Is 125 GeV techni-dilaton found at LHC?

0.16 MB·

by  Shinya Matsuzaki

MISC-2012-14
Is 125 GeV techni-dilaton found at LHC?
Shinya Matsuzaki1,∗ and Koichi Yamawaki2,†
1 Maskawa Institute for Science and Culture, Kyoto Sangyo University,
Motoyama, Kamigamo, Kita-Ku, Kyoto 603-8555, Japan.
2 Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI)
Nagoya University, Nagoya 464-8602, Japan.
(Dated: July 26, 2012)
A new particle at around 125 GeV has been observed at the LHC, which we show could be
identified with the techni-dilaton (TD) predicted in the walking technicolor and thus should be an
evidenceof walking technicolor. The TD is a pseudo Nambu-Goldstone boson for theapproximate
scale symmetry spontaneously broken by techni-fermion condensation, with its lightness being en-
2
suredbytheapproximatescaleinvarianceofthewalkingtechnicolor. Wetestthegoodness-of-fit of
1
the TD signatures using the presently available LHC data set, and show that the 125 GeV TD is
0
2 actuallyfavoredbythecurrentdatatoexplainthereportedsignalstrengthsintheglobalfitaswell
as in each channel including the coupling properties, most notably the somewhat large diphoton
l
u event rate. This is in sharp contrast to other dilaton/radion scenarios which tend to be disfavored
J bythe data, mainly dueto thesuppressed diphoton eventrate.

5
2
I. INTRODUCTION testing the goodness-of-fitofthe currentdata: The large

] diphoton event rate is achieved due to the presence of
h extratechni-fermionloopcontributions,a salientfeature
On July 4, the ATLAS and CMS groups [1] have re-
p
ported observation of a new boson at around 125 GeV of the techni-dilaton noted in the previous papers [7–9].
-
p in search for the decay channels such as γγ, WW∗ and It is also shown that, lacking such extra fermion contri-
e ZZ∗. Thoughthestatisticaluncertaintyisstilllarge,the butions,asimilardilatonmodel[10]andatypicalradion
h model [11] analyzed recently for LHC [12, 13] tend to
currentdataonthe diphotoneventrate[2,3]exhibitthe
[
signalstrengthabouttwotimeslargerthanthatexpected be disfavored by the data, mainly due to the suppressed

1 from the standard model (SM) Higgs boson, which may diphoton rate.
v imply the observation of a new boson beyond the SM.
1
One such a possibility is the techni-dilaton (TD), a
1 II. TD COUPLINGS
composite scalar boson, predicted in the walking tech-
9
5 nicolor (WTC) [4, 5] which is characterized by an ap-
. proximately scale-invariant (conformal) gauge dynamics The TD couplings to techni-fermions and the SM par-
7 and a large anomalous dimension γ = 1 (The WTC ticles have been discussed in detail in Ref. [9], which are
0 m
2 was subsequently studied without notion of anomalous completelyfixedbyWard-Takahashiidentitiesforthedi-
1 dimension and scale invariance/TD. [6]). The TD is latation current coupled to the TD. Those couplings are
: a pseudo Nambu-Goldstone boson for the spontaneous collected in an effective nonlinear Lagrangian invariant
v
breaking of the approximate scale symmetry triggered under the scale symmetry [9]:
i
X by techni-fermion condensation and hence its lightness, F2 F2
r say125GeV,isprotectedbytheapproximatescalesym- = πχ2Tr[ µU† µU]+ φ(∂µχ)2
a L 4 D D 2
metry inherent to the WTC. Thus the discovery of TD
would imply the discovery of the WTC. m χ 2−γm χ f¯f
f
In Refs. [7–9] we studied the LHC signatures of the − (cid:18)(cid:16)S(cid:17) · (cid:19)
TD. Particularly in Ref. [9] we have shown that the 125 χ β (g ) β (e)
+log F s G2 + F F2 + ,(1)
GeV TD can be consistent with the currently reported (cid:16)S(cid:17)(cid:26) 2gs µν 2e µν(cid:27) ···
diphoton signal as well as other signals such as WW∗
and ZZ∗, etc.. where χ = eφ/Fφ with the TD field φ and decay con-
Inthisarticle,weextendthepreviouslyreportedanal- stant Fφ, and U = e2iπ/Fπ with the techni-pion fields π
ysis[9]onthe125GeVTDbytestingthegoodness-of-fit and decay constant Fπ related to the electroweak (EW)
of the TD signatures, based on the presently available scale vEW 246 GeV by Fπ = vEW/√ND, in which
≃
LHC data set [2, 3]. We show that the 125 GeV TD is ND denotes the number of EW doublets formed by the
actually favored (slightly better than the SM Higgs) by techni-fermions. The SM gauge covariant µU term in-
D
cludestheweakgaugebosonmassesintheusualmanner.
