Contents lists available atScienceDirect
Physics
Letters
B
www.elsevier.com/locate/physletb
Identifying
a
light
charged
Higgs
boson
at
the
LHC
Run
II
Abdesslam Arhrib
a,
Rachid Benbrik
b,
c,
Rikard Enberg
d,
William Klemm
d,
e,
∗
,
Stefano Moretti
f,
Shoaib Munir
gaFacultédesSciencesetTechniques,AbdelmalekEssaadiUniversity,B.P.416,Tangier,Morocco bLPHEA,Semlalia,CadiAyyadUniversity,Marrakech,Morocco
cMSISMTeam,FacultéPolydisciplinairedeSafi,SidiBouzid,B.P.4162,Safi,Morocco
dDepartmentofPhysicsandAstronomy,UppsalaUniversity,Box516,SE-75120Uppsala,Sweden eSchoolofPhysics&Astronomy,UniversityofManchester,ManchesterM139PL,UK
fSchoolofPhysics&Astronomy,UniversityofSouthampton,SouthamptonSO171BJ,UK gSchoolofPhysics,KoreaInstituteforAdvancedStudy,Seoul130-722,RepublicofKorea
a
r
t
i
c
l
e
i
n
f
o
a
b
s
t
r
a
c
t
Articlehistory:
Received 23 June 2017
Received in revised form 22 September 2017
Accepted 2 October 2017 Available online 9 October 2017 Editor: G.F. Giudice
We dedicate this work to the late Professor Maria Krawczyk, a friend and inspiration to us all
We analyse the phenomenological implications of a light Higgs boson, h, within the CP-conserving 2-Higgs DoubletModel (2HDM)Type-I, forthe detectionprospectsofthe charged H± state atRun II ofthe LargeHadronCollider(LHC), assuming√s=13 TeV asenergyand O(100 fb−1) asluminosity. Whensufficientlylight,thish statecanopenupthebosonicdecaychannelH±→W±(∗)h,whichmay haveabranchingratiosignificantlyexceedingthoseofthe H±→
τ ν
and H±→cs channels.We per-formabroadscanofthe2HDMType-Iparameterspace,assumingtheheavierofthetwoCP-evenHiggs bosons,H,tobetheobservedSM-likestatewithamassnear125GeV.Throughthesescanswehighlight regionsinwhichmH±<mt+mbthatarestillconsistentwiththemostrecentlimitsfromexperimentalsearches.Wefindintheseregionsthat,whentheH±→W±(∗)h decaymodeisthedominantone,the h canbehighlyfermiophobic,withaconsiderablylarge decayrateinthe
γ γ
channel.Thiscanresult inthe totalcross sectionoftheσ
(pp→H±h→W±(∗)+4γ
) processreachinguptoO(100 fb).We thereforeinvestigatethepossibilityofobservingthisspectacularsignalattheLHCRunII.©2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
The discovery of a resonance around 125 GeV at the Large HadronCollider(LHC)[1,2]triggeredplentyofactivityinthe parti-clephysicscommunity.Comprehensiveanalysestoinvestigatethe spinandparityofthediscoveredparticlehaveconfirmeditsscalar nature.The measured signal ratesof thisscalar particle, Hobs,in
its dominant decaychannels, agree with those predictedfor the SMHiggsbosonatthe 2
σ
level [3].However, thepossibilitythat the Hobs couldbelong toamodelwithanextended Higgssector,such asthe SM withan extra singlet, doublet and/or triplet has not been ruled out. Amongst such higher Higgs representations, those withan extra doublet or triplet also contain one or more charged Higgs bosons in their scalar spectrum. The discovery of suchchargedHiggsbosonswouldbean eminentsignal ofan ex-tendedHiggssectorandclearevidenceofphysics BeyondtheSM (BSM).
*
Corresponding author.E-mailaddress:wklemm@berkeley.edu(W. Klemm).
Among the simplestextensions of SM is the 2-Higgs Doublet Model(2HDM)inwhichtheSM,containingacomplexscalar dou-blet,
φ
1, is augmented by another doublet,φ
2, in order to givemassesto all thefermions andgauge bosons.After Electro-Weak Symmetry Breaking (EWSB), out of the 8 degreesof freedom of the twoHiggs doublets,3 are eaten upby the EW gaugebosons tomakeuptheir longitudinalcomponents,whiletheremaining 5 shouldmanifestthemselvesasphysicalparticles.Therefore,the CP-conservingHiggssectorofthe2HDMcontainsthreeneutralHiggs bosons,twoscalars(h and H ,withmh
<
mH),apseudoscalar( A), andan H± pair.The requirement that one out ofh and H haveproperties consistent withthe Hobs puts rather stringentbounds
onthe2HDMparameterspace. Itiswellknownthat,ina2HDM, there exists a ‘decouplinglimit’, wheremH,A,H±
mZ [4,5],and the couplings ofthe h to the SM particles are identical tothose oftheSMHiggsboson.Alternatively,themodelalsopossessesan ‘alignment limit’, in which either one of h [6,7] or H [8,9] can mimictheSMHiggsboson.ThemassesoftheothertwoneutralHiggsbosonsaswellasthe
H± are alsostrongly constrainedby theresults fromtheir direct
https://doi.org/10.1016/j.physletb.2017.10.006
0370-2693/©2017 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.
