According to the Standard Model (SM), we expect to find a proton for each decaying neutron. However, the experiments counting the number of decayed neutrons and produced protons have a disagreement. This discrepancy suggests that neutrons might have an exotic decay to a Dark Sector (DS). In this paper, we explore a scenario where neutrons decay to a dark Dirac fermion $χ$ and a non-abelian dark gauge boson $W'$. We discuss the cosmological implications of this scenario assuming DS particles are produced via freeze-in. In our proposed scenario, DS has three portals with the SM sector: (1) the fermion portal coming from the mixing of the neutron with $χ$, (2) a scalar portal, and (3) a non-renormalizable kinetic mixing between photon and dark gauge bosons which induces a vector portal between the two sectors. We show that neither the fermion portal nor the scalar portal should contribute to the production of the particles in the early universe. Specifically, we argue that the maximum temperature of the universe must be low enough to prevent the production of $χ$ in the early universe. In this paper, we rely on the vector portal to connect the two sectors, and we discuss the phenomenological bounds on the model. The main constraints come from ensuring the right relic abundance of dark matter and evading the neutron star bounds. When dark gauge boson is very light, measurements of the Big Bang Nucleosynthesis impose a stringent constraint as well.
We discuss mechanisms for naturally generating GeV-scale hidden sectors in the context of weak-scale supersymmetry. Such low mass scales can arise when hidden sectors are more weakly coupled to supersymmetry breaking than the visible sector, as happens when supersymmetry breaking is communicated to the visible sector by gauge interactions under which the hidden sector is uncharged, or if the hidden sector is sequestered from gravity-mediated supersymmetry breaking. We study these mechanisms in detail in the context of gauge and gaugino mediation, and present specific models of Abelian GeV-scal…
We consider a generic abelian hidden sector that couples to the Standard Model only through gauge-invariant renormalizable operators. This allows the exotic Higgs boson to mix with the Standard Model Higgs boson, and the exotic abelian gauge boson to mix with the Standard Model hypercharge gauge boson. One immediate consequence of spontaneous breaking of the hidden sector gauge group is the possible decay of the lightest Higgs boson into four fermions through intermediate exotic gauge bosons. We study the implications of this decay for Higgs boson phenomenology at the Fermilab Tevatron Collide…
We add fermions to an abelian-gauged hidden sector. We show that the lightest can be the dark matter with the right thermal relic abundance, and discovery is within reach of upcoming dark matter detectors. We also show that these fermions change Higgs boson phenomenology at the Large Hadron Collider (LHC), and in particular could induce a large invisible width to the lightest Higgs boson state. Such an invisibly decaying Higgs boson can be discovered with good significance in the vector boson fusion channel at the LHC.
A general method for classifying the possible quark models of a multi-Higgs-doublet model, in the presence of Abelian symmetries, is presented. All the possible sets of textures that can be present in a given sector are shown, thus turning the determination of the flavor models into a combinatorial problem. Several symmetry implementations are studied for two and three Higgs doublet models. Some models implementations are explored in great detail, with a particular emphasis on models known as Branco-Grimus-Lavoura and nearest-neighbour-nnteraction. Several considerations on the flavor changing…
We introduce a new class of renormalisable models, consisting of a dark $SU(2)_D$ gauge sector connected to the Standard Model (SM) through a Vector-Like (VL) fermion mediator, not requiring a Higgs portal, in which a massive vector boson is the Dark Matter (DM) candidate. These models are labelled Fermion Portal Vector Dark Matter (FPVDM). Multiple realisations are possible, depending on the properties of the VL partner and of the scalar potential. One example is discussed in detail. FPVDM models have a large number of applications in collider and non-collider experiments, depending on the me…
We present a SUSY breaking scenario based on Abelian gaugino kinetic term mixings between hidden and observable sectors. If an extra U(1) gaugino in the observable sector obtains a large mass through this mixing effect based on SUSY breaking in the hidden sector, soft SUSY breaking parameters in the MSSM may be affected by radiative effects due to this gaugino mass. New phenomenological aspects are discussed in such a SUSY breaking scenario.
