We present a model of self-interacting dark matter based on QCD-like theories and inspired by the proximity of $a_0(980\pm 20)$ to the $K\bar{K}(990)$ threshold. Dark matter is comprised of dark pions which self-scatter via the $σ$ resonance close to the $ππ$ threshold. While the linear sigma model serves as a qualitative guide, a fully unitary description of the scattering in the strongly coupled regime is given by effective range theory. The introduction of a kinetically mixed dark photon allows the dark pion to either freeze-out or -in. We study the viable parameter space which explains the observed relic abundance while evading all current constraints. Searches for dark matter self interactions at different scales, (in)direct detection signals, and (in)visibly-decaying dark photons will test this model in the near future.
We discuss numerous mechanisms for production of sterile neutrinos, which can account for all or a fraction of dark matter, and which can range from warm to effectively cold dark matter, depending on the cosmological scenario. We investigate production by Higgs boson decay, $(B-L)$ gauge boson production at high temperature, as well as production via resonant and nonresonant neutrino oscillations. We calculate the effects on structure formation in these models, some for the first time. If two populations of sterile neutrinos, one warm and one cold, were produced by different mechanisms, or if …
The neutral member of a Majorana fermion triplet (Sigma^+,Sigma^0,Sigma^-) is proposed as a candidate for the dark matter of the Universe. It may also serve as the seesaw anchor for obtaining a radiative neutrino mass.
The propagation of sigma meson in nuclear matter is studied in the Walecka model, assuming that the sigma couples to a pair of nucleon-antinucleon states and to particle-hole states, including the in medium effect of sigma-omega mixing. We have also considered, by completeness, the coupling of sigma to two virtual pions. We have found that the sigma meson mass decreases respect to its value in vacuum and that the contribution of the sigma omega mixing effect on the mass shift is relatively small.
By combining the recent WMAP measurements of the cosmic microwave background anisotropies and the results of the recent luminosity distance measurements to type-Ia supernovae, we find that the normalization of the matter power spectrum on cluster scales, sigma_8, can be used to discriminate between dynamical models of dark energy (quintessence models) and a conventional cosmological constant model (LCDM).
We propose a new method to constrain elastic scattering between dark matter (DM) and standard model particles in the early Universe. Direct or indirect thermal coupling of non-relativistic DM with photons leads to a heat sink for the latter. This results in spectral distortions of the cosmic microwave background (CMB), the amplitude of which can be as large as a few times the DM-to-photon number ratio. We compute CMB spectral distortions due to DM-proton, DM-electron and DM-photon scattering for generic energy-dependent cross sections and DM mass m_DM >~ 1 keV. Using FIRAS measurements we set …
Within the standard LCDM model of cosmology, the recent Planck measurements have shown discrepancies with other observations, e.g., measurements of the current expansion rate H_0, the galaxy shear power spectrum and counts of galaxy clusters. We show that if LCDM is extended by a hot dark matter component, which could be interpreted as a sterile neutrino, the data sets can be combined consistently. A combination of Planck data, WMAP-9 polarisation data, measurements of the BAO scale, the HST measurement of H_0, Planck galaxy cluster counts and galaxy shear data from the CFHTLens survey yields …
An important role of the scalar isoscalar sigma-meson in the low-energy physics is discussed. The behavior of the sigma-meson in the hot and dense medium is studied. It is shown that in the vicinity of critical values of temperature(T) and chemical potential(m) the sigma-meson can become a sharp resonance. This effect can lead to a strong enhancement of the processes pi pi -> gamma gamma and pi pi-> pi pi near the two-pion threshold. Experimental observation of this phenomenon can be interpreted as a signal of approaching the domain where the chiral symmetry restoration and phase transition of…
The electroweak axion is identified with the fuzzy dark matter of a mass $m\simeq 10^{-20}$--$10^{-19}\,{\rm eV}$. The model predicts two components of dark matter, one is ultralight and the other is WIMP-like. The Chern-Simons-type interaction between the fuzzy dark matter and photon and the $B+L$ breaking proton decays are predicted.
