Dynamical Majorana Neutrino Masses and Axions II: Inclusion of Axial Background and Anomaly Terms
Nick E. Mavromatos, Alex Soto
备注：
24 pages revtex, eight figures incorporated. In this version, a brief discussion has been added in the introduction, on the justification of ignoring perturbative string-inspired axion-like particle potentials, and also in the conclusions on a comparison of the magnitude of the dynamical mass with ordinary QCD axion masses. No effects on conclusions
We extend the study of a previous publication \cite{amsot} on Schwinger-Dyson dynamical mass generation for fermions and pseudoscalar fields (axion-like particles (ALP)), in field theories containing Yukawa type interactions between the fermions and ALPs, by incorporating anomaly terms and/or (constant) axial background fields. The latter are linked to some Lorentz (and CPT) violating scenarios for leptogenesis in the early Universe. We discuss both Hermitian and non-Hermitian Yukawa interactions, anomaly terms and axial backgrounds, which are all motivated in the context of some scenarios for radiative (anomalous) Majorana sterile neutrino masses in string-isnpired, low-energy, effective field theories, including attractive four-fermion interactions. We show that, for a Hermitian Yukawa interaction, there is no (pseudo)scalar dynamical mass generation, but there is fermion dynamical mass generation, provided one adds a bare (pseudo)scalar mass. For this case, the hermitian anomaly terms play a similar role in inducing dynamical mass generation for fermions as the four-fermion attractive interactions. For antihermitian Yukawa interactions, an antihermitian anomaly resists mass generation. The axial background terms assist dynamical mass generation induced by antihermitian Yukawa interactions, in the sense that the larger the magnitude of the background, the larger the dynamical mass. For hermitian Yukawa interactions, however, the situation is the opposite, in the sense that the larger the background the smaller the dynamical mass. We also compare the anomaly-induced dynamical mass with the radiative fermion mass in models of sterile neutrinos, and find that in cases where the dynamical mass occurs, the latter dominates over the anomalously generated radiative sterile-neutrino mass.
Axions (in the general sense) may acquire qualitatively new couplings inside superfluids. Their conventional couplings to fermions, in empty space, involve purely imaginary masses; the new couplings involve emergent Majorana masses. The possibility of weak links for axions, recently put forward, is analyzed, rejected, and replaced with a non-local analogue.
The effect of quantum torsion in theories of quantum gravity is usually described by an axion-like field which couples to matter and to gravitation and radiation gauge fields. In perturbation theory, the couplings of this torsion-descent axion field are of derivative type and so preserve a shift symmetry. This shift symmetry may be broken, if the torsion-descent axion field mixes with other axions, which could be related to moduli fields in string-inspired effective theories. In particular, the shift symmetry may break explicitly via non-perturbative effects, when these axions couple to fermio…
We discuss dynamical mass generation for fermions and pseudoscalar fields (axion-like particles (ALP)), in the context of effective theories containing Yukawa type interactions between the fermions and ALPs. We discuss both Hermitian and non-Hermitian Yukawa interactions, which are motivated in the context of some scenarios for radiative (anomalous) Majorana sterile neutrino masses in some effective field theories. The latter contain shift-symmetry breaking Yukawa interactions between sterile neutrinos and ALPs. We show that, for a Hermitian Yukawa interaction, there is no (pseudo)scalar dynam…
New approach to quantization of the relativistic Majorana field is presented. It is based on expansion of the field into eigenfunctions of the axial momentum -- a novel observable introduced recently. Relativistic invariance is used as the main guiding principle instead of canonical formalism. Hidden structure of the quantized Majorana field in the form of real Clifford algebra of Hermitian fermionic operators is unveiled. Generators of the Poincaré transformations in the Fock space are found as solutions of certain operator equations, without invoking the principle of correspondence with clas…
The Kalb-Ramond (KR) antisymmetric tensor field arises naturally in the gravitational multiplet of string theory. Nevertheless, the respective low-energy field theory action, in which, for reasons of gauge invariance, the only dependence on the KR field is through its field strength, constitutes an interesting model \emph{per se}. In this context, the KR field strength also acts as a totally antisymmetric torsion field, while in four space-time dimensions is \emph{dual} to an (KR) axion-like pseudoscalar field. In this context, we review here first the rôle of quantum fluctuations of the KR ax…