The Hidden Abelian Higgs Model (HAHM) is an extension of the Standard Model based on the gauge group $G =SU(3)_{C} \times SU(2)_{L} \times U(1)_{Y} \times U(1)_{X}$ i.e. an extra $U(1)_{X}$ gauge group in addition to the SM gauge groups.In HAHM, an Abelian Hidden sector is coupled to the SM, and the resulting new Higgs boson H and new neutral gauge boson $Z_{HAHM}$ fields are allowed to mix with the corresponding SM fields. In this work, we search for the new neutral gauge boson $Z_{HAHM}$ and new Higgs boson in the context of the Hidden Abelian Higgs Model (HAHM) through the decay process $pp…
We propose a dark matter model in which the dark sector is gauged under a new SU(2) group. The dark sector consists of SU(2) dark gauge fields, two triplet dark Higgs fields, and two dark fermion doublets (dark matter candidates in this model). The dark sector interacts with the SM sector through kinetic and mass mixing operators. The model explains both PAMELA and Fermi LAT data very well and also satisfies constraints from both the DM relic density and Standard Model precision observables. The phenomenology of the model at the LHC is also explored.
In this paper, we explore a dark sector scenario with a gauged $SU(2)_R$ and a global $U(1)_X \times \mathbb{Z}_2$, where the continuous symmetries are spontaneously broken to a global $U(1)_D$. We show that in various regions of the parameter space we can have two, or three dark matter candidates, where these dark matter particles are either a Dirac fermion, a dark gauge boson, or a complex scalar. The phenomenological implications of this scenario are vast and interesting. We identify the parameter space that is still viable after taking into account the constraints from various experiments.…
In this paper we study the present and future sensitivities of the rare meson decay facilities KOTO, LHCb and Belle II to a light dark sector of the minimal dark abelian gauge symmetry where a dark Higgs $S$ and a dark photon $Z_D$ have masses $\lesssim 10$ GeV. We have explored the interesting scenario where $S$ can only decay to a pair of $Z_D$'s and so contribute to visible or invisible signatures, depending on the life-time of the latter. Our computations show that these accelerator experiments can access the dark Higgs (mass and scalar mixing) and the dark photon (mass and kinetic mixing)…
New fundamental particles, charged under new gauge groups and only weakly coupled to the standard sector, could exist at fairly low energy scales. In this article we study a selection of such models, where the secluded group either contains a softly broken U(1) or an unbroken SU(N). In the Abelian case new γv gauge bosons can be radiated off and decay back into visible particles. In the non-Abelian case there will not only be a cascade in the hidden sector, but also hadronization into new πv and ρv mesons that can decay back. This framework is developed to be applicable both for e+e- and pp co…
In strong (quasi-)Abelian fields, even at the one-loop level of the coupling constant, quantum fluctuations of fermions induce an effective Lagrangian density whose imaginary (absorptive) part is purely nonperturbative and known to be responsible for the fermion-antifermion pair creation. On the other hand, the induced real (dispersive) part has perturbative and nonperturbative contributions. In the one-loop case, we argue how to separate the two contributions from each other for any strength of the field. We show numerically that the nonperturbative contributions are in general comparable wit…
We study vortex solutions in a theory with dynamics governed by two weakly coupled Abelian Higgs models, describing a hidden sector and a visible sector. We analyze the radial dependence of the axially symmetric solutions constructed numerically and discuss the stability of vortex configurations for different values of the model parameters, studying in detail vortex decay into lower energy configurations. We find that even in a weak coupling regime vortex solutions strongly depend on the parameters of both the visible and hidden sectors. We also discuss on qualitative grounds possible implicat…
The Abelian decomposition of QCD which decomposes the gluons to the color neutral binding gluons (the neurons) and the colored valence gluons (the chromons) gauge independently naturally generalizes the quark model to the quark and chromon model which could play the central role in hadron spectroscopy. We discuss the color reflection symmetry, the fundamental symmetry of the quark and chromon model, and explain how it describes the glueballs and the glueball-quarkonium mixing in QCD. We present the numerical analysis of glueball-quarkonium mixing in $0^{++}$, $2^{++}$, and $0^{-+}$ sectors bel…
SU(N) Lie algebras possess discrete symmetries which can lead naturally to stable vector dark matter (DM). In this work, we consider the possibility that the dark SU(N) sector couples to the visible sector through the Higgs portal. We find that minimal CP-conserving hidden `Higgs sectors' entail stable massive gauge fields which fall into the WIMP category of dark matter candidates. For SU(N), N>2, DM consists of three components, two of which are degenerate in mass. In all of the cases, there are substantial regions of parameter space where the direct and indirect detection as well as relic a…
