Symmetries and composite dynamics for the 750 GeV diphoton excess

0.62 MB·

by  Diogo Buarque Franzosi

CP3-Origins-2015-023 DNRF90, DIAS-2015-23
Symmetries and composite dynamics for the 750 GeV diphoton excess
Diogo Buarque Franzosi
II. Physikalisches Institut, Universita¨t Go¨ttingen,
Friedrich-Hund-Platz 1, 37077 Go¨ttingen, Germany
Mads T. Frandsen
CP3-Origins and the Danish IAS, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
TheATLASandCMSexperimentsatLHCobservesmallexcessesofdiphotoneventswithinvari-
antmassaround750GeV.Herewestudythepossibilityofnearlyparitydegenerateandvector-scalar
degenerate spectra as well as composite dynamics in 2 scenarios for explaining the excess: Produc-
tion of a pseudo-scalar via gluon or photon fusion or via decay of a parent particle together with
soft additional final states. We discuss possible underlying realizations of the scenarios motivated
bydynamicalmodelsofelectroweaksymmetrybreaking(withoutnewcolouredstates)andfermion
masses.
TheATLASandCMS[1,2]experimentsobservelocal not need to couple significantly to SM fermions and the
6 excesses in diphoton final states with invariant masses branching to diphotons can be O(1). The small mass
1 around 750 GeV. If these excesses are interpreted as a splitting ensures that the additional final state particles
0
narrow resonance the local significances correspond to can be soft. Finally P can be off-shell when δm < 0,
RP
2
3.6 and 2.6 σ respectively leading to modest global sig- mimicking a finite width in the diphoton decays. If P

r nificances of 2σ in ATLAS and 1.2σ in CMS. The sig- and R are composite states of EW charged strongly in-
a
nificance is slightly higher in the ATLAS experiment if teractingfermions,involvedinEWSB,theO(1)diphoton
M
interpretedasaresonancewithawidthofabout50GeV branchingratiocanbeachievedandthesmallmasssplit-
8 while the CMS significance is decreased slightly. The re- tingrealizedbysymmetries. Forexampleparitydoubling
1 sultssuggestareconstructedresonancemassP ofaround of the spectrum in the large-N limit of the underlying
750 GeV with a production cross-section σ ∼5−10 fb. gauge group or via a vector-scalar symmetry such as in
P
] Although the significances of the results are rather mod- theheavyquarklimitofQCD.Thisscenario, withnegli-
h
estandhavebeenchallengedine.g[3]itiswellmotivated gible couplings of P to SM fermions allows the opposite
p
- toentertaintheideathattheseresultsmaybeduetonew extreme of scenario 1.
p physics. We outline specific underlying composite dynamics,
e
General phenomenological analyses indicate that the motivated by dynamical EWSB and fermion mass gen-
h
new state is of composite nature [4], even though other eration, able to provide the features needed to explain
[
interpretationsintermsofsimpleextensionsoftheStan- theexcessinbothscenarios. Theexperimentalsignature

2 dard Model (SM) [5], Supersymmetric models [6], Gold- distinguishing scenario 1 and scenario 2, independent of
v
stones, Radions and Dilatons [7], axions [8] as well as a thespecificrealizationswediscussaretheadditionalsoft
7
wide variety of models or interpretations [9], have been final states which may be difficult to detect.
5
3 contemplated. Implicationsforcosmologyanddarkmat-
5 ter have been discussed e.g. in [10]. To motivate the first scenario we note that for an
0 s-channel pseudo-scalar resonance P coupled to gluons
. In this study we present 2 scenarios for the diphoton and photons the excess and the best-fit width in the
1
0 excess motivated by composite dynamics for EWSB and ATLAS data are reproduced for ΓP/mP ∼ 0.05 and
6 spectral symmetries. In particular we examine if the Γ Γ /m2 ∼ 5 × 10−8 [4]. For a top Yukawa of 0.7
γγ gg P
1 signal can be achieved without invoking new coloured we have Γ /m ∼ 10−4 and Γ /m ∼ 0.05. For
gg P P→tt P
: states. Specific models of strong dynamics in which the a simple 2 Dirac flavor model of dynamical EWSB [13]
v
i new states carry color have been studied in [11]. with an additional lepton doublet and a low composite-
X In scenario 1 a pseudo scalar P with a large dipho- ness scale f (cid:46) 0.4v we find Γ /m (cid:39) 2 × 10−4
P EW γγ P
r ton partial width is produced in gluon fusion via a top not too far from the required values. Moreover the ratio
a
Yukawa of order 5×10−2 (cid:46) y (cid:46) 0.7. The upper limit m /f ∼ 10 for m = 750 GeV and f = 75 GeV is
Pt P P P P
is chosen so that Γ /m (cid:46)0.05, and the total width similar to the ratio m /f in QCD and not unnatural.
P→tt P η(cid:48) π
of P is near the best fit width from the ATLAS data. If
P isacompositeofnewEWchargedstronglyinteracting Asanalternativeweconsiderthatthe(pseudo-)scalar
fermions, involved in EWSB but with a decay constant resonance is produced in the decay R → XP(→ γγ) of
below v , a sufficiently large diphoton decay rate is a new ’parent’ resonance R either of spin-0 (S) or of
EW
possible in minimal models. spin-1 (V). The LHC diphoton analysis are inclusive
In scenario 2 the pseudo-scalar P is produced via de- so there could be interesting additional activity X along
cays of a parent resonance R (see e.g. [12]) with a small with the diphoton system, but in this study we require
mass splitting δm = m −m . Accordingly P does the additional final state(s) X to be soft.
