QFT derivation of the decay law of an unstable particle with nonzero momentum

  • We present a quantum field theoretical derivation of the nondecay probability of an unstable particle with nonzero three-momentum p. To this end, we use the (fully resummed) propagator of the unstable particle, denoted as Sto obtain the energy probability distribution, called dpS(E), as the imaginary part of the propagator. The nondecay probability amplitude of the particle S with momentum p turns out to be, as usual, its Fourier transform: ... (mth is the lowest energy threshold in the rest frame of S and corresponds to the sum of masses of the decay products). Upon a variable transformation, one can rewrite it as ... [here, ... is the usual spectral function (or mass distribution) in the rest frame]. Hence, the latter expression, previously obtained by different approaches, is here confirmed in an independent and, most importantly, covariant QFT-based approach. Its consequences are not yet fully explored but appear to be quite surprising (such as the fact that the usual time-dilatation formula does not apply); thus its firm understanding and investigation can be a fruitful subject of future research.

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Author:Francesco GiacosaORCiDGND
Parent Title (English):Advances in high energy physics
Place of publication:New York, NY
Contributor(s):Neelima G. Kelkar
Document Type:Article
Year of Completion:2018
Date of first Publication:2018/06/26
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2019/08/15
Issue:Art. 4672051
Page Number:8
First Page:1
Last Page:7
Copyright © 2018 Francesco Giacosa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.
Institutes:Physik / Physik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Licence (German):License LogoCreative Commons - Namensnennung 4.0