We present a 5D axion-neutrino model that explains the Standard Model fermion mass hierarchy and flavor structure, while simultaneously generating a high-quality axion. The axion and right-handed neutrinos transform under a 5D Peccei-Quinn gauge symmetry, and have highly suppressed profiles on the UV brane where the symmetry is explicitly broken. This setup allows neutrinos to be either Dirac, or Majorana with hierarchically small sterile neutrino masses. The axion decay constant originates from the IR scale, which in the holographically dual 4D description corresponds to the confinement scale…
Motivated by the SU(2)$_{\rm CMB}$ modification of the cosmological model $Λ$CDM, we consider isolated fuzzy-dark-matter lumps, made of ultralight axion particles whose masses arise due to distinct SU(2) Yang-Mills scales and the Planck mass $M_P$. In contrast to SU(2)$_{\rm CMB}$, these Yang-Mills theories are in confining phases (zero temperature) throughout most of the Universe's history and associate with the three lepton flavours of the Standard Model of particle physics. As the Universe expands, axionic fuzzy dark matter comprises a three-component fluid which undergoes certain depercola…
Axion like particles(ALPs) and right handed neutrinos~(RHNs) are two well-motivated dark matter(DM) candidates. However, these two particles have a completely different origin. Axion was proposed to solve the Strong CP problem, whereas RHNs were introduced to explain light neutrino masses through seesaw mechanisms. We study the case of ALP portal RHN DM taking into account existing constraints on ALPs. We consider the leading effective operators mediating interactions between the ALP and SM particles and three RHNs to generate light neutrino masses through type-I seesaw. Further, ALP-RHN neutr…
A low-background, high-purity germanium detector has been used to search for evidence of low-energy, bremsstrahlung-generated solar axions. An upper bound of $1.36\times 10^{-11}$ $(95% CL)$ is placed on the direct coupling of DFSZ model axions to electrons. The prospects for the sensitivity of the Majorana Demonstrator array of point-contact germanium detectors to solar axions are discussed in the context of the model-independent annual modulation due to the seasonal variation of the earth-sun distance.
We discuss here a specific field-theory model, inspired from string theory, in which the generation of a matter-antimatter asymmetry in the Cosmos is due to the propagation of fermions in a non-trivial, spherically asymmetric (and hence Lorentz violating) gravitational background that may characterise the epochs of the early universe. The background induces different dispersion relations, hence populations, between fermions and antifermions, and thus CPT Violation (CPTV) already in thermal equilibrium. Species populations may freeze out leading to leptogenesis and baryogenesis. More specifical…
It is well known that Majorana neutrinos have a pure axial neutral current interaction while Dirac neutrinos have the standard vector-axial interaction. In spite of this crucial difference, usually Dirac neutrino processes differ from Majorana processes by a term proportional to the neutrino mass, resulting in almost unmeasurable observations of this difference. In the present work we show that once the neutrino polarization evolution is considered, there are clear differences between Dirac and Majorana scattering on electrons. The change of polarization can be achieved in astrophysical enviro…
We present detailed arguments and calculations in support of our recent proposal to identify the axion arising in the solution of the strong CP problem with the Majoron, the (pseudo-)Goldstone boson of spontaneously broken lepton number symmetry. At low energies, the associated $U(1)_L$ becomes, via electroweak parity violation and neutrino mediation, indistinguishable from an axial Peccei-Quinn symmetry in relation to the strong interactions. The axionic couplings are then fully computable in terms of known SM parameters and the Majorana mass scales. The determination of these couplings invol…
We propose a model of Majorana fermions with quartic self-couplings. These Majorana fermions acquire masses via a type II seesaw mechanism in which the physical eigenstates are identified as a light Majorana fermion and another heavy Majorana fermion. On a physical basis, the quartic self-couplings involve axial currents of these Majorana fermions, and also the interaction of the axial current for the light particle with the heavy particle one. We introduce two auxiliaries gauge fields in this model, and we study the stability conditions of the correspondent effective potential of the model. T…