RP R P
2
For the spin-1 parent V we take a neutral isosin- split into the relevant pieces:
glet vector resonance with a mass splitting, δm =
bm-qVu−arkms.P,TrheelastiigvnealtoprPocaenssdiscoσu(pplpe(d¯bbp)r→edoVmi→nanPVtXlPy→to LV =(cid:88)f¯V/ (cid:0)gfV −gfAγ5(cid:1)f + Λ1V VµνF(cid:101)µνP , (2)
f
γγX) with X = {γsoft,Z∗} a soft additional photon or 1
off-shellZ boson. Havingdominantcouplingstob-quarks LP =iyPfPf¯γ5f + Λ PFµνF(cid:101)µν (3)
are preferred by the constraints on diphoton resonances P
L =y Sf¯f +Λ SPX (4)
from the 8 TeV run of LHC which favor a high increase S Sf S
in production cross-section from 8 to 13 TeV.
where f is a SM fermion, V = ∂ V − ∂ V and
µν µ ν ν µ
S Fmoarytbheeecnadsoewoefdawsitphins-i0zapbaleretnotp-tqhueasrckaclaoruprelisnognsaen.cge. F(cid:101)µν = 21(cid:15)µνρσFρσ with Fµν being the field strength of
the photon.
via mixing with the SM Higgs while fermion couplings
The partial widths from the above interactions are,
may be negligible for the pseudo scalar P — allowing a
ignoring light fermion masses and the mass of X,
large diphoton branching ratio for P.
N (f)
canEvaepnpeiafrtahsisamreisgohntanimceplwyitah finnaritreowwidwtihdtihf pfroordPuceidt ΓP,S→f¯f (cid:39) 8cπ yP2,SfmP (5)
snleigghattliyveo.ff-shell[12]whenδmSP =mS−mP issmalland ΓV→f¯f (cid:39) N1c2(πf)[(gfV)2+(gfA)2]mV (6)
We motivate the three scenarios by outlining compos- m3
Γ (cid:39) P (7)
ite models of dynamical electroweak symmetry breaking P→γγ 4πΛ2
P
and fermion masses that may realize them. The pseudo
1 (cid:18)m2 −m2 (cid:19)3
scalar P may be interpreted as a resonance analogous Γ = V P (8)
to the π0,η and η(cid:48) states in QCD with sizable dipho- V→Pγ 24πΛ2V mV
ton branching ratios. The V,S parent resonances can be Λ2 m2 −m2
Γ (cid:39) S S P (9)
thought of as analogues of e.g. the ω and σ mesons in S→PX 16π m3
S
QCD.
where N is the number of colors of the fermion.
The small mass splittings δm ,δm can e.g. be re- c
VP SP
To fit the peak cross-section of the diphoton excess we
alized in composite dynamics via parity doubling of the
assume m (cid:39) 750 GeV and require δm < 200 GeV,
spectrum in the large-N limit of the underlying gauge P RP
allowingforsomeadditionalfinalstateactivitygiventhe
group or via a vector-scalar symmetry such as in the
inclusivesearches. Theproductioncrosssectionsinunits
heavy quark limit of QCD. For certain fermion represen-
of the coupling squared are given in Fig. 1, in partic-
tations we indeed expect δm to be small and negative
SP
ular the production of P and S via top-induced gluon
in the large-N limit, allowing off-shell production [14].
fusion (solid purple) and the b-quark initiated produc-
Moreover, isosinglet ’ω-like’ vector resonances V will,
tion of V (blue dashed). The cross sections are derived
for some underlying realizations, not mass mix with the
at leading order with the factorization and renormaliza-
SM weak spin-1 bosons and only be coupled to SM
tion scales µ equal to the mass of the produced par-
fermions via higher dimensional operators [15]. See ap- F,R
ticle µ = µ = m and the NN23LO1 parton dis-
pendix of [16] for an explicit example. The higher di- F R R,P
tributions sets [19]. The loop induced processes have
mensionaloperatorsmaynaturallyinducedominantcou-
been computed with the model [20]. Next-to-leading or-
plings to the 3rd generation SM quarks, for example if
der K-factors have been computed for m =750 GeV
these operators are related to a dynamical SM fermion R,P
using the MadGraph aMC@NLO program. In the 5
mass generation mechanism like the so-called ’Extended
flavour scheme for b-quark initiated processes, we ob-
Technicolor’ construction [17, 18].
tained K(bb) = 0.99, see [21, 22]. For the light quark
initiated processes we used the SM UFO model and in-
creasedthemassoftheZ-boson,obtainingK(qq)=1.16.
Simplified Lagrangians and production cross-
We used the same K-factor for the scalar case for sim-
sections:
plicity. Forthegluonfusiontopologyweusedourownef-
We are interested in the signal processes fective gluon-Higgs model implementation and obtained
a factor of 2.3. However, we adopted K(gg)=2.7 which
σ(pp→P →2γ) , reproducesthecentralvalueofthecrosssectionreported
in [23] at NNLO+NNLL accuracy.