We study the impact of semi-annihilations x_i x_j <-> x_k X, where x_i is any dark matter and X is any standard model particle, on dark matter phenomenology. We formulate minimal scalar dark matter models with an extra doublet and a complex singlet that predict non-trivial dark matter phenomenology with semi-annihilation processes for different discrete Abelian symmetries Z_N, N>2. We implement two such example models with Z_3 and Z_4 symmetry in micrOMEGAs and work out their phenomenology. We show that both semi-annihilations and annihilations involving only particles from two different dark …
One of the open questions in modern cosmology is the small scale crisis of the cold dark matter paradigm. Increasing attention has recently been devoted to self-interacting dark matter models as a possible answer. However, solving the so-called "missing satellites" problem requires in addition the presence of an extra relativistic particle (dubbed dark radiation) scattering with dark matter in the early universe. Here we investigate the impact of different theoretical models devising dark matter dark radiation interactions on large scale cosmological observables. We use cosmic microwave backgr…
Mirror dark matter, and other similar dissipative dark matter candidates, need an energy source to stabilize dark matter halos in spiral galaxies. It has been suggested previously that ordinary supernovae can potentially supply the required energy. By matching the energy supplied to the halo from supernovae to that lost due to radiative cooling, we here derive a rough scaling relation, $R_{SN} \propto ρ_0 r_0^2$ ($R_{SN}$ is the supernova rate and $ρ_0, \ r_0$ the dark matter central density and core radius). Such a relation is consistent with dark matter properties inferred from studies of sp…
We study the bound nucleon sigma term and the quark condensate in nuclear matter. In the quark-meson coupling (QMC) model the nuclear correction to the sigma term is small and negative, i.e., it decelerates the decrease of the quark condensate in nuclear matter. However, the quark condensate in nuclear matter is controlled primarily by the scalar-isoscalar $σ$ field. Compared to the leading term, it moderates the decrease more than that of the nuclear sigma term alone at densities around and larger than the normal nuclear matter density.
We study the pion-nucleon sigma term in vacuum and in nuclear matter in the framework of global color model of QCD. With the effective gluon propagator being taken as the $δ$-function in momentum space of Munczek-Nomirovsky model, we estimate that the sigma term at chiral limit in the vacuum is 9/2 times the current quark mass and it decreases with the nuclear matter density. With the presently obtained in-medium pion-nucleon sigma term, we study the in-medium chiral quark condensate and obtain a reasonable variation behavior against the nuclear matter density.
Recent observations of the cosmic microwave background (CMB) anisotropies and the distribution of galaxies, galaxy clusters, and the Lyman Alpha forest have constrained the shape of the power spectrum of matter fluctuations on large scales k < few h/Mpc. We explore a new technique to constrain the matter power spectrum on smaller scales, assuming the dark matter is a Weakly Interacting Massive Particle (WIMP) that annihilates at early epochs. Energy released by dark matter annihilation can modify the spectrum of CMB temperature fluctuations and thus CMB experiments such as Planck have been abl…
Evidence has continued to accumulate over the last few decades as to the existence and nature of dark matter. Depending on the particle candidate, the dark matter can exhibit one of several cosmologically defined models: hot dark matter, cold dark matter, warm dark matter, self-interacting dark matter, and fuzzy dark matter. In this paper I review the relevance and status of these models, whether it is possible for more than one of these models to each constitute some fraction of the dark matter, and discuss the prospects for determining if any of these models can successfully describe the pro…
We present the cosmological constraints on the cross section of baryon-dark matter interactions for the dark matter mass below the MeV scale from the Planck CMB (cosmic microwave background) and SDSS (Sloan Digital Sky Survey) Lyman-$α$ forest data. To explore the dark matter mass $m_χ\lesssim 1$ MeV for which the dark matter's free-streaming effect can suppress the observable small scale density fluctuations, in addition to the acoustic oscillation damping in existence of the baryon-dark matter coupling, we apply the approximated treatment of dark matter free-streaming analogous to that of th…
We extend the formalism of dark matter directional detection to arbitrary one-body dark matter-nucleon interactions. The new theoretical framework generalizes the one currently used, which is based on 2 types of dark matter-nucleon interaction only. It includes 14 dark matter-nucleon interaction operators, 8 isotope-dependent nuclear response functions, and the Radon transform of the first 2 moments of the dark matter velocity distribution. We calculate the recoil energy spectra at dark matter directional detectors made of CF$_4$, CS$_2$ and $^{3}$He for the 14 dark matter-nucleon interactions…
