Leptogenesis from spin-gravity coupling following inflation

The energy levels of the left- and the right-handed neutrinos are split in the background of gravitational waves generated during inflation, which, in presence of lepton-number-violating interactions, gives rise to a net lepton asymmetry at equilibrium. Lepton number violation is achieved by the same dimension five operator which gives rise to neutrino masses after electroweak symmetry breaking. A net baryon asymmetry of the same magnitude can be generated from this lepton asymmetry by electroweak sphaleron processes.     

Baryogenesis from mixing of lepton doublets

It is shown that the mixing of lepton doublets of the Standard Model can yield sizable contributions to the lepton asymmetry, that is generated through the decays of right-handed neutrinos at finite temperature in the early Universe. When calculating the flavour-mixing correlations, we account for the effects of Yukawa as well as of gauge interactions. We compare the freeze-out asymmetry from lepton-doublet mixing to the standard contributions from the mixing and direct decays of right-handed neutrinos. The asymmetry from lepton mixing is considerably large when the mass ratio between the right-handed neutrinos is of order of a few, while it becomes Maxwell-suppressed for larger hierarchies. For an intermediate range between the case of degenerate right-handed neutrinos (resonant leptogenesis) and the hierarchical case, lepton mixing can yield the main contribution to the lepton asymmetry.     

Leptogenesis: The other cuts

For standard leptogenesis from the decay of singlet right-handed neutrinos, we derive source terms for the lepton asymmetry that are present in a finite density background but absent in the vacuum. These arise from cuts through the vertex correction to the decay asymmetry, where in the loop either the Higgs boson and the right-handed neutrino or the left-handed lepton and the right-handed neutrino are simultaneously on-shell. We evaluate the source terms numerically and use them to calculate the lepton asymmetry for illustrative points in parameter space, where we consider only two right-handed neutrinos for simplicity. Compared to calculations where only the standard cut through the propagators of left-handed lepton and Higgs boson is included, sizable corrections arise when the masses of the right-handed neutrinos are of the same order, but the new sources are found to be most relevant when the decaying right-handed neutrino is heavier than the one in the loop. In that situation, they can yield the dominant contribution to the lepton asymmetry.     

Precision neutral current asymmetry parameter measurements from the Tau polarization at LEP

Measurements of the lepton polarization and forward-backward polarization asymmetry near the Z resonance using the OPAL detector are described. The measurements are based on analyses of and decays from a sample of 144,810 candidates corresponding to an integrated luminosity of 151 pb. Assuming that the lepton decays according to V–A theory, we measure the average polarization near to be and the polarization forward-backward asymmetry to be , where the first error is statistical and the second systematic. Taking into account the small effects of the photon propagator, photon-Z interference and photonic radiative corrections, these results can be expressed in terms of the lepton neutral current asymmetry parameters: These measurements are consistent with the hypothesis of lepton universality and combine to give . Within the context of the Standard Model this combined result corresponds to . Combing these results with those from the other OPAL neutral current measurements yields a value of . Received: 5 March 2001 / Published online: 6 July 2001     

Constraints on two-lepton two-quark operators

Physics from beyond the Standard Model, such as leptoquarks, can induce four fermion operators involving a quark, an anti-quark, a lepton and an anti-lepton. We update the (flavour-dependent) constraints on the coefficients of such interactions, arising from collider searches for contact interactions, meson decays and other rare processes. We then make naive estimates for the magnitude of the coefficients, as could arise in texture models or from inverse hierarchies in the kinetic term coefficients. These “expectations” suggest that rare kaon decays could be a good place to look for such operators.     

First Principles Calculation of the Baryon Asymmetry of the Universe: Generalities and Application

We present a formalism that allows the computation of the lepton asymmetry of the universe from first principles of statistical physics and quantum field theory (this lepton asymmetry is then converted to a baryon asymmetry via sphaleron processes). This formalism includes a thermal bath of Standard Model particles (active neutrinos) coupled to a new sector that is out-of-equilibrium (sterile neutrinos). The key point that allows a first principles computation is that the number of sterile neutrinos produced during the relevant cosmological period remains small (we assume zero sterile neutrinos initially). In such a case, it is possible to expand the formal solution of Liouville's equation perturbatively and obtain a master formula for the lepton asymmetry expressed in terms of non-equilibrium Wightman functions. The master formula neatly separates CP-violating contributions from finite temperature correlation functions and satisfies all three Sakharov conditions. These correlation functions can then be evaluated perturbatively; the validity of the perturbative expansion depends on the parameters of the model considered. Here we choose the νMSM (i.e. a minimal extension of the Standard Model that includes three generations of sterile neutrinos with masses of the order of the electroweak scale) to illustrate the use of the formalism, but it could in principle be applied to other models.     

