Papers
Topics
Authors
Recent
Detailed Answer
Quick Answer
Concise responses based on abstracts only
Detailed Answer
Well-researched responses based on abstracts and relevant paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses
Gemini 2.5 Flash
Gemini 2.5 Flash 87 tok/s
Gemini 2.5 Pro 50 tok/s Pro
GPT-5 Medium 13 tok/s Pro
GPT-5 High 16 tok/s Pro
GPT-4o 98 tok/s Pro
GPT OSS 120B 472 tok/s Pro
Kimi K2 210 tok/s Pro
2000 character limit reached

Supercool exit: Gravitational waves from QCD-triggered conformal symmetry breaking (2303.02450v2)

Published 4 Mar 2023 in hep-ph and astro-ph.CO

Abstract: Classically conformal Standard Model extensions predict an intriguing thermal history of the early universe. In contrast to the common paradigm, the onset of the electroweak phase transition can be significantly delayed while the universe undergoes a period of thermal inflation. Then, a first-order chiral phase transition could not only trigger electroweak symmetry breaking but also initiate the exit from supercooling. To study the dynamics of this scenario, we focus on low-energy quark-based QCD effective models that exhibit a first-order transition. While a large amount of latent heat is naturally involved if thermal inflation ends, we find that a supercooling period prior to the QCD scale considerably enhances the timescale of the transition. This enhancement implies great observational prospects at future gravitational wave observatories. Our results are readily applicable to a wide class of scale-invariant SM extensions, as well as strongly coupled dark sectors.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (114)
  1. LISA collaboration, Laser Interferometer Space Antenna, arXiv e-prints , arXiv:1702.00786 (2017), arXiv:1702.00786 [astro-ph.IM] .
  2. P. Auclair et al. (LISA Cosmology Working Group), Cosmology with the Laser Interferometer Space Antenna (2022), arXiv:2204.05434 [astro-ph.CO] .
  3. M. Punturo et al., The Einstein Telescope: A third-generation gravitational wave observatory, Class. Quant. Grav. 27, 194002 (2010).
  4. C. Caprini and D. G. Figueroa, Cosmological Backgrounds of Gravitational Waves, Class. Quant. Grav. 35, 163001 (2018), arXiv:1801.04268 [astro-ph.CO] .
  5. E. Witten, Cosmic Separation of Phases, Phys. Rev. D 30, 272 (1984).
  6. C. J. Hogan, Nucleation of cosmological phase transitions, Physics Letters B 133, 172 (1983).
  7. M. S. Turner and F. Wilczek, Relic gravitational waves and extended inflation, Phys. Rev. Lett. 65, 3080 (1990).
  8. M. Kamionkowski, A. Kosowsky, and M. S. Turner, Gravitational radiation from first-order phase transitions, Phys. Rev. D 49, 2837 (1994).
  9. S. Profumo, M. J. Ramsey-Musolf, and G. Shaughnessy, Singlet Higgs phenomenology and the electroweak phase transition, JHEP 08, 010, arXiv:0705.2425 [hep-ph] .
  10. A. Ashoorioon and T. Konstandin, Strong electroweak phase transitions without collider traces, JHEP 07, 086, arXiv:0904.0353 [hep-ph] .
  11. J. R. Espinosa, T. Konstandin, and F. Riva, Strong Electroweak Phase Transitions in the Standard Model with a Singlet, Nucl. Phys. B 854, 592 (2012), arXiv:1107.5441 [hep-ph] .
  12. G. Kurup and M. Perelstein, Dynamics of Electroweak Phase Transition In Singlet-Scalar Extension of the Standard Model, Phys. Rev. D 96, 015036 (2017), arXiv:1704.03381 [hep-ph] .
  13. C.-Y. Chen, J. Kozaczuk, and I. M. Lewis, Non-resonant Collider Signatures of a Singlet-Driven Electroweak Phase Transition, JHEP 08, 096, arXiv:1704.05844 [hep-ph] .
  14. C.-W. Chiang, Y.-T. Li, and E. Senaha, Revisiting electroweak phase transition in the standard model with a real singlet scalar, Phys. Lett. B 789, 154 (2019), arXiv:1808.01098 [hep-ph] .
