We assume a dark $U_{D}$ symmetric hidden sector and explore its possible content such that neutrino mass and Dark Matter are generated through the scotogenic mechanism. The hidden sector is considered analogue to the Standard Model, namely the charge assignment of hidden fermions is chiral and anomaly-free. Moreover, $U_{D}$ is assumed broken by an only Higgs singlet that also generates masses to all hidden fermions, therefore the charge assignment is subjected to additional restriction. We search by computer program for charge assignments satisfying all these conditions, and identify the resulting minimal scotogenic models for Majorana neutrinos and Dirac neutrinos respectively in the sense of minimal number of messenger scalar involved. Particle spectrum, couplings, and phenomenologies of these minimal models are briefly discussed. DM is found multicomponent and always contains Dirac fermionic species.
We perform a systematic analysis of standard model extensions with an additional anomaly-free gauge $U(1)$ symmetry, to generate Dirac neutrino masses at one loop. Under such symmetry, standard model fields could either transform or be invariant, corresponding to an active $U(1)_X$ or a dark $U(1)_D$ symmetry, respectively. Having an anomaly-free symmetry imposes nontrivial conditions to the number and charges of the unavoidable new states. We perform an intensive scan, looking for non-anomalous solutions for given number of extra chiral fermions. In particular, we concentrate on solutions giv…
We study the gauged $U(1)_{L_μ-L_τ}$ scotogenic model with emphasis on latest measurement of LHCb $R_{K^{(*)}}$ anomaly and AMS-02 positron excess. In this model, neutrino masses are induced at one-loop level with $Z_2$-odd particles, i.e., right-handed neutrinos $N_\ell(\ell=e,μ,τ)$ and inert scalar doublet $η$ inside the loop. Meanwhile, the gauged $U(1)_{L_μ-L_τ}$ symmetry is broken spontaneously by the scalar singlet $S$, resulting to the massive gauge boson $Z'$. Provided certain couplings to quarks induced by heavy vector-like quarks, the gauge boson $Z'$ would contribute to the transiti…
Modular symmetries have been impeccable in neutrino and quark sectors. This motivated us, therefore, to propose a variant of scotogenic model based on modular $A_4$ symmetry to realize the neutrino mass generation at one-loop level through radiative mechanism. Alongside, the lepton flavour violating process $μ\to e γ$ and the muon $g-2$ anomaly are also addressed. The lightest Majorana fermions turn out to be potential dark matter candidates, made stable by suitable assignment of modular weights. The relic density of the same has been computed with annihilations mediated by inert scalars and n…
We show that the scotogenic dark symmetry can be obtained as a residual subgroup of the global $U(1)_{B-L}$ symmetry already present in Standard Model. We propose a general framework where the $U(1)_{B-L}$ symmetry is spontaneously broken to an even $\mathcal{Z}_{2n}$ subgroup, setting the general conditions for neutrinos to be Majorana and the dark matter stability in terms of the residual $\mathcal{Z}_{2n}$. Under this general framework, as examples, we build a class of simple models where, in the scotogenic spirit, the dark matter candidate is the lightest particle running inside the neutri…
We present a singly charged scalar extension of the Scotogenic model, ScotoZee, which resolves the recently reported deviations in $W$ boson mass as well as lepton $g-2$. The model admits a scalar or a fermionic dark matter while realizing naturally small radiative neutrino masses. The mass splitting of $\sim 100$ GeV, required by the shift in $W$ boson mass, among the inert doublets fields can be evaded by its mixing with the singlet scalar, which is also key to resolving $(g-2)_\ell$ anomaly within $1σ$. We establish the consistency of this framework with dark matter relic abundance while sa…
We construct the one-loop and two-loop scotogenic models for Dirac neutrino mass generation in the context of $U(1)_{B-L}$ extensions of standard model. It is indicated that the total number of intermediate fermion singlets is uniquely fixed by anomaly free condition and the new particles may have exotic $B-L$ charges so that the direct SM Yukawa mass term $\barν_Lν_R\overline{ϕ^0}$ and the Majorana mass term $(m_N/2)\overline{ν_R^C}ν_R$ are naturally forbidden. After the spontaneous breaking of $U(1)_{B-L}$ symmetry, the discrete $Z_{2}$ or $Z_{3}$ symmetry appears as the residual symmetry an…
We propose a scotogenic model for generating neutrino masses through a three-loop seesaw. It is a minimally extended inert doublet model with a spontaneously broken global symmetry $U(1)'$ and a preserved $\mathbb{Z}_2$ symmetry. The three-loop suppression allows the new particles to have masses at the TeV scale without fine-tuning the Yukawa couplings. The model leads to a rich phenomenology while satisfying all the current constraints imposed by neutrinoless double-beta decay, charged-lepton flavor violation, and electroweak precision observables. The relatively large Yukawa couplings lead t…
The latest results of anomalous muon magnetic moment at Fermilab show a discrepancy of 4.2 $σ$ between the Standard Model (SM) prediction and experimental value. In this work, we revisit $U(1)_{L_μ-L_τ}$ symmetry with in the paradigm of scotogenic model which explains muon ($g-2$) and neutrino mass generation, simultaneously. The mass of new gauge boson $M_{Z_{μτ}}$ generated after the spontaneous symmetry breaking of $U(1)_{L_μ-L_τ}$ is constrained, solely, in light of the current neutrino oscillation data to explain muon ($g-2$). In particular, we have obtained two regions I and II, around 1…
Measurement of the $γ3π$ process has revealed a possible conflict with what should be a solid prediction generated by the chiral anomaly. We show that inclusion of appropirate energy-momentum dependence in the matrix element reduces the discrepancy.
