Electroweak production of light scalar-pseudoscalar pairs from extended Higgs sectors

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Physics Letters B

www.elsevier.com/locate/physletb

Electroweak production of light scalar–pseudoscalar pairs from extended Higgs sectors

Rikard Enberg^a, William Klemm^a^,^b^,^∗, Stefano Moretti^c, Shoaib Munir^d

aDepartmentofPhysicsandAstronomy,UppsalaUniversity,Box516,SE-75120Uppsala,Sweden bSchoolofPhysics&Astronomy,UniversityofManchester,ManchesterM139PL,UK

cSchoolofPhysics&Astronomy,UniversityofSouthampton,SouthamptonSO171BJ,UK dSchoolofPhysics,KoreaInstituteforAdvancedStudy,Seoul130-722,RepublicofKorea

a r t i c l e i n f o a b s t ra c t

Articlehistory:

Received5August2016

Receivedinrevisedform2September2016 Accepted6November2016

Availableonline10November2016 Editor: G.F.Giudice

In models withextended Higgssectors, itis possible that the Higgs bosondiscovered atthe LHC is not thelightestone.Weshow thatinarealisticmodel (theTypeI 2-HiggsDoubletModel),whenthe sumofthemassesofalightscalarandapseudoscalar(h andA)issmallerthantheZ bosonmass,the Electroweak(EW)productionofanh A paircandominateoverQCDproductionbyordersofmagnitude,a factnotpreviouslyhighlighted.Thisisbecauseinthegg-initiatedprocess,h A productionviaaresonant Z inthes-channelisprohibitedaccordingtotheLandau–Yangtheorem,whichisnotthecaseforthe qq-initiated¯ process.We exploretheparameterspaceofthemodeltohighlightregionsgivingsuchh A solutionswhilebeingconsistentwithallconstraintsfromcollidersearches,b-physicsandEWprecision data.Wealsosingleoutafewbenchmarkpointstodiscusstheirsalientfeatures,includingtheh A search channelsthatcanbeexploitedatRunIIoftheLHC.

©²⁰¹⁶^TheÂuthor(s).^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

MostmodelsforphysicsbeyondtheStandardModel(SM)pre- dictextendedHiggssectors,withadditionalHiggs(pseudo)scalars.

Two-Higgs Doublet Models (2HDMs), which contain two Higgs doublets φ1 and φ2 (see [1] for a review), are among the sim- plestnon-trivial extensionsof theSM. The Higgs sector of a CP- conserving2HDMcontainsthreeneutralHiggsbosons,twoscalars andapseudoscalar(h, H ,withmh<mH,and A,respectively),and a charged pair H^±. One of the two CP-even Higgs bosons must havepropertiesconsistentwiththeobserved125 GeVstate[2–4], H_obs.AttheLargeHadronCollider(LHC),theneutralHiggsbosons ofa2HDMcanbeproducedbothsingly,dominantlyviagluonfu- sion,andinidentical ormixedpairs.We discussherea scenario inwhichtheh and A statesoftheType-I 2HDM(2HDM-I),¹ with massessatisfyingm_h+^mA<M_Z,canpassthepresentexperimen- talconstraintsfromtheLargeElectronPositron(LEP)collider,the

* Correspondingauthorat:SchoolofPhysics&Astronomy,UniversityofManch- ester,ManchesterM139PL,UK.

E-mailaddress:william.klemm@physics.uu.se(W. Klemm).

1 IntheTypeImodel,allfermionsgetmassfromYukawacouplingstoonlyone ofthedoublets,seebelow.

Tevatron andthe LHC, with the heavier H state beingidentiﬁed withH_obs.

TheLHCisahadroncolliderthatcanyieldcollisionswithvery smallmomentumfractionx ofthescatteredpartonsandverylarge squared momentum transfer Q². Becausethe proton hasa large gluondensityatsmallx,onewouldhopetoinitiate Z production fromgluon-gluon(gg)scattering(seetheleftdiagram ofFig. 1a), withthe h A ﬁnal state produced from Z decay.However, owing to theLandau–Yangtheorem [5,6], gg canonly scattervia a Z if itisnon-resonant (i.e.,off-shell,denotedby Z^∗) [7].Thisleads to amuchdepleted crosssection fortheh A signaland, additionally, to the inability of using Z mass reconstruction from the invari- antmassoftheh A (visible) decayproducts forsuppressingback- grounds.Inthecaseofthetree-levelquark-antiquark(qq)-initiated¯ process, however,the Z bosoncan be producedon-shell (leftdi- agram ofFig. 1b). The h A ﬁnal state can also be produced from doubleHiggs-strahlungoffheavy quarks(i.e.,b- andt-quarks),at theone-loop level(rightdiagram ofFig. 1a)andatthe treelevel (rightdiagram ofFig. 1b),inthecaseof gg andqq collisions,¯ respectively.

