Abstract
We show how the two physically-distinct sources of CP -asymmetry relevant to scenarios of leptogenesis: (i) resonant mixing and (ii) oscillations between different flavours can be unambiguously identified within the Kadanoff-Baym formalism. These contributions are isolated by analyzing the spectral structure of the non-equilibrium propagators without relying on the definition of particle number densities. The mixing source is associated with the usual mass shells, whereas the oscillation source is identified with a third intermediate shell. In addition, we identify terms lying on the oscillation shell that can be interpreted as the destructive interference between mixing and oscillation. We confirm that identical shell structure is obtained in both the Heisenberg- and interaction-picture realizations of the Kadanoff-Baym formalism. In so doing, we illustrate the self-consistency and complementarity of these two approaches. The interaction-picture approach in particular has the advantage that it may be used to analyze all forms of mass spectra from quasi-degenerate through to hierarchical.
References
Particle Data Group collaboration, K.A. Olive et al., Review of particle physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
A. Pais and O. Piccioni, Note on the decay and absorption of the θ 0, Phys. Rev. 100 (1955) 1487 [INSPIRE].
D. Boyanovsky and C.M. Ho, Nonequilibrium dynamics of mixing, oscillations and equilibration: a model study, Phys. Rev. D 75 (2007) 085004 [hep-ph/0610036] [INSPIRE].
D. Boyanovsky and L. Lello, Time evolution of cascade decay, New J. Phys. 16 (2014) 063050 [arXiv:1403.6366] [INSPIRE].
D. Boyanovsky, Space-time evolution of heavy sterile neutrinos in cascade decays, Nucl. Phys. B 888 (2014) 248 [arXiv:1406.5739] [INSPIRE].
D. Boyanovsky, Nearly degenerate heavy sterile neutrinos in cascade decay: mixing and oscillations, Phys. Rev. D 90 (2014) 105024 [arXiv:1409.4265] [INSPIRE].
B. Garbrecht and M. Herranen, Effective theory of resonant leptogenesis in the closed-time-path approach, Nucl. Phys. B 861 (2012) 17 [arXiv:1112.5954] [INSPIRE].
B. Garbrecht, F. Gautier and J. Klaric, Strong washout approximation to resonant leptogenesis, JCAP 09 (2014) 033 [arXiv:1406.4190] [INSPIRE].
P.S. Bhupal Dev, P. Millington, A. Pilaftsis and D. Teresi, Flavour covariant transport equations: an application to resonant leptogenesis, Nucl. Phys. B 886 (2014) 569 [arXiv:1404.1003] [INSPIRE].
P.S. Bhupal Dev, P. Millington, A. Pilaftsis and D. Teresi, Corrigendum to “Flavour covariant transport equations: an application to resonant leptogenesis”, Nucl. Phys. B 897 (2015) 749 [arXiv:1504.07640] [INSPIRE].
P.S. Bhupal Dev, P. Millington, A. Pilaftsis and D. Teresi, Kadanoff-Baym approach to flavour mixing and oscillations in resonant leptogenesis, Nucl. Phys. B 891 (2015) 128 [arXiv:1410.6434] [INSPIRE].
M. Fukugita and T. Yanagida, Baryogenesis without grand unification, Phys. Lett. B 174 (1986) 45 [INSPIRE].
S. Blanchet and P. Di Bari, The minimal scenario of leptogenesis, New J. Phys. 14 (2012) 125012 [arXiv:1211.0512] [INSPIRE].
V.A. Kuzmin, V.A. Rubakov and M.E. Shaposhnikov, On the anomalous electroweak baryon number nonconservation in the early universe, Phys. Lett. B 155 (1985) 36 [INSPIRE].
A. Pilaftsis, CP violation and baryogenesis due to heavy Majorana neutrinos, Phys. Rev. D 56 (1997) 5431 [hep-ph/9707235] [INSPIRE].
A. Pilaftsis, Heavy Majorana neutrinos and baryogenesis, Int. J. Mod. Phys. A 14 (1999) 1811 [hep-ph/9812256] [INSPIRE].
J.R. Ellis, M. Raidal and T. Yanagida, Observable consequences of partially degenerate leptogenesis, Phys. Lett. B 546 (2002) 228 [hep-ph/0206300] [INSPIRE].
T. Endoh, T. Morozumi and Z. Xiong, Primordial lepton family asymmetries in seesaw model, Prog. Theor. Phys. 111 (2004) 123 [hep-ph/0308276] [INSPIRE].
