P u b l i s h e d f o r SISSA b y S p r i n g e r R e c e i v e d: September 1, 2015
R e v i s e d: December 15, 2015 A c c e p t e d: January 13, 2016 P u b l i s h e d: January 28, 2016
Search for invisible decays of a Higgs boson using vector-boson fusion in pp collisions at √ s
=8 T eV with the A T L A S detector
T h e A T L A S collaboration
E -m a il: atlas.publications@cern.ch
Ab s t r a c t: A search for a Higgs boson produced via vector-boson fusion and decaying into invisible particles is presented, using 20.3 fb -1 of p ro to n -p ro to n collision d a ta a t a centre- of-mass energy of 8T eV recorded by th e ATLAS d etecto r a t th e LHC. For a Higgs boson w ith a m ass of 125 GeV, assum ing th e S tan d ard M odel prod uctio n cross section, an u p per b ound of 0.28 is set on th e branching fraction of H ^ invisible a t 95% confidence level, w here th e expected u p p er lim it is 0.31. T he results are in terp reted in m odels of Higgs- p o rta l d a rk m a tte r w here th e branching fraction lim it is converted into u p p e r bounds on th e d ark -m atter-n u cleo n scatterin g cross section as a function of th e d a rk -m a tte r particle m ass, and com pared to results from th e direct d a rk -m a tte r detection experim ents.
Ke y w o r d s: H adron-H adron scattering, Higgs physics
ArXiy ePr in t: 1508.07869
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C o n te n ts
1 I n tr o d u c tio n 1
2 D e t e c t o r 3
3 S im u la tio n 3
4 E v e n t s e le c tio n 5
5 B a c k g r o u n d e s tim a t io n s 7
5.1 D ata-d riv en estim atio n of th e m ultijet background 8 5.2 E stim atio n s of th e Z ( ^ v v )+ je ts and W ( ^ tv ) + je ts backgrounds 8
5.3 V alidation of d ata-d riv en estim ation s 14
6 S y s t e m a t ic u n c e r ta in t ie s 14
7 R e s u lts 15
8 M o d e l in te r p r e ta t io n 19
9 C o n c lu s io n s 20
T h e A T L A S c o lla b o r a tio n 28
1 In tr o d u c tio n
A strophysical observations provide strong evidence for d a rk m a tte r (see ref. [ 1] and th e references therein ). D ark m a tte r (DM) m ay be explained by th e existence of weakly in ter
actin g m assive particles (W IM P) [2, 3]. T h e observed Higgs boson w ith a m ass of ab o u t 125 GeV [4 , 5] m ight decay to d a rk m a tte r or n e u tra l long-lived massive particles [6- 10], provided this decay is kinem atically allowed. This is referred to as an invisible decay of th e Higgs boson [11- 18].
T his p a p e r presents a search for invisible decays of a Higgs boson produced via the vector-boson fusion (V B F) process. In th e S ta n d ard M odel (SM ), th e process H ^ Z Z ^ 4v is an invisible decay of th e Higgs boson, b u t th e branching fraction (BF) is 0.1% [19, 20], which is below th e sensitivity of th e search presented in th is pap er. In ad d itio n to th e V B F Higgs boson signal itself, th ere is a co n trib u tio n to Higgs boson p ro d uction from th e gluon fusion plus 2-jets (g g F + 2 -jets) process, which is sm aller th a n th e V B F signal in th e phase space of interest in th is search. T he g g F + 2 -jets co n trib u tio n is tre a te d as signal. T he search is perform ed w ith a d a ta se t corresponding to an integ rated lum inosity of 20.3 fb -1 of p ro to n -p ro to n collisions a t y fs = 8 TeV, recorded by th e ATLAS d e te c to r at th e LHC [21].
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T he signature of th is process is two je ts w ith a large sep aratio n in p seud orapid ity 1 and large m issing tran sv erse m o m entum 2 E™ ss. T he V B F process, in its m ost extrem e topology (high dijet invariant m ass for exam ple), offers strong rejection against th e QCD- in itiated (W, Z ) + je ts (V + je ts) backgrounds. T he resulting selection has a significantly b e tte r signal-to-background ratio th a n selections targ e tin g th e ggF process.
T he CMS C ollaboration obtained an up p er bound of 58% on th e branching frac
tio n of invisible Higgs boson decays using a com bination of th e V B F and Z H pro d uctio n m odes [22]. W eaker lim its were ob tained using th e Z ( ^ £ £ )H + E™ ss sign ature by b o th th e ATLAS and CMS collaborations [22, 23], giving u p p er lim its a t 95% CL of 75% and 83% on th e branching fraction of invisible Higgs boson decays, respectively. By com bining th e searches in th e Z ( ^ £ £ )H and Z ( ^ b b )H channels, CMS o b tained an up p er lim it of 81% [22]. Using th e associated p ro d uctio n w ith a vector boson, V H , w here th e vector- boson decays to jets and th e Higgs boson to invisible particles, ATLAS set a 95% CL up per bound of 78% on th e branching fraction of H ^ invisible [24]. O th e r searches for large Em iss in association w ith one or m ore je ts were rep o rted in refs. [25- 28]. These searches are less sensitive to H iggs-m ediated interactio ns th a n th e search presented here, because th ey are prim arily sensitive to th e ggF process and have significantly larger backgrounds.
Assum ing th a t th e couplings of th e Higgs boson to SM particles correspond to th e SM values, global fits to m easurem ents of cross sections tim es branching fractions of different channels allow th e e x tra ctio n of a lim it on th e Higgs boson’s branching fraction to invisible particles. T he 95% CL u p p er lim its on th is branching fraction set by ATLAS and CMS are 23% and 21% respectively [29, 30]. T here is an im p o rta n t com plem entarity betw een direct searches for invisible decays of Higgs bosons and indirect co n strain ts on th e sum of invisible and un d etected decays. A sim ultaneous excess would confirm a signal, while a non-zero branching fraction of H ^ invisible in th e global fit, b u t no excess in th e searches for Higgs boson decays to invisible particles, would point tow ard oth er u ndetected decays or m odel assum ptions as th e source of th e global fit result.
In th e search presented in th is paper, th e events observed in d a ta are consistent w ith th e background estim ations. An u p p er bound on th e cross section tim es th e branching fraction of th e Higgs boson decays to invisible particles is com puted using a m axim um - likelihood fit to th e d a ta w ith th e profile likelihood-ratio te st s ta tistic [31]. A co n strain t on th e branching fraction alone is obtain ed assum ing th e SM V B F and ggF p ro d uctio n cross sections, acceptances and efficiencies, for invisible decays of a Higgs boson w ith a m ass m H = 125 GeV.
In th e context of m odels w here d a rk m a tte r couples to th e SM particles p rim arily th ro u g h th e Higgs boson [32], lim its on th e branching fraction of invisible Higgs boson de
cays can be in terp reted in W IM P-nucleon in teraction m odels [33] and com pared to experi
1ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the z-axis along the beam direction. The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upward. Cylindrical coordinates (r, 0) are used in the transverse plane, 0 being the azimuthal angle around the beam direction. The pseudorapidity is defined as n = — ln ta n0/2, where 0 is the polar angle.
2The transverse momentum is the component of the momentum vector perpendicular to the beam axis.
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m ents which search for d a rk -m a tte r particles via th e ir direct in teraction w ith th e m aterial of a d etecto r [34- 42]. T he p a p e r is organized as follows. T he ATLAS d e te c to r is briefly de
scribed in section 2 . T he m odelling of th e signal and background is presented in section 3.
T he d a ta se t, triggers, event reconstruction, and event selection are described in section 4.