In this mini review, we discuss some recent developments regarding properties of (quantum) field-theory models containing anti-Hermitian Yukawa interactions between pseudoscalar fields (axions) and Dirac (or Majorana) fermions. Specifically, after motivating physically such interactions, in the context of string-inspired low-energy effective field theories, involving right-handed neutrinos and axion fields, we proceed to discuss their formal consistency within the so-called Parity-Time-reversal(PT)-symmetry framework, as well as dynamical mass generation, induced by the Yukawa interactions, fo…
We consider the presence of an axion like particle, $σ$, with a generic $CP$ violating axial coupling of the form $ (α\, σ/f) F \tilde{F}$, where $F_{μν}$ is the gauge field strength of a generic abelian $U(1)$ gauge group, not necessarily associated with the standard electromagnetism, and $f$ is the decay constant of the axion. It has previously been demonstrated that if the axion is identified with the inflaton, such an interaction can lead to measurable cosmological signatures (non-Gaussian modifications of the curvature perturbation spectrum) depending on the parameter $ξ= α\dotσ/ (f H)$. …
We study the Peccei-Quinn (PQ) symmetry of the sterile right-handed neutrino sector and the gauge symmetries of the Standard Model. Due to four-fermion interactions, spontaneous breaking of these symmetries at the electroweak scale generates top-quark Dirac mass and sterile-neutrino Majorana mass. The top quark channel yields massive Higgs, $W^\pm$ and $Z^0$ bosons. The sterile neutrino channel yields the heaviest sterile neutrino Majorana mass, sterile Nambu-Goldstone axion (or majoron) and massive scalar $χ$boson. Four-fermion operators effectively induce their tiny couplings to SM particles…
We derive the zero mode solutions for a Majorana fermion in the background of a cosmic string and contrast it with the zero mode solution for a (neutral) Dirac fermion. A Majorana zero mode carries no vector or axial charge, and it cannot be bosonised. We study the implications for vorton formation and stability. In the massless limit stability of the zero mode is guaranteed by energy-momentum conservation. However, zero modes obtain an effective mass on string loops. It is found that the conditions under which current formation can be effective are exactly those for which zero mode decay is m…
Martinus Veltman was the first to point out the inconsistency of the experimental value for the decay rate of $π^0\rightarrowγγ$ and its calculation by J. Steinberger with the very successful concept of the pion as the (pseudo)Nambu-Goldstone boson of the spontaneously broken global axial symmetry of strong interactions. That inconsistency has been resolved by J. Bell and R. Jackiw in their famous paper on the chiral anomalies. We review the connection between the decay amplitudes of an axion into two gauge bosons in Abelian vector-like and chiral gauge theories. The axion is the Nambu-Goldsto…
We propose a $SU(5) \times U(1)_X \times U(1)_{PQ}$ model, where $U(1)_X$ is the generalization of the $B-L$ (baryon minus lepton number) gauge symmetry and $U(1)_{PQ}$ is the global Peccei-Quinn (PQ) symmetry. There are four fermions families in $\bf{\overline 5} + \bf{10}$ representations of $SU(5)$, a mirror family in $\bf{5}+\bf{\overline {10}}$ representations, and three $SU(5)$ singlet Majorana fermions. The $U(1)_X$ related anomalies all cancel in the presence of the Majorana neutrinos. The $SU(5)$ symmetry is broken at $M_{GUT} \simeq (6-9)\times 10^{15}$ GeV and the proton lifetime $τ…
We survey a few minimal scalar extensions of the standard electroweak model that provide a simple setup for massive neutrinos in connection with an invisible axion. The presence of a chiral $U(1)$ à la Peccei-Quinn drives the pattern of Majorana neutrino masses while providing a dynamical solution to the strong CP problem and an axion as a dark matter candidate. We paradigmatically apply such a renormalizable framework to type-II seesaw and to two viable models for neutrino oscillations where the neutrino masses arise at one and two loops, respectively. We comment on the naturalness of the eff…
Each of neutrinos has a non - zero mass and regardless of whether it is a Dirac or a Majorana mass, can possess both anapole and electric dipole moments. Between their form factors appears a connection, for example, at the longitudinal neutrinos scattering on spinless nuclei. We discuss a theory, in which a mass consists of vector and axial - vector components responsible for separateness of leptonic current into the vector and axial - vector parts of the same charge or dipole moment. Such a model can explain the absence of truly neutral neutrinos vector interactions and the availability of an…