A spurion field S has been introduced so as to compen-
sate the scale invariance explicitly broken by the techni-
∗[email protected] fermion condensation itself, where S is set to 1 after all
†[email protected] calculations as in the case of other spurion methods.
2
The TD Yukawa coupling to the SM f-fermion arises Yukawa coupling as noted before (as well as Note added
from the second line of Eq.(1) as [5], of Ref. [9]), Eq.(5) is slightly different from Eq. (51) of
[9](whichusedγ =1)forthe numericalanalysisinthe
m
(3 γ )m
− m f φf¯f, (2) presentwork. Thefullexpressionsforthesecouplingsare
− Fφ presented in Appendix A of Ref. [9].
As seen from Eqs.(3) and (5), once the ratio v /F
alongwithscaledimensionoftechni-fermionbilinearop- EW φ
is fixed, the TD LHC phenomenological study can be
erator(3 γ ),wheretheanomalousdimensionisγ 1
− m m ≃ made just by quoting the SM Higgs coupling properties.
in WTC, which is crucial to obtain the realistic mass of
The TD decay constant F can actually be related to
the SM fermions of the first and the second generations φ
the TD mass M throughthe partially conserveddilata-
without suffering from the FCNC (flavor-changing neu- φ
tion current (PCDC) – which is analogous to the PCAC
tral current) problems [14]. However it was known for
(partially conserved axialvector current) relation for the
long time thatit is notenoughfor the massof the third-
QCD pion – involving the vacuum energy density :
generation SM f-fermions like t,b,τ: A simplest reso- Evac
lution would be the strong extended-technicolor (ETC) F2M2 = 16 . (6)
TC model [15] having much larger anomalous dimension φ φ − Evac
1<γm <2 due to the strong effective four-fermion cou- The vacuum energy density vac is saturated by the
pling from the ETC dynamics in addition to the walk- techni-gluon condensation inEduced from the techni-
ing gauge coupling. As was prescribed in Note added of fermion condensation, so is generically expressed as
Ref. [9], here we take γ 2, i.e., (3 γ ) 1, as in
m m
≃ − ≃
the strong ETC model [15] for the third-generation SM N N
= κ TC TF m4 , (7)
f-fermions like t,b,τ which are relevant to the current Evac − V (cid:18) 8π2 (cid:19) F
LHC data.
From the Lagrangian Eq.(1) one thus easily sees that where m denotes the dynamical techni-fermion mass
F
the TD couplings to W and Z bosons and fermions are and N = 2N + N including the number
TF D EW−singlet
related to those of the SM Higgs by a simple scaling: of dummy techni-fermions, N , which are sin-
EW−singlet
glet under the SM gauges. The overall coefficient κ is
g v V
φWW/ZZ EW
= , determined once a straightforward nonperturbative cal-
g F
hSMWW/ZZ φ culation is made. The dynamical techni-fermion mass
g v
φff = EW , for f =t,b,τ. (3) mF can,ontheotherhand,berelatedtothe techni-pion
ghSMff Fφ decay constant Fπ:
Inadditiontotheabovescaling,thecouplingstogluon N
and photon (G2 and F2 terms in Eq.(1)) involve the F2 =κ2 TCm2 , (8)
µν µν π F 4π2 F
betafunctions,β (g )andβ (e),inducedfromF-techni-
F s F
fermion loops [7]. This is the most crucial point [9] that with the overall coefficient κ and the property of N
F TC
distinguishes the TD from other similar models of dila- scaling taken into account.