T he background estim ation s are presented in section 5. In section 6, th e sy stem atic uncer
tain tie s are discussed. T he results are shown in section 7, and m odel in te rp re ta tio n s are given in section 8. Finally, concluding rem arks are presented in section 9 .
2 D e te c to r
ATLAS is a m u ltipurpose d e te c to r w ith a forw ard-backw ard sym m etric cylindrical geom etry, described in detail in ref. [21].
At small radii from th e beam line, th e inner detecto r, im m ersed in a 2 T m agnetic field produced by a th in su p erconducting solenoid located directly inside th e calorim eter, is m ade up of fine-granularity pixel and m icrostrip silicon detecto rs covering th e range |n| < 2.5, and a gas-filled straw -tu b e tran sitio n -rad ia tio n tracker (T R T ) in th e range |n| < 2. T he T R T com plem ents th e silicon tracker a t larger radii and also provides electron identification based on tra n sitio n radiation . T h e electrom agnetic (EM ) calorim eter is a lead /liq uid-arg on sam pling calorim eter w ith an accordion geom etry. T he E M calorim eter is divided into a barrel section covering |n| < 1.475 and two end-cap sections covering 1.375 < |n| < 3.2. For
|n| < 2.5 it is divided into th ree layers in d ep th , which are finely segm ented in n and ¢. An ad ditio n al th in presam pler layer, covering |n| < 1.8, is used to correct for fluctuations in energy losses betw een th e pro du ctio n vertex and th e calorim eter. H adronic calorim etry in th e region |n| < 1.7 uses steel absorbers, and scintillator tiles as th e active m edium . Liquid- argon calorim etry w ith copper absorbers is used in th e hadronic end-cap calorim eters, which cover th e region 1.5 < |n| < 3.2. A forw ard calorim eter using copper or tu n g ste n absorbers w ith liquid argon com pletes th e calorim eter coverage up to |n| = 4.9. T he m uon sp ectrom eter (MS) m easures th e cu rv atu re of m uon tra jec to rie s w ith |n| < 2.7, using th ree statio n s of precision drift tu b es, w ith cath o d e strip cham bers in th e innerm ost layer for |n| >
2.0. T he deflection is provided by a toroidal m agnetic field w ith an integral of approxim ately 3 T m and 6 T m in th e central and end-cap regions of th e ATLAS detecto r, respectively. T he MS is also in stru m en ted w ith dedicated trigger cham bers, nam ely resistive-plate cham bers in th e barrel and th in -g ap cham bers in th e end-cap, covering |n| < 2.4.
3 S im u la tio n
Sim ulated signal and background event sam ples are produced w ith M onte C arlo (MC) event generators, and passed th ro u g h a Ge a n t4 [43] sim ulation of th e ATLAS d e te c to r [21, 44], or a fast sim ulation based on a p aram eterizatio n of th e response to th e electrom agnetic and hadronic showers in th e ATLAS calorim eters [45] and a detailed sim ulation of o th er p a rts of th e d e te c to r and th e trigg er system . T he results based on th e fast sim ulation are validated against fully sim ulated sam ples and th e difference is found to be negligible. T he sim ulated events are reconstru cted w ith th e sam e software as th e d a ta . A dditional pp collisions in
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th e sam e and nearby bunch-crossings (pileup) are included by m erging diffractive and non- diffractive p p collisions sim ulated w ith P y th ia - 8 .1 6 5 [46]. T he m u ltiplicity d istrib u tio n of these pileup collisions is re-weighted to agree w ith th e d istrib u tio n in th e collision d a ta .
B o th th e V B F and ggF signals are m odelled using P o w H E g -B o x [47- 52] w ith CT10 p a rto n d istrib u tio n functions (P D F s) [53], and Py t h ia-8.165 sim ulating th e p a rto n shower, h ad ron ization and underlying ev en t.3 T he V B F and ggF Higgs boson p ro d u ctio n cross sections and th eir uncertain ties are tak en from ref. [54]. T he tran sv erse m om entum (px) d istrib u tio n of th e V B F -produced Higgs boson is re-weighted to reflect electrow eak (EW ) radiative corrections com puted by H A W K -2.0 [55]. These E W corrections am ou nt to 10
25% in th e Higgs boson p x range of 150-1000 GeV. T he ggF co n trib u tio n to th e signal is re-weighted [56, 57] so th a t th e px d istrib u tio n of th e Higgs boson in events w ith two or m ore associated je ts m atches th a t of th e next-to-leading-order (NLO) g g F + 2 -jets calculation in P o w H E g -B o x M iNLO [58], and th e inclusive distrib u tio n s in je ts m atch th a t of th e next-to- next-to-leading-order (NNLO) and next-to-next-to-lead ing -lo garithm (NNLL) calculation in H Re s-2.1 [59, 60]. T he effects of finite q uark masses are also included [52].
T he W ( ^ ^ v )+ je ts and Z ( ^ ££)+jets processes are generated using S h e rp a -1 .4 .5 [61]
including leading-order (LO) m a trix elem ents for up to five parto n s in th e final s ta te w ith CT10 P D F s and m atching these m a trix elem ents w ith th e p a rto n shower following the p rocedure in ref. [62]. T he W ( ^ ) + je ts and Z ( ^ ££)+ jets processes are divided into two com ponents based on th e num ber of electrow eak vertices in th e F eynm an diagram s.
D iagram s which have only two electrow eak vertices contain je ts th a t are produced via th e strong interaction, and are labelled “Q C D ” Z + je ts or W + je ts. D iagram s which have four electrow eak vertices contain je ts th a t are produced via th e electroweak interaction, and are labelled “E W ” Z + je ts or W + je ts [63]. T he MC predictions of th e QCD com ponents of W + je ts and Z + je ts are norm alized to NNLO in F E W Z [64, 65], while th e E W com ponents are norm alized to V B FN L O [66], including th e je t px and dijet invariant m ass requirem ents. T he interference betw een th e QCD and E W com ponents of Z + je ts and W + je ts is evaluated w ith S h e rp a -1 .4 .5 to be 7.5-18.0% of th e size of th e E W contri
b u tio n depending on th e signal regions. To account for this interference effect, th e E W c o n trib u tio n is corrected w ith th e estim ated size of th e interference term . F igure 1 shows F eynm an diagram s for th e signal and exam ple vector-boson backgrounds. T here are ad ditio nal small backgrounds from rt, single to p, diboson and m u ltijet production. T he t t process is m odelled using P o w H E g -B o x , w ith P y th ia - 8 .1 6 5 m odelling th e p a rto n shower, h ad ro nizatio n and underlying event. Single-top p ro d u ction sam ples are generated w ith M C @ N L O [67] for th e s- and W t-channel [68], while A c e rM C -v 3 .8 [69] is used for single
to p p ro d u ctio n in th e t-channel. A to p -q u ark m ass of 172.5 GeV is used consistently. T he A U ET2C (A U ET2B) [70] set of optim ized p aram eters for th e underlying event description is used for t t (single-top) processes, w ith CT10 (C TEQ 6L1) [71] P D F s. D iboson sam ples W W , W Z and Z Z (w ith leptonic decays) are norm alized a t NLO and generated using HERWig-6.5.20 [72] w ith CT10 P D F s, including th e p a rto n shower and hadronization, and
3The invisible decay of the Higgs boson is simulated by forcing the Higgs boson (with m H = 125 GeV) to decay via H ^ ZZ * ^ 4v.
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F ig u re 1. Example Feynman diagrams for the VBF H i n v i s i b l e ) signal and the vector-boson backgrounds.
