Search

With this article we introduce recent, improved machine learning methods from computer vision to the problem of event classification in particle physics. Supersymmetric scalar top decays to top quarks and weak scale bino-like neutralinos, where the neutralinos decay via the $UDD$ operator to three quarks, are difficult to search for and therefore weakly constrained. The jet substructure of the boosted decay products can be used to differentiate signal from background events. We apply transformer-based computer vision models CoAtNet and MaxViT to images built from jet constituents and compare the classification performance to a more classical convolutional neural network (CNN). We find that results from computer vision translate well onto physics applications and both transformer-based models perform better than the CNN. By replacing the CNN with MaxViT we find an improvement of $S/\sqrt{B}$ by a factor of almost 2 for some neutralino masses. We show that combining this classifier with additional features results in a strong separation of background and signal. We also find that replacing a CNN with a MaxViT model in a simple mock analysis can push the 95% C.L. exclusion limit of stop masses by about $100$ GeV and $60$ GeV for neutralino masses of $100$ GeV and $500$ GeV., Comment: 13 pages, 9 figures

Interactions between Dark Matter (DM) and nucleons relevant for direct search experiments can be organised in a model independent manner using a Galiliean invariant, non--relativistic effective field theory (NREFT). Here one expands the interactions in powers of the momentum transfer $\vec{q}$ and DM velocity $\vec{v}$. This approach generates many operators. The potentially most important subleading operators are odd under $T$, and can thus only be present in a theory with $CP$ violating interactions. We consider two such operators, called $\mathcal{O}_{10}$ and $\mathcal{O}_{11}$ in the literature, in simplified models with neutral spin$-0$ mediators; the couplings are chosen such that the coefficient of the leading spin independent (SI) operator, which survives for $\vec{v} \rightarrow 0$, vanishes at tree level. However, it is generically induced at the next order in perturbation theory. We perform a numerical comparison of the number of scattering events between interactions involving the $T-$odd operators and the corresponding loop induced SI contributions. We find that for ''maximal'' $CP$ violation the former can dominate over the latter. However, in two of the three models we consider, an electric dipole moment of the neutron (nEDM) is induced at two--loop order. We find that the experimental bound on the nEDM typically leads to undetectably small rates induced by ${\mathcal O}_{10}$. On the other hand, the model leading to a nonvanishing coefficient of ${\mathcal O}_{11}$ does not induce an nEDM., Comment: 49 pages, 17 figures, 4 tables

Polynomial inflation is a very simple and well motivated scenario. A potential with a concave ``almost'' saddle point at field value $\phi = \phi_0$ fits well the cosmic microwave background (CMB) data and makes testable predictions for the running of the spectral index and the tensor to scalar ratio. In this work we analyze leptogenesis in the polynomial inflation framework. We delineate the allowed parameter space giving rise to the correct baryon asymmetry as well as being consistent with data on neutrino oscillations. To that end we consider two different reheating scenarios. $(i)$ If the inflaton decays into two bosons, the reheating temperature can be as high as $T_\text{rh} \sim 10^{14}$ GeV without spoiling the flatness of the potential, allowing vanilla $N_1$ thermal leptogenesis to work if $T_\text{rh}> M_1$ where $N_1$ is the lightest right--handed neutrino and $M_1$ its mass. Moreover, if the dominant decay of the inflaton is into Higgs bosons of the Standard Model, we find that rare three--body inflaton decays into a Higgs boson plus one light and one heavy neutrino allow leptogenesis even for $T_\text{rh} < M_1$ if the inflaton mass is of order $10^{12}$ GeV or higher; in the polynomial inflation scenario this requires $\phi_0 \gtrsim 2.5~M_P$. This novel mechanism of non--thermal leptogenesis is quite generic, since the coupling leading to the three--body final state is required in the type I see--saw mechanism. $(ii)$ If the inflaton decays into two fermions, the flatness of the potential implies a lower reheating temperature. In this case inflaton decay to two $N_1$ still allows successful non--thermal leptogenesis if $\phi_0 \gtrsim 0.1~M_P$ and $T_\text{rh} \gtrsim 10^{6}$ GeV., Comment: V1: 19 pages, 3 figures, 1 new mechanism of leptogenesis via 3-body decay. V2: minor modification with a footnote 4 regarding washout effect, version accepted for publication in JCAP

