Dilaton at the LHC

Vernon Barger,1 Muneyuki Ishida,2 and Wai-Yee Keung3

1Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA2Department of Physics, Meisei University, Hino, Tokyo 191-8506, Japan

3Department of Physics, University of Illinois, Chicago, Illinois 60607, USA(Received 11 November 2011; published 26 January 2012)

The dilaton, a pseudo-Nambu-Goldstone boson appearing in spontaneous scale symmetry breaking at a

TeV scale f, may be found in Higgs boson searches. The dilaton couples to standard model fermions and

weak bosons with the same structure as the Higgs boson except for the overall strength. Additionally, the

dilaton couples to a Higgs boson pair. The couplings of the dilaton to a gluon pair and a photon pair,

appearing at loop level, are largely enhanced compared to the corresponding Higgs couplings. We present

regions of the mass and vacuum expectation value (VEV) of the dilaton allowed by WW, ZZ, and ��

limits from the LHC at 7 TeV with 1:0–2:3 fb�1 integrated luminosity. A scale of f less than 1 TeV is

nearly excluded. We discuss how the dilaton � can be distinguished from the Higgs boson h0 by

observation of the decays � ! �� and � ! h0h0 ! ðWWÞðWWÞ.DOI: 10.1103/PhysRevD.85.015024 PACS numbers: 14.80.Ec, 14.80.Va

Discovery of a standard model (SM) Higgs-boson h0 is atop priority of LHC experiments. However, an experimen-tal signature suggesting the existence of a scalar particledoes not necessarily mean the discovery of h0. There aremany candidate theories beyond the SM and almost allpredict the existence of new scalar particles. One of these isa dilaton [1], denoted as �, which appears as a pseudo-Nambu-Goldstone boson in spontaneous breaking of scalesymmetry [2]. The interesting case is that the scale f ofconformal symmetry breaking is larger than a weak scalev. In this case, the dilaton appears as a pseudo-Nambu-Goldstone boson with a mass m� � v � f in addition to

the Higgs boson that unitarizes the WW and ZZ scatteringamplitudes at the TeVenergy scale. This situation occurs inwalking technicolor models [3–9].

It is very important to distinguish the dilaton from h0 inobserved signals. The dilaton � has T�

� ðSMÞ couplings tothe SM particles, as will be explained later, which areproportional to the mass for the fermions and to masssquared for massive gauge bosons. The couplings arevery similar to the SM Higgs h0, except that the SMVEV is replaced by f. A distinctive difference is in thecouplings of massless gauge bosons. The dilaton has acoupling to the trace-anomaly T

��ðSMÞanom that is propor-

tional to the � function, while the SM Higgs has no suchcoupling and only triangle-loop diagrams of heavy parti-cles contribute to the gg and �� decays. Because of thisproperty, h0 ! �� is used as a channel searching for thefourth generation and the other heavy exotic particles.While for the dilaton, in the limit of high masses of theheavy particles in the loop, its contribution to the � func-tion exactly cancels the triangle diagram of the heavyparticles, and thus the dilaton couplings to gg and �� aredetermined only by � function contributions of light-particle loops.

In this paper, we evaluate the production and decays ofthe dilaton � appropriate to the LHC experiments at 7 TeV(LHC7) and consider the possibility that � could be foundinstead of the Higgs boson. We use the dilaton interactiongiven in Ref. [1], where the dilaton field � is introduced asa compensator for preservation of the nonlinear realizationof scale symmetry in the effective Lagrangian.The model parameters are the VEV f of the dilaton and

its mass m�. We derive allowed regions of parameters by

considering the latest LHC data relevant to the WW, ZZand �� decays of the dilaton. The tree-level couplings of �to SM particles are very similar to those of h0. We considera possible way to distinguish � from h0 in two specificdecays : � ! �� and � ! h0h0.Dilaton Production Cross Section The production of the

dilaton � at a hadron collider is mainly via gg fusionsimilar to the production of a Higgs boson h0. These crosssections are proportional to the respective partial decaywidths to gg.From calculations of the Higgs boson production cross

section at next-to-next-to leading order [10], we can di-rectly estimate the production cross section of � as

