Page 1

arXiv:0810.1952v3 [hep-ph] 21 Jul 2009

YITP-SB-08-44

Deciphering the spin of new resonances in Higgsless models

Alexandre Alves∗and O. J. P.´Eboli†

Instituto de F´ ısica, Universidade de S˜ ao Paulo, S˜ ao Paulo – SP, Brazil.

M. C. Gonzalez–Garcia‡

Instituci´ o Catalana de Recerca i Estudis Avan¸ cats (ICREA),

Departament d’Estructura i Constituents de la Mat` eria,

Universitat de Barcelona, 647 Diagonal, E-08028 Barcelona, Spain and

C.N. Yang Institute for Theoretical Physics, SUNY at Stony Brook, Stony Brook, NY 11794-3840, USA

J. K. Mizukoshi§

Centro de Ciˆ encias Naturais e Humanas, Universidade Federal do ABC, Santo Andr´ e – SP, Brazil.

We study the potential of the CERN Large Hadron Collider (LHC) to probe the spin of new

massive vector boson resonances predicted by Higgsless models. We consider its production via

weak boson fusion which relies only on the coupling between the new resonances and the weak

gauge bosons. We show that the LHC will be able to unravel the spin of the particles associated

with the partial restoration of unitarity in vector boson scattering for integrated luminosities of

150–560 fb−1, depending on the new state mass and on the method used in the analyses.

PACS numbers: 12.60.Fr, 14.70.Pw

I.INTRODUCTION

Despite the success of the Standard Model (SM) of

particle physics in describing electroweak physics below

∼ 100 GeV in terms of a non-abelian gauge theory with

spontaneously broken SU(2)L×U(1)Y gauge group, the

gauge symmetry does not predict the precise mechanism

of the electroweak symmetry breaking (EWSB). Indeed,

up to this moment, there is no direct experimental signal

of the mechanism of EWSB, being its search one of the

main goals of the LHC.

The EWSB mechanism plays an important role in the

high energy electroweak gauge boson scattering which

violates partial wave unitarity or becomes strongly inter-

acting at energies of the order of E ∼ 2 TeV, if there is

no new state to cut off its growth [1, 2]. In the context

of the SM, as well as in its supersymmetric realization,

electroweak symmetry is broken by the vacuum expecta-

tion value of some weakly coupled neutral scalar state(s),

the Higgs boson(s), which will contribute to electroweak

gauge boson scattering, preventing the unitarity violation

of the process.

Alternatively, Higgsless extensions of the SM [3, 4, 5]

have been proposed in which the electroweak symmetry

is broken without involving a fundamental Higgs field.

Generically on these models, the electroweak symmetry

∗Electronic address: aalves@fma.if.usp.br

†Electronic address: eboli@fma.if.usp.br

‡Electronic address: concha@insti.physics.sunysb.edu

§Electronic address: mizuka@ufabc.edu.br

is broken by boundary conditions in a higher dimensional

space.The originally proposed Higgsless models gave

large contributions to precision electroweak observables,

in particular to the S parameter [6] (ǫ3[7]) [8, 9, 10, 11,

12, 13]. Such problems could be overcome, for example,

by appropriate modifications of the fermion sector. In

this way, a variety of Higgsless models have been con-

structed [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24] which

ensure agreement with electroweak precision data.

From the point of view of unitarity, all Higgsless mod-

els share the common feature that new weakly interact-

ing spin-1 gauge bosons particles with the same quan-

tum numbers as the SM gauge bosons appear and they

are responsible for the partial restoration of unitarity

in vector boson scattering and for rendering a theory

weakly coupled to energies well above 2 TeV [25, 26, 27].

This property allows for an almost model independent

search for the lightest charged resonance V±

LHC through pp → V±

pp → V±

onance. The LHC experiments will be able to unravel the

existence of the charged state via these processes with

modest integrated luminosities of 10–60 fb−1. On the

contrary, the corresponding search for the neutral vector

resonance in gauge boson fusion is expected to be very

difficult, since a generic feature of this class of models

is the absence of coupling between the neutral resonance

and ZZ pairs. Reconstructing the heavy neutral vec-

tor resonance decaying into W+W−requires at least one

hadronic W decay, posing the challenge to dig it out from

the large SM backgrounds.

Once a clear signal of the charged resonance is observed

in the above channels, it is mandatory to study its spin

1

at the

1W∓or via weak boson fusion

1qq [28, 29], as long as V±

1remains a narrow res-

Page 2

2

to confirm that the new state is indeed a vector particle.

