6 pages, 5 figures. v2: discussion on BBN constraints added and BBN bounds implementend in figure 3, updated references. Version to appear on Phys.Lett.B
In a large class of models we show that the light scalar field responsible for the Sommerfeld enhancement in the annihilation of dark matter leads to observable direct detection rates, due to its mixing with the standard model Higgs. As a result the large annihilation cross-section of dark matter at present epoch, required to explain the observed cosmic ray anomalies, can be strongly constrained by direct searches. In particular Sommerfeld boost factors of order of a few hundred are already out of the CDMS-II upper bound at 90% confidence level for reasonable values of the model parameters.
We find model-independent upper limits on rates of dark matter annihilation in galactic halos. The Born approximation generally fails, while exotic threshold enhancements akin to "Sommerfeld factors" also turn out to be baseless The most efficient annihilation mechanism involves perturbatively small decay widths that have largely been ignored. Widths that are very small compared to TeV mass scales suffice to effectively saturate unitarity bounds on annihilation rates. Bound state formation in weakly coupled theories produces small effects due to wave function normalizations. Unitarity shows th…
We compute the present-day Wino dark matter annihilation cross-section including the one-loop radiative corrections together with the fully treated electroweak Sommerfeld effect. We discuss what is the consistent way of incorporating these two corrections simultaneously and why simply using the running coupling constants values at the Wino mass scale is not correct. The results show that up to a few TeV scale the full one-loop computation makes the cross-section smaller up to about 30% with respect to the Sommerfeld enhanced tree level result and are considerably larger than the tree or one-lo…
This paper concludes the presentation of the non-relativistic effective field theory formalism designed to calculate the radiative corrections that enhance the pair-annihilation cross sections of slowly moving neutralinos and charginos within the general minimal supersymmetric standard model (MSSM). While papers I and II focused on the computation of the tree-level annihilation rates that feed into the short-distance part, here we describe in detail the method to obtain the Sommerfeld factors that contain the enhanced long-distance corrections. This includes the computation of the potential in…
In models of dark matter (DM) with Sommerfeld-enhanced annihilation, where the annihilation rate scales as the inverse velocity, N-body simulations of DM structure formation suggest that the local annihilation signal may be dominated by small, dense, cold subhalos. This contrasts with the usual assumption of a signal originating from the smooth DM halo, with much higher velocity dispersion. Accounting for local substructure modifies the parameter space for which Sommerfeld-enhanced annihilating DM can explain the PAMELA and Fermi excesses. Limits from the inner galaxy and the cosmic microwave …
The first AMS-02 measurement confirms the existence of an excess in the cosmic-ray positron fraction previously reported by the PAMELA and Fermi-LAT experiments. If interpreted in terms of thermal dark matter (DM) annihilation, the AMS-02 result still suggests that the DM annihilation cross section in the present day should be significantly larger than that at freeze out. The Sommerfeld enhancement of DM annihilation cross section as a possible explanation for the observed excesses is subject to constraint from the DM thermal relic density, mainly due to the annihilation of DM particles into f…
We calculate how the relic density of dark matter particles is altered when their annihilation is enhanced by the Sommerfeld mechanism due to a Yukawa interaction between the annihilating particles. Maintaining a dark matter abundance consistent with current observational bounds requires the normalization of the s-wave annihilation cross section to be decreased compared to a model without enhancement. The level of suppression depends on the specific parameters of the particle model, with the kinetic decoupling temperature having the most effect. We find that the cross section can be reduced by…
We investigate the implication of unparticle exchange for the possible Sommerfeld enhancement in dark matter annihilation process. Assuming the unparticle exchange during WIMP collision, we solve the Schr\rm\ddot{o}dinger equation for the effective potential, and find that the Sommerfeld enhancement factor is dictated by the scale dimension of unparticle as 1/v^{3-2d_{\UP}}. Numerically the Sommerfeld enhancement could be {\cal O}(10-10^{3}).
In the last few years there has been some interest in WIMP Dark Matter models featuring a velocity dependent cross section through the Sommerfeld enhancement mechanism, which is a nonrelativistic effect due to massive bosons in the dark sector. In the first part of this article, we find analytic expressions for the boost factor for three different model potentials, the Coulomb potential, the spherical well and the spherical cone well and compare with the numerical solution of the Yukawa potential. We find that the resonance pattern of all the potentials can be cast into the same universal form…
We propose an analytic treatment for computing the relic abundances of non-relativistic particles whose annihilation rate at chemical decoupling is increased by Sommerfeld enhancement. We find approximate rational functions that closely fit the thermal average of Sommerfeld-enhanced cross sections in the massless limit of force carriers for s- and p-wave annihilations. We demonstrate that, with the approximate thermally-averaged cross sections implemented, the standard analytic method for the final relic abundances provides accuracy to within 1% even for the case of Sommerfeld enhancement.
