Dark matter interpretations of ATLAS searches for the electroweak production of supersymmetric particles in $\sqrt{s}=8$ TeV proton-proton collisions

P u b l i s h e d f o r S IS S A b y S p r i n g e r R e c e i v e d: August 3, 2016 A c c e p t e d: September 22, 2016 P u b l i s h e d: September 30, 2016

Dark matter interpretations of A T L A S searches for the electroweak production of supersymmetric

particles in √ s = 8 T e V proton-proton collisions

T h e A T L A S collaboration

E-m ail: atlas.publications@cern.ch

A b s t r a c t : A selection of searches by th e ATLAS experim ent a t th e LHC for th e elec- trow eak p ro duction of SUSY particles are used to stu d y th e ir im pact on th e con straints on d ark m a tte r candid ates. T he searches use 20 fb -1 of pro to n -p ro to n collision d a ta at

t/ s

= 8 TeV. A likelihood-driven scan of a five-dim ensional effective m odel focusing on th e gaugino-higgsino and Higgs sector of th e phenom enological m inim al supersym m etric S ta n d ard M odel is perform ed. This scan uses d a ta from direct d a rk m a tte r d etection experim ents, th e relic d ark m a tte r d ensity and precision flavour physics results. F u rth e r co n strain ts from th e ATLAS Higgs m ass m easurem ent and SUSY searches a t L E P are also applied. A subset of m odels selected from th is scan are used to assess th e im pact of th e selected ATLAS searches in th is five-dim ensional p a ra m ete r space. These ATLAS searches su b stan tially im pact those m odels for which th e m ass

of th e lightest n eu tralino is less th a n 65 GeV, excluding 86% of such models. T he searches have lim ited im pact on m odels w ith larger m (x 0) due to eith er heavy electroweakinos or com pressed m ass sp ectra w here th e m ass splittings betw een th e produced particles and th e lightest supersym m etric particle is small.

K

: H adron-H adron scatterin g (experim ents)

A

X

P

: 1608.00872

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Contents

1 I n tr o d u c tio n 1

2 A T L A S se a r c h e s 3

3 T h e o r e tic a l fra m e w o r k 4

3.1 Scanning stra te g y 4

3.2 E xperim ental co n strain ts in th e initial likelihood scan 6

3.3 Phenom enology of th e LSP 9

4 S ig n a l s im u la tio n a n d e v a lu a tio n o f A T L A S c o n s tr a in ts 10

5 I m p a c t o f t h e A T L A S e le c tr o w e a k S U S Y se a r c h e s 12

5.1 Im pact on th e electrow eakino masses 12

5.2 Im pact on th e E W K H m odel p aram eters 13

5.3 Im pact on d a rk m a tte r observables 14

6 C o n c lu s io n s 19

T h e A T L A S c o lla b o r a tio n 27

1 In tr o d u c tio n

Supersym m etry, or SUSY [1- 6], is a po p u lar c an d id ate for physics beyond th e S tan d ard M odel. It provides an elegant solution to th e hierarchy problem , which, in th e S tan d ard M odel, dem ands high levels of fine tu n in g to co u n teract large q u a n tu m corrections to th e m ass of th e Higgs boson [7- 10]. R -parity-conserving su persym m etric m odels can also provide a can d id a te for d ark m a tte r, in th e form of th e lightest supersym m etric particle (LSP) [11, 12].

T he ATLAS and CMS experim ents perform ed a large num ber of searches for SUSY du ring Run-1 of th e LHC and, in th e absence of a significant excess in any channel, exclusion lim its on th e masses of SUSY particles (sparticles) were calculated in num erous scenarios, usually in th e context of th e m inim al supersym m etric S tan d ard M odel (MSSM) [13, 14].

T hese scenarios include “high-scale” SUSY m odels such as m SU G R A [15- 17] or GMSB [18­

20], b o th of which specify a p a rticu la r SU SY -breaking m echanism . M ost searches also considered specific “simplified m odels” , which a tte m p t to c a p tu re th e behaviour of a small num ber of kinem atically accessible SUSY particles, often th ro u g h considering one p articu lar SUSY p ro d u ctio n process w ith a fixed decay chain.

A lthough th e high-scale and simplified m odel exclusions provide an easily in terp retab le p icture of th e sensitivity of analyses to specific areas of p a ra m ete r space, th ey are far from

J H E P 0 9 ( 2 0 1 6 ) 1 7 5

a full exploration of th e MSSM, which contains ab o u t 120 free p aram eters. T he num ber of p aram eters is reduced if th e phenom enological MSSM (pM SSM ) is considered instead. It is based on th e m ost general CP-conserving MSSM, w ith R -p arity conservation, and m inim al flavour violation [21, 22]. In addition, th e first two generations of sfermions are required to be degenerate and have negligible Yukawa couplings. T his leaves 19 in d ependent weak- scale p aram eters to be considered: te n sfermion m asses (five for th e degenerate first two generations and five for th e th ird g eneration), th ree trilin e ar couplings

which give th e couplings betw een th e Higgs field and th e th ird -g en eratio n sfermions, th e bino, wino and gluino m ass param eters M

,

,

, th e higgsino m ass p a ra m ete r ß, th e ratio of th e vacuum ex­

p e c ta tio n values of th e Higgs fields ta n ß , and th e m ass of th e pseudoscalar Higgs boson m ^ . T he m odel considered here, henceforth referred to as EW K H , is described by only five param eters: M 1, M 2, ß, and t a n ß to define th e gaugino-higgsino sector, and mA to define th e Higgs sector. B o th sectors are defined a t tre e level. T he coloured SUSY particles and sleptons are assum ed to be heavy such th a t th ey do not im pact th e phenomenology. This m odel is well m otivated from a d ark m a tte r perspective since th e d ark m a tte r can d idate of th e MSSM is th e lightest n eu tralin o whose properties are fully specified by these five param eters. These p aram eters therefore also d eterm ine th e relic density of th e n eu tralino for m uch of th e pM SSM p a ra m ete r space, i.e. if coannihilations w ith slepton, squarks and gluinos are neglected.

An in te rp re ta tio n of th e R un-1 SUSY searches in pM SSM m odels m ay be found in th e lite ra tu re (for instance refs. [23- 25]). In particu lar, ATLAS has previously perform ed a stu d y using a b o u t 300 000 pM SSM m odel points [26]. In th a t work, all 19 of th e pM SSM param eters were varied and th e strongest direct co n strain ts on sparticle pro du ction were o b tained in searches for squarks and gluinos. In th is article, a tte n tio n is restricted to a five-dim ensional (5D) sub-space of th e pM SSM in order to assess th e im pact of th e ATLAS R un-1 searches (using 20 fb

of d a ta a t

=

TeV) specifically on th e electrow eak p ro duc­

tio n of SUSY particles, and th e corresponding co n strain ts on d a rk m atte r. This provides a stu d y com plem entary to th a t in ref. [26] by decoupling stro ng -in teraction p ro d u ction pro­

cesses from th e phenomenology, and th u s allows m ore extensive exploration of th e regions of p a ra m ete r space relevant to electrow eak production. T h e scanning stra te g y used to select m odels is also different to ref. [26], w here m odels were sam pled from uniform d istri­

butions in th e pM SSM p aram eters, and th e n required to satisfy a variety of experim ental co n strain ts. In this study, an “initial likelihood scan” is perform ed to select models, using co n strain ts from d irect d a rk m a tte r searches, precision electroweak m easurem ents, flavour- physics results, previous collider searches, and th e ATLAS Higgs boson m ass m easurem ent.

