Yoshiharu Kawamura, Teppei Kinami, Takashi Miura
We derive sum rules among scalar masses for various boundary conditions of the hidden-visible couplings in the presence of hidden sector dynamics and show that they still can be useful probes of the MSSM and beyond.
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We study the hidden sector effects to the mass renormalization of a simplest gauge-mediated supersymmetry breaking scenario. We point out that possible hidden sector contributions render the soft scalar masses smaller, resulting in drastically different sparticle mass spectrum at low energy. In particular, in the ${\bf 5}+\bar{\bf 5}$ minimal gauge mediated supersymmetry breaking with high messenger scale (that is favored by the gravitino cold dark matter scenario), we show that stau can be the next lightest superparticle for moderate values of hidden sector self coupling. This provides a very…
We investigate the validity of an idea that the $B_μ$ problem is solvable via the renormalization effect in the strongly interacting hidden sector within the gauge mediated supersymmetry breaking scenario. Our analysis starts with a naive boundary condition, which is that the squared scalar masses experience $16π^2$ suppression. We use \texttt{softsusy} to get the low energy spectra of superparticles with the boundary condition at the scale ($Λ_{CFT}$) where the hidden sector is integrated out. We visit the low energy spectra and return to $Λ_{CFT}$ where the boundary conditions are given. We …
We consider a hidden sector with new vectorlike confining gauge theories like QCD. Then a scale $Λ_H$ would be generated in the hidden sector by dimensional transmutation, and chiral symmetry breaking occurs in the hidden sector. Then this scale $Λ_H$ can play a role of the SM Higgs mass parameter, triggering electroweak symmetry breaking (EWSB). Thus all the mass scales of the SM sector can arise from the hidden sector. Furthermore the lightest hadrons in the hidden sector is stable by the flavor conservation of the hidden sector strong interaction, and could be the cold dark matter (CDM). We…
We show that in the model of hidden sector of the Universe, interacting with the Standard-Model sector through the photonic portal, the Standard-Model Coulomb potential gets a tiny hidden-sector additive correction that might turn out to be either exciting or fatal for the verification of this model.
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 the phenomenological consequences of a hidden Higgs sector extending the Standard Model (SM), in which the matter content are uncharged under the SM gauge groups. We consider a simple case where the hidden sector is gauged under a U(1) with one Higgs singlet. The only couplings between SM and the hidden sector are through mixings between the neutral gauge bosons of the two respective sectors, and between the Higgs bosons. We find signals testable at the LHC that can reveal the existence and shed light on the nature of such a hidden sector.
We study the impact of a hidden sector beyond the Standard Model, e.g. a Hidden Valley model, on factorial moments and cumulants of multiplicity distributions in multiparticle production with a special emphasis on the prospects for LHC results.
In light of recent analyses that have shown that nontrivial hidden-sector dynamics in models of supersymmetry breaking can lead to a significant impact on the predicted low-energy supersymmetric spectrum, we extend these studies to consider hidden-sector effects in extensions of the MSSM to include a seesaw model for neutrino masses. A dynamical hidden sector in an interval of mass scales below the seesaw scale would yield renormalization-group running involving both the anomalous dimension from the hidden sector and the seesaw-extended MSSM renormalization group equations (RGEs). These effect…
We consider a hidden sector with a vectorlike confining gauge theory like QCD with $N_{h,c}$ colors and $N_{h,f}$ light quarks ${\cal Q}_h$ in the hidden sector. Then a scale $Λ_H$ would be generated by dimensional transmutation, and chiral symmetry breaking occurs in the hidden sector. This scale $Λ_H$ can play a role of the SM Higgs mass parameter, triggering electroweak symmetry breaking (EWSB). Furthermore the lightest mesons in the hidden sector is stable by flavor conservation of the hidden sector strong interaction, and could be a good cold dark matter (CDM). We study collider phenomeno…
Introducing a vacuum angle $θ_h$ in a strongly interacting hidden sector like QCD, we study how $θ_h$ affects physical quantities in a scale invariant extension of the standard model with that hidden sector. In this model the dynamical chiral symmetry breaking occurs in the hidden sector and generates a scale $ \vert \langle {\bar q} q \rangle \vert $ which triggers electroweak symmetry breaking. We find that the expression for a vacuum expectation value of the Higgs field depends on $θ_h$, while the condition which determines the Higgs particle mass does not. This model contains the hidden-se…
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.
