# Subproject B4: Production of unstable particles

Co-operation Partner:

Prof. Dr. M. Beneke

The systematic treatment of unstable particles (narrow resonances) in quantum field theories requires methods that go beyond the standard diagrammatic expansion in the coupling constant. The origin and solution of the problem lie in the existence of two separate scales, mass and width, which allow to construct an effective field theory (EFT). In this project the appropriate EFT has been developed and will be further refined. This EFT as well as the complex mass scheme are employed in parallel to predict quantum corrections to the production and subsequent decay of unstable particles, primarily weak gauge bosons and top quarks, in high-energy collisions.

To properly describe unstable particles in conventional perturbation
theory certain terms in the expansion in the coupling g
must be summed to all orders even when g is small. The question is
which terms must be selected to achieve a systematic approximation
of the production cross section (followed by the decay to a specific
final state, which defines the observable) in powers of
g^{2} and γ/M, where γ denotes the decay width
and M the mass of the unstable particle and where γ/M << 1
is always assumed. In gauge theories there is the additional
complication that the resummation procedure should be gauge-independent.

In high-energy physics (at the Tevatron, the Large Hadron Collider (LHC), and the planned International Linear Collider) the situations of interest are the s-channel production of massive particles (for example, weak gauge bosons, the Higgs particle, and perhaps, new particles in extensions of the Standard Model) or pair production (for instance of W and Z bosons, top quarks, and perhaps, superpartner particles). Both processes are instrumental in determining the masses and couplings of the produced resonances.

The project consists of
two parts: method development and collider-physics phenomenology.
In the first part we pursue the effective field theory approach
to unstable particle production developed earlier in this
project. This method is based on separating the scales M and
γ systematically. After matching, calculating with
the effective Lagrangian accomplishes the
required resummation and automatically constructs
a systematic expansion in g^{2} and γ/M of the
production and decay process including non-resonant processes.
In principle, this approach works to any desired order. So far,
this method has been applied mainly to inclusive quantities. The
focus is now the application of the effective field theory method
to observables with cuts, i.e. to amplitudes and phase-space
integrals as typically required for LHC measurements.

In the second part we consider specific processes with unstable particles where the width is phenomenologically important so that one would like to go beyond the narrow-width approximation. We employ the effective field theory approach or the complex mass scheme whenever one or the other is more suitable to the problem. The analysis of W-boson and top quark pair production, and Higgs production and decay is continued. In addition, we concentrate on radiative corrections including the interference between production and decay of resonances or pairs of resonances in hadron collisions at the LHC.

Last Change: 10th April 2012