In this work, our goal is to probe the V±

study of weak boson fusion production of V±

subsequent decay into leptons, i.e.

1

spin via the

with its

1

pp → V±

1jj → ℓ±νℓ′+ℓ′−jj (1)

with ℓ and ℓ′= e or µ, considering final states where the

W’s and Z’s decay into different and same flavor charged

leptons.To determine the spin of the state decaying

into W±Z we contrast the final state distributions aris-

ing from the production and decay of the vector charged

state with the ones stemming from the decay of a scalar

state; i.e. we work in the framework commonly used

to analyze the spin of supersymmetric particles [30, 31].

Here we show that it is possible to determine the spin of

a new heavy resonance decaying into W±Z at the LHC

with 99% CL for luminosities of ∼ 150–560 fb−1, de-

pending on the particle mass and the method used in the

analysis.

II.MODEL AND CALCULATION SETUP

The restoration of partial wave unitarity in Higgsless

models is due to new Kaluza–Klein resonances V±

V0

(i).The couplings V+

same Lorentz structure of the SM W+W−Z vertex with

a coupling constant g(i)

the dangerous terms in the scattering WZ → WZ that

depend on E2and E4, where E is the energy of the in-

coming W and Z in the center–of-mass system, the new

vector state coupling constants must satisfy the following

constraints:

(i)and

(i)W−Z (V0

(i)W−W+) have the

V WZ(g(i)

V WW). In order to cancel

gWWZZ= g2

ZWW+

?

??M2

3?M±

i

?

g(i)

VWZ

?2

,(2)

2?gWWZZ− g2

=

?

Eqs. (2) and (3) constrain the couplings of the lightest

charged Kaluza-Klein state to WZ pairs,

ZWW

W+ M2

Z

?+ g2

Z− M2

?M±

ZWW

M4

M2

?

Z

W

i

?

g(i)

VWZ

?2?

i

?2−(M2

W)2

?2

i

. (3)

g(1)

VWZ<

∼

gZWWM2

√3M±

Z

1MW

.(4)

In our analysis we assume that this bound is satu-

rated [32], which leads to the largest allowed value for

g(1)

VWZ, and we evaluate the quartic coupling gWWZZus-

ing Eq. (2). Moreover, we assume that the V±

to fermions are small and that the V±

into WZ pairs. This hypothesis is, in fact, realized in

some higgsless models [24].

Our study of the V±

1spin was carried out by comparing

the kinematic distributions of its decay products with

1 couplings

1’s mainly decay

the predictions for the production of a spin-0 resonance.

Since the signal for the new charged state is characterized

by peak in the WZ invariant mass distribution, we use

as template the kinematic distributions in a model which

is the SM without a Higgs plus a scalar charged state,

H±, with an interaction H±ZµW∓

H±ZµW∓

cross section is equal to the one for V±

also set the H±width equal to the V±

We performed a parton level study using the full tree

level amplitude for the final state processes in order to

keep track of spin correlations. The matrix elements were

generated using the package MADGRAPH [33], where

we included the higgsless (and template) model parti-

cles and interactions. We employed the CTEQ6L par-

ton distribution functions [34] with the factorization scale

?

momenta of the tagging jets. For the QCD backgrounds

we chose the renormalization scale µR = µF.

der to have a crude simulation of the detector perfor-

mance we smeared energies, but not directions, of all fi-

nal state partons with a Gaussian error. For the jets,

we assumed a resolution ∆E/E = 0.5/√E ⊕ 0.03, if

|ηj| ≤ 3, and ∆E/E = 1/√E ⊕ 0.07, if |ηj| > 3 (E

in GeV), while for charged leptons we used a resolution

∆E/E = 0.1/√E ⊕ 0.01. Furthermore, we considered

the jet tagging efficiency to be 0.75 × 0.75 = 0.56, while

the lepton detection efficiency is taken to be 0.93= 0.73.

µ. The coupling of the

µvertex is chosen such that the H±production

1after all cuts. We

1 one.

µF=

(p2

T j1+ p2

T j2)/2, where pT jiare the transverse

In or-

III. RESULTS

We analyzed the process

pp → ℓ±ℓ′+ℓ′−jj + / ET

with ℓ, ℓ′= e, µ

which contains the contribution of the vector boson fu-

sion production of new charged resonances decaying into

leptons; see Eq. (1). This process possesses a significant

irreducible background originating from electroweak and

QCD WZjj production. Moreover, the production of t¯t

pair in association with a jet exhibits a large cross sec-

tion after we demand the presence of two tagging jets [35]

and can lead to trilepton events when both t’s decay semi-

leptonically and the decay of one of the b’s leads to an

isolated lepton1.