Quantum leptogenesis I

Thermal leptogenesis explains the observed matter–antimatter asymmetry of the universe in terms of neutrino masses, consistent with neutrino oscillation experiments. We present a full quantum mechanical calculation of the generated lepton asymmetry based on Kadanoff–Baym equations. Origin of the asymmetry is the departure from equilibrium of the statistical propagator of the heavy Majorana neutrino, together with CP violating couplings. The lepton asymmetry is calculated directly in terms of Green’s functions without referring to “number densities”. Compared to Boltzmann and quantum Boltzmann equations, the crucial difference are memory effects, rapid oscillations much faster than the heavy neutrino equilibration time. These oscillations strongly suppress the generated lepton asymmetry, unless the standard model gauge interactions, which cause thermal damping, are properly taken into account. We find that these damping effects essentially compensate the enhancement due to quantum statistical factors, so that finally the conventional Boltzmann equations again provide rather accurate predictions for the lepton asymmetry.     

Realistic neutrinogenesis with radiative vertex correction

We propose a new model for naturally realizing light Dirac neutrinos and explaining the baryon asymmetry of the universe through neutrinogenesis. To achieve these, we present a minimal construction which extends the Standard Model with a real singlet scalar, a heavy singlet Dirac fermion and a heavy doublet scalar besides three right-handed neutrinos, respecting lepton number conservation and a Z₂$Z_2$ symmetry. The neutrinos acquire small Dirac masses due to the suppression of weak scale over a heavy mass scale. As a key feature of our construction, once the heavy Dirac fermion and doublet scalar go out of equilibrium, their decays induce the CP asymmetry from the interference of tree-level processes with the radiative vertex corrections (rather than the self-energy corrections). Although there is no lepton number violation, an equal and opposite amount of CP asymmetry is generated in the left-handed and the right-handed neutrinos. The left-handed lepton asymmetry would then be converted to the baryon asymmetry in the presence of the sphalerons, while the right-handed lepton asymmetry remains unaffected.     

Leptogenesis from first principles in the resonant regime

The lepton asymmetry generated by the out-of-equilibrium decays of heavy Majorana neutrinos with a quasi-degenerate mass spectrum is resonantly enhanced. In this work, we study this scenario within a first-principle approach. The quantum field theoretical treatment is applicable for mass splittings of the order of the width of the Majorana neutrinos, for which the enhancement is maximally large. The non-equilibrium evolution of the mixing Majorana neutrino fields is described by a formal analytical solution of the Kadanoff–Baym equations, that is obtained by neglecting the back-reaction. Based on this solution, we derive approximate analytical expressions for the generated asymmetry and compare them to the Boltzmann result. We find that the resonant enhancement obtained from the Kadanoff–Baym approach is smaller compared to the Boltzmann approach, due to additional contributions that describe coherent transitions between the Majorana neutrino species. We also discuss corrections to the masses and widths of the degenerate pair of Majorana neutrinos that are relevant for very small mass splitting, and compare the approximate analytical result for the lepton asymmetry with numerical results.     

Leptogenesis in flavor models with type I and II seesaws

In type I seesaw models with flavor symmetries accounting for the lepton mixing angles the CP asymmetry in right-handed neutrino decays vanishes in the limit in which the mixing pattern is exact. We study the implications that additional degrees of freedom from type II seesaw may have for leptogenesis in such a limit. We classify in a model independent way the possible realizations of type I and II seesaw schemes, differentiating between classes in which leptogenesis is viable or not. We point out that even with the interplay of type I and II seesaws there are generic classes of minimal models in which the CP asymmetry vanishes. Finally we analyze the generation of the lepton asymmetry by solving the corresponding kinetic equations in the general case of a mild hierarchy between the light right-handed neutrino and the scalar triplet masses. We identify the possible scenarios in which leptogenesis can take place.     

Probing lepton structure at the SSC

If quarks and leptons are composite objects with common constituents, then there exist two-quark-two-lepton contact interactions which could affect lepton pair production at the SSC. We show that for a range of compositeness scales and lepton pair invariant masses, the contact interaction contributions dominate the standard model contributions to the cross section. In this regime, we show that there should be a measurable and statistically significant front-back asymmetry.     