T he im pact of th e ATLAS searches in different regions of p a ra m ete r space is e sta b ­ lished by considering th e num ber of m odels selected by th e initial likelihood scan th a t are excluded by th e ATLAS electrow eak SUSY searches. Exclusion lim its are calculated using th e C Ls technique [27]. B o th particle-level

and reconstruction-level inform ation is used to calculate th e C Ls values (see section 4) , w here th e reconstruction-level inform ation makes

1Particle-level information constructs observables using the stable particles from MC generators, which account for the majority of interactions with the detector material [28].

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use of th e ATLAS d e te c to r sim ulation, data-d riv en background estim ations, and system atic un certainties and th eir correlations. T he C Ls calculations invoke th e sim plifying assum p­

tio n th a t th e reconstructio n of events selected a t particle level can be param eterised using an average efficiency factor th a t does not depend on th e d etails of th e SUSY model. T he reconstruction-level inform ation can th e n be used to directly m ap particle-level results to CLs values. T his “calib ration proced ure” significantly reduces th e co m p u tatio n al load of th e analysis and accounts, on average, for th e acceptance and efficiency across th e ensem ble of models.

2 A T L A S sea rch es

Four ATLAS R un-1 SUSY searches th a t ta rg e t electrow eak SUSY p ro d uction are consid­

ered, as listed in tab le 1. T heir com bined im pact on simplified m odels of electroweak sparti- cle production, as well as selected pM SSM and high-scale models, is sum m arised in ref. [29].

T he

analysis [30] targ e ts f -p air p ro d uction and

p ro d u ction (where X± decays via sleptons) w ith th re e signal regions, looking for an excess of events w ith e + e - , ß + ß - or e ± ß + and high stransverse m ass (m T2) [31, 32]. T hree addition al signal regions ta rg e t th e m ore difficult scenario of X+ Xi pro d u ctio n w here th e charginos decay via W bosons.

Finally, a seventh signal region requiring an opposite-sign light-lepton pair (e+ e - , ß + ß - ) w ith an invariant m ass consistent w ith a Z boson and an add ition al p air of je ts is used to ta rg e t Xi X2 p ro d u ction w here th e chargino decays via a W boson and th e n eu tralin o decays via a Z boson. T he 2 t analysis [33] uses four signal regions to search for f-p a ir, and Xi

p roduction, w here th e charginos and neutralinos decay via th ird -g en eratio n sleptons.

E vents w ith a pair of opposite-sign hadronically decaying t-le p to n s ( r had) and large m T2 are selected for th e search. T he

analysis [34] searches for weakly in teractin g SUSY particles in events w ith th ree light leptons ( e /ß ) , two light leptons and one Thad, or one light lepton and two Thad. Tw enty-four signal regions are defined to ta rg e t X1 X2 production, where charginos and n eutralinos decay via sleptons, staus, or th e SM bosons W , Z and h. T he

4 1

analysis [35] searches for higgsino-like X2X3 production, w here th e n eutralinos decay via sleptons, stau s or Z bosons. Nine signal regions are used to select events w ith large missing tran sv erse m om entum (whose m agn itude is denoted as E™ ss) and four light leptons, th ree light leptons and one Thad, or two light leptons and two Thad.

A lthough th is article is restricted to these four analyses, o th er SUSY searches could provide sensitivity in some regions of th e p a ra m ete r space considered in this article. For exam ple, th e ATLAS d isap p earing -track analysis [36] ta rg e ts d irect long-lived charginos w ith pro p er lifetimes O (1 n s) so it could have sensitivity to com pressed m odels w here th e m ass difference of th e lightest chargino and th e LSP is m uch less th a n 1GeV. C onsideration of this analysis is beyond th e scope of th is article. Furtherm ore, th e ATLAS m onojet search [37] ta rg e ts pair-produced d a rk m a tte r particles b u t makes no assu m ptio n of an underlying supersym m etric theory. These results do not yet have sensitivity to direct electrow eak SUSY prod u ctio n so is not considered fu rth e r in th is analysis.

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Analysis Target productio n processes

2JL

[30] X + X -, X±X°,

2 t

[33] X+Xi , X±X2,

[34] x ± x2

4 L

[35] x2x3

T a b le 1. ATLAS electrow eak SUSY searches re-in te rp rete d in th e pM SSM for th is article.

3 T h e o r e tic a l fram ew ork

T he th eoretical SUSY fram ew ork used in this article is an effective m odel of th e electroweak gauginos, higgsinos and th e Higgs sector of th e MSSM, collectively labelled EW K H . T he m odel is described by five p aram eters, w here four of th em define th e gaugino-higgsino sector at tre e level (M i, M 2, ß, and t a n ß ), and mA is added to define th e Higgs sector at tre e level. T he o th er soft sparticle masses are large to ensure th a t th e sfermions and gluinos are decoupled from th e effective theory, while th e trilin e ar couplings are not constrained.

T he specific values used are 5TeV for th e sferm ion soft-m asses, 4TeV for th e gluino m ass and 0.1TeV for th e trilin e ar couplings.

W hen scanning in th is fram ew ork, a Bayesian prior d istrib u tio n for these param eters is used as a device to co n cen trate th e p a ra m ete r scan in certain regions of p a ra m ete r space. Two different prior d istrib u tio n s are adopted: “flat priors” are uniform in all m odel param eters, while “log priors” are uniform in th e logarithm of all m odel p aram eters, except for ta n ß , for which a uniform prior is used for b o th sets. F la t priors ten d to concentrate sam pling tow ards large values of th e param eters (as m ost of volum e of th e prior lies th ere), while log priors co n cen trate th eir scan in th e lower m ass ( ^ 1TeV) region (since th is m etric gives every decade in th e p a ra m ete r values th e sam e a priori probability). T he p osterior sam ples resulting from th e flat and log prior scans are th e n m erged to achieve a reliable m apping of th e (prior-independent) profile likelihood function, as advocated in ref. [38].

Table 2 displays b o th of th e priors used and th e ir ranges.2 T he specific ranges are chosen because th ey contain th e interestin g d a rk m a tte r phenomenology.

T he profile likelihood m aps obtain ed from m erging th e sam ples g ath ered w ith bo th priors explore in detail b o th th e low-mass and th e high-m ass regions, for a m ore thorou gh scanning of th e entire p a ra m ete r space.

3.1 S c a n n in g s tr a t e g y

A B ayesian ap p roach is ad o pted for sam pling th e E W K H p a ra m ete r space, and th e sen­

sitivity of th e ATLAS SUSY electrow eak analyses is calculated for th e resulting p osterior sam ples. T his “initial likelihood scan” is driven by th e likelihood defined in section 3.2, which is a function of th e five pM SSM m odel p aram eters and ad ditio nal nuisance param -

2For parameters that span both negative and positive numbers the log prior is actually a piecewise function in order to be invertible. The log parameter

is mapped onto the linear, physical, parameter Oi as follows: if \Oi| > log10 e then Oi = sign(O^)10|s*|, otherwise Oi = O^e/ log10 e.

