Two interacting scalars system in curved spacetime — vacuum stability from the curved spacetime Effective Field Theory (cEFT) perspective

Abstract

In this article we investigated the influence of the gravity mediated higher dimensional operators on the issue of vacuum stability in a model containing two interacting scalar fields. As a framework we used the curved spacetime Effective Field Theory (cEFT) applied to the aforementioned system in which one of the scalars is heavy. After integrating out the heavy scalar we used the standard Euclidean approach to the obtained cEFT. Apart from analyzing the influence of standard operators like the non-minimal coupling to gravity and the dimension six contribution to the scalar field potential, we also investigated the rarely discussed dimension six contribution to the kinetic term and the new gravity mediated contribution to the scalar quartic self-interaction.

A preprint version of the article is available at ArXiv.

References

  1. [1]

    W. Buchmüller and D. Wyler, Effective Lagrangian analysis of new interactions and flavor conservation, Nucl. Phys. B 268 (1986) 621 [INSPIRE].

    ADS  Google Scholar 

  2. [2]

    B. Grzadkowski, M. Iskrzyński, M. Misiak and J. Rosiek, Dimension-six terms in the Standard Model Lagrangian, JHEP 10 (2010) 085 [arXiv:1008.4884] [INSPIRE].

    ADS  MATH  Google Scholar 

  3. [3]

    A. Dedes, M. Paraskevas, J. Rosiek, K. Suxho and L. Trifyllis, The decay h → γγ in the Standard-Model effective field theory, JHEP 08 (2018) 103 [arXiv:1805.00302] [INSPIRE].

    ADS  Google Scholar 

  4. [4]

    B. Henning, X. Lu and H. Murayama, How to use the Standard Model effective field theory, JHEP 01 (2016) 023 [arXiv:1412.1837] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  5. [5]

    B. Henning, X. Lu and H. Murayama, One-loop matching and running with covariant derivative expansion, JHEP 01 (2018) 123 [arXiv:1604.01019] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  6. [6]

    A. Drozd, J. Ellis, J. Quevillon and T. You, The universal one-loop effective action, JHEP 03 (2016) 180 [arXiv:1512.03003] [INSPIRE].

    ADS  Google Scholar 

  7. [7]

    S.A.R. Ellis, J. Quevillon, T. You and Z. Zhang, Extending the universal one-loop effective action: heavy-light coefficients, JHEP 08 (2017) 054 [arXiv:1706.07765] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  8. [8]

    L. Nakonieczny, Curved spacetime effective field theory (cEFT) — construction with the heat kernel method, JHEP 01 (2019) 034 [arXiv:1811.01656] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  9. [9]

    M. Sher, Electroweak Higgs potentials and vacuum stability, Phys. Rept. 179 (1989) 273 [INSPIRE].

    ADS  Google Scholar 

  10. [10]

    J. Elias-Miró, J.R. Espinosa, G.F. Giudice, G. Isidori, A. Riotto and A. Strumia, Higgs mass implications on the stability of the electroweak vacuum, Phys. Lett. B 709 (2012) 222 [arXiv:1112.3022] [INSPIRE].

    ADS  Google Scholar 

  11. [11]

    G. Degrassi et al., Higgs mass and vacuum stability in the Standard Model at NNLO, JHEP 08 (2012) 098 [arXiv:1205.6497] [INSPIRE].

    ADS  Google Scholar 

  12. [12]

    J.R. Espinosa et al., The cosmological Higgstory of the vacuum instability, JHEP 09 (2015) 174 [arXiv:1505.04825] [INSPIRE].

    ADS  MATH  Google Scholar 

  13. [13]

    O. Czerwińska, Z. Lalak and L. Nakonieczny, Stability of the effective potential of the gauge-less top-Higgs model in curved spacetime, JHEP 11 (2015) 207 [arXiv:1508.03297] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  14. [14]

    P. Burda, R. Gregory and I. Moss, Vacuum metastability with black holes, JHEP 08 (2015) 114 [arXiv:1503.07331] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  15. [15]

    P. Burda, R. Gregory and I. Moss, Gravity and the stability of the Higgs vacuum, Phys. Rev. Lett. 115 (2015) 071303 [arXiv:1501.04937] [INSPIRE].

