Electroweak corrections to the direct detection cross section of inert higgs dark matter
aa r X i v : . [ h e p - ph ] F e b Electroweak corrections to the directdetection cross section of inert higgsdark matter
Michael Klasen ∗ and Carlos E. Yaguna † Institut f¨ur Theoretische Physik, Universit¨at M¨unster,Wilhelm-Klemm-Straße 9, D-48149 M¨unster, Germany
Jos´e D. Ruiz- ´Alvarez ‡ Instituto de F´ısica, Universidad de Antioquia,A.A. 1226, Medell´ın, Colombia
MS-TP-13-01
Abstract
The inert higgs model is a minimal extension of the Standard Modelthat features a viable dark matter candidate, the so-called inert higgs( H ). In this paper, we compute and analyze the dominant electroweakcorrections to the direct detection cross section of dark matter withinthis model. These corrections arise from one-loop diagrams mediated bygauge bosons that, contrary to the tree-level result, do not depend onthe unknown scalar coupling λ . We study in detail these contributionsand show that they can modify in a significant way the prediction of thespin-independent direct detection cross section. In both viable regimesof the model, M H < M W and M H &
500 GeV, we find regions wherethe cross section at one-loop is much larger than at tree-level. We alsodemonstrate that, over the entire viable parameter space of this model,these new contributions bring the spin-independent cross section withinthe reach of future direct detection experiments.
Direct detection is possibly the most promising way of observing and identifyingthe dark matter –that mysterious form of matter that accounts for about 20%of the energy density of the Universe [1]. Direct detection experiments try toobserve, via recoil-energy, the scattering of dark matter particles with nucleiand to determine from it some fundamental properties of the dark matter par-ticle, such as its mass and its interactions. In recent years, these experiments,particularly XENON100 [2, 3], have made outstanding progress in this regardand have started to exclude interesting regions of the parameter space of com-mon models of dark matter –see e.g. [4, 5, 6, 7]. In the near future, planned ∗ [email protected] † [email protected] ‡ Now at IPNL, Lyon, France. jose@gfif.udea.edu.co Z symmetry. The lightest component ofthis doublet becomes automatically stable and, if neutral, a good dark mattercandidate, the so-called inert higgs ( H ). In recent years, the phenomenol-ogy of this model has been extensively studied in a number of works –see e.g.[11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]. In the inert dou-blet model, the tree-level direct detection cross section is determined by a higgs( h ) mediated diagram and will be suppressed whenever the coupling H H h ,which is proportional to a free parameter of this model, becomes small. Sinceat one-loop, H q scattering may proceed entirely via gauge processes ( W ± and Z mediated diagrams), it is not guaranteed that these one-loop corrections willbe smaller than the tree-level result. Motivated by this simple observation, wecalculate and analyze, in this paper, the dominant electroweak corrections tothe direct detection cross section of inert higgs dark matter. We will see thatthey may modify in a significant way the tree-level prediction within importantregions of the viable parameter space, sometimes giving the dominant contri-bution to the spin-independent direct detection cross section. Moreover, theyalways bring this cross section within the reach of future experiments such asXENON-1T.The rest of the paper is organized as follows. In the next section the inertdoublet model of dark matter is briefly reviewed, outlining its parameter spaceand its viable regions. Then, in section 3, we present the calculation of thedominant electroweak corrections to the direct detection cross section of inerthiggs dark matter and show its behavior as a function of the parameters ofthe model. Sections 4 and 5 contain our main results. They demonstrate theimpact of these electroweak corrections within the two viable regimes of themodel: the low mass one ( M H < M W ) in section 4 and the large mass one( M H &
500 GeV) in section 5. In both cases, we identify the regions where thecorrections are expected to be important. To further substantiate our findings,we perform a scan over the entire parameter space of the model and we analyzeit in some detail. Finally, our conclusions are presented in section 6.2
The inert doublet model