Leptogenesis from gravity waves in models of inflation

We present a new mechanism for creating the observed cosmic matter-antimatter asymmetry which satisfies all three Sakharov conditions from one common thread, gravitational waves. We generate lepton number through the gravitational anomaly in the lepton number current. The source term comes from elliptically polarized gravity waves that are produced during inflation if the inflaton field contains a CP-odd component. The amount of matter asymmetry generated in our model can be of realistic size for the parameters within the range of some inflationary scenarios and grand unified theories.     

Models of neutrino masses and baryogenesis

Majorana masses of the neutrino implies lepton number violation and is intimately related to the lepton asymmetry of the universe, which gets related to the baryon asymmetry of the universe in the presence of the sphalerons during the electroweak phase transition. Assuming that the baryon asymmetry of the universe is generated before the electroweak phase transition, it is possible to discriminate different classes of models of neutrino masses. While see-saw mechanism and the triplet Higgs mechanism are preferred, the Zee-type radiative models and the R-parity breaking models requires additional inputs to generate baryon asymmetry of the universe during the electroweak phase transition.     

Some Remarks about Semiclassical Trace Invariants and Quantum Normal Forms

In this paper we explore the connection between semi-classical and quantum Birkhoff canonical forms (BCF) for Schrödinger operators. In particular we give a “non-symbolic” operator theoretic derivation of the quantum Birkhoff canonical form and provide an explicit recipe for expressing the quantum BCF in terms of the semi-classical BCF.     

Scale of leptogenesis

We study the scale at which one can generate the lepton asymmetry of the universe which could then get converted to a baryon asymmetry during the electroweak phase transition. We consider the possibility that the Yukawa couplings could be arbitrarily small but sufficiently large to generate enough lepton asymmetry. This forbids the possibility of the breaking scale to be less than 10 TeV. Received: 14 April 1998 / Revised version: 8 August 1998 / Published online: 11 February 1999     

Semi-Classical States for Non-Self-Adjoint Schrödinger Operators

We prove that the spectrum of certain non-self-adjoint Schr?dinger operators is unstable in the semi-classical limit h→ 0. Similar results hold for a fixed operator in the high energy limit. The method involves the construction of approximate semi-classical modes of the operator by the JWKB method for energies far from the spectrum. Received: 7 April 1998 / Accepted: 12 June 1998     

Mass operator for a charged lepton in the Weinberg-Salam theory in a constant external field

An expression is found for the propagator of a charged W-boson in the presence of an arbitrary flat-wave electromagnetic field. The W-boson contribution to the mass operator of a charged lepton moving in a constant external electromagnetic field is computed in the second order of perturbation theory in the Weinberg-Salam model. A closed expression is obtained for the vacuum W-boson contribution (independent of the external field) to the anomalous magnetic moment of a charged lepton.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 55–57, December, 1985.     

Insensitivity of leptogenesis with flavor effects to low energy leptonic CP violation

If the baryon asymmetry of the Universe is produced by leptogenesis, CP violation is required in the lepton sector. In the seesaw extension of the standard model with three hierarchical right-handed neutrinos, we show that the baryon asymmetry is insensitive to the Pontecorvo-Maki-Nagakawa-Sakata phases: thermal leptogenesis can work for any value of the observable phases. This result was well known when there were no flavor effects in leptogenesis; we show that it remains true when flavor effects are included.     

Anomalous lepton moment in a non-Abelian gauge model in an intense electromagnetic field

The effect of an external electromagnetic field on the magnitude of the anomalous magnetic moment (AMM) of a lepton in the Weinberg model (1967) is investigated using the method of analytic continuation, previously applied to problems in quantum electrodynamics with an external field. The behavior of the AMM is studied as a function of the value of the dynamic parameter X=p_oH/mH_o.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 26–28, January, 1983.     

Leptogenesis and bi-unitary parametrization of neutrino Yukawa matrix

We analyze the neutrino Yukawa matrix by considering three constraints: the out-of-equilibrium condition of the lepton number-violating process responsible for leptogenesis, the upper bound of the branching ratio of the lepton flavor violating decay, and the prediction of large mixing angles using the see-saw mechanism. In a certain parametrization with a bi-unitary transformation, it is shown that the structure which satisfies the constraints can be characterized by only seven types of Yukawa matrices. The constraint of the branching ratio of LFV turns out to be redundant after applying the other two constraints. We propose that this parametrization can be the framework in which the CP asymmetry of a lepton number-violating process can be predicted in terms of observable neutrino parameters at low energy, if necessary, under assumptions following from a theory with additional symmetries. There is an appealing model of the neutrino Yukawa matrix considering the CP asymmetry for leptogenesis, giving a theoretical motivation to reduce the number of free parameters.Arrival of the final proofs: 24 June 2003