  15. M. Carena, Z. Liu, and Y. Wang, Electroweak phase transition with spontaneous Z22{}_{2}start_FLOATSUBSCRIPT 2 end_FLOATSUBSCRIPT-breaking, JHEP 08, 107, arXiv:1911.10206 [hep-ph] .
  16. L. Niemi, P. Schicho, and T. V. I. Tenkanen, Singlet-assisted electroweak phase transition at two loops, Phys. Rev. D 103, 115035 (2021), arXiv:2103.07467 [hep-ph] .
  17. P. Schwaller, Gravitational Waves from a Dark Phase Transition, Phys. Rev. Lett. 115, 181101 (2015), arXiv:1504.07263 [hep-ph] .
  18. A. J. Helmboldt, J. Kubo, and S. van der Woude, Observational prospects for gravitational waves from hidden or dark chiral phase transitions, Phys. Rev. D 100, 055025 (2019), arXiv:1904.07891 [hep-ph] .
  19. F. Ertas, F. Kahlhoefer, and C. Tasillo, Turn up the volume: listening to phase transitions in hot dark sectors, JCAP 02 (02), 014, arXiv:2109.06208 [astro-ph.CO] .
  20. E. Morgante, N. Ramberg, and P. Schwaller, Gravitational waves from dark SU(3) Yang-Mills theory, Phys. Rev. D 107, 036010 (2023), arXiv:2210.11821 [hep-ph] .
  21. K. A. Meissner and H. Nicolai, Conformal Symmetry and the Standard Model, Phys. Lett. B 648, 312 (2007), arXiv:hep-th/0612165 .
  22. S. Iso, N. Okada, and Y. Orikasa, Classically conformal B−L𝐵𝐿B-Litalic_B - italic_L extended Standard Model, Phys. Lett. B 676, 81 (2009a), arXiv:0902.4050 [hep-ph] .
  23. S. Iso, N. Okada, and Y. Orikasa, The minimal B-L model naturally realized at TeV scale, Phys. Rev. D 80, 115007 (2009b), arXiv:0909.0128 [hep-ph] .
  24. S. Iso and Y. Orikasa, TeV Scale B-L model with a flat Higgs potential at the Planck scale: In view of the hierarchy problem, PTEP 2013, 023B08 (2013), arXiv:1210.2848 [hep-ph] .
  25. A. Farzinnia, H.-J. He, and J. Ren, Natural Electroweak Symmetry Breaking from Scale Invariant Higgs Mechanism, Phys. Lett. B 727, 141 (2013), arXiv:1308.0295 [hep-ph] .
  26. M. Hashimoto, S. Iso, and Y. Orikasa, Radiative symmetry breaking at the Fermi scale and flat potential at the Planck scale, Phys. Rev. D 89, 016019 (2014), arXiv:1310.4304 [hep-ph] .
  27. V. V. Khoze, C. McCabe, and G. Ro, Higgs vacuum stability from the dark matter portal, JHEP 08, 026, arXiv:1403.4953 [hep-ph] .
  28. T. Hur and P. Ko, Scale invariant extension of the standard model with strongly interacting hidden sector, Phys. Rev. Lett. 106, 141802 (2011), arXiv:1103.2571 [hep-ph] .
  29. J. Kubo, K. S. Lim, and M. Lindner, Electroweak Symmetry Breaking via QCD, Phys. Rev. Lett. 113, 091604 (2014), arXiv:1403.4262 [hep-ph] .
  30. J. Kubo and M. Yamada, Scale and electroweak first-order phase transitions, PTEP 2015, 093B01 (2015), arXiv:1506.06460 [hep-ph] .
  31. H. Hatanaka, D.-W. Jung, and P. Ko, AdS/QCD approach to the scale-invariant extension of the standard model with a strongly interacting hidden sector, JHEP 08, 094, arXiv:1606.02969 [hep-ph] .
  32. P. Baratella, A. Pomarol, and F. Rompineve, The Supercooled Universe, JHEP 03, 100, arXiv:1812.06996 [hep-ph] .
  33. W. A. Bardeen, On naturalness in the standard model, Tech. Rep. (FERMILAB, Batavia, IL, 1995).
  34. T. Hambye and A. Strumia, Dynamical generation of the weak and Dark Matter scale, Phys. Rev. D 88, 055022 (2013), arXiv:1306.2329 [hep-ph] .