We study an extension of the minimal gauged $L_μ-L_τ$ model in order to explain the anomalous magnetic moments of muon and electron simultaneously. Presence of an additional scalar doublet $η$ and an in-built $Z_2$ symmetry under which the right handed singlet fermions and $η$ are odd, leads to light neutrino mass in scotogenic fashion along with a stable dark matter candidate. In spite of the possibility of having positive and negative contributions to $(g-2)$ from vector boson and charged scalar loops respectively, the minimal scotogenic $L_μ-L_τ$ model can not explain muon and electron $(g-…
Anomalies are an infrared effect, but are often realized in effective theories in a non-trivial way. We study the chiral anomaly in Soft Collinear Effective Theory (SCET), where the anomaly equation has terms contributing at different orders in the power expansion. The chiral anomaly equations in SCET are computed up to NNLO in the power counting with external collinear and/or ultrasoft gluons. We do this by expanding the QCD anomaly equation, using the tree level (LO in α_s) relations between QCD and SCET fields. The validity of this correspondence between the anomaly equations is confirmed b…
Within Wigner function formalism, the chiral anomaly arises naturally from the Dirac sea contribution in un-normal-ordered Wigner function. For massless fermions, the Dirac sea contribution behaves like a 4-dimensional or 3-dimensional Berry monopole in Euclidian momentum space, while for massive fermions, although Dirac sea still leads to the chiral anomaly but there is no Berry monopole at infrared momentum region. We discuss these points explicitly in a simple and concrete example.
The interplay between the chiral anomaly and the non-leptonic weak Hamiltonian is studied. The structure of the corresponding effective Lagrangian of odd intrinsic parity is established. It is shown that the factorizable contributions (leading in $1/N_C$) to that Lagrangian can be calculated without free parameters. As a first application, the decay $K^+ \ra π^+ π^0 γ$ is investigated.
Renormalization of the axial vector currents due to Goldstone loops is studied in a simple extension of Manohar - Georgi chiral quark model which incorporates $U(1)_A$ anomaly effects. The polarized strage quark sea in the polarized nucleon results from different renormalization of the flavor singlet and octet currents and is in reasonable agreement with the experiment.
Infra-red properties of the triangle anomaly and the ``anomaly pole'' are elaborated and applied to the study of high-energy scattering in QCD, when the gauge symmetry is partially broken to SU(2). It is shown that the chiral flavor anomaly provides a wee-gluon component for Goldstone bosons that combines with interactions due to the U(1) anomaly to produce an infra-red transverse momentum scaling divergence in scattering amplitudes. After the divergence is factorized out, as a wee-gluon condensate in the infinite momentum pion, the remaining physical amplitudes have confinement and chiral sym…
We determine the $η-η'$ mixing angle via a procedure relatively independent of theoretical assumptions by simultaneously fitting $η- eta'$ reactions involving the anomaly--$η,η'\toγγ, π^+π^-γ$. We extract reasonably precise renormalized values of the octet and singlet pseudoscalar decay constants $F_8,F_0$ as well as the mixing angle $θ$.
