t1
~
All limits at 95% CL
ATLAS
theory) σSUSY
1 Observed limit (±
exp) 1 σ Expected limit (±
σexp
2 Expected limit ±
0
χ1
∼
< m
t1
m~
Fig. 9.5:95% CL limit on stop-pair production with a 100% BR to ˜t→bf f0+ ˜χ01. The area enclosed by the dashed blue (solid black) line is excluded by the expected (observed) limit. Experimental uncertainties corresponding to±1σand±2σare shown as the green and yellow bands, respectively.
The impact of the theoretical cross section uncertainty is shown as the dotted curves around the observed limit.
Fig. 9.5 at 95% CL. As expected, the exclusion power close to the diagonal is similar to the stop-to-charm and sbottom-to-bottom scenarios, albeit slightly reduced due to higher experimental uncertainties, reaching m˜t ≈ 390 GeV. The exclusion power decreases rapidly for higher mass splittings. A previous limit on this scenario was set using Run 1 data and reached up to 280 GeV close to the diagonal [131]. Thus, the presented limit extends the reach by more than 100 GeV close to the diagonal. The observed limit is contained within the 2σ uncertainty of the expected limit.
9.3 Dark Matter Production
9.3.1 Signal Modelling
We focus on the dark matter production via an s-channel mediator exchange in the context of simplified models. A corresponding Feynman diagram has been introduced in Sec. 3.3, Fig. 3.7(b). WIMP production with an additional parton in the ME is generated with
Powheg-Boxv2 [165] at NLO precision. The PDF set is NNPDF30nlo. Pythia8and the A14 tune are used for the parton shower with the NNPDF23lo. The mediator has an axial-vector coupling to SM and DM particles with spin-1. The mediator width is modelled with a Breit-Wigner distribution. At generation level, a phase space cut is applied which leads to fully efficient sampling for 6ET > 250 GeV. The renormalisation and factorisation scales are set to HT/2 on an event-by-event basis, where HT is defined as HT = qm2χχ+p2T ,j1 +pT ,1. The transverse momentum of the leading jet is pT ,j1 and the invariant mass of the WIMP pair is mχχ. The couplings chosen aregq = 0.25 andgχ= 1. These values ensure the validity of the narrow width approximation and suppress a strong interplay between monojet and dijet constraints. WIMP masses are generated between 1 GeV and 1 TeV. Mediator masses range from 10 GeV to 10 TeV (the latter being useful for EFT interpretation). The different mass points in the mχ-mA grid generated are mostly in the off-shell regime (mA<2mχ). Further signal points in the on-shell regime are generated at truth level for the cross section calculation. The acceptance of the monojet analysis has been verified to be constant for a given mediator mass. The acceptances range for different dark matter and mediator mass combinations between ∼6% and ∼30% for 6ET >250 GeV. For higher6ET-cuts of up to 1 TeV the A ×εdecreases to 0.03-1.1%, depending on the particle masses.
9.3.2 Signal Uncertainties
The same uncertainties as for ADD and SUSY production are considered here and evaluated in a similar manner. Additional theory uncertainties enter the signal fit as individual nuisance parameters. To account for the uncertainty on the renormalisation and factorisation scale choice a flat 3% uncertainty is applied in all regions for all samples. The PDF uncertainty amounts to 20% for samples with mχ < 100 GeV or mχ > 1 TeV. All other samples assume a PDF uncertainty of 10%. Uncertainties on parton shower modelling are taken into account as a flat 20% uncertainty for all signal points. The usual experimental uncertainties are relevant for the signals: JER, JES, pileup reweighting and 6ET-uncertainties have an impact of around 1-3% on the signal region yields.
9.3.3 Exclusion Limits
The exclusion contour is obtained in a plane of mχ vs. mA. The on-shell signal strength limits are obtained by rescaling the fitted µsig of the points with mχ = 1 GeV and different mediator masses. The rescaling uses the cross sections provided by the truth MC samples:
µrescaled=µsig·σ1/σX, whereσ1 denotes the cross section formχ= 1 GeV samples to whichµsig corresponds andσX denotes the cross section with a varied WIMP massmχ=XGeV, but same mediator mass mA. The final result in terms of 95% CL limits is shown in Fig. 9.6. As usual, expected and observed exclusion contours are drawn along with their uncertainties. The grey hashed area indicates the phase space that violates perturbative unitary (mχ>pπ/2mA[166]).