σ(pp→R→PX →γγX) , (1)
Scenarios for the excess
with R either a spin-1 resonance V or a scalar resonance Based on the above simplified Lagrangian we now de-
S and X denoting additional (soft) final states. tail the two scenarios considered here.
The interaction Lagrangian linking the parent reso- In scenario 1 the excess arises from production of the
nances to P and to the standard model fermions can be pseudo-scalar P via top-quark loop induced gluon fusion
3
1000 100
]b 100 10
p
[ gg(t) qq
2
)/gq 10 gg(b) bb V] 1
->/RP 1 ΓGe[ 00..011000 Γ(tt)
p
p 0.10 Γ(gg)
(
σ 0.001 Γ(γγ)r=1.64/8
0.01 Γ(VV)r=1.64/8
10-4
750 800 850 900
0.0050.010 0.0500.100 0.500
M [GeV] 2
R/P yPt
FIG. 1. Production cross sections of the pseudo-scalar P,
FIG. 2. Required partial width Γ to explain the LHC
scalar S and vector V in units of the square of the fermion P→γγ
diphoton excess, σ ∼ 5 fb from gluon fusion production
couplings. The label gg refers to loop induced production γγ
of P via a top-loop and photon fusion, as a function of the
of (pseudo-) scalars, through a top-quark (t) or a bottom-
Yuakawa coupling y2 . The solid and dashed lines refer to
quark (b) loop. The solid lines refer to production of the Pt
r=1.64 and r=8 respectively.
pseudo-scalar P (identical to S in the quark initiated pro-
cesses), dashed lines refer to V production and dotted lines
refer to S production through gluon fusion.
large width can be achieved for r ∼ 8, also shown in
fig. (2).
production or photon fusion with the same mechanism The parameter targets in this scenario, in order to
of its subsequent decay into photons. If P couples dom- avoid experimental constraints, are
inantly to top-quarks in the SM and there are no new
• 2.5×10−3 (cid:38)y2 (cid:46)0.6
colored states, the cross section is well approximated by Pt
(3×10−4 (cid:38)Γ /m (cid:46)0.05)
P→tt P
Γ
σγγ (cid:39)(σgg→P,0yP2t+σγγ→P,0 ΓPγ→γ,γ0γ) (10) • ΓP→γγ/mP (cid:38)3−6×10−4 .
Γ
× P→γγ , (11)
Γ +Γ +Γ
P→γγ P→VV P→tt In scenario 2 we first consider the Drell-Yan produc-
where σ =1.9 pb is a reference cross-section with tion of a neutral isosinglet spin-1 resonance R=V with
gg→P,0
y = 1, σ (cid:39) 3 fb is a reference cross section for subsequent decay V → Pγ. Accordingly the branching
Pt γγ→P,0
photon-fusionwithΓ =0.34GeVbeingthediphoton ratio Br[P → γγ] ∼ O(1) is in principle possible as P
γγ,0
width for Λ =10 TeV. P will in general decay to weak need not couple significantly to SM fermions to be pro-
P
bosons, VV = WW, ZZ, γZ with Γ = rΓ duced. We adopt a minimum decay rate to weak bosons
P→VV P→γγ
and r (cid:38) 1.64 [24] unless isospin breaking couplings are with r =1.64 as discussed before. Additional final state
introduced. We will use r = 1.64 as a benchmark value. particles can be soft if the mass splitting δmVP is suffi-
The size of r is constrained by other searches. We have ciently small.
neglected Γ . The photon fusion contribution to the To get the minimal required production cross-section
P→gg
crosssectionisimportantforsmallSMfermioncouplings. σpp→V ∼ 5 fb, the minimum value of gbV or guV,d de-
We adopted a naive approximation, using MadGraph pend on the mass of the parent resonance V and is
withthephotondistributionfunctionoftheproton. The gb2 (cid:38)1(3)×10−3 formV =750(925)GeVand(guV,d)2 (cid:39)0
erroronthispiececanbelargeandwereferthereaderto or(gV )2 (cid:38)5×10−6−10−5. Thelatteriseasilyachieved
u,d
recent [9, 24] and on-going [25] studies for more details. viamixingofV withthehyperchargefield. Howeverthe
We show the required value of Γ as a function of former situation is preferred by the constraints from the
P→γγ
y2 in fig. (2) in order to reproduce σ ≥ 5 fb. Γ 8 TeV LHC run since the b-initiated cross-section grows
Pt γγ P→tt
and the top loop induced Γ are also shown. To with nearly a factor 5 from the 8 to 13 TeV run.