searches at various collider experiments. Moreover, indirect con-straintson thesecomefrom B-physics
[10–12]
andprecision EW measurements. Ingeneral, whenthe H± state islighter thanthe sumofthemassesofthetopandbottomquarks,itsdominant de-caymodeisτ ν
.TheATLAS andCMScollaborationshavereleased exclusionlimitsontheBranchingRatio(BR)ofageneric H±state inthisdecaymode [13–15].Theonly other decaychanneloftheH± probed atthe LHC in the light mass range so far is cs, but theresultinglimits[16,17]areratherweakcomparedtothosefor the
τ ν
channel. In fact, in a specific (socalled ‘flipped’) 2HDM, theH±→
cb decaycanalsoberelevant[18]
andhasindeedbeen searchedforbyCMS[19]
.However,ina recentstudy[20],itwas shownthatin another specific 2HDM (called Type-I, henceforth 2HDM-I) with an SM-likeh andmH±
<
mt+
mb,insteadoftheseconventionalchannels, W±(∗)h and/orW±(∗)A canalternativelybecomethedominant de-cay channels of the H±, thereby competing with the fermionic modes [21–23]. In another study [24] it was shown that, when insteadthe H isSM-like,itispossibleforh and A tohavemasses such that mh+
mA<
mZ, without being inconflict with the di-rect search limits. Two other important features of the relevant parameterspacewerealsonotedthere:i)forconsistencywiththe EWprecisionmeasurements, suchlighth and A areaccompanied by an H± not muchheavierthan the Z boson,andii)the h canbe extremely fermiophobic, so that its decays into SM fermions are highly suppressed, which can in turn result in a very large BR(h
→
γ γ
). In thisstudy, we further explore this possibility of alightH±inthe2HDM-Idecayingviasuchafermiophobich andthe W±(∗), along thelines of[25].When the H± is produced in the process qq
¯
→
W±(∗)→
H±h, due to the additional pair of photonscomingfromthesecondh,averycleanW±(∗)+
4γ
signal mayresult.Thepaperisorganisedasfollows.InSect.2webriefly review the various types of the 2HDM. In Sect. 3.1 we discuss parame-terspaceregions,satisfyingthetheoreticalandexperimental con-straintsavailable,wherealighth,accompaniedbyalight H± and an SM-like H ,can beobtained, whileinSect.3.2we analysethe
W±
+
4γ
signal.1 InSect.4wethen discussthepotentialvisibil-ityoftheH±inthisfinalstateatthe13TeV LHC.Wepresentour conclusionsinSect.5.
2. Typesofthe2HDM
Themostgeneral2HDMscalarpotentialwhichisbothSU
(2)
L⊗
U(1)
Y andCPinvariantiswrittenasV
(φ
1, φ
2)
=
m211φ
† 1φ
1+
m 2 22φ
† 2φ
2− [
m 2 12φ
† 1φ
2+
h.c.]
+
1 2λ
1(φ
† 1φ
1)
2+
1 2λ
2(φ
† 2φ
2)
2+ λ3
(φ
1†φ
1)(φ
2†φ
2)
+ λ4
(φ
1†φ
2)(φ
2†φ
1)
+ [
1 2λ
5(φ
† 1φ
2)
2+
h.c.],
(1)where
φ
1andφ
2 haveweakhyperchargeY= +
1,whilev1andv2are their respective Vacuum Expectation Values (VEVs). Through the minimisation conditions of the potential, m211 and m222 can be traded for v1 and v2 and the tree-levelmass relations allow
the quarticcouplings
λ
1–5 tobe substitutedby the four physicalHiggsbosonmassesandtheneutralsectormixingtermsin(β
−
α
),
whereβ
isdefinedthroughtanβ
=
v2/
v1,andα
isthemixingan-glebetweentheCP-eveninteractionstates.Thus,intotal,theHiggs
1 For the remainder of this letter, we suppress the “(∗)” superscript from any W±(∗) resulting from the decay of a charged Higgs. An off-shell W±∗ is implied
whenever mH±<mh+mW.
