On shell and off shell

Summary

In physics, particularly in quantum field theory, configurations of a physical system that satisfy classical equations of motion are called "on the mass shell" or simply more often on shell; while those that do not are called "off the mass shell", or off shell. In quantum field theory, virtual particles are termed off shell because they do not satisfy the energy–momentum relation; real exchange particles do satisfy this relation and are termed on shell (mass shell). In classical mechanics for instance, in the action formulation, extremal solutions to the variational principle are on shell and the Euler–Lagrange equations give the on-shell equations. Noether's theorem regarding differentiable symmetries of physical action and conservation laws is another on-shell theorem. Mass shell Mass shell is a synonym for mass hyperboloid, meaning the hyperboloid in energy–momentum space describing the solutions to the equation: :E^2 - |\vec{p} ,|^2 c^2 = m_0^2 c^4

Official source

https://en.wikipedia.org/wiki/On_shell_and_off_shell

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This Letter details and discusses the next-to-leading order QCD corrections to t-channel electro-weak W(+)bj production, where finite top-width effects are consistently taken into account. The computation is done within the AMC@NLO framework and includes both resonant and non-resonant contributions as well as interferences between the two. Results are presented for the LHC and compared to those of the narrow-width approximation and effective theory approaches. (C) 2013 Elsevier B.V. All rights reserved.

Elsevier Science Bv2013

Four-lepton production at hadron colliders: aMC@NLO predictions with theoretical uncertainties

Valentin Hirschi, Paolo Torrielli

We use aMC@NLO to study the production of four charged leptons at the LHC, performing parton showers with both HERWIG and PYTHIA6. Our underlying matrix element calculation features the full next-to-leading order O(alpha(S)) result and the O(alpha(2)(S)) contribution of the gg channel, and it includes all off-shell, spin-correlation, virtual-photon-exchange, and interference effects. We present several key distributions together with the corresponding theoretical uncertainties. These are obtained through a process-independent technique that allows aMC@NLO to compute scale and PDF uncertainties in a fully automated way and at no extra CPU-time cost.

2012

Heavy vector triplets: bridging theory and data

Duccio Pappadopulo, Andrea Thamm, Riccardo Torre, Andrea Wulzer

We introduce a model-independent strategy to study narrow resonances which we apply to a heavy vector triplet of the Standard Model (SM) group for illustration. The method is based on a simplified phenomenological Lagrangian which reproduces a large class of explicit models. Firstly, this allows us to derive robust model-independent phenomenological features and, conversely, to identify the peculiarities of different explicit realizations. Secondly, limits on sigma x BR can be converted into bounds on a few relevant parameters in a fully analytic way, allowing for an interpretation in any given explicit model. Based on the available 8TeV LHC analyses, we derive current limits and interpret them for vector triplets arising in weakly coupled (gauge) and strongly coupled (composite) extensions of the SM. We point out that a model-independent limit setting procedure must be based on purely on-shell quantities, like sigma x BR. Finite width effects altering the limits can be considerably reduced by focusing on the on-shell signal region. We illustrate this aspect with a study of the invariant mass distribution in di-lepton searches and the transverse mass distribution in lepton-neutrino final states. In addition to this paper we provide a set of online tools available at a dedicated webpage [1].

Springer2014