In existing dark matter models with global symmetries the relic abundance of dark matter is either equal to that of anti-dark matter (thermal WIMP), or vastly larger, with essentially no remaining anti-dark matter (asymmetric dark matter). By exploring the consequences of a primordial asymmetry on the coupled dark matter and anti-dark matter Boltzmann equations we find large regions of parameter space that interpolate between these two extremes. Interestingly, this new asymmetric WIMP framework can accommodate a wide range of dark matter masses and annihilation cross sections. The present-day …
It is pointed out that the hadron spectroscopy should be a study of the structure of the QCD vacuum, low-energy elementary excitations on top of which are hadrons. Concentrating on the dynamical breaking of the chiral symmetry in the QCD vacuum, we emphasize the importance to clarify what is going on with mesons in the $I=J=0$-channel, i.e., the sigma meson channel, because it is connected to the quantum fluctuations of the chiral order parameter. After summarizing the significance of the sigma meson in QCD and low-energy hadron phenomenology, we give a review on some theoretical and experimen…
We present a new realization of asymmetric dark matter in which the dark matter and lepton asymmetries are generated simultaneously through two-sector leptogenesis. The right-handed neutrinos couple both to the Standard Model and to a hidden sector where the dark matter resides. This framework explains the lepton asymmetry, dark matter abundance and neutrino masses all at once. In contrast to previous realizations of asymmetric dark matter, the model allows for a wide range of dark matter masses, from keV to 10 TeV. In particular, very light dark matter can be accommodated without violating ex…
The first direct detection limits on dark matter in the MeV to GeV mass range are presented, using XENON10 data. Such light dark matter can scatter with electrons, causing ionization of atoms in a detector target material and leading to single- or few-electron events. We use 15 kg-days of data acquired in 2006 to set limits on the dark-matter-electron scattering cross section. The strongest bound is obtained at 100 MeV where sigma_e < 3 x 10^{-38} cm^2 at 90% CL, while dark matter masses between 20 MeV and 1 GeV are bounded by sigma_e < 10^{-37} cm^2 at 90% CL. This analysis provides a first p…
The interior of compact stars is usually divided into two major parts, the outer part called crust and the inner part called core. There are several possibilities for the composition of these parts. One is a hybrid star, in which the crust contains nuclear matter, while the inner core contains quark matter. Since at large baryon densities one can work with effective models, and nuclear and quark matter are usually described by different models, some unification of the two parts is needed. We show two different approaches for a composite model and some recent developments in hybrid star constru…
We consider the inflation model of a singlet scalar field (sigma field) with both quadratic and linear non-minimal couplings where unitarity is ensured up to the Planck scale. We assume that a $Z_2$ symmetry for the sigma field is respected by the scalar potential in Jordan frame but it is broken explicitly by the linear non-minimal coupling due to quantum gravity. We discuss the impacts of the linear non-minimal coupling on various dynamics from inflation to low energy, such as a sizable tensor-to-scalar ratio, a novel reheating process with quartic potential dominance, and suppressed physica…
We suggest that two-to-two dark matter fusion may be the relaxation process that resolves the small-scale structure problems of the cold collisionless dark matter paradigm. In order for the fusion cross section to scale correctly across many decades of astrophysical masses from dwarf galaxies to galaxy clusters, we require the fractional binding energy released to be greater than v^n ~ [10^{-(2-3)}]^n, where n=1,2 depends on local dark sector chemistry. The size of the dark-sector interaction cross sections must be sigma ~ 0.1-1 barn, moderately larger than for Standard Model deuteron fusion, …
The paper brings a novel approach to unification of dark matter and dark energy in terms of a cosmic fluid. A model is introduced in which the cosmic fluid speed of sound squared is defined as a function of its equation of state (EoS) parameter. It is shown how logarithmic part of this function results in dynamical regimes previously not observed in cosmic fluid models. It is shown that in a particular dynamical regime the model behaves as a unification of dark matter and phantom dark energy. Further, it is shown that the model may describe dark matter - dark energy unification in which dark e…