In many well-motivated models of the electroweak scale, cascade decays of new particles can result in highly boosted hadronic resonances (e.g. $Z/W/h$). This can make these models rich and promising targets for recently developed resonant anomaly detection methods powered by modern machine learning. We demonstrate this using the state-of-the-art CATHODE method applied to supersymmetry scenarios with gluino pair production. We show that CATHODE, despite being model-agnostic, is nevertheless competitive with dedicated cut-based searches, while simultaneously covering a much wider region of parameter space. The gluino events also populate the tails of the missing energy and $H_T$ distributions, making this a novel combination of resonant and tail-based anomaly detection., Comment: 13 pages, 15 figures

In a non-standard cosmological scenario, heavy, long-lived particles, which we call moduli, dominate the energy density prior to Big Bang Nucleosynthesis. Weakly Interacting Massive Particles (WIMPs) may be produced non-thermally from moduli decays. The final relic abundance then depends on additional parameters such as the branching ratio of moduli to WIMPs and the modulus mass. This is of interest for WIMP candidates, such as a bino-like neutralino, where thermal production in standard cosmology leads to an overdensity. Previous works have shown that the correct dark matter (DM) relic density can then still be obtained if the moduli, with mass less than $10^{7}$ GeV, decay to WIMPs with a branching ratio of less than $10^{-4}$. This upper bound could easily be violated once higher order corrections, involving final states with more than two particles, are included. We compute the branching ratios of three- and four-body decays of a modulus into final states involving two DM particles for general couplings. We then apply these expressions to sparticle production within the Minimal Supersymmetric Standard Model (MSSM) with neutralino DM. We find that this upper bound on the branching ratio can be satisfied in simplified models through an appropriate choice of as yet undetermined couplings. However, in the MSSM, it requires sparticle masses to be very close to half the modulus mass, in contrast to the idea of weak-scale supersymmetry., Comment: 43 pages, 24 figures, 2 appendices; v2: figures and references updated, two footnotes added; v3: typos corrected, matches version accepted for publication in JCAP

Simple monomial inflationary scenarios have been ruled out by recent observations. In this work we revisit the next simplest scenario, a single--field model where the scalar potential is a polynomial of degree four which features a concave ``almost'' saddle point. We focus on trans--Planckian field values. We reparametrize the potential, which greatly simplifies the procedure for finding acceptbale model parameters. This allows for the first comprehensive scan of parameter space consistent with recent Planck and BICEP/Keck 2018 measurements. Even for trans--Planckian field values the tensor--to--scalar ratio $r$ can be as small as $\mathcal{O}(10^{-8})$, but the model can also saturate the current upper bound. In contrast to the small--field version of this model, radiative stability does not lead to strong constraints on the parameters of the inflaton potential. For very large field values the potential can be approximated by the quartic term; as well known, this allows eternal inflation even for field energy well below the reduced Planck mass $M_{\rm Pl}$, with Hubble parameter $H \sim 10^{-2} M_{\rm Pl}$. More interestingly, we find a region of parameter space that even supports {\em two phases of eternal inflation}. The second epoch only occurs if the slope at the would--be saddle point is very small, and has $H \sim 10^{-5} M_{\rm Pl}$; it can only be realized if $r \sim 10^{-2}$, within the sensitivity range of next--generation CMB observations., Comment: V1: 25 pages, 5 figures; V2: references updated, discussion on preheating included, version accepted for publication in JCAP; v3: a typo in footnote 11 corrected

We study the influence of leptophilic dark matter interactions on decays of muons and ground state mesons in existing experiments. We consider a secluded dark sector exclusively interacting with leptons via either a (leptophilic) scalar or vector mediator. These interactions will therefore influence leptonic decays and deform the energy spectra. We first study the Michel decay of muons, $\mu^+\rightarrow e^+\nu_e \bar{\nu}_\mu$, which allow us to constrain the parameter space reasonably well. Secondly, the rare $\pi^\pm$, $K^\pm$, $D^\pm$ and $D_s^\pm$ decays to $e\nu$ will be considered. Scalar mediators would remove the Standard Model helicity suppression, so that strong constraints can be derived. The resulting bounds on the couplings of the light mediators to electrons and muons still turn out to be somewhat weaker than those from searches at low--energy $e^+e^-$ colliders and the magnetic moment of the muon, respectively. Finally, we show that kaon and pion decays basically exclude a ''Co--SIMP'' scenario where a scalar dark matter particle has a dimension--5 coupling to electrons., Comment: 18 pages, 8 figures

