Ab initio approach to the non-perturbative scalar Yukawa model

Yang Li, V. A. Karmanov, P. Maris, J. P. Vary

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17 Scopus citations


We report on the first non-perturbative calculation of the scalar Yukawa model in the single-nucleon sector up to four-body Fock sector truncation (one "scalar nucleon" and three "scalar pions"). The light-front Hamiltonian approach with a systematic non-perturbative renormalization is applied. We study the n-body norms and the electromagnetic form factor. We find that the one- and two-body contributions dominate up to coupling α. ≈ 1.7. As we approach the coupling α. ≈. 2.2, we discover that the four-body contribution rises rapidly and overtakes the two- and three-body contributions. By comparing with lower sector truncations, we show that the form factor converges with respect to the Fock sector expansion.

Original languageEnglish (US)
Pages (from-to)278-283
Number of pages6
JournalPhysics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
StatePublished - Sep 2 2015

Bibliographical note

Funding Information:
We are indebted to A.V. Smirnov for kindly providing us some numerical benchmark results for the three-body truncation. We wish to thank J. Carbonell, J.-F. Mathiot and X. Zhao for valuable discussions. One of us (V.A.K.) is sincerely grateful to the Nuclear Theory Group at Iowa State University for kind hospitality during his visits. This work was supported in part by the Department of Energy under Grant Nos. DE-FG02-87ER40371 and DESC0008485 (SciDAC-3/NUCLEI) and by the National Science Foundation under Grant No. PHY-0904782 . Computational resources were provided by the National Energy Research Supercomputer Center (NERSC), which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231 .

Publisher Copyright:
© 2015 Published by Elsevier B.V.


  • Fock sector dependent renormalization
  • Light front hamiltonian
  • Scalar yukawa model


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