  35. C. D. Carone and R. Ramos, Classical scale-invariance, the electroweak scale and vector dark matter, Phys. Rev. D 88, 055020 (2013), arXiv:1307.8428 [hep-ph] .
  36. V. V. Khoze, Inflation and Dark Matter in the Higgs Portal of Classically Scale Invariant Standard Model, JHEP 11, 215, arXiv:1308.6338 [hep-ph] .
  37. S. Benic and B. Radovcic, Majorana dark matter in a classically scale invariant model, JHEP 01, 143, arXiv:1409.5776 [hep-ph] .
  38. S. Oda, N. Okada, and D.-s. Takahashi, Right-handed neutrino dark matter in the classically conformal U(1)’ extended standard model, Phys. Rev. D 96, 095032 (2017), arXiv:1704.05023 [hep-ph] .
  39. T. Hambye, A. Strumia, and D. Teresi, Super-cool Dark Matter, JHEP 08, 188, arXiv:1805.01473 [hep-ph] .
  40. K. Kawana, Cosmology of a supercooled universe, Phys. Rev. D 105, 103515 (2022), arXiv:2201.00560 [hep-ph] .
  41. V. V. Khoze and D. L. Milne, Gravitational waves and dark matter from classical scale invariance, Phys. Rev. D 107, 095012 (2023), arXiv:2212.04784 [hep-ph] .
  42. T. Konstandin and G. Servant, Cosmological Consequences of Nearly Conformal Dynamics at the TeV scale, JCAP 12, 009, arXiv:1104.4791 [hep-ph] .
  43. T. Konstandin and G. Servant, Natural Cold Baryogenesis from Strongly Interacting Electroweak Symmetry Breaking, JCAP 07, 024, arXiv:1104.4793 [hep-ph] .
  44. G. Servant, Baryogenesis from Strong C⁢P𝐶𝑃CPitalic_C italic_P Violation and the QCD Axion, Phys. Rev. Lett. 113, 171803 (2014), arXiv:1407.0030 [hep-ph] .
  45. V. V. Khoze and G. Ro, Leptogenesis and Neutrino Oscillations in the Classically Conformal Standard Model with the Higgs Portal, JHEP 10, 075, arXiv:1307.3764 [hep-ph] .
  46. P. Huang and K.-P. Xie, Leptogenesis triggered by a first-order phase transition, JHEP 09, 052, arXiv:2206.04691 [hep-ph] .
  47. R. Jinno and M. Takimoto, Probing a classically conformal B-L model with gravitational waves, Phys. Rev. D 95, 015020 (2017), arXiv:1604.05035 [hep-ph] .
  48. J. Kubo and M. Yamada, Scale genesis and gravitational wave in a classically scale invariant extension of the standard model, JCAP 12, 001, arXiv:1610.02241 [hep-ph] .
  49. L. Marzola, A. Racioppi, and V. Vaskonen, Phase transition and gravitational wave phenomenology of scalar conformal extensions of the Standard Model, Eur. Phys. J. C 77, 484 (2017), arXiv:1704.01034 [hep-ph] .
  50. S. Iso, P. D. Serpico, and K. Shimada, QCD-Electroweak First-Order Phase Transition in a Supercooled Universe, Phys. Rev. Lett. 119, 141301 (2017), arXiv:1704.04955 [hep-ph] .
  51. C. Marzo, L. Marzola, and V. Vaskonen, Phase transition and vacuum stability in the classically conformal B–L model, Eur. Phys. J. C 79, 601 (2019), arXiv:1811.11169 [hep-ph] .
  52. M. Aoki and J. Kubo, Gravitational waves from chiral phase transition in a conformally extended standard model, JCAP 04, 001, arXiv:1910.05025 [hep-ph] .
  53. T. Prokopec, J. Rezacek, and B. Świeżewska, Gravitational waves from conformal symmetry breaking, JCAP 02, 009, arXiv:1809.11129 [hep-ph] .
  54. J. Ellis, M. Lewicki, and V. Vaskonen, Updated predictions for gravitational waves produced in a strongly supercooled phase transition, JCAP 11, 020, arXiv:2007.15586 [astro-ph.CO] .