The trace anomaly term in the low energy chiral Lagrangian is established by deriving a low energy theorem for $γγ\rightarrow π^0π^0$ scattering. It contributes to $σ(γγ\rightarrow π^0π^0)$ in the same order as the previously computed pion loop contribution. The coherent sum of the two contributions explains the shape of the measured cross section, while the magnitude is determined by the anomalous dimension of the quark mass operator.
We calculate the $O(p^6)$ corrections to the anomalous form factors appearing in $π^+$, $K^+ \to e^+ νγ,\ μ^+νγ$ and $K_{l4}$ decays in Chiral Perturbation Theory. The relevant dimension $6$ terms of the lagrangian are evaluated assuming their saturation by the vector meson contribution.
We show on the basis of an effective theory of QCD that a wide variety of observables in the hadron world is governed by the chiral symmetry together with an interplay between the axial anomaly and the explicit symmetry breaking due to the current quark mass. We also discuss the nature of the chiral transition at finite temperature and related dynamical phenomena using the effective Lagrangian. Some phenomenological implications of the small vector coupling (``vector limit'') at high temperatures are suggested.
Using the formula of chiral anomaly, we discuss the pair production of quarks under color electric field $\vec{E}$ without addressing explicit formula of quark's wavefunctions. The production is assumed to occur under the effect of color magnetic field $\vec{B}$ as well as the color electric field. We obtain the life time $t_c$ of the color electric field in the limit of $B\gg E$. Applying it to the glasma in high-energy heavy-ion collisions, we find that $t_c\simeq 10Q_s^{-1}$ with saturation momentum $Q_s$.
To investigate $Z'$ phenomenology model-independent, we combine chiral effective theory with anomaly cancellation conditions without any other model input. We focus on $Z'$ mixings with $γ-Z$ in both mass and kinetic parts and calculate contributions to oblique $S,T,U$. The three sets of anomaly-free fermion $U(1)'$ charges parameterize the $Z'$ interactions with fermions. The cancellation of the $[U(1)']^3$ anomaly and mixing gravitational-gauge anomaly determines the number of right-handed neutrinos. We also find a novel relation between the charge assignments and Stueckelberg coupling in te…
A power expansion scheme is set up to determine the Wigner function that satisfies the quantum kinetic equation for spin-1/2 charged fermions in a background electromagnetic field. Vector and axial-vector current induced by magnetic field and vorticity are obtained simultaneously from the Wigner function. The chiral magnetic and vortical effect and chiral anomaly are shown as natural consequences of the quantum kinetic equation. The axial-vector current induced by vorticity is argued to lead to a local polarization effect along the vorticity direction in heavy-ion collisions.
The effect of perturbative QCD interactions on the high energy scattering of electroweak vector bosons, when the exchanged channel has pion quantum numbers, is considered. The chiral anomaly is shown to appear in the couplings of particular transverse momentum diagrams, producing an enhancement of the scattering amplitude by a power of the energy. At $O(α_s)$ a single large transverse momentum gluon is involved and, within the transverse momentum diagram framework, there is no cancelation. In higher orders, soft gluons, carrying both normal and anomalous color parity, are also present. The man…
An investigation is performed of all non-leptonic kaon decays sensitive to the chiral anomaly. Within the framework of chiral perturbation theory, there are two classes of anomalous amplitudes at $O(p^4)$: reducible and direct contributions. Only radiative transitions are affected by the anomaly. The phenomenology of the decays $K_L \to π^+ π^- γ$ and $K^+ \to π^+ π^0 γ$ is studied in detail. Including the dominant contributions of $O(p^6)$, the experimentally observed dependence of the direct emission amplitude for $K_L \to π^+ π^- γ$ on the photon energy can be understood. A survey is made o…
The ground-state (lightest) hybrid nonet with exotic quantum numbers $J^{PC}=1^{-+}$ and the nonet of their chiral partners with $J^{PC}=1^{+-}$ build a homochiral multiplet involving left- and right-handed currents, which under chiral transformation change just as (axial-)vector mesons. Masses and interactions of hybrids can be obtained in the context of the extended Linear Sigma Model. Here, we concentrate on the decays oh hybrids into two pseudoscalar mesons, such as $ηπ$ and $η^{\prime}π$ modes. Indeed, $π_{1}(1400)\rightarrowπη$ and $π_{1}(1600)\rightarrowπη^{\prime}$ have been seen in ex…
We study relation between Chiral Separation Effect (CSE) and Chiral Anomaly, and argue that CSE does not inherit the immutability of Chiral Anomaly. For QED in the leading order in electric charge, with point-splitting regularization in real-time formalism, we demontrate, in regularization-dependent way though, that CSE is an infrared (IR) effect, while the Anomaly is an ultra-violet (UV) phenomena. Thus, CSE in general is sensitive to non-perturbative interactions that alter the theory IR properties, while the Anomaly is fixed by Lorentz symmetry. The simplest example of such an interaction i…
The chiral anomaly in the context of an extended standard model with minimal Lorentz invariance violation is studied. Taking into account bounds from measurements of the speed of light, we argue that the chiral anomaly and its consequences are general results valid even beyond the relativistic symmetry.
