The Virtual Diphoton Excess

1.3 MB·

by  Daniel Stolarski

CERN-TH-2016-005
The Virtual Diphoton Excess
Daniel Stolarskia,b and Roberto Vega-Moralesc
aTheoretical Physics Department, CERN, Geneva, Switzerland
bOttawa-Carleton Institute for Physics, Carleton University,
1125 Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada
cDepartamento de F´ısica Teo´rica y del Cosmos and CAFPE, Universidad de Granada,
Campus de Fuentenueva, E-18071 Granada, Spain ∗
Interpretingtheexcessesaround750GeVinthediphotonspectratobethesignalofanewheavy
scalarϕdecayingtophotons,wepointoutthepossibilityoflookingforcorrelatedsignalswithvirtual
photons.Inparticular,weemphasizethattheeffectiveoperatorthatgeneratestheϕ→γγdecaywill
alsogeneratedecaysofϕ→2(cid:96)γ (2(cid:96)≡2e,2µ)andϕ→4(cid:96)(4(cid:96)≡2e2µ,4e,4µ)independentlyoftheϕ
couplings to Zγ and ZZ. Depending on the relative sizes of these effective couplings, we show that
the virtual diphoton component can make up a sizable, and sometimes dominant, contribution to
6 thetotalϕ→2(cid:96)γ andϕ→4(cid:96)partialwidths.Wealsodiscussmodificationstocurrentexperimental
1 cutsinordertomaximizethesensitivitytothesevirtualphotoneffects.Finally,webrieflycomment
0 on prospects for channels involving other Standard Model fermions as well as more exotic decay
2 possibilities of the putative resonance.

n
a
J INTRODUCTION ular emphasis on the leptonic ϕ→2(cid:96)γ (2(cid:96)≡2e,2µ) and

6 ϕ→4(cid:96) (4(cid:96)≡2e2µ,4e,4µ) channels.
2 Therehasbeentremendousinterestintheexcessesre- We also examine what effects cuts on the lepton in-

cently reported by both ATLAS [1] and CMS [2] in the variant masses have on the relative composition of the
]
h diphoton spectrum around 750 GeV. If this is a sign of a ϕ → 2(cid:96)γ and ϕ → 4(cid:96) partial widths. Should the dipho-
p new resonance, the simplest explanation for the decay is tonexcesspersist, thenknowing themass ofϕ willallow
p- through the photon field strength or dual field strength a search for ϕ → 2(cid:96)γ and ϕ → 4(cid:96) decays imposing only
e tensor. For concreteness we will consider the dual field minimalconstraintsonanysubsetofthefinalstates.We
h strength case via the dimension five operator take advantage of this to motivate modifying current ex-
[ perimental searches in the 2(cid:96)γ and 4(cid:96) channels in order
c
2 4γΛγ ϕFµνF(cid:101)µν, (1) to maximize the sensitivity to the virtual diphoton ef-
v fects. We also briefly discuss possibilities in the less ex-
04 where Fµν = ∂µAν −∂νAµ and F(cid:101)µν = 12(cid:15)µνρσFρσ. We perimentally clean decays to other SM fermions.
take Λ to be some new mass scale associated with this All of the results presented here are obtained by inte-
0
operator that will cancel in all the ratios we will con- gration of the analytic expressions for the ϕ → 2(cid:96)γ and
2
0 sider. Our choice of operator in Eq. (1) implies the new ϕ→4(cid:96)fullydifferentialdecaywidthsobtainedin[41–43]
. resonance ϕ is a parity odd scalar, but our considera- to which we refer the reader for further details.