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F la t priors Log priors

M i [TeV] ( —4, 4) sign(M i) logio |M i|/G e V (—3.6, 3.6) M

[TeV] (0.01, 4) log10 M

/G eV (1, 3.6) ß [TeV] ( —4, 4) sign (ß ) logio |ß |/G eV (—3.6, 3.6) m A [TeV] (0.01, 4) logio m ^ /G e V (1, 3.6)

ta n ß (2, 62) ta n ß (2, 62)

T a b le 2. E W K H p a ra m e te rs used in th e in itial likelihood scan an d th e prior ranges for th e tw o p rio r choices ad o p ted . “F la t p rio rs” are uniform in th e p a ra m e te r itself w ith in th e in d icated ranges, while “log p rio rs” are uniform in th e lo g arith m of th e p a ra m e te r w ith in th e in d icated ranges. T he physical ranges for b o th priors are identical for b o th th e “flat” an d “log” priors.

eters. T he dim ensionality of th e likelihood can be reduced to one or two p aram eters by m axim ising th e likelihood function over th e rem aining p aram eters. T he resulting function is called th e profile likelihood.

For exam ple, for a single p a ra m ete r of interest

and o th er undesired p aram eters F =

\ , . . . ,

i - \ ,

i+ \ , . . . ,

th e 1D profile likelihood is defined as:

L (0i) = m a x

F ) =

F ) , (3.1)

w here L(0i , F ) is th e likelihood function and F is th e conditional m axim um likelihood e stim ate (M LE) of F for a given 0i .

Confidence intervals/regions from th e resulting 1D /2D profile likelihood m aps are de­

term ined by ad o p tin g th e usual N eym an co n struction w ith th e profile likelihood ratio

as th e te st statistic:

m )

=

F ) , (

.

)

L(0i, F ) v ;

w here 6li and F are th e unconditional M LEs.

Intervals, or regions, corresponding to 68%, 95% and 99% CL can be estim ated by assum ing —2 ln A(0i) is x 2-d istrib u te d which is m otivated by W ilks’ theorem [39]. This te s t s ta tistic is used to select th e m odels of interest in this analysis. For each of th e final d istrib u tio n s in section 5 th e m odels included are those w ithin th e 95% confidence in terv al/reg io n of th e profile likelihood.

T he software used to sam ple th e p a ra m ete r space is

-v2.0, which is in­

terfaced w ith th e publicly available code

v2.18 [40, 41], an im plem entation of th e nested sam pling algorithm [42]. T his is an u p d a te d and im proved version of th e p u b ­ licly available

scanning package [43, 44]. T his B ayesian algorithm , originally designed to com pute a m odel’s likelihood and to accu rately m ap out th e posterior d istri­

bution, can also reliably evaluate th e profile likelihood, given ap p ro p riate settings [38].

SuperBayeS

-v2.0 is interfaced w ith th e following program s: S O F T S U S Y 3.3.10 [45, 46] for SUSY spectrum calculations; M ic r O M E G A s 2.4 [47, 48] to com pute th e abundance of d a rk m atter; D a r k S U S Y 5.0.5 [49, 50] for th e co m p u tatio n of , th e spin-independent

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S ta n d ard M odel H adronic

m t [GeV] 172.99 ± 0.91 [56]

0.0457 ± 0.0065 [57]

m b(m b)MS [GeV] 4.18 ± 0.03 [58]

0.0457 ± 0.0065 [57]

aE M (m z )MS - i

127.944 ± 0.014 [58] f Ts 0.043 ± 0.011 [59]

a s

) MS 0.1185 ± 0.0006 [58] A „ 0.787 ± 0.158 [60]

A strophysical

-0 .3 1 9 ± 0.066 [60]

ploc [GeV cm 3] 0.4 ± 0.1 [61]

-0 .0 2 0 ± 0.011 [60]

v© [kms 3] 230.0 ± 30.0 [61]

T a b le 3. S ta n d a rd M odel, astrophysical an d h adronie p a ra m e te rs used in th e analysis. T he s ta n d a rd d ev iatio n gives th e scale of th e u n c e rta in ty in each (alth o u g h th is is n o t used in th e analysis except in th e case of m t ). T he astrophysical q u a n titie s are th e local d a rk m a tte r density, p loc, an d th e velocity of th e Sun relative to th e G alactic rest fram e v©. For th e d a rk m a tte r velocity d istrib u tio n th e so-called M axw ellian d istrib u tio n is used. T he velocity dispersion is assum ed to be vd = v^3/2 v ©. T he h adronic m a trix elem ents, f Tu, f Td an d f Ts p ara m eterise th e co n trib u tio n s of th e light q u ark s to th e p ro to n com position for sp in -in d ep en d en t cross-section while A u , A d an d A s th e c o n trib u tio n s of th e light q u ark s to th e to ta l p ro to n spin for th e sp in -d ep en d en t neutralino- p ro to n sc a tte rin g cross-section.

(SI) X i-nucleon scatterin g cross-section, and CTSD, th e spin-dependent (SD) X i-proton sc at­

terin g cross-section; SüPE R lso 3.0 [51, 52] to com pute flavour-physics observables; and S

B S G 1.6 [53, 54] for th e d eterm in atio n of B R (B ^ X sy). For th e co m p u tatio n of th e electrow eak precision observables described below, th e com plete one-loop corrections and th e available M SSM two-loop corrections have been im plem ented, as have th e full S tan d ard M odel results [55].

U ncertain ties in th e m easured value of th e to p q u ark m ass, m t = 172.99±0.91G eV [56], can have a significant im pact on th e results of SUSY analyses. Therefore m t is included as a nuisance p a ra m ete r in th e scans, w ith a G aussian prior, in ad d itio n to th e m odel p aram eters described above. U ncertainties in o th er S tan d ard M odel param eters, as well as astrophysical and nuclear physics qu an tities th a t en ter th e likelihood for th e direct- detectio n experim ents (described in section 4) , have a very lim ited im pact on th e scan.

T hus to lim it th e dim ensionality of th e p a ra m ete r space considered, these o th er nuisance p aram eters are fixed in th e analysis. T he values used for all S ta n d ard M odel, astrophysical and hadronic param eters are shown in tab le 3 .