The inert doublet model is a simple extension of the Standard Model with oneadditional higgs doublet H and an unbroken Z symmetry, under which H isodd while all other fields are even. This discrete symmetry prevents the directcoupling of H to fermions and, crucial for dark matter, guarantees the stabilityof the lightest inert particle. The scalar potential of this model is given by V = µ | H | + µ | H | + λ | H | + λ | H | + λ | H | | H | + λ | H † H | + λ h ( H † H ) + h . c . i , (1)where H is the Standard Model higgs doublet, and λ i and µ i are real param-eters. Four new physical states are obtained in this model: two charged states, H ± , and two neutral ones, H and A . Either of them could account for thedark matter. In the following, we assume that H is the lightest inert parti-cle, M H < M A , M H ± , and, consequently, the dark matter candidate. Afterelectroweak symmetry breaking, the inert scalar masses take the following form M H ± = µ + 12 λ v ,M H = µ + 12 ( λ + λ + λ ) v ,M A = µ + 12 ( λ + λ − λ ) v , (2)where v = 246 GeV is the vacuum expectation value of H . Let us introduce atthis point the parameter λ defined by λ ≡ ( λ + λ + λ ) / . (3)This parameter is of particular relevance to our direct detection study as itdetermines the coupling H H h , and therefore the tree-level direct detectioncross section –see next section. In addition to λ , it is convenient to take M H , M A , and M H ± as the remaining free parameters of the inert sector. The tree-level direct detection cross section depends also on the higgs mass ( M h ). Giventhe small range to which M h has been constrained by recent data [26, 27], wehave simply set M h = 125 GeV throughout this paper.The new parameters of the inert doublet model are not entirely free, theyare subject to a number of theoretical and experimental constraints –see e.g. [8]and [10]. The requirement of vacuum stability imposes that λ , λ > , λ , λ + λ − | λ | > − p λ λ . (4)LEP data constrain the mass of the charged scalar, M H ± , to be larger than about90 GeV [28] while some regions in the plane ( M H , M A ) are also excluded, see[12]. In addition, the inert doublet, H , contributes to electroweak precisionparameters such as S and T , which must be small to remain compatible withcurrent data. Finally, the relic density of inert higgs dark matter should becompatible with the observed dark matter density [1]. To evaluate Ω h , we haveused micrOMEGAs [29], which automatically takes into account resonances andcoannihilation effects. Into micrOMEGAs we have incorporated the annihilation3 H H H H H H H H H H H H H H H WW WWW WWW H + H + H + A A A Z Z Z ZZ Z Z Zu u u u d u u u u uu d uu u uuduu u u h h
Figure 1:
The Feynman diagrams that give the dominant corrections to the directdetection cross section of inert higgs dark matter. into the three-body final state
W W ∗ ( H H → W W ∗ → W f ¯ f ′ ) which modifiesin a significant way the predicted relic density for M H . M W [19].In previous works [10], it had been found that the dark matter constraintcan not be satisfied for arbitrary values of M H . Two separate regions remainviable , one at low masses and the other at large masses. In the low massregime ( M H . M W ), the annihilation of dark matter is dominated by eitherthe b ¯ b final state or the three-body final state W W ∗ , and may be enhanceddue to the presence of the higgs resonance at M H ∼ M h /
2. Moreover, H - A coannihilations may also play a role in the determination of the dark matter relicdensity. In the large mass regime ( M H >
500 GeV), dark matter annihilateseither into gauge bosons ( W + W − , Z Z ) or into higgses. These annihilationchannels are usually very efficient, so the relic density tends to be suppressed.The observed value of the dark matter density can still be obtained in this regimebut only when the mass splitting between the inert particles is tiny. Since thesetwo dark matter compatible regimes have completely different phenomenologies,we will split our analysis and discuss our main results in two different sections,one dedicated to each regime. Before that, we present, in the next section, thecalculation of the electroweak corrections to the spin-independent cross sectionand obtain some preliminary results. In the inert doublet model, the dark matter direct detection cross section attree-level is given by σ SI (tree-level) = m r π (cid:18) λM H M h (cid:19) f m N , (5)where f is a quark form factor and m r is the reduced mass of the dark matter-nucleon system. This cross section arises from a higgs mediated diagram and Notice that, as anticipated in [20], the new viable region , M W < M H .