We study the effects of renormalization due to hidden-sector dynamics on observable soft supersymmetry-breaking parameters in the minimal supersymmetric extension of the Standard Model (MSSM), under various hypotheses about their universality at a high input scale. We show that hidden-sector renormalization effects may induce the spurious appearance of unification of the scalar masses at some lower scale, as in mirage unification scenarios. We demonstrate in simple two-parameter models of the hidden-sector dynamics that the parameters may in principle be extracted from experimental measurement…
A weak photon interaction with the hidden sector of the Universe, introduced recently to realize a "photonic portal", (to such a hypothetic sector responsible for cold dark matter), is conjectured to be embedded in a more extended weak interaction displaying electroweak symmetry spontaneously broken by the Standard-Model Higgs mechanism. This is a hypothetic new weak interaction between hidden and Standard-Model sectors of the Universe, appearing in our model in addition to the conventional electroweak interaction acting in the Standard-Model sector.
We study the phenomenology of a class of models describing modular invariant gaugino condensation in the hidden sector of a low-energy effective theory derived from the heterotic string. Placing simple demands on the resulting observable sector - such as proper electroweak symmetry-breaking, superpartner spectra consistent with current limits and neutralino relic densities of an acceptable magnitude - results in significant restrictions on the possible configurations of the hidden sector.
A hypothetic Hidden Sector of the Universe, consisting of sterile fermions ("sterinos") and sterile mediating bosons ("sterons") of mass dimension 1 (not 2!) - the last described by an antisymmetric tensor field - requires to exist also a scalar isovector and scalar isoscalar in order to be able to construct electroweak invariant coupling (before spontaneously breaking its symmetry).
We consider models with a vectorlike confining gauge theory in the hidden sector, and demonstrate that the origin of the electroweak symmetry breaking (EWSB) is due to the dimensional transmutation in the hidden sector gauge theory, and the lightest mesons in the hidden sector could be a good cold dark matter (CDM) candidate. There would be more than one neutral Higgs-like scalar bosons, and they could decay mainly into the CDM pair, if that decay channel is kinemtically allowed.
Hot vs cold hidden sectors and their effects on thermal relics
本文探讨了可见与隐藏扇区的同步热演化，发现隐藏扇区在重加热温度下的冷热状态会显著改变热遗迹密度和$ΔN_{\ m eff}$，并指出分别使用熵守恒的近似在极弱耦合下也无效。
QCD-like hidden sector models of supersymmetry breaking are considered which do not suffer from a cosmological problem due to the Polonyi field. Avoidance of a light gluino leads to introduction of quasi-symmetry -- symmetry broken explicitly only through gravitational effects.
The $μ$ parameter is calculated in supergravity models possessing the $U(1)_A\times U(1)_R$ symmetry. In one natural model without a free mass parameter below the Planck scale, the symmetry breaking scale is identified as the hidden sector squark condensation scale.
A new weak-isospin triplet of scalar bosons is introduced to the Standard Model in order to ensure the electroweak symmetry for a conjectured new weak coupling between a hidden sector of the Universe, responsible for cold dark matter, and the Standard-Model sector (involving now the new triplet). The considered coupling may be called "electroweak portal" to the structure of hidden sector. After spontaneously breaking the electroweak symmetry by the Standard-Model Higgs mechanism, it includes the so called "photonic portal" introduced by us previously.
