment: Invited Review for a special Gen.Rel.Grav. issue on Dark Energy, edited by G.F.R.Ellis, R.Maartens and H.Nicolai; revtex; 22 pages; 2 figure

Relativistic calculation of nuclear transparency in (e,e'p) reactions

Nuclear transparency in (e,e'p) reactions is evaluated in a fully relativistic distorted wave impulse approximation model. The relativistic mean field theory is used for the bound state and the Pauli reduction for the scattering state, which is calculated from a relativistic optical potential. Results for selected nuclei are displayed in a Q^2 range between 0.3 and 1.8 (GeV/c)^2 and compared with recent electron scattering data. For Q^2 = 0.3 (GeV/c)^2 the results are lower than data; for higher Q^2 they are in reasonable agreement with data. The sensitivity of the model to different prescriptions for the one-body current operator is investigated. The off-shell ambiguities are rather large for the distorted cross sections and small for the plane wave cross sections.Comment: 8 pages, 3 figure