A Soft-Wall Dilaton

We study the properties of the dilaton in a soft-wall background using two solutions of the Einstein equations. These solutions contain an asymptotically AdS metric with a nontrivial scalar profile that causes both the spontaneous breaking of conformal invariance and the generation of a mass gap in the particle spectrum. We first present an analytic solution, using the superpotential method, that describes a CFT spontaneously broken by a finite dimensional operator in which a light dilaton mode appears in the spectrum. This represents a tuning in the vanishing of the quartic coupling in the effective potential that could be naturally realised from an underlying supersymmetry. Instead, by considering a generalised analytic scalar bulk potential that quickly transitions at the condensate scale from a walking coupling in the UV to an order-one $\beta$-function in the IR, we obtain a naturally light dilaton. This provides a simple example for obtaining a naturally light dilaton from nearly-marginal CFT deformations in the more realistic case of a soft-wall background.Comment: 23 pages, 8 figures; v2: version published in JHE

Independently Parameterised Momenta Variables and Monte Carlo IR Subtraction

We introduce a system of parameters for the Monte Carlo generation of Lorentz invariant phase space that is particularly well-suited to the treatment of the infrared divergences that occur in the most singular, Born-like configurations of $1\to n$ QCD processes. A key feature is that particle momenta are generated independently of one another, leading to a simple parameterisation of all such IR limits. We exemplify the use of these variables in conjunction with the projection to Born subtraction technique at next-to-next-to-leading order. The geometric origins of this parameterisation lie in a coordinate chart on a Grassmannian manifold.Comment: 16 pages; v2: version published in JHE

Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system

Tipping points associated with bifurcations (B-tipping) or induced by noise (N-tipping) are recognized mechanisms that may potentially lead to sudden climate change. We focus here a novel class of tipping points, where a sufficiently rapid change to an input or parameter of a system may cause the system to "tip" or move away from a branch of attractors. Such rate-dependent tipping, or R-tipping, need not be associated with either bifurcations or noise. We present an example of all three types of tipping in a simple global energy balance model of the climate system, illustrating the possibility of dangerous rates of change even in the absence of noise and of bifurcations in the underlying quasi-static system.Comment: 20 pages, 8 figure

LHC Search for Right-handed Neutrinos in Z′Z^\prime Models

We consider right-handed neutrino pair production in generic $Z^\prime$ models. We propose a new, model-independent analysis using final states containing a pair of same-sign muons. A key aspect of this analysis is the reconstruction of the RH neutrino mass, which leads to a significantly improved sensitivity. Within the $U(1)_{(B-L)_{3}}$ model, we find that at the HL-LHC it will be possible to probe RH neutrino masses in the range $0.2\lesssim M_{N_R} \lesssim 1.1\,$TeV.Comment: 6 pages, 5 figure

Transport effects on the MHD stability of pinches

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Low-temperature thermochronology and thermokinematic modeling of deformation, exhumation, and development of topography in the central Southern Alps, New Zealand

Apatite and zircon (U-Th)/He and fission track ages were obtained from ridge transects across the central Southern Alps, New Zealand. Interpretation of local profiles is difficult because relationships between ages and topography or local faults are complex and the data contain large uncertainties, with poor reproducibility between sample duplicates. Data do form regional patterns, however, consistent with theoretical systematics and corroborating previous observations: young Neogene ages occur immediately southeast of the Alpine Fault (the main plate boundary structure on which rocks are exhumed); partially reset ages occur in the central Southern Alps; and older Mesozoic ages occur further toward the southeast. Zircon apparent ages are older than apatite apparent ages for the equivalent method. Three-dimensional thermokinematic modeling of plate convergence incorporates advection of the upper Pacific plate along a low-angle detachment then up an Alpine Fault ramp, adopting a generally accepted tectonic scenario for the Southern Alps. The modeling incorporates heat flow, evolving topography, and the detailed kinetics of different thermochronometric systems and explains both complex local variations and regional patterns. Inclusion of the effects of radiation damage on He diffusion in detrital apatite is shown to have dramatic effects on results. Geometric and velocity parameters are tuned to fit model ages to observed data. Best fit is achieved at 9 mm a−1 plate convergence, with Pacific plate delamination on a gentle 10°SE dipping detachment and more rapid uplift on a 45–60° dipping Alpine Fault ramp from 15 km depth. Thermokinematic modeling suggests dip-slip motion on reverse faults within the Southern Alps should be highest ∼22 km from the Alpine Fault and much lower toward the southeast

A Lower Bound for the First Passage Time Density of the Suprathreshold Ornstein-Uhlenbeck Process

We prove that the first passage time density $\rho(t)$ for an Ornstein-Uhlenbeck process $X(t)$ obeying $dX=-\beta X dt + \sigma dW$ to reach a fixed threshold $\theta$ from a suprathreshold initial condition $x_0>\theta>0$ has a lower bound of the form $\rho(t)>k \exp\left[-p e^{6\beta t}\right]$ for positive constants $k$ and $p$ for times $t$ exceeding some positive value $u$. We obtain explicit expressions for $k, p$ and $u$ in terms of $\beta$, $\sigma$, $x_0$ and $\theta$, and discuss application of the results to the synchronization of periodically forced stochastic leaky integrate-and-fire model neurons.Comment: 15 pages, 1 figur