A. Pilaftsis, Resonant τ leptogenesis with observable lepton number violation, Phys. Rev. Lett. 95 (2005) 081602 [hep-ph/0408103] [INSPIRE].
A. Pilaftsis and T.E.J. Underwood, Electroweak-scale resonant leptogenesis, Phys. Rev. D 72 (2005) 113001 [hep-ph/0506107] [INSPIRE].
T. Asaka and M. Shaposhnikov, The νMSM, dark matter and baryon asymmetry of the universe, Phys. Lett. B 620 (2005) 17 [hep-ph/0505013] [INSPIRE].
O. Vives, Flavor dependence of CP asymmetries and thermal leptogenesis with strong right-handed neutrino mass hierarchy, Phys. Rev. D 73 (2006) 073006 [hep-ph/0512160] [INSPIRE].
F.F. Deppisch and A. Pilaftsis, Lepton flavour violation and θ 13 in minimal resonant leptogenesis, Phys. Rev. D 83 (2011) 076007 [arXiv:1012.1834] [INSPIRE].
S. Blanchet, P. Di Bari, D.A. Jones and L. Marzola, Leptogenesis with heavy neutrino flavours: from density matrix to Boltzmann equations, JCAP 01 (2013) 041 [arXiv:1112.4528] [INSPIRE].
R. Barbieri, P. Creminelli, A. Strumia and N. Tetradis, Baryogenesis through leptogenesis, Nucl. Phys. B 575 (2000) 61 [hep-ph/9911315] [INSPIRE].
A. Abada, S. Davidson, F.-X. Josse-Michaux, M. Losada and A. Riotto, Flavour issues in leptogenesis, JCAP 04 (2006) 004 [hep-ph/0601083] [INSPIRE].
E. Nardi, Y. Nir, E. Roulet and J. Racker, The importance of flavor in leptogenesis, JHEP 01 (2006) 164 [hep-ph/0601084] [INSPIRE].
A. Abada et al., Flavour matters in leptogenesis, JHEP 09 (2006) 010 [hep-ph/0605281] [INSPIRE].
S. Blanchet and P. Di Bari, Flavour effects on leptogenesis predictions, JCAP 03 (2007) 018 [hep-ph/0607330] [INSPIRE].
S. Blanchet, P. Di Bari and G.G. Raffelt, Quantum Zeno effect and the impact of flavour in leptogenesis, JCAP 03 (2007) 012 [hep-ph/0611337] [INSPIRE].
S. Pascoli, S.T. Petcov and A. Riotto, Leptogenesis and low energy CP-violation in neutrino physics, Nucl. Phys. B 774 (2007) 1 [hep-ph/0611338] [INSPIRE].
G.C. Branco, A.J. Buras, S. Jäger, S. Uhlig and A. Weiler, Another look at minimal lepton flavour violation, leptogenesis and the ratio M ν /ΛLFV, JHEP 09 (2007) 004 [hep-ph/0609067] [INSPIRE].
A. De Simone and A. Riotto, On the impact of flavour oscillations in leptogenesis, JCAP 02 (2007) 005 [hep-ph/0611357] [INSPIRE].
A. Pilaftsis, Resonant CP-violation induced by particle mixing in transition amplitudes, Nucl. Phys. B 504 (1997) 61 [hep-ph/9702393] [INSPIRE].
A. Pilaftsis and T.E.J. Underwood, Resonant leptogenesis, Nucl. Phys. B 692 (2004) 303 [hep-ph/0309342] [INSPIRE].
M. Flanz, E.A. Paschos and U. Sarkar, Baryogenesis from a lepton asymmetric universe, Phys. Lett. B 345 (1995) 248 [Erratum ibid. B 382 (1996) 447] [hep-ph/9411366] [INSPIRE].
L. Covi and E. Roulet, Baryogenesis from mixed particle decays, Phys. Lett. B 399 (1997) 113 [hep-ph/9611425] [INSPIRE].
L. Covi, E. Roulet and F. Vissani, CP violating decays in leptogenesis scenarios, Phys. Lett. B 384 (1996) 169 [hep-ph/9605319] [INSPIRE].
W. Buchmüller and M. Plümacher, CP asymmetry in Majorana neutrino decays, Phys. Lett. B 431 (1998) 354 [hep-ph/9710460] [INSPIRE].
P.S. Bhupal Dev, P. Millington, A. Pilaftsis and D. Teresi, Flavour effects in resonant leptogenesis from semi-classical and Kadanoff-Baym approaches, J. Phys. Conf. Ser. 631 (2015) 012087 [arXiv:1502.07987] [INSPIRE].