150 GeV, hasalready been excluded by the recent XENON100 data [2, 3]. In our numerical evaluations, we use for the quark form factors f q the default values frommicrOMEGAs [29].
200 400 600 800 1000 M H [GeV] σ S I [ pb ] ∆ M = 1 GeV ∆ M = 10 GeV ∆ M = 20 GeV ∆ M = 50 GeV M A = M H + , λ = 0M h = 125 GeV ∆Μ = Μ Α −Μ Η Figure 2:
The purely one-loop contribution to the spin-independent cross section asa function of the dark matter mass for four different values of ∆ M = M A − M H = M H ± − M H : , , , and GeV (from top to bottom). In this figure we have set λ = 0 and M h = 125 GeV . is seen to be proportional to λ . In many models, the tree-level value of σ SI isaccurate enough for most purposes and there is no need to compute electroweakcorrections to it. The inert doublet model, however, may be an exception tothat rule. In fact, in this model not only can the coupling λ be very small (muchsmaller than the gauge couplings), but there are one-loop diagrams mediatedby the gauge bosons that contribute to σ SI which do not depend on λ andare instead entirely determined by the gauge couplings and the masses of theinert particles. It is quite possible, therefore, that the tree-level result, equation(5), fails to give the correct prediction for the spin-independent direct detectioncross section in certain regions of the parameter space. For that reason, in thispaper we compute the dominant electroweak corrections to σ SI and we analyzetheir importance in both the low and the large mass regime of the model. Acalculation similar to this was first presented in [30] and later applied to the inertdoublet model in [31]. It must be emphasized, however, that the model in [30]is not exactly the inert higgs model and that they considered only the regime M DM ≫ M W . Since their results can not be directly used for our study, we havecalculated these corrections ourselves without making any assumptions on themasses of the inert particles. We limit ourselves to those diagrams which mightbecome dominant when λ is small, that is to diagrams mediated by electroweakgauge bosons and independent on λ . The contributing diagrams are shown infigure 1. In the following, we denote by σ SI (tree-level) or simply by σ SI the valueof the spin-independent cross section that is obtained when these diagrams aretaken into account. Notice that these electroweak corrections depend only on5
00 200 300 M A [GeV] σ S I [ pb ] M H + = 100 GeVM H + = 200 GeV M H = 70 GeV, λ = 0M h = 125 GeV
600 650 700 750 800 M A [GeV] σ S I [ pb ] M H + = 650 GeVM H + = 700 GeV M H = 600 GeV, λ = 0M h = 125 GeV Figure 3:
The purely one-loop contribution to the spin-independent cross section asa function of M A for different sets of parameters. In the left panel, we consider alight dark matter particle, M H = 70 GeV , and M H ± = 100 ,
200 GeV . In the rightpanel, a heavy dark matter candidate is considered, M H = 600 GeV , and M H ± =650 ,
700 GeV . In both panels, λ = 0 and M h = 125 GeV . three unknowns : M H , M A , and M H ± . Next, we will numerically study σ SI as a function of these parameters and we will demonstrate that these one-loopcontributions may indeed be larger than the tree-level result.Figure 2 shows the purely one-loop contribution ( λ = 0) to σ SI as a func-tion of M H for four different values of the mass splitting ∆ M = M A − M H = M H ± − M H . From top to bottom, the lines correspond to ∆ M =1 , , ,
50 GeV. Notice that the electroweak corrections give a cross section oforder 10 − pb - 10 − pb depending slightly on the dark matter mass and onthe mass splitting. σ SI initially increases with M H but then reaches a constantvalue for large M H –a result compatible with that found in [30]. It is also clearfrom the figure that σ SI decreases with the mass splitting between the inertparticles.It is also interesting to look at the behavior of σ SI as a function of M A (or M H ± ) for a fixed value of the dark matter mass. In figure 3 we illustratethat for the low mass regime ( M H = 70 GeV, left panel) and the heavy massregime ( M H = 600 GeV, right panel). In each panel two different values of M H ± are considered. In both regimes we find that σ SI decreases with M A andwith M H ± and that it varies between 10 − pb and 10 − pb, as found