Abstract
Using the exact WKB analysis of the higher-order differential equations, we analyze the asymmetry in dynamical particle production of a complex scalar field. The solution requires the Stokes phenomena of the fourth-order differential equation. We found that the interference of different types of the Stokes phenomena causes matter-antimatter asymmetry. We also showed a specific example where asymmetry is forbidden in the exact calculation, but a false asymmetry appears in the perturbative expansion.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Planck collaboration, Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641 (2020) A6 [arXiv:1807.06209] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, PTEP 2020 (2020) 083C01 [INSPIRE].
A.D. Sakharov, Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe, Pisma Zh. Eksp. Teor. Fiz. 5 (1967) 32 [Sov. Phys. Uspekhi 34 (1991) 392].
A.G. Cohen and D.B. Kaplan, Thermodynamic Generation of the Baryon Asymmetry, Phys. Lett. B 199 (1987) 251 [INSPIRE].
A.G. Cohen and D.B. Kaplan, Spontaneous Baryogenesis, Nucl. Phys. B 308 (1988) 913 [INSPIRE].
A.G. Cohen, D.B. Kaplan and A.E. Nelson, Spontaneous baryogenesis at the weak phase transition, Phys. Lett. B 263 (1991) 86 [INSPIRE].
E.V. Arbuzova, A.D. Dolgov and V.A. Novikov, General properties and kinetics of spontaneous baryogenesis, Phys. Rev. D 94 (2016) 123501 [arXiv:1607.01247] [INSPIRE].
I. Affleck and M. Dine, A New Mechanism for Baryogenesis, Nucl. Phys. B 249 (1985) 361 [INSPIRE].
K. Enqvist and J. McDonald, B-ball baryogenesis and the baryon to dark matter ratio, Nucl. Phys. B 538 (1999) 321 [hep-ph/9803380] [INSPIRE].
S. Kasuya and M. Kawasaki, Q ball formation through Affleck-Dine mechanism, Phys. Rev. D 61 (2000) 041301 [hep-ph/9909509] [INSPIRE].
S. Enomoto and T. Matsuda, Asymmetric preheating, Int. J. Mod. Phys. A 33 (2018) 1850146 [arXiv:1707.05310] [INSPIRE].
Y.B. Zeldovich and A.A. Starobinsky, Particle production and vacuum polarization in an anisotropic gravitational field, Zh. Eksp. Teor. Fiz. 61 (1971) 2161 [INSPIRE].
A. Kusenko, K. Schmitz and T.T. Yanagida, Leptogenesis via Axion Oscillations after Inflation, Phys. Rev. Lett. 115 (2015) 011302 [arXiv:1412.2043] [INSPIRE].
L. Pearce, L. Yang, A. Kusenko and M. Peloso, Leptogenesis via neutrino production during Higgs condensate relaxation, Phys. Rev. D 92 (2015) 023509 [arXiv:1505.02461] [INSPIRE].
P. Adshead and E.I. Sfakianakis, Leptogenesis from left-handed neutrino production during axion inflation, Phys. Rev. Lett. 116 (2016) 091301 [arXiv:1508.00881] [INSPIRE].
P. Adshead and E.I. Sfakianakis, Fermion production during and after axion inflation, Journal of Cosmology and Astroparticle Physics 2015 (2015) 021.
S. Enomoto and T. Matsuda, The exact WKB and the Landau-Zener transition for asymmetry in cosmological particle production, JHEP 02 (2022) 131 [arXiv:2104.02312] [INSPIRE].
A. Kusenko, L. Pearce and L. Yang, Postinflationary Higgs relaxation and the origin of matter-antimatter asymmetry, Phys. Rev. Lett. 114 (2015) 061302 [arXiv:1410.0722] [INSPIRE].
L. Yang, L. Pearce and A. Kusenko, Leptogenesis via Higgs Condensate Relaxation, Phys. Rev. D 92 (2015) 043506 [arXiv:1505.07912] [INSPIRE].