    ADS  Google Scholar 

  16. [16]

    P. Burda, R. Gregory and I. Moss, The fate of the Higgs vacuum, JHEP 06 (2016) 025 [arXiv:1601.02152] [INSPIRE].

    ADS  MATH  Google Scholar 

  17. [17]

    M. Bounakis and I.G. Moss, Gravitational corrections to Higgs potentials, JHEP 04 (2018) 071 [arXiv:1710.02987] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  18. [18]

    C. Han, S. Pi and M. Sasaki, Quintessence saves Higgs instability, Phys. Lett. B 791 (2019) 314 [arXiv:1809.05507] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  19. [19]

    M. Herranen, T. Markkanen, S. Nurmi and A. Rajantie, Spacetime curvature and Higgs stability after inflation, Phys. Rev. Lett. 115 (2015) 241301 [arXiv:1506.04065] [INSPIRE].

    ADS  Google Scholar 

  20. [20]

    M. Herranen, T. Markkanen, S. Nurmi and A. Rajantie, Spacetime curvature and the Higgs stability during inflation, Phys. Rev. Lett. 113 (2014) 211102 [arXiv:1407.3141] [INSPIRE].

    ADS  Google Scholar 

  21. [21]

    O. Czerwińska, Z. Lalak, M. Lewicki and P. Olszewski, The impact of non-minimally coupled gravity on vacuum stability, JHEP 10 (2016) 004 [arXiv:1606.07808] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  22. [22]

    A. Rajantie and S. Stopyra, Standard Model vacuum decay with gravity, Phys. Rev. D 95 (2017) 025008 [arXiv:1606.00849] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  23. [23]

    T. Markkanen, A. Rajantie and S. Stopyra, Cosmological aspects of Higgs vacuum metastability, Front. Astron. Space Sci. 5 (2018) 40 [arXiv:1809.06923] [INSPIRE].

    ADS  Google Scholar 

  24. [24]

    J. Fumagalli, S. Renaux-Petel and J.W. Ronayne, Higgs vacuum (in)stability during inflation: the dangerous relevance of de Sitter departure and Planck-suppressed operators, JHEP 02 (2020) 142 [arXiv:1910.13430] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  25. [25]

    S.R. Coleman, The fate of the false vacuum. 1. Semiclassical theory, Phys. Rev. D 15 (1977) 2929 [Erratum ibid. 16 (1977) 1248] [INSPIRE].

  26. [26]

    S.R. Coleman and F. De Luccia, Gravitational effects on and of vacuum decay, Phys. Rev. D 21 (1980) 3305 [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  27. [27]

    A. Andreassen, D. Farhi, W. Frost and M.D. Schwartz, Direct approach to quantum tunneling, Phys. Rev. Lett. 117 (2016) 231601 [arXiv:1602.01102] [INSPIRE].

    ADS  Google Scholar 

  28. [28]

    U. Gen and M. Sasaki, False vacuum decay with gravity in nonthin wall limit, Phys. Rev. D 61 (2000) 103508 [gr-qc/9912096] [INSPIRE].

    ADS  Google Scholar 

  29. [29]

    F. Michel, Parametrized path approach to vacuum decay, Phys. Rev. D 101 (2020) 045021 [arXiv:1911.12765] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  30. [30]

    S.W. Hawking and I.G. Moss, Supercooled phase transitions in the very early universe, Phys. Lett. B 110 (1982) 35 [INSPIRE].

    ADS  Google Scholar 

  31. [31]

    A.R. Brown and E.J. Weinberg, Thermal derivation of the Coleman-De Luccia tunneling prescription, Phys. Rev. D 76 (2007) 064003 [arXiv:0706.1573] [INSPIRE].

    ADS  Google Scholar 

  32. [32]

    P. Chen, Y.-C. Hu and D.-H. Yeom, Two interpretations of thin-shell instantons, Phys. Rev. D 94 (2016) 024044 [arXiv:1512.03914] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  33. [33]

    C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation, W.H. Freeman, San Francisco, CA, U.S.A. (1973) [INSPIRE].