It is the purpose of this Letter to highlight the hitherto ne- glected predominanceofthe qq-initiated¯ tree-levelproduction of a light h A pair atthe LHC withrespect to the gg-initiatedone- loop productionina Type-I 2HDM. (See Ref.[8]for higherorder http://dx.doi.org/10.1016/j.physletb.2016.11.012

0370-2693/©²⁰¹⁶^TheÂuthor(s).^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

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Fig. 1. Diagramscontributingto(a)QCDproductionand(b)EWproductionofthe h A pair.

QCD correctionsto the corresponding diagrams.) We additionally outlinetheregionofthe2HDM-I parameterspacewherethefor- mercanbeaccessedaboveandbeyondtheyieldofthelatterand presentbenchmarkpoints toserveasaguidelineforprobingthis productionprocessatthecurrentLHCrun.

2. Model,parameterscanandconstraints

In general, in a 2HDM, depending on how the two doublets coupletofermions,FlavorChangingNeutralCurrents (FCNCs)can bemediatedby(pseudo)scalarsatthetreelevel.Therequirement ofvanishingFCNCs thusputsvery strongrestrictionsonthe cou- plingmatrices.ThesimplestwaytoavoidlargeFCNCsistoimpose aZ2symmetrysothateachtypeoffermiononlycouplestooneof thedoublets (“natural ﬂavor conservation”) [9,10].There are four basicwaysofassigning the Z2 charges,andhereweconsiderthe case where only the doublet φ2 couples to all fermions, known as the Type I model. The Higgs potential for the CP-conserving 2HDM-Iiswrittenas

V=^m²11φ₁^†φ₁+^m²22φ₂^†φ₂− [^m²12φ₁^†φ₂+^h.c.]

+¹

2λ1(φ₁^†φ1)²+¹

2λ2(φ₂^†φ2)²+ λ3(φ₁^†φ1)(φ₂^†φ2) + λ4(φ₁^†φ2)(φ₂^†φ1)+ [¹

2λ5(φ^†₁φ2)²+^h.c.], ⁽¹⁾

whichis invariantunder thesymmetry φ1→ −φ1 up tothe soft breakingtermproportionaltom²₁₂.Throughtheminimizationcon- ditions ofthe potential,m²₁₁ andm²₂₂ can be tradedfor thevac- uum expectation values, v1 and v2, of the two Higgs ﬁelds and the tree-levelmass relations allow thequartic couplings λ1−⁵ to be substituted by the fourphysical Higgs boson masses andthe neutralsector term sβ−α (short forsin(β−α), withthe angleβ deﬁnedthroughtanβ=^v2/v₁),where αmixestheCP-evenHiggs states.

In orderto test the consistency of solutions withm_h+^mA<

MZ in the 2HDM-I with the most crucial and relevant theoret- ical and experimental constraints (listed further below), we performed a scan of its parameter space² using 2HDMC-v1.7.0 [12].

The(randomly)scannedrangesofthefreeparameters(withmH= 125 GeV)aregiveninthesecondcolumnofTable 1.Becauseonly aselectregionoftheparameterspaceisallowedby currentcon- straints,weusedthedistributionsresultingfromthisinitialscanto

2 NotethatasimilarregionofparameterspacewascapturedbyRef.[11].

Table 1

2HDM-Iparametersandtheirscannedranges.

Parameter Initial range Reﬁned range

mh(GeV) (10, 80) (10, 2MZ/3)

mA(GeV) (10, MZ−mh) (mh/2, MZ−mh)

mH^±(GeV) (90, 500) (90, 150)

s_β−α (−^{1, 1)} ⁽−⁰.25, 0)

m²₁₂(GeV²) (0, m²_Asinβcosβ) (0, m²_Asinβcosβ)

tanβ (2, 25) (−0.95,−1.1)/sβ−α

determinethemostrelevantparameterranges,whichwefocused oninasecondscan,shownintherightmostcolumnofTable 1.