Heavy long-lived particles are abundant in BSM physics and will, under generic circumstances, get to dominate the energy density of the universe. The resulting matter dominated era has to end before the onset of Big Bang Nucleosynthesis through the decay of the heavy matter component of mass $M$ into a thermal bath of temperature $T$. The process of thermalization primarily involves near-collinear splittings of energetic particles into two particles with lower energy. The correct treatment of these processes requires the inclusion of coherence effects which suppress the splitting rate. We write down and numerically solve the resulting coupled Boltzmann equations including all gauge bosons and fermions of the Standard Model (SM). We then comment on the dependence of the nonthermal spectra on the ratio $M/T$, as well as on the matter decay rate and branching ratios into various SM particles.

Extending the Standard Model (SM) by a $U(1)_{L_\mu-L_\tau}$ group gives potentially significant new contributions to $g_\mu-2$, allows the construction of realistic neutrino mass matrices, incorporates lepton universality violation, and offers an anomaly-free mediator for a Dark Matter (DM) sector. In a recent analysis we showed that published LHC searches are not very sensitive to this model. Here we apply several Machine Learning (ML) algorithms in order to distinguish this model from the SM using simulated LHC data. In particular, we optimize the $3\mu$-signal, which has a considerably larger cross section than the $4\mu$-signal. Furthermore, since the $2$-muon plus missing $E_T$ final state gets contributions from diagrams involving DM particles, we optimize it as well. We find greatly improved sensitivity, which already for $36$ fb$^{-1}$ of data exceeds the combination of published LHC and non-LHC results. We also emphasize the usefulness of Boosted Decision Trees which, unlike Neural Networks, easily allow to extract additional information from the data which directly connect to the theoretical model through feature importance. The same scheme could be used to analyze other models., Comment: 39 pages, 10 figures

In this paper we introduce a light Dirac particle $\psi$ as thermal dark matter candidate in a $U(1)_{L_{\mu}-L_{\tau}}$ model. Together with the new gauge boson $X$, we find a possible parameter space with $m_X \simeq 20$ MeV, $U(1)_{L_{\mu}-L_{\tau}}$ coupling $g_X \simeq 5 \cdot 10^{-4}$ and $m_\psi \gtrsim m_X/2$ where the $(g-2)_\mu$ anomaly, dark matter, the Hubble tension, and (part of) the excess of $511$ keV photons from the region near the galactic center can be explained simultaneously. This model is safe from current experimental and astrophysical constraints, but can be probed by the next generation of neutrino experiments as well as low-energy $e^+e^-$ colliders., Comment: 19 pages, 4 figures; comments welcome; v2: typos corrected, discussion modified in sec.4 ,references updated

We revisit the Boltzmann equation governing the spectrum of energetic particles originating from the decay of massive progenitors during the process of thermalization. We assume that these decays occur when the background temperature $T$ is much less than the mass $M$ of the progenitor. We pay special attention to the IR cutoff provided by the thermal bath, and include the suppression resulting from the interference of multiple scattering reactions (LPM effect). We solve the resulting integral equation numerically, and construct an accurate analytical fit of the solutions., Comment: Including subsection 3.3 -- Published Journal Version

We revisit the renormalizable polynomial inflection point model of inflation, focusing on the small field scenario which can be treated fully analytically. In particular, the running of the spectral index is predicted to be $\alpha = -1.43 \times 10^{-3} +5.56 \times 10^{-5} \left(N_{\rm CMB}-65 \right)$, which might be tested in future. We also analyze reheating through perturbative inflaton decays to either fermionic or bosonic final states via a trilinear coupling. The lower bound on the reheating temperature from successful Big Bang nucleosynthesis gives lower bounds for these couplings; on the other hand radiative stability of the inflaton potential leads to upper bounds. In combination this leads to a lower bound on the location $\phi_0$ of the near inflection point, $\phi_0 > 3 \cdot 10^{-5}$ in Planckian units. The Hubble parameter during inflation can be as low as $H_{\rm inf} \sim 1$ MeV, or as high as $\sim 10^{10}$ GeV. Similarly, the reheating temperature can lie between its lower bound of $\sim 4$ MeV and about $4 \cdot 10^8 \ (10^{11})$ GeV for fermionic (bosonic) inflaton decays. We finally speculate on the "prehistory" of the universe in this scenario, which might have included an epoch of eternal inflation., Comment: v2: typos corrected, references updated; expanded discussion on preheating and inflaton scattering; version accepted by JCAP