We study the phenomenology of a class of models describing modular invariant gaugino condensation in the hidden sector of a low-energy effective theory derived from the heterotic string. Placing simple demands on the resulting observable sector, such as a supersymmetry-breaking scale of approximately 1 TeV, a vacuum with properly broken electroweak symmetry, superpartner masses above current direct search limits, etc., results in significant restrictions on the possible configurations of the hidden sector.
We briefly expose our model for generating open and hidden charm resonances and present the most interesting results.
Dark matter in scale-invariant gravity with hidden-sector condensation
该研究基于经典标度不变二次引力耦合强相互作用隐藏域的框架，将电弱标度起源、宇宙暴胀和暗物质统一，推导三类暗物质候选者的遗迹丰度。
In the Stueckelberg extension of the Standard Model (StSM), matter in the hidden sector can act as dark matter. Due to an interplay of mixings produced by the usual Higgs mechanism and the Stueckelberg mechanism in the neutral gauge boson sector, the hidden sector matter acquires a milli charge. The Stueckelberg extension also produces a narrow width Z prime which is detectable at the Large Hadron Collider. The hidden sector dark matter naturally explains the PAMELA positron excess by means of a Breit-Wigner enhancement through a Z prime resonance. We also discuss the origin of milli charge in…
A scale-invariant extension of the Standard Model with a singlet-scalar and hidden-QCD sector is studied. The scale of electroweak symmetry breaking is generated dynamically in an asymptotic-free hidden-QCD sector, and mediated by the Higgs-singlet coupling. Hidden-QCD pions are stable and can be a candidate of the cold dark matter. This presentation is based on a collaboration with D. W. Jung and P. Ko.
A pseudo-Goldstone boson for {\it quintessence} is known to require the decay constant $F_q\sim M_P$ and the height of the potential $(0.003 {\rm eV})^4$, and hence the pseudo-Goldstone boson mass of order $10^{-33}$ eV. The model-dependent axion in some superstring models is suggested as a good candidate for the quintessence. We realize this idea with a hidden-sector gauge group $SU(3)_H\times U(1)_H$. The hidden-sector instanton contribution to the quintessence potential is suppressed by the almost massless hidden-sector quarks. The model-independent axion is the QCD axion required for the s…
We continue the discussion of a proposed model of hidden sector of the Universe, consisting of sterile spin-1/2 Dirac fermions ("sterinos"), sterile spin-0 bosons ("sterons") with spontaneously nonzero vacuum expectation value, and sterile nongauge mediating bosons ("A bosons") described by an antisymmetric-tensor field (of dimension one). The Standard-Model electromagnetic field (of dimension two) multiplied by the steron vacuum expectation value becomes in a spontaneous way a source of A-boson field mediating new weak interactions in hidden sector and providing - due to the action of electro…
We study compact star made of degenerate hidden sector nucleons which will be a candidate for cold dark matter. A hidden sector like QCD is considered, and as the low energy effective theory we take (hidden sector) $ SU(2) $ chiral sigma model including hidden sector vector meson. With the mean field approximation, we find that one can treat the equation of state (EOS) of our model analytically by introducing a variable which depends on the Fermi momentum. The EOS is specified by the two parameters $ C'_{/sigma} $,$ C'_{/omega} $, and we discuss how these parameters affect on the mass-radius r…
We show under rather general assumptions that hidden sectors that never reach thermal equilibrium in the early Universe are also inaccessible for the LHC. In other words, any particle that can be produced at the LHC must either have been in thermal equilibrium with the Standard Model at some point or must be produced via the decays of another hidden sector particle that has been in thermal equilibrium. To reach this conclusion, we parametrise the cross section connecting the Standard Model to the hidden sector in a very general way and use methods from linear programming to calculate the large…
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 …
Most signatures of new physics in colliders have been studied so far on the transverse plane with respect to the beam direction. In this work however we study the impact of a hidden sector beyond the Standard Model (SM) on inclusive (pseudo)rapidity correlations and moments of the multiplicity distributions, with special emphasis in the LHC results.