ton/radion[10,11]. Here weshallemploythe one-family Thevaluesofκ andκ maybequotedfromthelatest
V F
model (1FM) with N = 4 as a WTC setting (see the result [16] on a ladder Schwinger-Dyson analysis for a
D
later discussions) for the SU(NTC) gauge group. The modern version of WTC [17–19]:
beta functions β (g )andβ (e)arethenexplicitly eval-
F s F
uated to be κV 0.7, κF 1.4, (9)
≃ ≃
g3 4
β (g ) = s N whereκF hasbeenestimatedbasedonthePagels-Stokar
F s (4π)23 TC formula [20]. In that case N is fixed by the criticality
TF
e3 16 condition for the walking regime as [18]
β (e) = N . (4)
F (4π)2 9 TC
N
TF
1. (10)
We thus find the scaling from the SM Higgs for the cou- 4N ≃
TC
plings to gg and γγ, which can approximately be ex-
The estimated values in Eqs.(9) and (10) are based on
pressed at around 125 GeV as
ladder approximation which are subject to certain un-
g v
φgg EW ((3 γ )+2N ) certainties up to 30% observed for the critical coupling
m TC
ghSMgg ≃ Fφ · − and hadron spectrum in QCD [21]. We may include this
g v 63 16(3 γ )32 30% uncertainty in estimation of each independent fac-
φγγ EW m
− − NTC , (5) tor κ , κ2 and the criticality condition N /(4N ).
ghSMγγ ≃ Fφ ·(cid:18) 47 47 (cid:19) V F TF TC
Putting these all together, we thus estimate v /F as
EW φ
where in estimating the SM contributions we have in-
corporated only the top and W boson loop contribu- vEW ND Mφ
(0.1 0.3) , (11)
tions. Note that since we used γm =2 for the top quark Fπ ≃ − ×(cid:18) 4 (cid:19)(cid:18)125GeV(cid:19)
3
and m (320 420)GeV 3/N for the 1FM with factors both from the gg and γγ couplings (See Eq.(5)),
F TC
≃ −
Fπ 123 GeV. p which can compensate the smallness of (vEW/Fφ) in
≃
FromEqs.(3)and(11)weseethatthe TD couplings to Eq.(11) for a moderately large N [9].
TC
WW,ZZ and ff¯are substantially smaller than those of This feature is in sharp contrast to other similar dila-
the SM Higgs. On the other hand, the TD couplings to ton models such as EW pseudo-dilaton [10] and Randall-
gg and γγ in Eq.(5) have extra factors (1+2N ) and Sundrum (RS) radion [11], where extra contributions be-
TC
(1 32N /47) coming from techni-fermions as well as yond the SM such as techni-fermions are absent so that
TC
−
the W and top quarks carrying the QCD color and elec- their diphoton rates are not enhanced, to be disfavored by
tromagnetic charges. The gluon fusion (GF) production thecurrentdiphotondataaswillbeshownmoreexplicitly
at the LHC thus becomes largerthan the SM Higgs case below.
due to this extra factor, while other productions such as We shall test the goodness-of-fit of the TD, based on
vector boson fusion (VBF) and vector boson associate the χ2 function:
(VBA) productions are significantly suppressed.