1
tions largely apply if it turns out to be a parity even or
0
6 CP violating scalar as well as a spin 2 resonance.
1 Assuming electroweak SU(2)×U(1) gauge symmetry DECAY OF ϕ TO 2(cid:96)γ
: holds in the UV, the operator in Eq. (1) must descend
v
i from a linear combination of the operators [3]: If there is indeed a new particle decaying to γγ, then
X
c c itwillalsodecayto2(cid:96)γ viaavirtualphoton.Therateof
ar 4WΛ ϕWµaνW(cid:102)aµν and 4BΛϕBµνB(cid:101)µν. (2) this decay is strongly sensitive to the phase space cuts,
particularly on the invariant mass of the lepton pair. In
Ashasalreadybeenpointedoutmanytimes[4–36],these
particular,ifanexperimentalanalysisallowsleptonpairs
operatorswillleadtocorrelatedsignalsinϕdecaystoZγ
withaninvariantmassbetweenM andM ,thenthe
and ZZ, as well as WW if c is non-zero. Searches for low high
W ratio of partial widths gives
dibosonresonanceshavebeenperformedbyATLAS[37–
39] and CMS [40] placing constraints on models which Γ(ϕ→γ∗γ →2(cid:96)γ) 4α (cid:18)M (cid:19)
≈ log high . (3)
can explain the diphoton resonance.
Γ(ϕ→γγ) 3π M
low
Inthisletter,weemphasizethattheoperatorinEq.(1)
alone is enough to produce ϕ→2fγ and ϕ→4f decays Thefactorofα/π comesfromtheadditionalphotoncou-
of the ϕ resonance through virtual photons, irrespective pling, while the log comes from integrating the photon
ofitsUVorigin.Weexamineunderwhichcircumstances propagator over the phase space. From this formula we
the virtual photon component makes up a sizable contri- see that if a search has a narrow invariant mass window
bution, or even dominates over the ZZ and Zγ compo- aroundtheZ pole,asintheATLASsearch[37]whichre-
nents, to these three and four body decays, with partic- quires65<M <120GeV,thentheeffectsfromvirtual
(cid:96)(cid:96)
2
photonswillbetiny.Ontheotherhand,makingasearch φ→2lγ(l=e,μ),M =750[GeV]
φ
as inclusive as possible will raise the rate from virtual
1 Γ(φ→γ*γ)/Γ(φ→γγ)
photons even in the absence of contributions from Z’s.
Γ(φ→Z*γ)/Γ(φ→γγ)
Of course most models that explain the diphoton ex- γγ) 0.100 Γ(φ→Z*γ/γ*γ)/Γ(φ→γγ) Γ
cess via Eq. (1) will also generate the Zγ operator → (φ
→
c2ZΛγ ϕFµνZ(cid:101)µν. (4) γ)/Γ(φ 0.010 γ)/Γ(φZ
2l 0.001 →
Naively, the effects from this operator should be para- → γγ
metrically larger than the the γ∗γ operator since the Z Γ(φ 10-4 ATLFAulSl )=2
can be produced on shell. However, the suppression is
not nearly so large for two important reasons: 10-5
0.0 0.5 1.0 1.5 2.0
• The Z coupling to leptons is suppressed relative to λZγ=cZγ/cγγ
that of the photon.
FIG.1. Theratioofϕ→2(cid:96)γeventsthatcomefromthethree
• Unlike the photon, there is no log enhancement underlying components: Z∗γ (red), γ∗γ (blue), and interfer-
when integrating the region of phase space away ence between the two (green), relative to the number of on-
shell ϕ→γγ events. The contributions are shown as a func-
from the Z pole.
tionofλ ,theratioofcouplingsdefinedinEq.(5).Weshow
Zγ
ratiosfortheinclusive(Full)phasespacecuts4<M <750
Therefore, if the phase space cuts are very inclusive, the (cid:96)(cid:96)
GeV(dashed)aswellasforATLAS-likecutswith65GeV<
off-shell photon can be an important effect.
M <115 GeV (solid). The vertical grey line corresponds to
(cid:96)(cid:96)
InFig.1weplotthethreedifferentcontributionstothe
Run I limits on λ derived from [37].
Zγ
process ϕ→2(cid:96)γ as a function of the ratio of couplings
λ =c /c . (5)
Zγ Zγ γγ
From the ATLAS 8 TeV search [37], one can bound
Wehavenormalizedthethreecomponentsofϕ→2(cid:96)γ to the cross section into 2(cid:96)γ, although the bound depends
the ϕ → γγ partial width so the ratio involving the γ∗γ onhowthecrosssectionscalesgoingfrom8to13TeV.In
component (blue curve) is flat. We plot these ratios for the case of gluon initiated production, the two body de-
both ATLAS-like phase space cuts (solid) and for much cayϕ→Zγ islimitedtobeabouttwiceϕ→γγ (seefor
moreinclusive‘Full’cuts1 with4GeV<M <750GeV example [10]) so we place a grey vertical line to indicate
(cid:96)(cid:96)
(dashed). The lower cutoff of 4 GeV is inspired by stud- this limit. The production mechanism could however be
ies looking for similar off-shell photon effects involving photon [47, 48] or quark [10, 49] initiated, or perhaps
the Higgs boson at 125 GeV [44–46]. We see that with some more exotic production mechanism [50–54]. There-
these relaxed phase space cuts, the γ∗γ component can fore, weshowresultsforevenlargervaluesofλ dueto
Zγ
be a few per cent of the on-shell rate because the log this uncertainty.