E.W. Kolb and S. Wolfram, Baryon number generation in the early universe, Nucl. Phys. B 172 (1980) 224 [Erratum ibid. B 195 (1982) 542] [INSPIRE].
M.A. Luty, Baryogenesis via leptogenesis, Phys. Rev. D 45 (1992) 455 [INSPIRE].
G. Sigl and G. Raffelt, General kinetic description of relativistic mixed neutrinos, Nucl. Phys. B 406 (1993) 423 [INSPIRE].
E.K. Akhmedov, V.A. Rubakov and A.Y. Smirnov, Baryogenesis via neutrino oscillations, Phys. Rev. Lett. 81 (1998) 1359 [hep-ph/9803255] [INSPIRE].
M. Shaposhnikov, The νMSM, leptonic asymmetries and properties of singlet fermions, JHEP 08 (2008) 008 [arXiv:0804.4542] [INSPIRE].
J.-S. Gagnon and M. Shaposhnikov, Baryon asymmetry of the universe without Boltzmann or Kadanoff-Baym equations, Phys. Rev. D 83 (2011) 065021 [arXiv:1012.1126] [INSPIRE].
T. Asaka, S. Eijima and H. Ishida, Kinetic equations for baryogenesis via sterile neutrino oscillation, JCAP 02 (2012) 021 [arXiv:1112.5565] [INSPIRE].
L. Canetti, M. Drewes, T. Frossard and M. Shaposhnikov, Dark matter, baryogenesis and neutrino oscillations from right-handed neutrinos, Phys. Rev. D 87 (2013) 093006 [arXiv:1208.4607] [INSPIRE].
B. Shuve and I. Yavin, Baryogenesis through neutrino oscillations: a unified perspective, Phys. Rev. D 89 (2014) 075014 [arXiv:1401.2459] [INSPIRE].
W. Buchmüller and S. Fredenhagen, Quantum mechanics of baryogenesis, Phys. Lett. B 483 (2000) 217 [hep-ph/0004145] [INSPIRE].
T. Prokopec, M.G. Schmidt and S. Weinstock, Transport equations for chiral fermions to order ℏ and electroweak baryogenesis: part I, Annals Phys. 314 (2004) 208 [hep-ph/0312110] [INSPIRE].
T. Prokopec, M.G. Schmidt and S. Weinstock, Transport equations for chiral fermions to order ℏ and electroweak baryogenesis: part II, Annals Phys. 314 (2004) 267 [hep-ph/0406140] [INSPIRE].
A. De Simone and A. Riotto, Quantum Boltzmann equations and leptogenesis, JCAP 08 (2007) 002 [hep-ph/0703175] [INSPIRE].
A. De Simone and A. Riotto, On resonant leptogenesis, JCAP 08 (2007) 013 [arXiv:0705.2183] [INSPIRE].
V. Cirigliano, A. De Simone, G. Isidori, I. Masina and A. Riotto, Quantum resonant leptogenesis and minimal lepton flavour violation, JCAP 01 (2008) 004 [arXiv:0711.0778] [INSPIRE].
A. Anisimov, W. Buchmüller, M. Drewes and S. Mendizabal, Nonequilibrium dynamics of scalar fields in a thermal bath, Annals Phys. 324 (2009) 1234 [arXiv:0812.1934] [INSPIRE].
M. Garny, A. Hohenegger, A. Kartavtsev and M. Lindner, Systematic approach to leptogenesis in nonequilibrium QFT: vertex contribution to the CP-violating parameter, Phys. Rev. D 80 (2009) 125027 [arXiv:0909.1559] [INSPIRE].
M. Garny, A. Hohenegger, A. Kartavtsev and M. Lindner, Systematic approach to leptogenesis in nonequilibrium QFT: self-energy contribution to the CP-violating parameter, Phys. Rev. D 81 (2010) 085027 [arXiv:0911.4122] [INSPIRE].
V. Cirigliano, C. Lee, M.J. Ramsey-Musolf and S. Tulin, Flavored quantum Boltzmann equations, Phys. Rev. D 81 (2010) 103503 [arXiv:0912.3523] [INSPIRE].
A. Anisimov, W. Buchmüller, M. Drewes and S. Mendizabal, Leptogenesis from quantum interference in a thermal bath, Phys. Rev. Lett. 104 (2010) 121102 [arXiv:1001.3856] [INSPIRE].
M. Garny, A. Hohenegger and A. Kartavtsev, Medium corrections to the CP-violating parameter in leptogenesis, Phys. Rev. D 81 (2010) 085028 [arXiv:1002.0331] [INSPIRE].