sectorofthe2HDMhas7independentparameters,whichinclude tan
β
,sin(β−
α
),
m212andthefourphysicalHiggsbosonmasses.If both the Higgsdoublets of a 2HDMcouple to all fermions, theycanmediateFlavorChangingNeutralCurrents(FCNCs) atthe tree level.Inorder toavoidlarge FCNCs, a Z2 symmetrymay be
imposed such that each type of fermion only couples to one of the doublets[26].Thepotential inEq.(1)isthus invariantunder thesymmetry
φ
1→ −φ
1uptothesoftbreakingtermproportionalto m212.DependingontheZ2chargeassignmentoftheHiggs
dou-blets, there are four basic Types of 2HDMs [4,5]. In the Type-I model, onlythe doublet
φ
2 couples toall the fermionsasin theSM. In the Type-X(or IV or‘lepton-specific’) model, thecharged leptons couple to
φ
1 while all the quarks couple toφ
2. In theType-II model
φ
2 couples to up-type quarks andφ
1 todown-type quarksandcharged leptons. Finally,in the Type-Y(or III or ‘flipped’)model
φ
2 couplestoup-typequarksandleptonsandφ
1todown-typequarks.Notethatforsin(β
−
α
)
≈
1,h hascouplings consistentwiththeSMHiggsboson,whileH is theSM-likeHiggs bosonforsin(β−
α
)
≈
0.The Yukawainteractions in terms of the neutral andcharged Higgsmasseigenstatesinageneral2HDMcanbewrittenas
−
L
2HDM Yukawa=
f=u,d, mf vξ
hf f f h+ ξ
Hf f f H−
iξ
Af fγ
5f A+
√
2Vud v u muξ
uAPL+
mdξ
dAPR dH++
√
2mξ
A vν
LRH +
+
h.c.,
(2)where v2
=
v21+
v22= (
2√
2GF)
−1, Vud is the top-left entry of the Cabibbo–Kobayashi–Maskawa (CKM) matrix, and PL and PR aretheleft- andright-handedprojectionoperators,respectively.In the2HDM-I,ξ
hf=
cosα
/
sinβ
andξ
fH=
sinα
/
sinβ,
for f=
u,
d,
l,while
ξ
dA= −
cotβ,ξ
uA=
cotβ,
andξ
lA= −
cotβ.As pointed out earlier,experimental searches can tightly con-strain the properties of the H± in a 2HDM, depending on its Type. For instance, in the Type-II and Type-Y 2HDMs, the mea-surement of the BR(b
→
sγ
) constrains mH± to be larger than about570 GeV[10–12],which makesthesemodelsirrelevant for thisstudy.Wethereforefocushereonthe2HDM-I,inwhich one can still obtain an H± with a mass as low as∼
100–200 GeV[11,12,27],providedthattan
β
≥
2.3. Productionviapp
→
H±h anddecaythroughH±→
W±hInouranalysis,weconcentrateonthescenariowhereH isthe SM-like Higgs, while h is lighter than 125 GeVand A could be eitherlighterorheavierthantheh.Inthissectionwefirstdiscuss the light CP-even Higgsh in our scenario,which can occur near the alignment limit (sin(β
−
α
)
≈
0) [24], and show how it can be highlyfermiophobic,decayingdominantlytotwo photons. We thenproceedto pp→
W±∗→
H±h productionvia s-channelW±exchange, followedby the H±
→
W±h decay mode,which could bethedominantone,allowingthe H± toescapetheTevatronand LHClimits,whicharebasedonthefermionicdecaymodes, H±→
τ ν
,
cs,
cb[13,14,19].3.1. Fermiophobich inthe2HDM-I
It iswell known that,in theSM, theh
→
γ γ
decayis domi-natedbythe W±loop,whichispartlycancelledbyasub-leading contribution from the top quarks; in the 2HDM, we additionally have an H± contribution.The W± loop depends onhW+W−∝
Table 1
Scanned ranges of the 2HDM-I parameters.
Parameter Scanned range
mh(GeV) (10, 120)
mA(GeV) (10, 500)
mH±(GeV) (80, 170) sin(β−α) (−1, 1)
m2
12(GeV2) (0, m2Asinβcosβ)
tanβ (2, 25)
sin(β
−
α
),
the fermionic loops on hf¯
f∝
cosα
/
sinβ,
and theH±contributionentersthroughthetriplescalarcouplinghH±H∓, whichdependsonthescalarparametersofthepotential.
Inour2HDM-IscenariowithH beingtheSM-likeHiggsboson, theW±loopsinh
→
γ γ
getsuppressedbythisfactorofsin(β−
α
)
≈
0.Forthefermionicloops,cosα
iscomputedthrough cosα
=
sinβ
sin(β
−
α
)
+
cosβ
cos(β
−
α
).
(3) Fornegative sin(β−
α
)
and positive cos(β−
α
),
it is clear that cosα
will vanishfora particular choiceof tanβ.
