Mirror Fermions Research Articles

Lattice regularization of reduced Kähler-Dirac fermions and connections to chiral fermions

We show how a path integral for reduced Kähler-Dirac fermions suffers from a phase ambiguity associated with the fermion measure that is an analog of the measure problem seen for chiral fermions. However, unlike the case of chiral symmetry, a doubler free lattice action exists which is invariant under the corresponding onsite symmetry. This allows for a clear diagnosis and solution to the problem using mirror fermions resulting in a unique gauge invariant measure. By introducing an appropriate set of Yukawa interactions which are consistent with ’t Hooft anomaly cancellation we conjecture the mirrors can be decoupled from low energy physics. Moreover, the minimal such Kähler-Dirac mirror model yields a light sector which corresponds, in the flat space continuum limit, to the Pati-Salam GUT model.

Propagator Zeros and Lattice Chiral Gauge Theories.

Symmetric mass generation (SMG) has been advocated as a mechanism to render mirror fermions massive without symmetry breaking, ultimately aiming for the construction of lattice chiral gauge theories. It has been argued that in an SMG phase, the poles in the mirror fermion propagators are replaced by zeros. Using an effective Lagrangian approach, we investigate the role of propagator zeros when the gauge field is turned on, finding that they act as coupled ghost states. In four dimensions, a propagator zero makes an opposite-sign contribution to the one-loop beta function as compared to a normal fermion. In two dimensional Abelian theories, a propagator zero makes a negative contribution to the photon mass squared. In addition, propagator zeros generate the same anomaly as propagator poles. Thus, gauge invariance will always be maintained in an SMG phase, in fact, even if the target chiral gauge theory is anomalous, but unitarity of the gauge theory is lost.

Sterile neutrinos in a left-right mirror model

In this work we investigate the possibility that one neutrino mirror plays the role of a sterile neutrinos with mass on the scale of a few eV ′ s, that is, mˆ 1 ∼ O(1 eV ). We consider the extension of the Standard Model with gauge symmetry SU(2)L ⊗ SU(2)R ⊗ U(1)Y ′ and additional exotic fermions known as mirror fermions. A double application of the seesaw type I approximation to the most general Majorana-type neutrino mass matrix and diagonalization is performed to study neutrino masses and mixing.

Fermi surface symmetric mass generation

Symmetric mass generation is a novel mechanism to give gapless fermions a mass gap by non-perturbative interactions without generating any fermion bilinear condensation. The previous studies of symmetric mass generation have been limited to Dirac/Weyl/Majorana fermions with zero Fermi volume in the free fermion limit. In this work, we generalize the concept of symmetric mass generation to Fermi liquid with a finite Fermi volume and discuss how to gap out the Fermi surfaces by interactions without breaking the U(1) loop group symmetry or developing topological orders. We provide examples of Fermi surface symmetric mass generation in both (1+1)D and (2+1)D Fermi liquid systems when several Fermi surfaces together cancel the Fermi surface anomaly. However, the U(1) loop group symmetry in these cases is still restrictive enough to rule out all possible fermion bilinear gapping terms, such that a non-perturbative interaction mechanism is the only way to gap out the Fermi surfaces. This symmetric Fermi surface reconstruction is in contrast to the conventional symmetry-breaking mechanism to gap the Fermi surfaces. As a side product, our model provides a pristine 1D lattice regularization for the (1+1)D U(1) symmetric chiral fermion model (e.g., the 3-4-5-0 model) by utilizing a lattice translation symmetry as an emergent U(1) symmetry at low energy. This opens up the opportunity for efficient numerical simulations of chiral fermions in their own dimensions without introducing mirror fermions under the domain wall fermion construction.

Type II Dirac seesaw portal to the mirror sector: Connecting neutrino masses and a solution to the strong CP problem

We present a version of the Type II seesaw mechanism for parametrically small Dirac neutrino masses. Our model starts from an $\mathrm{SU}(2{)}_{\mathrm{L}}\ensuremath{\bigotimes}\mathrm{SU}(2{)}^{\ensuremath{'}}\ensuremath{\bigotimes}\mathrm{U}(1{)}_{\mathrm{X}}$ gauge extension of the Standard Model involving a sector of mirror fermions. A bidoublet scalar with a very small vacuum expectation value connects the SM leptons with their mirror counterparts, and we can identify the mirror neutrino with the right-handed neutrino. Similar to the conventional Type II seesaw, our particle spectrum features singly and doubly charged scalars. The strong $CP$ problem is solved by a discrete exchange symmetry between the two sectors that forces the contributions of quarks and mirror quarks to the strong $CP$ phase to cancel each other. We discuss the low-energy phenomenology, comment on the cosmological implications of this scenario, and indicate how to realize successful Dirac leptogenesis.