In the Minimal Supersymmetric Extension of the Standard Model (MSSM) the higgsino mass parameter $\mu$ appears both in the masses of the Higgs bosons and in the neutralino mass matrix. Electroweak finetuning therefore prefers small values of $|\mu|$. On the other hand, bino--like neutralinos make a good dark matter candidate. We show that current direct search limits then impose a strong lower bound on $|\mu|$, in particular for $\mu > 0$ or if the masses of the heavy Higgs bosons of the MSSM are near their current limit from LHC searches. There is therefore some tension between finetuning and neutralino dark matter in the MSSM. We also provide simple analytical expressions which in most cases closely reproduce the numerical results., Comment: 15 Pages,6 figures

A non-relativistic effective field theory (NREFT) offers a bottom-up framework to classify Dark Matter (DM)-nucleon interactions relevant for scattering at direct detection experiments by organizing the interactions in powers of the momentum transfer $\vec{q}$ and DM velocity $\vec{v}$. This approach generates a number of operators including P-odd and T-odd operators; these can only be generated from a relativistic theory with CP violating interactions. We consider the leading order P-odd, T- odd operators viz. $\mathcal{O}_{10}$, $\mathcal{O}_{11}$ and $\mathcal{O}_{12}$ and compare the constraints on these operators from leading direct detection searches and from the bound on the neutron EDM (nEDM). We perform our analysis using simplified models with charged mediators and compute the loop diagrams contributing to the nEDM. We find that constraints on the DM scattering cross section from the bound on the nEDM are several orders of magnitude stronger than the limits from direct searches, and even well below the neutrino floor for such NREFT operators, for the entire sub-GeV to TeV DM mass range. This indicates that these operators need not be considered when analyzing data from present or future direct dark matter detection experiments., Comment: 15 pages, 4 figures, 3 tables, v2: typos corrected; published version is shorter without any major changes

The self coupling $\lambda$ of the Higgs boson in the Standard Model may show critical behavior, i.e. the Higgs potential may have a point at an energy scale $\sim 10^{17-18}$ GeV where both the first and second derivatives (almost) vanish. In this case the Higgs boson can serve as inflaton even if its nonminimal coupling to the curvature scalar is only ${\cal O}(10)$, thereby alleviating concerns about the perturbative unitarity of the theory. We find that just before the Higgs as inflaton enters the flat region of the potential the usual slow--roll conditions are violated. This leads to "overshooting" behavior, which in turn strongly enhances scalar curvature perturbations because of the excitation of entropic (non--adiabatic) perturbations. For appropriate choice of the free parameters these large perturbations occur at length scales relevant for the formation of primordial black holes. Even if these perturbations are not quite large enough to trigger copious black hole formation, they source second order tensor perturbations, i.e. primordial gravitational waves; the corresponding energy density can be detected by the proposed space-based gravitational wave detectors DECIGO and BBO., Comment: v3: updated Fig.11 by considering the kinematic effect of dark energy on the induced GW signatures; main conclusions remain unchanged; version published in EPJC

We apply LHC data to constrain a simplified extension of the Standard Model containing a new spin-1 mediator $R$, which does not couple to first generation quarks, and a spinor dark matter particle $\chi$. We recast ATLAS and CMS searches for final states containing one or more jet(s) + missing $E_T$, with or without $b$ tags, as well as searches for di-jet resonances with $b$ or $t$ tagging. We find that LHC constraints on the axial vector couplings of the mediator are always stronger than the unitarity bound, which scales like $m_R/m_t$. If $R$ has a sizable invisible branching ratio, the strongest LHC bound on both vector couplings and axial vector coupling comes from a di-jet + missing $E_T$ search with or without double $b$ tag. These bounds are quite strong for $m_R < 1$ TeV, even though we have switched off all couplings to valence quarks. Searches for a di-jet resonance with double $b$ tag lead to comparable bounds with the previous results even if $R \rightarrow \chi \bar \chi$ decays are allowed; these are the only sensitive LHC searches if the invisible branching ratio of $R$ is very small or zero., Comment: 13 pages, 2 figures