Initially we imposed the following jet acceptance cuts

designed to enhance events produced by vector boson

fusion,

pj

T> 20 GeV

|ηj1− ηj2| > 3.8 ,

,|ηj| < 4.9 ,

ηj1· ηj2< 0 .

(5)

1We considered a lepton to be isolated if the hadronic energy

deposited in a cone of size ∆R < 0.4 is smaller than 10 GeV

Page 3

3

cuts (5)–(6) cuts (5)–(7) cuts (5)–(8) cuts (5)–(10)

4.682.68

22.46.54

1.020.84

EW WZjj

t¯tj

2.40

1.85

0.78

0.265/0.166

0.024/0.0003

0.705

MV±

1

= 500 GeV

MV±

1

= 700 GeV0.360.320.30 0.25

TABLE I: SM background and signal cross sections after different set of cuts in fb. In the last column the top/bottom results

is obtained applying the top/bottom cut in Eq. (10).

We also applied lepton acceptance and isolation cuts

|ηℓ| ≤ 2.5

∆Rℓj≥ 0.4

,

,

pℓ

∆Rℓℓ≥ 0.4 .

T≥ 10 GeV

(6)

As we can see from Table I the SM background is still

quite large after these cuts with the t¯tj production be-

ing the dominant contribution. In order to reduce this

background we explore two features of the signal and

backgrounds. First of all, in the t¯tj production the lep-

ton coming from the b semi-leptonic decay is quite soft,

therefore, it can be reduced by imposing an additional

lepton transverse momentum cut:

pℓ

T> 25 GeV.(7)

Moreover, two of the leptons in the signal come from a

Z decay, consequently we also required that the events

present a pair of same flavor opposite charge leptons

(SFOC) with an invariant mass in a window around the

Z mass. Thus we further demanded

| MSFOC

ℓℓ

− MZ|< 10 GeV.(8)

The presence of just one neutrino in the signal final

state, Eq. (1), allows for full reconstruction of the neu-

trino momentum – up to a twofold ambiguity on its longi-

tudinal component – by imposing the transverse momen-

tum conservation and requiring that the invariant mass

of the neutrino–ℓ±pair, where ℓ is the charged lepton

not identified as coming from the Z decay, is compatible

with the W mass:

pν

L=

1

2pl

T

2

??M2

W+ 2(?pl

W+ 2(?pl

T·?/ pT)?pl

T·?/ pT)?2|? pl|2− 4(pl

L

±

??M2

TEl/ ET)2

?

(9)

Consequently, there are two distinct estimates for the

WZ invariant mass which we label Mrec,max

the maximum and minimum reconstructed values, re-

spectively. We show in left panel of Fig. 1 the Mrec,max

and Mrec,min

WZ

, as well as the true MWZ invariant mass

distributions for MV±

1

= 500 GeV. As seen in the fig-

ure, both reconstructed distributions present a clear peak

associated to the presence of a new charged resonance.

Moreover, the maximum (minimum) reconstructed WZ

WZ

and Mrec,min

WZ

WZ

invariant mass is a reasonable estimator of the true dis-

tribution for WZ invariant masses smaller (larger) than

the position of the resonance.

In order to isolate the contribution of the new charged

states, we imposed a cut on Mrec,min

WZ

400 GeV ≤ Mrec, min

WZ

≤ 550 GeV,for MV±

1

= 500 GeV

600 GeV ≤ Mrec, min

WZ

,for MV±

1

= 700 GeV

(10)

The effect of these cuts on the WZ invariant mass

spectrum can be seen in the right panel of Fig. 1 for

MV±

1

= 500 GeV and 700 GeV. As seen in the figure af-

ter these cuts, a good fraction of the peak signal events

are retained.

The predicted cross sections for the signal and SM

backgrounds after cuts (5)–(10) are listed in Table I.

From these numbers we conclude that the above cuts lead

to a good signal to background ratio of ≃ 2.4 (1.5) for

MV±

1

= 500 (700) GeV. Thus, a clear observation (5σ)

of the new charged resonances V±

mass in the leptonic channel requires a modest integrated

luminosity of 15 (66) fb−1, which can be achieved in the

low luminosity run of the LHC or in the early stages of

the high luminosity run.