CT or P problem and symmetric gapped fermion solution

An analogous ``strong $CP$ problem'' is identified in a toy model in two-dimensional spacetime: a general $1+1\mathrm{d}$ Abelian U(1) anomaly free chiral fermion and chiral gauge theory with a generic theta instanton term $\frac{\ensuremath{\theta}}{2\ensuremath{\pi}}\ensuremath{\int}F$. The theta term alone violates the charge-conjugation-time-reversal $CT$ and the parity $P$ discrete symmetries. The analogous puzzle here is the $CT$ or $P$ problem in $1+1\mathrm{d}$: Why can the $\overline{\ensuremath{\theta}}$ angle (including the effect of $\ensuremath{\theta}$ and the complex phase of a mass matrix) be zero or small for a natural reason? We show that this $CT$ or $P$ problem can be solved by a symmetric mass generation mechanism (SMG, namely generating a mass or energy gap while preserving an anomaly free symmetry). This $1+1\mathrm{d}$ toy model mimics several features of the $3+1\mathrm{d}$ Standard Model: chiral matter content, confinement, and Anderson-Higgs mass by Yukawa-Higgs term. One solution replaces some chiral fermion's Higgs-induced mean-field mass with SMG-induced non-mean-field mass. Another solution enriches this toy model by introducing several new physics beyond the Standard Model: a parity-reflection $PR$ discrete symmetry maps between the chiral and mirror fermions as fermion doubling localized on two domain walls at high energy, and SMG dynamically generates mass to the mirror fermion while still preserving the anomaly free chiral symmetry at an intermediate energy scale, much before the Higgs mechanism generates mass to the chiral fermion at lower energy. Without loss of generality, an arguably simplest $1+1\mathrm{d}$ U(1) symmetric anomaly free chiral fermion/gauge theory (e.g., Weyl fermions with ${3}_{L}\text{\ensuremath{-}}{4}_{L}\text{\ensuremath{-}}{5}_{R}\text{\ensuremath{-}}{0}_{R}$ U(1) charges) is demonstrated in detail. As an analogy to the superfluid-insulator or order-disorder quantum phase transition, in contrast to the conventional Peccei-Quinn solution sitting in the (quasi-long-range-order)-superfluid ordered phase, our solution is in the SMG insulator disordered phase.

NEUTRINO MASSES IN A LEFT-RIGHT MODEL WITH A LIGHT NEUTRINO MIRROR

In the framework of the extension of the Standard Model with gauge symmetry $SU(2)_{L} \otimes SU(2)_{R} \otimes U(1)_{Y^{\prime}}$ and additional exotic fermions known as mirror fermions, neutrino masses and mixing are studied. Starting from the most general Majorana neutrino mass matrix, we explore the possibility that one neutrino mirror plays the role of a sterile neutrino with mass on the scale of a few $eV's $, that is, $\hat{m}_1 \approx O(1\: eV)$.

Symmetric Mass Generation in the 1+1 Dimensional Chiral Fermion 3-4-5-0 Model.

Lattice regularization of chiral fermions has been a long-standing problem in physics. In this Letter, we present the density matrix renormalization group simulation of the 3-4-5-0 model of (1+1)D chiral fermions with an anomaly-free chiral U(1) symmetry, which contains two left-moving and two right-moving fermions carrying U(1) charges 3,4 and 5,0, respectively. Following the Wang-Wen chiral fermion model, we realize the chiral fermions and their mirror partners on the opposite boundaries of a thin strip of (2+1)D lattice model of multilayer Chern insulator, whose finite width implies the quantum system is effectively (1+1)D. By introducing two sets of carefully designed six-fermion local interactions to the mirror sector only, we demonstrate that the mirror fermions can be gapped out by the interaction beyond a critical strength without breaking the chiral U(1) symmetry, via the symmetric mass generation mechanism. We show that the interaction-driven gapping transition is in the Berezinskii-Kosterlitz-Thouless universality class. We determine the evolution of Luttinger parameters before the transition, which confirms that the transition happens exactly at the point when the interaction term becomes marginal. As the mirror sector is gapped after the transition, we check that the fermions in the light chiral fermion sector remain gapless, which provides the desired lattice regularization of chiral fermions.

