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 S, to obtain the energy probability distribution, called dSp(E), as the imagin...
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Wiley
2018-01-01
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| Series: | Advances in High Energy Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/4672051 |
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| author | Francesco Giacosa |
| author_facet | Francesco Giacosa |
| author_sort | Francesco Giacosa |
| collection | DOAJ |
| description | 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 dSp(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: aSp(t)=∫mth2+p2∞dEdSp(E)e-iEt (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 aSp(t)=∫mth∞dmdS0(m)e-imth2+p2t [here, dS0(m)≡dS(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. |
| format | Article |
| id | doaj-art-e971255fec2c43a6b533a326e8b26de9 |
| institution | Kabale University |
| issn | 1687-7357 1687-7365 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
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| series | Advances in High Energy Physics |
| spelling | doaj-art-e971255fec2c43a6b533a326e8b26de92025-02-03T01:31:40ZengWileyAdvances in High Energy Physics1687-73571687-73652018-01-01201810.1155/2018/46720514672051QFT Derivation of the Decay Law of an Unstable Particle with Nonzero MomentumFrancesco Giacosa0Institute of Physics, Jan-Kochanowski University, Ul. Swietokrzyska 15, 25-406 Kielce, PolandWe 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 dSp(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: aSp(t)=∫mth2+p2∞dEdSp(E)e-iEt (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 aSp(t)=∫mth∞dmdS0(m)e-imth2+p2t [here, dS0(m)≡dS(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.http://dx.doi.org/10.1155/2018/4672051 |
| spellingShingle | Francesco Giacosa QFT Derivation of the Decay Law of an Unstable Particle with Nonzero Momentum Advances in High Energy Physics |
| title | QFT Derivation of the Decay Law of an Unstable Particle with Nonzero Momentum |
| title_full | QFT Derivation of the Decay Law of an Unstable Particle with Nonzero Momentum |
| title_fullStr | QFT Derivation of the Decay Law of an Unstable Particle with Nonzero Momentum |
| title_full_unstemmed | QFT Derivation of the Decay Law of an Unstable Particle with Nonzero Momentum |
| title_short | QFT Derivation of the Decay Law of an Unstable Particle with Nonzero Momentum |
| title_sort | qft derivation of the decay law of an unstable particle with nonzero momentum |
| url | http://dx.doi.org/10.1155/2018/4672051 |
| work_keys_str_mv | AT francescogiacosa qftderivationofthedecaylawofanunstableparticlewithnonzeromomentum |