During the scan, each sampledmodel point was subjected to thefollowingconditions:

– Unitarity,perturbativity,andvacuumstabilityenforcedthrough thedefault2HDMCmethod.

– Consistencyat95%ConﬁdenceLevel(CL)withtheexperimen- talmeasurementsoftheobliqueparametersS,T andU ,again, calculatedby2HDMC.Wecomparethesetotheﬁtvalues[13], S=⁰.00±⁰.08 andT=⁰.05±⁰.07,inan ellipsewithacor- relationof90%.Allpointsfurthersatisfy U=⁰.05±⁰.10.

– Satisfactionofthe95%CLlimitsonb-physicsobservablescal- culatedwiththepubliccodeSuperIso-v3.4[14].

– Consistency withthe Z width measurement from LEP, Z = 2.4952±⁰.0023 GeV[13].Thepartialwidth(Z→^{h A})was requiredtofallwithinthe2σ experimentaluncertaintyofthe measurement.

– Consistency ofthe massand signal rates of H with the LHC data on H_obs.The combined 68% CL results fromATLAS and CMS for the most sensitive channels are [15]: μ^{γ γ}_ggF₊_t_¯_{t H} = 1.15⁺₋⁰₀^._.²⁸₂₅, μ^{γ γ}_VBF₊_{V H}=¹.17⁺₋⁰₀^._.⁵⁸₅₃, μ⁴=¹.40⁺₋⁰₀^._.³⁰₂₅. Werequired that the equivalent quantities, calculated with HiggsSignals- v1.3.2 [16], satisfy these measurements at 95% CL, assuming Gaussianuncertainties.

– Consistency of all Higgs states with the direct search con- straintsfromLEP,Tevatron,andLHCatthe95%CLtestedusing thepublictoolHiggsBounds-v4.3.1[17–20].

The points were alsorequired tosatisfy some additionalcon- straints fromLEP andLHC that havenot(yet) beenimplemented inHiggsBounds. Consistency withthecombinedLEP H^± searches inthe2HDM-I[21]wasensuredbyrequiringthatm_H±>90 GeV.

TheLEP-II constraintsone⁺e⁻→γ γbb¯ [22]werealsotakeninto account. While these constraints are mass dependent, we con- servatively required cos²(β−α)BR(h→γ γ)BR(A→^bb¯)<0.02.

Moreover, the results of the μμτ τ ﬁnal state studies performed byATLAS[23]aswellasofthe τ τ τ τ [24], μμτ τ [25]and μμbb¯ [26]analysesfromCMSweretestedagainst.

3. Scanresults

From the output of ourinitial scan, we noticed that the LHC observationofaverySM-like Hobs pushesthemodeltowardsthe alignment limit, sβ−α→^0. Additionally, strong constraints from LEP searchesleadtosuppressedh/A couplingstofermions,³ pro- ducing a strong correlation sβ−α≈ −¹/tanβ. We also find that a relativelylight chargedHiggs(m_H±^{120 GeV)} îs^necessary,âs a charged Higgs mass too far separated from mh or mA results

3 Inthe2HDM-I,thecouplingsofh and A tofermionsgoasg_hf_¯_f ∼^cosα/sinβ andg_{A f}_¯_f∼ ±^cotβ.

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in large contributions to the T -parameter.⁴ Existing searches for chargedHiggs bosons in this mass rangetypically focus on pro- ductionfromtopdecaysfollowedby chargedHiggsbosondecays to either τ ν or cs. For the points selected by the scan, these branching ratios typically fall below the percent level, in many cases by several orders of magnitude, with maximal values of BR(t→^H⁺^b)⁰.04,BR(H⁺→τ⁺ν_τ)⁰.01,andBR(H⁺→^c¯s) 6×¹⁰⁻³^.^This^places^them^well^below^existingconstraints,includ- ing recent LHC results [27–29] not yet included in HiggsBounds.

Insteadofthestandard decays,thelow massesofh and A inthe scenarioconsideredhereallowtheH^±todecaydominantlyinthe W^∗h or W^∗A channels (with the respective branching ratios al- ternativelynearunity),whichhavenot yetbeenexaminedatthe LHC.⁵

Numerousconstraintsrestrict thepossible massesofh and A.