Single top production via FCNC couplings at an $$e^{-}e^{+}$$ collider with center-of-mass energy $$\sqrt{s}=240$$ GeV

Aspects of top quark physics can be studied at a future Circular Electron-Positron Collider. In particular, flavor-changing neutral current interactions (FCNC) of the top quark can be studied even with a center-of-mass energy from \(\sqrt{s}\gtrsim m_t\) to \(\sqrt{s}=240\) GeV, through the production a single top quark in association with a charm quark, which can arise in several scenarios of new physics. We explore here this signal within the Left-Right Mirror Model, which is a Left-Right model that includes mirror fermions; this model is motivated as a possible solution to the strong CP problem and by its rich phenomenology. We find that for particular scenarios of the model parameters, which are in agreement with the most up-to-date experimental constraints, the signal coming from the process \(e^+e^-\rightarrow V \rightarrow tc\) (\(V=Z,\,Z^{\prime }\)) provides a detectable signal and thus, it can give evidence for FCNC interactions; in these scenarios, the mass of a new neutral gauge boson can be as high as \(m_{Z'}=7\) TeV.

Phenomenology of dark matter and mirror fermions from a left–right mirror model with singlet scalar

We investigate a left–right mirror model with SU(3) c × SU(2)L × SU(2)R × U(1) Y and a discrete symmetry, which introduces mirror fields that are copies of the standard model (SM) fields. The mirror fields have the opposite chirality to their SM counterpart fields. We also introduce singlet scalars as dark matter (DM). The new interaction between DM, SM fermions, and mirror fermions can account for DM abundance, charged lepton flavor violation, lepton anomalous magnetic moment, and flavor changing neutral current. We demonstrated that if we choose DM annihilation into muon as the dominant annihilation channel for leptophilic DM, both the observed DM abundance and the observed discrepancy between theory and experiment in the muon anomalous magnetic moment can be explained without contradicting the bound derived from charged lepton flavor violating processes. We briefly discuss how mirror fermions will be produced at the future linear collider, as mirror fermions can interact with neutral gauge bosons in this model. Finally, we discuss the lightest mirror neutrino decay mechanism, which will be highly abundant if stable.

Direct detection of mirror matter in Twin Higgs models

We explore the possibility of discovering the mirror baryons and electrons of the Mirror Twin Higgs model in direct detection experiments, in a scenario in which these particles constitute a subcomponent of the observed DM. We consider a framework in which the mirror fermions are sub-nano-charged, as a consequence of kinetic mixing between the photon and its mirror counterpart. We consider both nuclear recoil and electron recoil experiments. The event rates depend on the fraction of mirror DM that is ionized, and also on its distribution in the galaxy. Since mirror DM is dissipative, at the location of the Earth it may be in the form of a halo or may have collapsed into a disk, depending on the cooling rate. For a given mirror DM abundance we determine the expected event rates in direct detection experiments for the limiting cases of an ionized halo, an ionized disk, an atomic halo and an atomic disk. We find that by taking advantage of the complementarity of the different experiments, it may be possible to establish not just the multi-component nature of mirror dark matter, but also its distribution in the galaxy. In addition, a study of the recoil energies may be able to determine the masses and charges of the constituents of the mirror sector. By showing that the mass and charge of mirror helium are integer multiples of those of mirror hydrogen, these experiments have the potential to distinguish the mirror nature of the theory. We also carefully consider mirror plasma screening effects, showing that the capture of mirror dark matter particles in the Earth has at most a modest effect on direct detection signals.

Baryon asymmetry from left-right phase transition

We extend the standard model fermions by a mirror copy to realize a left-right symmetry. During a strongly first order phase transition of the spontaneous left-right symmetry breaking, the CP-violating reflections of the mirror fermions off the mirror Higgs bubbles can generate a mirror lepton asymmetry and an equal mirror baryon asymmetry. We then can obtain an ordinary baryon asymmetry through the mirror fermion decays where a dark matter scalar plays an essential role. Benefitted from a parity symmetry for solving the strong CP problem, the cosmic baryon asymmetry can be well described by the ordinary lepton mass matrices up to an overall factor. In this scenario, the Dirac CP phase in the Majorana neutrino mass matrix can provide a unique source for the required CP violation. Furthermore, the Higgs triplet for type-II seesaw as well as the first generation of mirror charged fermions can be allowed at the TeV scale.

