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  • Letter
  • Open Access

Positivity bounds without boosts: New constraints on low energy effective field theories from the UV

Tanguy Grall and Scott Melville

  • DAMTP, Centre for Mathematical Sciences, University of Cambridge, CB3 0WA, United Kingdom

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Phys. Rev. D 105, L121301 – Published 28 June, 2022

DOI: https://doi.org/10.1103/PhysRevD.105.L121301

Abstract

We derive new positivity bounds for low-energy effective field theories (EFTs) that are not invariant under Lorentz boosts. “Positivity bounds” are the low-energy manifestation of certain fundamental properties in the UV—to date, they have been used to constrain a wide variety of EFTs; however, since existing bounds require Lorentz invariance they are not directly applicable when this symmetry is broken, such as for most cosmological and condensed matter systems. Assuming that the low-energy degrees of freedom can be extended into the UV in a way consistent with the fundamental axioms of unitarity, analyticity, and locality, we derive an infinite family of bounds that (derivatives of) the 2→2 EFT scattering amplitude must satisfy even when Lorentz boosts are broken. We apply these bounds to the leading-order EFT of both a superfluid and the scalar fluctuations produced during inflation, comparing in the latter case with the current observational constraints on primordial non-Gaussianity, demonstrating that these bounds open a new window into the high-energy physics that lies beneath our low-energy measurements.

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References (109)

