2018/04/08 by Francesco Giacosa, Giacosa, Francesco
Computer Science · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1804.02728
openalex publication_date 2018/04/08 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We present a quantum field theoretical derivation of the nondecay probability\nof an unstable particle with nonzero three-momentum \p. To this end,\nwe use the (fully resummed) propagator of the unstable particle, denoted as\nS, to obtain the energy probability distribution, called dS\p\n(E), as the imaginary part of the propagator. The nondecay probability\namplitude of the particle S with momentum \p turns out to be, as\nusual, its Fourier transform: aS\p(t)=\∫_\√mth\n2+\p2\∞dEdS\p(E)e-iEt (mth is the\nlowest energy threshold in the energy frame, corresponding to the sum of masses\nof the decay products). Upon a variable transformation, one can rewrite it as\naS\p(t)=\∫_mth\∞dmdS\n\0(m)e^-i\√mth2+\p2t [here, dS\n\0(m)\≡ dS(m) is the usual spectral function (or mass\ndistribution) in the rest frame]. Hence, the latter expression, previously\nobtained by different approaches, is here confirmed in an independent and, most\nimportantly, covariant QFT-based approach. Its consequences are not yet fully\nexplored but appear to be quite surprising (such as the fact that usual\ntime-dilatation formula does not apply), thus its firm understanding and\ninvestigation can be a fruitful subject of future research.\n