In:
Advances in High Energy Physics, Hindawi Limited, Vol. 2018 ( 2018-06-26), p. 1-7
Abstract:
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 S , to obtain the energy probability distribution, called d S p ( 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: a S p ( t ) = ∫ m t h 2 + p 2 ∞ d E d S p ( E ) e - i E t ( m t h 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 a S p ( t ) = ∫ m t h ∞ d m d S 0 ( m ) e - i m t h 2 + p 2 t [here, d S 0 ( m ) ≡ d S ( m ) 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.
Type of Medium:
Online Resource
ISSN:
1687-7357
,
1687-7365
DOI:
10.1155/2018/4672051
Language:
English
Publisher:
Hindawi Limited
Publication Date:
2018
detail.hit.zdb_id:
2389407-6
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