�ðpp ! �XÞ ¼ �ðpp ! h0XÞ � �ð� ! ggÞ�ðh0 ! ggÞ ; (1)

where we can use the lowest-order results of �ð� ! ggÞand �ðh0 ! ggÞ, since in the approximation that the gg !� interaction is essentially pointlike, the QCD radiativecorrections to the gg ! h0 and gg ! � subprocessesshould be nearly equal. By use of the �ð� ! ggÞ partialwidth given later and �ðh0 ! ggÞ of the SM, we canpredict �ðpp ! �XÞ. The dilaton result for f ¼ 3 TeVis compared with the SM Higgs production in Fig. 1.The production of � is almost the same as that of the SM

Higgs boson of the same mass mh0 ¼ m� for the choice

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f ¼ 3 TeV used in this figure. The subprocess cross sec-tion �̂ðgg ! �Þ is proportional to 1=f2. Our prediction of�ð�Þ in Fig. 1 includes the �25% uncertainty associatedwith the theoretical uncertainty on �̂ðgg ! h0Þ.

Dilaton Decay The dilaton couplings to SM particles areobtained [1] by using the effective Lagrangian where � isintroduced as a compensator to preserve a nonlinear real-ization of scale symmetry. The � takes a VEV f in thespontaneous scale symmetry breaking and it is redefined by� ! fþ �. In the exact scale symmetric limit, the �couples to the SM particles through the trace of theenergy-momentum tensor T��ðSMÞ as

Ltrace ¼ �

fT�� ðSMÞ: (2)

T�� ðSMÞ ¼ T�

�ðSMÞtree þ T�� ðSMÞanom

T�� ðSMÞtree ¼ X

f

mf�ff� 2m2

WWþ�W

�� �m2ZZ�Z

�

þ 2m2hh

2 � @�h@�h

T�� ðSMÞanom ¼ � �s

8�bQCD

X

a

Fa��F

a�� � �

8�bEMF��F

��:

(3)

Here, T�� ðSMÞ, the trace of the SM energy-momentum

tensor, defined byffiffiffiffiffiffiffi�g

pT��ðSMÞ ¼ 2

ð ffiffiffiffiffi�gp

LSMÞg�� , is repre-

sented as a sum of the tree-level term T�� ðSMÞtree and the

trace anomaly term T�� ðSMÞanom for gluons and photons,

where Fa��ðF��Þ are the respective field strengths. The

T�� ðSMÞtree contributions are proportional to the fermion

masses and the squares of weak boson masses.

The b values of the � functions are

bQCD ¼ 11� ð2=3Þ6þ Ft and

bEM ¼ 19=6–41=6þ ð8=3ÞFt � FW (4)

which include the QCD top triangle-loop and the top andW EM triangle-loops. The triangle functions are given by

Ft ¼ tð1þ ð1� tÞfðtÞÞ;FW ¼ 2þ 3W þ 3Wð2� WÞfðWÞ

fðÞ ¼

8>>><>>>:

�Arcsin 1ffiffi

p�2

for � 1

� 14

�ln �þ

��� i�

�2

for < 1

(5)

�� ¼ 1� ffiffiffiffiffiffiffiffiffiffiffiffi1�

p; i �

�2mi

m�

�2

for i ¼ t;W: (6)

The dilaton couplings are very similar to those of the SMHiggs except that there is a distinctive difference in the ggand �� couplings. For the dilaton �, bQCD;EM in Eq. (4) are

given by

b�QCD ’8<:11� 2

3 5 m� < 2mt

11� 23 6 2mt < m�

;

b�EM ’

8>>><>>>:

� 809 m� < 2mW

� 359 2mW <m� < 2mt

� 173 2mt < m�

: (7)

Here, bQCD for m� < 2mt is represented as 11� 23nlight

with the number of light flavors nlight ¼ 5 as explained

above. For the case of the SM Higgs h0, the correspondingb values are

bh0

QCD ¼ Ft ’� 23 mh < 2mt

0 2mt < mh

;

bh0

EM ¼ 8

3Ft � FW ’

8><>:

� 479 mh < 2mW

�29 2mW <mh < 2mt

�2 2mt < mh

: (8)

There is a strong enhancement of gg and �� couplings of �compared to the h0, as previously discussed in Ref. [1].Another important dilaton decay channel is h0h0.