In addition, the line corresponding to models predicting the correct relic dark matter density as measured by the WMAP and Planck satellites [48, 167] is shown as the red curve. Models above this curve would predict an under-production of dark matter, and likewise an overproduction is expected below this curve. The observed exclusion crosses the red line at about mA ∼1.1 TeV and mχ ∼ 400 GeV. For low dark matter masses, mediator masses up to 1.55 TeV can be excluded. Most of the excluded area lies in the on-shell regime. The limit extends slightly into the off-shell regime for low mediator masses below 200 GeV. The monojet analysis loses sensitivity to off-shell scenarios due to the kinematically suppressed decay. The maximum
excluded WIMP mass is about 440 GeV, corresponding to a mediator mass of around 1.2 TeV.
This is also where the relic density curve crosses the observed limit. These limits extend the 2015 limits obtained by Atlas by about 500 GeV in mediator mass at low mχ and about 150 GeV in dark matter mass for mediator masses of ∼1 TeV. As in all other discussed limit plots, the observed limit is weaker than the expected by more than 1σ, but within 2σ reach. The limit in
[GeV]
ZA
m
0 1000 2000
[GeV]
χm
0 500
1000
Expected limit ± 2 σexpexp) σ
± 1 Expected limit (
PDF, scale) theory σ
± 1 Observed limit ( Perturbativity Limit Relic Density
= 13 TeV, 3.2 fb-1 s
ATLAS
ATLAS Preliminary
= 13 TeV, 36.1 fb-1 s
Axial-Vector Mediator Dirac Fermion DM
= 1.0 = 0.25, gχ gq
95% CL limits
χ = 2 m ZA
m
Fig. 9.6: 95% CL limit on WIMP pair production via an axial-vector mediator. The couplings gq = 0.25 andgχ= 1 are used. The area below the dashed blue (solid black) line is excluded by the expected (observed) limit. Experimental uncertainties corresponding to±1σand±2σare shown as the green and yellow bands, respectively. The impact of the theoretical cross section uncertainty is shown as the dotted curves around the observed limit. Additionally, the red curve corresponds to the models predicting the correct relic dark matter density [168]. The hashed area indicates the perturbativity violating phase space. The light blue curve shows the limit obtained with 3.2 fb−1 data [131].
themχ-mAplane can be translated into a WIMP-nucleon scattering cross section limit. This is done by using the relation as discussed in Ref. [169]:
σSD= 2.4·10−41cm2· gχgq
0.25 2
·
1 TeV mA
4
· µnχ
1 GeV 2
, (9.2)
whereσSDdenotes the spin dependent WIMP-nucleon scattering cross section andµnχis the re-duced WIMP-nucleon massµnχ= mmχχ+mmnn, wheremnis either the mass of the proton or neutron.
The derivation of the WIMP-nucleon scattering cross section limit as a function of the WIMP mass allows for a comparison of the collider sensitivity to WIMP production with the ones from dedicated direct detection search experiments. Therefore, the limits are derived at 90% CL as is conveniently done in direct detection search results. The results are compared in Fig. 9.7 for scattering with neutrons (a) and protons (b). The limit obtained by the monojet analysis excludes scattering cross sections above 2.9×10−43cm2 (3.3×10−43cm2) for WIMP masses
below 10 GeV (400 GeV), identically in both interactions with protons and neutrons (given the assumption that the mediator nucleon coupling is the same for all quarks). Beyond 400 GeV, this analysis is not able to establish lower limits on the scattering cross sections. In this regime of WIMP masses, the direct detection experiments are more sensitive. Below 400 GeV how-ever, the monojet analysis shows stronger sensitivity. It is important to note that the results obtained here are vastly dependent, while the direct detection searches are rather model-independent.
Alternative interpretations for WIMP dark matter models with a t-channel mediator or an s-channel pseudo-scalar mediator are briefly discussed in the Appendix, in Sec. A.2.
[GeV]
mχ
1 10 102 103 104
]2 -neutron) [cmχ(SDσ
43
10− 41
10− 39
10− 37
10− 35
10− 33
10− LUXAxial Vector Mediator
90% CL limits
Dirac Fermion DM = 1.0
= 0.25, gχ gq
C.Fischer PhD Thesis
= 13 TeV, 36.1 fb-1 s
(a)
[GeV]
mχ
1 10 102 103 104
]2 -proton) [cmχ(SDσ
42
10− 39
10− 36
10− 33
10− 30
10−
PICO-60 Axial Vector Mediator 90% CL limits
Dirac Fermion DM = 1.0
= 0.25, gχ gq
C.Fischer PhD Thesis
= 13 TeV, 36.1 fb-1 s
(b)
Fig. 9.7: Observed 90% CL limit exclusion contour in the plane of WIMP-nucleon scattering cross section versus WIMP mass: (a) the nucleon is neutron, (b) the nucleon is a proton. The regions above the curves are excluded. A comparison is shown with direct detection experiments: PICO [137]
for the scattering with protons and Lux [52] for the scattering with neutrons.