3 .2 E x p e r im e n ta l c o n s tr a in ts in t h e in itia l lik e lih o o d sc a n

A set of existing experim ental co n strain ts is used in th e initial likelihood scan over th e 5D pM SSM to select th e m odels in which to consider th e im pact of th e ATLAS SUSY searches. T hey are im plem ented w ith a jo in t likelihood function, whose logarithm takes th e following form:

ln Ljoint = ln L e w + ln Lb + ln L q ^ 2 + ln L d d + ln Lpiggs + ln

(3.3)

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Observable M ean value S ta n d ard deviation E x perim ental T heoretical

Ref.

m W [GeV] 80.385 0.015 0.01 [62]

s i n ^ r 0.23153 0.00016 0.00010 [63]

r z

[GeV] 2.4952 0.0023 0.001 [64]

r i f v [GeV] 0.499 0.0015 0.001 [62]

a had [nb] 41.540 0.037 — [64]

R0 20.767 0.025 — [64]

R 0 0.21629 0.00066 — [64]

R0 0.1721 0.003 — [64]

B R ( B ^ X s Y ) x

104

B R ( B u ^ r v ) B R ( Bu^ t v)

SM

B R (B 0 ^ ß + ß - )

109

3.55 1.62 2.9

0.26 0.57 1.1

0.30

0.38

[62]

[65]

[66]

QXh 2 0.1186 0.0031 0.012 [67]

m h

[GeV] 125.36 0.41 2.0 [68]

Lim it Ref.

m x v s. a xN ST XENON 100 2012 (224.6

34 kg days) [69]

m x v s. a SD SD XENON 100 2012 (224.6

34 kg days) [70]

m X v s. a xN ST LUX 2013 (118

85.3 kg days) [71]

C hargino mass L E P 2 [62]

T a b le 4 . S u m m ary of ex p erim en tal co n stra in ts th a t are used in th e likelihood. U p p er p art:

m easured observables, m odelled w ith a G au ssian likelihood w ith th e sta n d a rd d ev iatio n ( a2 + T 2)1/2, w here a is th e exp erim en tal and t th e th eo retical un certain ty . Lower p a rt: observables for w hich only lim its cu rre n tly exist. a0N an d a^D d en o te sp in -in d ep en d en t an d sp in -d ep en d en t L SP-nucleon sc a tte rin g cross-sections respectively. See te x t for fu rth e r in fo rm atio n a b o u t th e explicit form of th e likelihood function. All th e observables are described in section 3.

w here L e w represents electroweak precision observables, L B B -physics constrain ts,

m easurem ents of th e cosmological d a rk m a tte r relic density, L Dd direct d a rk m a tte r detec­

tio n constrain ts, L Biggs th e ATLAS m easurem ent of th e Higgs boson mass, and L LEp ^±

th e L E P 2 lim it on th e chargino mass.

Table 4 shows th e set of experim ental co n strain ts used in th e analysis. T h eir im ple­

m en tatio n is sum m arised below.

T he co n straints on th e electrow eak precision observables are obtain ed from Z -pole m ea­

surem ents a t L E P [64], and include th e co n strain t on th e effective electroweak m ixing angle for leptons sin2 6 ^ 7 , th e to ta l w id th of th e Z boson r z , th e invisible Z boson w id th T “ v , th e hadronic pole cross-section a 0ad, as well as th e decay w id th ratios R 0, R 0 and R 0. T he com ­ bined Tevatron and L E P W boson m ass (m W) e stim ate [62] is also included. T he B -physics

J H E P 0 9 ( 2 0 1 6 ) 1 7 5

co n strain ts include a num ber of world averages o b tained by th e Heavy F lavour Averaging G roup, including th e branching fraction B R (B ^ X sy) and th e ratio of th e branching frac­

tio n of th e decay

t v to its branching fraction predicted in th e S tan d ard M odel [62].

Finally, th e m easurem ent of th e rare decay branching fraction B R (B 0 ^ p + p - ) from th e L H C b experim ent a t th e LHC is used [66]. At th e tim e of th e initial likelihood scan a com patible m easurem ent from CMS [72] was also available. E ith e r of these m easurem ents could have been used w itho u t changing th e results, and th e L H C b value was chosen due to chronological precedence. A com bination of th e CMS and LH C b m easurem ents was later published [73] after th e initial m odel selection for this work had been perform ed. T he results from th e com bination are com patible w ith th e LH C b value and would not have a notice­

able im pact on th e final results. T he electroweak precision and B -physics co n strain ts are applied as G aussian likelihoods w ith m eans and sta n d a rd deviations as indicated in tab le 4.

For th e cosmological co n strain ts th e P lanck C o llab o ratio n ’s co n strain t on th e d ark m a tte r relic abundance is used, as this is th e m ost accu rate value available. T he co n strain t is im plem ented differently d epending on th e pro p o rtio n of d ark m a tte r a ttrib u te d to neu- tralinos. If th e n eu tralino were to m ake up all of th e d ark m a tte r in th e universe, th e result from P lanck te m p e ra tu re and lensing d a ta , “ x h 2 = 0.1186 ± 0.0031, would be applied as a G aussian likelihood [67]. B u t here, th e n eu tralin o is allowed to be a sub-dom inant d a rk m a tte r com ponent, and th e P lanck relic density m easurem ent is instead applied as an u p p er lim it. T he effective likelihood for th e u p p er lim it, tak in g into account th e error, is given by th e expression

f

œ i

Lq x h2

=

e-

(x -r*)2 x - 1 dx, (3.4)

J Q x h 2

/ CTpianck

as derived in th e ap p end ix of ref. [74]. L

is an irrelevant no rm alisation co n stan t, r* =

^ Planck/ o p lanck, and “ x h 2 is th e predicted relic density of n eutralinos as a function of th e m odel param eters. Here p Planck refers to th e value of “ x h 2 inferred by th e P lanck C ollaboration and upianck to its uncertainty. B o th num bers are given in tab le 4. A fixed th eoretical uncertainty,

= 0.012, is also added in q u a d ra tu re to th e experim ental error, in order to account for th e num erical uncertainties entering in th e calculation of th e relic density from th e SUSY param eters.

W hen n eutralinos are not th e only co n stitu e n t of d a rk m a tte r, th e ra te of events in a d irect-d etection experim ent is proportionally smaller, as th e local n eu tralino density, px , is now sm aller th a n th e to ta l local d a rk m a tte r density, pDM. T he suppression is given by th e factor £ = px / p DM. Following ref. [75], th e ratio of local n eu tralin o density to to ta l d ark m a tte r densities is assum ed to be equal to th a t for th e cosmic abundances, th u s a scaling ansatz is adopted:

£ = = 7 ^ . (3.5)

PDM “ DM

For “

, th e central value m easured by th e P lanck C ollaboration, “ DMh 2 = 0.1186, is used [67].

T he d irect-detectio n co n strain t uses th e recent results from X ENON 100, w ith 225 live days of d a ta collected betw een F ebruary 2011 and M arch 2012 w ith a 34 kg fiducial

J H E P 0 9 ( 2 0 1 6 ) 1 7 5

volum e [69]. T he tre a tm e n t of XENON 100 d a ta is described in detail in ref. [76]. T he likelihood function is built as a Poisson d istrib u tio n for observing N recoil events when N s(0 ) signal plus N b background events are expected. T he expected num ber of background events th e XENON 100 ru n is N b = 1.0± 0.2, while th e collaboration rep o rted N = 2 events observed in th e pre-defined signal region. An u p d a te d version of th e likelihood function described in refs. [76, 77] is used. For th e spin-independent cross section, th e LU X d a ta from 85.3 live-days w ith a fiducial volum e of 118 kg [71] is used, as this result becam e available in tim e to be included in th e analysis. T h e LU X lim it was included using th e likelihood com puted by th e LU XCalc package [78]. T he likelihood is con stru cted from a Poisson d istrib u tio n in which th e num bers of observed and background events are 1 and 0.64, respectively. Im proved spin-independent [79, 80] and new spin-dependent [81] lim its have in th e m eantim e been published by LUX, b u t have not been included in th is work as th ey becam e available as th is analysis was being finalized. Such lim its are not expected to lead to significantly different results for th is analysis.