We exemplify earlier general considerations on flavor symmetry breaking employing a hidden sector and exploiting supersymmetry in a specific model. The model is at best a caricature of reality, but it is sufficient to display mechanisms for the natural emergence of minimal low-energy Higgs structure, non-trivial texture zeros and symmetry, and coupling to the standard model only through Higgs fields, which could be considerably more general.
If supersymmetry is dynamically broken in a hidden sector, the gauginos typically have unacceptably small masses. This situation can be corrected if a non-Abelian gauge interaction becomes strong at a scale of order 1 TeV and induces dynamical gaugino masses. We discuss the typical signals of this scenario at present and future colliders.
Recently there has been much interest in hidden sectors, especially in the context of dark matter and dark forces, since they are a common feature of beyond standard model scenarios like string theory and SUSY and additionally exhibit interesting phenomenological aspects. Various laboratory experiments place limits on the so-called hidden photon and continuously further probe and constrain the parameter space; an updated overview is presented here. Furthermore, for several hidden sector models with light dark matter we study the viability with respect to the relic abundance and direct detectio…
We introduce a new dark matter candidate, the lightest U-parity particle (LUP). We suggest it as a good dark matter candidate especially in the R-parity violating supersymmetric model.
Thermal leptogenesis and supergravity are attractive scenarios for physics beyond the standard model. However, it is well known that the super-weak interaction of the gravitino often leads to problems with primordial nucleosynthesis in the standard scenario of matter parity conserving MSSM + three right-handed neutrinos. We will present and compare two related solutions to these problems: 1) The conflict between BBN and leptogenesis can be avoided in presence of a hidden sector with light supersymmetric particles which open new decay channels for the dangerous long-lived particles. 2) If there…
In the effective field theory framework, we consider the effect of supersymmetry breaking via gaugino condensation and supergravity in the hidden sector gauge group on the hidden sector vacuum angle $θ_h$. The $θ_h$ parameter dependence of the potential yields phenomenologically acceptable invisible axion solutions if the $U(1)_R$ symmetry is broken down to a discrete subgroup $Z_N$ with $N\ge 3$ (N=4 is marginal). Anomalous U(1) superstring models are good candidates for this invisible axion resolution of the strong CP puzzle.
This work examines the confining-deconfining phase transition in a hidden Yang Mills sector with scale $Λ\sim 10^{14}$ GeV appropriate to dilaton stabilization and SUSY-breaking via formation of a gaugino consensate. If the transition is assumed to take place through homogenous nucleation, then under reasonable assumptions it is found that a critical bubble, formed at a temperature which provides enough supercooling, is not large enough to accommodate an adequate number $(\gsim 100)$ of quanta of the confined phase (`hidden hadrons') to allow a consistent thermodynamic description. Thus, a fir…
We present a detailed study of the oscillations and optical properties for vacuum, in a model for the dark sector that contains axion-like particles and hidden photons. In this model, both can couple to photons. We provide bounds for the couplings versus the mass, using current results from ALPS-I and PVLAS. We also discuss the challenges for the detection of models with more than one hidden particle in light shining trough wall-like experiments.
Hidden sectors in connection with GeV-scale dark forces and dark matter are not only a common feature of physics beyond the Standard Model such as string theory and SUSY but are also phenomenologically of great interest regarding recent astrophysical observations. The hidden photon in particular is also searched for and constrained by laboratory experiments, the current status of which will be presented here. Furthermore, several models of hidden sectors containing in addition a dark matter particle will be examined regarding their consistency with the dark matter relic abundance and direct de…
The Higgs boson offers a unique window to hidden sector fields S_i, singlets under the Standard Model gauge group, via the renormalizable interactions |H|^2 S_i^2. We prove that such interactions can provide new patterns for electroweak breaking, including radiative breaking by dimensional transmutation consistent with LEP bounds, and trigger the strong enough first order phase transition required by electroweak baryogenesis.