    Google Scholar 

  34. [34]

    E.W. Kolb and A.J. Long, Superheavy dark matter through Higgs portal operators, Phys. Rev. D 96 (2017) 103540 [arXiv:1708.04293] [INSPIRE].

    ADS  Google Scholar 

  35. [35]

    G. Arcadi, A. Djouadi and M. Raidal, Dark matter through the Higgs portal, Phys. Rept. 842 (2020) 1 [arXiv:1903.03616] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  36. [36]

    A.O. Bärvinsky and G.A. Vilkovisky, Covariant perturbation theory. 2. Second order in the curvature. General algorithms, Nucl. Phys. B 333 (1990) 471 [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  37. [37]

    A.O. Bärvinsky, Y. Gusev, V.V. Zhytnikov and G.A. Vilkovisky, Covariant perturbation theory. 4. Third order in the curvature, arXiv:0911.1168 [INSPIRE].

  38. [38]

    I.G. Avramidi, The covariant technique for calculation of one loop effective action, Nucl. Phys. B 355 (1991) 712 [Erratum ibid. 509 (1998) 557] [INSPIRE].

  39. [39]

    A.O. Bärvinsky, Y. Gusev, V.F. Mukhanov and D.V. Nesterov, Nonperturbative late time asymptotics for heat kernel in gravity theory, Phys. Rev. D 68 (2003) 105003 [hep-th/0306052] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  40. [40]

    Maplesoft, a division of Waterloo Maple Inc., Maple, Waterloo, ON, Canada (2020).

  41. [41]

    W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Numerical recipes — the art of scientific computing, Cambridge University Press, Cambridge, U.K. (2007).

    Google Scholar 

  42. [42]

    J.W. York, Role of conformal three geometry in the dynamics of gravitation, Phys. Rev. Lett. 28 (1972) 1082 [INSPIRE].

    ADS  Google Scholar 

  43. [43]

    G.W. Gibbons and S.W. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].

    ADS  Google Scholar 

  44. [44]

    A.D. Barvinsky and S.N. Solodukhin, Nonminimal coupling, boundary terms and renormalization of the Einstein-Hilbert action and black hole entropy, Nucl. Phys. B 479 (1996) 305 [gr-qc/9512047] [INSPIRE].

    ADS  MATH  Google Scholar 

  45. [45]

    S.W. Hawking and N. Turok, Open inflation without false vacua, Phys. Lett. B 425 (1998) 25 [hep-th/9802030] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  46. [46]

    V. Branchina and E. Messina, Stability, Higgs boson mass and new physics, Phys. Rev. Lett. 111 (2013) 241801 [arXiv:1307.5193] [INSPIRE].

    ADS  Google Scholar 

  47. [47]

    Z. Lalak, M. Lewicki and P. Olszewski, Higher-order scalar interactions and SM vacuum stability, JHEP 05 (2014) 119 [arXiv:1402.3826] [INSPIRE].

    ADS  Google Scholar 

  48. [48]

    V. Branchina, E. Messina and M. Sher, Lifetime of the electroweak vacuum and sensitivity to Planck scale physics, Phys. Rev. D 91 (2015) 013003 [arXiv:1408.5302] [INSPIRE].

    ADS  Google Scholar 

  49. [49]

    F. Loebbert and J. Plefka, Quantum gravitational contributions to the Standard Model effective potential and vacuum stability, Mod. Phys. Lett. A 30 (2015) 1550189 [arXiv:1502.03093] [INSPIRE].

    ADS  MATH  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Łukasz Nakonieczny.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

ArXiv ePrint: 2004.12327

Rights and permissions

Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Lalak, Z., Nakonieczna, A. & Nakonieczny, Ł. Two interacting scalars system in curved spacetime — vacuum stability from the curved spacetime Effective Field Theory (cEFT) perspective. J. High Energ. Phys. 2020, 132 (2020). https://doi.org/10.1007/JHEP11(2020)132

Download citation

Keywords

  • Effective Field Theories
  • Solitons Monopoles and Instantons
  • Cosmology of Theories beyond the SM
  • Classical Theories of Gravity