Jim m y [73] to m odel th e underlying event, w hereas th e W W , W Z , and Z Z ( ^ ££qq, v v q q ) processes are g enerated to g eth e r w ith E W W + je ts and Z + je ts sam ples. D iboson W W , W Z and Z Z ( ^ £ £ q q ,v v q q ) sam ples generated using S h e rp a -1 .4 .5 w ith CT10 P D F s and norm alized to NLO in QCD [74] are used as a cross-check. M ultijet and Y + jet sam ples are gen erated using P y th ia - 8 .1 6 5 w ith CT10 P D F s.
4 E v en t se le c tio n
T he d a ta used in th is analysis were recorded w ith an ETplss trig g er during periods when all ATLAS sub-detectors were o p eratin g under nom inal conditions. T he trigger consists of th ree levels of selections. T he first two levels, L1 and L2, use as in p u ts coarse-spatial- g ran u larity analog (L1) and digital (L2) sum s of th e m easured energy. In th e final level, calib rated clusters of cell energies in th e calorim eter [75] are used. A t each level, an increas
ingly string ent threshold is applied. T he m ost stringen t requirem ent is ETplss > = 80G eV . B ecause of fu rth e r corrections m ade in th e offline recon structed ETpiss and th e resolutions of th e L1 and L2 calculations, th is trigg er is not fully efficient until th e offline ETpiss is g reater th a n 150 GeV.
J e ts are reconstructed from calib rated energy clusters [76, 77] using th e an ti-kt algo
rith m [78] w ith radius p a ra m ete r R = 0.4. Je ts are corrected for pileup using th e event-by- event je t-a re a su b tra c tio n m eth od [79, 80] and calib rated to particle level by a m ultiplicative je t energy scale factor [76, 77]. T he selected je ts are required to have p T > 20 GeV and
|n| < 4.5. To discrim inate against je ts o riginating from m inim um -bias interactions, selec
tio n c riteria are applied to ensure th a t at least 50% of th e j e t ’s sum m ed scalar tra c k p T , for je ts w ithin |n| < 2.5, is associated w ith tracks originating from th e p rim ary vertex, which is taken to be th e vertex w ith th e highest sum m ed pT of associated tracks. Inform ation a b o u t th e tracks and clusters in th e event is used to co n stru ct m ultiv ariate discrim inators to veto events w ith b-jets and hadronic T-jets. T he requirem ents on these discrim inators identify b-jets w ith 80% efficiency (estim ated using t t events) [81- 83], one-track jets from hadronic t decays w ith 60% efficiency (m easured w ith Z ^ t t events), and m ultiple-track je ts from hadronic T decays w ith 55% efficiency [84].
E lectron cand id ates are recon structed from clusters of energy deposits in th e electro
m agnetic calorim eter m atched to tracks in th e inner d e te c to r [85]. M uon cand idates are
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Requirement SR1 SR2a SR2b
Leading Jet p T >75 GeV >120 GeV >120 GeV
Leading Jet Charge Fraction N/A >10% >10%
Second Jet pT >50 GeV >35 GeV >35 GeV
mjj >1 TeV 0.5 < m jj < 1 TeV > 1 TeV
% i x j <0
|A% j| >4.8 >3 3 < |A% j| < 4.8
| A j | <2.5 N/A
Third Jet Veto p T Threshold 30 GeV
|A^ j,E ™ | >1.6 for j i , >1 otherwise >0.5 zrmiss
Et >150GeV >200 GeV
T ab le 1. Summary of the main kinematic requirements in the three signal regions.
reco nstructed by requiring a m atch betw een a tra c k in th e inner d e te c to r and a tra c k in th e m uon sp ectrom eter [86].
T he selection defines th re e orthogonal signal regions (SR), SR1, SR2a and SR2b. T hey are distinguished p rim arily by th e selection requirem ents on th e invariant m ass m jj of th e two highest-pT jets and th e ir sep aration in p seudorapidity A j as shown in tab le 1. T he SR1 selection requires events to have two jets: one w ith p T > 75 GeV and one w ith p T > 50 GeV. T he E™ ss is co n stru cted as th e negative vectorial sum of th e transverse m om enta of all calibrated objects (identified electrons, m uons, photons, hadronic decays of T-leptons, and jets) and an additional term for transverse energy in th e calorim eter n ot included in any of these objects [87]. E vents m ust have E “ iss > 150 GeV in order to suppress th e background from m ultijet events. To fu rth e r suppress th e m ultijet background, th e two leading jets are required to have an azim uthal opening angle | A j | < 2.5 radians and an azim uthal opening angle w ith respect to th e E J flss of |A ^ j Emiss | > 1.6 radians for th e leading je t and |A 0 j EimiSS | > 1 rad ian otherw ise. In th e V B F process, th e forw ard jets ten d to have large separations in pseudorapidity ( A j ), w ith correspondingly large dijet m asses, and little hadronic activ ity betw een th e two jets. To focus on th e V B F production, th e leading je ts are required to be w ell-separated in pseudorapidity |A p jj | > 4.8, and have an invariant m ass m jj > 1 TeV. E vents are rejected if any je t is identified as arising from th e decay of a b-quark or a t -lepton. T he rejection of events w ith b-quarks suppresses to p -q u ark backgrounds. Similarly, rejection of events w ith a t -lepton suppresses th e W ( ^ t v ) + j e t s background. F u rth er, events are vetoed if th ey contain any reco n structed leptons passing th e transverse m om entum thresholds pT > 10 GeV for electrons, pT > 5 GeV for muons, or pT > 20 GeV for T-leptons. Finally, events w ith a th ird je t having p T > 30 GeV and
|n| < 4.5 are rejected. T he SR2 selections are m otivated by a search for new phenom ena in final states w ith an energetic je t and large m issing transverse m om entum [25], and differ from those of SR1. F irst, th e leading je t 4 is required to have p T > 120 GeV and |n| < 2.5.
4The “charge fraction” of this jet is defined as the ratio of the of tracks associated to the jet to the
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A dditionally, th e sub-leading je t is required to have p T > 35 GeV, th e A j requirem ent is removed, th e requirem ent on A ^-,Emiss is relaxed to |A 0 j,Emiss| > 0.5, and th e E™ ss requirem ent is tig h tened to E™ ss > 200 GeV. A com m on threshold of p t = 7 GeV is used to veto events w ith electrons and muons, and no T-lepton veto is applied. Finally in SR2, th e ETpiss co m p u tatio n excludes th e m uon co n trib u tio n and tre a ts hadronic tau s like je ts (this allows th e m odelling of W + je ts and Z + je ts in th e control regions and signal regions using th e sam e ETpiss variable as discussed in section 5) . SR2 is fu rth e r subdivided into SR2a w ith 500 < m — < 1000 GeV, — x n j2 < 0, and |A j | > 3, and SR2b w ith m - j > 1000 GeV, — x nj2 < 0 and 3 < lA p— | < 4.8.
5 B a ck g ro u n d e stim a tio n s
In order to reduce th e im pact of theo retical and experim ental u ncertainties, th e m ajo r back
grounds, Z ^ vv and W ^ t v , are determ ined from m easurem ents in a set of control sam ples consisting of Z ^ t t or W ^ t v events ( t = e /p ) . In each of these control regions (C R ), two ad ditio n al jets are required, following th e sam e requirem ents as th e signal regions. T he Z ^ t t control sam ples consist of events w here th e invariant m ass of two sam e-flavour and opposite-sign leptons is consistent w ith th e Z -boson mass, and so backgrounds in these control regions are small enough th a t th ey are tak en from th e ir MC predictions ra th e r th a n from d ata-d riv en m ethods. In th e W ^ t v control regions, th e background from jets m isidentified as leptons is m ore im p o rta n t, at least for th e case of W ^ e v . In SR1, th e background from jets m isidentified as leptons in th e W ^ t v control regions is norm alized using a fit th a t takes advantage of th e distinctive shape of th e transv erse m ass d istrib u tio n
m T = ^2pTETpiss 1 — c o s ( A ^ )Emiss) (5.1) of th e lepton and ETpiss, and th e charge asy m m etry in W + / W - events. In SR2, th e back
ground from jets m isidentified as leptons in th e W ^ t v control regions is reduced by th e requirem ents on m T and ETpiss as discussed in section 5.2.