  1. C. Cheung, P. Creminelli, A. L. Fitzpatrick, J. Kaplan, and L. Senatore, J. High Energy Phys. 03 (2008) 014.
  2. L. Senatore and M. Zaldarriaga, J. High Energy Phys. 04 (2012) 024.
  3. F. Piazza and F. Vernizzi, Classical Quantum Gravity 30, 214007 (2013).
  4. B. Finelli, G. Goon, E. Pajer, and L. Santoni, J. Cosmol. Astropart. Phys. 05 (2018) 060.
  5. D. Son, arXiv:hep-ph/0204199.
  6. D. Son, Phys. Rev. Lett. 94, 175301 (2005).
  7. S. Dubovsky, L. Hui, and A. Nicolis, Phys. Rev. D 89, 045016 (2014).
  8. S. Dubovsky, L. Hui, A. Nicolis, and D. T. Son, Phys. Rev. D 85, 085029 (2012).
  9. A. Nicolis, arXiv:1108.2513.
  10. A. Nicolis, R. Penco, and R. A. Rosen, Phys. Rev. D 89, 045002 (2014).
  11. L. V. Delacrétaz, A. Nicolis, R. Penco, and R. A. Rosen, Phys. Rev. Lett. 114, 091601 (2015).
  12. A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis, and R. Rattazzi, J. High Energy Phys. 10 (2006) 014.
  13. A. Jenkins and D. O’Connell, arXiv:hep-th/0609159.
  14. B. Bellazzini, J. High Energy Phys. 02 (2017) 034.
  15. C. de Rham, S. Melville, A. J. Tolley, and S.-Y. Zhou, Phys. Rev. D 96, 081702 (2017).
  16. C. de Rham, S. Melville, A. J. Tolley, and S.-Y. Zhou, J. High Energy Phys. 03 (2018) 011.
  17. G. N. Remmen and N. L. Rodd, Phys. Rev. D 105, 036006 (2022).
  18. B. Bellazzini, J. Elias Miró, R. Rattazzi, M. Riembau, and F. Riva, Phys. Rev. D 104, 036006 (2021).
  19. A. J. Tolley, Z.-Y. Wang, and S.-Y. Zhou, J. High Energy Phys. 05 (2021) 255.
  20. S. Caron-Huot and V. Van Duong, J. High Energy Phys. 05 (2021) 280.
  21. X. Li, C. Yang, H. Xu, C. Zhang, and S.-Y. Zhou, Phys. Rev. Lett. 127, 121601 (2021).
  22. N. Arkani-Hamed, T.-C. Huang, and Y.-T. Huang, J. High Energy Phys. 05 (2021) 259.
  23. T. Trott, J. High Energy Phys. 07 (2021) 143.
  24. T. N. Pham and T. N. Truong, Phys. Rev. D 31, 3027 (1985).
  25. B. Ananthanarayan, D. Toublan, and G. Wanders, Phys. Rev. D 51, 1093 (1995).
  26. M. R. Pennington and J. Portoles, Phys. Lett. B 344, 399 (1995).
  27. J. Distler, B. Grinstein, R. A. Porto, and I. Z. Rothstein, Phys. Rev. Lett. 98, 041601 (2007).
  28. L. Vecchi, J. High Energy Phys. 11 (2007) 054.
  29. Y.-J. Wang, F.-K. Guo, C. Zhang, and S.-Y. Zhou, J. High Energy Phys. 07 (2020) 214.
  30. B. Bellazzini and F. Riva, Phys. Rev. D 98, 095021 (2018).
  31. C. Zhang and S.-Y. Zhou, Phys. Rev. D 100, 095003 (2019).
  32. Q. Bi, C. Zhang, and S.-Y. Zhou, J. High Energy Phys. 06 (2019) 137.
  33. S.-Y. Zhou, Proc. Sci., EPS-HEP2019 (2020) 667.
  34. K. Yamashita, C. Zhang, and S.-Y. Zhou, J. High Energy Phys. 01 (2021) 095.
  35. B. Fuks, Y. Liu, C. Zhang, and S.-Y. Zhou, Chin. Phys. C 45, 023108 (2021).
  36. C. Zhang and S.-Y. Zhou, Phys. Rev. Lett. 125, 201601 (2020).
  37. G. N. Remmen and N. L. Rodd, Phys. Rev. Lett. 125, 081601 (2020).
  38. G. N. Remmen and N. L. Rodd, J. High Energy Phys. 12 (2019) 032.
  39. G. Dvali, A. Franca, and C. Gomez, arXiv:1204.6388.
  40. B. Bellazzini, C. Cheung, and G. N. Remmen, Phys. Rev. D 93, 064076 (2016).
  41. C. Cheung and G. N. Remmen, Phys. Rev. Lett. 118, 051601 (2017).
  42. X. O. Camanho, J. D. Edelstein, J. Maldacena, and A. Zhiboedov, J. High Energy Phys. 02 (2016) 020.
  43. A. Gruzinov and M. Kleban, Classical Quantum Gravity 24, 3521 (2007).
  44. M. Herrero-Valea, R. Santos-Garcia, and A. Tokareva, Phys. Rev. D 104, 085022 (2021).
  45. L. Alberte, C. de Rham, S. Jaitly, and A. J. Tolley, Phys. Rev. D 102, 125023 (2020).
  46. L. Alberte, C. de Rham, S. Jaitly, and A. J. Tolley, Phys. Rev. D 103, 125020 (2021).
  47. C. Cheung and G. N. Remmen, J. High Energy Phys. 04 (2016) 002.
  48. J. Bonifacio, K. Hinterbichler, and R. A. Rosen, Phys. Rev. D 94, 104001 (2016).
  49. B. Bellazzini, F. Riva, J. Serra, and F. Sgarlata, Phys. Rev. Lett. 120, 161101 (2018).
  50. C. de Rham, S. Melville, and A. J. Tolley, J. High Energy Phys. 04 (2018) 083.
  51. C. de Rham, S. Melville, A. J. Tolley, and S.-Y. Zhou, J. High Energy Phys. 03 (2019) 182.
  52. L. Alberte, C. de Rham, A. Momeni, J. Rumbutis, and A. J. Tolley, J. High Energy Phys. 03 (2020) 097.
  53. L. Alberte, C. de Rham, A. Momeni, J. Rumbutis, and A. J. Tolley, J. High Energy Phys. 07 (2020) 121.
  54. Z.-Y. Wang, C. Zhang, and S.-Y. Zhou, J. High Energy Phys. 04 (2021) 217.
  55. J. Bonifacio and K. Hinterbichler, Phys. Rev. D 98, 045003 (2018).
  56. B. Bellazzini, F. Riva, J. Serra, and F. Sgarlata, J. High Energy Phys. 10 (2019) 189.
  57. S. Melville, D. Roest, and D. Stefanyszyn, J. High Energy Phys. 02 (2020) 185.
  58. C. Cheung and G. N. Remmen, J. High Energy Phys. 12 (2014) 087.
  59. C. Cheung, J. Liu, and G. N. Remmen, J. High Energy Phys. 10 (2018) 004.
  60. Y. Hamada, T. Noumi, and G. Shiu, Phys. Rev. Lett. 123, 051601 (2019).
  61. C. Cheung, J. Liu, and G. N. Remmen, Phys. Rev. D 100, 046003 (2019).
  62. B. Bellazzini, M. Lewandowski, and J. Serra, Phys. Rev. Lett. 123, 251103 (2019).
  63. A. M. Charles, arXiv:1906.07734.
  64. A. Nicolis, R. Rattazzi, and E. Trincherini, J. High Energy Phys. 05 (2010) 095; 11 (2011) 128(E).
  65. Z. Komargodski and A. Schwimmer, J. High Energy Phys. 12 (2011) 099.
  66. H. Elvang, D. Z. Freedman, L.-Y. Hung, M. Kiermaier, R. C. Myers, and S. Theisen, J. High Energy Phys. 10 (2012) 011.
  67. C. de Rham, S. Melville, A. J. Tolley, and S.-Y. Zhou, J. High Energy Phys. 09 (2017) 072.
  68. V. Chandrasekaran, G. N. Remmen, and A. Shahbazi-Moghaddam, J. High Energy Phys. 11 (2018) 015.
  69. S. Melville and J. Noller, Phys. Rev. D 101, 021502 (2020); 102, 049902(E) (2020).
  70. J. Kennedy and L. Lombriser, Phys. Rev. D 102, 044062 (2020).

  71. Our assumption that the free equation of motion for π has the form (1) is what allows the use of relativistic Mandelstam-like variables—in cases where the dispersion relation is far from linear, there would be little motivation for forming sab combinations and in that case the nonrelativistic problem is best treated in terms of the energies directly (c.f. the Kramers-Kronig relations).

