Measurements of neutral vector resonance in Higgsless models at the LHC

0.33 MB·English

by  Masaki Asano

TU-874
Measurements of neutral vector resonance in
1
Higgsless models at the LHC
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n
a
J Masaki Asanoa and Yasuhiro Shimizua,b

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aDepartment of Physics, Tohoku University, Sendai 980-8578, Japan

] bIIAIR, Tohoku University, Sendai 980-8578, Japan
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2 Abstract
v
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In Higgsless models, new vector resonances appear to restore the unitarity of
3
2 theWLWL scattering amplitudewithouttheHiggs boson. Intheidealdelocalized
5 threesiteHiggsless model,oneoflargeproductioncrosssection oftheneutralvec-
0. tor resonance (Z′) at the Large Hadron Collider is the W-associated production,
1 pp Z′W± W∓W±W±. Although the dileptonic decay channel, lνl′ν′jj, is
0 → →
experimentally clean to search for the Z′ signals, it is difficult to reconstruct the
1
: Z′ invariant mass due to the two neutrinos in the final state. We study collider
v
i signatures of Z′ using the MT2-Assisted On-Shell (MAOS) reconstruction of the
X
missing neutrino momenta. We show the prospect of the Z′ mass determination
r
a in the channel, lνl′ν′jj, at the Large Hadron Collider.
1 Introduction
The Large Hadron Collider (LHC) experiments are now operating. At the LHC, a new
electroweak signalwillbediscovered becausetheunitarity oftheW W scatteringamplitude
L L
is violated atthescalehigheraround1TeVduetotheE2 dependence. Oneof thecandidates
is a signal from a scalar SU(2) doublet, called the Higgs boson. Due to the contribution
L
from the Higgs boson, the E2 dependence of the W W scattering amplitude vanishes in the
L L
standard model (SM).
Ontheotherhand,itis alsopossibletomaintain theunitarity withouttheHiggs scalar in
Higgsless models [1, 2]. In Higgsless models, vector resonances which are responsible for the
restoration of the unitarity of the W W scattering amplitude will be produced at the LHC.
L L
The masses are less than around 1 TeV to avoid the unitarity violation, but such particles
are strictly constrained by direct observation if their couplings to SM fermions are similar
to the SM ones [3]. Also the coupling induces a large correction to electroweak precision
measurements at the tree level. To avoid the constraints, the couplings should be suppressed
and it is realized by the fermion delocalization [4, 5, 6, 7, 8, 9]. The vector resonances
therefore have only small coupling to the SM fermions in Higgsless models.
Fermiophobic vector resonances can be produced mainly by the weak gauge boson as-
sociated process or the vector boson fusion process and mainly decay into the weak gauge
bosons at the LHC. The measurements of charged vector resonance have been studied [10,
11, 12, 13, 14]. However, in a case that the W-associated production is dominant, the mass
determination of the neutral vector resonance (Z′) is very difficult because there are three W
bosons in the final state. A way using W±W±W∓ l±νl′±ν′jj mode is proposed by Tao
→
Han et.al.[14], and they showed that the mass can be read off by an endpoint of the m(ljj)
distribution from the parton level study.
In this paper, we show that neutral vector resonance can be reconstructed even in
WWW lνl′ν′jj finalstateusingM AssistedOn-Shell(MAOS)reconstruction ofmissing
T2
→
momenta [15, 16, 17]. Since MAOS momenta equal true neutrino four momenta at the M
T2
[18] endpoint of WW lνl′ν′ system, the Z′ mass will be determined by the peak of the
→
invariant mass of reconstructed W±W∓ bosons.
This article is organized as follows. In the next section, we briefly review the Higgsless
models. In our study, we focus on the three site Higgsless model [19] as a benchmark model.
In section 3, we briefly review the MAOS momenta. The Monte Carlo simulation study for