In this study, we apply LHC data to constrain the extension of the Standard Model by an anomaly-free $U(1)_{L_\mu-L_\tau}$ gauge group; this model contains a new gauge boson ($Z^\prime$) and a scalar dark matter particle ($\phi_{\rm DM}$). We recast a large number of LHC analyses from ATLAS and CMS of multi-lepton final states. We find that for $10$ GeV $< m_{Z^\prime} < 60$ GeV the strongest constraint comes from a dedicated $Z^\prime$ search in the $4\mu$ final state by the CMS collaboration; for larger $Z^\prime$ masses, searches for final states with three leptons plus missing $E_T$ are more sensitive. Searches for final states with two leptons and missing $E_T$, which are sensitive to $Z^\prime$ decays into dark matter particles, can only probe regions of parameter space that are excluded by searches in the $3$ and $4$ lepton channels. The combination of LHC data excludes values of $Z^\prime$ mass and coupling constant that can explain the deficit in $g_\mu-2$ for $4$ GeV $\leq m_{Z^\prime} \leq 500$ GeV. However, for much of this range the LHC bound is weaker than the bound that can be derived from searches for trident events in neutrino-nucleus scattering., Comment: 15 pages, 4 figures

I begin by briefly reviewing the evidence for the existence of Dark Matter (DM), emphasizing that {\em many} observations, at length scales between kpc (the size of the smallest galaxies) and Gpc (the Hubble radius) can be described by the same simple model, $\Lambda$CDM. I will then argue that primordial black holes, the only DM candidates that can be realized within the Standard Model (SM) of particle physics, are very unlikely to provide all of DM. After giving a (probably incomplete) list of possible DM candidates, I end by mentioning some recent developments in the theory of Weakly Interacting Massive Particles (WIMPs)., Comment: Plenary Talk delivered at ICHEP 2018, Seoul, Korea; 10 pages, no figures

We investigate the production of neutralino dark matter in a cosmological scenario featuring an early matter dominated era ending at a relatively low reheating temperature. In such scenarios different production mechanisms of weakly interacting massive particles (WIMPs), besides the well--studied thermal production, can be important. This opens up new regions of parameter space where the lightest neutralino, as the best--known supersymmetric (SUSY) WIMP, obtains the required relic abundance. Many of these new sets of parameters are also compatible with current limits from colliders as well as direct and indirect WIMP searches. In particular, in standard cosmology bino--like neutralinos, which emerge naturally as lightest neutralino in many models, can have the desired relic density only in some finetuned regions of parameter space where the effective annihilation cross section is enhanced by co--annihilation or an $s-$channel pole. In contrast, if the energy density of the universe was dominated by long--lived PeV--scale particles (e.g. moduli or Polonyi fields), bino--like neutralinos can obtain the required relic density over wide regions of supersymmetric parameter space. We identify the interesting ranges of mass and decay properties of the heavy long--lived particles, carefully treating the evolution of the temperature of the thermal background., Comment: 27 pages, 6 figures, updated references, minor modifications, as published

We apply data taken at the $e^+e^-$ collider LEP in the 1990's at center-of-mass energy up to 209 GeV to constrain Dark Matter models with a light leptophobic spin-1 mediator $R$. We assume that the dark sector particle (DSP) is a spin-1/2 fermion $\chi$. This scenario is well studied in the context of LHC searches for mediator mass from 100 GeV to several TeV. Emission of the mediator off a quark or antiquark at LEP gives rise to di-jet plus missing energy and 4-jet signatures, which we use to limit the relevant couplings. We focus on scenarios with $2 m_\chi > m_R$, which are poorly constrained by LHC data. We recast published searches by the ALEPH collaboration. For $m_\chi < 20$ GeV the best bounds result from an analysis at $\sqrt{s} \simeq M_Z$ of di-jet plus missing energy events. For heavier DSP but $m_R < 70$ GeV meaningful bounds can be derived from a four jet analysis at $\sqrt{s} = 183$ GeV. Unfortunately published searches using four jet final states at $\sqrt{s} \simeq M_Z$ use only a small fraction of the total data sample. Moreover, all published searches for di-jet plus missing energy final states at $\sqrt{s} \geq 130$ GeV have poor efficiency for our model; we therefore design new cuts that combine good background rejection with higher efficiency. Re-analyzing the higher energy data using our new cuts, and an analysis of the complete four jet data sample taken at $\sqrt{s}\simeq M_Z$, can explore new regions of parameter space., Comment: 28 pages, 16 figures