in Eq. (3) is large, while with current cuts the virtual The central observation of this study is that the in-
photon contribution is an order of magnitude smaller. variant mass spectrum of the lepton pair (rather than
WealsoseeinFig.1thatforsmallλZγ,theγ∗γcompo- the full (cid:96)(cid:96)γ system) contains significant information on
nent dominates, while for large λZγ the Z∗γ component the couplings of the new resonance to gauge bosons. In
dominates as expected. Another expected feature is that Fig. 2 we plot the normalized invariant mass distribu-
thecontributionfromZ∗γisrelativelyunalteredbythese tions for two extreme values (10 and 0.1) of the ratio of
cutssincetheybothcontaintheZ-pole.Theinterference couplings λ defined in Eq. (5). We also show the two
Zγ
between the two components is always small, but is sig- simple cases of c = 0 (red) and c = 0 (green) using
W B
nificantly enhanced by the more inclusive cuts, making the SU(2)×U(1) operators in Eq. (2). These predict
√ √
this effect potentially observable with a large number of λ = 2tanθ ≈ 0.8 and λ = 2cotθ ≈ 2.6
Zγ W Zγ W
ϕdecays.Thistypeofinterferencealsoopensupthepos- respectively [3], where θ is the Weinberg angle. Un-
W
sibility of observing CP violation in the ϕ → 2(cid:96)γ three surprisingly, we see that larger values of λ raises the
Zγ
body decays as proposed for the Higgs boson [43]. height of the peak around the Z pole, while lower values
raises the value at low M . A perhaps more unexpected
(cid:96)(cid:96)
feature, is that for low values of the ratio there are also
more events at high M above the Z peak. This comes
(cid:96)(cid:96)
1 Note that we have only considered cuts on the lepton invariant fromthefactthatthedistributionsarenormalizedsothe
masses and not on the lepton pT or rapidity. Since the rate is peak is not as large.
dominatedbythepolestructureofthevectorbosonpropogators,
thissimplificationscapturesqualitativelythefeatureswewishto We can exploit the fact that the virtual photon and
emphasizeinthisstudy. Z have very different distributions in the invariant mass
3
0.100 φ→2lγ,Mφ =750[GeV],4<Mll <750[GeV]
φ→2lγ
Mφ=750[GeV]
llφ→γ 0.010 4<Mll<750[GeV] 0.8
Γ 0.001 λ =10
)/ Zγ
Mll
d 10-4 λZγ= 2 cotθW (cB =0) 0.6 Γ
/γ Δ) (φ
dΓllφ→ 10-5 λλZZγγ==0.21 tanθW (cW =0) R(Z0.4 Δ=2.5[GeV] →γ)/ΓZ
( 10-6 Δ=10[GeV] (φ
0.2 Δ=30[GeV] →
γ
γ
10-7 Δ=50[GeV] )
0 100 200 300 400 500 =
0.0 2
M [GeV]
ll 0.0 0.5 1.0 1.5 2.0
λ
Zγ
FIG. 2. Normalized (over 4 < M < 750 GeV) lepton pair
(cid:96)(cid:96)
invariant mass distribution shown for two extreme values 10
FIG.3. R (∆),thefractionofeventsneartheZ poledefined
(orange) and 0.1 (blue) of the ratio of couplings λ defined Z
Zγ inEq.(6)asafunctionofλ ,theratioofcouplingsdefined
inEq.(5).Wealsoshowthetwosimplecasesofc =0(red) Zγ
W in Eq. (5). We plot ∆ = 2.5, 10, 30, 50 GeV going from
and c = 0 (green) if the ϕZγ and ϕγγ operators descend
B bottom to top. The total phase space is defined via the cuts
from the SU(2)×U(1) invariant operators in Eq. (2). See
4 GeV < M < 750 GeV shown at the top. Again, we also
text for more information. (cid:96)(cid:96)
showthelimit(verticalline)fromZγ searches[37]at8TeV.