Generalized matter couplings to four-dimensional supersymmetric sigma models on general Kaehler manifolds are presented, preserving all holomorphic symmetries. Our generalization allows assignment of arbitrary U(1) charges to additional matter fermions, in all representations of (the holomorphic part of) the isometry group. This can be used to eliminate unwanted gamma_5 anomalies, in particular for the U(1) symmetry arising from the complex structure of the target space. A consistent gauging of this isometry group, or any of its subgroups, then becomes possible. When gauged in the presence of …
We present a comprehensive study of mass modifications of scalar, pseudo-scalar, vector, and axial-vector mesons in nuclear matter using the three-flavor extended Linear Sigma Model (eLSM) and the two-flavor Parity Doublet Model (PDM). The meson masses in nuclear matter are determined by calculating the one-loop nucleon corrections to the meson mean fields. As a result, we find all spin-$0$ meson masses except those of the pion, kaon, and the lightest scalar-isoscalar mesons decrease at finite baryon density. For spin-$1$ mesons, masses of all axial-vector mesons decrease in medium, and the de…
The SU(4) Polyakov linear sigma model (PLSM) is extended towards characterizing the chiral condensates, $σ_l$, $σ_s$ and $σ_c$ of light, strange and charm quarks, respectively and the deconfinement order-parameters $ϕ$ and $\barϕ$ at finite temperatures and densities (chemical potentials). The PLSM is considered to study the QCD equation of state in the presence of the chiral condensate of charm for different finite chemical potentials. The PLSM results are in a good agreement with the recent lattice QCD simulations. We conclude that, the charm condensate is likely not affected by the QCD phas…
In single-component theories of dark matter, the $2\to 2$ amplitudes for dark-matter production, annihilation, and scattering can be related to each other through various crossing symmetries. These crossing relations lie at the heart of the celebrated complementarity which underpins different existing dark-matter search techniques and strategies. In multi-component theories of dark matter, by contrast, there can be many different dark-matter components with differing masses. This then opens up a new, "diagonal" direction for dark-matter complementarity: the possibility of dark-matter decay fro…
We study energy transport by asymmetric dark matter in the interiors of very low-mass stars and brown dwarfs. Our motivation is to explore astrophysical signatures of asymmetric dark matter, which otherwise may not be amenable to conventional indirect dark matter searches. In viable models, the additional cooling of very-low mass stellar cores can alter stellar properties. Asymmetric dark matter with mass 4 < Mx/GeV < 10 and a spin-dependent (spin-independent) cross sections of sigma \sim 10^{-37} cm^2 (sigma \sim 10^{-40} cm^2) can increase the minimum mass of main sequence hydrogen burning, …
Modified dark matter (MDM) is a phenomenological model of dark matter, inspired by gravitational thermodynamics. For an accelerating Universe with positive cosmological constant ($Λ$), such phenomenological considerations lead to the emergence of a critical acceleration parameter related to $Λ$. Such a critical acceleration is an effective phenomenological manifestation of MDM, and it is found in correlations between dark matter and baryonic matter in galaxy rotation curves. The resulting MDM mass profiles, which are sensitive to $Λ$, are consistent with observational data at both the galactic…
We study the effects of dark matter self-interactions on the local dark matter distribution in selected Milky Way-like galaxies in the EAGLE hydrodynamical simulations. The simulations were run with two different self-interacting dark matter models, a constant and velocity-dependent self-interaction cross-section. We find that the local dark matter velocity distribution of the Milky Way-like halos in the simulations with dark matter self-interactions and baryons are generally similar to those extracted from cold collisionless dark matter simulations with baryons. In both cases, the local dark …
We show that the recently measured UV luminosity functions of ultra-faint lensed galaxies at z= 6 in the Hubble Frontier Fields provide an unprecedented probe for the mass m_X of the Warm Dark Matter candidates independent of baryonic physics. Comparing the measured abundance of the faintest galaxies with the maximum number density of dark matter halos in WDM cosmologies sets a robust limit m_X> 2.9 keV for the mass of thermal relic WDM particles at a 1-sigma confidence level, m_X> 2.4 keV at 2-sigma, and m_X> 2.1 keV at 3-sigma. These constitute the tightest constraints on WDM particle mass d…
We show that hidden hot dark matter, hidden-sector dark matter with interactions that decouple when it is relativistic, is a viable dark matter candidate provided it has never been in thermal equilibrium with the particles of the standard model. This hidden hot dark matter may reheat to a lower temperature and number density than the visible Universe and thus account, simply with its thermal abundance, for all the dark matter in the Universe while evading the typical constraints on hot dark matter arising from structure formation. We find masses ranging from ~3 keV to ~10 TeV. While never in e…