In order to use th e control regions ra th e r th a n th e MC predictions for settin g th e W + je ts and Z + je ts background norm alizations, th e MC predictions in each of th e three signal regions and six corresponding Z ( ^ e e /p p ) + je ts and W ( ^ e v /p v ) + je ts control regions are scaled by free p aram eters fcj. T here is one k for each signal region and th e corresponding control regions. In SR1 for exam ple, o m ittin g factors th a t m odel system atic u ncertainties, th e expected num ber of events for Z ( ^ v v )+ je ts in th e signal region is Z SR1 = k 1ZSR1, for Z ( ^ t t ) + j e t s in th e Z ^ t t control region Z CR = fc^CR?, and for W ( ^ tv ) + je ts in th e W ^ t v control region WCR = fo W C R . T h e scale factors k are com m on for th e Z + je ts and W + je ts background norm alizations. T he scale factors k are determ ined from th e m axim um Likelihood fit described in section 7. T he Z ( ^ t t ) + j e t s and th e W ( ^ tv ) + je ts MC predictions th u s affect th e final estim ates of Z ( ^ v v )+ je ts calibrated jet pT ; this quantity must be at least 10% of the maximum fraction of the jet energy deposited in one calorimeter layer. The charged fraction requirement was shown to suppress fake jet backgrounds from beam-induced effects and cosmic-ray events [25].
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and W ( ^ ) + je ts in th e signal region th ro u g h an im plicit dependence on th e MC ratios Zs r/ Zcr and Zs r/Wcr for Z ( ^ v v )+ je ts , and Wsr/Wcr for W ( ^ ^ v )+ jets:
v ( *7 I *7 \ MC r^data Z SR — (zSR/zCR) x Z CR j
Zsr - (Zs r/Wc r)MC x WCRta , (5.2) Wsr — (Wsr/Wc r)MC x WCRta .
U nique estim ates of th e Z ( ^ v v )+ je ts and W ( ^ ^ v )+ je ts backgrounds in th e signal region result from th e sim ultaneous m axim um likelihood fit to th e control regions and signal region.
T he m u ltijet background is estim ated from data-d riv en m ethods as presented in sec
tio n 5.1. T he d ata-d riv en norm alizations for th e Z + je ts and W + je ts backgrounds are described in section 5.2. T he background estim ation s are validated in control regions w ith no signal contam ination, and are in good agreem ent w ith observations in th e validation control regions, as discussed in section 5.3. In SR1 and SR2, th e sm aller backgrounds of tt, single to p and dibosons are taken from th e ir MC predictions.
B ackground contribu tio ns from th e visible Higgs boson decay channels are suppressed by th e signal region requirem ents described in section 4 .
5.1 D a ta -d r iv e n e s tim a t io n o f t h e m u ltije t b a c k g r o u n d
M u ltijet events which have no p ro m p t (from th e p rim ary interactions) neutrinos can pass th e E™ ss selection due to in stru m en tal effects such as th e m is-m easurem ent of th e je t energy. B ecause of th e very large rejection from th e ETpiss requirem ent, it is not p ractical to sim ulate th is background, so it is estim ated using d ata-d riv en m eth od s instead.
In th e SR2 selections, th e m u ltijet background is estim ated from d a ta , using a je t sm earing m ethod as described in ref. [88], which relies on th e assum ption th a t th e E™ ss of m ultijet events is dom in ated by fluctuations in th e d e te c to r response to je ts m easured in th e d a ta . T he estim ated m u ltijet background in SR2 is 24 ± 24 events (a 100% u ncertain ty is assigned to th e estim ate).
In SR1, th e m ultijet background is estim ated from d a ta as follows. A control region is defined w here th e A ^ -,Emiss requirem ent is inverted, so th a t th e ETpiss vector is in th e direc
tio n of a je t in th e event. T he resulting sam ple is dom inated by m ultijet events. T he signal region requirem ents on th e leading and sub-leading je t p t and on th e ETpiss trigger are ap plied as described in section 4 . T he efficiency of each subsequent requirem ent is determ ined using th is sam ple and assum ed to apply to th e signal region w ith th e nom inal A ^ - E:miss re
quirem ent. A system atic u n certain ty is assessed based on th e accuracy of this assum ption in a control region w ith | A j | < 3.8 and in a control region w ith th re e jets. To account for th e A ^ j Emiss requirem ent itself, th e A j - requirem ent is inverted, requiring back-to-back jets in 0. T his sam ple is also m u ltijet-d o m inated. Com bining all th e efficiencies w ith th e observed control region yield gives an e stim ate of 2 ± 2 events for th e m ultijet background in SR1.
5 .2 E s t im a t io n s o f t h e Z( ^ v v ) + j e t s a n d W ( ^ l v) + j e t s b a c k g r o u n d s
To estim ate th e Z ( ^ v v )+ je ts background, b o th th e Z ( ^ e e / j ) + j e t s and W ( ^ e v /^ v ) + je ts control regions are employed. T he W + je ts background is estim ated using
J H E P 0 1 ( 2 0 1 6 ) 1 7 2
W ( ^ e v /p v )+ je ts control regions. In th e Z ( ^ e e )+ je ts control sam ples for SR1 and W ( ^ tv ) + je ts control sam ples for SR1 or SR2, electrons and m uons are required to be isolated. E lectron isolation is not required in th e SR2 Z ( ^ e e )+ je ts control sam ple. For electrons, th e norm alized calorim eter isolation tran sverse energy, i.e. th e ratio of th e isola
tio n transverse energy to lepton p T , is required to be less th a n 0.28 (0.05) for SR1 (SR2), and th e norm alized tra c k isolation is required to be less th a n 0.1 (0.05) w ithin a cone A R = \ J(A p )2 + ( A ^ ) 2 = 0.3 for SR1 (SR2). In th e SR1 selections, m uons m ust have a norm alized calorim eter isolation less th a n 0.3 (or < 0.18 if p t < 25 GeV) and a norm alized tra c k isolation less th a n 0.12 w ithin A R = 0.3, w hereas in th e SR2 selections, th e scalar sum of th e transverse m om entum of tracks in a cone w ith radius 0.2 around th e muon can d id a te is required to be less th a n 1.8 GeV. E lectrons and m uons are also required to point back to th e p rim ary vertex. T he tran sverse im pact p a ra m ete r significance m ust be less th a n 3ct for b o th th e electrons and muons, while th e longitudinal im pact p aram eter m ust be < 0.4(1.0) m m for electrons (m uons).
T he Z ( ^ e e /p p ) + je ts control regions are defined by selecting events containing two same-flavour, oppositely charged leptons w ith p T > 20 GeV and |m « — m Z | < 25 GeV, w here m u and m Z are th e d ilepton invariant m ass and th e Z -boson m ass, respectively. In th e control sam ple corresponding to th e SR1 selection, th e leading lepton is required to have p T > 30 GeV. Triggers requiring a single electron or m uon w ith p T > 24 GeV are used to select th e control sam ples in SR1; in SR2, eith er a single-electron or ETpiss trig ger is used.
