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Bayesian Analysis of $χ$EFT at Leading Order in a Modified Weinberg Power Counting Approach (2302.12624v2)

Published 24 Feb 2023 in nucl-th

Abstract: We present a Bayesian analysis of renormalization-group invariant nucleon-nucleon interactions at leading order in chiral effective field theory ($\chi$EFT) with momentum cutoffs in the range 400--4000 MeV. We use history matching to identify relevant regions in the parameter space of low-energy constants (LECs) and subsequently infer the posterior probability density of their values using Markov chain Monte Carlo. All posteriors are conditioned on experimental data for neutron-proton scattering observables and we estimate the $\chi$EFT truncation error in an uncorrelated limit. We do not detect any significant cutoff dependence in the posterior predictive distributions for two-nucleon observables. For all cutoff values we find a multimodal LEC posterior with an insignificant mode harboring a bound $1{S}_0$ state. The $3P_0$ and $3P_2$ phase shifts emerging from the Bayesian analysis are less constrained and typically more repulsive compared to the results of a phase shift optimization. We expect that our inference will impact predictions for nuclei. This work demonstrates how to perform inference in the presence of limit-cycle-like behavior and spurious bound states, and lays the foundation for a Bayesian analysis of renormalization-group invariant $\chi$EFT interactions beyond leading order.

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References (58)
  1. S. Weinberg, Phenomenological Lagrangians, Physica A 96, 327 (1979).
  2. S. Weinberg, Nuclear forces from chiral Lagrangians, Phys. Lett. B 251, 288 (1990).
  3. S. Weinberg, Effective chiral Lagrangians for nucleon - pion interactions and nuclear forces, Nucl. Phys. B 363, 3 (1991).
  4. U. van Kolck, The Problem of Renormalization of Chiral Nuclear Forces, Front. Phys. 8, 79 (2020a), arXiv:2003.06721 [nucl-th] .
  5. P. F. Bedaque and U. van Kolck, Effective field theory for few nucleon systems, Ann. Rev. Nucl. Part. Sci. 52, 339 (2002), arXiv:nucl-th/0203055 .
  6. E. Epelbaum, H.-W. Hammer, and U.-G. Meissner, Modern Theory of Nuclear Forces, Rev. Mod. Phys. 81, 1773 (2009), arXiv:0811.1338 [nucl-th] .
  7. R. Machleidt and D. R. Entem, Chiral effective field theory and nuclear forces, Phys. Rep. 503, 1 (2011), arXiv:1105.2919 [nucl-th] .
  8. H. W. Hammer, S. König, and U. van Kolck, Nuclear effective field theory: status and perspectives, Rev. Mod. Phys. 92, 025004 (2020), arXiv:1906.12122 [nucl-th] .
  9. I. Stetcu, B. R. Barrett, and U. van Kolck, No-core shell model in an effective-field-theory framework, Phys. Lett. B 653, 358 (2007), arXiv:nucl-th/0609023 .
  10. C. J. Yang, Do we know how to count powers in pionless and pionful effective field theory?, Eur. Phys. J. A 56, 96 (2020), arXiv:1905.12510 [nucl-th] .
  11. J. A. Melendez, S. Wesolowski, and R. J. Furnstahl, Bayesian truncation errors in chiral effective field theory: nucleon-nucleon observables, Phys. Rev. C 96, 024003 (2017), arXiv:1704.03308 [nucl-th] .
  12. I. Svensson, A. Ekström, and C. Forssén, Bayesian parameter estimation in chiral effective field theory using the hamiltonian monte carlo method, Phys. Rev. C 105, 014004 (2022).
  13. I. Svensson, A. Ekström, and C. Forssén, Bayesian estimation of the low-energy constants up to fourth order in the nucleon-nucleon sector of chiral effective field theory, Phys. Rev. C 107, 014001 (2023), arXiv:2206.08250 [nucl-th] .
  14. B. Hu et al., Ab initio predictions link the neutron skin of 208208{}^{208}start_FLOATSUPERSCRIPT 208 end_FLOATSUPERSCRIPTPb to nuclear forces, Nature Phys. 18, 1196 (2022), arXiv:2112.01125 [nucl-th] .