before.So far in our analysis we have made two important simplifications: i) wehave set λ = 0, or equivalently we have limited ourselves to the purely one-loopcontribution; ii) we have not yet enforced the constraints on the parametersof the inert doublet model. In the next two sections, where our main resultsare presented, we will get rid of these simplifications. Ultimately, what weactually want to know is how important these electroweak corrections are withinthe viable regions of the inert doublet model. In particular, we would like todetermine if they can give the dominant contribution to σ SI and in which regionsthat happens. We also want to know how these corrections modify the prospectsfor the direct detection of dark matter in future experiments. To that end, weshould move away from the λ = 0 limit considered in this section and we shouldensure that σ SI is evaluated only for models that are compatible with all the The total amplitude (tree + one-loop) will depend also on λ and M h . Since the latter isfixed, the total amplitude depends on 4 parameters. M H [GeV] λ M A = M H + 10 GeVM A = M H + 50 GeV M H + = M H + 50 GeVM h = 125 GeV Ω h = 0.11
50 55 60 65 70 75 M H [GeV] σ S I ( - l oop ) / σ S I ( t r ee - l e v e l ) M A = M H + 10 GeVM A = M H + 50 GeV M H + = M H + 50 GeVM h = 125 GeV Ω h = 0.11 Figure 4:
Left: The viable parameter space of the inert doublet model in the plane( M H , λ ) for two different values of M A − M H :
10 GeV (dotted-dashed line) and
50 GeV (dashed line). In this figure, M H ± − M H was set to
50 GeV and M h to
125 GeV . Along the lines, the dark matter constraint, Ω h = 0 . , is satisfied. Noticethat the coupling λ can reach values as small as − . Right: The correction to thespin-independent direct detection cross section as a function of the dark matter massalong the viable regions from the left panel. known phenomenological and cosmological constraints. In this section, we examine the implications of the electroweak corrections to σ SI within the low mass regime of the inert doublet model. To begin with, we show,in the left panel of figure 4, the viable parameter space in the plane ( M H , λ )for M H ± = M H + 50 GeV and two different values of M A − M H : 10 GeVand 50 GeV. Along the lines, the dark matter relic density is compatible withcurrent observations, Ω h = 0 .
11. Since coannihilation effects are importantfor M A = M H + 10 GeV (dash-dotted line) the required value of λ is alwayssmaller than that for M A = M H + 50 GeV (dashed line), where they are not.Close to the higgs resonance, M H = M h / . λ has to be very small to avoid depleting theabundance of dark matter in the early Universe. For M H ∼ −
72 GeV, theannihilation into the three-body final state
W W ∗ [19], a process dominated bythe gauge interactions, is sufficient to account for the observed dark matter so λ must be small to suppress the additional higgs-mediated annihilations (whosestrength increases with λ ). The main lesson from this figure is that there areregions in the viable parameter space of the inert doublet model where the scalarcoupling λ is indeed much smaller than the gauge couplings, reaching values aslow as 10 − .In such regions, we expect the one-loop corrections to modify in a significantway the prediction of the inert higgs direct detection cross section, and perhapsto give a contribution larger than the tree-level one. To illustrate the effect of theelectroweak corrections, in the following we will either compare σ SI (tree-level)with σ SI (1-loop) in the same figure or study their ratio as a function of theparameters of the model.The right panel of figure 4 shows the ratio σ SI (1-loop) /σ SI (tree-level) along7 M H [GeV] σ S I [ pb ] Tree-level1-loop
Xenon100Xenon1T M A = M H + = M H + 50 GeV Figure 5:
A comparison between the tree-level and the one-loop direct detection crosssection for one of the viable regions of figure 4. the viable lines from the left panel. As expected, the correction is large where λ is small and vice versa. We see that the one-loop correction can indeed bemuch larger than the tree-level result, with σ SI (1-loop) /σ SI (tree-level) reachingvalues as high as ∼
30 for M H ∼
71 GeV and ∼
100 for M H ∼ M h /