When this sce-nariotakesplace,sinceits couplingstofermionsare proportional tocosα
,theh becomesfermiophobic[28].Therefore,h→
f¯
f and h→
gg vanish. Moreover, since the h of interest here is lighter than 120 GeV, implying that the h→
V V∗ decayis phase–space suppressed,sotheh→
γ γ
decaychannelisexpectedtodominate inthislimit.Todemonstratethiseffect,weperformedasystematic numer-icalscan ofthe 2HDM-I parameters over theranges indicated in
Table 1(withmH fixed to125GeV)usingthe2HDMC-v1.7.0 [29] program.Intheleft panelof
Fig. 1
weshow theloop factors, Fx, corresponding to W±, fermions, and H± as functionsof the re-ducedcouplinghf¯
f=
cosα
/
sinβ
forthepointsobtainedfromour scan.TheseloopfactorsaredefinedasFf
=
i−
2τ
2f NfQ 2 fξ
hf(
τ
f+ (
τ
f−
1)
I(
τ
f)),
FH±=
ghH±H∓τ
H2± m2W m2H±(
τ
H±−
I(
τ
H±)),
(4) FW=
sin(β
−
α
)
τ
2 W(
2τ
W2+
3τ
W+
3(
2τ
W−
1)
I(
τ
W)),
where ghH±H∓=
1 2m2 W((
2m2H±−
m2h)
sin(β
−
α
)
+
cos(β
−
α
)
sinβ
2cosβ
2(
m 2 hsinβ
cosβ
−
m212)),
(5)τ
x=
m2h/(4m
2x),
and the scalar function I(
x)
is given by (from, e.g.,[30],butusingtheoppositesignconvention)I
(
x)
=
[
sin−1(
√
x)
]
2,
x≤
1−
1 4[
ln(
√ x+√x−1 √ x−√x−1)
−
iπ
]
2,
x>
1.
(6)It isclear fromthefigure that, inmostof thecases, the W±
loopisdominantandinterferesdestructivelywiththeH±and top-quark loops. Inthe exactalignment limit,where sin(β
−
α
)
→
0, the W± loopsvanishandonly the H± andtoploopscontribute, interferingdestructively.Awayfromtheexactalignmentlimit,for certain values ofsin(β−
α
)
and tanβ, cosα
vanishes. Therefore, as intimated, h becomes fermiophobic, and consequently, asthe right panel of Fig. 1further illustrates, the BR(h→
γ γ
)
can be-come100%forcosα
/
sinβ
=
0.SeveralsearchesforfermiophobicHiggsbosonshavebeen per-formedbytheLEPandTevatroncolliders,imposingstringent lim-its.AtLEP-II,afermiophobicHiggsbosonwassearchedforthrough
e+e−
→
Zh, where h decays to 2 photons [31,32], and a lower limitoforder100 GeVwassetonthemassofanSM-likeh. Teva-tron also searched for a fermiophobic Higgs boson produced via Higgs-strahlung, pp→
V h (V=
W±,
Z ), aswell asvector boson fusion, qq→
qqh, withsimilar results [33] to those obtainedat LEP-II. In our 2HDM-I scenario, since the V V h coupling is sup-pressedduetosin(β−
α
)
≈
0,theselimitsfromLEPandTevatron would apply only weakly. However, one can also produce such Higgs bosons in association with a CP-odd Higgs boson throughe+e−
→
h A,whichdependsonthecoupling Zh A∝
cos(β−
α
).
The complementarity of theseh Z andh A searches withh→
γ γ
allowedthe DELPHIcollaborationto placestringentlimitsonmh and mA in fermiophobic models [31]. These constraints only applytoexactlyfermiophobicmodels,whereasinthisworkweare mostinterestedintheparameterspacecloseto,butnotnecessarily at,thefermiophobiclimit.ThecombinedLEPh Z limitscanreadily beappliedtomodelswhicharenotatthefermiophobiclimit,and theseare testedwithHiggsBounds[34], butasimilar application oftheDELPHIfermiophobich A results,whichdependonmh and mA, is less straightforward and not included in HiggsBounds. In
Appendix A,wedescribeamethodforapproximatingtheh A limits
moregenerally,whichweapply toourscan inSect.3.2.Wenote that the OPAL collaboration performeda similar search [35], but theirlimitsareweakerthantheonesweapplyhere.
Followingthe work ofRefs. [36,37],the CDFcollaboration has alsosearchedforfermiophobicHiggsbosons[38]intheW±
+
4γ
channel highlighted in this paper. This search should in princi-plehavesensitivitytosomeoftheparameterspaceclosest tothe fermiophobiclimit.However,theCDFlimitsarepresentedonlyfor
Fig. 1. Left:
Contribution,
Fx, defined in the text, to the h→γ γdecay, corresponding to the W±(red), fermions (blue), and H±(green) loops. Right: BRs of the h→γ γ (green) and h→bb (red)¯decays. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. Left:σ(qq→H±h)at √s=13 TeV as a function of mhfor the points passing the parameter space scan, with mH±indicated by the colour map. Right: BR(H±→W±h) as a function of mH±, with mhindicated by the colour map.
theexactly fermiophobic scenarioand arenot readily extendable toourmoregeneralsearch.
