Dark Matter Particle Candidates
Paolo Gondolo University of Utah Evidence for cold dark matter
0.04175±0.00004 pJ/m3 photons
37.6±0.2 pJ/m3 ordinary matter
1 to 4 pJ/m3 neutrinos 535±7 pJ/m3 dark energy Cold Dark 201±2 pJ/m3 cold dark matter Matter
The observed energy content of the Universe matter p≪ρ radiation p=ρ/3 -12 Planck (2015) 1 pJ = 10 J vacuum p=-ρ TT,TE,EE+lowP+lensing+ext 2 3 ρcrit=1688.29 h pJ/m Is cold dark matter an elementary particle?
is the particle of light
couples to the plasma
disappears too quickly
HiggsH boson
No known particle can be nonbaryonic cold dark matter! What particle model for cold dark matter?
• It should have the cosmic cold dark matter density • It should be stable or very long-lived (≳1024 yr) • It should be compatible with collider, astrophysics, etc. bounds • Ideally, it would be possible to detect it in outer space and produce it in the laboratory • For the believer, it would explain claims of dark matter detection (annual modulation, positrons, X-ray line, γ-ray excess, etc.) Particle dark matter
• SM neutrinos (hot) • lightest supersymmetric particle (cold) thermal relics • lightest Kaluza-Klein particle (cold) • sterile neutrinos, gravitinos (warm) • Bose-Einstein condensates, (cold) axions, axion clusters non-thermal relics • solitons (Q-balls, B-balls, ...) (cold) • supermassive wimpzillas (cold)
Mass range Interaction strength range 10-22 eV (10-59kg) B.E.C.s Only gravitational: wimpzillas -8 +22 10 M⦿ (10 kg) axion clusters Strongly interacting: B-balls Particle dark matter
Hot dark matter - relativistic at kinetic decoupling (last scattering, start of free streaming) - big structures form first, then fragment light neutrinos
Cold dark matter - non-relativistic at kinetic decoupling - small structures form first, then merge neutralinos, axions, WIMPZILLAs, solitons
Warm dark matter - semi-relativistic at kinetic decoupling - smallest structures are erased sterile neutrinos, gravitinos Particle dark matter
Thermal relics - in thermal equilibrium with the plasma in the early universe - produced in collision of plasma particles - insensitive to initial conditions
neutralinos, other WIMPs, ....
Non-thermal relics
- not in thermal equilibrium with the plasma in the early universe - produced in decays of heavier particles or extended structures - have a memory of initial conditions
axions, WIMPZILLAs, solitons, .... Particle dark matter
- in plasma reactions DM production collider searches - from decays of decoupled species cosmic density - emitted from extended objects
DM-DM annihilation - self-conjugate DM indirect detection χ+χ̅ →anything - asymmetric DM cosmic density hot/cold/warm DM—SM scattering - elastic/inelastic scattering halo (sub)structure χ+SM→χ′+SM - short-/long-range interactions direct detection DM—DM scattering - collisionless dark halo structure χ+χ→χ+χ - self-interacting - stable DM decay - long-lived indirect detection χ→anything - ensemble of short-lived particles Particle dark matter Some factors affecting the particle dark matter cosmic density — Production mechanism: • produced in reactions of plasma (thermal) particles - reaching reaction equilibrium WIMP freeze-out, … - not reaching reaction equilibrium FIMP freeze-in, … - coannihilating with similar mass particles neutralinos, … • produced in decays of non-thermal particles gravitinos, … • emitted from extended objects axions, …
— Dark matter-antimatter asymmetry: • self-conjugate Majorana fermions, neutralinos, axions, gravitinos, …
• not self-conjugate Dirac fermions, asymmetric dark matter, …
— Hubble expansion rate before nucleosynthesis: • standard vs nonstandard cosmology low temperature reheating, kination, … The magnificent WIMP (Weakly Interacting Massive Particle)
0.04175±0.00004 pJ/m3 photons • One naturally obtains the 37.6±0.2 pJ/m3 ordinary matter right cosmic density of 1 to 4 pJ/m3 neutrinos 201±2 WIMPs 3 535±7 pJ/m pJ/m3 dark energy Thermal production in cold dark matter hot primordial plasma.
• One can experimentally test the WIMP hypothesis The same physical processes that produce the right density of WIMPs make their detection possible the WIMP The power of Indirect detection Colliders (—) B ør ge K i l e G j e l s t e n , U n i v e r s i t y o f O s l o Annihilation Production 4 4 I D M , A u g 20 0 8 f f (—) Cosmic density Cosmic density Scattering Large scale structure Direct detection Neutrinos Cosmic density of massive neutrinos
Active neutrinos ~ few GeV preferred cosmological mass Excluded as cold dark matter (1991) Lee & Weinberg 1977
Direct Searches
LEP bound Z ⌫⌫¯ ! Sterile neutrino dark matter
Standard model + right-handed neutrinos Active and sterile neutrinos oscillate into each other.
case 1 case 2 -4 -4 10 LMC 10 LMC
MW 6 MW 6 M31 10 n / s M31 -6 10 n / s -6 ν ν e Sterile neutrinos can be warm 10 e MW 10 MW 0.0 SPI 0.0 SPI dark matter (mass > 0.3 keV) -8 -8 10 DM density 10 θ θ
Dodelson, Widrow 1994; Shi, Fuller 2 2 2 -10 2 -10 1999; Laine, Shaposhnikov 2008 10 2 10 2 sin Lyman-α sin 4 4 (SDDS) 25 16 12 25 16 12 8 8 -12 70 -12 70 10 250 10 250 700 700 2500 2500 -14 -14 10 10
-16 -16 νMSM 10 0 1 2 10 0 1 2 10 10 10 10 10 10 Laine, Shaposhnikov 2008 M1 / keV M1 / keV
Figure 4: The central region of Fig. 3, M1 =0.3 ...100.0keV,comparedwithregionsexcluded by various X-ray constraints [22, 25, 30, 31], coming from XMM-Newton observations of the Large Magellanic Cloud (LMC), the Milky Way (MW), and the Andromedagalaxy(M31).SPImarksthe constraints from 5 years of observations of the Milky Way galactic center by the SPI spectrometer on board the Integral observatory.
dark matter simulations, which have not been carried out withactualnon-equilibriumspec- tra so far. Nevertheless, adopting a simple recipe for estimating the non-equilibrium effects (cf. Eq. (5.1)), the results of refs. [34, 35] can be re-interpreted as the constraints M1 > 11.6 ∼ keV and M1 > 8 keV, respectively (95% CL), at vanishing asymmetry [12]. Very recently limits stronger∼ by a factor 2–3 have been reported [36]. We return to how the constraints change in the case of a non-zero lepton asymmetry in Sec. 5. We note, however, that the most conservative bound, the so-called Tremaine-Gunn bound[52,53],ismuchweakerand reads M1 > 0.3keV[54],whichwehavechosenasthelowerendofthehorizontal axes in Figs. 4, 6. ∼ In Fig. 5 we show examples of the spectra, for a relatively small mass M1 =3keV(like in Fig. 1), at which point the significant changes caused by theasymmetrycanbeclearly identified. The general pattern to be observed in Fig. 5 is thatforasmallasymmetry,the distribution function is boosted only at very small momenta.Quantitiesliketheaverage momentum q then decrease, as can be seen in Fig. 6. For large asymmetry, the resonance ⟨ ⟩s affects all q;thetotalabundanceisstronglyenhancedwithrespecttothecasewithouta resonance, but the shape of the distribution function is lessdistortedthanatsmallasymmetry, so that the average momentum q returns back towards the value in the non-resonant case. ⟨ ⟩s Therefore, for any given mass, we can observe a minimal value of q s in Fig. 6, q s > 0.3 q a. ⟨ ⟩ ⟨ ⟩ ∼ ⟨ ⟩ This minimal value is remarkably independent of M1,butthevalueofasymmetryatwhich
15 Sterile neutrino dark matter Radiative decay of sterile neutrinos An unidentified 3.5-keV X-ray line has been reported in galaxy ⌫s ⌫a E = ms/2 ! clusters and the Andromeda galaxy. 2 -11 mν = 7.1 keV sin (2θ) = 7×10 Bulbul et al 2014; Boyarski et al 2014; case 1 case 2 Iakubovskyi et al 2015 -4 -4 10 LMC 10 LMC )
-1 MW 6 MW 0.8 XMM-MOS 6 M31 10 n / s M31 keV 3.57 ± 0.02 (0.03) -6 -6 ν
-1 10 n / s Full Sample ν e 0.7 6 Ms 10 e MW 10 MW 0.0 SPI 0.0 SPI 0.6 stacked clusters Flux (cnts s 0.02 -8 -8 0.01 10 DM density 10
0 θ θ 2 2 2 2 Residuals -0.01 -10 -10 2 2 -0.02 10 10 sin Lyman-α sin
) 4
2 315 4 310 (SDDS) 25 16 12 25 16 12 8 8 70 70 305 -12 -12 10 250 10 250 300 700 700 Eff. Area (cm 2500 2500 3 3.2 3.4 3.6 3.8 4 Energy (keV) -14 -14 10 10
Fuller, Lowenstein,Jeltema, -16 -16 νMSM 10 0 1 2 10 0 1 2 Kusenko, Abazajian, Smith 10 10 10 10 10 10 (Thursday) Laine, Shaposhnikov 2008 M1 / keV M1 / keV
Figure 4: The central region of Fig. 3, M1 =0.3 ...100.0keV,comparedwithregionsexcluded by various X-ray constraints [22, 25, 30, 31], coming from XMM-Newton observations of the Large Magellanic Cloud (LMC), the Milky Way (MW), and the Andromedagalaxy(M31).SPImarksthe constraints from 5 years of observations of the Milky Way galactic center by the SPI spectrometer on board the Integral observatory.
