TY - JOUR
A2 - Kelkar, Neelima G.
AU - Giacosa, Francesco
PY - 2018
DA - 2018/06/26
TI - QFT Derivation of the Decay Law of an Unstable Particle with Nonzero Momentum
SP - 4672051
VL - 2018
AB - 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.
SN - 1687-7357
UR - https://doi.org/10.1155/2018/4672051
DO - 10.1155/2018/4672051
JF - Advances in High Energy Physics
PB - Hindawi
KW -
ER -