Dark Matter and the Higgs in Natural SUSY

Null results from dark matter (DM) direct detection experiments and the 125 GeV Higgs both pose serious challenges to minimal supersymmetry. In this paper, we propose a simple extension of the MSSM that economically solves both problems: a"dark sector"consisting of a singlet and a pair of $SU(2)$ doublets. Loops of the dark sector fields help lift the Higgs mass to 125 GeV consistent with naturalness, while the lightest fermion in the dark sector can be viable thermal relic DM, provided that it is mostly singlet. The DM relic abundance is controlled by s-wave annihilation to tops and Higgsinos, leading to a tight relation between the relic abundance and the spin-dependent direct detection cross section. As a result, the model will be fully probed by the next generation of direct detection experiments. Finally we discuss the discovery potential at LHC Run II.

Fine tuning measure: ! ! FT exponentially worse as k u decreases. This requires (Different from Bino-Higgsino system where ) Direct Detection DM direct detection experiments are probing couplings of DM to nucleons ⇠ SI q (¯ )(qq) + ⇠ SD q (¯ 5 µ )(q 5 µ q) SI controlled by c h and SD controlled by c Z .
Thermal relic density ! ! DM slowly moving at freeze out (v 2~0 .1), so all else being equal, annihilation rate dominated by s-wave.
Initial state (pair of identical Majorana fermions) is CP odd, so no s-wave through s-channel Higgs. This leaves s-channel Z and t-channel.
Additional simplifications in large M L limit...
Thermal relic density Comments: • s-wave annihilation is to tt and Higgsinos to leading order in v 2 /M L 2 . • Annihilation to dibosons is always subdominant for the parameter space that we study. • c Z controls both the SD DD cross section and the annihilation to tt.
• Confirms analytics of DD bounds. • Confirms estimates of FT via one-loop Higgs mass.
IceCube SD HttL c Z LUX SD c Z

Conclusions
We studied an economic extension of the MSSM that gives a 125 GeV Higgs mass with a fine-tuning as low as 10% and provides a natural thermal WIMP DM candidate.
The main annihilation channels in our model are s-wave annihilation to tt and Higgsinos.
Imposing the relic density constraint immediately implies a particular value for the SD cross-section. This value is not ruled out yet, but the next generation of DM experiments (e.g.\ Xenon1T , LZ) should completely rule out or discover this model.

Blind Spot
To satisfy LUX SI bounds, need a mild blind spot cancellation (factor of ≲ 2)

Landau Pole Problem
Generally there is a Landau pole well before the GUT scale. Theory needs to be UV completed --or extended with gauge interactions to deflect the Yukawas... Let's focus on the more important couplings (g 3 , y t , k u , k d ) and of other couplings in finding the scale of Landau poles. Starting functions we have Since the new particles are not coloured, g 3 's beta function is the We define the Landau pole scale (⇤ LP ) for a Yukawa coupling k(µ which k(⇤ LP ) = 4⇡. Solving the RGEs of our model numerically, we

Electroweak Precision Tests
Model is totally safe from EWPT --in mostly singlet regime, thermal relic constraint requires doublet mass ≳ 1 TeV...  With limits set on p,n the allowed region in a p a n space can be found following the procedure detailed in [40]: where A p,n are the limits on the proton/neutron-only cross sections, for the isotope with mass number A. The excluded region is shown in Figure 2. Typically only the most sensitive channel of the two cross sections is shown. In this case the limits in the a p a n plane can be found following the method detailed in Ref. [41], which is a good approximation if a p a n or vice-versa. This result improves the constraint on a n over previous experiments. The lines are parts of elongated elipses and the orientation depends on the sensitivity to both a p and a n . The angle of the ellipse for LUX and XENON100 is not the same due to di↵erences in the spin structure functions used and the energy scale in the analysis (which affects the signal spectrum). XENON100 also had slightly di↵erent abundances of 129 Xe and 131 Xe. This plot also emphasises the complementarity between the di↵erent detector materials.
In conclusion, we have set the most stringent limits on LUX 1602.03489  Figure 7: Limits on the spin-dependent WIMP-proton cross-section from IC79, for a range of di↵erent annihilation final states. The canonical hard (W + W and ⌧ + ⌧ ) and soft (bb) channels bracket the possible limits for di↵erent models reasonably well. More extreme channels (hardest: ⌫⌫, softest: gg) less often found in SUSY can lead to even stronger or weaker constraints. For the ⌫⌫ channel we have assumed equal branching fractions for all three neutrino flavours. The ability to easily and quickly compute full limits for any combination of final states is a particular feature of the method and tools we present in this paper.
are up to a factor of 4 stronger than the previous analysis at multi-TeV masses. The latest update of WIMPSim fixes an issue with propagation of neutrinos in the Sun that a↵ected the version used to derive the original IC79 limits [1]. This resulted in conservative limits for WIMP masses above ⇠500 GeV, ranging from a factor of 1.05 at 500 GeV to 1.2 at 1 TeV Official ttbar limit is new; previously had to be recasted (see e.g. Cheung, Hall & Ruderman '12).