dark matter simulations, which have not been carried out withactualnon-equilibriumspec- tra so far. Nevertheless, adopting a simple recipe for estimating the non-equilibrium effects (cf. Eq. (5.1)), the results of refs. [34, 35] can be re-interpreted as the constraints M1 > 11.6 ∼ keV and M1 > 8 keV, respectively (95% CL), at vanishing asymmetry [12]. Very recently limits stronger∼ by a factor 2–3 have been reported [36]. We return to how the constraints change in the case of a non-zero lepton asymmetry in Sec. 5. We note, however, that the most conservative bound, the so-called Tremaine-Gunn bound[52,53],ismuchweakerand reads M1 > 0.3keV[54],whichwehavechosenasthelowerendofthehorizontal axes in Figs. 4, 6. ∼ In Fig. 5 we show examples of the spectra, for a relatively small mass M1 =3keV(like in Fig. 1), at which point the significant changes caused by theasymmetrycanbeclearly identified. The general pattern to be observed in Fig. 5 is thatforasmallasymmetry,the distribution function is boosted only at very small momenta.Quantitiesliketheaverage momentum q then decrease, as can be seen in Fig. 6. For large asymmetry, the resonance ⟨ ⟩s affects all q;thetotalabundanceisstronglyenhancedwithrespecttothecasewithouta resonance, but the shape of the distribution function is lessdistortedthanatsmallasymmetry, so that the average momentum q returns back towards the value in the non-resonant case. ⟨ ⟩s Therefore, for any given mass, we can observe a minimal value of q s in Fig. 6, q s > 0.3 q a. ⟨ ⟩ ⟨ ⟩ ∼ ⟨ ⟩ This minimal value is remarkably independent of M1,butthevalueofasymmetryatwhich
15 Neutralinos Supersymmetric models
The CMSSM* is in dire straights, but there are many supersymmetric models *Constrained Minimal Supersymmetric Standard Model
mSUGRA
CMSSM SplitSUSY
Pure Gravity SM-18 pMSSM Mediation MSSM-25 AMSB GMSB
non-universalSUGRA MSSM-63
MSSM-124
NMSSM are highly detectable by IC/DC. We observe that all such WMAP-saturating well-tempered neutralinos with masses mLSP 500 GeV should be excluded by the IC/DC search (c.f.,the magenta points in Fig. 8).
Neutralino dark matter: impact of LHC Cahill-Rowell et al 1305.6921 pMSSM (phenomenological MSSM) “the only pMSSM models µ, mA, tan ,Ab,At,A⌧ ,M1,M2,M3,
remainingdensities. Of course, even[with for masses neutralino up to 1-2 TeV, XENON1T being still provides quite decentmQ1 ,mQ3 ,mu1 ,md1 ,mu3 ,md3 , model coverage in this parameter plane. As noted already, most of the impact of the LHC is at present seen to be at lower LSP masses below 500 GeV. The LHC coverage is relatively 100% of CDM] are those⇠ with uniform as far as the value of the relic density is concerned except in the case of very lightmL1 ,mL3 ,me1 ,me3 LSPs where the coverage is very strong. Of course, we again remind the reader that we binostill need tocoannihilation” add the additional information coming from the new 8 TeV LHC analyses not included here as well as the extrapolations to 14 TeV so that the coverage provided by the(19 parameters) LHC should be expected to improve substantially.
only a few red points have 100% CDM
CDM
Ω “IceCube”
Figure 13: Thermal relic density as a function of the LSP mass for all pMSSM models, surviving after all searches, color-coded by the electroweak properties of the LSP. Compare “Direct Detection” with Fig.Figure 2. 8: IC/DC signal event rates as a function of LSP mass (upper-left), thermal annihi- lation cross-section R2 (upper-right) and thermal elastic scattering cross-sections Finally, Fig. 13 shows the impact of combining all of the di↵erent searches in this same SD,p 2 h i ⌦h -LSPand mass plane which(lower should be panels). compared with that In for all the panels original model the set as gray points represent generic models in our full generated that is shownSI,p in Fig. 2. Here we see that (i)themodelsthatwereinthelighth pMSSM model set, while WMAP-saturating models with mostly bino, wino, Higgsino or mixed ( 80% of each)23 LSPs in are highlighted in red, blue, green and magenta, respectively. The red line denotes a detected flux of 40 events/yr, our conservative estimate for exclusion.
6 Complementarity: Putting It All Together
Now that we have provided an overview of the various pieces of data that go into our analysis, we can put them together to see what they (will) tell us about the nature of the neutralino
16 CONSTRAINED NEXT-TO-MINIMAL SUPERSYMMETRIC ... PHYSICAL REVIEW D 87, 115010 (2013) We include the constraint in our likelihood function taking 2 2 2 2 2 2 Vsoft mH Hu mH Hd mS S into account both theoretical and experimental uncertain- ¼ u j j þ d j j þ j j 1 3 ties, as will be described below. ASHuHd AS H:c: ; (2) The other important update was the top pole mass by the þ þ 3 þ Particle Data Group, obtained from an average of data from where A and A are soft trilinear terms associated with the Tevatron and the LHC at ps 7 TeV, Mt 173:5 and terms in the superpotential. The vev s, determined 1:0 GeV [38]. As we shall see¼ below this is a¼ welcomeÆ ffiffiffi by the minimization conditions of the Higgs potential, is increase relative to its previous value in the context of the effectively induced by the SUSY-breaking terms in Eq. (2), Higgs sector of constrained SUSY models as it pushes the and is naturally set by MSUSY, thus solving the -problem mass of h1 up, closer to the experimentally observed of the MSSM. Higgs-like resonance mass. We define the CNMSSM in terms of five continuous In this article, we present the first global Bayesian input parameters and one sign, analysis of the CNMSSM after the observation of the SM m ;m ;A ; tan ; ; sgn ; (3) Higgs-like boson. We separately consider the cases of this 0 1=2 0 ð effÞ boson being h1, or h2, or a combination of both. We test the where unification conditions at a high scale require that all parameter space of the model against the currently pub- the scalar soft SUSY-breaking masses in the superpotential lished, already stringent constraints from SUSY searches at (except mS) are unified to m0, the gaugino masses are the LHC and other relevant constraints from colliders, CONSTRAINED NEXT-TO-MINIMAL SUPERSYMMETRIC ... PHYSICAL REVIEW D 87, 115010 (2013) unified to m1=2, and all trilinear couplings, including A b-physics and dark matter (DM) relic density. Our goal is the posterior distribution. For the same reason R ZZ degenerate light scalars. However, the posterior pdf in and A, are unified to A0. This leaves us with two addi- h1 ð Þ to map out the regions of the parameter space of the tional free parameters: and the singlet soft-breaking mass cannot be perfectly fitted either, though its contribution the (Rh h , Rh h ZZ ) plane is remarkably similar CNMSSM1þ 2 ð Þ that1þ are2 ð favoredÞ by these constraints. As in 2 2 to the total 2 is smaller than 0.5 units of 2,makingthis to the one shown in Fig. 9(a), due to the large singlet m . The latter is not unified to m for both theoretical and our CMSSM study [30], the CMS razor limit based on S 0 observable equally ineffective in constraining the component of h2, and we refrain from showing it again phenomenological reasons. From the theoretical point of posterior. over4:4 here.=fb of In fact, data in is case implemented 3 we were not through able to find an aapproximate single but view, it has been argued [39] that the mechanism for SUSY In Fig. 9(b) we present the posterior distribution for pointaccurate with the likelihood enhanced function.rate. Since We case also 3 is study a subset the of effects of breaking might treat the singlet field differently from the case 2. Once again, R can hardly become larger h2 caserelaxing 2 in terms the ofg the2 favoredconstraint. parameter space, and the ð Þ ð À Þ other superfields. From the phenomenological point of than 1 over the preferred parameter space. The 95% cred- ratesThe in the article and is organizedZZ channel as do follows. not show In interesting Sec. II we briefly ible region lies far from the central value of the observed view, the freedom in mS allows for easier convergence features,revisit we the will model, not consider highlighting it separately some from of its the salient other features. enhancement and, in fact, even covers values lower than in cases any further. when the renormalization group equations (RGEs) are In Sec. III we detail our methodology, including our sta- case 1. Rh ZZ presents similar behavior, although the evolved from the GUT scale down to M . It also yields, 2 ð Þ SUSY suppression of the reduced cross section is highly welcome tisticalD. approachProspects for and DM our direct construction detection of and the likelihoods for in the limit 0, and with s fixed, effectively the for this observable, as it places the calculated value closer the BR B signal, the CMS razor 4:4=fb, and ! s BRþ BÀs þÀ CMSSM plus a singlet and singlino fields that both to the rate observed at CMS. Smaller than 1 signal rates the CMSð Higgs! searches.