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 enhancement 2pi/(l!)^2 (alpha/ v)^{2l+1} (v relative velocity), e.g. for the P wave the enhancement 2pi(alpha/ v)^3.
Size Dependence of the Sommerfeld Enhancement for Puffy Dark Matter
Chengdu Technological University（成都工业学院）；Henan Normal University（河南师范大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Nanjing Normal University（南京师范大学）
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.
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…
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}).
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 have investigated neutralino dark matter in the framework of minimal supersymmetric Standard Model focusing on the coannihilatioin region. In this region, where the particle whose mass is tightly degenerated with the neutralino dark matter exists, we can solve the Lithium problem in the case of lepton flavor being violated. It turns out that Sommerfeld enhancement is important in the coannihilation region so that the dark matter signal becomes large enough to be observed by the current sensitivity of indirect experiments.
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 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…
We present an analysis of the Sommerfeld enhancement to dark matter annihilation in the presence of an excited state, where the interaction inducing the enhancement is purely off-diagonal, such as in models of exciting or inelastic dark matter. We derive a simple and accurate semi-analytic approximation for the s-wave enhancement, which is valid provided the mass splitting between the ground and excited states is not too large, and discuss the cutoff of the enhancement for large mass splittings. We reproduce previously derived results in the appropriate limits, and demonstrate excellent agreem…
We point out that the exchange of a Goldstone pseudo-scalar can provide an enhancement in the dark matter annihilation rate capable of explaining the excess flux seen in high energy cosmic ray data. The mechanism of enhancement involves the coupling of s and d waves through the tensor force that is very strong and, in fact, singular at short distances. The results indicate that large enhancements require some amount of fine tuning. We also discuss the enhancement due to other singular attractive potentials, such as WIMP models with a permanent electric dipole.
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, …
A calculation of the Sommerfeld enhancement is presented and applied to the problem of s-wave non-relativistic dark matter annihilation. The difference from previous computations in the literature is that the effect of the underlying short-range scattering process is consistently included together with the long-range force in the effective QM Schrödinger problem. Our procedure satisfies partial-wave unitarity where previous calculations fail. We provide analytic results for some potentials of phenomenological relevance.
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 study the Sommerfeld enhancement experienced by a scattering object that couples to a tower of mediators. This can occur in, e.g., models of secluded dark matter when the mediator scale is generated naturally by hidden-sector confinement. Specializing to the case of a confining CFT, we show that off-resonant values of the enhancement can be increased by ~ 20% for cases of interest when (i) the (strongly-coupled) CFT admits a weakly-coupled dual description and (ii) the conformal symmetry holds up to the Planck scale. Larger enhancements are possible for lower UV scales due to an increase in…
We present a detailed discussion of Sommerfeld enhancements in neutralino dark matter relic abundance calculations for several popular benchmark scenarios in the general MSSM. Our analysis is focused on models with heavy wino- and higgsino-like neutralino LSP and models interpolating between these two scenarios. This work is the first phenomenological application of effective field theory methods that we have developed in earlier work and that allow for the consistent study of Sommerfeld enhancements in non-relativistic neutralino and chargino co-annihilation reactions within the general MSSM,…
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…
Analysis of p-Wave Sommerfeld Resonance Behavior in Finite-Size Dark Matter
School of Integrated Circuits, Chengdu Technological University（成都工业学院集成电路学院）；Center for Theoretical Physics, Henan Normal University（河南师范大学理论物理中心）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；State Key Laboratory of Dark Matter Physics, Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学汤川研究所暗物质物理国家重点实验室）；Key Laboratory for Particle Astrophysics and Cosmology (MOE) & Shanghai Key Laboratory for Particle Physics and Cosmology, Shanghai Jiao Tong University（上海交通大学粒子天体物理与宇宙学教育部重点实验室及上海粒子物理与宇宙学重点实验室）
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…
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 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 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…
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…
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 have developed a general formalism to compute Sommerfeld enhancement (SE) factors for a multi-state system of fermions, in all possible spin configurations and with generic long-range interactions. We show how to include such SE effects in an accurate calculation of the thermal relic density for WIMP dark matter candidates. We apply the method to the MSSM and perform a numerical study of the relic abundance of neutralinos with arbitrary composition and including the SE due to the exchange of the W and Z bosons, photons and Higgses. We find that the relic density can be suppressed by a facto…
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…
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…
Much attention has been given to dark matter explanations of the PAMELA positron fraction and Fermi electronic excesses. For those theories with a TeV-scale WIMP annihilating through a light force-carrier, the associated Sommerfeld enhancement provides a natural explanation of the large boost factor needed to explain the signals, and the light force-carrier naturally gives rise to hard cosmic ray spectra without excess pi0 gamma rays or anti-protons. The Sommerfeld enhancement of the annihilation rate, which at low relative velocities v scales as 1/v, relies on the comparatively low velocity d…
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 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 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…
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…
Vector Dark Matter in the Fundamental Representation of $SU(2)_{L}$: Sommerfeld Enhancement and Indirect Detection
Universidad Técnica Federico Santa María（弗雷德里科·圣塔马利亚技术大学）；Millennium Institute for Subatomic Physics at High Energy Frontier – SAPHIR（高能前沿亚原子物理千年研究所 - SAPHIR）；Centro Científico-Tecnológico de Valparaíso, Universidad Técnica Federico Santa María（瓦尔帕莱索科学技术中心，弗雷德里科·圣塔马利亚技术大学）
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…
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 …
EFT Approaches to Sommerfeld Enhancement and Bound States in Singular Potentials
Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器）；Department of Physics, Harvard University（哈佛大学物理系）；Center for Theoretical Physics – a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院莱因韦伯理论物理中心）；Radcliffe Institute for Advanced Study at Harvard University（哈佛拉德克利夫高等研究院）
The scattering of neutrinos assuming a "secret" interaction at low energy is considered. To leading order in energy, the two-body potential is a $δ$-potential, and it is used as a motivation to study generic short-range elastic interactions between neutrinos. The scattering cross section and Sommerfeld enhancement depend on two phenomenological parameters deriving from the exact form of the potential, akin to "renormalized" coupling constants. Repulsive potentials lead to a decrease in the total cross section, resulting in an enhancement of the neutrino density. For attractive potentials of th…
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.
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 annihilation of heavy particles close to thermal equilibrium, which plays a prominent role in the chemical equilibration of heavy quarks in the Quark-Gluon Plasma (QGP) as well as in many classic dark matter scenarios, is reexamined. We derive a scattering amplitude that resums near-threshold attractive interaction of the annihilating particles in terms of the non-relativistic scattering $T$-matrix and Green's function, thereby capturing the pertinent Sommerfeld enhancement from both nonperturbative scattering state and bound state solutions. The derived formula is of such generality that …
Sommerfeld Enhancement in Spin-1 Electroweak Dark Matter
Tokyo University of Science（东京科学大学）；Kyushu University（九州大学）；University of Toyama（富山大学）；Nagoya University（名古屋大学）；Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University（名古屋大学小林-益川粒子起源研究所）；Kavli IPMU (WPI), UTIAS, University of Tokyo（东京大学理化学研究所木下国际数学·物理联合中心）
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…
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 <…