We investigate the screening masses of neutral pions and sigma mesons in hot and magnetized quark matter in the framework of a two-flavor lattice-improved Nambu-Jona-Lasinio (NJL) model with a magnetic field dependent coupling constant, which is determined by utilizing the results from lattice QCD simulations. Since such model can well reproduce inverse magnetic catalysis (IMC), by comparing with the standard NJL model, we systemically analyze the impacts of IMC on the temperature and magnetic field dependences of the longitudinal and transverse screening masses of the chiral partners, i.e. π^…
We study the cosmological consequences of co-decaying dark matter - a recently proposed mechanism for depleting the density of dark matter through the decay of nearly degenerate particles. A generic prediction of this framework is an early dark matter dominated phase in the history of the universe, that results in the enhanced growth of dark matter perturbations on small scales. We compute the duration of the early matter dominated phase and show that the perturbations are robust against washout from free-streaming. The enhanced small scale structure is expected to survive today in the form of…
The simplest renormalizable effective field theories with asymmetric dark matter bound states contain two additional gauge singlet fields one being the dark matter and the other a mediator particle that the dark matter annihilates into. We examine the physics of one such model with a Dirac fermion as the dark matter and a real scalar mediator. For a range of parameters the Yukawa coupling of the dark matter to the mediator gives rise to stable asymmetric dark matter bound states. We derive properties of the bound states including nuggets formed from $N\gg1$ dark matter particles. We also consi…
We present a model for describing nuclear matter at finite density based on quarks interacting with chiral fields, sigma and pion. The chiral Lagrangian also includes a logarithmic potential, associated with the breaking of scale invariance. We provide results for the soliton in vacuum and at finite density, using the Wigner-Seitz approximation. We show that the model can reach higher densities respect to the Linear-sigma model, up to approximately 3 rho_0 for m_sigma=1200 MeV.
Soft-photon emission rates are calculated within the linear sigma model. The investigation is aimed at answering the question to which extent the emissivities map out the phase structure of this particular effective model of strongly interacting matter.
The existence of dark matter and dark energy in cosmology is implied by various observations, however, they are still unclear because they have not been directly detected. In this Letter, an unified model of dark energy and dark matter that can explain the evolution history of the Universe later than inflationary era, the time evolution of the growth rate function of the matter density contrast, the flat rotation curves of the spiral galaxies, and the gravitational experiments in the solar system is proposed in mimetic matter model.
Since neither supersymmetry nor dark matter WIMPs have yet been observed, pessimism about their reality has been growing. Here we discuss a new supersymmetric theory and a new dark matter candidate which are naturally consistent with current experimental results, but which imply a plethora of new phenomena awaiting discovery within the foreseeable future.
We present a simple extension of the standard model that gives rise to baryogenesis a has a dark matter candidate of O(GeV) mass. A minimal set of new fields required for baryogenesis includes two O(TeV) colored scalars and a singlet fermion. The fermion also becomes a viable dark matter candidate when its is nearly degenerate in mass with the proton. Dark matter and baryon asymmetry are produced form the decay of heavy scalars, which can lead to a natural explanation of the baryon-dark matter coincidence problem. The dark matter candidate escapes direct and indirect detection, but can be prob…
We propose a unified scenario to generate the masses of Dirac neutrinos and cold dark matter at the TeV scale, understand the origin of dark energy and explain the matter-antimatter asymmetry of the universe. This model can lead to significant impact on the Higgs searches at LHC.
We introduce an $SU(2)_X^{}$ dark sector without any fermions and then realize a non-abelian kinetic mixing between the dark $SU(2)_X^{}$ gauge fields and the standard model $SU(2)_L^{}\times U(1)_Y^{}$ gauge fields. While one of the dark gauge bosons becomes a dark photon, the others can keep stable to form a dark matter particle. The nearly degenerate masses of dark photon and dark matter could be tested if the dark photon and the dark matter are both observed in the future.