T he inefficiency of th e triggers w ith respect to th e offline requirem ents is negligible. In order to em ulate th e effect of th e offline m issing tran sverse m om entum selection used in th e signal region, th e ETpiss q u a n tity is corrected by vectorially adding th e electron (SR1 and SR2) and m uon tran sverse m om enta (SR1 only). All th e Z ( ^ e e /p p ) + je ts events are th e n required to pass th e o th er signal region selections. B ackgrounds from processes o th er th a n Z ( ^ e e /p p ) + je ts are small in these control regions; th e co ntribu tion s from n o n -Z backgrounds are estim ated from MC sim ulation. For Z ^ ee (Z ^ p p ), th e non -Z background is a t a level of 1.6% (0.9%) of th e sam ple. T here is 50% u n certain ty (m ainly due to the lim ited num bers of MC events) on th e n o n -Z background co n tam in atio n in th e Z control regions. T he observed yield in th e SR1 Z control region, shown in tab le 2, is larger th a n the expected yield by 16% b u t is com patible w ithin th e com bined sta tistic a l un certain ties of MC sim ulation and d a ta . In th e SR2 control regions, th e observed and expected yields differ by 10% as shown in tab le 3 b u t are com patible w ithin th e to ta l sta tistic a l and sy stem atic u n certain ties (see section 6) . T he em ulated ETpiss d istrib u tio n s for th e Z control regions are shown in figures 2 and 3 for SR1 and SR2 respectively. Because th e m uon m om entum is excluded from th e E “ iss definition in SR2, th e “em u lated ” label is o m itted from figure 3 b .
T he W ( ^ e v /p v ) + je ts control regions are sim ilarly defined by selecting events con
tain in g one lepton w ith tran sv erse m om entum p T > 30 GeV (25 GeV) in th e case of SR1 (SR2), and no ad ditio n al leptons w ith p T > 20 GeV. T he ETpiss is em ulated in th e same way as for th e Z ^ e e /p p control region and events are required to pass th e signal region selections on je ts and ETpiss. In SR1, th e co ntrib utio ns of th e th re e lepton flavours to th e to ta l W ^ t v background after all th e requirem ents are 20% for W ^ e v , 20% for W ^ p v , and 60% for W ^ t v. T he equal contrib utio ns from W ^ ev and W ^ p v
J H E P 0 1 ( 2 0 1 6 ) 1 7 2
SR1 Z Control Regions Background Z ( ^ ee)+ jets Z ( ^ ^ ) + j e t s QCD Z ^ U 10.4 ± 1.5 14.0 ± 1.5 EW Z ^ U 7.4 ± 0.8 8.2 ± 0.8 O ther Backgrounds 0.3 ± 0.2 0.2 ± 0.1
Total 18.1 ± 1.7 22.4 ± 1.7
D ata 22 25
Table 2. Expected and observed yields for the SR1 Z e e / p , p , ) + j e t s control sample in 20.3 fb-1 of 2012 data. Expected contributions are evaluated using MC simulation, and the uncertainties are statistical only.
SR2 Z Control Regions SR2a SR2b
Background Z ( ^ ee)+ jets Z ( ^ ^ ) + j e t s Z ( ^ ee)+ jets Z ( ^ ^ ) + j e t s
QCD Z ^ U 116 ± 3 121 ± 4 26 ± 2 28 ± 2
EW Z ^ U 17 ± 1 17 ± 1 16 ± 1 16 ± 2
O ther backgrounds 8 ± 1 10 ± 2 2 ± 1 3 ± 1
Total 141 ± 3 148 ± 5 44 ± 3 47 ± 3
D ata 159 139 33 38
Table 3. Expected and observed yields for the SR2 Z ( ^ ee/p,p,)+jets control sample in 20.3 fb-1 of 2012 data. Expected contributions are evaluated using MC simulation, and the uncertainties are statistical only.
F ig u re 2. Data and MC distributions of the emulated Emlss (as described in the text) in the SR1 Z ( ^ ee/yU,yU,)+jets control region.
J H E P 0 1 ( 2 0 1 6 ) 1 7 2
Figure 3. Data and MC distributions of the Emiss (as described in the text) in the SR2 Z +jets control regions (a) Z ( ^ ee)+jets and (b) Z ( ^ p,p,)+jets.
suggest th a t these are events where the lepton is below its pT threshold or sufficiently far forward to escape the jet veto, and not events where the lepton is misidentified as a tag jet (since muons deposit little energy in the calorimeter and would therefore not be identified as a jet). This expectation is checked explicitly for the case of W ^ t v , by using MC tru th information about the direction of the T-lepton to find the A R between the T-lepton and the nearest reconstructed tag jet. The component with A Rj , T < 0.4 is completely negli
gible after the signal region requirements, indicating th a t the lepton tends to be recoiling against the tag jets rather than being aligned with them. For SR1, four W control regions are considered using different charge samples for W + / W - ^ e v /^ v since W ( ^ )+ jets is not charge symmetric as shown in table 4, whereas in SR2, only two control regions W ( ^ e v /^ v )+ je ts are used as shown in table 5.
In the W ( ^ e v /^ v )+ je ts control regions corresponding to the SR1 selection, a fit to the transverse mass defined in eq. (5.1) is used to estim ate the m ultijet background. In order to obtain an explicit measurement and uncertainty for the background from multi
jets, no requirements are made on Emiss and m T . Because the m ultijet background does not have a prom pt neutrino, the Eipiss tends to be lower and to point in the direction of the jet th a t was misidentified as a lepton. As a result, the m ultijet background tends to have significantly lower m x th a n the W + jets contribution. Control samples modelling the jets misidentified as leptons in m ultijet events are constructed by selecting events th a t pass the W + jets control region selection, except for certain lepton identification criteria: for electrons, some of the EM calorimeter shower shape requirements are loosened and fully identified electrons are removed, while for muons, the transverse impact param eter (d0) requirement which suppresses muons originating from heavy-flavour jets is reversed. To ob
tain the normalization of the multijet background in the W + jets control region, tem plates of the m T distribution for processes with prom pt leptons are taken from MC simulation.
Shape tem plates for the backgrounds from m ultijet events are constructed by summing the observed yields in control samples obtained by inverting the lepton identification and d0
J H E P 0 1 ( 2 0 1 6 ) 1 7 2
SR1 W C ontrol Regions
B ackground W + ^ ev W ^ ev W + ^ ^ v W ^ ^ v QCD W ^ fv 92.3 ± 7.2 55.1 ± 5.3 85.5 ± 7.0 43.8 ± 4.6 E W W ^ fv 99.4 ± 4.0 52.5 ± 2.9 81.9 ± 3.7 39.1 ± 2.5 QCD Z ^ f f 3.4 ± 0.6 4.4 ± 0.9 6.4 ± 1.1 5.0 ± 0.9 E W Z ^ f f 2.5 ± 0.3 2.9 ± 0.3 2.7 ± 0.3 3.2 ± 0.3 M u ltijet 28.0 ± 6.8 28.0 ± 6.8 1.6 ± 2.6 1.6 ± 2.6 O th er backgrounds 4.0 ± 0.7 1.8 ± 0.4 3.2 ± 0.7 1.0 ± 0.3
T otal 230 ± 11 145 ± 9 181 ± 8 93.7 ± 5.9
D a ta 225 141 182 98
T able 4. Expected and observed yields for the SR1 W ^ fv control sample, after all requirements in 20.3 fb-1 of 2012 data. The multijet background is estimated using the data-driven method described in the text; all other contributions are evaluated using MC simulation. Only the statistical uncertainties are shown.