We study fermions derivatively coupled to axion-like or pseudoscalar fields, and show that the axial vector current of the fermions is not conserved in the limit where the fermion is massless. This apparent violation of the classical chiral symmetry is due to the background axion field. We compute the contributions to this anomalous Ward identity due to the pseudoscalar field alone, which arise in Minkowski space, as well as the effects due to an interaction with an external gravitational field. For the case of massless fermions, these interactions induce terms in the axion effective action th…
In this work we compute the axion mass and, from this (exploiting a well-known relation), we also derive an expression for the QCD topological susceptibility in the finite-temperature case, both below and above the chiral phase transition at $T_c$, making use of a chiral effective Lagrangian model which includes the axion, the scalar and pseudoscalar mesons and implements the $U(1)$ axial anomaly of the fundamental theory. We also provide a numerical estimate of the topological susceptibility at $T=0$ (in the physical case of three light quark flavors) and discuss the question of the temperatu…
The smallness of neutrino mass, the strong CP problem, and the existence of dark matter are explained in an economical way. The neutrino mass is generated by the colored version of a radiative seesaw mechanism by using color adjoint mediators. The Majorana mass term of the adjoint fermion, which carries lepton number U(1)_L, is induced by its spontaneous breaking, resulting in a Majoron which doubles as the QCD (quantum chromodynamics) axion, thereby solving the strong CP problem. The breaking of U(1)_L sets simultaneously the seesaw scale for neutrino mass and the Peccei-Quinn breaking scale.…
The CPT odd contribution to the effective electromagnetic action deriving from the vacuum polarization tensor in a large class of fermionic systems exhibiting Lorentz invariance violation (LIV) is calculated using thermal field theory methods, focusing upon corrections depending on the chemical potential. The systems considered exhibit the axial anomaly and their effective actions are described by axion electrodynamics whereby all the LIV parameters enter in the coupling $Θ(x)$ to the unmodified Pontryagin density. A preliminary application to type-I tilted Weyl semimetals is briefly presented…
We show that the interaction of an axion field, or in general a pseudoscalar field, with the axial-vector current generated by an electron through a derivative-type coupling can give rise to a time-dependent mixing of opposite-parity states in atomic and molecular systems. Likewise, the analogous interaction of an axion field with the axial-vector current generated by a nucleon can give rise to time-dependent mixing of opposite-parity states in nuclear systems. This mixing can induce oscillating electric dipole moments, oscillating parity non-conservation effects and oscillating anapole moment…
Beam dump experiments have been used to search for new particles, $ϕ$, with null results interpreted in terms of limits on masses $m_ϕ$ and coupling constants $ε$. However these limits have been obtained by using approximations [including the Weizsäcker-Williams (WW) approximation] or Monte-Carlo simulations. We display methods to obtain the cross section and the resulting particle production rates without using approximations on the phase space integral or Monte-Carlo simulations. In our previous work we examined the case of the new scalar boson production; in this paper we explore all possib…
We review scenarios of baryogenesis through leptogenesis at early epochs of the universe, in string-inspired minimal extensions of the Standard Model (SM), involving heavy right-handed Majorana neutrinos. Spontaneous violation of CPT symmetry is induced by appropriate (in general, temperature-dependent) backgrounds of the Kalb-Ramond (KR) axion field, which has its origins in the (bosonic) massless string multiplet. As interesting features of the model, we also discuss two issues associated with quantum (chiral) anomalies: (i) the non-contribution of the KR axion background to the (anomalous) …
Once a light axionlike scalar field couples to the electroweak gauge bosons, its classical motion during reheating induces an effective chemical potential for the fermion number. In the presence of rapid lepton number (L)-violating processes in the plasma, such a chemical potential provides a favorable opportunity for baryogenesis via leptogenesis. We are able to demonstrate that L violation due to the exchange of heavy Majorana neutrinos is sufficient for a successful realization of this idea. Our mechanism represents a novel and minimal alternative to thermal leptogenesis, which turns out to…
