Unitarity and causality in a renormalizable field theory with unstable particles

Veltman, M.J.G.

doi:10.1016/s0031-8914(63)80277-3

Cited by 408 publications

(464 citation statements)

References 10 publications

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“…Taking the imaginary part amounts to performing all possible cuts of the self-energy insertions while the unstable particle is not cut [28]. To obtain the total cross section for a flavourspecific four-fermion final state, only the cuts through these specific fermion lines have to be taken into account.…”

Section: Production Vertex Production-decay Vertices and The Leadingmentioning

confidence: 99%

Four-fermion production near the W pair-production threshold

et al. 2008

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We perform a dedicated study of the four-fermion production process e − e + → µ −ν µ ud X near the W pair-production threshold in view of the importance of this process for a precise measurement of the W boson mass. Accurate theoretical predictions for this process require a systematic treatment of finite-width effects. We use unstable-particle effective field theory (EFT) to perform an expansion in the coupling constants, Γ W /M W , and the non-relativistic velocity v of the W boson up to next-to-leading order in Γ W /M W ∼ α ew ∼ v 2 . We find that the dominant theoretical uncertainty in M W is currently due to an incomplete treatment of initial-state radiation. The remaining uncertainty of the NLO EFT calculation translates into δM W ≈ 10 -15 MeV, and to about 5 MeV with additional input from the NLO four-fermion calculation in the full theory.

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Section: Production Vertex Production-decay Vertices and The Leadingmentioning

confidence: 99%

Four-fermion production near the W pair-production threshold

et al. 2008

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“…The generalized set of diagrams includes 2 n such diagrams if the original diagram had n vertex and sources. These diagrams obey the so-called "largest time equation" [52,53]. If one examines these diagrams before the times at the vertices and sources have been integrated out, and assumes that the vertex or source with the largest time is numbered i, it is easy to prove that…”

Section: Cutting Rulesmentioning

confidence: 99%

Particle production in field theories coupled to strong external sources, I: Formalism and main results

2006

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We develop a formalism for particle production in a field theory coupled to a strong time-dependent external source. An example of such a theory is the Color Glass Condensate. We derive a formula, in terms of cut vacuum-vacuum Feynman graphs, for the probability of producing a given number of particles. This formula is valid to all orders in the coupling constant. The distribution of multiplicities is non-Poissonian, even in the classical approximation. We investigate an alternative method of calculating the mean multiplicity. At leading order, the average multiplicity can be expressed in terms of retarded solutions of classical equations of motion. We demonstrate that the average multiplicity at next-to-leading order can be formulated as an initial value problem by solving equations of motion for small fluctuation fields with retarded boundary conditions. The variance of the distribution can be calculated in a similar fashion. Our formalism therefore provides a framework to compute from first principles particle production in proton-nucleus and nucleus-nucleus collisions beyond leading order in the coupling constant and to all orders in the source density. We also provide a transparent interpretation (in conventional field theory language) of the well known Abramovsky-Gribov-Kancheli (AGK) cancellations. Explicit connections are made between the framework for multi-particle production developed here and the framework of Reggeon field theory.

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“…This is an old well-known problem [16,20]. However, we cannot get rid of the t-channel singularity when we replace the troublesome W + (i) by the well-defined asymptotic state e + ν e and consider instead 3 → 2 or 3 → 3 processes like e + ν e ν e → ν e W + .…”

Section: ))mentioning

confidence: 99%

On gauge invariance of Breit-Wigner propagators

Nowakowski

Pilaftsis

1993

Z. Phys. C - Particles and Fields

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We present an approach to bosonic (Z 0 , W ± ) as well as fermionic (top-quark) Breit-Wigner propagators which is consistent with gauge invariance arguments. In particular, for the Z 0 -boson propagator we extend previous analyses and show that the part proportional to k µ k ν /M 2 must be modified near the resonance. We derive a mass shift which agrees with results obtained elsewhere by different methods. The modified form of a resonant heavy fermion propagator is also given.

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Unitarity and causality in a renormalizable field theory with unstable particles

Cited by 408 publications

References 10 publications

Four-fermion production near the W pair-production threshold

Four-fermion production near the W pair-production threshold

Particle production in field theories coupled to strong external sources, I: Formalism and main results

On gauge invariance of Breit-Wigner propagators

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