We study the impact of the Sommerfeld enhancement on the thermal relic density of the lightest neutralino in the case of large co-annihilation effects with a scalar particle. The proper way of including the Sommerfeld effect in this case is discussed, and the appropriate formulas for a general scenario with a set of particles with arbitrary masses and (off-)diagonal interactions are provided. We implement these results to compute the relic density in the neutralino sfermion co-annihilation regions in the mSUGRA framework. We find non-negligible effects in whole sfermion co-annihilation regimes…
For models in which dark matter annihilation is Sommerfeld-enhanced, the annihilation cross section increases at low relative velocities. Dwarf spheroidal galaxies (dSphs) have low characteristic dark matter particle velocities and are thus ideal candidates to study such models. In this paper we model the dark matter phase space of dSphs as isotropic and spherically-symmetric, and determine the $J$-factors for several of the most important targets for indirect dark matter searches. For Navarro-Frenk-White density profiles, we quantify the scatter in the $J$-factor arising from the astrophysica…
We study the multi-Sommerfeld enhancement in the case where $V(r)$ is composed of different kinds of potentials. We show that there are special properties of the multi-Sommerfeld enhancement. The physical content of the multi-Sommerfeld mechanism is carefully demonstrated. The multi-Sommerfeld enhancement might play a role in dark matter annihilation.
Anomalies in direct and indirect detection have motivated models of dark matter consisting of a multiplet of nearly-degenerate states, coupled by a new GeV-scale interaction. We perform a careful analysis of the thermal freezeout of dark matter annihilation in such a scenario. We compute the range of "boost factors" arising from Sommerfeld enhancement in the local halo for models which produce the correct relic density, and show the effect of including constraints on the saturated enhancement from the cosmic microwave background (CMB). We find that boost factors from Sommerfeld enhancement of …
Sommerfeld-enhanced dark matter (DM) annihilation through $s$-wave has been widely considered as a consistent explanation for both the observed cosmic-ray (CR) positron excess and the DM thermal relic density. However, as the $s$-wave Sommerfeld-enhanced annihilation cross section increases monotonically with decreasing DM velocity, severe constraints appear from the data of gamma rays from dwarf spheroidal satellite galaxies (dSphs) and the cosmic microwave background (CMB), as the relevant typical DM velocities are even lower than that in the Galactic halo. In this work, we consider Sommerfe…
We consider dark matter consisting of weakly interacting massive particles (WIMPs) and revisit in detail its thermal evolution in the early universe, with a particular focus on models where the annihilation rate is enhanced by the Sommerfeld effect. After chemical decoupling, or freeze-out, dark matter no longer annihilates but is still kept in local thermal equilibrium due to scattering events with the much more abundant standard model particles. During kinetic decoupling, even these processes stop to be effective, which eventually sets the scale for a small-scale cutoff in the matter density…
The substructures of the Galactic dark matter halo such as dark matter subhalos and dwarf galaxies have very low velocity dispersions, which makes them useful in constraining the scenario of Sommerfeld-enhanced dark matter annihilation. We calculate the velocity distribution of dark matter particles in dark matter halo substructures using the Eddington's formula with NFW density profile. We parametrize the effect of Sommerfeld enhancement of s-wave dark matter annihilation on the gamma-ray flux as the Sommerfeld-enhanced J-factors, and explicitly calculate their values for 15 known dwarf spher…
We investigate stau-antistau annihilation into heavy quarks in the phenomenological Minimal Supersymmetric Standard Model within the DM@NLO project. We present the calculation of the corresponding cross section including corrections up to $\mathcal{O}(α_s)$ and QED Sommerfeld enhancement. The numerical impact of these corrections is discussed for the cross section and the dark matter relic density, where we focus on top-quark final states and consider either neutralino or gravitino dark matter. Similarly to previous work, we find that the presented corrections should be included when calculati…
We use the suite of Milky Way-like galaxies in the Auriga simulations to determine the contribution to annihilation radiation from dark matter subhalos in three velocity-dependent dark matter annihilation models: Sommerfeld, p-wave, and d-wave models. We compare these to the corresponding distribution in the velocity-independent s-wave annihilation model. For both the hydrodynamical and dark-matter-only simulations, only in the case of the Sommerfeld-enhanced annihilation does the total annihilation flux from subhalos exceed the total annihilation flux from the smooth halo component within the…
We examine the constraints on models of weakly interacting massive particle (WIMP) dark matter from the recent observations of the Galactic center by the High Energy Spectroscopic System (HESS) telescope. We analyze canonical WIMP annihilation into Standard Model particle final states, including b/b-bar, t/t-bar and W^+ W^-. The constraints on annihilation into b/b-bar is within an order of magnitude of the thermal cross section at ~3 TeV, while the tau^+/tau^- channel is within a factor of ~2 of thermal. We also study constraints on Sommerfeld-enhanced dark matter annihilation models, and fin…
We investigate the evolution of the abundance of the asymmetric thermal Dark Matter when its annihilation rate at chemical decoupling is boosted by the Sommerfeld enhancement. We perform the detailed analysis of the effect of $s$-- and $p$--wave Sommerfeld enhanced annihilation cross section on the relic abundances of asymmetric Dark Matter particle and anti--particle both in numerical and analytical way. The constraints on the coupling and asymmetric factor are given by using the observational data of the relic density of Dark Matter.