Recent developments constraining the SUSY parameter space are reviewed within the framework of SUGRA GUT models. The WMAP data is seen to reduce the error in the density of cold dark matter by about a factor of four, implying that the lightest stau is only 5 -10 GeV heavier than the lightest neutralino when m_0, m_{1/2} < 1 TeV. The CMD-2 re-analysis of their data has reduced the disagreement between the Standard Model prediction and the Brookhaven measurement of the muon magnetic moment to 1.9 sigma, while using the tau decay data plus CVC, the disagreement is 0.7 sigma. (However, the two set…
A brief overview of our current understanding of abundance and properties of dark energy and dark matter is presented. A more focused discussion of supersymmetric dark matter follows. Included is a frequentist approach to the supersymmetric parameter space and consequences for the direct detection of dark matter.
The predicted size of dark matter substructures in kilo-parsec scales is model-dependent. Therefore, if the correlations between dark matter mass densities as a function of the distances between them are measured via observations, we can scrutinize dark matter scenarios. In this paper, we present an assessment procedure of dark matter scenarios. First, we use Gaia's data to infer the single-body phase-space density of the stars in the Fornax dwarf spheroidal galaxy. The latter, together with the Jeans equation, after eliminating the gravitational potential using the Poisson equation, reveals t…
A simple model of the Majorana neutrino with the see-saw mechanism is studied, assuming that two light neutrinos are the hot dark matters with equal mass of 2.4 eV in the cold plus hot dark matter model of cosmology. We find that the heavy neutrino, which is the see-saw partner with the remaining one light neutrino, can be the cold dark matter, if the light neutrino is exactly massless. This cold dark matter neutrino is allowed to have the mass of the wide range from 5.9 x 10^2 eV to 2.2 x 10^7 eV.
We attempt to answer whether neutrinos and antineutrinos, such as those in the cosmic neutrino background, would clusterize among themselves or even with other dark-matter particles, under certain time span, say 1 Gyr. With neutrino masses in place, the similarity with the ordinary matter increases and so is our confidence for neutrino clustering if time is long enough. In particular, the clusterings could happen with some seeds (cf. see the text for definition), the chance in the dark-matter world to form dark-matter galaxies increases. If the dark-matter galaxies would exist in a time span o…
Even though the sensitivity of direct dark matter search experiments reach the level about $10^{-45}~{\rm cm}^2$, there is no confident signal of dark matter been observed. We point out that, if dark matter is a vector boson, the null result in direct dark matter search experiments may due to the destructive effects in dark-matter-nucleon elastic scattering. We illustrate the scenario using a modified Higgs portal model that includes exotic quarks. The significant cancellation can occur for certain mass gap between heavy quark and dark matter. As a result, the spin-independent dark-matter-nucl…
The linear sigma model with quarks at very low temperatures provides an effective description for the thermodynamics of the strong interaction in cold and dense matter, being especially useful at densities found in compact stars and protoneutron star matter. Using the MSbar one-loop effective potential, we compute quantities that are relevant in the process of nucleation of droplets of quark matter in this scenario. In particular, we show that the model predicts a surface tension of Σ~ 5-15 MeV/fm^2, rendering nucleation of quark matter possible during the early post-bounce stage of core colla…
The anomalous magnetic moment of the muon has been measured to 0.5 ppm in a series of precision experiments at the Brookhaven Alternating Gradient Synchrotron. The individual results for each sign: a(mu+)= 11 659 204(7)(5) E-10 and a(mu-) = 11 659 214(8)(3) E-10 are consistent with each other, so that we can write the average anomaly as a(mu)(exp) = 11 659 208(6) E-10 (0.5 ppm). A discrepancy between the measured value and the Standard Model (Delta a(mu)) is a signal for new physics. Assuming that such a discrepancy is due to contributions from supersymmetric particles provides a framework whi…
The equation of state provided by effective models of strongly interacting matter should comply with the restrictions imposed by current astrophysical observations of compact stars. Using the equation of state given by the (axial-)vector meson extended linear sigma model, we determine the mass-radius relation and study whether these restrictions are satisfied under the assumption that most of the star is filled with quark matter. We also compare the mass-radius sequence with those given by the equations of state of somewhat simpler models.
The pion-nucleon sigma term is a quantity involved in many important aspects of particle and nuclear physics. In this review I show its origin and how it is connected to important questions as the origin of mass of the ordinary matter, studies of dark matter detection and nucleosynthesis. I mention the most common methods used to obtain the sigma term, and comment on the extracted values. As it is shown, the accepted value of the sigma term has been moving from relatively low ($\sim 40$ MeV) to larger ones ($\sim 60$ MeV) until today, where this controversy still persist.