Why is the mission impossible? Decoupling the mirror Ginsparg–Wilson fermions in the lattice models for two-dimensional Abelian chiral gauge theories

AbstractIt is known that the four-dimensional Abelian chiral gauge theories of an anomaly-free set of Wely fermions can be formulated on the lattice preserving the exact gauge invariance and the required locality property in the framework of the Ginsparg–Wilson relation. This holds true in two dimensions. However, in the related formulation including the mirror Ginsparg–Wilson fermions, and therefore having a simpler fermion path-integral measure, it has been argued that the mirror fermions do not decouple: in the 345 model with Dirac– and Majorana–Yukawa couplings to the XY-spin field, the two-point vertex function of the (external) gauge field in the mirror sector shows a singular non-local behavior in the paramagnetic strong-coupling phase. We re-examine why the attempt seems to be a “Mission: Impossible” in the 345 model. We point out that the effective operators to break the fermion number symmetries (‘t Hooft operators plus others) in the mirror sector do not have sufficiently strong couplings even in the limit of large Majorana–Yukawa couplings. We also observe that the type of Majorana–Yukawa term considered is singular in the large limit due to the nature of the chiral projection of the Ginsparg–Wilson fermions, but a slight modification without such a singularity is allowed by virtue of their very nature. We then consider a simpler four-flavor axial gauge model, the $1^4(-1)^4$ model, in which the U(1)$_A$ gauge and Spin(6)(SU(4)) global symmetries prohibit the bilinear terms but allow the quartic terms to break all the other continuous mirror fermion symmetries. We formulate the model so that it is well behaved and simplified in the strong-coupling limit of the quartic operators. Through Monte Carlo simulations in the weak gauge-coupling limit, we show numerical evidence that the two-point vertex function of the gauge field in the mirror sector shows regular local behavior, and we argue that all you need is to kill the continuous mirror fermion symmetries with would-be gauge anomalies non-matched, as originally claimed by Eichten and Preskill. Finally, by gauging a U(1) subgroup of the U(1)$_A$$\times$ Spin(6)(SU(4)) of the previous model, we formulate the $2 1 (-1)^3$ chiral gauge model, and argue that the induced fermion measure term satisfies the required locality property and provides a solution to the reconstruction theorem formulated by Lüscher. This gives us “A New Hope” for the mission to be accomplished.

The full lepton flavor of the littlest Higgs model with T-parity

We re-examine lepton flavor violation (LFV) in the Littlest Higgs model with T-parity (LHT) including the full T-odd (non-singlet) lepton and Goldstone sectors. The heavy leptons induce two independent sources of LFV associated with the couplings necessary to give masses to the T-odd mirror fermions and to their partners in right-handed SO(5) multiplets, respectively. The latter, which have been neglected in the past, can be decoupled from gauge mediated processes but not from Higgs mediated ones and must therefore also be included in a general analysis of LFV in the LHT. We also further extend previous analyses by considering on-shell Z and Higgs LFV decays together with the LFV processes at low momentum transfer. We show that current experimental limits can probe the LHT parameter space up to global symmetry breaking scales f ∼ 10 TeV. For lower f values ≳ 1 TeV, μ − e transitions require the misalignment between the heavy and the Standard Model charged leptons to be ≲ 1%. Future LFV experiments using intense muon beams should be sensitive to misalignments below the per mille level. For τ LFV transitions, which could potentially be observed at Belle II and the LHC as well as future lepton colliders, we find that generically they can not discriminate between the LHT and supersymmetric models though in some regions of parameter space this may be possible.

A low scale left-right symmetric mirror model

A left-right symmetric mirror model restoring parity at a high scale in a way such that the mirror fermions and mirror gauge sector simultaneously could exist at TeV scale is discussed. We also provide an ultraviolet completion of the model with vector-like fermions, and discuss some theoretical and phenomenological implications of this model.