AsfortheLHC,despitethefactthataphenomenological frame-workfora 4-photonsearch was setupin [39](also coveringthe
H±h productionmodeaddressedhere),noATLAS andCMS exper-imentalanalysesontheselinesexisttodate.Onethushastorely on Ref. [40], which uses data for the 2-photon Higgs search to constrainthescenario where4photonsareproduced.This study, however,doesnotexcludetheregionofparameterspacediscussed here, while the H±h
→
W±hh→
W±+
4γ
analysisof Ref. [39]capturesasomewhatdifferentregionofparameterspacefromthe one considered here, withmH±
>
100 GeVandmh>
40 GeV, and onlyconsiderstheexactfermiophobiclimit.Ourpresentstudy ex-tendstomuchlower massesofbothoftheseHiggsbosons (down tomH±≈
80 GeVandmh≈
10 GeV)andconsidersalessrestrictive rangeofvaluesfortheothermodelparameters.23.2. pp
→
H±h anditsW±+
4γ
finalstateWeperformedanumericalscanoftheparameterspacegivenin
Table 1toinvestigatethescenarioswhichcanresultinasignificant crosssectionfortheW±
+
4γ
finalstate.3Thisrepresentsabroad,though not exhaustive,regionof the2HDMparameter space. For example, whereas requiring tanβ >2 helps to evade B-physics
constraints,tan
β
caninprincipletakevalueslargerthan25; how-ever,wefindthat thislimitismorethansufficient tofindpoints whichsaturatethe H±→
W±h branchingratio.Duringthescan, all points were required to pass theoretical bounds on unitarity, perturbativity,andvacuumstabilityasimplementedinthe2HDMC code.Thesepointswere furthercheckedforconsistencywith var-ious experimental constraints from direct Higgs boson searches,B-physics, andEW precision data. The complete list ofthe con-straintsimposed can be foundin Sect. 2of[24].We additionally requiredthesepointstosatisfythelimitsfromsearchesfor fermio-phobich viae+e−
→
h A production,asdescribedinAppendix A
.Thedirectsearchconstraintswerecheckedusingthelatest sta-ble version (v4.3.1) of the public code HiggsBounds [34].
Higgs-2 Furthermore, we perform here a detailed kinematical analysis of the 4-photon
signal and background which was missing in[39].
3 The original scan, where all the input parameters were scanned uniformly, was
supplemented by uniform scans of the ranges mh<62.5 GeV and 62.5 <mh< 90 GeV in order to obtain an appreciable density of points in each range. Appar-ent discontinuities in some figures at the resulting mh boundaries are a result of this choice (within a given range, the points represent a uniform scan). Each scan produced approximately 900 points.
Bounds 4doesnotincludesearchesfromthe13TeVLHC aswell assomeLEPsearchesforchargedHiggsbosons;wehavetherefore additionally checked our results against a beta version of Higgs-Bounds 5, which includesthese searches.4 We findthat the only
searches unique to HiggsBounds 5 betawhich exclude additional pointscomefromLEPsearchesfore+e−
→
H+H−[41],which re-moveasmallfractionofpointswithmH± justabove80 GeV.While inprincipletheLEPresults[41]allowthechargedHiggstotakeon a massbelow80 GeV,they placestrongexclusionsinthisregion, sowekeepahardlowerlimitof80 GeVinourscantoavoid rely-ingsolelyonthebetaversionofHiggsBounds 5.For calculating the cross section for the process qq
→
H±hwithq
=
u,
d,
s,
c,
b (i.e.,inthefive-flavourscheme)at√
s=
13TeV,we used 2HDMCcombined withMadGraph5_aMC@NLO [42]. We
haveusedNNPDFv2.3partondistributionswithdynamicalscales set by MadGraph. In the left panel of Fig. 2 we show the cross section pp
→
W±∗→
H±h for the points obtained in our scan that pass all the constraints. The cross section has two sources ofenhancement: thefirst isthe H±W∓h coupling, whichis pro-portionalto cos(β−
α
)
andhence near-maximalin ourscenario, whilethe secondisthe largephasespaceafforded duetoalighth and/or H±. It is clear that thisproduction cross section could reach the pb level for relatively light h, inthe range 10–60 GeV, andlight,80–110GeV, H±.Thesecrosssectionscanbe compara-bleto,andinsomecasesexceed,theproductionofalightcharged Higgsviatopdecay,e.g. pp
→ ¯
tt→ ¯
tbH+,especiallyatlarger val-uesoftanβ,
wherethecouplingof H± tofermionsissuppressed in2HDM-I models.Furthermore,thetbH¯
+ channel doesnotgive risetothelow-backgroundW±+
4γ
signatureconsideredhere.Similar to the H±h production, the decay H±
→
W±h alsoenjoys the enhancement factor from cos(β
−
α
)
≈
1. The right panel of Fig. 2 illustrates that the BR(H±→
W±h)
can reach 100% for a very light h. In the left panel of Fig. 3we show the BR(h→
γ γ
) as function of mh, with the other 2HDM-I param-eters varying in the ranges given in Table 1. We notice in the figure that before the opening of the h→
W W∗ channel, the BR(h→
γ γ
) could reach 100% for small values of cosα
/
sinβ.