For th e im plem entation of th e Higgs boson likelihood th e m ost recent m easurem ent by th e ATLAS experim ent of th e m ass of th e Higgs boson is used, m h = 125.36 ± 0.37 ± 0.18GeV, w here th e first error is sta tistic a l and th e second erro r is sy stem atic [68]. This is fully com patible w ith th e m ost recent CMS m easurem ent [82]. A th eo retical error of 2GeV [83] is added in q u a d ra tu re to th e quoted u ncertainties. T he observed u p p er lim it of 0.23 on th e branching fraction for Higgs boson decays into invisible particles [84] (e.g.

v, Xi) is not included. Including th is bound would exclude at th e 95% confidence level (CL) 5% of m odels surviving th e initial likelihood scan, and 8% of those rem aining after th e electrow eak SUSY analysis co n strain ts have been applied.

Finally, th e likelihood associated w ith th e m(Xu ) co n strain t from L E P 2 d a ta is tak en from equ atio n (3.5) of ref. [85], w here an experim ental lower bound of 92.4GeV [62] and a th eo retical uncertain ty of 5% from th e S O F T S U S Y 3.3.10 prediction of th e spectrum is assum ed.

3 .3 P h e n o m e n o lo g y o f t h e L S P

As m entioned in section 3.1, th e results of th e likelihood scan are used to select m odels upon which to consider th e sensitivity of th e electroweak SUSY searches. F igure 1 displays th e LSP com position of those m odels w ithin th e 95% CL 2D contours, and th e ir d istrib u tio n in th e Xu versus Xu m ass plane. T he colours encode th e Xu com position of th e models.

T hree d istin ct regions are seen, which correspond to different m echanism s to enhance th e a n nih ilatio n cross-section and th u s avoid having a cosmological relic density larger th a n observed. T here is th e so-called Z -funnel region, w here th e LSP m ass is close to 45GeV and it is m ostly bino-like. In th is case, th e ann ihilatio n ra te is pro po rtio nal to th e higgsino fraction of th e Xu. T he region centred on m (X i) ~ 60GeV corresponds to a Xu th a t annihilates th ro u g h a m echanism sim ilar to th a t in th e Z -funnel b u t involving th e lightest Higgs boson instead. This is th e so-called h-funnel, and th e annih ilation ra te is p roportional to th e higgsino fraction as well as th e com bined bino and wino fraction. In each funnel, th e Xu annih ilation ra te is enhanced due to a pole in th e p ro p ag ato r (2m(Xu) ~ m z or m h , respectively) and th u s th e P lanck co n strain t can be satisfied. Finally, there is a

J H E P 0 9 ( 2 0 1 6 ) 1 7 5

F i g u r e 1. S c a tte r p lot of m odels in th e m (X i) vs. m (X ± ) plane w ith th e colour encoding which categ o ry of X? com position th e m odel belongs to. T he X? is defined as bino-like (B -like), wino-like (TT-like) or higgsino-like (HH-like) if th e relevant fractio n is a t least 80%. A m ixed Xi has a t least 20% of each d en o ted com ponent and < 20% of any o th e r com ponent. T he m odels considered are all w ith in th e 95% confidence region found using th e in itial likelihood scan.

com pressed region, w here m (Xi) ~ m (X± ). Here, th e LSP com position is less constrained

— in p articu lar, higgsino-like and wino-like sta te s are likely, as well as wino-higgsino m ixed states. Some m odel points w ith m (X?) > 200GeV have a non-com pressed spectru m and a nearly pure bino-like LSP. These correspond to th e so-called A -funnel region, w here d ark m a tte r annihilates th ro u g h th e pseudoscalar Higgs boson pole.

4 S ig n a l sim u la tio n an d e v a lu a tio n o f A T L A S c o n str a in ts

C o n strain ts from ATLAS SUSY searches are im posed on th e 570 599 m odels generated in th e initial likelihood scan by generating and sim ulating events from a subset of these m od­

els. T he m odels are split into th ree categories: those considered to be already excluded by pre-existing co n strain ts and having a Xu lighter th a n 1TeV (108 740 m odels); those where th e considered analyses are assum ed to be insensitive w itho ut perform ing a detailed anal­

ysis (134 624 m odels); and those th a t are sim ulated to assess th e im pact of th e searches in tab le 1 (326 951 m odels).

T he pre-existing co n strain t defining th e first category of m odels is th e L E P 2 lim it on th e m ass of th e lightest chargino, m (Xi ) > 92.4GeV. T h e second category, consisting of m odels for which th e considered searches are not expected to have any sensitivity, is defined by estim atin g th e to ta l pro du ction cross-section for SUSY particle production, using P r o s p in o 2 [86- 90]. T he searches are not optim ised for detecting th e decay prod u cts of sparticles very close in m ass to th e LSP, and therefore a process

is only included in th e cross-section calculation if Am (% p LSP) or A m (% j, LSP) is g rea ter th a n

J H E P 0 9 ( 2 0 1 6 ) 1 7 5

5GeV. M odels w ith a to ta l cross-section for all considered electrow eak SUSY production processes below 0.25 fb are placed in th e second category and not processed fu rth e r at this stage. T hey are, however, included as unexcluded m odels in section 5.

T he rem aining 326 951 models, in th e th ird category, are sim ulated at p article level using M

G

1.5.12 [91] w ith th e C T E Q 6L1 p a rto n density function set [92] and P

6.427 [93] w ith th e A U ET2B [94] set of tu n e d p aram eters. M

G

is used to generate th e initial p air of sparticles and up to one addition al p a rto n , while P

is used for all sparticle decays and p a rto n showering. T

[95] and P

[96] are used to handle th e decays of T-leptons and th e final-state rad iatio n of photons, respectively.

E xp ected signal region yields are calculated for each of th e four considered analyses using these sim ulated events.

To avoid th e co m p u tatio n al cost of processing every m odel w ith th e ATLAS d etecto r sim ulation, a “calib ratio n procedu re” is used to e x tra c t C Ls values for th e m odels using th e particle-level signal region yields described above. Of th e 326 951 sim ulated models, a random sam ple of 500 m odels was selected and processed using a fast

-based [97]

sim ulation of th e ATLAS d etecto r, w ith a p aram eterisatio n of th e perform ance of th e ATLAS electrom agnetic and hadronic calorim eters [98] and full event reconstruction. T he selected m odels follow ap proxim ately th e initial likelihood scan and th u s span th e relevant p a ra m ete r space. T h e num ber of events generated for each of these m odels corresponds to ap proxim ately four tim es th e recorded in teg rated lum inosity collected at

= 8 TeV, i.e.

80 fb- 1 . For these sim ulated models, signal cross-sections are calculated a t next-to-leading (NLO) order in th e stro n g coupling c o n stan t using P r o s p w o 2 [88]. These cross-sections are in agreem ent w ith th e NLO calculations m atched to resum m ation at th e next-to-leading- logarithm ic accuracy (N L O +N L L ) w ithin ~ 2% [99- 101]. T he nom inal cross-section and th e u n certain ty are tak en from an envelope of cross-section predictions using different p a rto n d istrib u tio n function sets and facto risatio n and renorm alisation scales, as described in ref. [102].

