We show that hadron colliders have an excellent reach for positivity tests on a class of diphoton operators. Due to the helicity selection rules, the relevant dimension-6 operators either do not contribute or are highly constrained by other experimental observables. We demonstrate, for the first time, that the LHC can probe the positivity of the dimension-8 operators involving colored particles. The kinematic differential distributions of the diphoton final states are utilized to perform the $ \chi^2$ analysis. Through a global fit, the effective scale for these operators can be inclusively probed up to around 2 TeV at HL-LHC and over 5 TeV at future 100 TeV FCC-hh at 95% C.L., providing a powerful test of the positivity bounds up to the multi-TeV scale.

United States

Zhen Liu

Kun-Feng Lyu

Tong Arthur Wu

LHC shines on positivity * Zhen Liu and Kun-Feng Lyu are supported in part by U.S. Department of Energy (DESC0011842); Zhen Liu is also supported in part by a Sloan Research Fellowship from the Alfred P. Sloan Foundation at the University of Minnesota

<p>Symmetry under a particular class of nonstrictly canonical transformation may be used to identify, and subsequently excise degrees of freedom which do not contribute to the closure of the algebra of dynamical observables. Such redundant degrees of freedom may physically be identified with empirically inaccessible measures of global scale. In this article, we present a mathematical framework which extends the symmetry reduction procedure to theories of classical fields, in both the Lagrangian and Hamiltonian settings. In order to maintain Lorentz covariance, while simultaneously working with a finite-dimensional phase space, we employ the De Donder-Weyl formalism, for which the natural description is formulated in terms of the fibered manifolds of multisymplectic geometry. We subsequently analyze a number of simple examples, and provide a discussion of the broader implications of our construction.</p>

United Kingdom

Callum Bell

David Sloan

Dynamical similarity in multisymplectic field theory

Abstract Recently, lattice formulations of Abelian chiral gauge theory in two dimensions have been devised on the basis of the Abelian bosonization. A salient feature of these 2D lattice formulations is that the gauge invariance is exactly preserved for anomaly-free theories and thus is completely free from the question of the gauge mode decoupling. In the present paper, we propose yet another lattice formulation sharing this desired property. A particularly unique point in our formulation is that the vertex operator of the dual scalar field, which carries the vector charge of the fermion and the “magnetic charge” in the bosonization, is represented by a “hole” excised from the lattice; this is the excision method formulated recently by Abe et al. in a somewhat different context.

Japan

Okuto Morikawa

Soma Onoda

Hiroshi Suzuki

Yet Another Lattice Formulation of 2D (1) Chiral Gauge Theory via Bosonization David Tong: lectures on gauge theory

All measurements are comparisons. The only physically accessible degrees of freedom (DOFs) are dimensionless ratios. The objective description of the universe as a whole thus predicts only how these ratios change collectively as one of them is changed. Here we develop a description for classical Bianchi IX cosmology implementing these relational principles. The objective evolution decouples from the volume and its expansion degree of freedom. We use the relational description to investigate both vacuum dominated and quiescent Bianchi IX cosmologies. In the vacuum dominated case the relational dynamical system predicts an infinite amount of change of the relational DOFs, in accordance with the well known chaotic behaviour of Bianchi IX. In the quiescent case the relational dynamical system evolves uniquely though the point where the decoupled scale DOFs predict the big bang/crunch. This is a non-trivial prediction of the relational description; the big bang/crunch is not the end of physics – it is instead a regular point of the relational evolution. Describing our solutions as spacetimes that satisfy Einstein's equations, we find that the relational dynamical system predicts two singular solutions of GR that are connected at the hypersurface of the singularity such that relational DOFs are continuous and the orientation of the spatial frame is inverted.

Mexico

Tim A. Koslowski

Canada

Italy

Flavio Mercati

Through the big bang: Continuing Einstein's equations beyond a cosmological singularity