of the lepton pair to make a crude but very simple mea-
dominant.Thedominantbackgroundhasbeencalculated
surement of λ . The idea is to simply take the fraction
Zγ very precisely in both the qq¯ and gg initial states [58–
of events that have leptons near the Z pole:
71].Acrudeestimateusingtree-levelMadgraph[72]sim-
N(M +∆>M >M −∆) ulation finds that opening the lepton invariant mass cut
R (∆)= Z (cid:96)(cid:96) Z , (6)
Z totalnumberof events from being just around the Z pole to simply requiring
M > 4 GeV roughly doubles the background. This
where the total number of events is defined by the inclu- (cid:96)(cid:96)
shouldalsogiveareasonableestimateforthefakephoton
sive phase space cuts 4 GeV < M < 750 GeV. As can
(cid:96)(cid:96) background because the underlying process is Z(∗)/γ(∗)
be seen in Fig. 3, R is strongly dependent on λ . We
Z Zγ
+ jets, so the invariant mass distribution when a photon
plot various different values of the mass window ∆, and
is replaced with a jet should be similar. Ultimately, the
we see that for λ (cid:46)0.7, the slope of the curve is large
Zγ
background is smooth and rapidly falling in the center
andthisvariablebecomesquitesensitive.Forlargercou-
of mass energy, allowing for good background discrimi-
plings, the virtual photon contribution to this channel
nation with a simple side-band analysis. Therefore, we
becomes subdominant and this observable becomes less
donotexpectrelaxingthecutsontheleptonpairinvari-
sensitive.Inthiscase,however,thetotalrateofϕ→2(cid:96)γ
ant mass to be an obstruction for enhancing the virtual
events will be larger so a more statistically precise mea-
diphoton signal.
surement will be possible.
Onecouldimaginevarying∆inanexperimentalanal-
ysis to get more information about this coupling ra-
DECAYS TO FOUR LEPTONS
tio. Taking this to the extreme and using the full phase
space information contained in the differential mass dis-
We now turn to ϕ→4(cid:96) four body decays where again
tributioneventbyeventwouldallowforevenbettermea-
4(cid:96)=2e2µ,4e,4µ. In this case the operator
surements. Of course using a so-called matrix element
c
mdiefftehroendtwiahledreectahyewliikdetlhihuosoidngisaclolnosbtsreurcvtaebdlefrsoimn ϕth→efu2l(cid:96)lγy 4ZΛZ ϕZµνZ(cid:101)µν (7)
uses the maximum amount of information. Furthermore, will also contribute and is naively the dominant effect
at 750 GeV these kinematic observables may be more due to the fact that both Z bosons can be on-shell at
discriminating than was found for a 125 GeV Higgs bo- 750GeV.Therearehowever, stillcontributionsfromthe
son[55]decayingto2(cid:96)γ.However,weleaveafullydiffer- c and c operators studied in the previous section. If
γγ Zγ
ential analysis utilizing all observables in ϕ→2(cid:96)γ using these operators descend only from the SU(2)×U(1) in-
the framework of [41–43, 56] to ongoing work [57]. variant operators of Eq. (2), then there are only two un-
Finally, we briefly comment on backgrounds. The knowns and the system is over-constrained. Therefore,
dominant background around 750 GeV in the current measuringthecontributionofallthreeoperatorsisanon-
search [37] comes from genuine 2(cid:96)γ, while a jet faking trivialtestoftheSMgaugesymmetryatthescaleofthe
a photon is the second most important but highly sub- mass of the new resonance. While the ϕ→4(cid:96) rate alone
4
is not enough to measure all three operators, a fully dif- 3.0
0.035
ferential analysis may be able to determine all three in a Γ(φ → 4l)
0.04
single channel [57], but we do not explore this here.