T hese 500 m odels are th e n analysed using th e full sta tistic a l fram ew ork [103] of th e orig­

inal ATLAS electroweak SUSY analyses and a C Ls value is calculated for each of them . One difference w ith respect to th e published analyses is th a t signal regions th a t would norm ally be statistically com bined in th e likelihood fit are now tre a te d as sep arate signal regions, and CLs values are calculated for each region. Similarly, for binned signal regions each bin is tre a te d separately. T he results from th e 500 m odels are used to fit a “calib ratio n fu nctio n”

betw een th e particle-level yields and th e C L s values for each signal region. T his accounts for th e SM background prediction in each signal region, to g eth er w ith th e observed d a ta . T here is one rem aining free p aram eter, which roughly corresponds to th e average selection efficiency for SUSY events th a t pass th e particle-level selection. O nly those signal regions w here th e average efficiency could be determ ined w ith a sta tistic a l precision of b e tte r th a n 20% are considered in th e final analysis. In addition, it is required th a t at least one of th e 500 m odels is excluded, w ith expected and observed C Ls < 0.05. Of th e original 44 signal regions, 25 pass these requirem ents. T he 19 rejected signal regions typically have a low ac­

ceptance for th e E W K H m odels, due to eith er very strin gent kinem atic criteria, or a require­

m ent for Thad candid ates, which have a low yield in th e E W K H m odels considered, due to

J H E P 0 9 ( 2 0 1 6 ) 1 7 5

th e very high m ass of th e stau. T he real selection efficiency varies from m odel to model, and th e calib ratio n procedure therefore can only gives accurate results w hen averaged over m any models. No additio n al system atic u n certain ty for m odel-to-m odel variations is applied.

T his simplified m eth od provides an efficient way to calculate th e im pact of th e elec- trow eak searches and th e calibratio n functions are used to e x tra c t C Ls values for all 326 951 considered models. T he best co n straints on any signal m odel would be obtained from a s ta tistic a l com bination of all relevant signal regions; however, th is is not possible w ith this simplified approach so instead a conservative approach is used w here th e C Ls value is tak en from th e signal region w ith th e sm allest expected C L s value.

5 Im p a c t o f th e A T L A S elec tr o w ea k S U S Y sea rch es

In th is section th e im pact of th e A TLA S electrow eak SU SY searches is discussed in term s of 1D and 2D distrib u tio n s. T he m odels considered for each d istrib u tio n are those w ithin th e 95% confidence region according to th e initial likelihood scan outlined in section 3.

T here are 438 589 and 472 933 such m odels in th e 1D and 2D case, respectively.

A m odel is considered to be excluded by th e A TLA S electrow eak SU SY searches if th e observed CLs value, calculated as explained in section 4 , is less th a n 0.05. For th e 1D d istrib u tio n s in th is section, stacked plots are used to indicate th e co n tribu tion s of th e 2L,

3 £

and

searches. T he 2 t search is found to be insensitive, relative to th e oth er searches, due to th e lack of light stau s in these m odels. Signal regions of th e 3L and 4L searches th a t require Thad can d id ates are sim ilarly insensitive to these models. If m ore th a n one search can exclude a m odel, th e one w ith th e sm allest expected C Ls value is chosen, following th e procedure in section 4 . For th e 2D plots th e colours represents th e fraction of m odels which are excluded by ATLAS d a ta at 95% CL. In all of th e d istrib u tio n s th e fractions displayed correspond to th e p ro p o rtio n of m odels excluded for a given bin in th e p a ra m ete r space.

Of th e 472 933 m odels w ithin th e tw o-dim ensional 95% CL bound before th e ATLAS electrow eak SUSY analyses are considered, approxim ately 3% are excluded by th e searches considered (listed in tab le 1) . T he 3L search is th e m ost powerful of th e four analyses across these models, having th e signal region w ith th e lowest expected C L s for 63.3% of th e excluded models. T he high sensitivity of th is search is largely due to a signal region th a t is binned in kinem atic q u an tities such as th e dilepto n invariant m ass and E™ ss (the signal region is called SR0

a in ref. [34]). T he 20 bins of SR0

a are tre a te d here as 20 individual signal regions, th e m ost powerful of which (for these models) is bin 16, requiring a Z boson can d id a te and strin gen t lower lim its on th e transv erse m ass (m T) and ETpiss.

T he 2L and 4L searches exclude sm aller fractions of models, alth oug h th ey have areas of unique sensitivity, as discussed below.

5.1 I m p a c t o n t h e e le c tr o w e a k in o m a ss e s

T he fractions of m odels excluded as a function of m (X i), m (X ±), and m (x 2 ) are shown as 2D and 1D d istrib u tio n s in figures 2 and 3 , respectively. Areas w here no m odels survive th e initial likelihood scan are left w hite in figure 2 and figure 3 . For exam ple, chargino masses below 100GeV are strongly disfavoured due to th e L E P 2 co n strain t, which also im pacts th e

J H E P 0 9 ( 2 0 1 6 ) 1 7 5

range of X

masses th a t can be considered. T he

- and h-funnel regions are also clearly visible in b o th figures 2(a) and 3 (a ).

T hese results show th a t th e considered searches effectively co nstrain th e Z - and h- funnel regions of th e p a ra m ete r space, w ith th e greatest im pact when m(Xa ) < 300GeV.

In th is scenario th e leptons produced in th e decay of th e produced electroweakinos to th e LSP have a large signal acceptance, and th e p ro d u ction cross-section of wino- and higgsino- like particles can reach O (pb ) w ith these masses. T he searches have a negligible im pact in th e com pressed region w here m (X i) ~ m(Xa ), since th e reconstruction efficiency of low-pT leptons (pT % 5GeV) is small.

Overall, th e results are dom in ated by th e

search, as explained above. T he 4£

search is uniquely sensitive to a small fraction of m odels in a p a rticu la r region of th e p a­

ram e te r space w here all of th e electroweakinos have masses sm aller th a n approxim ately 300GeV. These m odels also have a p a rticu la r p a tte rn of w ino/higgsino m ixing th a t es­

pecially favours th e SR0Z signal region, which requires a Z c an d id ate and significant E T - 8 [35]. T he signal process pp ^

X

^ Z

Z X

was already considered in th e 4£

search p a p e r as a simplified model; however, th e relatively light (m < 300GeV) wino- like X

and X± particles supplem ent th e search sensitivity via long cascades such as

+

^ (Z X + )(W _

2) ^

+ X i)(W - Z

i). T he 2£ search is m ainly used to exclude m odels w ith extrem ely light higgsino-like particles (m (Xi , X

) ~ 100-130GeV), w ith a bino- like LSP in th e Z - or h-funnel region. T he exclusion power arises m ostly from th e signal region SR-W W a, which is optim ised for processes such as pp ^

- ^ (W + *

i) ( W 2 *

i ) w here m (

) — m (X i) < m W [30]. T he wino-like electroweakinos are usually significantly m ore m assive (m (X

,X

) % 300GeV), such th a t th e search is m ainly sensitive to

+

, x2Xi and X4Xi p air production.