By puttingtogether all theseobservations – thelarge H±h crosssections, dominant H±
→
W±h decays, and the possibility of a fermiophobic h that could decay primarily into two photons – one can immediatelyanticipate asignificant crosssection fortheW±hh
→
W±+
4γ
finalstate.Thisisconfirmedbytherightpanel of Fig. 3, in which one sees that the total cross section for ourFig. 3. Left:
BR
(h→γ γ)as a function of the mass of h,with the heat map showing
|cosα/sinβ|. Right: Signal cross section, σ(±ν+4γ)as a function of mh, with the heat map showing the mass of H±. The five selected benchmark points are highlighted in yellow circles. (For interpretation of the references to colour in this figure legend,the reader is referred to the web version of this article.)
Table 2
Input parameters, parton-level cross sections (in fb), and selected branching ratios corresponding to the selected BPs. All masses are in GeV and for all points mH=125 GeV. Here σ(W±+4γ)=σ(qq→H±h)×BR(H±→W±h)×BR(h→γ γ)2for the LHC at 13 TeV (in contrast to Figs. 3 and6, a factor of B R(W±→ ±ν)is not included here).
BP mh mH± mA sin(β−α) m212 tanβ cosα/sinβ σ(W±+4γ)[fb] B R(H±→W±h) B R(h→γ γ) B R(A→bb¯)
1 24.2 152.2 111.1 −0.048 19.0 20.9 1.1×10−4 359 1.00 0.94 4 .6×10−3 2 28.3 83.7 109.1 −0.050 31.3 20.2 −5.9×10−5 2740 1.00 0.97 7.4×10−3 3 44.5 123.1 119.9 −0.090 30.8 10.9 6.8×10−4 285 1.00 0.70 0.031 4 56.9 97.0 120.3 −0.174 243.9 5.9 −6.5×10−3 39 0.90 0.22 0.18 5 63.3 148.0 129.2 −0.049 173.1 20.7 −4.2×10−4 141 1.00 0.71 0.017
signal,
σ
(
qq→
H±h→
W±hh→
+ν
+
4γ
)
(which wecalculate asσ
(
qq→
H±h)
×
BR(H±→
W±h)
×
BR(h→
γ γ
)
2×
BR(W±→
±
ν
)
with=
e,
μ
),canreachthepblevelforlowmh.From thesepoints, we haveselected a few benchmark points (BPs),highlightedintherightpanelof
Fig. 3
,thespecificsofthese BPs are given inTable 2. TheseBPs are chosen mainly to repre-sentavarietyofvaluesformh andmH± whichleadtosignificant W±+
4γ
crosssections,withBP3 lying somewhat centrally and theother pointslying closertotheextremal valuesof(
mh,
mH±) withsignificantcrosssections.Thesemassesareimportantbothin determiningthe pp→
H±h crosssection, asseenabove inFig. 2
, andthekinematicselection,asshowninthefollowingsection.All ofthebenchmarkpointshaveahighlyfermiophobich,dueto val-uesofsin(β−
α
)
andtanβ whichgiverisetosmallhf f couplings,andhavesignificant hH±W∓ couplings dueto small sin(β
−
α
).
Thebranching ratios H±→
W±h and h→
γ γ
are then closeto maximal,withthenotableexceptionofBP4,whichisthefurthest fromthefermiophobiclimitandhasasmallerB R(
h→
γ γ
).
4. Discoverypotential
Nextweconsider thepotential forthe 13TeV LHCtoobserve this W±
+
4γ
→
±ν
+
4γ
signature. Fig. 4showsthe distribu-tions ofthetransverse momenta(pT’s)forone theBPs, forboth thelepton and the softest photon. Both of them resultfrom de-caysofrelativelylightintermediatestates,sothedistributionsare skewed towards low pT. The photon pT, in particular, peaks at lower values for BPs with smaller mh. The lepton pT distribu-tion is sensitive to both mh andmH±,as is evident for the dis-tribution corresponding to BP4,wherein the lepton coming from the off-shell W± tends toward low pT, owing to the fact that mH±−
mh is much smaller than mW±. Noting also that these distributions fall offrapidly inthe pT ranges that might reason-ably be used to select events, the discovery potential could bevery sensitive to thechoice of triggers andeventselection crite-ria.
The experiments cannot trigger on such low-pT single pho-tonsorleptons, though,sothe necessarytriggers willhavetobe oncombinationsofmultipleobjects.Forexample,theATLAShigh level trigger (HLT)selection [43,44] for a single isolated electron ormuongoesdownto26 GeV,withofflineselectiononlyslightly higher. Triggering on two muons, however, reduces the required momentato14 GeV.Similarly,asinglephotonrequires120 GeVin theHLT,buttwotightphotonsrequire22 GeVeach.Itistherefore conceivablethatthecombinationsrequiredfortheanalysisweare proposing, forexample, a lepton plus a photon trigger,or a four photontrigger, withlow enoughtransversemomenta10–15GeV, couldbeaddedtothetriggermenu.