  55. X. Wang, F. P. Huang, and X. Zhang, Phase transition dynamics and gravitational wave spectra of strong first-order phase transition in supercooled universe, JCAP 05, 045, arXiv:2003.08892 [hep-ph] .
  56. M. Kierkla, A. Karam, and B. Swiezewska, Conformal model for gravitational waves and dark matter: A status update, JHEP 03, 007, arXiv:2210.07075 [astro-ph.CO] .
  57. R. D. Pisarski and F. Wilczek, Remarks on the Chiral Phase Transition in Chromodynamics, Phys. Rev. D 29, 338 (1984).
  58. E. Witten, Cosmological Consequences of a Light Higgs Boson, Nucl. Phys. B 177, 477 (1981).
  59. B. von Harling and G. Servant, QCD-induced Electroweak Phase Transition, JHEP 01, 159, arXiv:1711.11554 [hep-ph] .
  60. D. Bödeker, Remarks on the QCD-electroweak phase transition in a supercooled universe, Phys. Rev. D 104, L111501 (2021), arXiv:2108.11966 [hep-ph] .
  61. S. Ipek and T. M. P. Tait, Early Cosmological Period of QCD Confinement, Phys. Rev. Lett. 122, 112001 (2019), arXiv:1811.00559 [hep-ph] .
  62. D. Croon, R. Houtz, and V. Sanz, Dynamical Axions and Gravitational Waves, JHEP 07, 146, arXiv:1904.10967 [hep-ph] .
  63. S. R. Coleman and E. J. Weinberg, Radiative Corrections as the Origin of Spontaneous Symmetry Breaking, Phys. Rev. D 7, 1888 (1973).
  64. D. H. Lyth and A. Riotto, Particle physics models of inflation and the cosmological density perturbation, Phys. Rept. 314, 1 (1999), arXiv:hep-ph/9807278 .
  65. J. Braun and H. Gies, Chiral phase boundary of QCD at finite temperature, JHEP 06, 024, arXiv:hep-ph/0602226 .
  66. G. Aarts et al., Phase Transitions in Particle Physics – Results and Perspectives from Lattice Quantum Chromo-Dynamics (2023) arXiv:2301.04382 [hep-lat] .
  67. Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. ii, Phys. Rev. 124, 246 (1961).
  68. S. P. Klevansky, The Nambu-Jona-Lasinio model of quantum chromodynamics, Rev. Mod. Phys. 64, 649 (1992).
  69. M. Buballa, NJL model analysis of quark matter at large density, Phys. Rept. 407, 205 (2005), arXiv:hep-ph/0402234 .
  70. T. Kunihiro, Effects of the UA⁢(1)subscriptUA1{\rm U}_{\rm A}(1)roman_U start_POSTSUBSCRIPT roman_A end_POSTSUBSCRIPT ( 1 ) anomaly on the Quark Condensates and Meson Properties at Finite Temperature, Phys. Lett. B 219, 363 (1989), [Erratum: Phys.Lett.B 245, 687 (1990)].
  71. P. Rehberg, S. P. Klevansky, and J. Hufner, Hadronization in the SU(3) Nambu-Jona-Lasinio model, Phys. Rev. C 53, 410 (1996), arXiv:hep-ph/9506436 .
  72. G. ’t Hooft, Symmetry breaking through bell-jackiw anomalies, Phys. Rev. Lett. 37, 8 (1976).
  73. M. Kobayashi and T. Maskawa, Chiral symmetry and η−X𝜂𝑋\eta-Xitalic_η - italic_X mixing, Prog. Theor. Phys. 44, 1422 (1970).
  74. M. Kobayashi, H. Kondo, and T. Maskawa, Symmetry breaking of the chiral U(3)×\times×U(3) and the quark model, Prog. Theor. Phys. 45, 1955 (1971).
  75. T. Kunihiro and T. Hatsuda, A Selfconsistent Mean Field Approach to the Dynamical Symmetry Breaking: The Effective Potential of the Nambu-Jona-Lasinio Model, Prog. Theor. Phys. 71, 1332 (1984).