ð Þ! In Sec.Þ IV we present the results indicate less of a SM-like character for h , which is caused In this subsection we will discuss the impact of decouple from the rest of the spectrum. Through the mini- 2 limitsfrom from our directscans DM and searches discuss theiron the novel preferred features. para- We sum- 2 by the suppression of the SM couplings induced by its mization equations of the Higgs potential, mS can then be increased singlet component. metermarize space our of findings the CNMSSM. in Sec. ThisV. kind of experiments traded for tan (the ratio of the vev’s of the neutral The posterior distributions presented in Figs. 9(a) and are complementary to direct LHC SUSY searches, as they components of the Hu and Hd fields) and either sgn eff 9(b) indicate that, in both case 1 and case 2 it is in are capable of testing neutralino mass ranges beyond the ð Þ II. THE NMSSM WITH GUT-SCALE or . We choose sgn eff for conventional analogy with general extremely difficult to obtain the signal enhance- current and future reach of the LHC, and therefore could ð Þ ment in the channel. The scan naturally tends to stay add new pieces of informationUNIVERSALITY to the global picture. the CMSSM. Both and tan are defined at MSUSY. Our CONSTRAINED NEXT-TO-MINIMALin the regions of parameter SUPERSYMMETRIC space favored by... all con- At presentPHYSICAL the most REVIEW stringent limit D 87, on115010 the spin- (2013) choice of the parameter space is the same as the one used SI straints. It is therefore no surprise that among the points independentThe NMSSM cross section is an economicalp comes from extension XENON100 of the MSSM, by one of us in a previous Bayesian analysis [31], of which We include the constraint inNeutralino our likelihood function dark taking matter:V[78 inimpact]. which Inm supersymmetric2 oneH 2 adds ofm models a 2LHC gauge-singletH it2 can thenm2 beS superfield2 plotted as S whose scanned for case 1 only two presented a rate in the soft Hu u Hd d S this paper is, in some sense, an update. Of course, there into account both theoreticalrange 1.2–2, and thanks experimental to the reduced uncertain- coupling of the signal ascalar function¼ component ofj the neutralinoj þ couples massj only inj theþ to form thej ofj two an exclu- MSSM Higgs SI 1 1 exist different possibilities that have been explored in the Higgs bosonKowalska to the et bottomal 1211.1693 quarks. [PRD Such points87(2013)115010] present sion limit in the (m , p ) plane. 3 ties, as will be described below. doublets HuAandSHHuHd atd the treeA level.S HThe:c: scale-invariant; (2) 2 contributions to the relic density of order several 10s, We want to point out that the theory uncertainties literature. Some authors have studied the more constrained The other important update was the top pole mass by the superpotentialþ of the modelþ 3 has theþ form 2 2 2 are very large (up to a factor of 10) and strongly affect version of the CNMSSM, characterized by m m [26]. and the contribution to BR Bs þÀ is of order S ¼ 0 Particle Data Group, obtained100. In case from 2 we an found average a dozen ofð data such! from points,Þ forwhere which A theNMSSMand impactA are of (Next-to-MSSM) softthe experimental trilinear terms limit associated on the parameter with the But it is also true that the underlying assumption employed CNMSSM: Alive and well! Tevatron and the LHCthe contribution at ps 7 to TeV the relic, M densityt 173 is even:5 worse. and termsspace [41 in]. the It wassuperpotential. shown that,3 when The smearing vev s, determined out the here, of a different treatment of the singlet field by the CONSTRAINEDIn case NEXT-TO-MINIMAL 3 one¼ could expect to SUPERSYMMETRIC¼ obtain an enhancementÆ ... of XENON100W SH limitPHYSICALuH withd a theoreticalS REVIEWMSSM uncertainty D 87, Yukawa115010 of order terms (2013); (1) 1:0 GeV [38]. As we shall see below this is a welcome by the minimization¼ conditionsþ 3 SI ofþð the Higgs potential, isÞ SUSY breaking mechanism, would allow for freedom in Rh byffiffiffi adding the individual rates for both almost 10 times the given value of p , the effect on the posterior increase relativeWe include to its the previoussig ð constraintÞ value in our in the likelihood context function of the takingeffectively induced by2 the SUSY-breaking2 2 2 terms2 2 in Eq. (2), A at the GUT scale [39]. We will give some comment in Vsoft mH Hu mH Hd mS S Higgs sectorinto of account constrained both SUSY theoretical models and experimental as it pushes theuncertain- ¼ u j j þ d j j þ j j the Conclusions about the possible impact of relaxing the and is naturallywhere set byandMSUSY are, thus dimensionless solving1 the couplings.-problem Upon 3 unification condition for A. mass of h1ties,up, as closer will be to described the experimentally below. observed of the MSSM.spontaneous symmetryASHuH breaking,d A theS scalarH:c: Higgs; (2) field S þ þ 3 þ Higgs-like resonanceThe other mass. important update was the top pole mass by the We definedevelops the CNMSSM a vev, s inS terms, and the of five first continuous term in Eq. (1) Particle Data Group,CDM obtained from an average of data from h i III. STATISTICAL TREATMENT OF In this article, we present the first global Bayesian whereassumesA and theA are role soft of trilinear the effective terms associated-term of with the the MSSM, Ω input parametersConstrained and one NMSSM sign, Tevatron and the LHC at ps 7 TeV, Mt 173:5 EXPERIMENTAL DATA analysis of the CNMSSM after the observation of the SM andefftermss in. The the superpotential. soft SUSY-breaking The vev termss, determined in the Higgs 1:0 GeV [38]. As we shall see¼ below this is a¼ welcomeÆ ¼ ffiffiffi by thesector minimizationm0 are;m1 then=2;A given0 conditions; tan by ; ; sgn of theeff Higgs; potential,(3) is We explore the parameter space of the model with the Higgs-like boson.increase We relative separately to its previous consider value the casesin the contextof this of the ð Þ effectivelyGUT induced & radiative by the EWSB SUSY-breaking terms in Eq. (2), help of Bayesian formalism. We follow the procedure boson beingHiggsh1, or sectorh2, or of a constrained combination SUSY of both. models We as test it pushes the thewhereand unification is naturally conditions set by M at a, high thus solving scale require the -problem that all 1For simplicity we willSUSY be using the same notation for super- outlined in detail in our previous papers [30,40,41], of parameter spacemass of ofh the1 up, model closer against to the the experimentally currently pub- observedthe scalarof the soft MSSM. SUSY-breaking masses in the superpotential lished, alreadyHiggs-like stringent resonance constraints mass. from SUSY searches at fields and their bosonic components. which we give a short summary here. Our aim is to map (except WemS) define are unified the CNMSSM to m0, in the terms gaugino of five masses continuous are the LHC andIn other this article, relevant we constraints present the from first colliders, global Bayesian input parameters and one sign, unified to m1=2, and all trilinear couplings, including A b-physics andanalysis dark of matter the CNMSSM (DM) relic after density. the observation Our goal of is the SM Higgs-like boson. We separately consider the cases of thisand A, are unifiedm0;m to 1A=20;A. This0; tan leaves ; ; sgn us witheff ; two addi-(3) to map out the regions of the parameter space of the tional freeMarginalized parameters: 2D andposterior the singlet PDF soft-breakingð Þ mass 115010-3 boson being h1, or h2, or a combination of both. We test the CNMSSM that are favored by these constraints. As in 2 where unification conditions at2 a high scale require that all parameter space of the model against the currently pub-mS. Theof latter global is analysis not unified including to m0 LHC,for both theoretical and our CMSSM study [30], the CMS razor limit based on the scalar soft SUSY-breaking+ − masses in the superpotential lished, already stringent constraints from SUSY searchesphenomenological at WMAP, (g-2) reasons.