The measurement of the anomalous magnetic moment of the muon provides a stringent test of the standard model and of any physics that lies beyond it. There is currently a deviation of $3.1σ$ between the standard model prediction for the muon's anomalous magnetic moment and its experimental value. We calculate the contribution to the anomalous magnetic moment in theories where the muon couples to a particle in a hidden sector (that is, uncharged under the standard model) and a connector (which has nontrivial standard model gauge and hidden sector quantum numbers).
A variety of supergravity and string based models contain hidden sectors which can play a role in particle physics phenomena and in cosmology. In this note we discuss the possibility that the visible sector and the hidden sectors in general live in different heat baths. Further, it is entirely possible that dark matter resides partially or wholly in hidden sectors in the form of dark Dirac fermions, dark neutralinos or dark photons. A proper analysis of dark matter and of dark forces in this case requires that one deals with a multi-temperature universe. We discuss the basic formalism which in…
Little experimental data bears on the question of whether there is a spontaneously broken hidden sector that has no Standard Model quantum numbers. Here we discuss the prospects of finding evidence for such a hidden sector through renormalizable interactions of the Standard Model Higgs boson with a Higgs boson of the hidden sector. We find that the lightest Higgs boson in this scenario has smaller rates in standard detection channels, and it can have a sizeable invisible final state branching fraction. Details of the hidden sector determine whether the overall width of the lightest state is sm…
In this letter we study a novel effect of a hidden sector coupling to the standard model Higgs boson: an enhancement of the Higgs pair production cross section near threshold due to bound state effects. After summing the ladder contributions of the hidden sector to the effective $ggHH$ coupling, we find the amplitude for gluon-gluon scattering via a Higgs loop. We relate this amplitude to the double Higgs production cross section via the optical theorem. We find that enhancements of the order of 100 for the partonic cross section near the threshold region can be obtained for a hidden sector st…
In this note we establish LHC limits on a variety of benchmark models for hidden sector physics using 2011 and 2012 data. First, we consider a "hidden" U(1) gauge boson under which all Standard Model particles are uncharged at tree-level and which interacts with the visible sector either via kinetic mixing or higher dimensional operators. Second, we constrain scalar and pseudo-scalar particles interacting with the Standard Model via dimension five operators and Yukawa interactions, in particular including so-called axion-like particles. In both cases we consider several different final states,…
By including the effects of superstring thresholds, we reconsider minimal string unification together with the requirement of producing a supersymmetry-breaking gluino condensate in the hidden sector. This gives, for examples of phenomenologically-viable $Z_8'$ and other related orbifolds, the constraint that $0.1215 \leq α_s(M_Z) \leq 0.1270$. In such models, a hidden photino can be a source of cosmological dark matter detectable by gravitational microlensing.
The existence of light hidden sectors is an exciting possibility that may be tested in the near future. If DM is allowed to decay into such a hidden sector through GUT suppressed operators, it can accommodate the recent cosmic ray observations without over-producing antiprotons or interfering with the attractive features of the thermal WIMP. Models of this kind are simple to construct, generic and evade all astrophysical bounds. We provide tools for constructing such models and present several distinct examples. The light hidden spectrum and DM couplings can be probed in the near future, by me…
We calculate the production rate of gauge-boson pairs at the SSC in a model with a ``hidden'' electroweak symmetry breaking sector. We show that the signal of electroweak symmetry breaking is lower than the background and that we cannot necessarily rely on gauge boson pairs as a signal of the dynamics of symmetry breaking.
