Quark mass effects in high energy neutrino nucleon scattering

We evaluate the neutrino nucleon charged current cross section at next-to-leading order in quantum chromodynamic corrections in the variable flavor number scheme and the fixed flavor number scheme, taking into account quark masses. The number scheme dependence is largest at the highest energies considered here, $10^{12}$ GeV, where the cross sections differ by approximately 15 percent. We illustrate the numerical implications of the inconsistent application of the fixed flavor number scheme.Comment: 8 pages, 8 figures, v2: updated pdfs, version accepted for publicatio

Target Mass Corrections to Electro-Weak Structure Functions and Perturbative Neutrino Cross Sections

We provide a complete and consistent framework to include subasymptotic perturbative as well as mass corrections to the leading twist (tau=2) evaluation of charged and neutral current weak structure functions and the perturbative neutrino cross sections. We revisit previous calculations in a modern language and fill in the gaps that we find missing for a complete and ready-to-use "NLO xi-scaling" formulary. In particular, as a new result we formulate the mixing of the partonic and hadronic structure function tensor basis in the operator approach to deep inelastic scattering. As an underlying framework we follow the operator product expansion a la Georgi & Politzer that allows the inclusion of target mass corrections at arbitrary order in QCD and we provide explicit analytical and numerical results at NLO. We compare this approach with a simpler collinear parton model approach to xi-scaling. Along with target mass corrections we include heavy quark mass effects as a calculable leading twist power suppressed correction. The complete corrections have been implemented into a Monte Carlo integration program to evaluate structure functions and/or integrated cross sections. As applications, we compare the operator approach with the collinear approximation numerically and we investigate the NLO and mass corrections to observables that are related to the extraction of the weak mixing angle from a Paschos-Wolfenstein-like relation in neutrino-iron scattering. We expect that the interpretation of neutrino scattering events in terms of oscillation physics and electroweak precision physics will benefit from our results.Comment: 26 pages, 5 figures, note added, to appear in PR

Nonparametric Stochastic Volatility

Using recent advances in the nonparametric estimation of continuous-time processes under mild statistical assumptions as well as recent developments on nonparametric volatility estimation by virtue of market microstructure noise-contaminated high-frequency asset price data, we provide (i) a theory of spot variance estimation and (ii) functional methods for stochastic volatility modelling. Our methods allow for the joint evaluation of return and volatility dynamics with nonlinear drift and diffusion functions, nonlinear leverage effects, jumps in returns and volatility with possibly state-dependent jump intensities, as well as nonlinear risk-return trade-offs. Our identification approach and asymptotic results apply under weak recurrence assumptions and, hence, accommodate the persistence properties of variance in finite samples. Functional estimation of a generalized (i.e., nonlinear) version of the square-root stochastic variance model with jumps in both volatility and returns for the S&P500 index suggests the need for richer variance dynamics than in existing work. We find a linear specification for the variance's diffusive variance to be misspecified (and inferior to a more flexible CEV specification) even when allowing for jumps in the variance dynamics.Spot variance, stochastic volatility, jumps in returns, jumps in volatility, leverage effects, risk-return trade-offs, kernel methods, recurrence, market microstructure noise.

Ultrahigh energy neutrinos, small x and unitarity

The ultrahigh energy cross section for neutrino interactions with nucleons is reviewed, and unitarity constraints are discussed. We argue that existing QCD extrapolations are self-consistent, and do not imply a breakdown of the perturbative expansion in the weak coupling.Comment: 5 pages, 2 figures, RevTeX4, contribution to Snowmass 200