We analyze the compatibility between abelian symmetries acting in two different sectors of a theory using the Smith Normal Form method. We focus on N-Higgs-doublet models (NHDMs) and on the compatibility between symmetries in the Higgs potential and in the Yukawa interactions, which were separately analyzed previous works. It is shown that two equal (isomorphic) symmetry groups that act in two separate sectors are not necessarily compatible in the whole theory and an upper bound is found for the size of the group that can be implemented in the entire NHDM. We also develop useful techniques to …
We discuss one loop generation of the term connecting gauge fields from a local hidden $SU(2)_H$ and the standard model $U(1)_Y$ introducing an $SU(2)_H$ doublet fermion with non-zero hypercharge and a scalar field in adjoint representation. Then we obtain a kinetic mixing term between $SU(2)_H$ and $U(1)_Y$ gauge fields after the adjoint scalar field developing vacuum expectation value. We illustrate such a concrete scenario introducing a dark matter model in an ultraviolet (UV) completion with local $SU(2)_H$ symmetry where the scalar doublet is our dark matter candidate and its stability is…
New physics can be light if it is hidden, coupling very weakly to the Standard Model. In this work we investigate the discovery prospects of Abelian hidden sectors in lower-energy fixed-target and high-precision experiments. We focus on a minimal supersymmetric realization consisting of an Abelian vector multiplet, coupled to hypercharge by kinetic mixing, and a pair of chiral Higgs multiplets. This simple theory can give rise to a broad range of experimental signals, including both commonly-studied patterns of hidden vector decay as well as new and distinctive hidden sector cascades. We find …
We show a simple mechanism for a dynamical CPT violation in the neutron sector. In particular, we show a {\it CPT-violating see-saw mechanism}, generating a Majorana mass and a CPT violating mass for the neutron. CPT-violating see-saw involves a sterile partner of the neutron, living in a hidden sector, in which CPT is spontaneously broken. In particular, neutrons (antineutrons) can communicate with the hidden sector through non-perturbative quantum gravity effects called {\it exotic instantons}. Exotic instantons dynamically break R-parity, generating one effective vertex between the neutron …
We investigate the detailed phenomenology of a light Abelian hidden sector in the Randall-Sundrum framework. Relative to other works with light hidden sectors, the main new feature is a tower of hidden Kaluza-Klein vectors that kinetically mix with the Standard Model photon and Z. We investigate the decay properties of the hidden sector fields in some detail, and develop an approach for calculating processes initiated on the ultraviolet brane of a warped space with large injection momentum relative to the infrared scale. Using these results, we determine the detailed bounds on the light warped…
Classifying the symmetries of the scalar sector in multi-Higgs-doublet models is the main focus of this thesis. We have found certain symmetries that are always broken in models with more than two doublets, which we name "frustrated symmetries". In the attempt towards the classification of possible symmetries in the scalar sector of the NHDM, we find that these symmetry groups are either subgroups of the maximal torus, or certain finite Abelian groups which are not subgroups of maximal tori. For the subgroups of the maximal torus, we present an algorithmic strategy that gives the full list of …
Quantum interferometric probe of neutron--hidden neutron oscillations
Università di Salerno（萨莱诺大学）；INFN – Gruppo Collegato di Salerno（意大利国家核物理研究所萨莱诺协作组）；University of Camerino（卡梅里诺大学）；Technical University of Munich（慕尼黑工业大学）
In the present study we analyse, within the scalar sector of the Standard-Model Extension (SME) framework, the influence of a spontaneous Lorentz symmetry breaking on gravitational quantum states of ultracold neutrons. The model is framed according to the laboratory conditions of the recent high-sensitivity GRANIT and $q$Bounce experiments. The high-precision data achieved in such experiments allow us to set bounds on the symmetry breaking parameters of the model. The effective Hamiltonian governing the neutron's motion along the axis of free fall is derived explicitly. It describes a particle…
An extra Abelian gauge symmetry is motivated in many new physics models in both supersymmetric and nonsupersymmetric cases. Such a new gauge symmetry may interact with both the observable sector and the hidden sector. We systematically investigate the most general residual discrete symmetries in both sectors from a common Abelian gauge symmetry. Those discrete symmetries can ensure the stability of the proton and the dark matter candidate. A hidden sector dark matter candidate (lightest U-parity particle or LUP) interacts with the standard model fields through the gauge boson Z', which may sel…
We summarize our recent proposal of explaining the discrepancy between the bottle and beam measurements of the neutron lifetime through the existence of a dark sector, which the neutron can decay to with a branching fraction 1%. We show that viable particle physics models for such neutron dark decays can be constructed and we briefly comment on recent developments in this area.