Models with f > v predict the scalar unitarizing WW,ZZ scattering amplitudes to have mass in the TeV region,but there is no compelling reason to forbid the situationmh <m�=2. Observing � ! h0h0 ! ðWWÞðWWÞ,ðWWÞðZZÞ, or ðZZÞðZZÞ is a decisive way to distinguish� from h0.The kinetic and mass terms of � are given [1] by

L � ¼ 1

2@��@

���m2�

2�2 �m2

�

2f�3 þ � � � ; (9)

100 500200 300150

0.1

0.2

0.5

1.

2.

5.

10.

20. LHC7

SM h

Dilatonf 3 TeV

FIG. 1 (color online). The inclusive dilaton production crosssection in pb from gg fusion (solid blue), compared with that ofthe SM Higgs of the same mass mh0 ¼ m� (solid red). The VEV

f of � is taken to be 3 TeV. The dilaton production cross sectionscales with a factor ð3 TeV

f Þ2. The overall theoretical uncertainties[10] are denoted by the dashed lines.

VERNON BARGER, MUNEYUKI ISHIDA, AND WAI-YEE KEUNG PHYSICAL REVIEW D 85, 015024 (2012)

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where we consider an explicit scale symmetry breakingparameter with dimension 2 by having a Higgs mass termin the SM. This L� duplicates the SM Higgs interactions

when f is replaced by v.For the � decay channels � ! AB, we consider AB ¼

gg, ��,WþW�, ZZ, b �b, t�t, c �c, þ�, and h0h0. The decaybranching fractions of � are given in Fig. 2. The QCDradiative correction in next-to-next-to leading order[11,12] is taken into account for the gg channel. TheQCD radiative corrections to b �b, c �c and t�t at next-toleading order are included. The off-shell WW and ZZdecays are treated as in Ref. [14].

A large gg branching fraction at m� & 140 GeV is a

characteristic of � decay in comparison with h0 decayswhere h0 ! b �b is the dominant channel for mh0 &140 GeV, as pointed out in Ref. [1].

Dilaton Detection compared to SM Higgs Next, weconsider the detection of � in the WþW�, ZZ and ��channels. The � detection ratio (DR) to h0 in the �XXchannel is defined [15] by

DR � ��!gg��! �XX=�tot�

�h0!gg�h0! �XX=�toth0; (10)

where �XX ¼ WþW�, ZZ, and ��. The DR are plottedversus m� ¼ mh0 in Fig. 3 for f ¼ 3 TeV.

DRðWWÞ ¼ DRðZZÞ in all mass regions. DR of theWW, ZZ, and �� are all relatively large in the mass range160<m� < 260 GeV, between theWW threshold and the

h0h0 threshold. DRð��Þ is larger than those ofWW, ZZ inall mass regions because of the enhancement evident inEq. (7).

The cross section of a putative Higgs boson signal,relative to the standard model cross section, as a functionof the assumed Higgs boson mass, is widely used by theexperimental groups to determine the allowed and ex-cluded regions of mh0 . By use of the DR in Fig. 3, wecan determine the allowed regions of f and m�. First, we

consider the quantity ð1=DRÞ � ð�exp=�ðh0 ! �XXÞÞ. Thisis the signal of the Higgs boson decaying into �XX relativeto the dilaton cross section ½�ð� ! �XXÞ ¼ �ðh0 !�XXÞ �DR for �XX ¼ WW, ZZ, ��. DR is proportionalto ð1=fÞ2. The f corresponding to the 95% CL upper limitof �exp gives the lower limit on the allowed region of f.