measurements of neutral vector resonance at the LHC are discussed in section 4, where we
2
show the mass will be measured with an integrated luminosity of 100 fb−1 at √s = 14TeV.
Section 5 is devoted to summary and discussion.
2 Higgsless models
In continuum five-dimensional gauge theory, the cancellations of E2 and E4 dependence of
W W scattering amplitude are guaranteed by following sum rules [1, 20]:
L L
∞
g2 = g g2 g2 , (1)
ZiWW WWWW − ZWW − γWW
i=1
X
∞
3 g2 M2 = 4g M2 3g2 M2,
ZiWW Zi WWWW W − ZWW Z
i=1
X
where g , g and g are the SM WWWW, WWZ and γWW coupling con-
WWWW ZWW γWW
stants, respectively. The Z represents the i-th KK excitation and Z is also denoted Z′ in
i 1
this paper. The Z′ mass should be less than the unitarity violation scale √8πv 1.2 TeV if
∼
there is no Higgs boson nor other vector resonances.
In this paper, we study the collider signatures of the three site Higgsless model [19] as
a benchmark model of Higgsless models. The model contains many essential ingredients of
Higgsless models and a gauge invariant four-dimensional effective theory of Higgsless models.
We briefly review the three site Higgsless model.
The three site Higgsless model is a deconstructed Higgsless model with only three sites ∗.
The model is based on two nonlinear (SU(2) SU(2))/SU(2) sigma models. The non-linear
×
sigma fields, U and U , are given as
1 2
U = eiπiaτa/fi for i = 1,2, (2)
i
whereπa areNambu-Goldstonebosonsandτa arethePaulimatrices. Themodelincorporates
i
SU(2) SU(2) U(1) gauge symmetry with gauge coupling strengths g , g and g , respec-
0 1 2
× ×
tively. The vacuum expectation values (VEVs) f and f break the SU(2) SU(2) U(1)
1 2
× ×
∗ The gauge sector is equivalent to the Breaking Electroweak Symmetry Strongly (BESS) model [21, 22]
one.
3
Particles SU(2) SU(2) U(1)
0 1 2
q , l 2 1 1/6, 1/2
L0 L0
−
q , l 1 2 1/6, 1/2
L1 L1
−
q , l 1 2 1/6, 1/2
R1 R1
−
u , d , e 1 1 2/3, 1/3, 1
R2 R2 R2
− −
Table 1: Quantum numbers of fermion fields.
gauge symmetry to U(1) :
em
2 f2 2 1
= i Tr (D U )†(DµU ) Tr[V Vµν], (3)
Lgauge 4 µ i i − 2 iµν i
Xi=1 h i Xi=0
τa
D U ∂ U +ig V U ig U V , V = Va for i =0,1,
µ i ≡ µ i (i−1) (i−1)µ i− i i iµ iµ 2 iµ
a=1,2,3
X
τ3
V ∂ V ∂ V +ig [V ,V ], V = V3 ,
iµν ≡ µ iν − ν iµ i iµ iν 2µ 2 2µ
where the Va is the gauge field for the SU(2) gauge group at the site 0(1) and V3 is the
0(1) 2
gauge field for the U(1) gauge group at the site 2 which is embedded as the τ generator
3
of SU(2). Therefore, this model contains charged and neutral gauge bosons, W′ and Z′, in
addition to the SM W, Z and photon. The combinations of V1,2 correspond to the W′ and
0,1
W. On the other hand, the combination of V3 are the Z′, Z and photon, respectively. For
0,1,2
simplicity, we take f = f =√2v in this study.
1 2
The left-handed fermions ψ and ψ are SU(2) doublets coupling to the groups at the
L0 L1
sites 0 and 1, respectively. On the other hand, the right handed fermions ψ are SU(2)
R1
doublets coupling to the group at site 1 and u , d and e are singlets coupling to the
R2 R2 R2
group at site 2. The quantum numbers of the fermions are shown in Table 1. The Yukawa
couplings are written by
λ′ 0 u
= λf ψ¯ U ψ +f ψ¯ U u R2 +Mψ¯ ψ +h.c. (4)
LYukawa 1 L0 1 R1 2 L1 2(cid:18) 0 λ′d(cid:19)(cid:18)dR2(cid:19) L1 R1
ε 0 ψ
= ψ¯ ψ¯ M L R1 +h.c.,
L0 L1 1 ε u ,d
uR,dR R2 R2
(cid:18) (cid:19)(cid:18) (cid:19)
(cid:0) (cid:1)
where Mε = λf m and Mε = λ′ f m′ . In this paper, we assume that the m
L 1 ≡ uR,dR u,d 2 ≡ u,d
and M are universal for the generation and quark-lepton.
In the limit, g /g 1 and g /g 1, the gauge boson masses are given by
0 1 2 1
≪ ≪
g2 1 g 2 1 g 2
M 0v2 1 0 , M g2v2 1+ 0 , (5)
W ∼ 4 − 4 g W′ ∼ 1 4 g
" (cid:18) 1(cid:19) # " (cid:18) 1(cid:19) #
g2 (c2 s2)2 g 2 1 g 2
MZ ∼ 4c02v2 1− 4−c2 g0 , MZ′ ∼ g12v2 1+ 4c2 g0 .
" (cid:18) 1(cid:19) # " (cid:18) 1(cid:19) #
4
Here s= sinθ, c= cosθ, and tanθ = g /g . In the ε 1 limit, fermion masses are written