At natural values of parameters of the model dicussed, the contribution of the chromoelectric dipole moment of the s-quark to the neutron electric dipole moment (EDM) exceeds considerably the experimental upper limit for the neutron EDM. As strict bounds on the parameters of the model are derived from the atomic experiment with odd isotope of mercury.
We show that neutron star binaries can be ideal laboratories to probe hidden sectors with a long range force. In particular, it is possible for gravitational wave detectors such as LIGO and Virgo to resolve the correction of waveforms from ultralight dark gauge bosons coupled to neutron stars. We observe that the interaction of the hidden sector affects both the gravitational wave frequency and amplitude in a way that cannot be fitted by pure gravity.
Recent neutrino experiments have made very significant progresses and our knowledge of neutrino masses and mixing has considerably improved. In a model independent Monte Carlo approach, we have examined a very large class of textures, in the context of non abelian horizontal symmetries; we have found that neutrino data select only those charged lepton matrices with left-right asymmetric texture. The large atmospheric mixing angle needs m_{23} ~= m_{33}. This result,if combined with similar recent findings for the quark sector in the B oscillations, can be interpreted as a hint for SU(5) unific…
We analyse the properties of generic models based on an SU(3) family symmetry providing a full description of quark charged lepton and neutrino masses and mixing angles. We show that a precise fit of the resulting fermion textures is consistent with CP being spontaneously broken in the flavour sector. The CP violating phases are determined by the scalar potential and we discuss how symmetries readily lead to a maximal phase controlling CP violation in the quark sector. In a specific model the CP violation to be expected in the neutrino sector is related to that in the quark sector and we deter…
All pieces of concrete evidence for phenomena outside the standard model (SM) - neutrino masses and dark matter - are consistent with the existence of new degrees of freedom that interact very weakly, if at all, with those in the SM. We propose that these new degrees of freedom organize themselves into a simple dark sector, a chiral SU(3) x SU(2) gauge theory with the smallest nontrivial fermion content. Similar to the SM, the dark SU(2) is spontaneously broken while the dark SU(3) confines at low energies. At the renormalizable level, the dark sector contains massless fermions - dark leptons …
The neutron lifetime anomaly has been used to motivate the introduction of new physics with hidden-sector particles coupled to baryon number, and on which neutron stars provide powerful constraints. Although the neutron lifetime anomaly may eventually prove to be of mundane origin, we use it as motivation for a broader review of the ways that baryon number violation, be it real or apparent, and dark sectors can intertwine and how neutron star observables, both present and future, can constrain them.
There is strong evidence in favor of the idea that dark matter is self interacting, with the cross section-to-mass ratio $σ/ m \sim 1\,\mathrm{cm^2/g} \sim 1\,\mathrm{barn/GeV}$. We show that viable models of dark matter with this large cross section are straightforwardly realized with non-Abelian hidden sectors. In the simplest of such models, the hidden sector is a pure gauge theory, and the dark matter is composed of hidden glueballs with a mass around $100\,\mathrm{MeV}$. Alternatively, the hidden sector may be a supersymmetric pure gauge theory with a $\sim 10\,\mathrm{TeV}$ gluino therma…
The possibility of neutron swapping between the ordinary and mirror sectors is today a subject of a great many theoretical and experimental studies. In this paper, we investigate the neutron-mirror neutron transitions in different environments from vacuum to neutron star. Our approach is based on the density matrix formalism, Lindblad and Bloch equations and the implication of the seesaw mechanism to the Hamiltonian diagonalization.