µ, Bs→µ Fromµ etc. the theoretical point of (except mS) are unified to m0, the gaugino masses are 4:4=fb of datathe is LHC implemented and other through relevant an constraints approximate from but colliders, view,unified it has been to m argued1=2, and [39 all] trilinear that the couplings, mechanism including for SUSYA accurate likelihoodb-physics function. and dark matter We also (DM) study relic the density. effects Our of goal is SI FIG. 10 (color online). Marginalized 2D posterior pdf inbreaking the mand ; p mightAplane, are of treat the unified CNMSSM the to singletA constrained0. This field leaves by differently the experiments us with from two listed addi- the relaxing thetog map2 outinconstraint. the Table regionsI in (a) case of 1 the and (b) parameter case 2. The space solid red of line the showsð the 90%Þ C.L. exclusion bound by XENON100 (not included in the ð À Þ othertional superfields. free parameters: From the and phenomenological the singlet soft-breaking point mass of The articleCNMSSM is organizedlikelihood), that areas follows. favoredand the dashed In by Sec. these gray lineII constraints.we the projectedbriefly sensitivity As in form XENON1T.2. The latter The iscolor not code unified is the to samem2 asfor in Fig. both2. theoretical and view, theS freedom in mS allows for0 easier convergence revisit the model,our CMSSM highlighting study [ some30], the of CMS its salient razor features. limit based on phenomenological reasons. From the theoretical point of 4:4=fb of data is implemented through an approximate butwhen the renormalization group equations (RGEs) are In Sec. III we detail our methodology, including our sta- evolvedview, from it has the been GUT argued scale [39 down] that to theM mechanism. It also for yields, SUSY accurate likelihood function. We also study the effects of 115010-15breaking might treat the singlet fieldSUSY differently from the tistical approachrelaxing and the ourg construction2 constraint. of the likelihoods for in the limit 0, and with s fixed, effectively the ð À Þ other superfields. From the phenomenological point of the BR Bs Theþ articleÀ signal, is organized the CMS as follows. razor In4:4 Sec.=fb,II andwe brieflyCMSSM plus! a singlet and singlino fields that both the CMSð Higgs! searches.Þ In Sec. IV we present the results view, the freedom in mS allows for easier convergence revisit the model, highlighting some of its salient features.decouplewhen from the the renormalization rest of the spectrum. group equations Through (RGEs) the mini- are from our scansIn Sec. andIII discusswe detail their our novel methodology, features. including We sum- our sta- 2 mizationevolved equations from the of GUT the Higgs scale down potential, to MSUSYmS. Itcan also then yields, be marize ourtistical findings approach in Sec. andV. our construction of the likelihoods fortradedin for thetan limit (the0 ratio, and of with thes vev’sfixed, of effectively the neutral the the BR Bs þÀ signal, the CMS razor 4:4=fb, and CMSSM plus! a singlet and singlino fields that both the CMSð Higgs! searches.Þ In Sec. IV we present the resultscomponents of the Hu and Hd fields) and either sgn eff or .decouple We choose fromsgn the rest offor the conventional spectrum. Through analogy theð mini- withÞ II.from THE our NMSSM scans and WITH discuss GUT-SCALE their novel features. We sum- mization equations ofeff the Higgs potential, m2 can then be the CMSSM. Both ðand tanÞ are defined at MS . Our marize ourUNIVERSALITY findings in Sec. V. traded for tan (the ratio of the vev’s of theSUSY neutral choicecomponents of the parameter of the H spaceand H is thefields) same and as either the onesgn used The NMSSM is an economical extension of the MSSM, by one of us in a previousu Bayesiand analysis [31], of whichð effÞ II. THE NMSSM WITH GUT-SCALE or . We choose sgn eff for conventional analogy with in which one adds a gauge-singlet superfield S whose ð Þ UNIVERSALITY this paperthe CMSSM. is, in some Both sense, and tan an update.are defined Of course, at MSUSY there. Our scalar component couples only to the two MSSM Higgs exist differentchoice of possibilitiesthe parameter that space have is the been same explored as the one in used the The NMSSM is an economical1 extension of the MSSM, doublets Hu and Hd at the tree level. The scale-invariant literature.by one Some of us authors in a previous have Bayesian studied the analysis more [31 constrained], of which in which one adds a gauge-singlet superfield S whose superpotential of the model has the form versionthis of paper the CNMSSM, is, in some characterized sense, an update. by m Of2 course,m2 [ there26]. scalar component couples only to the two MSSM Higgs exist different possibilities that have been exploredS ¼ 0 in the 1 But it is also true that the underlying assumption employed doublets Hu and Hd at the tree level. The scale-invariant literature. Some authors have studied the more constrained superpotential 3 of the model has the form here, of a different treatment of the singlet field2 by2 the W SHuHd S MSSM Yukawa terms ; (1) version of the CNMSSM, characterized by mS m0 [26]. ¼ þ 3 þð Þ SUSYBut breaking it is also mechanism, true that the underlying would allow assumption for freedom¼ employed in 3 A athere, the GUT of a scale different [39]. treatment We will of give the some singlet comment field by the in W SHuHd S MSSM Yukawa terms ; (1) where and ¼ are dimensionlessþ 3 þð couplings. UponÞ the ConclusionsSUSY breaking about mechanism, the possible would impact allow of for relaxing freedom the in spontaneous symmetry breaking, the scalar Higgs field S unificationA at the condition GUT scale for [A39.]. We will give some comment in where and are dimensionless couplings. Upon the Conclusions about the possible impact of relaxing the develops a vev, s S , and the first term in Eq. (1) unification condition for A . assumes thespontaneous role of theh symmetryi effective breaking,-term the of scalar the MSSM, Higgs field S III. STATISTICAL TREATMENT OF develops a vev, s S , and the first term in Eq. (1) EXPERIMENTAL DATA s. The soft SUSY-breaking h i terms in the Higgs III. STATISTICAL TREATMENT OF eff ¼ assumes the role of the effective -term of the MSSM, sector are then givens. by The soft SUSY-breaking terms in the Higgs We explore the parameterEXPERIMENTAL space of DATA the model with the eff ¼ sector are then given by help ofWe Bayesian explore the formalism. parameter We space follow of the the model procedure with the 1For simplicity we will be using the same notation for super- outlinedhelp in of detail Bayesian in our formalism. previous We papers follow [30 the,40 procedure,41], of fields and their1For bosonic simplicity components. we will be using the same notation for super-whichoutlined we give in a detail short in summary our previous here. papers Our aim [30 is,40 to,41 map], of fields and their bosonic components. which we give a short summary here. Our aim is to map
115010-3 115010-3 Neutralino dark matter 4 Neutralino dark matter with decoupled (heavy) sfermions
4 tan β=10 4 tan β=10 Excluded by LEP, 3 HESS3 , LUX D D 2 2 TeV TeV @ @ 2 2 M M All can be tested 1 by1 LZ, CTA, and a 100-TeV pp 0 collider40
4 D 3 3 3 4 2 2 2 1 TeV 0 @
-1 1 1 -2 1 3 4 M -4 -3 m TeV M 1 2 1 LSP mass 0 TeV 0 -2 -1 -4 -3 mχ 0= ●0.1 |●0.2 |●0.5 |●1.0 |●1.5 |●2.0 |●2.5 TeV m TeV 1 Wino fraction of LSP @ @ D No Sommerfeld = ● ●<0.01 | ●0.1 | ●0.3 | ●0.5 | ●0.7 | ●0.9 | ●0.95 |●>0.99 D Baer, Nanopoulos @ D Bramante, Desai, Fox, Martin, Ostdiek, Plehn 2015 (Thursday) Figure 1. Left panel: Combinations of neutralino mass parameters M1,M2,µthat produce the correct relic abundance, accounting for Sommerfeld-enhancement, along with the LSP mass. The relic surface without Sommerfeld enhancement is underlain in gray. Regions excluded by LEP are occluded with a white box. Right panel: The wino fraction of the lightest neutralino. sfermions are also motivated by models of split supersymmetry, where most scalar supersymmetric partners are decoupled [58–71].