SR2 W Control Regions SR2a SR2b
Background W ( ^ ev)+jets W ( ^ p,v)+jets W ( ^ ev)+jets W ( ^ p,v)+jets
QCD W ^ fv 595 ± 12 906 ± 15 122 ± 5 201 ± 7
EW W ^ fv 149 ± 5 214 ± 6 121 ± 4 184 ± 5
QCD Z ^ ff 5.8 ± 0.9 23 ± 1.6 1.6 ± 0.4 4.5 ± 0.6
EW Z ^ ff 0.4 ± 0.1 0.5 ± 0.2 2.0 ± 0.4 2.7 ± 0.8
Multijet 13 ± 3 0 ± 0 3 ± 1 0 ± 0
Other backgrounds 44 ± 4 78 ± 7 13 ± 2 19 ± 3
Total 807 ± 14 1222 ± 18 263 ± 7 411 ± 9
Data 783 1209 224 295
T able 5. Expected and observed yields for the SR2 W ( ^ ev /^v )+ jets control sample in 20.3 fb-1 of 2012 data. Expected contributions are evaluated using MC simulation, and the uncertainties are statistical only. The discrepancy in the W ( ^ p,v)+jets SR2b control region is due to a mis- modelling of the W p T. The agreement improves when the systematic uncertainties (discussed in section 6) are included.
requirem ents, and su b tra c tin g th e expected co ntribu tion s from W + je ts and Z + je ts events using MC. Since th e m isidentified-jet sam ples are expected to be charge-sym m etric, th e sam e shape tem p la te and norm alization factor is used to m odel b o th charge categories of a given lepton flavour (e or ^ ). To determ ine th e W ( ^ f v )+ je ts background norm aliza
tion, a fit to th e tran sv erse m ass m T of th e lepton and Em iss is used. T he W ( ^ f v )+ je ts co n tribu tio n, however, is not charge sym m etric, so th e different charge sam ples are kept sep arate in th e sim ultaneous fit to four m T d istribu tion s, one for each lepton flavour and charge com bination shown in figure 4 . T here are th re e free norm alizations in th e fit: one
J H E P 0 1 ( 2 0 1 6 ) 1 7 2
F ig u re 4. The transverse mass distributions used in the SR1 W +jets control regions after all requirements except for the Eiplss > 150 GeV requirement: (a) W + ^ e+v, (b) W - ^ e- v, (c) W + ^ ^ + v and (d) W - ^ .
for events w ith a pro m p t lepton, one for events w here a je t is m isidentified as an electron, and one for events w here a je t is m isidentified as a muon. T he norm alization factor for th e p ro m p t leptons in th e m T fit is 0.95 ± 0.05 (sta t).
In th e W ^ ev control region corresponding to th e SR2 selections, th e background from m ultijet events is rejected by requiring th a t th e Em iss (corrected by vectorially adding th e electron tran sv erse m om entum ) be larger th a n 25 GeV and th a t th e tran sv erse m ass be in th e range 40 < m T < 100 GeV. T he selected electron is required to pass b o th th e tra c k and calorim eter isolation requirem ents. T he tig h t requirem ents on electron isolation and E™ ss greatly reduce th e m u ltijet background relative to th e o th er backgrounds. T he residual m ultijet background in th e W ^ ev control region is at th e level of 1% of th e to ta l control region background, w ith an u n certain ty of 100%. For th e W ^ ^ v control region corresponding to th e SR2 selections, th e selected m uon is required to pass only th e tra c k isolation requirem ent and th e transverse m ass is required to be in th e range 30 < m T < 100 GeV. An a tte m p t is m ade to estim ate th e residual m u ltijet background in th e W ^ ^ v control region using a control sam ple w ith inverted m uon isolation. T he
J H E P 0 1 ( 2 0 1 6 ) 1 7 2
Figure 5. The transverse mass distributions in the SR2 W +jets control regions after all require
ments: (a) W ^ ev and (b) W ^ p v.
residual background from multijet events is negligible. Figure 5 shows the m T distributions in the SR2 W + jets control regions.
5 .3 V a lid a tio n o f d a ta -d r iv e n e s tim a t io n s
To validate the background estim ates for SR1, two signal-depleted neighbouring regions are defined by (1) reversing the veto against three-jet events and requiring th a t the third jet in the event has transverse momentum pT > 40 GeV, and (2) reversing both the jet veto with a p T > 30 GeV requirement and the jet rapidity gap with a l A j | < 3.8 requirement.
Good agreement between expectation and observation is found in these validation regions, as shown in table 6.
6 S y s t e m a t i c u n c e r t a i n t i e s
The experimental uncertainties on the MC predictions for signals and backgrounds are dom inated by uncertainties in the jet energy scale and resolution [76]. This includes effects such as the n dependence of the energy scale calibration and the dependence of the energy response on the jet flavour composition, where flavour refers to the gluon or light quark initiating the jet. Uncertainties related to the lepton identification in the control regions and lepton vetoes are negligible. Luminosity uncertainties [89] are applied to the signal and background yields th a t are obtained from MC simulation.
Theoretical uncertainties on the W + jets and Z + jets contributions to both the signal and control regions are assessed using Sh e r p a, and cross-checked with M C F M [74]
and V B F N L O [66] for the EW and QCD processes respectively, and by a comparison between Sh e r p a and Al p g e n [90] for the latter process. In all cases, the uncertainties are determined by independently varying the factorization and renormalization scales by factors of 2 and 1/2, keeping their ratio within 0.5-2.0. The parton distribution function
J H E P 0 1 ( 2 0 1 6 ) 1 7 2
Process 3-jet 3-jet and l A j | < 3.8
ggF signal 6.2 ± 3.1 -
V B F signal 19.9 ± 1.4 4.7 ± 0.6
Z ( ^ v v )+ je ts 97 ± 10 111 ± 10 W ( ^ tv ) + je ts 78.5 ± 6.5 73 ± 10
M u ltijet 19.9 ± 21.8 -
O th er backgrounds 2.2 ± 0.3 0.5 ± 0.1
Total 198 ± 25 185 ± 14
D a ta 212 195
T able 6. Expected and observed yields for the validation regions in 20.3 fb-1 of data. 3-jet:
reversal of the veto against three-jet events by requiring pi]3 > 40 GeV; and 3-jet and | A j | < 3.8:
requirements of both | A j | < 3.8 and p T > 30 GeV. Contributions from W +jets and Z +jets are normalized to data-driven estimates. The W +jets and Z +jets uncertainties include MC statistics from both the selected region and the corresponding control region, and the number of data events in the control regions. The other numbers are evaluated using MC simulation and their uncertainties indicate only statistical uncertainty.
u ncertain ties are evaluated w ith th e CT10 error sets [53]. T he u n certain ty on th e ggF yield due to th e je t selection is evaluated using Stew art-T ackm ann m eth od [91]. U n certain ty in th e p T d istrib u tio n of th e Higgs boson in ggF is evaluated from scale v ariations in H Res
following th e re-weighting of th e p T d istrib u tio n [59, 60] as m entioned in section 1. To assess th e level of th eo retical u n certain ty on th e je t veto, th e variation in th e predicted V B F cross section w ith respect to shifts in th e renorm alization and factorization scales as well as w ith respect to u n certain ty in th e parton-show er m odelling is m easured using Po w h e g-bo x NLO g en erator m atched to Py t h ia and to He r w ig. T he effect of th e p a rto n shower on th e QCD W + je ts and Z + je ts background estim ations is o b tain ed by com paring sim ulated sam ples w ith different p a rto n shower models. As shown in tab le 7, w here th e m ain system atic uncertainties are sum m arized, using th e M C predictions of Zs r/Wcr and Wsr/Wcr ratio s reduces th e system atic uncertain ties in th e final Z + je ts and W + je ts background estim ates. T he Z t t ) + j e t s / W t v ) + j e t s ratio is checked in d a ta and MC, and no discrepancy larger th a n 10% is observed, consistent w ith th e residual th eory uncertain ties on th e Z SR/W CR ratios shown in tab le 7.