Experimental results indicate a possible relation between the lepton and quark mixing matrices of the form U_PMNS \approx V_CKM^\dagger U_X, where U_X is a matrix with special structure related to the mechanism of neutrino mass generation. We propose a framework which can realize such a relation. The main ingredients of the framework are the double seesaw mechanism, SO(10) Grand Unification and a hidden sector of theory. The latter is composed of singlets (fermions and bosons) of the GUT symmetry with masses between the GUT and Planck scale. The interactions in this sector obey certain symmetr…
We argue that the hidden sector potential energy is generically of order the intermediate scale although the true cosmological constant does vanish. This would significantly change the predicted values of soft parameters for a variety of supergravity models including those derived from string theory. We stress that this point is particularly relevant for supergravity models in which the soft masses of observable fields vanish at tree level. Implications of a nonzero hidden sector potential energy for low energy phenomenology are also studied.
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 describe more precisely the mechanism of spontaneous mass generation in the previously proposed model of hidden sector of the Universe. The hidden sector is conjectured to consist of sterile spin-1/2 fermions (sterinos) whose mass is spontaneously generated by sterile scalar bosons (sterons), while their interactions are mediated by sterile antisymmetric-tensor bosons (A bosons). Such a sector communicates with the familiar Standard Model sector through a photonic portal acting weakly between both sectors (but stronger than the universal gravity). This is due to photons which, beside sterin…
There is a growing appreciation that hidden sector dynamics may affect the supersymmetry breaking parameters in the visible sector (supersymmetric standard model), especially when the dynamics is strong and superconformal. We point out that there are effects that have not been previously discussed in the literature. For example, the gaugino masses are suppressed relative to the gravitino mass. We discuss their implications in the context of various mediation mechanisms. The issues discussed include anomaly mediation with singlets, the mu (B mu) problem in gauge and gaugino mediation, and disti…
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…
The sequestering of supersymmetry (SUSY) breaking parameters, which is induced by superconformal hidden sector, is one of the solutions for the mu/B_mu problem in gauge-mediated SUSY-breaking scenario. However, it is found that the minimal messenger model does not derive the correct electroweak symmetry breaking. In this paper we present a model which has the coupling of the messengers with the SO(10) GUT-symmetry breaking Higgs fields. The model is one of the realistic extensions of the gauge mediation model with superconformal hidden sector. It is shown that the extension is applicable for a…
We investigate the possibility of detecting hidden vector gauge bosons at ILC linear collider. The study is performed in the framework of hidden sector extension of Standard Model with 3 degenerate dark gauge bosons. By studying the cross section of pair dark gauge boson with photon at initial state radiation we found that at the energy $\sqrt{s} \approx$ 1300 GeV the cross section can be as large as $48fb$, the same order ($\mathcal{O}(fb)$) with the irreducible background of the Standard Model. Hence more methods needed to be done to eliminate the background for this model.
We show that supersymmetric "Dark Force" models with gravity mediation are viable. To this end, we analyse a simple string-inspired supersymmetric hidden sector model that interacts with the visible sector via kinetic mixing of a light Abelian gauge boson with the hypercharge. We include all induced interactions with the visible sector such as neutralino mass mixing and the Higgs portal term. We perform a detailed parameter space scan comparing the produced dark matter relic abundance and direct detection cross sections to current experiments.
In this letter we discuss a certain class of Hidden Valley models where the dynamics in the hidden sector are close to a strongly coupled conformal fixed point. We show that these models can explain the excess in cosmic ray muon events with high muon multiplicities that has been reported from cosmic ray studies with the ALEPH and DELPHI detectors. We further point out that these models can also at least partially account for the excess in multi-muon events that was found by the CDF experiment. Finally we discuss possible signatures of these models at the LHC.
The short distance behavior of dark matter (DM) at galaxy scales exhibits several features not explained by the typical cold dark matter (CDM) with velocity-independent cross-section. We discuss a particle physics model with a hidden sector interacting feebly with the visible sector where a dark fermion self-interacts via a dark force with a light dark photon as the mediator. We study coupled Boltzmann equations involving two temperatures, one for each sector. We fit the velocity-dependent DM cross-section to the data from scales of dwarf galaxies to clusters consistent with relic density cons…
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