1 Neutralinos in the MSSM are mixtures of the spin- 2 superpartners of the weak gauge bosons, hypercharge gauge bosons, and Higgs bosons. After electroweak symmetry is broken, the neutral and charged states mix to form neutralinos and charginos, respectively. We identify the neutralinos 0 ˜ ˜0 ˜ 0 ˜ 0 ˜ ˜ ˜ ˜ ˜ 0 ˜ 0 as ˜i = Nij(B,W , Hu, Hd ) and the charginos as ˜i± = Vij(W ±, H±). Here B,W,Hd , Hu, are the bino, wino, and higgsino fields; Nij and Vij are the neutralino and chargino mixing matrices in the bino-wino basis, such that i and j index mass and gauge respectively [72]. The bino, wino, and higgsino mass parameters are M1,M2, and µ, and tan defines the ratio of up- and down-type Higgs boson vacuum expectation values in the MSSM.
Assuming that all scalar superpartners are heavy, when the universe cools to Trad < TeV during radiation dominated expansion, MSSM neutralinos freeze out to a relic abundance determined by their rate of annihilation to Standard Model particles. For neutralinos with masses below 1 TeV, it is often su cient to use tree-level annihilation cross-sections and ignore the initial state exchange of photons and weak bosons between annihilating neutralinos. On the other hand, the exchange of gauge bosons between two initial-state particles can substantially alter the annihilation probability of neutralinos with masses above 1 TeV. At threshold this higher-order correction can diverge like 1/v,wherev is the relative velocity of the two incoming states. For a Yukawa-like potential, mediated for example by a Z-boson, this e↵ect is cut o↵ at v m /m , leading to large e↵ects for ⇡ Z ˜ a large ratio of LSP vs weak boson masses. This non-relativistic modification of the potential of two incoming states is called the Sommerfeld e↵ect. For freeze-out temperatures below the mass of electroweak bosons (Tfreeze-out m ˜/20 . 0.1 TeV), and thus for lighter LSPs, the contribution of ⌘ m /T W ± exchange to the e↵ective potential of neutralino pairs is suppressed by factors of e W rad [56]. To understand when the Sommerfeld enhancement will a↵ect the freeze-out of mixed neutralinos, it is useful to first consider the thermal relic abundance of pure neutralino states. With decoupled scalars, two neutralinos or charginos can either annihilate through an s-channel Z or Higgs boson, or through a t-channel neutralino or chargino. For the lightest neutralinos the relevant couplings QCD axions QCD axions as dark matter
Hot Produced thermally in early universe 8 Important for ma>0.1eV (fa<10 ), mostly excluded by astrophysics
Cold Produced by coherent field oscillations around minimum of the axion potential (Vacuum realignment)
Produced by decay of topological defects
(Axionic string decays) Still a very complicated and matsu et al 2012 uncertain calculation!e.g. Hira QCD axions as cold dark matter
10-12 18 10 qi=0.0001
q =0.001 16 i 10 Axion Isocurvature 10-9 Fluctuations
D qi=0.01 D 1014 PQ symmetry breaks before inflation ends eV @ GeV
@ q =0.1 i -6 a PQ symmetry breaks after inflation ends
a 10 m f 1012 ADMX W > W qi=1 p a c 2 H I mass axion 10 = -3 Fraction of axion 10 f a 10 ê density from decays of 108 White Dwarfs Cooling Time topological defects 104 106 108 1010 1012 1014 PQ symmetryPQ scale breaking 6/7 HI GeV m = (71 2) µeV (1 + ↵ ) a ± d Expansion rate at end of inflation @ D Sikivie (today), Visinelli, Gondolo 2009, 2014 Carosi, Brubaker, Baer (Thursday) Anapole dark matter Anapole dark matter
The anapole moment is a C and P violating, but CP-conserving, electromagnetic moment Zeldovich 1957
First measured experimentally in Cesium atoms Wood et al 1997
Anapole dark matter spin-1/2 Majorana fermion Excluded g µ 5 ⌫ = ¯ @ Fµ⌫ DAMA L 2⇤2 g H = ~ ~ B~ ⇤2 · r⇥
Direct detection limits with standard dark halo
Del Nobile, Gelmini, Gondolo, Huh 2014 Anapole dark matter 2 2 d 2m e g 2 2 2 2 = 2 2 v vmin FL(ER)+FT (ER) dER ⇡v ⇤ h i
Excluded For anapole dark DAMA matter, the lowest DAMA bins may be compatible with null searches
The modulation amplitude would need to be large
Del Nobile, Gelmini, Gondolo, Huh 2014 Scalar phantoms Scalar phantom dark matter
“Gauge singlet scalar dark matter” Minimalist dark matter “Singlet scalar dark matter” “Scalar singlet dark matter” do not confuse with minimal dark matter “Scalar Higgs-portal dark matter” “The minimal model of dark matter”
Gauge singlet scalar field S stabilized by a Z2 symmetry (S→−S)
1 µ 1 2 2 S 4 2 = @ S@ S + µ S S H†HS L 2 µ 2 S 4 HS
Silveira, Zee 1985 Andreas, Hambye, Tytgat 2008 Djouadi, Falkowksi, Mambrini, Quevillon 2012 Cline, Scott, Kainulainen, Weniger 2013 “Scalar phantom” is the original 1985 name Scalar phantom dark matter
101
Fermi
100
WS < WDM LUX 2 -1 a HS 10 Invisible
Higgs decays
10-2 WS > WDM
10-3 50 100 150 200 250 300
mS GeV
Figure 1. AlongNot theexcluded cyan line the by real LUX scalar at singlet mS gives ≈60 the GeV correct and dark m matterS >1 relic TeV abundance. The region belowNo density this line corresponds rescaling to overabundance and is excluded, while most of the region above is excluded by experimental constraints. The@ strongestD limits are from direct detection (LUX [37]): they exclude the region above the blackFeng, line. GoingProfumo, to masses Ubaldi below 201 a5 few GeV the most important constraint comes from invisible Higgs decays searches [40], which exclude the region above the purple line. We show several lines for the constraints from gamma-ray line searches (Fermi [38]): the plain lines correspond to the annihilation SS , the dashed lines to SS Z. If density is rescaled according! to ΩS, LUX and ! The colors correspond to di↵erent dark matter density profiles: red is for Einasto, blue for NFW, green for Isothermal.FERMI Fermi exclusion excludes the regions area above these are lines. very The onlydifferent small region which is not yet excluded is the white area on the lower left part of the plot, close to the resonance mS = mh/2. We zoom into the resonant region in Fig.Cline,2. Scott, Kainulainen, Weniger 2013
where µ2 < 0, is the quartic coupling for the Higgs, and ( µ2/ )1/2 = v. This potential is bounded from below, at tree level, provided that ,b 0, and b a2 for negative a . 4 4 2 2 The singlet mass is, at tree level,
2 2 mS = b2 + a2v . (2.3)
The phenomenology of this model is completely determined by the parameters a2 and b2 (or mS), since the self-interaction quartic coupling b4 does not play any phenomenologically observable role (see e.g. [26, 39]). In this paper we study experimental bounds on the two-dimensional parameter space a ,m and we update the results of our previous work [26]. Since then, the Higgs has { 2 S} been discovered [35, 36], thus its mass is no longer a free parameter. In addition, we also now have constraints on the invisible Higgs decay h SS [40–42], and both direct [37] ! and indirect [38] detection limits have improved significantly.