We perform a careful study of the infrared sector of massless non-abelian gauge theories in four-dimensional Minkowski spacetime using the covariant phase space formalism, taking into account the boundary contributions arising from the gauge sector of the theory. Upon quantization, we show that the boundary contributions lead to an infinite degeneracy of the vacua. The Hilbert space of the vacuum sector is not only shown to be remarkably simple, but also universal. We derive a Ward identity that relates the n-point amplitude between two generic in- and out-vacuum states to the one computed in …
We consider the cosmology and phenomenology of a dark photon portal to a simple dark sector consisting of a single, light, fermionic dark matter particle species with mass in the MeV range. We entertain three possible kinetic mixing structures of a new Abelian gauge group U(1)$_{\text{dark}}$ with the visible sector through U(1)$_{\text{e.m.}}$, U(1)$_{\text{Y}}$ and T[SU(2)$_{\text{L}}$]. We assume the dark photon to be massive and around the MeV scale, thus close to the mass scale of the dark matter candidate. We compute the dark matter relic density via freeze-out and freeze-in, entertainin…
The influence of vector backgrounds with restored Lorentz invariance on non-abelian gauge field theories is studied. Lorentz invariance is ensured by taking the average over a Lorentz invariant ensemble of background vectors. Like in the abelian case [hep-ph/0506210], the propagation of fermions is suppressed over long distances. Contrary to the fermionic sector, pure gauge configurations of the background suppress the long-distance propagation of the bosons only partially, i.e. not beyond the leading contribution for a large number of colours.
We discuss the implications of a gauged Abelian hidden-sector communicating with the Standard Model (SM) fields via kinetic mixing with the SM hypercharge gauge field, or via the Higgs quartic interaction. We discuss signatures of the hidden-sector gauge boson at the LHC in the four-lepton channel. We show that a hidden-sector fermion can be a natural dark-matter candidate with the correct relic-density, discuss direct-detection prospects, and show how Higgs signatures may be altered at the LHC.
Following a previous proposal, lepton number is considered as the result of a spontaneously broken non-Abelian gauge $SU(2)_N$ symmetry. New fermions are added to support this new symmetry, the spontaneous breaking of which allows these new fermions to be part of the dark sector, together with the vector gauge boson which communicates between them and the usual leptons. A byproduct is a potential significant contribution to the muon anomalous magnetic moment.
The relation between the mixing matrices of leptons and quarks: $U_{\rm{PMNS}} \approx V_{\rm{CKM}}^\dagger U_0$, where $U_0$ is a matrix of special forms (e.g. BM, TBM), can be a clue for understanding the lepton mixing and neutrino masses. It may imply the Grand unification and existence of a hidden sector with certain symmetry which generates $U_0$ and leads to the smallness of neutrino masses. We apply the residual symmetry approach to obtain $U_0$. The residual symmetries of both the visible and hidden sectors are $\mathbb{Z}_{2} \times \mathbb{Z}_{2}$. Their embedding in a unified flavor…
We apply a generalized field ansatz to describe the spherically symmetric sector of classical solutions of the electroweak theory. This sector contains Abelian magnetic monopoles labeled by their magnetic charge $n=\pm 1,\pm 2,\ldots$, the non-Abelian monopole for $n=\pm 2$ found previously by Cho and Maison (CM), and also the electric oscillating solutions. All magnetic monopoles have infinite energy. We analyze their perturbative stability and use the method of complex spacetime tetrad to separate variables and reduce the perturbation equations to multi-channel Schroedinger-type eigenvalue p…
In anomaly-mediated supersymmetry breaking (AMSB) models, superpartner masses are proportional to couplings squared. Their hidden sectors therefore naturally contain WIMPless dark matter, particles whose thermal relic abundance is guaranteed to be of the correct size, even though they are not weakly-interacting massive particles (WIMPs). We study viable dark matter candidates in WIMPless AMSB models with non-Abelian hidden sectors and highlight unusual possibilities that emerge in even the simplest models. In one example with a pure SU(N) hidden sector, stable hidden gluinos freeze out with th…
The possibility that a neutron can be transformed to a hidden sector particle remains intriguingly open. Proposed theoretical models conjecture that the hidden sector can be represented by a mirror sector, and the neutron n can oscillate into its sterile mirror twin n', exactly or nearly degenerate in mass with n. Oscillations n - n' can take place in vacuum and in the environment of the regular matter and the magnetic field where only neutron will be subject of interaction with the environment. We describe the propagation of the oscillating n - n' system as a particle of the cold neutron beam…