C om paring figures 2(b) and 3(c) shows th a t these searches are in general only sensitive to m odels w here th e X

m ass is sm aller th a n ab o u t 300GeV. T he p rop ortion of excluded m odels approaches 30% in th e best case, for m (X2) ~ 120GeV. This subset of m odels corresponds m ost closely to th e canonical sig natu re targ e te d by th e 2£, 3£ and 4£ searches, w here wino- or higgsino-like particles decay to a bino-like LSP and eith er a W or Z boson (which m ay be off-shell). These searches are expected to be less sensitive in th e case where th e x2 and

m asses are not degenerate, as seen in figure 2 (b ). T hen, even if th e

is accessible, typically th is implies th a t it and th e LSP are b o th m ostly wino-like, w ith a very sm all m ass difference th a t prevents d etectio n by th e considered analyses. T he ATLAS search for disap p earin g tracks [36] targ e ts th is kind of signature, in th e case w here th e mass difference is small enough th a t th e X i can traverse a significant p o rtio n of th e d etecto r before it decays (A m < 200MeV). A full consideration of th is search would lead to fu rth e r co n strain ts in th is p a rt of th e p a ra m ete r space as shown in ref. [26].

5 .2 I m p a c t o n t h e E W K H m o d e l p a r a m e te r s

Figures 4 and 5 display th e fraction of m odels excluded for th e five E W K H param eters:

M 1, M 2,

and t a n ß . As before, regions of th e p a ra m ete r space are visible where no m odels are allowed. For exam ple, th ere are no m odels w ith

or |p| less th a n 80GeV due to th e L E P 2 co n strain t on th e X i m ass. T he m easured value of B R (B 0 ^

) is

J H E P 0 9 ( 2 0 1 6 ) 1 7 5

(a) (b)

F i g u r e 2. T he bin-by-bin fraction of m odels excluded as a 2D function of sp article masses. T he colour encodes th e fraction of m odels excluded. T he m odels considered are all w ith in th e 2D 95%

confidence region found using th e in itial likelihood scan. No such m odels are in th e w hite regions, a n d therefore th e coloured bins in d ica te th e 95% CL contours for th e in itial likelihood scan.

com patible w ith th e S ta n d ard M odel prediction, disfavouring th e region w ith mA % 500GeV in figure 5(d) as co n trib utio n s to th a t process typically scale as ~ ta n 6

Finally, values of ta n

10 (figure 5(e)) are strongly favoured because th e tree-level co n trib u tio n to th e Higgs boson m ass is m axim ised.

As seen in figures 4 and 5(a)- 5 (c), th e considered searches have th e strongest im pact w hen |M i|, M 2 and |ß| are all small ( ^ 1TeV), w here th e SUSY particle p rod u ction cross­

section is large. T he searches have th e strongest im pact w here th e Xi is light and bino-like;

ap proxim ately 86% of m odels w ith |M 1| < 85GeV are excluded, which corresponds to th e re­

gion m (X i) < 65GeV in figure 3. T he im pact on M 2 and ß is less severe, w here th e excluded fraction peaks a t ab o u t 4%. In th e case of M 2, a small num ber of m odels w ith M 2 > 1TeV are excluded, corresponding to m odels w ith a light higgsino spectrum and a bino-like LSP.

T he considered searches can only provide indirect co n strain ts on th e rem aining m odel p aram eters, mA and ta n ß . Therefore, th e features in figures 5(d) and 5(e) are driven by th e p roperties of m odels w ith a low-mass LSP in th e Z - or h-funnel. A lthough th e pseudoscalar boson does not en ter directly into th e phenom enology of th e considered elec- trow eak searches, th e p ro po rtio n of excluded m odels is g reatest for values of mA below 1TeV, while th e excluded m odels span a wide range of ta n ß betw een a b o u t 20 and 50.

5 .3 I m p a c t o n d a rk m a tt e r o b s e r v a b le s

Finally, th e im pact of th e considered electrow eak searches in several 2D p a ra m ete r spaces relevant to d a rk m a tte r phenom enology is shown in figure 6 . F igure 6(a) shows th e fraction of m odels excluded in th e Xi relic abundance versus Xi m ass plane. T he Z - and h-funnel regions can again be clearly seen. T he exclusion power of th e considered searches depends only weakly upon th e relic density, which can be as sm all as ~ 10-3 depending on th e higgsino com ponent of th e LSP and th u s th e efficiency of th e s-channel annihilation.

J H E P 0 9 ( 2 0 1 6 ) 1 7 5

(a) (b)

F i g u r e 3. T he n u m b er of m odels sam pled by th e in itial likelihood scan, an d th e stacked bin-by- b in n u m b er of m odels excluded by th e R u n 1 ATLAS SUSY searches as a 1D function of m (X?), m (X i ), an d m (X?). T he lower p a rt of each figure shows th e fraction of m odels excluded by th e R u n 1 ATLAS SUSY searches. T he red bins in d icates th e fraction th a t is excluded by a 21 SR, th e green by a 3^ SR, an d blue by a 4^ SR. T he m odels considered are all w ith in th e 1D 95% confidence interval found using th e in itial likelihood scan.

T he region a t higher LSP m ass corresponds to th e region w here th e X± and Xi are close in m ass (cf. figure 1) . Efficient coannihilation betw een these sta te s (and th e X2, if relevant) reduces th e relic density w ith respect to a pure bino-like particle. P u re higgsino-like states w ith m (X i) ~ 1TeV and pure wino-like sta te s w ith m (

i) ~ 2TeV s a tu ra te th e relic density.

Below these masses, m ixed sta te s can give rise to th e full range of relic densities illu strated in th e plot. Finally, th e A -funnel region can be seen in th e m odels w ith m (X i) > 200GeV away from th e com pressed sp ectru m strip in figure 2 (a ). In th is region th e Xi is m ostly bino- like. As discussed above, th e considered searches have a negligible im pact on these regions.

J H E P 0 9 ( 2 0 1 6 ) 1 7 5

(a) (b)

F i g u r e 4 . T h e bin-by-bin fraction of m odels excluded as a 2D function of m odel p aram eters. T he colour encodes th e fraction of m odels excluded. T he m odels considered are all w ith in th e 2D 95%

confidence region found using th e in itial likelihood scan. No such m odels are in th e w hite regions, a n d therefore th e coloured bins in d icate th e 95% CL co n to u rs for th e in itial likelihood scan. T he p lo ts are tru n c a te d in |M i | an d |p,| to highlight th e region of ATLAS electrow eak SUSY sensitivity.

F igure 6(b) shows th e SI X i-proton scatterin g cross-section versus th e Xi m ass. This shows th a t each of th e th re e regions w ith different d a rk m a tte r an nih ilation m echanism s spans a large cross-section range. Large values of th e cross-section are not penalised in th e likelihood scan because th e scaling factor £ given in E q u a tio n (3.5) reduces th e predicted n um ber of recoil events, w eakening b o th th e XENON 100 and LUX constrain ts. T he largest cross-sections are achieved w hen th e Xi acquires some higgsino com ponent, w hereas cross­

sections are suppressed when th e Xi has an increased bino or wino com ponent in th e lo w /in term ed iate Xi m ass regions. Very low values of ^ 10- i6 pb are rare, b u t occur in some m odels due to cancellations betw een th e contrib utio ns from th e two n eu tral CP- even Higgs bosons. T he SUSY searches considered here exclude a large p o rtio n of th e p a ra m ete r space w ith m (X i) < 65GeV, including a t sm aller scatterin g cross-sections where cu rren t and fu tu re tonne-scale underground d a rk m a tte r d irect-d etectio n experim ents will have less sensitivity.