–3– 750-GeV portal The 750-GeV resonance at the LHC
A possible spin-0 resonance decaying into a pair of photons
104 ATLAS Preliminary Data 103 -1 Background-only fit CMS Preliminary 2.6 fb (13 TeV)
Events / 40 GeV EBEB category 102 s = 13 TeV, 3.2 fb-1 2.6σ excess in CMS 102
10 10
Events / ( 20 GeV ) Data 1 1 Fit model ± 1 σ 10−1 10-1 ± 2 σ 200 400 600 800 1000 1200 1400 1600 15 10 mγγ [GeV]
5 stat 4 0 σ 2 −5 0 −10 -2 2σ excess in ATLAS -4 −15 (data-fit)/ Data - fitted background 2 2 2 3 3 200 400 600 800 1000 1200 1400 1600 3×10 4×10 5×10 10 2×10 mγ γ (GeV) mγγ [GeV] ATLAS note CONF-2015-081 (2015/12/15) CMS PAS EXO-15-004 (2015/12/18)
There are many models and analyses relating the 750-GeV resonance to dark matter, too numerous to list here. 750-GeV portal with Majorana dark matter D’Eramo, de Vries, Panci 1601.01571
� �� ��� Scalar resonance �� ��������� �� ��������� ����� ������ -� ����� ������ �χ� · ���/Λ = �π ��� Excluded gg S �� �χ� = �π
� σ �� � ± � ! ! - = ������ Ω��� c σ GG ��� ± � a µ⌫ � = ������ c SS ¯ + SG G � Ω��� µ⌫ a �� ��� Excluded ⇤ � χ
Λ �
-� � )/ Γ�/�� = ���%(���/Λ≃���� ��� )
�� -� � �� �+��� (�χ� = ����) ��
· ��� � �� ��������� Strongest constraints from χ Γ /� = �% (� /Λ ≃ ���� ���-�) � � � �� - ( �� � -� ��������� -� invisible width, jets, and LUX �� ���� ���-�≲ � /Λ≲���� ���-� ���/Λ = ���� ��� �� �� -� -� -� -� -� �� ���⨯�� ��� ≲ ���/Λ≲���� ��� ���/Λ≃��� ⨯ �� ��� ���/Λ = � ���/Λ = � -� ��-� �� � � Can be fully probed by LZ �� ��� �� �� �� ���� �� ��� �� ���� �� ���
Figure 8: Same as Fig. 7 but for the gluon fusion case.Figure The 6: indirect DM analysis detection in the constraints gluon fusion in regime. The notation is the same as in Fig. 5. � � �� 1 �� the right�� panel ��������� are given for cBB/⇤ 0.01 TeV . Pseudoscalar resonance ' �� ��������� ����� ������ ����� ������ -� and we show results for this scenario in Fig. 6. The couplings to gluons for a scalar mediator is �χ� · ���/Λ = �π ��� Excluded responsible for�χ� = quite�π large direct detection rates. As an example, the RG analysis in Section (3.2) gg P the (m�� ,c ScBB/⇤) plane of Fig. 7. A thermal relic consistent with S 45 GeV then requires �� 2 46 2 � yields a direct detection' cross section SI c S 2.2 10 cm for m =1TeVandcGG/⇤ ! ! c - S 2.42. If resonance e↵ects are����� negligible, the relic density line is a universal function of Ω 1 ����� ' ⇥ · ' ' �� ���� � � 0.03 TeV . Limits from mono-jet events are not relevant in this DM mass range (see Eq. (40)). c ScBB/⇤ and we have explicitly= checked that����� this rescaling invariance works perfectly for lower c˜ � ������ GG a µ⌫ The thermal����� relic line for m �
)/ -� ⇤ Γ�/�� = ���%(���/Λ≃���� ��� ) � value of c S suddenly drops and a thermal relic is consistent with LUX bounds. However, the
relic�� with-� S mS. As can be seen from Figs. 3 and 4, this corresponds to a larger coupling
� ��
· �+���'(� = ����) entire parameter space will be deeply probed by LZ. Although the results in Fig. 6 are presented cBB/⇤ 0.53 TeV,χ� and a thermal relic would then require c S 6.77. The net result on the � �� ��������� χ ' Γ /� = �% (� /Λ ≃ ���� ���-�) for a fixed value' of c /⇤,itisstraightforwardtorescaletheresults.DDboundsscalelinearly Strongest constraints from � � � �� GG relic( density is a combination of two e↵ects: a large overall coupling in the cross section and a ��-� -� with cGG/��������� ⇤.Thisistruealsoforthethereliclinebutonlyform Proposed as solution to ‘cusp vs core’ and ‘too big to fail’ puzzles in collisionless dark matter simulations. Spergel, Steinhardt 1999 Tested on cluster and galaxy collisions σ/m < 0.7 cm2/g mass loss in Bullet Cluster Randall et al 2008 σ/m < 0.47 cm2/g 72 cluster collisions Harvey et al 2015 σ/m = (1.7±0.7)×10-4 cm2/g in Abell 3827 (?) Massey et al 2015 Several particle models exist Light mediator Feng, Kaplinghat, Yu; Buckley, Fox 2009; Tulin, Yu, Zurek 2013 Hidden vector dark matter (HVDM) Hambye 2008 Dark matter is 3 gauge bosons of a hidden SU(2) group spontaneously broken by a hidden Higgs doublet coupled to the SM Higgs. Allowed in some regimes Bernal et al 2015 Yu, Bullock, Boddy (Thursday) 1 barn/GeV = 0.6 cm2/g Dynamical dark matter 11 Dynamical dark matter KEITH R. DIENES AND BROOKS THOMAS PHYSICAL REVIEW D 85, 083523 (2012) yields the relation d R3 pd R3 , from which it im- Dienes, Thomas 2011, 2012 ð Þ¼À ð Þ 3 3 effective total abundance (w>0) mediately follows that p dR =R d or Dienes, Kumar, Thomas 2012, 2013 3 p d logR d. Recognizingð þ Þ p ¼À1 w total abundance Significance: tot andð þd logÞR Hdt¼Àwhere H is the Hubbleþ parameter,¼ð þ weÞ Σ Σ Σ Σ Σ 1 2 A vast 3ensemble of4 fields 5 thus have ¼ log(abundance) decaying from one to another d log FIG. 2: Contours of the minimum significance level with which agivenDDMensembleisconsistentwithAMS-02data, 3H 1 w : (6) − − individual component abundances plotted within the (m0, α + γ)DDMparameterspaceforα = 3(leftpanel)andα = 2(rightpanel).Thecolored (each with w=0) ð þ Þ¼À dt regions correspond to DDM ensembles which successfully reproduce theExample: AMS-02 data Kaluza-Klein while simultaneously tower satisfying of all of the applicable phenomenological constraints outlined in Sect. IV, while theaxions white regions in extra-dimensions of parameter space correspond toDDM This is a completely general relation which makes no ensembles which either cannot simultaneously satisfy theseconstraintsorwhichfailtomatchtheAMS-02positron-excess data individual assumptions about the time-(in)dependence of w.We states at the 5σ significance level or greater. The slight difference between the results shown in the two panels is a consequence of decay may therefore take this to be our fundamental definition the differences in the CMB constraints for the two corresponding values of α. for weff t —i.e., matter− ð Þ dominated log(time) 1 d logtot weff t 1 FIG. 2. A sketch of the total dark-matter abundance in our ð ÞÀ3H dt þ scenario during the final, matter-dominated era. Even though 1 d log tot for RH=MD eras eachPhenomenology dark-matter component individually has w 0 , the spec- 2 d logt mn = m0 + n m, À trum of lifetimes and abundances of these components¼ conspire 8 (7) obtained through ¼ > to produce a time-dependent total dark-matter↵ abundance > 2 d log tot 1 for RD era. ⇢n m , ⌧n m tot < 3 d logt 3 whichscaling corresponds laws to an effective equation⇠ n of state with⇠ w>n 0. À þ > Note that while:> our derivation has thus far been completely in all cosmological eras, the presence of an effective weff general, we have specialized to specific cosmological eras which differs (however slightly) from zero would then in passing to the final expressions in Eq. (7). Specifically, Thissignify model a departure can fit from the traditional dark-matter we have written and taken 3H =t where tot ¼ tot crit thescenarios. positron excess 2 (RH=MD), 3=2 (RD). ¼ ¼ andWe has can no also cut understand off. this at a mathematical level. The The final expressions in Eq. (7) are easy to interpret fact that each individual dark-matter component has an physically, since the double-logarithmic derivatives which abundance which follows the behavior in Eq. (1) with w appear in these expressions are nothing but the slopes in the FIG. 3: Predicted combined fluxes Φe+ + Φe− (left panel) and positron fractions Φe+/(Φe+ + Φe− )(rightpanel)corresponding ¼ 0 does not guarantee that their sum tot must follow the sketches in Figs. 1 and 2. However, the important point of to the DDM parameter choices lying within those regions of Fig. 2 for which our curves agree with AMS-02 data to within 3σ. same behavior. Indeed, the two effects which can alter the this derivation has been to demonstrate that weff defined as These curves are therefore all consistent with current combined-flux data to within 3σ and also consistent with current positron- fraction data to within 3σ (with the color of the curve indicating the precise quality offit,usingthesamecolorschemeintime-evolution of the sum tot in our scenario are a pos- in Eq. (7) continues to have a direct interpretation as a true Fig. 2). These curves are also consistent with all other applicable phenomenological constraints discussed in Sect. IV.However,sible staggered turn-on at early times, and the individually equation-of-state parameter