  15. A. Manohar and H. Georgi, Chiral Quarks and the Nonrelativistic Quark Model, Nucl. Phys. B 234, 189 (1984).
  16. A. Nogga, R. G. E. Timmermans, and U. van Kolck, Renormalization of one-pion exchange and power counting, Phys. Rev. C 72, 054006 (2005), arXiv:nucl-th/0506005 .
  17. B. Long and C. J. Yang, Short-range nuclear forces in singlet channels, Phys. Rev. C 86, 024001 (2012a), arXiv:1202.4053 [nucl-th] .
  18. B. Long, Improved convergence of chiral effective field theory for 1S0 of NN scattering, Phys. Rev. C 88, 014002 (2013), arXiv:1304.7382 [nucl-th] .
  19. B. Long and C.-J. Yang, Renormalizing chiral nuclear forces: Triplet channels, Phys. Rev. C 85, 034002 (2012b).
  20. M. P. Valderrama and E. Ruiz Arriola, Renormalization of chiral two-pion exchange NN interactions with Delta-excitations: Central Phases and the Deuteron, Phys. Rev. C 79, 044001 (2009), arXiv:0809.3186 [nucl-th] .
  21. M. C. Birse, Power counting with one-pion exchange, Phys. Rev. C 74, 014003 (2006), arXiv:nucl-th/0507077 .
  22. D. B. Kaplan, M. J. Savage, and M. B. Wise, A New expansion for nucleon-nucleon interactions, Phys. Lett. B 424, 390 (1998), arXiv:nucl-th/9801034 .
  23. B. Long and U. van Kolck, Renormalization of Singular Potentials and Power Counting, Ann. Phys. 323, 1304 (2008), arXiv:0707.4325 [quant-ph] .
  24. E. Epelbaum and U. G. Meissner, On the Renormalization of the One-Pion Exchange Potential and the Consistency of Weinberg‘s Power Counting, Few Body Syst. 54, 2175 (2013), arXiv:nucl-th/0609037 .
  25. E. Epelbaum and J. Gegelia, Regularization, renormalization and ’peratization’ in effective field theory for two nucleons, Eur. Phys. J. A 41, 341 (2009), arXiv:0906.3822 [nucl-th] .
  26. A. M. Gasparyan and E. Epelbaum, Is the RG-invariant EFT for few-nucleon systems cutoff independent?, arxiv  (2022), arXiv:2210.16225 [nucl-th] .
  27. H. Hergert, A Guided Tour of a⁢b𝑎𝑏abitalic_a italic_b i⁢n⁢i⁢t⁢i⁢o𝑖𝑛𝑖𝑡𝑖𝑜initioitalic_i italic_n italic_i italic_t italic_i italic_o Nuclear Many-Body Theory, Front. Phys. 8, 379 (2020), arXiv:2008.05061 [nucl-th] .
  28. K. Hebeler, Three-nucleon forces: Implementation and applications to atomic nuclei and dense matter, Phys. Rep. 890, 1 (2021), arXiv:2002.09548 [nucl-th] .
  29. H. W. Griesshammer, A Consistency Test of EFT Power Countings from Residual Cutoff Dependence, Eur. Phys. J. A 56, 118 (2020), arXiv:2004.00411 [nucl-th] .
  30. E. Epelbaum, H. Krebs, and U. G. Meißner, Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order, Eur. Phys. J. A 51, 53 (2015), arXiv:1412.0142 [nucl-th] .
  31. U. van Kolck, Naturalness in nuclear effective field theories, Eur. Phys. J. A 56, 97 (2020b).
  32. T. Barford and M. C. Birse, A Renormalization-group approach to two-body scattering with long range forces, AIP Conf. Proc. 603, 229 (2001), arXiv:nucl-th/0108024 .
  33. T. Barford and M. C. Birse, A Renormalization group approach to two-body scattering in the presence of long range forces, Phys. Rev. C 67, 064006 (2003), arXiv:hep-ph/0206146 .
  34. M. P. Valderrama, Perturbative renormalizability of chiral two pion exchange in nucleon-nucleon scattering, Phys. Rev. C 83, 024003 (2011), arXiv:0912.0699 [nucl-th] .