The ATLAS exclusion of h0 is obtained by combiningWWand ZZ data for mh0 > 150 GeV, and including �� for

100 200 300 400 500 60010 5

10 4

0.001

0.01

0.1

1

hh

WW

ZZ

gg

tt

bb

cc

Dilaton

FIG. 2 (color online). Decay branching fractions of � versusm�ðGeVÞ. mh0 is taken to be 130 GeV. The result is independent

of the value of f.

100 200 300 400 500 600

0.05

0.1

0.5

1.

5.

10.

Dilaton

WW ZZ

FIG. 3 (color online). � Detection ratio ðDRÞ to the SM Higgsh0 of Eq. (9) for the �XX ¼ WþW� (solid blue) and �� (solidblack) final states versus m�ðGeVÞ. Note that DRðZZÞ ¼DRðWWÞ. f is taken to be 3 TeV. DR scales with a factorð3 TeV

f Þ2.

500200 300150200

500

1000

2000

5000

ATLAS WW ZZ

Excluded:95 CL

FIG. 4 (color online). The allowed regions of dilaton parame-ters ðf;m�Þ in GeVat the 95% confidence level, determined from

ATLAS data. We use DRðWWÞ for the ATLAS [16] combinedresult (blue points and solid line), which are obtained from theresults for H ! WW ! l�l� (1:70 fb�1), H ! ZZ ! llll(1:96–2:28 fb�1), H ! ZZ ! llqq (1:04 fb�1), and H ! ZZ !ll�� (1:04 fb�1) at mH > 150 GeV. At m� < 150 GeV, the

constraint from �� data with 1:08 fb�1 (black points and solidlines), improves on the WW=ZZ constraints. See also relatedprevious [17] and subsequent [18,19] works. The dashed linerepresents a prediction of a walking technicolor model, f ’14132 ð600 GeV

m�Þ GeV [20] in a partially gauged one-doublet model

[21,22] with ðNTC; NTFÞ ¼ ð2; 8Þ or (3, 12).

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mh0 < 150 GeV. We can use the DRðWWÞ for the ATLAScombined result since the model prediction is DRðWWÞ ¼DRðZZÞ<DRð��Þ which is valid in all mass regions, ascan be seen in Fig. 3. Figure 4 shows the exclusion regionsof dilaton parameters at 95% confidence level.

The �� final state is very promising for � detection,because the � detection ratio to h0 is generally very large inall the mass range of m�, as is evident in Fig. 3. For m� >

150 GeV, the detection of a �� signal can be a key todistinguish � and h0, although the �� BF of � is itselfsmall.

Concluding Remarks We have investigated a search forthe dilaton � at LHC7. The VEV f < 1 TeV is not favor-able, but large allowed regions of f and m� are consistent

with the present data. The forthcoming 5 fb�1 integratedluminosity at LHC7 will substantially extend the discoveryor exclusion regions. The coupling of � is very similar tothe h0; however, it is possible to distinguish it from the SM

h0 by observing the �� decay rate relative to WW. The� ! h0h0 decay is a distinguishing feature of the dilatonfrom the SM Higgs, It will give ðWWÞðWWÞ, ðWWÞðZZÞ,and ðZZÞðZZÞ final states, which have low backgrounds.If the LHC7 finds no signal of a scalar in forthcoming

5 fb�1 data, we still have a possibility of a low-massdilaton with f > 3 TeV. In this case, the walking techni-color models [3–9] are promising wherein the Higgs scalarunitarizing the WW, ZZ scattering amplitudes appears inthe TeV region.

M. I. is very grateful to the members of phenomenologyinstitute of University of Wisconsin-Madison for hospital-ities. This work was supported in part by the U.S.Department of Energy under Grants No. DE-FG02-95ER40896 and No. DE-FG02-84ER40173, in part byKAKENHI (2274015, Grant-in-Aid for Young Scientists(B), and in part by Meisei University.

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