Invariant Description of Peripheral Three-particle Final States

We present several implementations of the Metropolis method, an adaptive Monte Carlo algorithm, which allow for the calculation of multi-dimensional integrals over arbitrary on-shell four-momentum phase space. The Metropolis technique reveals itself very suitable for the treatment of high energy processes in particle physics, particularly when the number of final state objects and of kinematic constraints on the latter gets larger. We compare the performances of the Metropolis algorithm with those of other programs widely used in numerical simulations.Comment: 28+3 pages, To appear in Computer Physics Communications. One proof revised, to appear as Erratum in CP

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“…This way, one could benefit from the use of mappings which can cancel the ME singularities (e.g., see eqs. (13) and (14) in Sect. 3.3).…”

Section: Discussionmentioning

confidence: 99%

The Metropolis algorithm for on-shell four-momentum phase space

Kharraziha

Moretti

2000

Computer Physics Communications

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“…. Equations (35) and (36), together with use of the 3-phase space variables of Section IV provide a fully covariant formalism capable of exact treatment of both hadronic and electromagnetic sectors of a given model. Within the physical limitations implicit in a given model, it makes no further assumptions or approximations.…”

Section: B Emission From All Diagramsmentioning

confidence: 99%

“…is the basic three-particle kinematic function [35], which for equal masses (m a = m b = m 1 = m 2 ) has the more familiar form λ(s, m 2 , m 2 ) = s(s − 4m 2 ), and g ab = (2S a + 1)(2S b + 1) is the spin degeneracy factor which for pions is unity. K 1 is the modified Bessel function.…”

Section: Dilepton Ratesmentioning

confidence: 99%

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Dilepton bremsstrahlung from pion-pion scattering in a relativistic one boson exchange model

et al. 1996

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We have made a detailed and quantitative study of dilepton production via bremsstrahlung of a virtual photon during collisions of two free pions. Most calculations of electromagnetic radiation from strong interaction processes rely on the soft photon approximation ͑SPA͒. The conditions underlying this approximation are generally violated when dilepton spectra are calculated in terms of their invariant mass, so that an approach going beyond the SPA becomes necessary. Superseding previous derivations, we derive an exact formula for the bremsstrahlung cross section. The resulting formulation is compared to various forms based on the SPA, the two-particle phase space approximation, and Rückl's formula using a relativistic one boson exchange ͑OBE͒ model. Within the OBE approach, we show that approximations to the bremsstrahlung dilepton cross sections often differ greatly from the exact result; discrepancies become greater both with rising temperature and with invariant mass. Integrated dilepton production rates are overestimated by Rückl-based approximations by factors 1.5-8.0. The largest discrepancies occur for the reaction ϩ ϩ → ϩ ϩ l ϩ l Ϫ , where such approximations overestimate the exact rate by factors ranging from 2 to 30 for invariant masses between 10 and 500 MeV. Our findings, combined with recent estimates of the Landau-Pomeranchuk effect, indicate that bremsstrahlung dilepton rates in ultrarelativistic heavy ion collisions should be even more suppressed than had been thought before.

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“…Some applications of the new identity in high-energy physics are considered, including the possibility of significant shortening of the expressions for the traces of products of 10 and more Dirac γ matrices. 1 We use a metric in which a µ = ( a, a 4 = ia 0 ), ab = a µ b µ = a b − a 0 b 0 .…”

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confidence: 99%