2. Outsidethese regions, the correction is small but not necessarily negligible and mayeasily account for a 20% increase in σ SI .A direct comparison between σ SI (1-loop) and σ SI (tree-level) is shown infigure 5. Here, we have selected, from the two viable lines discussed in theprevious figure, the one featuring M A = M H + 50 GeV. For illustration, thecurrent bound from XENON100 and the expected sensitivity of XENON-1Tare also displayed. The former already excludes the regions M H >
53 GeVand 64 < M H / GeV <
70 in this parameter space. The effect of the one-loopcorrections is clearly seen close to the higgs resonance, where it prevents thecross section from going below about 10 − pb. A similar effect takes place alsoat the largest allowed value of M H .One may be tempted to conclude, from the above figures, that in the lowmass regime the one-loop corrections to σ SI can become very large only aroundtwo specific values of M H , M h / λ = 10 − , − , − and M H ± = M H + 50 GeV. Because in this case H - A coannihilations play a prominentrole in obtaining the right value of the dark matter density, it makes sense todisplay the parameter space in the plane ( M H , M A − M H ). For λ = 10 − (dash-dotted line) it is always possible to find a value of M A − M H that gives8 M H [GeV] M A - M H [ G e V ] λ = 0.01 λ = 0.001 λ = 0.0001 M H + = M H + 50 GeVM h = 125 GeV Ω h = 0.11
50 55 60 65 70 75 M H [GeV] σ S I ( - l oop ) / σ S I ( t r ee - l e v e l ) λ = 0.01 λ = 0.001 λ = 0.0001 M H + = M H + 50 GeVM h = 125 GeV Ω h = 0.11 Figure 6:
Left: The parameter space of the inert doublet model in the plane( M H , M A − M H ) for three different values of the coupling λ : − (solid line), − (dashed line) and − (dashed-dotted line). The value of M H ± was set to M H + 50 GeV . Along the lines the relic density constraint, Ω h = 0 . , is satis-fied –mainly via H - A coannihilations. Notice that for λ = 10 − and λ = 10 − thereis a range in M H with no viable points. Right: The correction to the spin-independentdirect detection cross section as a function of the dark matter mass along the viablelines from the left panel. Notice that in this case the correction only slightly dependson M H . the observed value of the dark matter density, but that is not true for λ = 10 − or λ = 10 − . Notice that the required mass splitting increases significantlyclose to the higgs resonance and near the maximum allowed value of M H . Thesmall bump observed at M H ∼ . A - A annihilations on the relic density. The right panel of figure 6 shows the correctionto σ SI along such viable regions. We see that in this case the correction doesnot strongly depend on M H : it is of order of several percent for λ = 10 − (solidline), a factor 2 to 4 for λ = 10 − (dashed line) and it reaches almost a factor100 for λ = 10 − (dash-dotted line). In all cases there is a slight increase in thecorrection with the dark matter mass. Clearly, large electroweak corrections to σ SI are not confined to M H ∼ M h / M H ∼
70 GeV but can actuallybe found for any value of M H . At the end, it is the size of λ and not M H what determines how important the corrections are, and λ can vary over severalorders of magnitude within the viable regions of the model.To assess in all generality, and independently of the specific slice of parameterspace examined, the relevance of the electroweak corrections to σ SI , we havescanned, using Markov Chain Monte Carlo techniques [32], the entire parameterspace of the inert doublet model. After allowing the parameters to vary withinthe following ranges 80 GeV > M H >
50 GeV , (6) M A > M H , (7) M H ± >
90 GeV , (8)1 > λ > − , (9)and imposing all the experimental bounds (collider, precision, dark matter, etc.)we obtained a sample of about 10 viable models to analyze. Figure 7 shows ascatter plot of these models in the plane ( M H , σ SI ). The (blue) squares show9 M H [GeV] σ S I [ pb ] Tree level1-loop
Xenon100Xenon1T
Figure 7:
A scatter plot of the spin-independent direct detection cross section attree-level and at one-loop as a function of the dark matter mass. In this figure all theparameters of the inert higgs model were allowed to vary randomly (see text for details)and all experimental bounds were taken into account. σ SI (tree-level) and the (red) circles σ SI (1-loop). Two classes of models can beeasily distinguished in this figure: the annihilating models that are concentratedalong a narrow band similar to that observed in figure 5 and the coannihilating models which are scattered in the region below that band. They are absentbelow M H ∼