Furthermore, it should be noted that the freedom of choice in selecting the optimal triggers is enabled by the fact that the background for this process is essentially non-existent. We
es-timated the irreducible SM W±
+
4γ
background usingMad-Graph5_aMC@NLO. Requiring, e.g., four photons and one lepton, all with pT
>
10 GeV, along with pseudorapidity and isola-tion cuts described below, we find a cross section of less than 10−6 pb. In fact, we expect that instrumental backgrounds (e.g.,mis-identification of a lepton or a jet as a photon [45,46]), will not change this conclusion, as long as all 4 photons are indeed reconstructed.
With thisin mind, we consider two sets of cuts: (i) requires that all photons have pγT
>
10 GeV and the charged lepton haspT
>
20 GeV, whereas (ii) imposes that pγT>
20 GeV and pT>
10 GeV. In both cases, we require pseudorapidity|
η
|
<
2.5 for the lepton and each photon, while all objects are required to havean isolationR
=
(
η
)
2+ (φ)
2>
0.4.Todetermine theefficiencies of these cuts, we calculated event rates for various masses and determined the corresponding selection efficiencies,
=
σ
(cuts)/
σ
(no cuts).
The results are shownin Fig. 5forboth choices of cuts, and demonstrate a strong dependence on theFig. 4. Transverse momentum distributions for the softest photon (left) and the lepton (right) for the±ν+4γ signal for the various BPs.
Fig. 5. Efficiency,=σ(cuts)/σ(no cuts), for the ±ν+4γfinal state for the two choices (i) and (ii) of cuts described in the text (left and right, respectively). All masses are in GeV. No values are shown for mH±≤mh, where the H±→W∗h decay
is not kinematically allowed.
Fig. 6. Signal
cross section
σ(±ν+4γ)times selection efficiency for the two choices (i) and (ii) of cuts described in the text (left and right, respectively). The cross section is calculated as σ(±ν+4γ)=σ(qq→H±h)×BR(H±→W±h)×BR(h→γ γ)2×BR(W±→ ±ν). The five selected BPs are once again highlighted in yellow circles. (Forinterpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
massesinvolved.Theeffectofthesecutsonthesignal yieldfrom our scan is shown in Fig. 6, with numerous points representing different regions of phase space yielding post-trigger cross sec-tions above thefemtobarnlevel.Giventhe negligiblebackground forthisprocess,itisclearthatthereisregionofparameterspace
that shouldbe within reach5 alreadyattheLHC RunII assuming
standardluminositiesoforder100 fb−1.
5 A full detector-level sensitivity analysis of this signature is beyond the scope of
Table 3
Average centre-of-mass energies and integrated luminosities of the DELPHI analysis.
√
s [GeV] 182.6 188.6 191.6 195.5 199.6 201.6 205.0 206.5 206.8 L[pb−1] 49.3 153.0 25.1 76.0 82.7 40.2 80.0 59.2 81.8
5. Conclusions
Intheframeworkofthe2HDM-I,thereexiststhepossibilityofa scenarioinwhich: H istheobservedCP-evenSM-likeHiggsboson,
h islighterthan125 GeV(infact,possiblyaslightasabout10 GeV orso),andH±liesinthe80–160GeVmassrange,stillbeing con-sistentwithallLHC,LEPTevatronandB-physicsdata.Furthermore, inthisscenario,for cos
α
≈
0 and someparticular choicesofthe other parameters, h could be highly fermiophobic, decayingfully ordominantlyintotwophotons,whilethe H±coulddecay domi-nantlytoW±h,escapingtheexistingLHClimitsonH±→
fermion signatures.Undertheseconditions,wehaveshownthattheassociated pro-ductionofthechargedHiggsbosonwiththelight CP-evenHiggs,
pp
→
H±h, could be substantial and would lead to a W±+
4γ
final statewitha rathersignificant eventyield. Infact, after rea-sonable cuts on the pT of each of the photons and the lepton, underplausibletriggerassumptions,alongsidethosein
η
andR,
the emerging W±
+
4γ
signal can still enjoy a cross section of theorder 10 fbandmore inan essentially background-free envi-ronment.We note inpassing that thisdecay channel of the H±could also be of great significance ata lepton collider.There, as long asthe H± is not tooheavy, its pair-production would pro-ceedvia the tree-level mechanism e+e−
→
H±H∓, leading to a cleanW±W∓4γ
finalstate.We look forward to the ATLAS and CMS experiments testing this hitherto neglected scenario against their data, as establish-ing the signature discussed here will provide not only a direct indication of a non-minimal Higgssector butalso circumstantial evidenceofaspecific2HDMstructure.
Acknowledgements
This project has received funding/support from the European
Union’s Horizon 2020 research and innovation programme
un-dertheMarieSkłodowska-CuriegrantagreementNo.690575.The
work of RE and SMo is funded through the grant
H2020-MSCA-RISE-2014 No. 645722 (NonMinimalHiggs). SMo is supported in partthrough theNExT Institute andSTFCConsolidatedGrant ST/ J000396/1. AA and RB are supported by the Moroccan Ministry ofHigherEducation andScientific ResearchMESRSFC andCNRST: Project PPR/2015/6.WKthanksSofiaAndringaforhelpfulfeedback. WethankElinBergeås KuutmannandRichardBrennerforhelpful discussions ofexperimental prospects andTim Stefaniak forhelp withHiggsBounds5.