P→gg
reproduce the signal cross-section σ ∼ 5−10 fb and We therefore focus on the b-dominated case. Near the
γγ
the width Γ ∼ 0.05m , marginally preferred by the minimum possible value of the b-coupling (gV)2 (cid:39) 10−3
P P b
ATLAS results over a narrow resonance (locally 3.6 vs we need Br[V → Pγ → γγγ ] (cid:39) 1. In fig. (3)
soft soft
3.9 σ), we need y2 ∼ 0.5 leading to Γ /m ∼ 3− therequiredpartialwidthΓ andthecorresponding
Pt P→γγ P V→Pγ
6×10−4. Thett¯productionviaP →t¯tconstrainsy2 (cid:46) values of Λ are shown: As gV is increased the needed
Pt V b
1.5 [26], even though interference effects between signal branchingratiorapidlydecreasetoanearconstantvalue.
and background not taken into account in the analysis For large values of gV the branching to b¯b is likely to
b
should relax this bound. Alternatively, for low y2 , the dominate. If that is the case, i.e. Br[V →bb]>Br[V →
Pt
4
Λ
S
5000
Λ
1000 MR=775GeV V
MR=925GeV
]V 100 ΓR→ff eV] 1000
e G
G
[
[PX 10 ΛR 500
/γ
P
→
R 1
Γ
100
0.1
750 800 850 900
104
M[GeV]
5000 ΛV(gb2)
ΛS(ySt2) FIG.4. ThescaleΛ infrontoftheRPX verticesrequiredto
R
1000 fitthediphotonexcess,witheitherR=V aspin-1resonance
]V 500 (blacksolid),orR=Sascalarresonance(dashed). Thescale
e
G isindependentofgV for(gV)2 (cid:38)3×10−2(asseeninthelower
b b
[
R paneloffig.3). Thedottedcurvecorrespondtotheoff-shell
Λ 100 regionwiththeorangedottedcurvereferringtocaseB,along
50 which mP increases and mS =750 GeV is kept fix.
10
ingwiththeSMHiggswhileP canhavenegligiblemixing
0.01 0.1 1.
with the Higgs due to parity and negligible couplings to
coupling2 fermions. Finally the decay S → PX can be large and
dominateS →ttevenforsizableYukawacouplings. The
FIG.3. Top: ThepartialwidthsΓ andΓ required finalstatesX couldincludesoftQCDprocesses,(param-
S→PX V→Pγ
to explain the di-photon excess as a function of the Yukawa eterizedeg. viaamixingofP withpseudo-scalarslikethe
coupling,yStandthevector-fermioncouplinggbV. Alsoshown η and π ), or additional new but light composite states
thepartialwidthtotop(bottom)-quarkpairintheS(V)case that mix with P as in [28].
for m = 775 GeV. Bottom: The corresponding scales Λ ,
R S In order to reproduce the di-photon signal in this sce-
Λ derived from eq. (9).
V nario the minimal production cross section, σ ∼ 5
pp→S
fb, demands a Yukawa coupling y2 (cid:38) 4 × 10−3, for
Pt
m = 775 GeV, while for m = 925 GeV, y2 (cid:38) 0.01.
Pγ], thensincetheproductioncouplinggrowslike(gV)2 S S Pt
therequiredbranchingtoPγbecomes(gV)2independbent The required partial widths and ΛS as a function of yP2t
b are also shown, with dashed lines, in fig. (3). The decay
andonlydependsonm duetothephasespacesuppres-
V widthtofermionsisalsoshownforcomparison. Different
sioninEq.9andpartondistributionsuppression. Specif-
fromthevectorscenario,theeffectofthekineticsuppres-
ically we require Γ (cid:104) 0.22−0.63 GeV (or equiva-
R→Pγ sion is milder and the different resonance mass converge
lently Λ (cid:104) 85−820 GeV) for m = 775−925 GeV.
V V to similar Λ values for large Yukawa, shown in fig. (4).
S
In Fig. 4 we show the range of relevant scales Λ as a
R TheATLASresultsmarginallypreferaresonancewith
function of m and with m = 750 GeV. As is evident,
R P a non-negligible width (locally 3.6 vs 3.9 σ). While com-
therangeisverysensitivetothephasespacesuppression
posite dynamics can generate a sizeable diphoton par-
δm .
RP tial width Γ it is hard to account for a Γ ∼
Forlargem ,di-jetsearchesimposethelimits(gV)2 (cid:46) P→γγ P
V b 0.05mP. If such a total width is corroborated the P
0.6(0.8) for m =900(800) GeV [27].
V could be produced off-shell and mimic a finite width for
Finally the above discussion assumed a maximum
m < m + m [12]. In fig. (5), case A, we show
V P X
branching ratio of P to di-photons Br[P → γγ] = the diphoton distribution of a slightly off-shell P∗ pro-
1/(1+r)=0.38with(r=1.64)andnegligiblecouplingsof
duced together with a light (pseudoscalar) state X for
P to SM fermions. In specific models that last assump-
m = m = 750 GeV and m = 0,10,20,30 GeV. In
P S X
tionmaynotbetrue,andinonediscussedbelow,indeed fig. (6), case B, we take m = 0 and force P∗ off-shell
X
P decays also to b-quark pairs.
from requiring m = m + δm and m = 750 GeV
P S S
with δm = 0,10,20,30 GeV while in fig. (7), case C,
Inscenario2theparentresonancemayalsobeascalar we fix m = 750 GeV and take m = 760−δm, again
P S
resonance S in a (nearly) parity doubled spectrum of for δm = 0,10,20,30 GeV. In the three cases it can be
scalar(s) S and pseudo-scalar(s) P. The scalar S may seen that a broad distribution which tracks the ATLAS
then e.g. be endowed with top-quark couplings via mix- data reasonably with the 40 GeV experimental binning
5
5GeV 5GeV
40GeV 40GeV
FIG. 5. Case A: Diphoton distribution from the process FIG. 6. Case B: Same as fig. 5 but with m = 750 GeV,
S
pp → S → PX with m = m = 750 GeV and m = m =0 and m =m +δm, for δm=0,10,20,30 GeV.