!
Factor of a few weaker ttbar vs WW makes a big difference for our model! Indirect detection ealizations of the two data sets. Because the Pass 8 six-year and Pass 7 Reprocessed fourear event samples have a shared fraction of only 20-40%, the two analyses are nearly statistically ndependent. For masses below 100 GeV, the upper limits of [1] were near the 95% upper bound f the expected sensitivity band while the limits in the present analysis are within one standard eviation of the median expectation value. No official ttbar limits, but probably ineffective above 100 GeV...

Conclusions
We studied an economic extension of the MSSM that gives a 125 GeV Higgs mass with a fine-tuning as low as 10% and provides a natural thermal WIMP DM candidate. The constraints on the parameter space are:

Conclusions
We studied an economic extension of the MSSM that gives a 125 GeV Higgs mass with a fine-tuning as low as 10% and provides a natural thermal WIMP DM candidate. The constraints on the parameter space are:

Introduction: two questions
In minimal SUSY, the answer to both questions is basically NO.
• Higgs at 125 GeV in the MSSM requires multi-TeV A-terms or 10 TeV stops. Either way it is fine tuned at the sub-percent level or worse.
• WIMP dark matter in the MSSM requires either a heavy SUSY scale or contrived numerical coincidences (blind spots, funnels, co-annihilation).
So if SUSY solves the hierarchy problem, the source of both DM and the Higgs mass likely lies beyond the MSSM.

Introduction
In this talk, we will study a simple, economical extension of the MSSM that includes both DM and the source of the Higgs mass.
We will see that it is possible to achieve ~10% fine-tuning, a 125 GeV Higgs, and thermal relic DM consistent with all experimental constraints, by just adding a singlet and pair of vector-like doublets to the MSSM.
The Model Then much of the physics (thermal relic density, direct detection, LHC signatures, ...) controlled by DM-DM-Higgs and DM-DM-Z couplings. (Cheung & Sanford '13;Calibbi et al '15) In our model, these are given by: Part of a broader framework of Higgs and Z-portal dark matter (cf e.g. Giudice, de Simone and Strumia '14) blind spot Higgs mass and fine-tuning (M L =1200 GeV, M S =300 GeV) Need k u >1 to avoid same fate as MSSM stops. For k u~1 .5, can achieve Δ ~ 10. At leading order in 1/ML, only s-wave annihilation is to ttbar, and it's controlled by c Z ! c Z Thermal relic density Comments: • SI controlled by c h and SD controlled by c Z .  With limits set on p,n the allowed region in a p a n space can be found following the procedure detailed in [40]: where A p,n are the limits on the proton/neutron-only cross sections, for the isotope with mass number A. The excluded region is shown in Figure 2. Typically only the most sensitive channel of the two cross sections is shown. In this case the limits in the a p a n plane can be found following the method detailed in Ref. [41], which is a good approximation if a p a n or vice-versa. This result improves the constraint on a n over previous experiments. The lines are parts of elongated elipses and the orientation depends on the sensitivity to both a p and a n . The angle of the ellipse for LUX and XENON100 is not the same due to di↵erences in the spin structure functions used and the energy scale in the analysis (which affects the signal spectrum). XENON100 also had slightly di↵erent abundances of 129 Xe and 131 Xe. This plot also emphasises the complementarity between the di↵erent detector materials.
In conclusion, we have set the most stringent limits on LUX 1602.03489  Figure 7: Limits on the spin-dependent WIMP-proton cross-section from IC79, for a range of di↵erent annihilation final states. The canonical hard (W + W and ⌧ + ⌧ ) and soft (bb) channels bracket the possible limits for di↵erent models reasonably well. More extreme channels (hardest: ⌫⌫, softest: gg) less often found in SUSY can lead to even stronger or weaker constraints. For the ⌫⌫ channel we have assumed equal branching fractions for all three neutrino flavours. The ability to easily and quickly compute full limits for any combination of final states is a particular feature of the method and tools we present in this paper.
are up to a factor of 4 stronger than the previous analysis at multi-TeV masses. The latest update of WIMPSim fixes an issue with propagation of neutrinos in the Sun that a↵ected the version used to derive the original IC79 limits [1]. This resulted in conservative limits for WIMP masses above ⇠500 GeV, ranging from a factor of 1.05 at 500 GeV to 1.2 at 1 TeV Official ttbar limit is new; previously had to be recasted (see e.g. Cheung, Hall & Ruderman '12).

!
Factor of a few weaker ttbar vs WW makes a big difference for our model! Indirect detection ealizations of the two data sets. Because the Pass 8 six-year and Pass 7 Reprocessed fourear event samples have a shared fraction of only 20-40%, the two analyses are nearly statistically ndependent. For masses below 100 GeV, the upper limits of [1] were near the 95% upper bound f the expected sensitivity band while the limits in the present analysis are within one standard eviation of the median expectation value. igure 1: Constraints on the DM annihilation cross section at 95% CL for the bb (left) and t + t (right) hannels derived from a combined analysis of 15 dSphs. Bands for the expected sensitivity are calculated by epeating the same analysis on 300 randomly selected sets of high-Galactic-latitude blank fields in the LAT ata. The dashed line shows the median expected sensitivity while the bands represent the 68% and 95% uantiles. For each set of random locations, nominal J-factors are randomized in accord with their measure-