Change of variables and equivalence theorems in quantum field theories

We study the deviations from the exponential decay law, both in quantum field theory (QFT) and quantum mechanics (QM), for an unstable particle which can decay in (at least) two decay channels. After a review of general properties of non-exponential decay in QFT and QM, we evaluate in both cases the decay probability that the unstable particle decays in a given channel in the time interval between t and t + dt. An important quantity is the ratio of the probability of decay into the first and the second channel: this ratio is constant in the Breit-Wigner limit (in which the decay law is exponential) and equals the quantity Γ1/Γ2, where Γ1 and Γ2 are the respective tree-level decay widths. However, in the full treatment (both for QFT and QM) it is an oscillating function around the mean value Γ1/Γ2 and the deviations from this mean value can be sizable. Technically, we study the decay properties in QFT in the context of a superrenormalizable Lagrangian with scalar particles and in QM in the context of Lee Hamiltonians, which deliver formally analogous expressions to the QFT case.

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“…A related difficulty is the (in)dependence on the representation choice [24], see also the corresponding discussions in Ref. [14].…”

Section: Vanishing Of P ′ (0) and The Definition Of The 'Zeno-time'mentioning

confidence: 99%

Non-exponential Decay in Quantum Field Theory and in Quantum Mechanics: The Case of Two (or More) Decay Channels

Giacosa

2012

Found Phys

104

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“…(19) scalar fluctuations are automatically canonical. Second, one is free to choose this parametrization of scalar fluctuations: a general theorem [12] guarantees that this different parametrization does not change the physics.…”

Section: An Efficient Way Of Dealing With Scalar Fluctuationsmentioning

confidence: 99%

Scalar loops in little Higgs models

Espinosa¹,

No²

2007

J. High Energy Phys.

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Loops of the scalar particles present in Little Higgs models generate radiatively scalar operators that have been overlooked before in Little Higgs analyses. We compute them using a technique, recently proposed to deal with scalar fluctuations in non-linear sigma models, that greatly simplifies the calculation. In particular models some of these operators are not induced by loops of gauge bosons or fermions, are consistent with the Little Higgs symmetries that protect the Higgs boson mass, and must also be included in the Lagrangian. In general, scalar loops multiplicatively renormalize the tree-level scalar operators,] with large N (e.g. N ∼ 20 for the Littlest Higgs), suggesting a true UV cutoff Λ < ∼ 4πf / √ N significantly below the estimate 4πf of naive dimensional analysis. This can have important implications for the phenomenology and viability of Little Higgs models.

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“…(27) scalar fluctuations are automatically canonical. Second, we are free to choose this parametrization of scalar fluctuations: a general theorem [15] guarantees that this different parametrization does not change the physics. Finally, using eq.…”

Section: Effective Potential (T =0)mentioning

confidence: 99%

Symmetry nonrestoration at high temperature in little Higgs models

2005

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A detailed study of the high temperature dynamics of the scalar sector of Little Higgs scenarios, proposed to stabilize the electroweak scale, shows that the electroweak gauge symmetry remains broken even at temperatures much larger than the electroweak scale. Although we give explicit results for a particular modification of the Littlest Higgs model, we expect that the main features are generic. As a spin-off, we introduce a novel way of dealing with scalar fluctuations in nonlinear sigma models, which might be of interest for phenomenological applications.

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Change of variables and equivalence theorems in quantum field theories

Cited by 180 publications

References 21 publications

Non-exponential Decay in Quantum Field Theory and in Quantum Mechanics: The Case of Two (or More) Decay Channels

Non-exponential Decay in Quantum Field Theory and in Quantum Mechanics: The Case of Two (or More) Decay Channels

Scalar loops in little Higgs models

Symmetry nonrestoration at high temperature in little Higgs models

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