P S X X P S
0,10,20,30 GeV.
5GeV
is achieved. The second peak, seen with the finer 5 GeV
40GeV
binning, emerges when the parent S∗ goes off shell while
P is on shell. It cannot be resolved with current data,
but with sufficient future LHC data this can serve as a
diagnostic of the off-shell processes considered here.
To compute the distributions, the simplified La-
grangiansineq.(4)wereimplementedintheUFOformat
[29] using the Feynrules package [30]. The Yukawa cou-
pling is set to y = 0.1 and an effective gluon operator
t
SGa Gµν,a/Λ with Λ = 6.82×104 was implemented
µν G G
to reproduce the corresponding production cross section
induced by a top loop, although the full loop structure
ingeneralwouldleadtomodificationinthedistribution.
We used a fiducial scale Λ = 750(1000) GeV for the
S
distributions in cases A and B (C). The correct values
FIG. 7. Case C: Same as fig. 5 but with m = 750 GeV,
to reproduce the required branching ratios to diphotons P
m =0 and m =760−δm, for δm=0,10,20,30 GeV.
are larger and shown in the dotted lines in fig. (4) for X S
cases B (orange dotted line, on the horizonthal axis M
referstom )andC.Thecrosssectionstodiphotonshave
P although in the models we will discuss it is more natural
been rescaled accordingly. The correction to the total
to have Γ(P →γγ)(cid:46)0.3, and Λ (cid:38)10 TeV. In fig. (8)
widthsusedinthefiguresarenegligible. Weperformeda P
this effect is taken into account in the determination of
simple parton level analysis implementing the kinemat-
the partial widths, Γ(V → Pγ) and Γ(S → PX) and
ical cuts used in the ATLAS analysis: Eγ1 > 40 GeV,
T the effect is found to be small but can interplay with
Eγ2 > 30 GeV, Eγ1/m > 0.4 and Eγ2/m > 0.3,
T T γγ T γγ the parent decay topology to produce the correct excess.
whereγ aretheleading(subleading)photonsintrans-
1,2 For scenario 1 on the other hand, there is no freedom in
verse energy, E . Below we discuss explicit underlying
T choosing Λ and therefore the photon fusion contribu-
gaugetheorieswhichinthelarge-N limitrealizethis[14]. P
tion is also fixed - we nevertheless also show the effect of
To summarize our primary parameter target in sce-
neglecting it in the figure.
nario 2 with a scalar parent S are
• 5×10−3 (cid:46)(yPt)2 (cid:46)0.7, P →γγ and R→PX decay widths
If P arises from composite dynamics we may estimate
• 1(cid:38)Br[S →PX →γγX](cid:38)5×10−3,
itscouplinganddiphotondecaywidth,fromloopsofnew
• δm ≡m −m (cid:28)m . stronglyinteractingfermionsQ,byanalogywithpseudo-
SP S P P
scalars such as the π0,η and η(cid:48) in QCD.
In both V and S scenarios, a contribution from direct
Thetwo-photondecaywidthoftheπ0 inQCDisgiven
production of P via photon fusion will be present, relax-
roughlybyΓ /m (cid:39)6×10−8 [31]inexcellentagree-
ing the requirements on Λ and Λ . Contrary to sce- π→γγ π
nario 1, the decay rate P →S γγ canV vary almost freely, ment with the formula Γπ→γγ (cid:39) 6α42πm3f2π2 with fπ = 93
π
6
100 This may be compared to the minimal unavoidable de-
50 Γ(P→γγ) cay width of V into b-quarks, Γ /m (cid:38) 10−4 from
V→bb P
Γ(V→Pγ) the required production couplings in this scenario. Cor-
Γ(S→PX) respondly ΛV ∼ 32fP in Eq. (8). Because of the strong
10
suppressionofthebranchingfromthephasespacefactor
]GeV 5 (frδommmVVPth)3isitQisChDa-rsdcatloedgeetstsiumffiactieenwtidthipohuottoanddcirtoiossn-aslechtaiornd
[
Γ activity in the final state: e.g. ΓV→Pγ ∼ 10−4 for
1 mV
δm =2f =150 GeV.
VP P
0.5
We finally consider the case of a spin-0 parent reso-
nance S. From eq. (9) we have
0.001 0.010 0.100 1 Γ Λ2δm
S→PX (cid:39) S SP (15)
coupling2 mS 8πm3S
sin2(θ)m δm
(cid:39) S SP (16)
FIG.8. Effectofphotonfusionontherequiredpartialwidths. 16π f2
ThedashedlinesincludesthephotoncontributionwithΛ = P
P
1th0eTeeffVecwthoiflenethgleecstoilnidglpinheotnoenglfeucstioint.inFotrhePs→olidγγlinwee, wshhoilwe In the last line we have taken ΛS ∼ mfP2S sin(θ), by as-
thedot-dashedoneistheusualpredictionwithphotonfusion suming a vertex of the form L = m2SSPP (equiva-
included. We used m =825 GeV and r=1.64. fP
R lent to the SM linear sigma model) and by introduc-
ing an angle θ that parameterizes the mixing between
P and X. This can be compared to the minimum width
MeV. This formula includes the factor Tr[τ Q2] = 1
3 Γ /m (cid:38)5×10−4 arising if S is produced at a level
where Q is the charge matrix of the u,d fermions and S→tt S
of σ ∼ 5 fb purely via a top-induced gluon fusion. No-
the trace includes color. For the iso-singlet P, similar to S
tably the smaller phase space suppression, as compared
the η and η(cid:48) in QCD, this becomes a sum over charges
to V →Pγ allows to achieve the cross-section more eas-
squared rather than a difference. For a discussion of the
ily.