Y.-P. Wu, L. Yang and A. Kusenko, Leptogenesis from spontaneous symmetry breaking during inflation, JHEP 12 (2019) 088 [arXiv:1905.10537] [INSPIRE].
K. Freese, J.A. Frieman and A.V. Olinto, Natural inflation with pseudo nambu-goldstone bosons, Physical Review Letters 65 (1990) 3233.
F.C. Adams, J.R. Bond, K. Freese, J.A. Frieman and A.V. Olinto, Natural inflation: Particle physics models, power law spectra for large scale structure, and constraints from COBE, Phys. Rev. D 47 (1993) 426 [hep-ph/9207245] [INSPIRE].
S.R. Coleman, Q-balls, Nucl. Phys. B 262 (1985) 263 [INSPIRE].
A. Kusenko and M.E. Shaposhnikov, Supersymmetric Q balls as dark matter, Phys. Lett. B 418 (1998) 46 [hep-ph/9709492] [INSPIRE].
B.-H. Liu, L.D. McLerran and N. Turok, Bubble nucleation and growth at a baryon number producing electroweak phase transition, Phys. Rev. D 46 (1992) 2668 [INSPIRE].
T. Matsuda, Baryon number violation, baryogenesis and defects with extra dimensions, Phys. Rev. D 66 (2002) 023508 [hep-ph/0204307] [INSPIRE].
T. Matsuda, Electroweak baryogenesis mediated by locally supersymmetry breaking defects, Phys. Rev. D 64 (2001) 083512 [hep-ph/0107314] [INSPIRE].
T. Matsuda, On the cosmological domain wall problem in supersymmetric models, Phys. Lett. B 436 (1998) 264 [hep-ph/9804409] [INSPIRE].
L. Kofman, A.D. Linde, X. Liu, A. Maloney, L. McAllister and E. Silverstein, Beauty is attractive: Moduli trapping at enhanced symmetry points, JHEP 05 (2004) 030 [hep-th/0403001] [INSPIRE].
S. Enomoto, S. Iida, N. Maekawa and T. Matsuda, Beauty is more attractive: particle production and moduli trapping with higher dimensional interaction, JHEP 01 (2014) 141 [arXiv:1310.4751] [INSPIRE].
L. Kofman, A.D. Linde and A.A. Starobinsky, Towards the theory of reheating after inflation, Phys. Rev. D 56 (1997) 3258 [hep-ph/9704452] [INSPIRE].
G.N. Felder, L. Kofman and A.D. Linde, Instant preheating, Phys. Rev. D 59 (1999) 123523 [hep-ph/9812289] [INSPIRE].
J.H. Traschen and R.H. Brandenberger, Particle Production During Out-of-equilibrium Phase Transitions, Phys. Rev. D 42 (1990) 2491 [INSPIRE].
A. Dolgov and K. Freese, Calculation of particle production by Nambu Goldstone bosons with application to inflation reheating and baryogenesis, Phys. Rev. D 51 (1995) 2693 [hep-ph/9410346] [INSPIRE].
A. Dolgov, K. Freese, R. Rangarajan and M. Srednicki, Baryogenesis during reheating in natural inflation and comments on spontaneous baryogenesis, Phys. Rev. D 56 (1997) 6155 [hep-ph/9610405] [INSPIRE].
H.L. Berk, W.M. Nevins and K.V. Roberts, New Stokes’ line in WKB theory, Journal of Mathematical Physics 23 (1982) 988.
T. Aoki, T. Kawai, S. Sasaki, A. Shudo and Y. Takei, Virtual turning points and bifurcation of Stokes curves for higher order ordinary differential equations, Journal of Physics A Mathematical General 38 (2005) 3317 [math-ph/0409005].
S. Enomoto and T. Matsuda, The exact WKB for cosmological particle production, JHEP 03 (2021) 090 [arXiv:2010.14835] [INSPIRE].