µ µexp 2
χ2 = i− i , (15)
(cid:18) σ (cid:19)
III. TD SIGNAL AT LHC i∈Xevents i
where µexp denote the best-fit strengths for each chan-
i
As done in Refs. [8, 9], we can calculate the TD pro- nel reported in Refs [2, 3] and σ the corresponding one
i
duction cross sections and decay widths including loop sigmaerrors. Taking(v /F )asafreeparametersoas
EW φ
contributions from the SM particles, by quoting the cor- to satisfy the theoretically expected range in Eq.(11), in
respondingformulasforthe SMHiggs[22]. (The explicit Fig.1weplottheχ2 functionforthe125GeVTDinthe
expressions of the formulas for TD are given in Ref. [9].) 1FMwith N =4,5. The best-fit values are as follows:
TC
HerewefocusontheGFandVBFproductionsfordecay
channels to WW∗, ZZ∗, τ+τ− and γγ, and VBA pro- N (v /F ) χ2 /d.o.f
duction for b¯b channel, to which the ATLAS and CMS 4TC EW0.22φ best 12m/1in3 0.9 , (16)
experiments have so far reported the significant data in ≃
5 0.17 10/13 0.7
search for the SM Higgs [2, 3]. ≃
Thesignalstrengthµ σ/σ forb¯bchannelat√s=
7,8 TeV is thus evaluate≡d as SM which are compared with the SM Higgs case, χ2min|SM ≃
14/14=1.0,implyingthattheTDismorefavorablethan
σφ (s) BR(φ b¯b) the SM Higgs (µi = 1). This nice goodness of fit is due
µb¯b = σVVhSBBMAA(s)BR(hSM→→b¯b) tcoomthinegsfirgonmificthanetseecnthoarnbceeymonendtthineSthMe(dtiepchhontio-fnercmhiaonnnse),l
σ (s)+σ (s) BR(φ b¯b) as was also noted in Ref. [23]: The techni-fermion loop
Wφ Zφ
= → . (12)
σ (s)+σ (s)BR(h b¯b) contributions as in Eq.(5) become large enough to com-
WhSM ZhSM SM → pensatethesmallnessoftheoverall(v /F )inEq.(11).
EW φ
For X = WW∗, ZZ∗ and τ+τ− channels we take the In Fig. 1 also has been shown a comparison with
signal strengths to be inclusive: other similar models, EW pseudo-dilaton [10] and RS
radion [11]. These dilaton/radionscenarios are actually
σφ (s)+σφ (s) BR(φ X) disfavored mainly due to the absence of enhancement of
µ = GF VBF → . (13)
X σGhSFM(s)+σVhSBMF(s)BR(hSM →X) diphoton rate, in sharp contrast to the TD [24]. This
resultisinaccordwithothersimilaranalysesinRef.[25]
On the other hand, γγ +0j and γγ +2j channels are for the EW pseudo-dilaton and in Ref. [26] for the RS
treatedtobe exclusivebydistinguishingtheTDproduc- radion performed in light of the 125 GeV LHC events.
tion processes: although we have not included the Tevatron results on
the ¯bb channel [27].
µ = σGφF(s) BR(φ→X) , Finally,inFig.2weexplicitlycomparethebest-fitsig-
γγ0j σGhSFM(s)BR(hSM →X) nalstrengthsofTD with those estimatedby the ATLAS
and CMS analyses for each channel. Note first that the
ξ σφ (s)+ξ σφ (s)
µ = GF· GF VBF· VBF mostprecisemeasurementhascurrentlybeendoneinthe
γγ2j ξGF·σGhSFM(s)+ξVBF·σVhSBMF(s) diphotonchannelwith 0 jet (γγ0j)which exhibits about
BR(φ γγ) 2 times larger signal strengths than the SM Higgs pre-
→ , (14) diction (µ =1.9 0.5 for ATLAS 7TeV + 8TeV and
×BR(h γγ) γγ0j
SM ±
→ µ = 1.7 0.5 for CMS 7TeV + 8TeV [2, 3]). The
γγ0j
where the corresponding acceptances multiplied by dijet χ2 fit is ther±efore fairly sensitive to the γγ0j category,
tagefficienciesξ andξ arereadofffromRefs.[2,3]. and hence currently the TD can be more favorable than
GF VBF
We then combine the 7 TeV and 8 TeV signal strengths the SM Higgs due to the enhancement of the diphoton
with the luminosities accumulated for each event cate- rate which happens when N 4. On the other hand,
TC
≥
gory. It turns out that µ can be enhanced by the theTDsignalstrengthinthediphotonplusdijetchannel
γγ0j
4
(γγ2j)tendstobesmallerthantheSMHiggsprediction, nelslike2l2ν+2j andτ+τ−+2j aswellasb¯boriginated
simply because ofthe suppressionof the overallTD cou- fromthe VBAandVBFproductions. Thusmoreprecise
pling compared to the SM Higgs (v /F ) in Eq.(11). measurementsinsuchotherexclusiveevents woulddraw
EW φ
Similarsuppressionsarealsoseeninotherexclusivechan- a moredefinite conclusionthatthe TDis favoredornot.