Γ(φ → γγ)
2.5 Γ(φ→ZZ)/Γ(φ→γγ)=6
ThecurrentbestlimitsfordecaystoZZ inRunIcome
from the (cid:96)(cid:96)¯qq¯ channel [38] from which one can extract
that the ϕ decay to ZZ is at most a factor of six bigger 0.02 0.02
2.0
than the rate to γγ [10] assuming that ϕ is produced
γ
fhriogmhegrluborannicnhiitniaglrsatatitoest.hTahnisthchea4n(cid:96)neclhhanasneal,sibguntifiscuaffnetlrys cc/ZZγ1.5 Mφ=750[GeV] Γ(φ→Z
from a worse signal to background ratio. Therefore, this = Full:4<M1,2<750[GeV] γ)/Γ
search requires that both pairs of objects are roughly λZZ ATLA1S2:<50M<2M<112<01[2G0e[VG]eV], (φ→γ
on the Z pole. There is also a search for decays to four 1.0 γ)
=
2
leptons [39] which has a significantly smaller rate, but
is experimentally much cleaner. In this search, there is 0.004
0.5 0.004
also a requirement that one lepton pair invariant mass
be between 50 and 120 GeV while the second is required
0.0005
tobebetween12and120GeV.Thisnotonlyreducesthe 0.0005
0.0
totalsignalrate,butalsotherelativesizeofanynon-ZZ 0.0 0.5 1.0 1.5 2.0
contributiontoϕ→4(cid:96),analogoustothethreebodycase λZγ=cZγ/cγγ
of ϕ→2(cid:96)γ described above.
Here we will study ratios of partial widths involving FIG. 4. Contours for the ratio of the rate of ϕ → 4(cid:96) (4(cid:96) ≡
ϕ → 4(cid:96) in the two dimensional parameter space of λ 2e2µ+4e+4µ) over the rate of ϕ → γγ in the plane of
Zγ
coupling ratios λ and λ defined in Eq. (5) and Eq. (8),
defined in Eq. (5) and a second ratio of couplings, Zγ ZZ
respectively. We show inclusive phase space cuts 4<M <
1,2
λ =c /c . (8) 750 GeV (dashed orange) as well as ATLAS-like cuts [38]
ZZ ZZ γγ
with 50 < M < 120 GeV and 12 < M < 120 GeV (solid
1 2
The kinematics of ϕ → 4(cid:96) are more complicated than blue). We also put the limits on the coupling ratios coming
2(cid:96)γ and have been studied at length in the context of from ϕ→ZZ and ϕ→Zγ searches assuming ϕ is produced
a heavy Higgs decay (see for example [73–77]). Although from gluon initial states as in [10].
therearemultipleangularobservableswhichcontainuse-
ful information, in this simplified study we focus on the
informationcontainedinthetwoinvariantmassdistribu- to be roughly the same as for the 125 GeV Higgs boson
tionsoftheleptonpairs.Inparticular, aswithourstudy where this ratio is ∼ 2.5% [80, 81]. As the Higgs boson
of ϕ → 2(cid:96)γ, we examine how the ϕ → 4(cid:96) rate as well as was discovered in both h → γγ and h → 4(cid:96) [82, 83],
its composition in terms of the ZZ,Zγ∗, and γ∗γ∗ com- thisgivessomehopethatifthe750GeVdiphotonexcess
ponents is affected by phase space cuts on the invariant persists, a signal in ϕ→4(cid:96) may also be observable soon.
mass of the lepton pairs. From Fig. 4, we also see that the rate can be en-
We label the lepton pair invariant masses M and M hanced by going to more inclusive phase space cuts:
1 2
and define M1 > M2 following the conventions and def- 4<M1,2 <750GeV,comparedtothoseusedbytheAT-
initions in [41, 42]. Since we are considering only rates, LAS search [38] which requires 50<M1 <120 GeV and
the difference between the 2e2µ and 4e/4µ channels due 12<M2 <120GeV.TheeffectislargestwhenλZZ (cid:28)1
toidenticalfinalstateinterferenceisnegligible.However, sinceinthiscasetheZγ∗ andγ∗γ∗ componentsmakeup
as pointed out in [45], these identical final state effects a larger fraction of ϕ → 4(cid:96). Thus phase space cuts have
can greatly influence event selection and these channels a larger effect compared to when ZZ dominates, since
shouldbetreatedseparatelyinamorecompletefullydif- in that case both Z bosons can be on-shell in either the
ferential likelihood analysis [42, 45, 56, 78]. Since these more inclusive or the ATLAS-like cuts. We again show
subtleties are not relevant for current purposes, we sim- values of λZZ and λZγ larger than allowed by ϕ → ZZ
ply study the 2e2µ channel and multiply by a factor of andϕ→Zγ searches[10]duetothevariousassumptions
two to include 4e and 4µ. which go into these limits as discussed above.