7 R e su lts
Figures 6 and 7 show th e E™ ss and th e m j j distrib u tio n s after im posing th e requirem ents of SR1 and SR2 respectively. T here is good agreem ent betw een th e d a ta and th e background ex pectations from th e SM, and no statistically significant excess is observed in d a ta . T he lim it on th e branching fraction of H ^ invisible is com puted using a m axim um - likelihood fit to th e yields in th e signal regions and th e W ( ^ e v /p v ) + je ts and Z ( ^ e e /p p ) + je ts control sam ples following th e C LS m odified frequentist form alism [92] w ith
J H E P 0 1 ( 2 0 1 6 ) 1 7 2
U n certainty V B F ggF Z or W Zs r/Wcr or Ws r/Wcr
J e t energy scale 16 9
43 12
17-33 0-11
3-5 1-4 J e t energy resolution Negligible
3.1
Negligible 3.2
Negligible 0.2-7.6
Negligible 0.5-5.8
L um inosity 2.8 2.8 2.8 Irrelevant
QCD scale 0.2 7.8 5-36
7.5-21
7.8-12 1-2
P D F 2.3
2.8 7.5 3-5
0.1-2.6
1-2
P a rto n shower
4.4 41 9-10 5
Veto on th ird je t 29
Negligible Negligible
Higgs boson p T Negligible 9.7 Irrelevant Irrelevant
MC statistics 2
0.6
46 13
2.3-6.4
0.8-4.5 3.3-6.6
T able 7. Detector and theory uncertainties (%) after all SR or CR selections. For each source of uncertainty, where relevant, the first and second rows correspond to the uncertainties in SR1 and SR2 respectively. The ranges of uncertainties in the Z or W column correspond to uncertainties in the Z +jets and W +jets MC yields in the SR or CR. The search uses the uncertainties in the ratios of SR to CR yields shown in the last column.
a profile likelihood-ratio te s t s ta tistic [31]. E x pected signal and background d istrib u tio n s in th e signal and control regions are determ ined from MC predictions, w ith th e exception of th e m u ltijet backgrounds, which use th e data-d riv en m ethods described in section 5.
S y stem atic uncertain ties are param eterized as G aussian con strained nuisance param eters.
T h e nuisance p a ra m ete r for each individual source of u n c e rtain ty is shared am ong th e expected yields so th a t its correlated effect is tak en into account. T he relative weight of th e Z ( ^ e e / ^ ) + j e t s and W ( ^ e v / p v)+ je ts in th e control regions is determ ined by th e m axim ization of th e likelihood function.
O ne global likelihood function including all th re e signal regions and th e six correspond
ing control regions is co n stru cted w ith only th e signal yields and correlated uncertainties coupling th e search regions. T he th eoretical un certainties are tak e n to be uncorrelated betw een th e E W and Q C D processes and uncorrelated w ith th e scale u n certain ty on th e signal. T he uncertainties which are tre a te d as correlated betw een th e regions are:
J H E P 0 1 ( 2 0 1 6 ) 1 7 2
F ig u re 6. Data and MC distributions after all the requirements in SR1 for (a) ET?lss and (b) the dijet invariant mass m jj. The background histograms are normalized to the values in table 8. The VBF signal (red histogram) is normalized to the SM VBF Higgs boson production cross section with B F(H ^ invisible) = 100%.
F ig u re 7. Data and MC distributions after all the requirements in SR2 for (a) ET?lss and (b) the dijet invariant mass m jj. The background histograms are normalized to the values in table 8.
The VBF signal is normalized to the SM VBF Higgs boson production cross section with B F (H ^ invisible) = 100%.
• U n certain ty in th e lum inosity m easurem ents. T his im pacts th e predicted rates of th e signals and th e backgrounds th a t are estim ated using MC sim ulation, nam ely ggF and V B F signals, and tt, single top , and diboson backgrounds.
• U ncertainties in th e absolute scale and resolution of th e reco nstru cted je t energy.
• U ncertainties in th e m odelling of th e p a rto n shower.
• U ncertainties in renorm alization and factorization scales.
J H E P 0 1 ( 2 0 1 6 ) 1 7 2
S ig n a l r e g io n Process
SR1 SR2a SR2b
ggF signal 2 0 ± 15 5 8 ± 22 19± 8
V B F signal 2 86± 57 182± 19 105±15
Z ( ^ v v )+ je ts 3 39± 37 1580± 90 335±23 W ( ^ ^ v )+ je ts 2 35 ± 42 1010± 50 225±16
M u ltijet 2 ± 2 2 0 ± 20 4 ± 4
O th e r backgrounds 1±0.4 6 4 ± 9 19± 6 T otal background 577± 62 2680±130 583±34
D a ta 539 2654 636
T able 8. Estimates of the expected yields and their total uncertainties for SR1 and SR2 in 20.3 fb-1 of 2012 data. The Z ( ^ vv)+jets, W ( ^ f'v)+jets, and multijet background estimates are data- driven. The other backgrounds and the ggF and VBF signals are determined from MC simulation.
The expected signal yields are shown for mH = 125 GeV and are normalized to B F (H ^ invisible) = 100%. The W +jets and Z +jets statistical uncertainties result from the number of MC events in each signal and corresponding control region, and from the number of data events in the control region.
R esults E xpected + 1 a —1a + 2 a —2 a Observed
SR1 0.35 0.49 0.25 0.67 0.19 0.30
SR2 0.60 0.85 0.43 1.18 0.32 0.83
Com bined R esults 0.31 0.44 0.23 0.60 0.17 0.28
T able 9. Summary of limits on B F (H ^ invisible) for 20.3 fb 1 of 8 TeV data in the individual search regions and their combination, assuming the SM cross section for m H = 125 GeV.
Table 8 shows signal, background and d a ta events after th e global fit including th e effects of system atic uncertainties, M C sta tistic a l uncertainties in th e control and signal regions, and th e d a ta sta tistic a l uncertain ties in th e control regions. T h e post-fit values of th e Z + je ts and W + je ts background norm alization scale factors hp discussed in section 5, are 0.95 ± 0.21, 0.87 ± 0.17 and 0.74 ± 0.12 for SR1, SR2a and SR2b and th e ir control regions, respectively. As shown in tab le 8 , th e signal-to-background ratio is 0.53 in SR1, and 0.09 and 0.21 in SR2a and SR2b respectively, for B F (H ^ invisible) = 100%. F its to th e likelihood function are perform ed sep arately for each signal region and th eir com bination, and th e 95% CL lim its on B F (H ^ invisible) are shown in tab le 9 .