M. Beneke, B. Garbrecht, M. Herranen and P. Schwaller, Finite number density corrections to leptogenesis, Nucl. Phys. B 838 (2010) 1 [arXiv:1002.1326] [INSPIRE].
M. Beneke, B. Garbrecht, C. Fidler, M. Herranen and P. Schwaller, Flavoured leptogenesis in the CTP formalism, Nucl. Phys. B 843 (2011) 177 [arXiv:1007.4783] [INSPIRE].
B. Garbrecht, Leptogenesis: the other cuts, Nucl. Phys. B 847 (2011) 350 [arXiv:1011.3122] [INSPIRE].
A. Anisimov, W. Buchmüller, M. Drewes and S. Mendizabal, Quantum leptogenesis I, Annals Phys. 326 (2011) 1998 [Erratum ibid. 338 (2011) 376] [arXiv:1012.5821] [INSPIRE].
M. Garny, A. Kartavtsev and A. Hohenegger, Leptogenesis from first principles in the resonant regime, Annals Phys. 328 (2013) 26 [arXiv:1112.6428] [INSPIRE].
M. Drewes and B. Garbrecht, Leptogenesis from a GeV seesaw without mass degeneracy, JHEP 03 (2013) 096 [arXiv:1206.5537] [INSPIRE].
B. Garbrecht, Baryogenesis from mixing of lepton doublets, Nucl. Phys. B 868 (2013) 557 [arXiv:1210.0553] [INSPIRE].
T. Frossard, M. Garny, A. Hohenegger, A. Kartavtsev and D. Mitrouskas, Systematic approach to thermal leptogenesis, Phys. Rev. D 87 (2013) 085009 [arXiv:1211.2140] [INSPIRE].
M. Drewes, The phenomenology of right handed neutrinos, Int. J. Mod. Phys. E 22 (2013) 1330019 [arXiv:1303.6912] [INSPIRE].
B. Garbrecht and M.J. Ramsey-Musolf, Cuts, cancellations and the closed time path: the soft leptogenesis example, Nucl. Phys. B 882 (2014) 145 [arXiv:1307.0524] [INSPIRE].
A. Hohenegger and A. Kartavtsev, Leptogenesis in crossing and runaway regimes, JHEP 07 (2014) 130 [arXiv:1404.5309] [INSPIRE].
S. Iso, K. Shimada and M. Yamanaka, Kadanoff-Baym approach to the thermal resonant leptogenesis, JHEP 04 (2014) 062 [arXiv:1312.7680] [INSPIRE].
S. Iso and K. Shimada, Coherent flavour oscillation and CP-violating parameter in thermal resonant leptogenesis, JHEP 08 (2014) 043 [arXiv:1404.4816] [INSPIRE].
G. Baym and L.P. Kadanoff, Conservation laws and correlation functions, Phys. Rev. 124 (1961) 287 [INSPIRE].
L.P. Kadanoff and G. Baym, Quantum statistical mechanics, Benjamin, New York U.S.A. (1962).
J.-P. Blaizot and E. Iancu, The quark gluon plasma: collective dynamics and hard thermal loops, Phys. Rept. 359 (2002) 355 [hep-ph/0101103] [INSPIRE].
J. Berges, Introduction to nonequilibrium quantum field theory, AIP Conf. Proc. 739 (2004) 3 [hep-ph/0409233] [INSPIRE].
J.S. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys. 2 (1961) 407 [INSPIRE].
L.V. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz. 47 (1964) 1515 [INSPIRE].
R.D. Jordan, Effective field equations for expectation values, Phys. Rev. D 33 (1986) 444 [INSPIRE].
E. Calzetta and B.L. Hu, Nonequilibrium quantum fields: closed time path effective action, Wigner function and Boltzmann equation, Phys. Rev. D 37 (1988) 2878 [INSPIRE].
E. Calzetta and B.L. Hu, Closed time path functional formalism in curved space-time: application to cosmological back reaction problems, Phys. Rev. D 35 (1987) 495 [INSPIRE].
P. Millington and A. Pilaftsis, Perturbative nonequilibrium thermal field theory, Phys. Rev. D 88 (2013) 085009 [arXiv:1211.3152] [INSPIRE].
P. Millington and A. Pilaftsis, Perturbative non-equilibrium thermal field theory to all orders in gradient expansion, Phys. Lett. B 724 (2013) 56 [arXiv:1304.7249] [INSPIRE].