  76. T. Hatsuda and T. Kunihiro, QCD phenomenology based on a chiral effective Lagrangian, Phys. Rept. 247, 221 (1994), arXiv:hep-ph/9401310 .
  77. T. Hatsuda and T. Kunihiro, Fluctuation effects in hot quark matter: Precursors of chiral transition at finite temperature, Phys. Rev. Lett. 55, 158 (1985).
  78. K. Fukushima, Phase diagrams in the three-flavor Nambu-Jona-Lasinio model with the Polyakov loop, Phys. Rev. D 77, 114028 (2008), [Erratum: Phys.Rev.D 78, 039902 (2008)], arXiv:0803.3318 [hep-ph] .
  79. H. Kohyama, D. Kimura, and T. Inagaki, Regularization dependence on phase diagram in Nambu–Jona-Lasinio model, Nucl. Phys. B 896, 682 (2015), arXiv:1501.00449 [hep-ph] .
  80. K. Fukushima and C. Sasaki, The phase diagram of nuclear and quark matter at high baryon density, Prog. Part. Nucl. Phys. 72, 99 (2013), arXiv:1301.6377 [hep-ph] .
  81. A. M. Polyakov, Compact Gauge Fields and the Infrared Catastrophe, Phys. Lett. B 59, 82 (1975).
  82. P. N. Meisinger, T. R. Miller, and M. C. Ogilvie, Phenomenological equations of state for the quark gluon plasma, Phys. Rev. D 65, 034009 (2002), arXiv:hep-ph/0108009 .
  83. K. Fukushima and V. Skokov, Polyakov loop modeling for hot QCD, Prog. Part. Nucl. Phys. 96, 154 (2017), arXiv:1705.00718 [hep-ph] .
  84. P. N. Meisinger and M. C. Ogilvie, Chiral symmetry restoration and Z(N) symmetry, Phys. Lett. B 379, 163 (1996), arXiv:hep-lat/9512011 .
  85. K. Fukushima, Chiral effective model with the Polyakov loop, Phys. Lett. B 591, 277 (2004), arXiv:hep-ph/0310121 .
  86. C. Ratti, M. A. Thaler, and W. Weise, Phases of QCD: Lattice thermodynamics and a field theoretical model, Phys. Rev. D 73, 014019 (2006), arXiv:hep-ph/0506234 .
  87. B.-J. Schaefer, J. M. Pawlowski, and J. Wambach, The Phase Structure of the Polyakov–Quark-Meson Model, Phys. Rev. D 76, 074023 (2007), arXiv:0704.3234 [hep-ph] .
  88. L. D. McLerran and B. Svetitsky, Quark Liberation at High Temperature: A Monte Carlo Study of SU(2) Gauge Theory, Phys. Rev. D 24, 450 (1981).
  89. L. Fister and J. M. Pawlowski, Confinement from Correlation Functions, Phys. Rev. D 88, 045010 (2013), arXiv:1301.4163 [hep-ph] .
  90. A. D. Linde, Fate of the False Vacuum at Finite Temperature: Theory and Applications, Phys. Lett. B 100, 37 (1981).
  91. C. G. Callan and S. Coleman, Fate of the false vacuum. ii. first quantum corrections, Phys. Rev. D 16, 1762 (1977).
  92. S. Coleman, Erratum: Fate of the false vacuum: semiclassical theory, Phys. Rev. D 16, 1248 (1977).
  93. O. Gould and J. Hirvonen, Effective field theory approach to thermal bubble nucleation, Phys. Rev. D 104, 096015 (2021), arXiv:2108.04377 [hep-ph] .
  94. C. L. Wainwright, CosmoTransitions: Computing Cosmological Phase Transition Temperatures and Bubble Profiles with Multiple Fields, Comput. Phys. Commun. 183, 2006 (2012), arXiv:1109.4189 [hep-ph] .
  95. A. H. Guth and S. H. H. Tye, Phase transitions and magnetic monopole production in the very early universe, Phys. Rev. Lett. 44, 631 (1980).
  96. A. H. Guth and E. J. Weinberg, Cosmological consequences of a first-order phase transition in the su5subscriptu5{\mathrm{u}}_{5}roman_u start_POSTSUBSCRIPT 5 end_POSTSUBSCRIPT grand unified model, Phys. Rev. D 23, 876 (1981).