H. Taya, T. Fujimori, T. Misumi, M. Nitta and N. Sakai, Exact WKB analysis of the vacuum pair production by time-dependent electric fields, JHEP 03 (2021) 082 [arXiv:2010.16080] [INSPIRE].
H. Kitamoto, No-go theorem of anisotropic inflation via Schwinger mechanism, Phys. Rev. D 103 (2021) 063521 [arXiv:2010.10388] [INSPIRE].
S. Hashiba and Y. Yamada, Stokes phenomenon and gravitational particle production — How to evaluate it in practice, JCAP 05 (2021) 022 [arXiv:2101.07634] [INSPIRE].
A. Voros, The return of the quartic oscillator — The complex WKB method, Ann. Inst. Henri Poincare 39 (1983) 211.
E. Delabaere, H. Dillinger and F. Pham, Resurgence de Voros et peeriodes des courves hyperelliptique, Annales Inst. Fourier 43 (1993) 163.
V.L. Pokrovskii and I.M. Khalatnikov, On the Problem of Above-Barrier Reflection of High-Energy Particles, Zh. Eksp. Teor. Fiz. 40 (1961) 1713 [Sov. Phys. JETP 13 (1961) 1207].
E. Brezin and C. Itzykson, Pair production in vacuum by an alternating field, Physical Review D 2 (1970) 1191.
M.V. Berry and K.E. Mount, Semiclassical approximations in wave mechanics, Rept. Prog. Phys. 35 (1972) 315 [INSPIRE].
D.J.H. Chung, Classical Inflation Field Induced Creation of Superheavy Dark Matter, Phys. Rev. D 67 (2003) 083514 [hep-ph/9809489] [INSPIRE].
S. Enomoto, N. Maekawa and T. Matsuda, Preheating with higher dimensional interaction, Phys. Rev. D 91 (2015) 103504 [arXiv:1405.3012] [INSPIRE].
H. Shen and H.J. Silverstone, Observations on the JWKB treatment of the quadratic barrier, in Algebraic analysis of differential equations: From microlocal analysis to exponential asymptotics, Springer Tokyo, Japan (2008), pp. 237–250 [DOI].
Y. Takei, Sato’s conjecture for the Weber equation and transformation theory for Schrödinger equations with a merging pair of turning points, RIMS Kokyuroku Bessatsu B10 (2008) 205, [https://www.kurims.kyoto-u.ac.jp/~kenkyubu/bessatsu/open/B10/pdf/B10_011.pdf].
T. Aoki, T. Kawai and Y. Takei, The bender-wu analysis and the voros theory, in ICM-90 Satellite Conference Proceedings, pp. 1–29, Springer Tokyo, Japan (1991) [DOI].
Takashi Aoki, Kohei Iwaki, Toshinori Takahashi, Exact WKB Analysis of Schrödinger Equations with a Stokes Curve of Loop Type, Funkcial. Ekvac 62 (2019) 1.
N.D. Birrell and P.C.W. Davies, Quantum Fields in Curved Space, Cambridge University Press (1982) [DOI].
C. Zener, Nonadiabatic crossing of energy levels, Proc. Roy. Soc. Lond. A 137 (1932) 696 [INSPIRE].
P.B. Greene and L. Kofman, Preheating of fermions, Physics Letters B 448 (1999) 6.
M. Peloso and L. Sorbo, Preheating of massive fermions after inflation: Analytical results, JHEP 05 (2000) 016 [hep-ph/0003045] [INSPIRE].
N. Shimada and A. Shudo, Numerical verification of the exact WKB formula for the generalized Landau-Zener-Stueckelberg problem, Phys. Rev. A 102 (2020) 022213.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2203.04497
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.
About this article
Cite this article
Enomoto, S., Matsuda, T. The Exact WKB analysis for asymmetric scalar preheating. J. High Energ. Phys. 2023, 88 (2023). https://doi.org/10.1007/JHEP01(2023)088
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2023)088