55 GeV because the mass splitting required for coannihilationsto be important becomes inconsistent with collider bounds [12]. Notice thatwhereas σ SI (tree-level) may be as small as 10 − pb, σ SI (1-loop) does not gobelow 10 − pb or so. From the figure we also see that some regions are alreadyexcluded by the XENON100 bound [3] (solid line). The most important result,however, is the fact that the one-loop corrections always bring σ SI within thereach of future direct detection experiments and in particular very close to theXENON-1T expected sensitivity.Figure 8 shows the same sample of viable models, but in two additionalplanes. The right panel shows σ SI (1-loop) /σ SI (tree-level) as a function of M H . The annihilating and coannihilating models can again be clearly dis-tinguished in this figure. Notice that the correction can be very large, say σ SI (1-loop) /σ SI (tree-level) ∼ M H . Theright panel displays the same ratio but now as a function of λ . The general be-havior is as anticipated, with the correction increasing for decreasing λ . It canalso be seen in this figure that σ SI (1-loop) becomes larger than σ SI (tree-level)for λ & − , as we had found before. The small spread observed in thisfigure clearly demonstrates that it is the size of λ that determines how large σ SI (1-loop) /σ SI (tree-level) is.Summarizing, we have seen that in the small mass regime of the inert doubletmodel, M H < M W , the electroweak corrections to the spin-independent directdetection cross section can be quite relevant, giving in certain cases the dominant10 M H [GeV] σ S I ( - l oop ) / σ S I ( t r ee - l e v e l ) Ω h = 0.11 λ σ S I ( - l oop ) / σ S I ( t r ee - l e v e l ) Ω h = 0.11 Figure 8:
Left: A scatter plot of σ SI ( ) /σ SI ( tree-level ) as a function of M H .Right: A scatter plot of σ SI ( ) /σ SI ( tree-level ) as a function of λ . In this figureall the parameters of the inert higgs model were allowed to vary randomly (see text fordetails) and all experimental bounds were taken into account. contribution to σ SI . We have observed that these corrections become large when λ . − . Such values of λ are compatible with the dark matter constraintthanks to coannihilations (for a wide range of M H ), resonant annihilations(for M H . M h / M H ∼
72 GeV). We have also noticed that in contrast to σ SI (tree-level), which can bearbitrarily small, σ SI (1-loop) is never below ∼ − pb. Thus, over the entirelow mass regime, the electroweak corrections we have studied bring σ SI withinthe reach of future direct detection experiments. We now focus our attention on the heavy mass regime of the model, M H &
500 GeV. Figure 9 shows viable regions of the inert doublet model in theplane ( M H , M A − M H ) for different values of the scalar coupling λ . Forconcreteness, in this figure we have set M H ± = M A and we have restrictedthe mass range to M H < M H = 1 TeV, for instance, it amountsto no more than 7 GeV. This is a generic and well-known feature of the largemass regime of the inert doublet model: only for small values of M A − M H and M H ± − M H can the relic density constrained be satisfied, see e.g. [31].In the figure we see that the viable parameter space starts at M H ∼
520 GeVfor λ = 10 − , − and around 600 GeV for λ = 0 .
1. In this regime thereare neither resonances nor thresholds, so the analysis is much simpler. As wesaw in figure 2, the one-loop correction to σ SI initially increases with M H whereas the tree-level value of σ SI decreases with M H (see equation 5). Since,in addition, λ can be made arbitrarily small in this regime, we expect that theelectroweak corrections to σ SI be more relevant than for the low mass regime.Figure 10 shows σ SI (1-loop) /σ SI (tree-level) along the viable lines of figure 9.As expected, the correction is larger the smaller λ is. We also observe thatas M H increases, the correction indeed becomes more important. It amountsto a factor between 1 and 2 for λ = 0 .
1, about a factor 10 for λ = 0 .