H.A. Weldon, Thermalization of boson propagators in finite-temperature field theory, Phys. Rev. D 45 (1992) 352 [INSPIRE].
T. Altherr and D. Seibert, Problems of perturbation series in nonequilibrium quantum field theories, Phys. Lett. B 333 (1994) 149 [hep-ph/9405396] [INSPIRE].
T. Altherr, Resummation of perturbation series in nonequilibrium scalar field theory, Phys. Lett. B 341 (1995) 325 [hep-ph/9407249] [INSPIRE].
P.F. Bedaque, Thermalization and pinch singularities in non-equilibrium quantum field theory, Phys. Lett. B 344 (1995) 23 [hep-ph/9410415] [INSPIRE].
I. Dadić, Two mechanisms for elimination of pinch singularities in out of equilibrium thermal field theories, Phys. Rev. D 59 (1999) 125012 [hep-ph/9801399] [INSPIRE].
C. Greiner and S. Leupold, Interpretation and resolution of pinch singularities in non-equilibrium quantum field theory, Eur. Phys. J. C 8 (1999) 517 [hep-ph/9804239] [INSPIRE].
B. Garbrecht and M. Garny, Finite width in out-of-equilibrium propagators and kinetic theory, Annals Phys. 327 (2012) 914 [arXiv:1108.3688] [INSPIRE].
M. Garny, A. Hohenegger and A. Kartavtsev, Quantum corrections to leptogenesis from the gradient expansion, arXiv:1005.5385 [INSPIRE].
A. Hohenegger and A. Kartavtsev, Basis invariant measure of CP-violation and renormalization, Nucl. Phys. B 899 (2015) 476 [arXiv:1309.1385] [INSPIRE].
A.D. Sakharov, Violation of CP invariance, C asymmetry and baryon asymmetry of the universe, Pisma Zh. Eksp. Teor. Fiz. 5 (1967) 32 [INSPIRE].
C. Fidler, M. Herranen, K. Kainulainen and P.M. Rahkila, Flavoured quantum Boltzmann equations from cQPA, JHEP 02 (2012) 065 [arXiv:1108.2309] [INSPIRE].
R.F. Hoskins and J.S. Pinto, Theories of generalised functions: distributions, ultradistributions and other generalised functions, Woodhead Publishing, Cambridge U.K. (2005), pp. 48-50.
N. Nakanishi, A theory of clothed unstable particles, Prog. Theor. Phys. 19 (1958) 607.
T. Petrosky, I. Prigogine and S. Tasaki, Quantum theory of non-integrable systems, Physica A 173 (1991) 175.
M. Le Bellac, Thermal field theory, Cambridge University Press, Cambridge U.K. (2000).
M.J.G. Veltman, Unitarity and causality in a renormalizable field theory with unstable particles, Physica 29 (1963) 186 [INSPIRE].
M. Plümacher, Baryon asymmetry, neutrino mixing and supersymmetric SO(10) unification, Nucl. Phys. B 530 (1998) 207 [hep-ph/9704231] [INSPIRE].
A. Hohenegger, A. Kartavtsev and M. Lindner, Deriving Boltzmann equations from Kadanoff-Baym equations in curved space-time, Phys. Rev. D 78 (2008) 085027 [arXiv:0807.4551] [INSPIRE].
J.M. Cornwall, R. Jackiw and E. Tomboulis, Effective action for composite operators, Phys. Rev. D 10 (1974) 2428 [INSPIRE].
R.E. Norton and J.M. Cornwall, On the formalism of relativistic many body theory, Annals Phys. 91 (1975) 106 [INSPIRE].
F. Hahn-Woernle, M. Plümacher and Y.Y.Y. Wong, Full Boltzmann equations for leptogenesis including scattering, JCAP 08 (2009) 028 [arXiv:0907.0205] [INSPIRE].
A. Kartavtsev and D. Besak, Baryogenesis via leptogenesis in an inhomogeneous universe, Phys. Rev. D 78 (2008) 083001 [arXiv:0803.2729] [INSPIRE].
W. Buchmüller, P. Di Bari and M. Plümacher, Leptogenesis for pedestrians, Annals Phys. 315 (2005) 305 [hep-ph/0401240] [INSPIRE].
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Kartavtsev, A., Millington, P. & Vogel, H. Lepton asymmetry from mixing and oscillations. J. High Energ. Phys. 2016, 66 (2016). https://doi.org/10.1007/JHEP06(2016)066
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DOI: https://doi.org/10.1007/JHEP06(2016)066
Keywords
- Thermal Field Theory
- Effective field theories