η(cid:48) in QCD we refer to [32].
Up to non-perturbative factors we therefore estimate
Model Frameworks:
the diphoton decay width of an isosinglet P via
We focus on minimal composite models of EWSB as
ΓPm→γγ ∼ 6α42πm3f2π2mf22P((cid:88)d(RQ)e2Q)2 (12) rtoealmizeaatniontsheofsoeucrtoarbobvreeaskceinngariEoWs. McoinnitmaianlswaehfeewretEaWke
P π P Q doublets of strongly interacting fermions without QCD
m2 (cid:88) colour. Additional interactions are required to generate
∼3×10−8 P( d(R )e2)2 (13)
f2 Q Q theSMfermionmassesandYukawacouplingsofthecom-
P Q posite states to the SM fermions. This can be done via
’ETC’ interactions where 4-fermion operators bilinear in
where we sum over the the strongly interacting con-
the SM fields [17, 18] generate the required couplings,
stituents Q of P, having factored out the dimension of
’partial fermion compositeness’ where the 4 fermion op-
the representation d(R ) under the strongly interacting
Q
erators are linear in the SM fields [33] or by coupling the
gauge group.
strong sector to fundamental scalar fields with Yukawa
couplings [34].
Thus we can get a large diphoton decay rate to mass
A low compositeness scale f < v = 175 GeV
ratioΓ /m withrespecttotheΓ /m ifthera- P EW
P→γγ P π→γγ π where f is the analogue of f in QCD can lead to a
tioofmasstodecayconstantm /f islargeandifthere P π
P P large photon decay rate of P. This arises in compos-
is a sufficiently large number of underlying fermionic de-
ite models with multiple fermion representations [35] or
greesoffreedom. Belowwegiveexplicitexamples. From
when the composite sector is coupled to, and induces
the above estimates and eq. (9) we identify the scale
vacuum expectation values for, fundamental scalars [34].
ΛP ∼ (cid:80)6Q×d1(0R3QfP)e2Q. The 125 GeV scalar may then be (partially) composite
SimilarlywemayestimatethedecayrateofV intoPγ, and identified with one of these scalars.
from the analogous decay rates ω → π0γ/ηγ in QCD. As explicit examples of scenario 1 and the signal pro-
From Γ(ω →π0γ)/m ∼10−3 we find cess
ω
Γ Γ(ω →π0γ) f2 m2 δm σ(pp→P →2γ) (17)
V→Pγ ∼8 π V ( VP)3
m m m2 f2 m
V ω ω P V we first consider the minimal SU(3) MWT model (or
S
∼10−4m2V (δmVP)3 . (14) NexttoMinimalWalkingTecthnicolor)model[36]which
f2 m features a single doublet of Dirac fermions Q = (U,D)
P V
7
in the 2-index symmetric representation of SU(3) with Such a kinetic mixing may equivalently be rewritten
d(R ) = 6 and charges e = −e = 1 leading to as a mass mixing of interaction eigenstates. However,
Q U D 2
(cid:80) (d(R )e2)2 = 9. Assuming f /v ∼ 0.5 we if V is composite this mass mixing with the SM weak
Q Q Q P EW
find a diphoton decay width corresponding to Γγγ(P) ∼ bosons does not arise for certain anomaly free choices of
mP weakchargesoftheunderlyingfermions[15]. Anexplicit
3×10−5.
example is the SU(3) MWT model above as shown ex-
S
Another minimal model is a variant of the SU(2)
Adj plicitly in the appendix of [16]. Instead V may still have
MWTmodel,orsimplyMWTmodel[36],featuringasin-
’direct’ couplings to the SM fermion currents J in-
f,µ
gledoubletofDiracfermionsbutintheadjointrepresen-
duced via higher dimensional operators. If V is a com-
tationofSU(2)withd(RQ)=3. DuetoaWittenglobal posite bilinear of the form Vµ ∼ Q¯γµQ ≡ Jµ, where Q
anomaly this model requires an additional heavy lepton Q
represents the constituents of V, such a coupling arises
doublet(ξ,ν )inthespectrumandagaugeanomalyfree
ξ via the dimension 6 operator:
charge assignment is [13]
1 1
JµJ ∼ Q¯γµQ¯bγ b (21)
Q(U)=1,Q(D)=0,Q(ξ)=−2,Q(νξ)=−1, (18) Λ2 Q b,µ Λ2 µ
b b
If we assume late Yukawa couplings of the leptons to P where Λb is related to the mass scale of the interactions
thisleadsto(cid:80) (d(R )e2)2 =64. Assumingf /v = mediating the 4-fermion operators.
