Kinematical singularities, crossing matrix and kinematical constraints for two-body helicity amplitudes

Cohen-Tannoudji, Gilles; Morel, A.; Navelet, H.

doi:10.1016/0003-4916(68)90243-1

Cited by 258 publications

(51 citation statements)

References 14 publications

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“…The vacuum state functional for a theory with a Hamiltonian operator (2) is assumed to take the approximate form (8) where | vac) is given by (8), /(x,y) is given by (10), and the complex-valued c-number function ipix) is to be determined. By applying the Rayleigh-Ritz procedure to the energy functionality associated with (15), (16) we find that \j/(x) must satisfy the relativistic wave equation^…”

Section: Stationary States In the Modelmentioning

confidence: 99%

Relativistic Particle-Antiparticle Stationary States in a Model Quantum Field Theory: Mesons from Quarks

Rosen

1968

Phys. Rev.

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Relativistic two-quantum particle-antiparticle bound states and scattering states are derived in a renormalized complex scalar field theory model which features a Heisenberg-type self-interaction term Xo(^V)^ in the Lagrangian. The analysis is based on the Rayleigh-Ritz procedure for functionalities-a nonperturbative solutional method requiring the assumption that physically reasonable stationary states exist in the model. It is shown that the mass of a particle-antiparticle bound state can be one or more orders of magnitude less than the mass associated with a one-particle state. This property of the model suggests that a Heisenberg-type theory for a self-interacting quark spinor field may yield a physically realistic quark-antiquark meson with a mass one or two orders of magnitude less than the mass of a constituent quark.

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Section: Stationary States In the Modelmentioning

confidence: 99%

Relativistic Particle-Antiparticle Stationary States in a Model Quantum Field Theory: Mesons from Quarks

Rosen

1968

Phys. Rev.

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“…So far reactions involving two body states with two 1 − particles have not been dealt with. The technique applied in this work has been used previously in studies of two-body scattering systems with photons, pions and nucleons [5,[16][17][18][19][20][21][22][23][24]. A possibly related approach is by Chung and Friedrich [25,26].…”

Section: Introductionmentioning

confidence: 99%

On kinematical constraints in boson-boson systems

Lutz

Vidaña

2012

Eur. Phys. J. A

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We consider the scattering of two-bosons with negative parity and spin 0 or 1. Starting from helicity partial-wave scattering amplitudes we derive transformations that eliminate all kinematical constraints. Such amplitudes are expected to satisfy partial-wave dispersion relations and therefore provide a suitable basis for data analysis and the construction of effective field theories. Our derivation relies on a decomposition of the various scattering amplitudes into suitable sets of invariant functions. A novel algebra was developed that permits the efficient computation of such functions in terms of computer algebra codes.

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“…Considering the fact that ei"''=V .da(P,Pa, P2) 1 = vs(sin f}_a, 2 _)-1 (cos~J-1 , at .ds (P, Pa, P2) = 0. A similar procedure can be made at .d3 C!,.Pa, Pi) =0 (i=3, 4) and finally we get the helicity amplitude by combining the result of 3A):(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) This is free from kinematical singularities at .d8 (P, Pa, Pi) =. 0 (i = 1, 2, 3, 4).…”

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confidence: 97%

The Crossing Matrix, Kinematical Singularities and Reggeization for the Six-Body Helicity Amplitude

Inagaki

1973

Prog. Theor. Phys.

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We treat the six-body helicity amplitude of massive particles and study its various properties including crossing relations, kinematical singularities and Reggeizations. We also apply them to the one-particle inclusive reaction and the inclusive polarization and obtain many interesting results which cannot be seen in four-body case. § I. IntroductionThe differential cross section for the one-particle inclusive production 111 the inclusive reaction1s proportional to the discontinuity of the six-body forward scattering amplitude a+b+c~a+b+c across the cut of the missing mass variable Mi. If particles in the reaction (1·1) have spins, it should be possible to measure experimentally various polarizations}l• 2 l For instance, we can define the proton target asymmetry E for the reaction as follows:where 7! + P ~7! + anythingand H;.~'4";•l (sab• t, Mi) is the six-body forward helicity amplitude for· n+ P+ 7!~ n+ p + 7! in the physical region, sab>O, Mi>O and t

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Kinematical singularities, crossing matrix and kinematical constraints for two-body helicity amplitudes

Cited by 258 publications

References 14 publications

Relativistic Particle-Antiparticle Stationary States in a Model Quantum Field Theory: Mesons from Quarks

Relativistic Particle-Antiparticle Stationary States in a Model Quantum Field Theory: Mesons from Quarks

On kinematical constraints in boson-boson systems

The Crossing Matrix, Kinematical Singularities and Reggeization for the Six-Body Helicity Amplitude

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