We first consider the ratio of the ϕ → 4(cid:96) rate to the In Fig. 5 we show the relative contribution of the
ϕ→γγdecayrateasshownFig.4.AswiththeHiggsbo- naively subdominant components to ϕ → 4(cid:96), namely
sonat125GeV,thisratiowillnotbeverylarge,butthis those arising from Zγ∗ (blue) and γ∗γ∗ (orange). Again
is compensated by the very high precision with which it we see that expanding the phase space cuts gives signifi-
can be measured [79]. Depending on the coupling ratios, cantlymoresensitivitytothesecomponentsthancurrent
theϕ→4(cid:96)ratewillnotbebiggerthanO(2−3%)ofthe ATLAS cuts. The absolute size of the ZZ component is
ϕ→γγ rateforcouplingratioswhicharestillallowedby relatively unaffected when λ (cid:38) 1 and λ (cid:28) 1 as
ZZ Zγ
ϕ→ZZ and ϕ→Zγ direct searches [10]. This happens can also be inferred from Fig. 4 because the inclusive
5
3.0 0.005 Mφ=750[GeV],4<M1,2<750[GeV]
0.001
Γ(φ→ V*γ* → 2e2μ) 3.0
Γ(φ→ 2e2μ) 4<M1<750[GeV],Δ2=5[GeV] 0.8
2.5 Γ(φ→ZZ)/Γ(φ→γγ)=6 Δ1=5[GeV],Δ2=5[GeV]
0.01 2.5 Γ(φ→ZZ)/Γ(φ→γγ)=6
0.01
γ*γ* 0.2 Γ(φ
2.0 →
cc=/ZZγγ1.5 0.01 AFMuTφlLl=:A47S5<1:025M[0<G1,<2Me<VM2]7<15<1021[02G0[eG[VGe]Ve]V], 0.2 c/ZZγγ2.0 φRZ→(Δ21,eΔ22μ) γ)/Γ(φ→γγ)Z
λZZ Γ(φ c= 1.5 =2
→
1.0 Z*γ* γ)/Γ(φ→Z 0.005 λZZ1.0 0.65 0.5
γ
γ 0.5
)=
0.5 2
0.1
0.5
0.1
0.1
0.0 00.9.9 0.9 0.9 0.01
0.0 0.5 1.0 1.5 2.0 0.0 0.1
λZγ=cZγ/cγγ 0.0 0.5 1.0 1.5 2.0
λ =c /c
Zγ Zγ γγ
FIG. 5. Contours for the fraction of 2e2µ events that come
from Zγ∗ (blue) and γ∗γ∗ (orange) in the plane of coupling
FIG.6. ContoursofR asdefinedinEq.(9)intheplaneof
ZZ
ratios λ and λ defined in Eq. (5) and Eq. (8), respec-
Zγ ZZ coupling ratios λ and λ defined in Eq. (5) and Eq. (8)
Zγ ZZ
tively. Again the dashed lines correspond to inclusive phase
respectively. We show R for ∆ = ∆ = 5 GeV (blue
ZZ 1 2
space cuts while the the solid lines correspond to the phase
solid) and ∆ = 5 GeV with 4 < M < 750 GeV (dashed
2 1
space cuts used in the ATLAS search [38] as defined in fig-
orange). We also show the limits on the coupling ratios as-
ure.Wealsoshowlimitsonthecouplingratiosassumingϕis
suming ϕ is produced from gluon initial states as in [10].
produced from gluon initial states as in [10].