F igure 6(c) shows th e ATLAS co n straints in a plane of th e SI Xu-proton cross-section versus th e Xi relic density. Since th is stu d y assum es th a t th e local Xi density scales w ith th e cosmological abundance, th e XENON 100 and LUX lim its are shifted tow ards larger SI cross-section values for m odels w ith a relic density sm aller th a n th e value m easured by P lanck. This tra n sla te s into a negative correlation for large values of th e SI scatterin g cross-section (> 10-8 pb).

For th e sm allest values of Qx h 2 ( ~ 10- 4 ) th e m ost favoured region of p a ra m ete r space is a narrow b an d stretch in g along th e cu rren tly largest allowed SI cross-section values of a b o u t 10- i pb. In th is region, th e low relic density is achieved by m odels th a t sit on th e A -funnel resonance. T he Xi for these m odels is m ostly bino b u t w ith a sizeable higgsino content which explains th e large SI cross-section. This large SI cross-section also p u ts these m odels w ithin reach of fu tu re d irect-detectio n searches. For larger relic densities, th e SI

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(e)

Figure 5. T he num ber of m odels sam pled by th e in itial likelihood scan, an d th e stacked bin-by-bin n u m b er of m odels excluded by th e R u n 1 ATLAS SUSY searches as a 1D function of th e E W K H m odel p aram eters. T he lower p a rt of each figure shows th e fraction of m odels excluded by th e R un 1 ATLAS SUSY searches. T he red bins in d icates th e fraction th a t is excluded by a 21 SR, th e green by a 3£ SR, an d blue by a 4£ SR. T h e m odels considered are all w ith in th e 1D 95% confidence interval found using th e in itial likelihood scan. T h e p lo ts are tru n c a te d in \M 1\ and |p,| to highlight th e region of ATLAS electrow eak SUSY sensitivity.

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(a) (b)

F i g u r e 6. T he bin-by-bin fraction of m odels excluded as a 2D function of th e d a rk m a tte r observ­

ables. T h e colour encodes th e fraction of m odels excluded. T he m odels considered are all w ith in th e 2D 95% confidence region found using th e in itial likelihood scan. No such m odels are in th e w hite regions, and therefore th e coloured bins in d icate th e 95% C L contours for th e in itial likelihood scan.

cross-section is small as long as th e higgsino ad m ix tu re is small, b u t, in th e case w here th e Xi becomes higgsino-like (wino-like), annihilation is still efficient provided th e higgsino-like (wino-like) Xi has a m ass m (X i) < 1(2)TeV. In this scenario th e relic abundance is low, corresponding to th e region 10-4 < Qx h 2 < 10- i . Finally, when th e Xi is eith er bino-like (w ith a m ass of ~ 50GeV or a few hundred GeV), wino-like (w ith a m ass of a b o u t 2TeV) or higgsino-like (w ith a m ass of ab o u t 1TeV) th e n th e relic density m atches th e m easurem ent from th e P lanck C ollaboration. In these cases th e SI cross-section reaches lower values because of th e g reater p u rity of th e Xi.

T he im pact of th e electrow eak SUSY searches is stronger for th e region of th e p a ra m ete r space w here 10-2 < Ux h 2 < 10- i and th e SI cross-section is low. T here is also a mild im pact for larger SI cross-sections (10- i l - 1 0 -8 pb) w hen th e relic density extends down to Qx h 2 ~ 10- 3 .

Taken togeth er, these results show th a t d irect searches for th e electroweak production of SUSY particles w ith th e ATLAS experim ent have a significant im pact on th e phe-

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nom enologically relevant Z - and h-funnel regions in th e pM SSM , w ith out relying on th e p ro d u ction of squarks and gluinos. T he exclusions weaken if m (X i ) > 300GeV, which m o­

tiv ates fu rth e r stu d y w ith R un-2 d a ta collected a t

/

= 13TeV. T he considered searches have lim ited sensitivity in regions of th e p a ra m ete r space th a t favour Xi-X1 coannihilation and th e A-funnel, altho u g h p a rts of these regions could be explored using o th er search channels not considered here. T he im pact of th e considered searches is com plem entary to o th er co n strain ts, and th ey probe regions of th e p a ra m ete r space th a t are difficult to reach w ith d irect-detectio n d a rk m a tte r experim ents.

6 C o n c lu sio n s

T he ATLAS C ollaboration perform ed a set of ded icated searches for electrow eak SUSY p article pro duction durin g th e first run of th e LHC, using pp collisions w ith centre-of-m ass energy of 8TeV and an in teg rated lum inosity of 20.3 fb- i . In this work these searches are in terp reted in a five-dim ensional realisation of th e pM SSM called EW K H . T his effective m odel param eterises th e relevant d a rk m a tte r phenom enology and defines th e Higgs sector a t tree level of th e whole pMSSM.

T he p a ra m ete r space of th e th eo ry was initially sam pled using a likelihood-driven m ethod. T he com bined likelihood contains term s for previous collider searches, electroweak precision m easurem ents, flavour physics results, th e d ark m a tte r relic density and direct d a rk m a tte r searches, as well as th e Higgs boson mass. T he dim ensionality of th e initial likelihood scan was reduced to one or two p aram eters by m axim ising th e likelihood func­

tio n over th e rem aining p aram eters. This produced 472 933 m odels w ithin th e 2D 95%

confidence-level region.

C o n strain ts from ATLAS searches for electrow eak SUSY particle p ro d u ction in events w ith two, th re e and four charged leptons were th e n applied by tak in g th e C Ls value of th e signal region w ith th e best expected sensitivity for each model. M odels w ith C L s < 0.05 were considered to be excluded at 95% confidence level. D ue to th e num ber of m odels involved, a new m eth od for estim atin g th e C Ls values of different signal regions was de­

veloped, which uses only generator-level inform ation in add ition to a calib ratio n sam ple of 500 m odels th a t were passed th ro u g h th e full ATLAS d etecto r sim ulation. T he fraction of m odels excluded as a function of m odel param eters and m asses was th e n studied.

T he d a rk m a tte r relic density m easurem ent from th e P lan ck C ollaboration allows only four regions of p a ra m ete r space. These correspond to th re e m echanism s th a t achieve a high enough d a rk m a tte r an nih ilatio n cross-section. These regions are: th e Z-funnel w ith m (X i) ~ 45GeV; th e h-funnel w ith m (X i) ~ 60GeV; th e coannihilation region w ith m (X i) ~ m (X l ) which extends up to m (X i) ~ 2TeV; and th e A-funnel w ith 0.2 < m (X i) <

2TeV. T he considered searches exclude 86% of th e m odels in th e Z - and h-funnel regions (m (X i) < 65GeV) while having negligible sensitivity to th e coannihilation and A-funnel regions. T he m ass spectru m in th e co annihilation region is, by definition, com pressed, and any leptons produced in th e decays of these particles are to o soft for th e considered searches. It is possible th a t an existing search, not considered here, for events w ith a dis­

a pp earin g tra c k would be sensitive to th e po rtio n of this region w here th e m ass sp littin g is

< 200MeV, leading to a m etastab le chargino th a t would decay in th e d etecto r. In addition,

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