  97. J. Ellis, M. Lewicki, and J. M. No, On the Maximal Strength of a First-Order Electroweak Phase Transition and its Gravitational Wave Signal, JCAP 04, 003, arXiv:1809.08242 [hep-ph] .
  98. C. Caprini et al., Detecting gravitational waves from cosmological phase transitions with LISA: an update, JCAP 03, 024, arXiv:1910.13125 [astro-ph.CO] .
  99. M. S. Turner, E. J. Weinberg, and L. M. Widrow, Bubble nucleation in first-order inflation and other cosmological phase transitions, Phys. Rev. D 46, 2384 (1992).
  100. M. Lewicki and V. Vaskonen, Gravitational waves from bubble collisions and fluid motion in strongly supercooled phase transitions, Eur. Phys. J. C 83, 109 (2023), arXiv:2208.11697 [astro-ph.CO] .
  101. M. Lewicki, O. Pujolàs, and V. Vaskonen, Escape from supercooling with or without bubbles: gravitational wave signatures, Eur. Phys. J. C 81, 857 (2021), arXiv:2106.09706 [astro-ph.CO] .
  102. M. Lewicki and V. Vaskonen, Gravitational wave spectra from strongly supercooled phase transitions, Eur. Phys. J. C 80, 1003 (2020), arXiv:2007.04967 [astro-ph.CO] .
  103. J. T. Giblin and J. B. Mertens, Gravitional radiation from first-order phase transitions in the presence of a fluid, Phys. Rev. D 90, 023532 (2014), arXiv:1405.4005 [astro-ph.CO] .
  104. D. Bodeker and G. D. Moore, Can electroweak bubble walls run away?, JCAP 05, 009, arXiv:0903.4099 [hep-ph] .
  105. Y. Gouttenoire, R. Jinno, and F. Sala, Friction pressure on relativistic bubble walls, JHEP 05, 004, arXiv:2112.07686 [hep-ph] .
  106. A. Sesana et al., Unveiling the gravitational universe at μ𝜇\muitalic_μ-Hz frequencies, Exper. Astron. 51, 1333 (2021), arXiv:1908.11391 [astro-ph.IM] .
  107. J. Crowder and N. J. Cornish, Beyond LISA: Exploring future gravitational wave missions, Phys. Rev. D 72, 083005 (2005), arXiv:gr-qc/0506015 .
  108. B. Sathyaprakash et al., Scientific Objectives of Einstein Telescope, Class. Quant. Grav. 29, 124013 (2012), [Erratum: Class.Quant.Grav. 30, 079501 (2013)], arXiv:1206.0331 [gr-qc] .
  109. T. Robson, N. J. Cornish, and C. Liu, The construction and use of LISA sensitivity curves, Class. Quant. Grav. 36, 105011 (2019), arXiv:1803.01944 [astro-ph.HE] .
  110. F. Cuteri, O. Philipsen, and A. Sciarra, On the order of the QCD chiral phase transition for different numbers of quark flavours, JHEP 11, 141, arXiv:2107.12739 [hep-lat] .
  111. A. Ekstedt, P. Schicho, and T. V. I. Tenkanen, DRalgo: A package for effective field theory approach for thermal phase transitions, Comput. Phys. Commun. 288, 108725 (2023), arXiv:2205.08815 [hep-ph] .
  112. J. I. Kapusta, Quantum Chromodynamics at High Temperature, Nucl. Phys. B 148, 461 (1979).
  113. R. D. Pisarski, Computing Finite Temperature Loops with Ease, Nucl. Phys. B 309, 476 (1988).
  114. R. R. Parwani, Resummation in a hot scalar field theory, Phys. Rev. D 45, 4695 (1992), [Erratum: Phys.Rev.D 48, 5965 (1993)], arXiv:hep-ph/9204216 .
Citations (18)
View on Semantic Scholar
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Ai Generate Text Spark Streamline Icon: https://streamlinehq.com

Paper Prompts

Sign up for free to create and run prompts on this paper using GPT-5.

List Streamline Icon: https://streamlinehq.com Explore 10 Community Prompts
Dice Question Streamline Icon: https://streamlinehq.com

Follow-up Questions

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now