  72. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevD.105.L121301 for further details of the analyticity and unitarity properties of the boost-breaking scattering amplitude.
  73. M. Gell-Mann, M. L. Goldberger, and W. E. Thirring, Phys. Rev. 95, 1612 (1954).
  74. H. J. Bremermann, R. Oehme, and J. G. Taylor, Phys. Rev. 109, 2178 (1958).
  75. K. Hepp, Helv. Phys. Acta (Switzerland) 37, 639 (1964).
  76. R. J. Eden, P. V. Landshoff, D. I. Olive, and J. C. Polkinghorne, S-Matrix Theory of Strong Interactions’ (Cambridge University Press, Cambridge, England, 1966).
  77. D. Baumann, D. Green, H. Lee, and R. A. Porto, Phys. Rev. D 93, 023523 (2016).
  78. G. Ye and Y.-S. Piao, Eur. Phys. J. C 80, 421 (2020).
  79. S. Kim, T. Noumi, K. Takeuchi, and S. Zhou, J. High Energy Phys. 12 (2019) 107.
  80. M. Herrero-Valea, I. Timiryasov, and A. Tokareva, J. Cosmol. Astropart. Phys. 11 (2019) 042.
  81. A. Martin, Phys. Rev. 129, 1432 (1963).
  82. M. Froissart, Phys. Rev. 123, 1053 (1961).
  83. C. Cordova, J. Maldacena, and G. J. Turiaci, J. High Energy Phys. 11 (2017) 032.
  84. K. Aoki, S. Mukohyama, and R. Namba, J. Cosmol. Astropart. Phys. 10 (2021) 079.

  85. We stress that subtracting up to sb with M held fixed corresponds to energies ωb/Λ∼sb/MΛ, and so the effective cutoff for the EFT amplitude A˜s in the complex s plane is set by the product ΛM.

  86. C. de Rham and S. Melville, Phys. Rev. D 95, 123523 (2017).
  87. T. Grall and S. Melville, J. Cosmol. Astropart. Phys. 09 (2020) 017.
  88. Y. Akrami et al. (Planck Collaboration), Astron. Astrophys. 641, A1 (2020).

  89. This corresponds to setting γ=1 in (20). This bound can be improved by using a larger value for γ, but one must ensure that it corresponds to kinematics which are both subhorizon (24) and within the resolving power of the EFT—see e.g., the cutoffs identified in [87].

  90. J. R. Fergusson, D. M. Regan, and E. P. S. Shellard, arXiv:1012.6039.
  91. K. M. Smith, L. Senatore, and M. Zaldarriaga, arXiv:1502.00635.
  92. A. Nicolis and F. Piazza, J. High Energy Phys. 06 (2012) 025.
  93. A. Nicolis, R. Penco, F. Piazza, and R. A. Rosen, J. High Energy Phys. 11 (2013) 055.
  94. S. Endlich, A. Nicolis, and R. Penco, Phys. Rev. D 89, 065006 (2014).
  95. A. Nicolis, R. Penco, F. Piazza, and R. Rattazzi, J. High Energy Phys. 06 (2015) 155.
  96. L. V. Delacretaz, T. Noumi, and L. Senatore, J. Cosmol. Astropart. Phys. 02 (2017) 034.
  97. E. Pajer and D. Stefanyszyn, J. High Energy Phys. 06 (2019) 008.
  98. L. Alberte and A. Nicolis, J. High Energy Phys. 07 (2020) 076.
  99. T. Grall, S. Jazayeri, and D. Stefanyszyn, J. High Energy Phys. 11 (2020) 097.
  100. G. Gubitosi, F. Piazza, and F. Vernizzi, J. Cosmol. Astropart. Phys. 02 (2013) 032.

  101. This will likely require replacing the scattering amplitude with an equal-time correlator or wavefunction coefficients—see [102, 103, 104, 105, 106, 107, 108, 109] for recent progress in this direction.

  102. N. Arkani-Hamed, D. Baumann, H. Lee, and G. L. Pimentel, J. High Energy Phys. 04 (2020) 105.
  103. N. Afkhami-Jeddi, S. Kundu, and A. Tajdini, J. High Energy Phys. 10 (2018) 156.
  104. D. Baumann, D. Green, and T. Hartman, J. High Energy Phys. 12 (2019) 134.
  105. D. Baumann, C. Duaso Pueyo, A. Joyce, H. Lee, and G. L. Pimentel, J. High Energy Phys. 12 (2020) 204.
  106. D. Baumann, C. Duaso Pueyo, A. Joyce, H. Lee, and G. L. Pimentel, SciPost Phys. 11, 071 (2021).
  107. S. Céspedes, A.-C. Davis, and S. Melville, J. High Energy Phys. 02 (2021) 012.
  108. H. Goodhew, S. Jazayeri, and E. Pajer, J. Cosmol. Astropart. Phys. 04 (2021) 021.
  109. E. Pajer, J. Cosmol. Astropart. Phys. 01 (2021) 023.

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Phys. Rev. D 105, L121301– Published 28 June, 2022
  • Received 7 March 2021
  • Accepted 11 June 2022
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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