relating energy density and ∼ despite these constraints, the behavior of the positron-fraction curves beyond Ee± 350 GeV is entirely unconstrained except decaying dark-matter components at late times. Thus pressure, even when weff is time-dependent. No other by the internal theoretical structure of the DDM ensemble. Their relatively flat shape in this energy range thus serves as a the time-dependence of need not necessarily follow definition of weff would have had this property. prediction (and indeed a “smoking gun”) of the DDM framework.DatafromAMS-02[1],HEAT[2],AMS-01[3],PAMELA[6], tot Eq. (1) with w 0. The results in Eq. (7) provide a relation between weff and FERMI [7, 9], PBB-BETS [45], ATIC [46], and HESS [47] are also shown for reference. ¼ One possibility, of course, is that will continue to tot t . However, it is also possible to derive a similar tot ð Þ follow Eq. (1), but with some other effective value weff. relation between weff and . Assuming that we restrict However, even this outcome requires that our individual our attention to periods of time after all staggered turn- dark-matter components exhibit certain relationships ons are complete (so that the identity of the dark-matter between their abundances and lifetimes which need not component associated with 0 is fixed), it trivially follows actually hold for our dark-matter ensemble. Therefore, in from the definition of in Eq. (5) that general, we expect that tot might exhibit a time- dependence which does not resemble that given in d log tot RH=MD eras d log 1 À d logt Eq. (1) for any constant weff. Or, to phrase this somewhat ð À Þ 8 (8) differently, we expect that in general, our effective d logt ¼ > d log tot 1 RD era: < À d logt þ 2 equation-of-state parameter weff might itself be time- :> dependent. We therefore seek to define a function weff t Using the results in Eq. (7), we therefore find that which parametrizes a time-dependent equation of state forð Þ our dynamical dark-matter ensemble as a whole. 1 d log 1 ð À Þ RH=MD eras In order to define such an effective function w t , let us 2 d logt effð Þ w t 8 (9) first recall that the traditional parameter w is fundamentally eff > ð Þ¼> 2 d log 1 defined through the relation p w where p and are, < 3 d logð Àt Þ RD era: ¼ respectively, the pressure and energy density of the ‘‘fluid’’ > in question. Of course, in an FRW universe with radius R, It therefore follows:> that decreasing corresponds to posi- the conservation law for energy density dE pdV tive w , and vice versa. As a self-consistency check, we ¼À eff 083523-8 Asymmetric dark matter Asymmetric dark matter • Dark matter in a hidden mirror sector (“dark sector”) • Dark matter asymmetry similar to baryon asymmetry, generated by similar mechanisms n n ⇡ p • Dark matter mass is a few times the proton mass m ⌦ ⌦p (a few) ⌦p ⇡ mp ⇡ Nussinov 1985; Gelmini, Hall, Lin 1986; Hooper, March-Russell, West 2008; Kouvaris 2008; Kaplan, Luty, Zurek 2009; Hall, March-Russell, West 2010; Buckley, Randall 2010; Dutta, Kumar 2011; Cohen, Phalen, Pierce, Zurek 2010; Falkowski, Ruderman, Volansky 2011; Frandsen, Sarkar, Schmidt-Hoberg 2011; etc. Model-agnostic dark matter All particle physics models - Consider all possible interactions between dark matter and standard model particles - This program has been carried out in some limits (e.g., contact interactions, non-relativistic kinematics) χ χ Four-particle effective operators (mediator mass ≫ exchanged energy) O q,g q,g There are many possible operators. Interference is important although often neglected. Long-distance interactions are often not included. Effective operators: LHC & direct detection Name Operator Coefficient 3 Name Operator Coefficient D1 χχ¯ qq¯ mq/M∗ † 2 5 3 C1 χ χqq¯ mq/M∗ D2 χγ¯ χqq¯ imq/M∗ † 5 2 5 3 C2 χ χq¯γ q imq/M∗ D3 χχ¯ q¯γ q imq/M∗ † µ 2 5 5 3 C3 χ ∂µχq¯γ q 1/M∗ D4 χγ¯ χq¯γ q mq/M∗ † µ 5 2 C4 χ ∂µχq¯γ γ q 1/M µ 2 ∗ D5 χγ¯ χq¯γµq 1/M∗ C5 χ†χG Gµν α /4M 2 µ 5 2 µν s ∗ D6 χγ¯ γ χq¯γµq 1/M∗ † µν 2 C6 χ χGµν G˜ iαs/4M µ 5 2 ∗ D7 χγ¯ χq¯γµγ q 1/M∗ R1 χ2qq¯ m /2M 2 µ 5 5 2 q ∗ D8 χγ¯ γ χq¯γµγ q 1/M∗ R2 χ2q¯γ5q im /2M 2 µν 2 q ∗ D9 χσ¯ χq¯σµν q 1/M∗ 2 µν 2 5 2 R3 χ Gµν G αs/8M∗ D10 χσ¯ µν γ χq¯σαβq i/M∗ R4 χ2G G˜µν iα /8M 2 µν 3 µν s ∗ D11 χχ¯ Gµν G αs/4M∗ 5 µν 3 D12 χγ¯ χGµν G iαs/4M∗ Table of effective operators relevant for ˜µν 3 D13 χχ¯ Gµν G iαs/4M∗ the collider/direct detection connection 5 ˜µν 3 D14 χγ¯ χGµν G αs/4M∗ Goodman, Ibe, Rajaraman, Shepherd, Tait, Yu 2010 TABLE I: Operators coupling WIMPs to SM particles. The operator names beginning with D, C, RapplytoWIMPSthatareDiracfermions,complexscalarsorreal scalars respectively. III. COLLIDER CONSTRAINTS A. Overview We can constrain M∗ for each operator in the table above by considering the pair pro- duction of WIMPs at a hadron collider: pp¯(pp) χχ + X. (2) → Since the WIMPs escape undetected, this leads to events with missingtransverseenergy, recoiling against additional hadronic radiation present in the reaction. The most significant Standard Model backgrounds to this process are events where a Z boson decays into neutrinos, together with the associated production of jets. This back- ground is irreducible. There are also backgrounds from events where a particle is either missed or has a mismeasured energy. The most important of these comes from events pro- 7 Effective operators: LHC & direct detection LHC limits on WIMP-quark and WIMP-gluon interactions are competitive with direct searches Beltran et al, Agrawal et al., Goodman et al., Bai et al., 2010; Goodman et al., Rajaraman et al. Fox et al., 2011; Cheung et al., Fitzptrick et al., March-Russel et al., Fox et al., 2012...... 16 10-36 Spin-independent monojet PICASSO 10-35 10-38 m razor c g c q gm q These bounds do not combined DAMA XENON 10 DAMA D 2 D -40 H L I M apply to SUSY,q ±etc.33 % 2 10 -37 COUPP CoGeNT q ± 33 % 10 cm cm monojet @ @ SIMPLE SI razor SD -42 s CRESST H L 10 combined H L s Complete theories contain sums CDMS -39 10 m 5 5 of operatorsc g g c (interference)q gm g q and 10-44 XENON - 100 not-so-heavy mediators (Higgs) m mn Spin-dependent c g c as Gmn G Spin-independent -41 I M I M 10-46 10 0.1 1 10 100 1000 0.1 1 10 100 1000 H L I mM c GeV mc GeV Fox, Harnik, Primulando, Yu 2012 FIG. 6: Razor limits on spin-independent@ D (LH plot) and spin-dependent@ (RHD plot) DM-nucleon scattering compared to limits from the direct detection experiments. We also include the mono- jet limits and the combined razor/monojet limits. We show the constraints on spin-independent scattering from CDMS [2], CoGeNT [36], CRESST [37], DAMA [38], and XENON-100 [3], and the constraints on spin-dependent scattering from COUPP [39], DAMA [38], PICASSO [40], SIM- PLE [41], and XENON-10 [42]. We have assumed large systematic uncertainties on the DAMA quenching factors: q =0.3 0.1 for sodium and q =0.09 0.03 for iodine [43], which gives Na ± I ± rise to an enlargement of the DAMA allowed regions. All limits are shown at the 90% confidence level. For DAMA and CoGeNT, we show the 90% and 3 contours based on the fits of [44], and for CRESST, we show the 1 and 2 contours. energy required to create a pair of DM is higher. In addition to the direct detection bounds, we can also convert the collider bounds into a DM annihilation cross-section, which is relevant to DM relic density calculations and indirect detection experiments. The annihilation rate is proportional to the quantity v , where h reli is the DM annihilation cross section, vrel is the relative velocity of the annihilating DM and . is the average over the DM velocity distribution. The quantity v for and h i rel OV OA operators is 5 1 m2 8m4 4m2 m2 +5m4 v = 1 q 24(2m2 + m2)+ q q v2 (14) V rel 16⇡⇤4 m2 q m2 m2 rel q s q X ✓ ◆ 1 m2 8m4 22m2 m2 +17m4 v = 1 q 24m2 + q q v2 (15) A rel 16⇡⇤4 m2 q m2 m2 rel q s q X ✓ ◆ 5 A comprehensive study of di↵erent types of operators can be found in Ref. [8]. of particles of spin one or less (i.e. at most quadratic in either S~ or ~v). In any Lorentz-invariant local quantum field theory, CP-violation is equivalent to T-violation, so let us first consider operators that respect time reversal symmetry. These operators are 1, S~ S~ ,v2,i(S~ ~q) ~v, i~v (S~ ~q), (S~ ~q)(S~ ~q) (4) · N ⇥ · · N ⇥ · N · ~v? S~ , ~v? S~N ,iS~ (S~N ~q). of particlesEffective