Abstract
We reemphasize the momentum dependence of the coefficients of the derivative expansion as already explained in our paper [1]. We also discuss how the momentum dependence plagues the time-dependent HALQCD method and what is a necessary condition for the method to yield valid results being independent of the choice of the interpolating operators.
Highlights
Once again we stress the momentum dependence of the coefficients in the derivative expansion as already explained in Ref. [1] and how the momentum dependence affects the time-dependent HALQCD method [2].1 We show a necessary condition to obtain valid results from the method, which should be independent of the choice of the interpolating operators in the source time slice
We discuss how the momentum dependence plagues the time-dependent HALQCD method and what is a necessary condition for the method to yield valid results being independent of the choice of the interpolating operators
K dependence of the expansion coefficient ViðxÞ of the reduced BS wave function hðx; kÞ is inevitable in a practical determination by lattice calculations, as far as the expansion is truncated at some finite order [1]
Summary
CP-PACS Collaboration has shown that its x dependence gives the consistent momentum with the one determined from the two-particle energy [9] This is a confirmation that the BS wave function outside the interaction range can be used to obtain the scattering amplitude. The complexity of the method introduces additional serious systematic uncertainties such as the convergence of the derivative expansion and inability of specifying momenta where the correct scattering amplitudes should be obtained It is not clear whether the expansion converges or not by investigating the convergence properties with only a few terms as in Ref. The magnitude of these systematic errors are hardly estimated by the HALQCD method itself, which is a typical feature of model calculation, so that the results should be always checked by other methods
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