InFig. 2weshowthepointspassingalltheconstraintsmentioned abovein the(m_h,m_A)plane. Because theh A Z couplingis maxi- mizedinthefavoreds_β−α→^{0 limit,}^the ^constraint^fromZ,the 1σ and2σ contours forwhich arealsoshown, isparticularlyse- vere.We note two distinctregions witha largedensityof points inthe figure. The region nearthe top left corner corresponds to themA>m_h (heavier A) scenario.Thisregioncutsoffsharplyat mA=^mH/2 due to thepossibility ofthe H→^{A A decay}ârising, whichpotentiallyleadstoasuppressionofthesignalstrengthsfor theSM-like H (forthe2HDM-Iscenariosweconsider,thesesignal strengths are always below1to beginwith). Thispossibility can beavoidedwitha sufficientlysuppressed H A A coupling,asare- sultofwhichadditionalpointssatisfyingallconstraintsappearin theregioncorrespondingtothem_h>m_A(heavierh)scenarionear thelowerrightcornerofthefigure.Whenm_h>2mA,theh→^{A A} decay channel opens up, and the model is severely constrained by LEP searches for processes such as e⁺e⁻→^{h A}→ (^{A A})A→ (bbb¯ b¯)bb¯ [31]. Consequently, we did not find acceptable points withm_h>2mA.

Thecolormap in Fig. 2 depictsthetotal crosssection forthe qq¯→h A process, which evidently grows larger as one moves awayfromthediagonalandm_h+^mA getssmaller.Forcalculating this cross section, we used the 2HDMC model [12] with Mad- Graph5_aMC@NLO[32],considering both 4- (q=û,d,c,s)and5- (q=û,d,c,s,b) flavor schemes. The 5-flavor scheme predictions differby less than3% from those ofthe 4-flavor one dueto the small b-quark couplings. Also highlighted in the figure are the three Benchmark Points (BPs) selected to demonstrate the typi- calcharacteristicsoftheinterestingparameterspaceregions.These BPswillbediscussedindetaillater.

4. EWvs.QCDproduction

In order to be able to compare the relative strengths of the qq¯→h A productionmode andthe gg→^{h A mode,}^we ^also^cal- culatedthecrosssection forthe latterforeachpoint usingcodes developedwithMadGraph5_aMC@NLO[32]forHiggspairproduc- tion [33]. The comparisonis shown in Fig. 3, where one notices that the maximal cross section achievable forQCD production is aboutthree orders of magnitudesmaller than that for EW production,whichcan reachashighas∼^{90 pb.}^Also, ^for^the ^points shown, while the maximal cross section for EW production is consistent across the two (m_h,mA) regions, which can be dis- tinguishedthroughthe colormap in mA,QCD production clearly preferstheheavier A scenario.

4 Thisrequirement ofalight charged Higgsprevents usfrom ﬁnding similar pointsinType-IImodels,whereahighermH±isrequiredbyB-physicsconstraints.

5 ThesedecaymodesoftheH^±willbediscussedfurtherin[30].

Fig. 2. Constraintsandacceptedpointsinthe(mh,mA)plane.Shadedareas:Red– mh>2mA,allowingh→A A decays;Blue–theoreticalpredictionofthe Z→h A partialwidthexceedsexperimentaluncertaintyatthe1σ(lighter)and2σ(darker) levels,inthelimitcos(β−α)=^1;^Orange^–^mh+^mAabovethemZthreshold,not consideredinthisstudy.Thecolormapcorrespondstothetotalcrosssectionfor theqq¯→h A processat√

s=^{13 TeV,}^and^the^three^benchmark^points^have^been highlightedinyellow.(Forinterpretationofthereferencestocolorinthisﬁgure legend,thereaderisreferredtothewebversionofthisarticle.)

Fig. 3. Crosssectionsforqq- vs.¯ gg-initiatedh A productionattheLHCwith√ s= 13 TeV,forpointssatisfyingalltheconstraintsdescribedinthetext.Thecolormap indicatesmA.(Forinterpretationofthereferencestocolorinthisﬁgurelegend,the readerisreferredtothewebversionofthisarticle.)

5. Benchmarks

The input parameters for the three BPs shown in Fig. 2 are given in Table 2 along with the corresponding cross sections in thetwoh A productionchannelsanalyzed.BP1correspondstothe heavierh scenariowhileBP2andBP3correspondtotheheavier A scenario.

In Table 3 we list the BRs of h and A in the most impor- tant decaychannelsforeach BP.Theallowed points inthe heavier h scenario all have characteristics similar to BP1 – a highly fermiophobic h which consequently decays dominantly to Z^∗A anda light A which decaysprimarily into pairs of third genera-