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  "authors": [
    {
      "affiliations": [
        {
          "country": "Japan", 
          "value": "Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, , , Kyoto 606-8502, , , Japan"
        }, 
        {
          "country": "Japan", 
          "value": "Theoretical Research Division, Nishina Center, , , RIKEN, Saitama 351-0198, , , Japan"
        }
      ], 
      "surname": "Aoki", 
      "email": "saoki@het.ph.tsukuba.ac.jp", 
      "full_name": "Aoki, Sinya", 
      "given_names": "Sinya"
    }, 
    {
      "affiliations": [
        {
          "country": "Japan", 
          "value": "Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), , , RIKEN Saitama 351-0198, , , Japan"
        }
      ], 
      "surname": "Yazaki", 
      "given_names": "Koichi", 
      "full_name": "Yazaki, Koichi"
    }
  ], 
  "titles": [
    {
      "source": "OUP", 
      "title": "Derivative expansion in the HAL QCD method for a separable potential"
    }
  ], 
  "dois": [
    {
      "value": "10.1093/ptep/ptab168"
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      "journal_title": "Progress of Theoretical and Experimental Physics", 
      "material": "article", 
      "journal_volume": "2022", 
      "artid": "033B04", 
      "year": 2021, 
      "journal_issue": "3"
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  "page_nr": [
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      "url": "https://creativecommons.org/licenses/by/4.0/", 
      "license": "CC-BY-4.0"
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  "copyright": [
    {
      "statement": "\u00a9 The Author(s) 2021. Published by Oxford University Press on behalf of the Physical Society of Japan.", 
      "year": "2021"
    }
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      "primary": "Progress of Theoretical and Experimental Physics"
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  "abstracts": [
    {
      "source": "OUP", 
      "value": "Abstract We investigate how the derivative expansion in the HAL QCD method works to extract physical observables, using a separable potential in quantum mechanics, which is solvable but highly non-local in the coordinate system. We consider three cases for inputs to determine the HAL QCD potential in the derivative expansion: (1) energy eigenfunctions, (2) time-dependent wave functions as solutions to the time-dependent Schr\u00f6dinger equation with some boundary conditions, and (3) a time-dependent wave function made by a linear combination of a finite number of eigenfunctions at low energy to mimic the finite volume effect. We have found that, for all three cases, the potentials provide reasonable scattering phase shifts even at the leading order of the derivative expansion, and they give more accurate results as the order of the expansion increases. By comparing the above results with those from the formal derivative expansion for the separable potential, we conclude that the derivative expansion is not a way to obtain the potential but a method to extract physical observables such as phase shifts and binding energies, and that the scattering phase shifts from the derivative expansion in the HAL QCD method converge to the exact ones much faster than those from the formal derivative expansion of the separable potential."
    }
  ], 
  "imprints": [
    {
      "date": "2021-12-31", 
      "publisher": "OUP"
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