T he agreem ent betw een th e d a ta and th e background exp ectation s in SR1 is also expressed as a m odel-independent 95% CL u p p er lim it on th e fiducial cross section
f i d = a x B F x A, N
£ x e
(7.1) (7.2) w here th e acceptance A is th e fraction of events w ithin th e fiducal phase space defined a t th e M C t r u th level using th e SR1 selections in section 4 , N th e accepted num ber of
J H E P 0 1 ( 2 0 1 6 ) 1 7 2
SR1 Expected + 1 o —1o + 2 o —2o Observed Fiducial cross section [fb] 4.78 6.32 3.51 8.43 2.53 3.93
T ab le 10. Model-independent 95% CL upper limit on the fiducial cross section for non-SM pro
cesses <7fld in SR1.
events, L th e integ rated lum inosity and e th e selection efficiency defined as th e ratio of selected events to those in th e fiducial phase space. Only th e system atic un certain ties on th e backgrounds and th e in teg rated lum inosity are tak en into account in th e u p p er lim it on o fid, shown in tab le 10. In SR1, th e acceptance and th e event selection efficiency, estim ated from sim ulated V B F H ^ Z Z ^ 4 v events, are (0.89 ± 0.04)% and (94 ± 15)% respectively.
T h e un certain ties have been divided such th a t th e th eo ry un certainties are assigned to th e acceptance and th e experim ent uncertainties are assigned to th e efficiency.
8 M o d e l in te r p r e ta tio n
In th e H iggs-portal d a rk -m a tte r scenario, a d a rk sector is coupled to th e S ta n d a rd M odel via th e Higgs boson [9 , 10] by intro du cing a W IM P d a rk -m a tte r singlet x th a t only couples to th e SM Higgs doublet. In th is m odel, assum ing th a t th e d a rk -m a tte r particle is lighter th a n half th e Higgs boson m ass, one would search for Higgs boson decays to un d etected (invisible) d a rk -m a tte r particles, e.g. H ^ x x . T he u p p er lim its on th e branching fraction to invisible particles directly determ ine th e m axim um allowed decay w id th to th e invisible particles
r inv = B F (H ^ invisible) r H 1 — B F (H ^ invisible) H,
w here r H is th e SM decay w idth of th e Higgs boson. A dopting th e form ulas from ref. [10], th e decay w idth of th e Higgs boson to th e invisible particles can be w ritte n as
r H v_ SS = A H s s v 2 p s , (8.2)
64nm H V !
inv A h v v v m, HQ v ( \ , ,
TH% v v = - H V V 1 — 4 —£ + 12— V- , (8.3)
H^ v v 256nmV y m 2H m % ) y 1
A2TTff v 2m H Q3
r H % ff = H f f J f , (8.4)
H ^ f f 32nA 2 ’ v ;
for th e scalar, vector and M ajorana-ferm ion d a rk m a tte r, respectively. T h e p aram eters AHSS, AHVV, A H f f / A are th e corresponding coupling con stan ts, v is th e vacuum expec
ta tio n value of th e SM Higgs doublet, Qx = ^ 1 — 4 m 2L/m?H (x = S, V , f ), and m x is th e W IM P m ass. In th e H iggs-portal model, th e Higgs boson is assum ed to be th e only m ediator in th e W IM P-nucleon scatterin g, and th e W IM P-nucleon cross section can be w ritte n in a general spin-independent form. Inserting th e couplings and m asses for each spin scenario gives:
Osi = AH ss m N f N (8 5)
S N 167Tm 4H ( m s + m N)2 , .
(8.1)
J H E P 0 1 ( 2 0 1 6 ) 1 7 2
Vacuum expectation value Higgs boson mass
Higgs boson width Nucleon mass
v / ^ 2 174 GeV 125 GeV r H 4.07 MeV m N 939 MeV Higgs-nucleon coupling form factor f N 0.33+q
Table 11. Parameters in the Higgs-portal dark-m atter model.
(8.6)
^si = ^ H v v m N f N VN l 6 n m 4H (m V + m N ) 2 ’ _SI = AH ff m N m / f N
f N 4nA 2mH ( m f + m N )2 ’ (8.7)
where m N is the nucleon mass, and f N is the form factor associated to the Higgs boson- nucleon coupling and com puted using lattice QCD [10]. The numerical values for all the param eters in the equations above are given in table 11.
The inferred 90% CL branching fraction limit for H ^ invisible, translated into an upper bound on the scattering cross section between nucleons and WIMP, is shown in figure 8 compared to the results from direct detection experiments. The WIMP-nucleon cross-section limits resulting from searches for invisible Higgs boson decays extend from low W IM P mass to half the Higgs boson mass, and are complementary to the results provided by direct detection experiments th a t have limited sensitivity to W IM P with mass of the or
der of 10 GeV and lower [34, 36- 40, 42]. This is expected as the LHC has no limitations for the production of low-mass particles, whereas the recoil energies produced in the interac
tions of sub-relativistic W IM P with nuclei in the apparatus of a direct detection experiment are often below the sensitivity threshold for small W IM P masses. The aforementioned cor
relation between the branching fraction of Higgs boson decays to invisible particles and the WIM P-nucleon cross section is presented in the effective field theory framework, assum
ing th a t the new physics scale is O (afew )TeV , well above the scale probed at SM Higgs boson mass. Adding a renormalizable mechanism for generating the fermion and vector W IM P masses could modify the correlation between the WIM P-nucleon cross section and the branching fraction of Higgs boson decays to invisible particles [93].
9 C o n c l u s i o n s
A search for Higgs boson decays to invisible particles is presented. The search uses d ata events with two forward jets and large missing transverse momentum, collected with the ATLAS detector from 20.3 fb-1 of pp collisions at yfs = 8TeV at the LHC. Assuming the SM production cross section, acceptance and efficiency for invisible decays of a Higgs boson with a mass of 125 GeV, a 95% CL upper bound is set on the B F (H ^ invisible) at 0.28. The results are interpreted in the Higgs-portal dark-m atter model where the 90% CL limit on the B F (H ^ invisible) is converted into upper bounds on the dark-m atter nucleon
J H E P 0 1 ( 2 0 1 6 ) 1 7 2
Figure 8. The WIMP-nucleon cross section as a function of the WIMP mass. The exclusion limits [34- 38] of the direct detection experiments are compared to the ATLAS results from the B F (H ^ invisible) limit in the Higgs-portal scenario, translated into the WIMP-nucleon cross section using the formulas from ref. [10]. The exclusion limits are shown at 90% CL. The error bands on the ATLAS results indicate the uncertainty coming from the different estimations of the Higgs-nucleon coupling form factor [94, 95].
scattering cross section as a function of the dark-m atter particle mass. The ATLAS limits are complementary to the results from the direct dark-m atter detection experiments.
A c k n o w l e d g m e n t s
We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions w ithout whom ATLAS could not be operated efficiently.
We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Aus
tralia; BMWF, Austria; AHAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Brazil;
NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Repub
lic; DNRF, DNSRC and Lundbeck Foundation, Denmark; ARTEMIS, European Union;
IN2P3-CNRS, CEA-DSM /IRFU, France; GNAS, Georgia; BMBF, DFG, HGF, M PG and AvH Foundation, Germany; GSRT, Greece; ISF, MINERVA, GIF, DIP and Benoziyo Cen
ter, Israel; INFN, Italy; M EXT and JSPS, Japan; CNRST, Morocco; FOM and NWO, Netherlands; RCN, Norway; MNiSW, Poland; GRICES and FCT, Portugal; MERYS (M ECTS), Romania; MES of Russia and ROSATOM, Russian Federation; JINR; MSTD, Serbia; MSSR, Slovakia; ARRS and MVZT, Slovenia; D ST /N R F , South Africa; MICINN, Spain; SRC and Wallenberg Foundation, Sweden; SER, SNSF and Cantons of Bern and Geneva, Switzerland; NSC, Taiwan; TAEK, Turkey; STFC, the Royal Society and Lever- hulme Trust, United Kingdom; DOE and NSF, United States of America.