01, and11
00 600 700 800 900 1000 M H [GeV] M A - M H [ G e V ] λ = 0.1 λ = 0.01 λ = 0.001 M H + = M A M h = 125 GeV Ω h = 0.11 Figure 9:
The viable parameter space of the inert doublet model in the plane( M H , M A − M H ) for different values of λ . In this figure we consider the largemass regime of the model and we set M H ± = M A and M h = 125 GeV . Notice thatthe required mass splitting is always very small. more than 200 for λ = 10 − . Notice, for example, that in the large mass regime σ SI (1-loop) /σ SI (tree-level) ∼ λ = 0 . λ at least one order ofmagnitude smaller.We have also scanned the parameter space of this regime by allowing theinert masses to vary in the range1 TeV > M H >
500 GeV , (10) M H ± > M H , (11) M A > M H . (12)After imposing all the relevant constraints, we obtained a sample of approxi-mately 10 viable models. Figure 11 shows this sample of models in two differentplanes. The left panel displays σ SI (1-loop) /σ SI (tree-level) as a function of λ . Itdemonstrates that σ SI (1-loop) /σ SI (tree-level) is a decreasing function of λ , asexpected, and that it becomes much larger than 1, say ∼
10, for λ ∼ − . Thesmall spread of models in this plane again indicates that it is fundamentally λ the parameter that determines the size of σ SI (1-loop) /σ SI (tree-level). Theright panel compares the tree-level and one-loop value of σ SI as a function of M H . Notice that whereas at tree-level σ SI could be as small as 10 − pb atone-loop it is never below 10 − pb. From the figure we see that this regionis not being currently probed by direct detection experiments –see the presentXENON100 bound (solid line). The future prospects, however, are very goodbecause the one-loop corrections bring σ SI within the reach of planned direct12
00 600 700 800 900 1000 M H [GeV] σ S I ( - l oop ) / σ S I ( t r ee - l e v e l ) λ = 0.1 λ = 0.01 λ = 0.001 M H + = M A M h = 125 GeV Ω h = 0.11 Figure 10:
The correction to the spin-independent direct detection cross section as afunction of the dark matter mass along the viable lines of figure 9. detection experiments.
We have computed and studied the dominant electroweak corrections to thedirect detection cross section of inert higgs dark matter. These corrections arisefrom one-loop diagrams mediated by the electroweak gauge bosons and do notdepend on the scalar coupling λ that controls the tree-level cross section. Wehave analyzed the behavior of these one-loop contributions as a function of theparameters of the model, and have calculated their effect within the regions thatare compatible with the dark matter constraint for the two distinct regimes ofthis model: the low mass regime ( M H < M W ) and the large mass regime( M H &
500 GeV). In both regimes, we have found regions where the one-loopcorrections not only become significant but can even be larger than the tree-levelresult. In the low mass regime, this happens when λ . − , a value that can becompatible with the dark matter constraint via annihilation through the higgsresonance, annihilation into the three-body final state W W ∗ , or coannihilations.The first two require respectively M H ∼ M h / M H ∼
72 GeV whereascoannihilations allow for a much wider range of M H . In the heavy mass regime,we found the effect of the electroweak corrections to be larger, with correctionsof order 100% already for λ = 0 .
1. Thus, they must be necessarily taken intoaccount when assessing the prospects for the direct detection of inert higgs darkmatter. From the scans over the full parameter space of the model, we alsoobserved that these one-loop contributions always bring σ SI within the reach offuture direct detection experiments. 13 e-05 0.0001 0.001 0.01 0.1 1 λ σ S I ( - l oop ) / σ S I ( t r ee - l e v e l ) Ω h = 0.11
500 600 700 800 900 1000 M H [GeV] σ S I [ pb ] Tree level1-loop
Xenon100
Figure 11:
Some results of the scan over the parameters of the model for the largemass regime. Left: A scatter plot of the correction to σ SI as a function of λ . Right:A comparison between the tree-level and the one-loop value of σ SI as a function of M H . The solid line shows the current bound from XENON100 whereas the dashedline corresponds to the expected sensitivity of XENON-1T. Acknowledgments
This work is supported by the “Helmholtz Alliance for Astroparticle PhyicsHAP” funded by the Initiative and Networking Fund of the Helmholtz Associ-ation. J.D.R. would like to thank D. Restrepo for his collaboration.
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