Boost factors of dark matter annihilation into antiprotons and electrons/positrons due to the clumpiness of dark matter distribution are studied in detail in this work, taking the Sommerfeld effect into account. It has been thought that the Sommerfeld effect, if exists, will be more remarkable in substructures because they are colder than the host halo, and may result in a larger boost factor. We give a full calculation of the boost factors based on the recent N-body simulations. Three typical cases of Sommerfeld effects, the non-resonant, moderately resonant and strongly resonant cases are co…
Recently, possible indications of line spectral features in the Fermi-LAT photon spectrum towards the galactic center have been reported. If the distinct line features arise from dark matter (DM) annihilation into $γX (X=γ, Z^{0} or h^{0})$, the corresponding annihilation cross-section is unnaturally large for typical loop-induced radiative processes. On the other hand, it is still too small to be responsible for the observed DM relic density. We show that the mechanism of Sommerfeld enhancement with scalar force-carrier can provide a simple solution to these puzzles. The possibly large Sommer…
Thermal pair annihilation of heavy particles, such as dark matter or its co-annihilation partners, can be strongly influenced by attractive interactions. We investigate the case that pair annihilation proceeds through a velocity-suppressed $p$-wave operator, in the presence of an SU(3) gauge force. Making use of a non-relativistic effective theory, the thermal average of the pair-annihilation rate is estimated both through a resummed perturbative computation and through lattice simulation, in the range $M/T \sim 10 ... 30$. Bound states contribute to the annihilation process and enhancement fa…
The recently introduced Sommerfeld enhancement of the dark matter annihilation cross section has important implications for the detection of dark matter annihilation in subhalos in the Galactic halo. In addition to the boost to the dark matter annihilation cross section from the high densities of these subhalos with respect to the main halo, an additional boost caused by the Sommerfeld enhancement results from the fact that they are kinematically colder than the Galactic halo. If we further believe the generic prediction of CDM that in each subhalo there is an abundance of substructure which i…
Dark matter that possesses a particle-antiparticle asymmetry and has thermalised in the early universe, requires a larger annihilation cross-section compared to symmetric dark matter, in order to deplete the dark antiparticles and account for the observed dark matter density. The annihilation cross-section determines the residual symmetric component of dark matter, which may give rise to annihilation signals during CMB and inside haloes today. We consider dark matter with long-range interactions, in particular dark matter coupled to a light vector or scalar force mediator. We compute the coupl…
We extend the analysis of asymmetric Dark Matter relic density with Sommerfeld enhancement to the case where the mediator is massive. In asymmetric Dark Matter models, the asymmetric Dark Matter is assumed to couple to light scalar or vector boson. Asymmetric Dark Matter annihilation cross section is enhanced by the Sommerfeld effect which exists due to the distortion of wavefunction of asymmetric Dark Matter particle and anti--particle by long--range interactions. The impacts of Sommerfeld enhancement on the relic densities of asymmetric Dark Matter particle and anti--particle are discussed. …
We investigate the evolution of abundance of the asymmetric thermal Dark Matter when its annihilation rate at chemical decoupling is boosted by the Sommerfeld enhancement. Then we discuss the effect of kinetic decoupling on relic abundance of asymmetric Dark Matter when the interaction rate depends on the velocity. Usually the relic density of asymmetric Dark Matter is analyzed in the frame of chemical decoupling. Indeed after decoupling from the chemical equilibrium, asymmetric Dark Matter particles and anti--particles were still in kinetic equilibrium for a while. It has no effect on the cas…