We consider the effect of density dependent dark matter on the neutron star mass, radius, and tidal deformability. Nuclear matter (normal matter) as well as the fermionic dark matter sector is considered in a mean field model. We adopt the two fluid formalism to investigate the effect of dark matter on the neutron star properties. In the two fluid picture, there is no direct interaction between the dark matter and the nuclear matter. Rather these two sectors interact only through gravitational interaction. The nuclear matter sector is described by the $σ-ω-ρ$ meson interaction in the "FSU2R" p…
Non-Abelian dark gauge forces that do not couple directly to ordinary matter may be realized in nature. The minimal form of such a dark force is a pure Yang-Mills theory. If the dark sector is reheated in the early universe, it will be realized as a set of dark gluons at high temperatures and as a collection of dark glueballs at lower temperatures, with a cosmological phase transition from one form to the other. Despite being dark, the gauge fields of the new force can connect indirectly to the Standard Model through non-renormalizable operators. These operators will transfer energy between th…
We present the possible mixing effects associated with the low-energy limit of a Standard-Model extension by two abelian gauge groups U(1)_1 x U(1)_2. We derive general formulae and approximate expressions that connect the gauge eigenstates to the mass eigenstates. Applications using the well-studied groups U(1)_B, U(1)_(B-L), U(1)_(L_alpha - L_beta) (L_alpha being lepton flavor numbers), and U(1)_DM (a symmetry acting only on the dark matter sector) are discussed briefly.
Gauge theory is the foundation of the particle physics Standard Model (SM). Considering the multiple gauge sectors for one gauge transformation, we study the generalized Abelian and non-Abelian (Yang-Mills theory) gauge theories. We first point out that the U(1) gauge theory has a few unique properties, which provide the motivations for the generalized Yang-Mills theory. Also, we consider the generalized Abelian gauge theory, and study the Higgs mechanism with new interesting properties. In addition, we propose the simple and generic generalizations of Yang-Mills theory. In the simple generali…
Freeze-in Production of Non-Abelian Millicharged Vector Dark Matter
National Center for Theoretical Sciences, National Taiwan University（台湾大学理论科学中心）；Phenikaa Institute for Advanced Study, Phenikaa University（phenikaa 大学先进研究院）；Institute of Physics, Academia Sinica（中央研究院物理研究所）
Assuming that finite family symmetries are gauged, we derive discrete anomaly conditions for various non-Abelian groups. We thus provide new constraints for flavor model building, in which discrete non-Abelian symmetries are employed to explain the tri-bimaximal mixing pattern in the lepton sector.
The supersymmetric standard model (SSM) has a CP-violating phase in its gauge-Higgs sector. This new source of CP violation induces the electric dipole moments (EDMs) of the neutron and electron at the one-loop level. The same CP-violating phase generates the EDM of the $W$ boson through one-loop diagrams mediated by the charginos and neutralinos, which leads to the EDMs of the neutron and electron at the two-loop level. We discuss these EDMs, assuming that the CP-violating phase has the magnitude of order 0.1--1 which may be suggested from the baryon asymmetry of the universe. Even at the two…
The weak-scale $U(1)_{Y}$ Abelian Higgs Model (AHM) is the spontaneous-symmetry-breaking gauge theory of a complex scalar $ϕ= \frac{1}{\sqrt{2}}(H + i π)$ and a vector $A_μ$. Global $U(1)_{Y}\otimes BRST$ symmetry emerges: when it is realized that on-shell T-matrix elements enjoy an extra $U(1)_{Y}$ global symmetry beyond the Lagragian's BRST symmetry. The symmetries co-exist: $U(1)_{Y}$ generators $δ_{U(1)_Y}$ commute with BRST generators s and $[δ_{U(1)_Y},s]{\cal L} = 0$. Two towers of Ward Takahashi identities (WTI), which include all-loop-orders quantum corrections, emerge: a tower of rel…
Motivated by the recent proliferation of observed astrophysical anomalies, Arkani-Hamed et al. have proposed a model in which dark matter is charged under a non-abelian "dark" gauge symmetry that is broken at ~ 1 GeV. In this paper, we present a survey of concrete models realizing such a scenario, followed by a largely model-independent study of collider phenomenology relevant to the Tevatron and the LHC. We address some model building issues that are easily surmounted to accommodate the astrophysics. While SUSY is not necessary, we argue that it is theoretically well-motivated because the GeV…
