We use the worldline formalism to derive integral representations for three classes of amplitudes in scalar field theory: (i) the scalar propagator exchanging N momenta with a scalar background field (ii) the “half-ladder” with N rungs in x-space (iii) the four-point ladder with N rungs in x-space as well as in (off-shell) momentum space. In each case we give a compact expression combining the N! Feynman diagrams contributing to the amplitude. As our main application, we reconsider the well-known case of two massive scalars interacting through the exchange of a massless scalar. Applying asymptotic estimates and a saddle-point approximation to the N-rung ladder plus crossed ladder diagrams, we derive a semi-analytic approximation formula for the lowest bound state mass in this model.
Integral representations combining ladders and crossed-ladders / F. Bastianelli; A. Huet; C. Schubert; R. Thakur; A. Weber. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - ELETTRONICO. - 07(2014):(2014), pp. 07(2014)066.1-07(2014)066.29. [10.1007/JHEP07(2014)066]
Integral representations combining ladders and crossed-ladders
BASTIANELLI, FIORENZO;
2014
Abstract
We use the worldline formalism to derive integral representations for three classes of amplitudes in scalar field theory: (i) the scalar propagator exchanging N momenta with a scalar background field (ii) the “half-ladder” with N rungs in x-space (iii) the four-point ladder with N rungs in x-space as well as in (off-shell) momentum space. In each case we give a compact expression combining the N! Feynman diagrams contributing to the amplitude. As our main application, we reconsider the well-known case of two massive scalars interacting through the exchange of a massless scalar. Applying asymptotic estimates and a saddle-point approximation to the N-rung ladder plus crossed ladder diagrams, we derive a semi-analytic approximation formula for the lowest bound state mass in this model.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.