We investigate the Sommerfeld enhancement (SE) in the generalized scotogenic model with large electroweak multiplets. We focus on scalar dark matter (DM) candidate of the model and compare DM annihilation cross sections to $WW$, $ZZ$, $γγ$ and $γZ$ at present day in the galactic halo for scalar doublet and its immediate generalization, the quartet in their respective viable regions of parameter space. We find that larger multiplet has sizable Sommerfeld enhanced annihilation cross section compared to the doublet and because of that it is more likely to be constrained by the current H.E.S.S. re…
We demonstrate that the Sommerfeld correction to CDM annihilations can be appreciable if even a small component of the dark matter is extremely cold. Subhalo substructure provides such a possibility given that the smallest clumps are relatively cold and contain even colder substructure due to incomplete phase space mixing. Leptonic channels can be enhanced for plausible models and the solar neighbourhood boost required to account for PAMELA/ATIC data is plausibly obtained, especially in the case of a few TeV mass neutralino for which the Sommerfeld-corrected boost is found to be $\sim10^4-10^5…
Extending previous work, we calculate the electroweak potentials for all co-annihilation channels of wino dark matter at the one-loop order and obtain the wino relic abundance including the Sommerfeld effect at the next-to-leading order (NLO).
The chemical equilibration of heavy quarks in a quark-gluon plasma proceeds via annihilation or pair creation. For temperatures T much below the heavy quark mass M, when kinetically equilibrated heavy quarks move very slowly, the annihilation in the colour singlet channel is enhanced because the quark and antiquark attract each other which increases their probability to meet, whereas the octet contribution is suppressed. This is the so-called Sommerfeld effect. It has not been taken into account in previous calculations of the chemical equilibration rate, which are therefore incomplete for T <…
If the annihilation products of dark matter (DM) are non-relativistic and if there is some long-range force between them, there can be Sommerfeld effect for the final state particles. We study this effect on DM relic abundance in the thermal freeze-out scenario. As a proof of concept, we consider the case of a DM pair annihilation into a final state pair, assuming that the mutual interactions between the two final state particles give rise to a Coulomb-like potential, and that the masses of the initial and final state particles are similar, so that both the initial and final state particles ar…
We calculate the SU(2)$\times$U(1) electroweak static potential between a fermionic triplet in the broken phase of the Standard Model in the one-loop order (NLO). The one-loop correction provides the leading non-relativistic correction to the large Sommerfeld effect in the annihilation of wino or wino-like dark matter particles $χ^0$. We find sizeable modifications of the $χ^0χ^0$ annihilation cross section and determine the shifts of the resonance locations due to the loop correction to the wino potential.
The annihilation cross section of thermal relic dark matter determines both its relic density and indirect detection signals. We determine how large indirect signals may be in scenarios with Sommerfeld-enhanced annihilation, subject to the constraint that the dark matter has the correct relic density. This work refines our previous analysis through detailed treatments of resonant Sommerfeld enhancement and the effect of Sommerfeld enhancement on freeze out. Sommerfeld enhancements raise many interesting issues in the freeze out calculation, and we find that the cutoff of resonant enhancement, …
We derive cosmological constraints on the annihilation cross section of dark matter with velocity-dependent structure, motivated by annihilating dark matter models through Sommerfeld or Breit-Wigner enhancement mechanisms. In models with annihilation cross section increasing with decreasing dark matter velocity, big-bang nucleosynthesis and cosmic microwave background give stringent constraints.