Q Q Q P EW
0.4 we find Γ (P)/m ∼ 2×10−4 and with a top cou- The effective Lagrangian for the composite states can
γγ P
pling y2 (cid:46) 0.1 a signal cross-section of σ (cid:38) 5 fb can be described via a chiral (vector resonance) Lagrangian
Pt γγ withthegoldstonebosonscontainedinanon-linearsigma
be accommodated see fig. (2).
field U such that we can identify
Interestingly,bynaivescalingofQCD,andidentifying
P withtheanalogueoftheη(cid:48) statesuchadecayconstant Jµ →f2Tr(iDµUU†)→f2g˜Vµ (22)
f would correspond to a P mass of about 750 GeV. Q P P
P DµU = ∂µU −ig˜VµU (23)
While it is clear that it is not immediate to explain
theobservedsignalcross-sectionwithoutintroducingnew where the nonlinear sigma field on the vacuum is nor-
colored states to enhance production of P we have here malized to (cid:104)U(cid:105) = 1 and g˜ (cid:46) 4π is the effective strong
demonstrated that it is possible, even in relatively mini- interactioncoupling. InQCDg˜wouldberelatedtog
ρππ
mal models of dynamical EWSB. In models with more where we identified the ’pion’ decay constant with f .
P
strongly interacting fermions carrying color, it is cer- Then from the above composite operator we find
tainly possible [11] to get a sufficient rate. Alterna-
tivelythecompositeP canbecoupledtonewvectorlike 1 JµJ → fP2g˜VµJ , (24)
coloured fermions [8] or to heavy quarks responsible for Λ2 Q b,µ Λ2 b,µ
b b
(Witten) anomaly cancellation [37].
and require g˜Λf2P2 (cid:38) 4.2(5.6) × 10−2 for δmVP =
b
Asexplicitexamplesofscenario2wefirstconsiderthe 75(175) GeV togetaproductioncross-sectionofatleast
case of a spin-1 parent and the signal process 5 fb. Even for larger couplings, e.g. g˜fP2 (cid:38) 0.1 the scale
Λ2
b
varies little around f ∼ Λ /32 ∼ 10(20) GeV for mass
σ(pp→V →P γ →γγγ ). (19) P S
soft soft
splitting δm = 75(175) GeV, which is very small -
PV
A relatively small mass splitting δm of the even if the constituent quarks have large masses. The
VP (cid:113) √
vector/pseudo-scalar system V −P may be accidental. corresponding values of Λ (cid:46) g˜ f ∼ g˜32(63) GeV
In composite dynamics it arises if V and P share one or b 0.1 P
are around the weak scale v (cid:39)175 GeV for g˜∼4π.
more constituent fermions which are heavy with respect EW
These interactions may e.g be induced via ETC type
to the confinement scale generating the bound state. A
interactions of the form
well known example of this is the vector-scalar mass de-
1
generacy in the heavy quark limit of QCD. Q¯ σµb Q σµ¯b , (25)
In general the symmetries of the SM allow an interac- Λ2 L L R R
b
tion term
where we identify Λ ∼ M /g with the ratio of
b ETC,b ETC
L=−4(cid:15)V(cid:98)µνB(cid:98)µν (20) mUpasosnaFniderzcoruepalrirnagngoefmaenntexacnhdancgoenddeEnTsaCtiognauogfeQb’sostohnis.
leads to a mass term for the b-quark and will include
where V(cid:98)µν is the field strength tensor of the interac- interaction terms of the form
tteiornacteiiognenesitgaetnestsaptien-h1ypreerscohnaarngceefiV(cid:98)elda.nTdhBi(cid:98)sµmνixisintgheterinm- Λc12Q¯γµQ¯bγµb+ Λc22Q¯γ5Q¯bγ5b+... (26)
willcouplethemasseigenstateVµ roughlyuniversallyto b b
the fermion currents with a coupling of the size (cid:15)g(cid:48)Y(f) wherec areO(1)numbers. Gettingasufficientlylarge
1,2 √
whereg(cid:48) isthehyperchargecouplingandY(f)isthehy- coupling requires M ∼ g g˜32(63) GeV which
ETC,b ETC
per charge of the fermion f. still for g˜∼4π,g ∼4 is low for typical ETC models.
ETC
8
Again the scenario is borderline able to account for mass splitting becomes sizable the tell-tale sign of the
theobservedexcessofphotonsatLHC.Inparticularthe vector realization V → P γ/Z of scenario 2 will be the
analysis has neglected Clebsch-Gordon coefficients from the production of an additional photon or an on shell Z
the fierzing of group structure matrices in the ETC in- boson reconstructing the V invariant mass above the P
teractions. We leave it as a proof of principle that an mass.
underlying composite model can be constructed to real-
ize our scenario 2. Variations:
We finally consider the case of a spin-0 parent reso- In other realizations than the one considered here it is
nance S and the signal process possible to motivate larger couplings of the vector reso-
nance to b-quarks which in turn would allow a broader
σ(pp→S →PX →γγX). (27)
resonance P while still achieving the observed signal
We identify S with a (partially composite) scalar with cross-section. At the prize of increased tension with
sizable Yukawa couplings either from mass mixing with LHC8 data it is also simply possible that R is produced
a fundamental scalar as in [34] or via 4-fermion interac- viathelightSMfermions. Thiswouldbethecaseincom-
tions[17,18,33]. LiketheσresonanceinQCDweexpect posite models of a vector R=V and underlying fermion
asignificantcouplingtopseudoscalarpairsL=Λ SPP chargesallowingadirectmass-mixingbetweenV andthe
S
with ΛS ∼ mfP2S leading to an O(1) width for ΓS→PP for SMAnhoytpheerrchinartgereeBstinfigeldp.ossibility is the regime where P
massless Ps. With m (cid:39) 750 GeV the decay mode is
P
is extremely light such that the decay of P via V →
closed kinematically but we imagine that P mixes with
(P → γγ)γ would lead to a highly collimated diphoton
lighter state(s) of the same quantum numbers. An inter-
pair [38]. This spectrum would be possible if P were a
esting possibility is the scenario in [28] where a new few
nearly exact Goldstone boson.
