Il Nuovo Cimento (1955-1965)

, Volume 32, Issue 1, pp 103–121 | Cite as

On the masses and lifetimes of unstable particles

  • H. P. Stapp


Apparent ambiguities of definitions of masses and lifetimes of unstable particles that depend either on the introduction of unperturbed Hamiltonians and their eigenstates, or on an assumed correspondence between resonances and elementary fields, are noted. TheS-matrix definition is unambiguous; the positions of poles in the first unphysical sheets are given by the zeros of the Fredholm denominator function, which is a function only of an appropriate center-of-mass energy. The mass and lifetime of a particle are consequently independent of the variables of the scattering process or of the particular process to which the particle contributes. The invariance of the Fredholm denominator under charge conjugation, which is a consequence of CPT invariance, ensures the equality of masses and lifetimes of relatively conjugate antiparticles. Unstable particles are closely akin to stable ones; by the factorization of the residues of unstable-particle poles, unstable-particle scattering functions quite analogous to ordinary scattering functions can be unambiguously defined. Like ordinary scattering functions they are defined only on the mass shell, the fixed masses of the unstable particles being well-defined complex numbers. The needed factorizability of the residue is an immediate consequence of Fredholm’s second theorem. The continuation, by means of unitarity, through the multiparticle physical cuts onto unphysical sheets is discussed.


Si fanno notare apparenti ambiguità nella definizione delle masse e vite medie delle particelle instabili, che dipendono o dalla introduzione di hamiltoniani non perturbati e dai loro autostati, o da una supposta corrispondenza fra risonanze e campi elementari. La definizione della matriceS è priva di ambiguità; le posizioni dei poli nei primi foglietti non fisici sono date dagli zeri della funzione denominatore di Fredholm, che è funzione solo di un’appropriata energia nel centro di massa. La massa e la vita media di una particella sono conseguentemente indipendenti dalle variabili del processo di scattering o del particolare processo al quale la particella contribuisce. L’invarianza del denominatore di Fredholm rispetto alla coniugazione della carica, che è una conseguenza dell’invarianza CPT, assicura l’eguaglianza delle masse e vite medie di anti-particelle reciprocamente coniugate. Le particelle instabili sono strettamente simili a quelle stabili; fattorizzando i residui dei poli delle particelle instabili, si possono definire in modo privo di ambiguità funzioni di scattering delle particelle instabili del tutto analoghe alle funzioni di scattering ordinarie. Come le funzioni di scattering ordinarie esse sono definite solo sul guscio di massa, essendo le masse fisse delle particelle instabili numeri complessi ben definiti. La necessaria fattorizzabilità del residuo è una conseguenza immediata del secondo teorema di Fredholm. Ricorrendo all’unitarietà, si discute la continuazione su foglietti non fisici per mezzo di tagli fisici a molte particelle.


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Copyright information

© Società Italiana di Fisica 1964

Authors and Affiliations

  • H. P. Stapp
    • 1
  1. 1.Lawrence Radiation LaboratoryUniversity of CaliforniaBerkeley

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