In a wino LSP scenario the annihilation cross section of winos gravitationally bound in galaxies can be boosted by a Sommerfeld enhancement factor which arises due to the ladder of exchanged W bosons between the initial states. The boost factor obtained can be in the range S ~ 10^4 if the mass is close to the resonance value of M ~ 4 TeV. In this paper we show that if one takes into account the Sommerfeld enhancement in the relic abundance calculation then the correct relic density is obtained for 4 TeV wino mass due to the enhanced annihilation after their kinetic decoupling. At the same time…
Traditional computations of the dark matter (DM) relic abundance, for models where attractive self-interactions are mediated by light force-carriers and bound states exist, rely on the solution of a coupled system of classical on-shell Boltzmann equations. This idealized description misses important thermal effects caused by the tight coupling among force-carriers and other charged relativistic species. We develop for the first time a comprehensive ab-initio derivation for the description of DM long-range interactions in the presence of a hot and dense plasma background directly from non-equil…
The Sommerfeld enhancement plays an important role in dark matter (DM) physics, and can significantly enhance the annihilation cross section of non-relativistic DM particles. In this paper, we study the effect of neutrino forces, which are generated by the exchange of a pair of light neutrinos, on the Sommerfeld enhancement. We demonstrate that in certain cases, a neutrino force can cause a significant correction to the Sommerfeld enhancement. Models that can realise DM-neutrino interactions and sizeable Sommerfeld enhancement are also briefly discussed, together with the impacts on DM phenome…
Sommerfeld enhancement and Breit-Wigner enhancement of the dark matter annihilation have been proposed to explain the "boost factor" which is suggested by observed cosmic ray excesses. Although these two scenarios can provide almost indistinguishable effects on the cosmic ray fluxes, the cross sections of the self-interaction in those enhancement mechanisms are drastically different. As a result, we show that they can be distinguished by examining the effects of the self-interaction on the halo shapes. In Sommerfeld enhancement models with m_phi<100MeV and m_DM<3TeV, the self-interaction can l…
Dark matter with Sommerfeld-enhanced annihilation has been proposed to explain observed cosmic ray positron excesses in the 10 GeV to TeV energy range. We show that the required enhancement implies thermal relic densities that are too small to be all of dark matter. We also show that the dark matter is sufficiently self-interacting that observations of elliptical galactic dark matter halos exclude large Sommerfeld enhancement for light force carriers. Resonant Sommerfeld enhancement does not modify these conclusions, and the astrophysical boosts required to resolve these discrepancies are disf…
We present analytical formulae for the Sommerfeld corrections to the annihilation of massive colored particles into quarks and gluons through the strong interaction. These corrections are essential to accurately compute the dark matter relic density for coannihilation with colored partners. Our formulae allow to compute the Sommerfeld effect, not only for the lowest term in the angular momentum expansion of the amplitude, but for all orders in the partial wave expansion. In particular, we carefully account for the effects of the spin of the annihilating particle on the symmetry of the two-part…
Assuming that two incoming annihilating particles interact by a generally massive attractive vector potential,we find, by taking the non-relativistic limit of the field theory ladder diagrams, that the complete annihilation amplitude A is equal to: the convolution of a solution of the Schroedinger equation (including the vector potential) with the Fourier transform of the bare (i.e. ignoring the attraction) annihilation amplitude A0. The main novelty is that A0 is completely arbitrary. In particular for a massless vector potential we find for the l-partial-wave cross-section the Sommerfeld enh…
In the cold dark matter scenario, galactic dark matter halos are populated with a large number of smaller subhalos. Previous work has shown that dark matter annihilations in subhalos can generate a distinctive, non-Poisson signal in the gamma-ray photon counts probability distribution function (PDF). Here we show that the gamma-ray PDF also carries information about the velocity dependence of the dark matter annihilation cross section. After calculating the PDF assuming $s$-wave and Sommerfeld-enhanced annihilation, we perform a mock data analysis to illustrate how current and future observati…
We calculate the effective $J$-factors, which determine the strength of indirect detection signals from dark matter annihilation, for 25 dwarf spheroidal galaxies (dSphs). We consider several well-motivated assumptions for the relative velocity dependence of the dark matter annihilation cross section: $σ_A v$: $s$-wave (velocity independent), $p$-wave ($σ_A v \propto v^2$), $d$-wave ($σ_A v \propto v^4$), and Sommerfeld-enhancement in the Coulomb limit ($σ_A v \propto 1/v$). As a result we provide the largest and most updated sample of J-factors for velocity-dependent annihilation models. For …
We calculate the full one-loop SUSY-QCD corrections to stop annihilation into gluons and light quarks including the Sommerfeld enhancement effect and discuss their impact on the neutralino relic density in the MSSM.
Sommerfeld Effect and Bound State Formation for Dark Matter Models with Colored Mediators with SE+BSF4DM
Università degli Studi di Padova（帕多瓦大学）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Johannes Gutenberg-Universität Mainz（约翰内斯·古腾堡美因茨大学）；Technical University of Munich（慕尼黑工业大学）