GeV scale of a neutral composite sector is present and
provides DM candidates. If X denotes a peudoscalar
state then P can mix with it. Summary:
At the minimal Yukawa coupling y required to re- We have considered 2 scenarios for explaining the re-
St
producethedi-photonexcessexclusivelyviathetop-loop centlyobservedexcessesindiphotonfinalstatesnear750
inducedprocess,thescaleΛ aswellastherequiredpar- GeV invariant masses by the ATLAS and CMS collabo-
S
tial width of S →PX diverges, and f tends to vanish. rations [1, 2]. Our motivation was to connect the signal
P
Nearthislowvaluesofy photonfusionplaysanimpor- tomodelsof(dynamical)electroweaksymmetrybreaking
St
tant role in the production of the P state, as discussed and flavor and to avoid having to invoke new vector-like
in scenario 1. Fixing the previously introduced mixing colored states.
angle sin(θ) = 0.1, in order to get f (cid:38) 15 GeV it is In both scenarios we assume the excess is due to a
P
necessary y2 ∼ 0.012 for δm = 25 GeV and photon pseudo-scalar resonance produced either directly in top-
St SP
fusionmaystillplaysanimportantrolefortypicalvalues induced gluon fusion or via a parent resonance R close
of Λ . in mass. We take the parent resonance R to be either
P
For larger values of y2 (cid:38) 0.1 the top-quark domi- spin-1 or spin-0. With a small mass splitting between R
St
nates both the production via loop and decay widths of and P the additional activity in the final state beyond
S, making Λ , f and the partial width S → PX vary- the diphoton pair can be soft. We further assumed the
S P
ing little in y . For y = 0.1 and sin(θ) = 0.1 we have spin-1 parent couples dominantly to b-quarks in order to
St St
f = 73, 107, 119 GeV for δm = 25, 75, 175 GeV. havealargeenhancementoftheproductioncross-section
P SP
We conclude that our scenario 2 is more easily achieved from the 8 TeV to the 13 TeV run. While such mass de-
with a scalar parent resonance than with a vector. generacies and couplings are in general ad hoc we moti-
Finally we note that in this scenario 2, where P may vatedtheminsymmetrylimitsofscenariosofweakscale
havenegligiblecouplingstoSM,P maystillbeproduced composite dynamics.
directly via photon-fusion, given the sizable diphoton InallscenariosasignificantcouplingofP tophotonsis
couplings that can be achieved. inducedbynew(dynamically)heavystronglyinteracting
fermions.
Possible signatures: Ifthesignalisduetoapseudo-scalarproducedingluon
InthelimitwhereP isproducedoff-shelladistinctfea- fusion via an order 1 top Yukawa, producing a width
ture which can identify this scenario 2 over the photon Γ ∼0.05m the pseudo-scalar must have a very signif-
P P
fusion, or the gluon fusion production of P in scenario icant partial width into photons. We found that this is
1, is the double peak, or peak plus tail, structure in the possibleeveninrelativelyminimal,butlowscalecompos-
diphoton signal, which can be resolved with more statis- ite models of EWSB. Thus an additional sector playing
tics and finer binning, see figs.5-7. a role in EW symmetry breaking must in this case be
Once P is produced on-shell but with the additional present.
finalstate(s)X verysoft,itwillbecomplicatedtodistin- If the signal is instead due to production of P via a
guish from additional activity in the simple gluon fusion parent resonance the branching of P into diphotons can
production in scenario 1. Finally in the limit where the be O(1). We discussed the possibility of a spin-1parent
9
resonance coupled dominantly to b-quarks, motivated by shell Z (for sufficiently small mass splittings) in the final
the ω meson in QCD and by the dominant third genera- state, while in the third scenario with a scalar parent,
tioncouplingsinducedfrom’ExtendedTechnicolor’-type there would be additional soft hadronic activity. The
interactions. However in this case it is hard to reach the most important motivation for our study is the connec-
require cross-section. tion of the diphoton excess to underlying models of dy-
Finally if the parent resonance is a scalar S, top cou- namical EWSB.
plings of S might be induced due to mass mixing with
the 125 GeV Higgs, while fermion couplings of P could
be negligible. In that case we could have a very narrow
ACKNOWLEDGMENTS
resonancewithabranchingratiointophotonsoforder1.
If a large width of the excess observed in ATLAS data
persiststhiscouldbeduetoaslightlyoff-shellproduction We thank E. Molinaro, F. Sannino and N. Vignaroli
of P. forcommentsanddiscussions. TheCP3-Originscentreis
The distinct experimental signature of the second sce- partially funded by the Danish National Research Foun-
nario is the presence of an additional soft photon or off- dation, grant number DNRF90.
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