We attempt to identify a phenomenologically viable solution to the strong $CP$ problem in which the axion is composed entirely out of Standard Model fermion species. The axion consists predominantly of the $η'$ meson with a minuscule admixture of a pseudoscalar bilinear composite of neutrinos, $η_ν$. The Peccei-Quinn symmetry is an axial symmetry that acts on the up quark and the neutrino species and is spontaneously broken by the QCD condensate of quarks as well as the condensate of neutrinos triggered by chiral gravitational anomaly. The up-quark mass is spontaneously generated by the neutri…
We investigate the most interesting decay processes involving axions, photons and the lightest pseudoscalar mesons, making use of a chiral effective Lagrangian model with $L=3$ light quark flavors, which also includes the flavor-singlet pseudoscalar meson and implements the $U(1)$ axial anomaly of the fundamental theory. In particular, we compute the electromagnetic coupling of the axion to photons and we compare our result with the prediction of the Chiral Effective Lagrangian with $L=2$ light quark flavors. Moreover, we study the decay channels $η/η'\rightarrow ππa$ and we estimate the corre…
A neutrino possesses the anapole and electric dipole moments. Their interaction with field of emission can also lead to the neutrino elastic scattering by spinless nuclei. In this letter, we present some implications implied from the process cross sections. One of them states that there exists a hard connection between the neutrino magnetic and anapole moments. An equation for the anapole and electric dipole form factors is also obtained. They define the electronic neutrino axial-vector moments. All findings are generalized to the case of a Majorana neutrino.
In this talk, I present a novel and minimal alternative to thermal leptogenesis, which builds upon the assumption that the electroweak gauge bosons are coupled to an axion-like scalar field, as it is, for instance, the case in certain string compactifications. The motion of this axion-like field after the end of inflation generates an effective chemical potential for leptons and antileptons, which, in the presence of lepton number-violating scatterings mediated by heavy Majorana neutrinos, provides an opportunity for baryogenesis via leptogenesis. In contrast to thermal leptogenesis, the final…
We show that a recently proposed framework that provides a simple connection between Majorana neutrinos and an invisible axion in minimal scalar extensions of the standard electroweak model can be naturally embedded in a classically scale-invariant setup. The explicit breaking of the scale invariance à la Coleman-Weinberg generates the Peccei-Quinn and electroweak scales. The spontaneous breaking of the chiral $U(1)_{PQ}$ triggers the generation of neutrino masses via Type-II seesaw and, at the same time, provides a dynamical solution to the strong CP problem as well as the axion as a dark mat…
We argue that there are both experimental and theoretical reasons to reconsider the construction of KSVZ-like axion models. From the experimental side, predictions for the axion-photon coupling are not consistent with the collection of astrophysical hints. From the theoretical side, we find that the construction can be conceptually simplified. In particular, it contains an unnecessary assumption on the type of the gauge theory involved which has far-reaching consequences for low energy axion phenomenology. In order to relax this assumption, we allow heavy fermions of the KSVZ-like models to ca…
We propose a minimal model in which the flavour anomaly in the $b \to s μ^+ μ^-$ transition is connected to the breaking of Peccei-Quinn (PQ) symmetry. The flavour anomaly is explained from new physics contribution by introducing one generation of heavy quark and heavy lepton which are vector-like under the standard model (SM) gauge group but charged under a local $U(1)_X$ group. They mix with the SM quarks and leptons, inducing flavour-changing $Z^\prime$ couplings, which generates the $b \to s μ^+μ^-$ anomaly at tree level. On the other hand the new fermions are chiral under the global Pecce…
In the hot and dense medium of a supernova (SN) core, the nucleon spins fluctuate so fast that the axial-vector neutrino opacity and the axion emissivity are expected to be significantly modified. Axions with $m_a\alt10^{-2}\,{\rm eV}$ are not excluded by SN~1987A. A substantial transfer of energy in neutrino-nucleon ($νN$) collisions is enabled which may alter the spectra of SN neutrinos relative to calculations where energy-conserving $νN$ collisions had been assumed near the neutrinosphere.