Similar sensitivity could be obtained by cutting, in-

stead, on Mrec,max

WZ

, though in general the cuts have to

be chosen tighter and dependent on the MV±

This is so because the SM background is a decreasing

function of the WZ mass, therefore when cutting on

the maximum reconstructed WZ mass, the number of

miss–reconstructed background events in the signal re-

gion tends to be larger.

After the new state coupled to WZ is discovered, it is

important to probe its spin. The best way to accomplish

that is to study angular correlations of the final state par-

ticles. In principle, useful information on the spin could

be also extracted from the production cross section, how-

ever, at the LHC one measures the production cross sec-

tion times the decay branching ratio, requiring additional

information to disentangle these quantities. Here we em-

1with a 500 (700) GeV

1

mass.

Page 4

4

MV1±=500 GeV

MV1±=500 GeV

MV1±=700 GeV

FIG. 1: Left : WZ invariant mass distribution reconstructed

using the largest (dash-dotted line) and smallest (full line) es-

timate [see Eq. (9)], as well as the true distribution (shadowed

region) for two values of MV±

and minimum (line) reconstructed WZ invariant mass distri-

butions after the cuts in Eq. (10).

1. Right: The true (shadow)

ploy two methods to unravel the spin of the new charged

state based exclusively on the kinematic distribution of

the final state particles. In the first method, we contrast

the kinematic distributions of the charged leptons pro-

duced in the decay of vector and scalar charged states,

much in the spirit of the analysis carried out to study

the spin of supersymmetric particles at the LHC [30, 31].

A virtue of this method is that it does not rely on the

reconstruction of the neutrino momentum (besides the

invariant mass cut). In our second analysis, we used the

reconstructed neutrino momentum to obtain the polar

angle of the produced Z’s in the WZ center–of–mass sys-

tem.

In order to contrast the spin-0 and spin-1 resonances,

we focused on the leptons whose momenta can be well

determined. In previous studies [30], it has been shown

that a convenient variable for such analysis is

cosθ∗

ℓℓ≡ tanh

?∆ηℓℓ

2

?

, (11)

where ∆ηℓℓ is the rapidity difference between the same

charge leptons. Notice that this quantity is invariant un-

der longitudinal boosts. We plot in Fig. 2 the expected

cosθ∗

ℓℓdistributions for the SM background and the pro-

duction of scalar and vector resonances with mass 500

(700) GeV in the left (right) panel after cuts (5)–(10). In

obtaining this figure, we imposed that the cross section

for the production of spin-0 resonances is the same of the

one for spin-1 states. We also display the SM background

alone to show its impact on the distributions.

These figures clearly show that the cosθ∗

for spin-1 and and spin-0 resonances are quite different

and they can be used to quantify the required integrated

luminosity needed to discriminate between them at a

given CL. A simple χ2analysis of the distributions shown

ℓℓdistribution

in Fig. 2 yields a 99% CL discrimination between spin-0

and spin-1 resonances of mass 500 (700) GeV for an in-

tegrated luminosity of 170 (215) fb−1, considering only

the statistical errors.

In order to eliminate possible normalization systemat-

ics in the angular distributions, we have also estimated

the integrated luminosity needed to decipher the spin of

the new charged state by constructing an angular asym-

metry

Aℓℓ=σ(|cosθ∗

σ(|cosθ∗

Considering only the statistical errors, this asymmetry

allows a 99% CL distinction between spin-0 and spin-

1 resonances of mass 500 (700) GeV for an integrated

luminosity of 440 (560) fb−1. With these choices of inte-

grated luminosities, we have Aℓℓ(scalar) = +0.104±0.05

and Aℓℓ(vector) = −0.07 ± 0.05, for MV±

and Aℓℓ(scalar) = −0.036 ± 0.06 and Aℓℓ(vector) =

−0.27±0.06, for MV±

1

only the statistical errors.

We also studied the resolving power of the recon-

structed Z polar angle (θWZ) distribution evaluated in

the WZ center–of–mass frame. We display in Fig. 3 the

cosθWZ distribution for spin-1 charged states after cuts

(5)–(10). Since the reconstructed neutrino momentum

has a twofold ambiguity, there is also a twofold ambiguity

in the reconstructed Z polar angle in the WZ center–of–

mass frame which lead to the two distributions shown in

the figure. The dashed (dotted) lines correspond to the

reconstructed Z polar angle distribution using the neu-

trino momentum that leads to the maximum (minimum)

WZ invariant mass. As we can see, the two distributions

differ appreciably for cosθWZ close to zero. However, as

shown in the figure, the average of the two distributions

has a better behavior in the central region of the detec-

tor and resembles the true distribution. Consequently,

we have considered the average of the two reconstructed

distributions as discriminating observable.