of spin one or less (i.e.operator at most quadratics: indirect either S~ or ~vdetection). In any Lorentz-invariant· · · ⇥ local quantum field theory, CP-violation isThe equivalent operators to T-violation, in the first line so let of useq. first (4) are consider parity conserving, while those of the second line operators thatAll respectnon-relativistic time reversal contact symmetry.are operators parity These violating. operators classified In are addition, there are T-violatingFitzpatrick operators:et al. 2012 2 1, S~ S~ ,v,i(S~ ~q) ~v, i~v (S~ ~q), (S~ ~q)(S~ ~q) iS~N ~q,(4) iS~ ~q, (5) · N ⇥ · · N ⇥ · N · · · ~v? S~ , ~v? S~ ,iS~ (S~ ~q). (iS~N ~q)(~v? S~ ), (iS~ ~q)(~v? S~N ). · · N · N ⇥ · · · · The operators in the first line of eq. (4) are parityIn order conserving, to determine while those the interaction of the second of DM line particles with the nucleus, the above oper- are parity violating.Global analysis In addition, there are T-violatingators need operators:to be insertedExperimental between nuclearlimits states. Experimentally, the relevant question is thus what sort of nuclear responses these operators illicit when DM couples to the nucleus. Catena, Gondolo 2014 iS~ ~q, iS~ ~q, Schneck et al. (SuperCDMS) 2015(5) N ·We find · that there are six basic responses corresponding to single-nucleon operators labeled 40 ~ 200 ~ ~ ~ ˜ (iSN ~q)(~v? S M),J;(p,niS, ⌃~qJ0 )(;p,n~v?, ⌃SJ00N;p,n)., J;p,n, J0 ;pn, J00;p,n in our discussion of section 3. Five of these re- 20 · 100 · · · 2 v 2 v sponses (MJ;p,n, ⌃0 , ⌃00 , J;p,n, 00 )ariseinCPconservinginteractions(duetothe m m 0 J;p,n J;p,n J;p,n 0 5 3 c In order toc determine the interaction of DM particles with the nucleus, the above oper- -20 -100 exchange of spin one or less), and we therefore primarily focus on this smaller set. Although a ators need to be inserted between nuclear states. Experimentally, the relevant question is -40 -200 certain CP-violating interaction can be viable (see section 6), finding a UV-model which will thus what sort- of0.02 nuclear-0.01 0.00 responses0.01 0.02 these operators-5 0 illicit5 when DM couples to the nucleus. 2 2 ˜ c m resultc4m in the response J0 ;pn seems more challenging. In this paper we provide form factors in We find that there are six1 v basic responses correspondingv to single-nucleon operators labeled 3000 detail for some commonly used elements, however, it is useful to have a heuristic description 200 MJ;p,n, ⌃0 2000, ⌃00 , J;p,n, ˜ 0 , 00 in our discussion of section 3. Five of these re- J;p,n J;p,n J;pn J;p,n for the responses. M is the standard spin-independent response. ⌃0, ⌃00 are the transverse 1000 100 2 v sponses (MJ;p,n, ⌃J0 ;p,n, ⌃J00;p,n, J;p,n2 v , J00;p,n)ariseinCPconservinginteractions(duetothe m m 0 0 9 6 and longitudinal (with respect to the momentum transfer) components of the nucleon spin c c exchange of spin-1000 one or less), and we therefore primarily focus on this smaller set. Although a -100 (either p or n). They favor elements with unpaired nucleons. A certain linear combination -2000 certain CP-violating interaction can be-200 viable (see section 6), finding a UV-model which will -3000 of them is the usual spin-dependent coupling. at zero-momentum transfer measures the -10 -5 ˜ 0 5 10 -10 -5 0 5 10 result in the response J0 ;pn2 seems more challenging.c m2 In this paper we provide form factors in c4mv net angular-momentum8 v of a nucleon (either p or n). This response can be an important detail for some commonly used elements, however, it is useful to have a heuristic description LUX m = 10 TeVcontribution0 to the coupling of DM to elements with unpaired nucleons, occupying an orbital Figure 4. 95% CL profile-likelihood upper limits on the coupling constants ci (i =1, 3,...,11) that for the responses.can in principle exhibitM correlations,is the for standard the LUX experiment spin-independent and a dark matter particle mass m = response. 10 ⌃0, ⌃00 are the transverse 0 0 0 0 TeV. There is negligible correlation between c4 and c5 and between shellc8 and c9, with positive correlation non-zero angular momentum. Finally, 00, at zero-momentum transfer is related to 0 0 0 0 and longitudinalbetween c1 and (withc3, and negative respect correlation betweento thec4 and momentumc6. transfer) components of the nucleon spin (L~ S~)n,p. It favors elements with large, not fully occupied, spin-partner angular-momentum 0 0 · (either p orfor an given). experiment They at favor a given m elements and ⌘ are ellipses with in the ci unpairedorbitals–cj plane. These (i.e. ellipses nucleons. can when Aorbitals certainj linear= ` combination1 are not fully occupied). As all these responses view be obtained without random sampling in parameter space by writing ± 2 of them is the usual spin-dependent0 2 0 0 coupling.0 2 at zero-momentum transfer measures the aii(ci ) +2aijci cj + ajj(cj ) = µSconstnuclei, di↵erently,(5.4) a completely model independent treatment of the experiments requires data net angular-momentum of a nucleon (either p or n). This response can be an important where µSconst is the desired value of µS (e.g., its upper limit)to and the be coe considered cients aii, aij, for each response separately (up to interference e↵ects). and ajj are obtained using Eqs. (2.3), (2.5), (4.1), (4.2), and (B.1). The relative size of these contributioncoe tocients, the and thus coupling the shape of of the ellipses,DM isto essentially elements fixed by the with nuclear unpaired structure nucleons, occupying an orbital 0Our0 paper is organized as follows. In section 2, we describe in detail the e↵ective field functions W . The correlation coe cient rij for the pair of variables ci and cj follows as shell with non-zero angular momentum. Finally, 00, at zero-momentum transfer is related to aij theory, emphasizing the non-relativistic building blocks of operators and their symmetry rij = . (5.5) ~ ~ paiiajj (L S)n,p. It favors elements with large, notproperties, fully occupied, and demonstrate spin-partner that angular-momentum the operators in (4,5) describe the most general low-energy · Fig. 4 shows the ellipses (5.4) for LUX at m = 101 TeV, with µSconst corresponding to the orbitals (i.e.LUX upper when limit. Weorbitals see that out ofj the= four` possible2 cases,are two exhibitnot negligible fully correlations occupied). As all these responses view (with r = 0.027 and r =0.054), one has positive± correlationtheory (c0 and c0 with givenr =0.90) our assumptions. In section 3, we discuss the relevant nuclear physics, and in 45 89 1 3 13 nuclei di↵erently,and one has negative a completely correlation (c0 and modelc0 with r independent= 0.64). These correlations treatment survive of the experiments requires data 4 6 46 when all experiments are included in the profile likelihood analysis,particular as seen next. we thoroughly analyze the possible nuclear response function in a partial wave to be considered for each response separatelybasis, (up which to interference is the standard e↵ects). formalism for such physics. In section 4, we give an overview of Our paper is organized as follows. In sectionthe various 2, we new describe nuclear in responses,detail the e with↵ective an fieldemphasis on their relative strength at di↵erent – 21 – theory, emphasizing the non-relativistic buildingelements. blocks In section of operators 5, we summarize and their these symmetry results in a format that can be easily read o↵ and properties, and demonstrate that the operators in (4,5) describe the most general low-energy theory given our assumptions. In section 3, we discuss the relevant nuclear physics, and4 in particular we thoroughly analyze the possible nuclear response function in a partial wave basis, which is the standard formalism for such physics. In section 4, we give an overview of the various new nuclear responses, with an emphasis on their relative strength at di↵erent elements. In section 5, we summarize these results in a format that can be easily read o↵ and 4 Summary • There have been many candidates for nonbaryonic dark matter over the years. There seem to be even more now. • Particle physicists do not lack ideas and are able to escape stronger and stronger experimental constraints. • The time is ripe for experiments to conclusively find a particle of dark matter.