50
EW pseudo-dilaton
40
RS radion
30
2Χ
20
SM Higgs
10 TD NTC=5 TD NTC=4
0
0.10 0.15 0.20 0.25 0.30
vEW(cid:144)FΦ
FIG. 1: The plot of χ2 as a function of vEW/Fφ in the case of the 1FM with NTC = 4 (black dashed curve) and NTC = 5
(black solid curve). Comparison with theEW pseudo-dilaton [10](bluedottedcurve)and RSradion [13](green dotted curve)
is also shown, along with the SM Higgs case (red dotted line). Here χ2 /d.o.f = 12/13(10/13) ≃ 0.9(0.7) for the TD with
min
NTC =4(5), χ2min/d.o.f =37/13≃2.8 for theEW pseudo-dilaton and χ2min/d.o.f =30/13≃2.3 for theRS radion.
ATLAS&CMS data
SM Higgs
dotted TD NTC=3
dashed TD NTC=4
solid TD NTC=5
dot-dashed TD NTC=6
æ æàìò æ CMS 8TeV ΓΓ2j (loose)
æ àæìòæ CMS 8TeV ΓΓ2j (tight)
æàìòæ æ CMS7TeV ΓΓ2j
æàìòæ æ ATLAS8TeV ΓΓ2j
æ æ àæìò CMS 7TeV+8TeV ΓΓ0j
æ æ à æìò ATLAS 7TeV+8TeV ΓΓ0j
æ òìæàæ CMS 7TeV+8TeV ΤΤ
òæìæàæ ATLAS 7TeV ΤΤ
òìææàæ CMS 7TeV+8TeV ZZ*(4l)
òìæàææ ATLAS 7TeV+8TeV ZZ*(4l)
òæìæàæ CMS 7TeV+8TeV WW*(2l2Ν)
òìæàææ ATLAS 7TeV+8TeV WW*(2l2Ν)
ìòæà æ æ CMS 7TeV+8TeV bb
ìòæà æ æ ATLAS 7TeV bb
0 5 10 15
Μ=Σ(cid:144)Σ
SM
FIG. 2: The best-fit signal strengths of the125 GeV TD, for thedecay channels categorized as WW∗(2l2ν), ZZ∗(4l), τ+τ−,
γγ0j and γγ2j [2, 3].
IV. SUMMARY WW∗, ZZ∗, τ+τ− and γγ. We found that the 125 GeV
TDisactuallyfavoredbythecurrentdatatoexplainthe
reported signal strengths including the coupling proper-
In summary, we have tested the goodness-of-fit of the ties involving somewhat large diphoton event rate. It
125 GeV TD signatures, using the presently available was also shown that other dilaton and radion scenarios
LHC data set by focusing on the decay channels to b¯b,
5
tend to be disfavored by the data, mainly due to the Acknowledgments
suppressed diphoton event rate.
The issue to be studied in future is a reliable non-
perturbative estimate of the TD mass: There has been
onlyacrudeestimatebasedontheladderapproximation
(see references cited in e.g. Ref.[9]). The holographic ThisworkwassupportedbytheJSPSGrant-in-Aidfor
method [28] may give some hint and the lattice simula- Scientific Research (S) #22224003 and (C) #23540300
tions eventually give us the definite answer. (K.Y.).
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