Abstract
The anti-kaon nucleon scattering lengths resulting from a Hamiltonian effective field theory analysis of experimental data and lattice QCD studies are presented. The same Hamiltonian is then used to compute the scattering length for the K−d system, taking careful account of the effects of recoil on the energy at which the K¯N T-matrices are evaluated. These results are then used to estimate the shift and width of the 1S levels of anti-kaonic hydrogen and deuterium. The K−p result is in excellent agreement with the SIDDHARTA measurement. In the K−d case the imaginary part of the scattering length and consequently the width of the 1S state are considerably larger than found in earlier work. This is a consequence of the effect of recoil on the energy of the K¯N energy, which enhances the role of the Λ(1405) resonance.
Highlights
The kaon has played an important role in advancing particle physics since it was discovered in cosmic rays
After the resummation of contributions from kaon multiple scatterings between the two nucleons in the deuteron, solving the full three-body Hamiltonian or Faddeev equations, the energy shift for kaonic deuterium has been found to be of order 700∼900 eV, while the width has been reported to be in the range 800∼1200 eV [28,29,30,31,32,33]
The difference between the (1405) resonance and the K N threshold is less than 30 MeV and, its 50 MeV width means they overlap to some extent
Summary
The kaon has played an important role in advancing particle physics since it was discovered in cosmic rays. After the resummation of contributions from kaon multiple scatterings between the two nucleons in the deuteron, solving the full three-body Hamiltonian or Faddeev equations, the energy shift for kaonic deuterium has been found to be of order 700∼900 eV, while the width has been reported to be in the range 800∼1200 eV [28,29,30,31,32,33]. The difference between the (1405) resonance and the K N threshold is less than 30 MeV and, its 50 MeV width means they overlap to some extent In such a case, even if the recoiling nucleon shifts the center-of-mass energy of K N a relatively small distance from the threshold, the scattering amplitude may be very different from that at threshold, which the static approximation uses.
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