Particle theory

Abstract:

Lund diagrams, a theoretical representation of the phase space within jets, have long been used in discussing parton showers and resummations. We point out that they can be created for individual jets through repeated Cambridge/Aachen declustering, providing a powerful visual representation of the radiation within any given jet. Concentrating here on the primary Lund plane, we outline some of its analytical properties, highlight its scope for constraining Monte Carlo simulations and comment on its relation with existing observables such as the $z_g$ variable and the iterated soft-drop multiplicity. We then examine its use for boosted electroweak boson tagging at high momenta. It provides good performance when used as an input to machine learning. Much of this performance can be reproduced also within a transparent log-likelihood method, whose underlying assumption is that different regions of the primary Lund plane are largely decorrelated. This suggests a potential for unique insight and experimental validation of the features being used by machine-learning approaches.

Abstract:

We identify a set of transforms on the Picard lattice of non-singular complex projective surfaces that map effective line bundles to nef line bundles, while preserving the dimension of the zeroth cohomology. These transforms can often be used in conjunction with vanishing theorems to compute the dimension of the zeroth cohomology in terms of a topological index. The method is illustrated on del Pezzo and Hirzebruch surfaces.

Abstract:

Adopting the Standard Halo Model (SHM) of an isotropic Maxwellian velocity distribution for dark matter (DM) particles in the Galaxy, the most stringent current constraints on their spin-dependent scattering cross-section with nucleons come from the IceCube neutrino observatory and the PICO-60 C$_3$F$_8$ superheated bubble chamber experiments. The former is sensitive to high energy neutrinos from the self-annihilation of DM particles captured in the Sun, while the latter looks for nuclear recoil events from DM scattering off nucleons. Although slower DM particles are more likely to be captured by the Sun, the faster ones are more likely to be detected by PICO. Recent N-body simulations suggest significant deviations from the SHM for the smooth halo component of the DM, while observations hint at a dominant fraction of the local DM being in substructures. We use the method of Ferrer et al. (2015) to exploit the complementarity between the two approaches and derive conservative constraints on DM-nucleon scattering. Our results constrain $\sigma_{\mathrm{SD}} \lesssim 10^{-39} \mathrm{cm}^2$ ($10^{-38} \mathrm{cm}^2$) at $\gtrsim 90\%$ C.L. for a DM particle of mass 1~TeV annihilating into $\tau^+ \tau^-$ ($b\bar{b}$) with a local density of $\rho_{\mathrm{DM}} = 0.3~\mathrm{ GeV/cm}^3$. The constraints scale inversely with $\rho_{\mathrm{DM}}$ and are independent of the DM velocity distribution.