shown in many studies of the Higgs boson, these inter-
and ATLAS cut contours become very similar in that
ference effects would give us access to the CP properties
region. We also see in Fig. 5 that the Zγ∗ component
of ϕ and to potential CP violating effects. An investiga-
dominates when λ (cid:28) 1,λ (cid:38) 1, and that the γ∗γ∗
ZZ Zγ tionoftheseinterestingpossibilitiesusingtheframework
dominates when λ (cid:28) 1,λ (cid:28) 1. Finally, we note
ZZ Zγ of [41–43, 56] is ongoing [57].
the sharply rising slope for the size of the γ∗γ∗ compo-
In an experimental analysis, backgrounds must of
nent when λ (cid:46)0.3 and λ (cid:46)0.5, indicating a strong
ZZ Zγ coursebetakenintoaccount,but,aswithHiggsdecaysto
sensitivity in this regime.
fourleptons,thebackgroundisverysmall.Thedominant
We again propose a simple way to measure λ and
Zγ source of background is quark initiated ZZ production,
λ analogous to the one from the previous section for
ZZ with the one-loop gluon process also contributing, but
ϕ→2(cid:96)γ. Namely we define a similar ratio
again is very subdominant [39]. As far as we know, there
are no higher order calculations of these backgrounds,
N(M +∆ >M >M −∆ )
R (∆ )= Z 1,2 1,2 Z 1,2 .(9) but that is partially because they are quite small. As
ZZ i totalnumberof events
with the 2(cid:96)γ case, enlarging the mass window from the
where again the total number of events is defined by the current searches will increase the background, but it will
inclusive phase space with 4 < M1,2 < 750 GeV. We still be small and smooth, so a sideband analyses can
show contours of RZZ in Fig. 6 where we see that it is again be used. Of course using a fully differential likeli-
very sensitive to λZZ for λZZ (cid:46)1 while less sensitive to hood analysis would increase the ability to discriminate
λZγ. The stronger sensitivity to λZZ can be understood signalfrombackgroundfurther[84],butwedonotinves-
from the pole structure of the two Z bosons which can tigatethispossibilityhere.Forpresentpurposeswehave
both be on-shell at 750 GeV. Again we also see the ben- simplyusednaiveestimatestoensurethatthedominant
efits of using more inclusive cuts to enhance the non-ZZ background can easily be controlled.
components.
We have not discussed interference between the dif-
ferent intermediate states since it has a negligible ef- NON-LEPTONIC AND EXOTIC DECAYS
fect on the rates. However, in a fully differential analysis
whereshapeinformationisused,theseinterferenceeffects If the diphoton excess proves to be more than a sta-
can potentially be important. In particular, as has been tistical fluctuation and indeed due to a new scalar ϕ,
6
φ→2fγ,Mφ=750[GeV],4<Mff <750[GeV] experimentally challenging. They are expected however
tohavemuchlargerratesthanϕ→4(cid:96)inmuchofthepa-
γ) 1 rameterspace,particularlywhentheϕγγ couplingisnot
γ
→ 0.500 parametrically larger than for Zγ and ZZ. One can also
φ consider WW decays to (cid:96)ν(cid:96)ν or other channels. While
Xγ)/Γ( 00..015000 Γ(φ→Z tthoethceosmepcuatsaestioansswueltli,litzheedeixnptehriismwenotraklcaannalybseesexbteecnodmede
=Γ(φ→ 00..000150 RRlqlγqγ==(l(q==e,uμ,,dτ,)c,s,b) γ)/Γ(φ→γγ mcaorreefudlliyffi.cIufltthaendresboancakngcreouantds75h0avGeetVo btuertnrseaotuetdtmoobree
Xγ Rννγ )= genuine new physics, fully understanding all these chan-
R RZγ*BRZll 2 nels will be crucial to characterizing the new state and
0.001
any theory it might be associated with.