We investigate dark matter (DM) production in an early matter dominated era where a heavy long-lived particle decays to radiation and DM. In addition to DM annihilation into and thermal DM production from radiation, we include direct DM production from the decay of the long-lived particle. In contrast to earlier treatments the temperature dependence of the number of degrees of freedom $g_*$ in the Standard Model (SM) plasma is treated carefully. Besides the well-known cases of thermal hot and cold DM, additional regions of parameter space with the approximately correct DM relic density appear. In some of these regions the temperature dependence of $g_*$ can change the final DM density by several hundred percent. Furthermore, we analyze the effect of allowing nonvanishing initial abundances for radiation and DM. We find an upper bound on the mass of the long-lived particle if the DM annihilation cross section is below that corresponding to thermal WIMP (Weakly Interactive Massive Particle) DM in standard cosmology., Comment: 29 pages, 7 figures, updated references, minor modifications, as published

We study the Standard Model singlet ("right-handed") sneutrino $\tilde \nu_R$ dark matter in a class of $U(1)'$ extensions of the MSSM that originate from the breaking of the $E_6$ gauge group. These models, which are referred to as UMSSM, contain three right--handed neutrino superfields plus an extra gauge boson $Z'$ and an additional SM singlet Higgs with mass $\simeq M_{Z'}$, together with their superpartners. In the UMSSM the right sneutrino is charged under the extra $U(1)'$ gauge symmetry; it can therefore annihilate via gauge interactions. In particular, for $M_{\tilde \nu_R} \simeq M_{Z'}/2$ the sneutrinos can annihilate by the exchange of (nearly) on--shell gauge or Higgs bosons. We focus on this region of parameter space. For some charge assignment we find viable thermal $\tilde \nu_R$ dark matter for mass up to $\sim 43$ TeV. This is the highest mass of a good thermal dark matter candidate in standard cosmology that has so far been found in an explicit model. Our result can also be applied to other models of spin$-0$ dark matter candidates annihilating through the resonant exchange of a scalar particle. These models cannot be tested at the LHC, nor in present or near--future direct detection experiments, but could lead to visible indirect detection signals in future Cherenkov telescopes., Comment: 29 pages, 6 figures, 1 table

We analyse the constraints on models of WIMP Dark Matter that can be derived from upper bounds on the "monojet" cross section at the LHC. These constraints were originally interpreted in the context of an effective field theory (EFT) where the Standard Model is extended by a dimension--6 operator whose coefficient is $1/\Lambda^2$. We show that combining the 8 TeV data of the ATLAS and CMS collaborations improves the bounds only slightly. We then analyze this final state in the context of simplified models with $s-$channel mediator. We show that if the decay width of the mediator is small, these simplified models can be accurately modeled by the effective field theory only if the mediator mass is above 5 TeV. Finally, we point out that even if the EFT accurately describes the ${\cal O}(\Lambda^{-2})$ contributions to the matrix element, for values of $\Lambda$ near the current bound it receives significant contributions of order $\Lambda^{-4}$, in the context of simplified models, these correspond to diagrams where two mediators are exchanged. This observation challenges the internal consistency of the EFT description since dimension$-8$ operators, which would also contribute to ${\cal O}(\Lambda^{-4})$ to the matrix element, are not included., Comment: 21 pages, 6 figures

Weakly Interactive Massive Particles (WIMPs) are the most widely studied candidate particles forming the cold dark matter (CDM) whose existence can be inferred from a wealth of astrophysical and cosmological observations. In the framework of the minimal cosmological model detailed measurements on the cosmic microwave background by the PLANCK collaboration fix the scaled CDM relic density to $\Omega_{c}h^2=0.1193\pm0.0014$, with an error of less than 1.5%. In order to fully exploit this observational precision, theoretical calculations should have a comparable or smaller error. In this paper we use recent lattice QCD calculations to improve the description of the thermal plasma. This affects the predicted relic density of "thermal WIMPs", which once were in chemical equilibrium with Standard Model particles. For WIMP masses between 3 and 15 GeV, where QCD effects are most important, our predictions differ from earlier results by up to 9% (12%) for pure S-wave (P-wave) annihilation. We use these results to compute the thermally averaged WIMP annihilation cross section that reproduces the correct CDM relic density, for WIMP masses between 0.1 GeV and 10 TeV., Comment: 14 pages, 6 figures