Fig. 4 depicts such averaged distributions for charged

vector and scalar resonances, where we are included the

SM background prediction for assessment of its impact

on the spin determination. Clearly, the production of V±

leads to more WZ pairs produced at small polar angles

while the scalar resonance leads to more central events,

as expected. As above, in order to quantify the discrimi-

nating power between the scalar and vector productions

we constructed the asymmetry

ℓℓ| < 0.5) − σ(|cosθ∗

ℓℓ| < 0.5) + σ(|cosθ∗

ℓℓ| > 0.5)

ℓℓ| > 0.5).(12)

1

= 500 GeV,

= 700 GeV, where we have quoted

1

AWZ=σ(|cosθWZ| < 0.5) − σ(|cosθWZ| > 0.5)

σ(|cosθWZ| < 0.5) + σ(|cosθWZ| > 0.5).

(13)

We find that for the new state mass of 500 (700) GeV,

it is necessary 400 (550) fb−1to separate the two pos-

sibilities at 99% CL. With these choices of integrated

luminosities, we have AWZ(scalar) = +0.057 ± 0.05 and

AWZ(vector) = −0.125 ± 0.05, for MV±

1

= 500 GeV,

Page 5

5

SM background

L=300 fb-1

MV1±=500 GeV

SM background

MV1±=700 GeV

L=300 fb-1

FIG. 2: cosθ∗

error bars), and the production of charged scalars (solid line). In the left (right) panel the mass of the new resonance is 500

(700) GeV and we considered an integrated luminosity of 300 fb−1.

ℓℓdistribution for the SM background (dashed line), the production of a vector charged resonance (solid line with

and AWZ(scalar) = −0.04 ± 0.06 and AWZ(vector) =

−0.28±0.06, for MV±

1

quoted only the statistical errors. Furthermore the use of

a χ2analysis of the cosθWZdistribution is able to reveal

the spin of the new state at 99% CL for an integrated

luminosity of 150 (220) fb−1, for MV±

= 700 GeV, where we have again

1

= 500 (700) GeV.

IV.CONCLUSIONS

The observation of new charged vector resonances in

Higgsless models decaying into WZ pairs can be carried

out via weak boson production at the LHC and their

subsequent decays into charged leptons [28, 29]. Here

we show how the LHC will be able to determine the

spin of these new states using two different methodolo-

gies. In the first method, only the observed charged lep-

tons are used to discriminate between spin-0 and spin-

1 resonances using the variable defined in Eq. (11). In

this case, an integrated luminosity of 170 (215) fb−1is

needed to establish the spin of the 500 (700) GeV reso-

nance at 99% CL via a χ2analysis of the cosθ∗

bution. On the other hand, the use of the asymmetry

given by Eq. (12) requires 440 (560) fb−1to determine

the new resonance spin for a mass 500 (700) GeV. The

second method is based on the two–folded reconstruction

ℓℓdistri-

of the escaping neutrino momentum to obtain the WZ

polar angle distribution in its center–of–mass frame. This

procedure requires a good understanding and calibration

of the hadronic calorimeters, therefore, being subject to

larger systematic uncertainties. We determined that the

later method can distinguish between spin-1 and spin-0

states at 99% CL for integrated luminosities of 150 (220)

fb−1for MV±

1

= 500 (700) GeV, respectively, when we

perform a χ2fit of the cosθWZdistribution. If we use the

asymmetry defined in Eq. (13) to perform the analysis,

the integrated luminosities are 400 and 550 fb−1, respec-

tively. All results above only account for statistical errors

and the inclusion of systematic uncertainties may render

the efficiencies of the two methods rather similar.

Acknowledgments

We thank G. Burdman for a careful reading of the

manuscript. This work was supported in part by Con-

selho Nacional de Desenvolvimento Cient´ ıfico e Tec-

nol´ ogico (CNPq) and by Funda¸ c˜ ao de Amparo ` a Pesquisa

do Estado de S˜ ao Paulo (FAPESP); M.C.G-G is sup-

ported by National Science Foundation grant PHY-

0354776 and by Spanish Grants FPA-2007-66665-C02-01,

and FPA2006-28443-E.

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MV1±=500 GeV

MV1±=700 GeV

FIG. 3: cosθWZ distributions for a vector resonance of 500 GeV (left panel) and 700 GeV (right panel). The dashed (dotted)

line stands for the reconstructed distribution using the neutrino momentum that leads to the maximum (minimum) WZ

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