Kopnin spectral flow force acting on quantized vortices in superfluid and superconductors is discussed. Kopnin force represents the first realization of the chiral anomaly in condensed matter.
We study the Schwinger model at finite temperature and show that a temperature dependent chiral anomaly may arise from the long distance behavior of the electric field. At high temperature this anomaly depends linearly on the temperature $T$ and is present not only in the two point function, but also in all even point amplitudes.
It is known that in the zeta function regularization and in the Fujikawa method chiral anomaly is defined through a coefficient in the heat kernel expansion for the Dirac operator. In this paper we apply the heat kernel methods to calculate boundary contributions to the chiral anomaly for local (bag) boundary conditions. As a by-product some new results on the heat trace asymptotics are also obtained.
We discuss the type of the general macroscopic parity-violating effects, when there is the current along the vortex, which is concentrated in the vortex core. We consider vortices in superfluids, which contain the Weyl points. In the vortex core the positions of the Weyl points form the skyrmion structure. We show that the mass current concentrated in such a core is provided by the spectral flow through the Weyl points according to the Adler-Bell-Jackiw equation for chiral anomaly.
The important role played by chiral symmetry and axial anomaly in QCD in nuclear physics is reviewed. Some recent topics on possible chiral restoration in hot and/or dense matter are picked up. We also discuss so called {\em effective} restoration of chiral anomaly hot and/or dense matter, as may be seen in a character change of $η'$ meson.
Through more detailed calculations on QED$_{1+1}$ and QED$_{3+1}$ emplying a new treatment of Feynman Amplitudes, we attribute the regularization independent and hence definite origin of chiral anomaly in perturbation theory to an unambiguous term which is a rational function in momentum space. Some relevant remarks are presented.
Universidad Autónoma de Madrid（马德里自治大学）；IFT-UAM/CSIC（理论物理研究所（马德里自治大学/西班牙高等科学研究委员会））；Simons Center for Geometry and Physics, State University of New York Stony Brook（纽约州立大学石溪分校西蒙斯几何与物理中心）；CERN（欧洲核子研究组织）；Universidad Complutense de Madrid (UCM)（马德里康普顿斯大学）
The generation of a chiral shift parameter in the normal ground state of magnetized relativistic matter is discussed. The chiral shift contributes to the axial current density, but does not modify the conventional axial anomaly relation. The analysis based on gauge invariant regularization schemes suggests that this finding is also valid in gauge theories. We argue that the chiral shift parameter can affect observable properties of compact stars. In the regime of heavy ion collisions, the chiral shift parameter can modify the key features of the chiral magnetic effect.
A calculation of the chiral anomaly on a finite lattice without fermion doubling is presented . The lattice gauge field is defined in the spirit of noncommutative geometry. Standard formulas for the continuum anomaly are obtained as a limit.
Gribov viewed the axial anomaly as a manifestation of the collective motion of charged fermions with arbitrarily high momenta in the vacuum. In the presence of an external magnetic field and a chirality imbalance, this collective motion becomes directly observable in the form of the electric current - this is the chiral magnetic effect (CME). I give an elementary introduction into the physics of CME, and discuss some recent developments.
We revisit the chiral anomaly in the quantum kinetic theory in the Wigner function formalism under the background field approximation. Our results show that the chiral anomaly is actually from the Dirac sea or the vacuum contribution in the un-normal-ordered Wigner function. We also demonstrate that this contribution modifies the chiral kinetic equation for antiparticles.