  35. M. Pavon Valderrama, Perturbative Renormalizability of Chiral Two Pion Exchange in Nucleon-Nucleon Scattering: P- and D-waves, Phys. Rev. C 84, 064002 (2011), arXiv:1108.0872 [nucl-th] .
  36. B. Long and C.-J. Yang, Renormalizing chiral nuclear forces: A case study of P03superscriptsubscript𝑃03{}^{3}\phantom{\rule{-1.60004pt}{0.0pt}}{P}_{0}start_FLOATSUPERSCRIPT 3 end_FLOATSUPERSCRIPT italic_P start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT, Phys. Rev. C 84, 057001 (2011).
  37. R. Workman et al. (Particle Data Group), Review of particle physics, to be published (2022).
  38. K. Erkelenz, R. Alzetta, and K. Holinde, Momentum space calculations and helicity formalism in nuclear physics, Nucl. Phys. A 176, 413 (1971).
  39. G. E. Brown, A. D. Jackson, and T. T. S. Kuo, Nucleon-nucleon potential and minimal relativity, Nucl. Phys. A 133, 481 (1969).
  40. M. I. Haftel and F. Tabakin, Nuclear saturation and the smoothness of nucleon-nucleon potentials, Nucl. Phys. A 158, 1 (1970).
  41. J. Bystricky, F. Lehar, and P. Winternitz, Formalism of Nucleon-Nucleon Elastic Scattering Experiments, J. Phys. (France) 39, 1 (1978).
  42. K. M. Case, Singular potentials, Phys. Rev. 80, 797 (1950).
  43. W. Frank, D. J. Land, and R. M. Spector, Singular potentials, Rev. Mod. Phys. 43, 36 (1971).
  44. H.-W. Hammer and B. G. Swingle, On the limit cycle for the 1/r2 potential in momentum space, Ann. Phys. 321, 306 (2006).
  45. S. Wu and B. Long, Perturbative n⁢n𝑛𝑛nnitalic_n italic_n scattering in chiral effective field theory, Phys. Rev. C 99, 024003 (2019).
  46. J. R. Taylor, Scattering Theory: The quantum Theory on Nonrelativistic Collisions (Wiley, New York, 1972).
  47. R. Navarro Pérez, J. E. Amaro, and E. Ruiz Arriola, Partial-wave analysis of nucleon-nucleon scattering below the pion-production threshold, Phys. Rev. C 88, 024002 (2013).
  48. R. N. Pérez, J. E. Amaro, and E. R. Arriola, Coarse-grained potential analysis of neutron-proton and proton-proton scattering below the pion production threshold, Phys. Rev. C 88, 064002 (2013).
  49. I. Vernon, M. Goldstein, and R. Bower, Galaxy formation: a bayesian uncertainty analysis, Bayesian Anal. 5(4), 619 (2010).
  50. I. Vernon, M. Goldstein, and R. Bower, Galaxy formation: Bayesian history matching for the observable universe, Statist. Sci. 29, 81 (2014).
  51. Y. Kondo et al., First observation of 2828{}^{28}start_FLOATSUPERSCRIPT 28 end_FLOATSUPERSCRIPTO, Nature 620, 965 (2023).
  52. V. Joseph, Space-filling designs for computer experiments: A review, Qual. Eng. 28, 28 (2016).
  53. F. Pukelsheim, The three sigma rule, Am. Stat. 48, 88– (1994).
  54. P. Gregory, Bayesian Logical Data Analysis for the Physical Sciences: A Comparative Approach with Mathematica® Support (Cambridge University Press, 2005).
  55. W. Glöckle, The Quantum Mechanical Few-body Problem (Springer-Verlag, Berlin Heidelberg, 1983).
  56. R. H. Landau, Quantum mechanics II: a second course in quantum theory, 2nd ed. (Wiley, New York, 1996).
  57. R. Machleidt, The High precision, charge dependent Bonn nucleon-nucleon potential (CD-Bonn), Phys. Rev. C 63, 024001 (2001), arXiv:nucl-th/0006014 .
  58. J. M. Blatt and L. C. Biedenharn, The Angular Distribution of Scattering and Reaction Cross Sections, Rev. Mod. Phys. 24, 258 (1952).
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