Deciphering the spin of new resonances in Higgsless models

Abstract

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. Comment: 7 pages, 4 figures. Version published in Physical Review D

Full text

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 GeV0.36 0.320.300.25
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.
[1] B. W. Lee, C. Quigg, and H. B. Thacker, Phys. Rev.
Lett. 38, 883 (1977).
[2] B. W. Lee, C. Quigg, and H. B. Thacker, Phys. Rev. D
16, 1519 (1977).
[3] C.Csaki, C.Grojean,H. Murayama,L.Pilo,
and J. Terning, Phys. Rev. D 69, 055006 (2004)
[arXiv:hep-ph/0305237].
[4] C. Csaki, C. Grojean, L. Pilo, and J. Terning, Phys. Rev.
Lett. 92, 101802 (2004) [arXiv:hep-ph/0308038].
[5] Y. Nomura, J. High Energy Phys. 0311, 050 (2003)