Appendix A. e+e−
→
h A limitThe DELPHI collaboration performeda search for the process
e+e−
→
h A,withthe decaysh→
γ γ
and A→
bb or¯
A→
Zh→
Zγ γ
,whenkinematicallyallowed[31].Thisenabledthemtoplace limits on sin2(β
−
α
),
assuming an exactly fermiophobic h, and that A decaysentirelyinto eitherbb or¯
Zh.These limitsdepend on mh and mA and are explicitly given for mA=
50 GeV and mA=
115 GeV.Here, we deriveapproximatelimitsforother val-uesof mA, which allows one to constrain models which are not exactly fermiophobic.The centre-of-mass energies,√
s, and inte-gratedluminosities,L,
usedintheanalysisare showninTable 3
. Foragivenmodel,theexpectednumberofobservedeventsisNh Aexp
(
mh,
mA)
=
BR(
h→
γ γ
)
×
BR(
A→
X)
×
{s}
σ
h A(
s,
mh,
mA)
L
(
s)
(
s,
mh,
mA).
(A.1) Here, X iseitherbb or¯
Z(
h→
γ γ
)
and(
s,
mh,
mA)
isthesignal selectionefficiencyoftheanalysis.Ifweassumethatthevariations oftheefficiencyarenottoolarge,wecanreplaceitwithan effec-tiveefficiency¯
,whichwemaythenpulloutsideofthesumand absorbintoN˜
=
Nh Aexp/
¯
,giving˜
N(
mh,
mA)
=
N0(
mh,
mA)
cos2(β
−
α
)
×
BR(
h→
γ γ
)
×
BR(
A→
X),
(A.2) where N0(
mh,
mA)
=
{s}σ
0(
s,
mh,
mA)
×
L
(
s).
(A.3) Here wehaveintroducedσ0
,which isthee+e−→
h A cross sec-tionwhencos(β−
α
)
=
0.Wecan thentranslate agivenlimit, sβlimα , onsin(β
−
α
)
intoa limiton N,˜
giventhestatedassumptionsthatBR(A→
X)
=
1 and BR(h→
γ γ
)
isforanexactlyfermiophobich≡
hf:˜
Nmax
(
mh,
mA)
=
N0(
mh,
mA)(
1− (
slimβα(
mh,
mA))
2)
×
BR(
hf→
γ γ
).
(A.4) We onlyhave valuesof slimβα formh= {
50,115}
GeV, butsince the experimental efficiencies vary slowly [47] over our region of interestinthe2HDM-Iparameterspace,weapproximate N˜
max asa constant. To choose a suitable value, we consider the average valuesofthetwolimitingcurvesoverrelevantvaluesofmh:
˜
Navgmax
(
40<
mh<
90,
mA=
50)
=
8.
4,
˜
Nmaxavg
(
25<
mh<
70,
mA=
115)
=
9.
1.
(A.5) FormA=
50 GeV, we choose a lower limit formh of40 GeV, aswe haveonlyafew pointswithmh+
mA muchbelowmZ due tolimitsfromthe Z widthmeasurement.Furthermore,above the upper limit of90 GeV very few points have cross sectionsof in-terestto thisstudy.FormA=
115 GeV, wechoosean upperlimit ofmh=
70 GeV,above which mh+
mA√
s for some LEP runs. Thelowerlimitof25 GeVoccursaroundmA
=
mh+
mZ,wherethe A→
Zh analysisisused.ItisnotablethatbothvaluesofmA give similarresults,andforourlimitweconservativelychooseavalue of8.4.Wemaythenimposealimitforallvaluesof(
mh,
mA)
given bycos2
(β
−
α
)
×
BR(
h→
γ γ
)
×
BR(
A→
X)
≤
N˜
maxN0
(
mh,
mA)
,
(A.6) withN
˜
max=
8.4.Finally,wenotethatthe A→
Zh searchrequiredan on-shell Z boson, so it isonly applicable inthe region mA
>
mh+
mZ.Inthatregion,however,the A→
bb channel¯
isreported tostillhavesensitivitycomparabletothe A→
Zh channel[31],so that,whenconstrainingaparticularpointintheparameterspace, wetakethelargerofthetwo:BR
(
A→
X)
=
⎧
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎩
BR(
A→
bb¯
),
if mA<
mh+
mZ maxBR
(
A→
bb¯
),
BR(
A→
h Z)
×
BR(
h→
γ γ
)
if mA>
mh+
mZ.
(A.7) TheresultinglimitsforN˜
max=
8.4 areshowninFig. 7
.Fig. 7. Estimated
limits on cos
2(β−α)×BR(h→γ γ)×BR(A→bb¯/Zγ γ)with ˜Nmax=8.4. BPs from the text are indicated in yellow circles. The dashed line
in-dicates where mA=mh+mZ, above which the on-shell A→Zh decay
is possible.
(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)References
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