A Majorana neutrino is characterized by just one flavor diagonal electromagnetic form factor: the anapole moment, that in the static limit corresponds to the axial vector charge radius <r^2_A>. As is the case for the vector charge radius of a Dirac neutrino, proving that this is a well defined physical quantity is non trivial. I will first describe briefly the origin of the long standing controversy about the physical or non physical nature of the neutrino charge radius. Then I will argue that, in contrast to Dirac neutrino electromagnetic form factors, for Majorana neutrinos cosmological and …
We re-examine the very stringent limits on the axion mass based on the strength and duration of the neutrino signal from SN 1987A, in the light of new measurements of the axial-vector coupling strength of nucleons, possible suppression of axion emission due to many-body effects, and additional emission processes involving pions. The suppression of axion emission due to nucleon spin fluctuations induced by many-body effects degrades previous limits by a factor of about 2. Emission processes involving thermal pions can strengthen the limits by a factor of 3-4 within a perturbative treatment that…
We propose a search of galactic axions with mass about 0.2 microeV using a large volume resonant cavity, about 50 m^3, cooled down to 4 K and immersed in a moderate axial magnetic field of about 0.6 T generated inside the superconducting magnet of the KLOE experiment located at the National Laboratory of Frascati of INFN. This experiment, called KLASH (KLoe magnet for Axion SearcH) in the following, has a potential sensitivity on the axion-to-photon coupling, g_agg, of about 6x10^-17 GeV-1, reaching the region predicted by KSVZ and DFSZ models of QCD axions.
Recently, the LHC collaborations, ATLAS and CMS, have announced an excess in the diphoton channel with local significance of about $3\,σ$ around an invariant mass distribution of $\sim 750$ GeV, after analyzing new data collected at centre-of-mass energies of $\sqrt{s} = 13~{\rm TeV}$. We present a possible physical interpretation of such a signature, within the framework of a minimal UV-complete model with a massive singlet pseudo-scalar state $a$ that couples to a new TeV-scale coloured vector-like fermion $F$, whose hypercharge quantum number is a non-zero integer. The pseudo-scalar state $…
The connection between the axion and right-handed neutrinos is explored in the framework of the minimal SUSY SO(10) model. The former is related to the Peccei-Quinn (PQ) solution to the strong CP problem and the latter is to the light Majorana neutrinos through the see-saw mechanism. In this model, a relative phase between $({\bf 10,1,3}) (\equiv {\bf \barΔ}_R) \subset {\bf \bar{126}}$ and $({\bf \bar{10},1,3}) (\equiv {\bf Δ}_R) \subset {\bf 126}$ multiplets of ${\rm SU}(4) \times {\rm SU}(2)_L \times {\rm SU}(2)_R \subset {\rm SO}(10)$ becomes a physical degree of freedom identified with the…