0.0 0.5 1.0 1.5 2.0
λ =c /c Finally, we note that the simplified analysis presented
Zγ Zγ γγ
here is also useful if the new physics is not one simple
FIG. 7. The ratio of the ϕ → 2fγ partial width relative to resonance decaying to diphoton but is instead multiple
ϕ→γγ.Thisisplottedasafunctionoftheratioλ defined resonances [10, 85], not a resonance [50–54], or a reso-
Zγ
in Eq. (5). We plot f to be leptons (solid red), light quarks nancethatdecaysthroughacascade[8,25,86–88].Each
(dashedblue),andneutrinos(dashedgreen).Theon-shellZγ ofthesekindsofmodelshasdifferentpredictionsforboth
contribution times branching ratio into leptons (dashed red)
thecorrelatedsearchesviaZγandZZ aswellaswithvir-
isshownforcomparison.Wealsoshowthelimit(verticalline)
tual photons. Furthermore, the improved signal to back-
obtained from Zγ searches [10] at 8 TeV.
groundratio,particularlyinthecaseoffourleptons,will
allow a more precise measurement of the line-shape al-
lowing discrimination of many possibilities. Should the
we will want to search for ϕ decays in as many chan-
excess persist, an exploration of these cases would also
nels as possible, not just the experimentally clean ones
be interesting.
with leptons. Furthermore, our considerations of the vir-
tual diphoton contributions to ϕ→2(cid:96)γ and ϕ→4(cid:96) also
apply when one considers other charged fermions in the
CONCLUSIONS AND OUTLOOK
SM, though of course experimentally these channels are
much less cleanly measured. While the branching ratios
In this work, we interpret the excess observed by AT-
and couplings of the Z and photon are well measured,
LAS and CMS in the diphoton spectra around 750 GeV
looking for decays in ϕ → 2fγ and ϕ → 2f2f(cid:48) is an
to be indicative of a new scalar resonance ϕ decaying to
importanttesttoseeifthereisothernewphysicsorcou-
photons. We show in particular that the effective oper-
plings of ϕ to SM fermions.
ator responsible for the ϕ → γγ decay will also lead to
In Fig. 7 we consider the ϕ → Vγ → 2fγ (where a signal in ϕ → 2fγ and ϕ → 2f2f(cid:48) (where f is a SM
V = Z,γ∗) partial width normalized to ϕ → γγ for the fermion) decays independently of the effective couplings
various light SM fermions. We see that for small λZγ the ofϕtoZγ andZZ.Wehavefocusedinparticularonthe
leptons(solidred)dominate.Bycomparingthesolidred leptonic ϕ → 2(cid:96)γ and ϕ → 4(cid:96) channels ((cid:96) = e,µ). De-
curve, which is the full ϕ → 2(cid:96)γ decay width, to the pending on the relative sizes of these effective couplings,
dashed red curve which is only the on-shell Zγ mediated we show that the virtual diphoton component can make
ϕ→2(cid:96)γ width,weseethatthelowλZγ behaviorisdom- up a sizable, and sometimes dominant, contribution to
inated by photon contributions. This explains why the the total ϕ→2(cid:96)γ and ϕ→4(cid:96) partial widths.
leptons are the largest contribution at small λZγ, since Wehavealsoexploredtheeffectsthatphasespacecuts
theyhavelargerelectricchargethanSMquarks.Atlarger ontheinvariantmassoftheleptonpairshaveonthetotal
λZγ, decayswithquarksandneutrinosbecomemoreim- rates and composition of ϕ→2(cid:96)γ and ϕ→4(cid:96). We have
portant. While these are experimentally more difficult, emphasized the contribution from virtual photons and
kinematic shape information can perhaps be used to un- pointedoutthatcurrentexperimentalsearchesshouldbe
cover the signal from the background, though we do not modified in order to enhance the sensitivity to these vir-
explore this issue here. We also note that if one imposes tual photon effects. We find that a more inclusive phase
the ϕ → Zγ limit (vertical line) derived from [10], this space cut (while still requiring the full system to be at
implies a limit on ϕ → 2(cid:96)γ ((cid:96) = e,µ,τ) and ϕ → 2qγ theresonancemass)wouldallowanincreasedsignalrate
(q = u,d,c,s,b) of ∼ 40% and ∼ 90% of the γγ rate, andlargercontributionsfromallcomponentsofϕ→2(cid:96)γ
respectively. Of course, all the caveats discussed above and ϕ → 4(cid:96). The virtual photon contributions in par-
about the production mechanism still apply. ticular can be increased by an order of magnitude. This
For the case of four fermion decays, there are many allowsustostudyϕinmoredetailwhilestillkeepingthe
more possibilities including (cid:96)(cid:96)νν and (cid:96)(cid:96)qq¯which are also backgrounds under control.
7
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