A fast charged particle crossing the boundary between the chiral matter and vacuum radiates the transition radiation. Its most remarkable features --- the resonant behavior at a certain emission angle and the circular polarization of the spectrum --- depend on the parameters of the chiral anomaly in a particular material/matter. The chiral transition radiation can be used to investigate the chiral anomaly in such diverse media as the quark-gluon plasma, the Weyl semimetals, and the axionic dark matter.
In this comment to the Nature paper of Bevan et al I point out that their interpretation of experimental data is based on a double counting of the `chiral anomaly' due to a vortex motion: using the calculation far away from the vortex core (Berry phase) to cancel the equivalent calculation at the core (spectral flow). The relaxation time approximation in force or momentum balance equation involved in their theory is also wrong, which has been rigorous proved in transport theory since 60's. Hence their affirmative conclusion is premature.
We report our recent progress on the search of Chiral Magnetic Effect (CME) by developing new measurements as well as by hydrodynamic simulations of CME and background effects, with both approaches addressing the pressing issue of separating flow-driven background contributions and possible CME signal in current heavy ion collision measurements.
We study the resonance properties within chiral perturbation theory by explicitly taking into account the U_A(1) anomaly effect. This assures we have the appropriate degrees of freedom of low energy QCD in the large Nc limit. We calculate the various resonance properties, such as mass, width and residues, for the physical case, i.e. Nc=3. Then we extrapolate the values of Nc to study the trajectories of resonance poles.
We propose an effective chiral Lagrangian with a chiral scalar introduced as a dilaton associated with broken conformal symmetry and responsible for the trace anomaly in QCD and discuss the properties of hadronic matter at high density and temperature. As the "dilaton limit" is taken, which drives a system from nuclear matter density to near chiral restoration density, a linear sigma model emerges from the highly non-linear structure. A striking prediction is that as the dilaton limit is approached, the omega-nucleon interaction gets strongly suppressed at high density. This is shown to be a f…
Chiral anomaly and the novel quantum phenomena it induces have been widely studied for Dirac and Weyl fermions. In most typical cases, the Lorentz covariance is assumed and thus the linear dispersion relations are maintained. However, in realistic materials, such as Dirac and Weyl semimetals, the non-linear dispersion relations appear naturally. We develop a kinetic framework to study the chiral anomaly for Weyl fermions with non-linear dispersions by using the methods of Wigner function and semi-classical equations of motion. In this framework, the chiral anomaly is sourced by Berry monopoles…
We use strongly coupled lattice QED with two flavors of massless staggered fermions to model the physics of pions in two-flavor massless QCD. Our model has the right chiral symmetries and can be studied efficiently with cluster algorithms. In particular we can tune the strength of the QCD anomaly and thus study its effects on the chiral phase transition. Our study confirms the widely accepted view point that the chiral phase transition is first order in the absence of the anomaly. Turning on the anomaly weakens the transition and turns it second order at a critical anomaly strength. The anomal…
Axial anomaly and nesting is elucidated in the context of the inhomogeneous chiral phase. Using the Gross-Neveu models in 1+1 dimensions, we shall discuss axial anomaly and nesting from two different points of view: one is homogeneous chiral transition and the other is the Ferrel-Fulde-Larkin-Ovchinnikov (FFLO) state in superconductivity, which are closely related to each other by way of duality. It is shown that axial anomaly leads to a particular kind of the FFLO state within the two dimensional Nambu-Jona Lasinio model, where axial anomaly is manifested in a different mode. Nesting is a dri…
It is known that the contribution of torsion to the equation for the chiral Weyl fermions can be equivalently considered in terms of the axial $U(1)$ gauge field. In this scenario the gravitational field transforms to the $U(1)$ gauge field. Here we show that in chiral superconductors the opposite scenario takes place: the electromagnetic $U(1)$ field serves as the spin connection for the Bogoliubov fermionic quasiparticles. As a result the electromagnetic field gives rise to the gravitational anomaly, which contains the extra factor $1/3$ in the corresponding Adler-Bell-Jackiw equation as com…
Exact chiral symmetry at finite lattice spacing would preclude the axial anomaly. In order to describe a continuum quantum field theory of Dirac fermions, lattice actions with purported exact chiral symmetry must break the flavor-singlet axial symmetry. We demonstrate that this is indeed the case by using a minimally doubled fermion action. For simplicity we consider the Abelian axial anomaly in two dimensions. At finite lattice spacing and with gauge interactions, the axial anomaly arises from non-conservation of the flavor-singlet current. Similar non-conservation also leads to the axial ano…
