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A unitary coupled-channel three-body amplitude with pions and kaons
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A unitary coupled-channel three-body amplitude with pions and kaons
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Three-body dynamics above threshold is required for the reliable extraction of many amplitudes and resonances from experiment and lattice QCD. The S-matrix principle of unitarity can be used to construct dynamical coupled-channel approaches in which three particles scatter off each other, re-arranging two-body subsystems by particle exchange. This paper reports the development of a three-body coupled-channel, amplitude including pions and kaons. The unequal-mass amplitude contains two-body S- and P-wave subsystems ("isobars") of all isospins, $I=0,\,1/2,\,1,\, 3/2, \, 2$, and it also allows for transitions within a given isobar. The $f_0(500)\, ("\sigma"),\,f_0(980),\,\rho(700), K_0^*(700)\,("\kappa")$, and $K^*(892)$ resonances are included, apart from repulsive isobars. Different methods to evaluate the amplitude for physical momenta are discussed. Production amplitudes for $a_1$ quantum numbers are shown as a proof of principle for the numerical implementation.
Forward citations
Cited by 8 Pith papers
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Emergence of the $\pi(1300)$ Resonance from Lattice QCD
Lattice QCD plus three-body scattering formalism yields a π(1300)-like pole at (1169±46)−i(62−62+168) MeV, consistent with experiment.
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The $a_1(1420)$ in a Unitary Coupled-Channel Three-Body Approach
Nine-channel unitary three-body fits to COMPASS lineshapes reproduce the a1(1420) enhancement by triangle singularity without requiring a genuine a1(1420) pole.
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Production Effects and Final-state Interactions in $\pi_1 \to 3\pi$
A Khuri-Treiman model with contact and one-pion-exchange production terms fits COMPASS's π1→3π freed-isobar data and produces a smooth 1.6 GeV structure in the extracted production strengths.
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Three-body unitary determination of the $f_1(1285)$ and $f_1(1420)$ pole positions
Fitting a spectator-isobar three-body unitary amplitude to BESIII K0S K0S pi0 data yields poles at (1277±2±1)-i(12±1±0) MeV for f1(1285) and (1435±2±7)-i(40±2±1) MeV for f1(1420), with the latter traced to a K Kbar* q...
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Coupled-channel approach to isotensor $\pi\pi\pi$ scattering from lattice QCD
The I=2 three-pion spectrum from lattice QCD is described by a repulsive rho-pi S-wave interaction, consistent with a leading-order effective Lagrangian.
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The $a_1(1420)$ in a Unitary Coupled-Channel Three-Body Approach
Unitary coupled-channel three-body model fitted to COMPASS data reproduces the a1(1420) enhancement via triangle singularity, indicating no genuine resonance pole is required.
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Two bodies left behind
In quasi-free high-energy breakup of a heavy-light bound state, the leading amplitude factors as the product of the remnant light-particle scattering amplitude, a probe-dependent dynamical function, and a real bound-s...
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Effects of Final State Interactions on Landau Singularities
Triangle singularities mimicking resonances are analyzed in the presence of final-state rescattering using Landau equations and a scattering formalism enforcing two- and three-body unitarity.
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