WIMP dark matter in the parity solution to the strong CP problem

We extend the Standard Model (SM) with parity symmetry, motivated by the strong CP problem and dark matter. In our model, parity symmetry is conserved at high energy by introducing a mirror sector with the extra gauge symmetry, SU(2)R × U(1)R. The charges of SU(2)R × U(1)R are assigned to the mirror fields in the same way as in the SM, but the chiralities of the mirror fermions are opposite to respect the parity symmetry. The strong CP problem is resolved, since the mirror quarks are also charged under the SU(3)c in the SM. In the minimal setup, the mirror gauge symmetry leads to stable colored particles which would be inconsistent with the observed data, so that we introduce two scalars in order to deplete the stable colored particles. Interestingly, one of the scalars becomes stable because of the gauge symmetry and therefore can be a good dark matter candidate. We especially study the phenomenology relevant to the dark matter, i.e. thermal relic density, direct and indirect searches for the dark matter. The bounds from the LHC experiment and the Landau pole are also taken into account. As a result, we find that a limited region is viable: the mirror up quark mass is around [600 GeV, 3 TeV] and the relative mass difference between the dark matter and the mirror up quark or electron is about mathcal{O} (1–10%). We also discuss the neutrino sector and show that the right-handed neutrinos in the mirror sector can increase the effective number of neutrinos or dark radiation by 0.14.

CP Properties of Leptons within the Mirror Mechanism

Formation of quark and lepton mass matrices through intermediate states of heavy mirror fermions is capable of reproducing main qualitative properties of weak mixing matrices (CKM and PMNS matrices). The reproduction includes the hierarchy of CKM matrix elements, a general form of the PMNS matrix, involving the smallness of the neutrino mixing angle \theta_{13}, and leads to very small neutrino masses. For leptons, these properties appear only for the Dirac nature of SM neutrino and its inverse spectrum. In such a lepton system, not only do spontaneous mirror symmetry violation and the observed mass hierarchy of charged leptons (e,\mu,\tau) govern the structure of the PMNS matrix but also permit assessment of its allowed complexity, that is, the CP properties of leptons. The PMNS matrix then contains no Majorana phases and its Dirac phase \delta_{CP} corresponds to |\sin\delta_{CP}|, which is significantly smaller than unity.

Muon-to-electron conversion in mirror fermion model with electroweak scale non-sterile right-handed neutrinos

The muon-to-electron conversion in aluminum, titanium and gold nuclei is studied in the context of a class of mirror fermion model with non-sterile right-handed neutrinos having masses at the electroweak scale. We show that the electric and magnetic dipole operators from the photon exchange diagrams provide the dominant contributions, which enables us to derive a simple formula to relate the conversion rate with the on-shell radiative decay rate of muon into electron at the limit of zero momentum transfer and large mirror lepton masses. Current experimental limits (SINDRUM II) and projected sensitivities (Mu2e, COMET and PRISM) for the muon-to-electron conversion rates in various nuclei and latest limit from MEG for the radiative decay rate of muon into electron are used to put constraints on the parameter space of the model. Sensitivities to the new Yukawa couplings can reach the range of one tenth to one hundred-thousandth, depending on the mixing scenarios and mirror fermion masses in the model as well as the nuclei targets used in future experiments.

Electron electric dipole moment in mirror fermion model with electroweak scale non-sterile right-handed neutrinos

The electric dipole moment of the electron is studied in detail in an extended mirror fermion model with the following unique features of (a) right-handed neutrinos are non-sterile and have masses at the electroweak scale, and (b) a horizontal symmetry of the tetrahedral group is used in the lepton and scalar sectors. We study the constraint on the parameter space of the model imposed by the latest ACME experimental limit on electron electric dipole moment. Other low energy experimental observables such as the anomalous magnetic dipole moment of the muon, charged lepton flavor violating processes like muon decays into electron plus photon and muon-to-electron conversion in titanium, gold and lead are also considered in our analysis for comparison. In addition to the well-known CP violating Dirac and Majorana phases in the neutrino mixing matrix, the dependence of additional phases of the new Yukawa couplings in the model is studied in detail for all these low energy observables.

Left-handed and right-handed U(1) gauge symmetry

We propose a model with the left-handed and right-handed continuous Abelian gauge symmetry; U(1)L × U(1)R. Then three right-handed neutrinos are naturally required to achieve U(1)R anomaly cancellations, while several mirror fermions are also needed to do U(1)L anomaly cancellations. Then we formulate the model, and discuss its testability of the new gauge interactions at collider physics such as the large hadron collider (LHC) and the international linear collider (ILC). In particular, we can investigate chiral structure of the interactions by the analysis of forward-backward asymmetry based on polarized beam at the ILC.