2 0 L
≪
as the following:
mm′
m t,b , M M2+m′2, (6)
t,b ∼ M2+m′2 T,B ∼ t,b
t,b q
q
where we show the masses of the third-generation quarks as an example. The M (M ) is
T B
the new heavy top(bottom) quark mass.
The couplings between the light fermions and the heavy gauge bosons are constrained by
direct heavy gauge boson search and the electroweak precision measurements. The coupling
can be small by delocalizing fermion and ε is a parameter which denotes the degree of the
L
delocalization. In the case, ε = (1+ε2 )2 (g /g )2/2+ ((g /g )4)+ , the coupling
L fR { 0 1 O 0 1 ···}
constants are given by
g = 0. (7)
ffW′
This case is called ideal delocalization in which the precision electroweak corrections are
minimized at tree level [8] †. In the ideal delocalization case, the lower bound of W′ mass,
380 GeV, is given by the bound on the triple gauge vertex from the LEP-II experiments [19].
3 MAOS momentum
In this section, we briefly review the MAOS momentum [15, 16, 17]. The MAOS momentum
is defined using the M formula [18]. In the WW l(p)ν(k)l′(p′)ν′(k′) system, the M
T2 T2
→
valuable is written by
M2 = min max M2(p ,k ),M2(p′ ,k′ ) , (8)
T2 T T T T T T
kT+k′T=p/T
(cid:2) (cid:8) (cid:9)(cid:3)
where p/ is the missing transverse momentum and the transverse mass, M , is defined by
T T
M2(p ,k ) = 2( p k p k ), (9)
T T T | T|| T|− T · T
where the lepton masses are neglected.
The MAOS momenta, kMAOS and k′MAOS, are defined by the following. Assuming p/ =
T
(p +p′ ), the transverse momenta of kMAOS and k′MAOS are defined by
− T T
kMAOS = p′ , k′MAOS = p , (10)
T − T T − T
† At the1-loop level, the parameter does not satisfy theelectroweak precision measurements [23]. But we
take the parameter in the following analysis since the correction to the signal in our collider study is small
even if we takea parameter which satisfies theelectroweak precision measurements at the1-loop level.
5
m [GeV] m [GeV] M [GeV] g σ(Z′W) [fb] σ(Z′qq) [fb] Br(Z′ WW)
Z′ W′ Z′WW
| | →
380 378 4000 0.071 593 144 97%
500 498 4000 0.054 178 42 99%
Table2: Representativepointsinthisstudy. Theσ(Z′W)andσ(Z′qq)arethepp Z′W production
′ →
cross section and pp Z qq production cross section, respectively.
→
and
M (p ,p′ ,p/ ) = √2 p kMAOS p kMAOS , (11)
T2 T T T | T|| T |− T · T
q
= √2 (cid:0) p′ k′MAOS p′ k′MAOS(cid:1) .
| T|| T |− T · T
q
(cid:0) (cid:1)
The MAOS momenta are also required to satisfy the following conditions in the WW
→
l(p)ν(k)l′(p′)ν′(k′) system:
kMAOS 2 = k′MAOS 2 = 0, (12)
p+(cid:0)kMAOS(cid:1)2 = (cid:0)p′+k′M(cid:1)AOS 2 = M2 .
T2
(cid:0) (cid:1) (cid:0) (cid:1)
From these equations, the longitudinal momenta of kMAOS and k′MAOS are also determined
by
kMAOS k′MAOS
kMAOS( ) = | T |p , k′MAOS( )= | T |p′ . (13)
L ± p L L ± p′ L
| T| | T|
AttheM endpoint,theMAOS momentabecomeequalto thefinalstate neutrinomomenta
T2
k,k′, respectively.
In the next section, we show that the fermiophobic Z′ can be reconstructed using MAOS
momenta of neutrinos at the LHC through Monte Carlo simulations. The Z′ mass can be
measured by the invariant mass peak of the reconstructed WW.
4 Monte Carlo Simulation
WestudythepossibilityofZ′ reconstructionthroughMonteCarlosimulationsinthissection.
We investigate the ideal delocalized three site Higgsless model as a benchmark model and
the parameters at the representative points are summarized in Table 2. For the Monte Carlo
simulation, we have produced the signal parton events by Madgraph/Madevent [24, 25] and
they have been hadronized by PYTHIA [26]. For the SM backgrounds, we have generated
the events using ALPGEN [27] and HERWIG [28, 29]. Our detector simulation is based on
ACERDET [30]. Hereafter we assume an integrated luminosity of = 100 fb−1.
L
6
W∓ j W∓ l∓
j′ ν
Z′ l± Z′ ν′
W± W± ν W± W± l′±
ν′ j
j′
W± l′± W±
Figure 1: (Left) Feynman diagram for the same sign dilepton mode. (Right) Feynman
diagram for the opposite sign dilepton mode.
In our analysis, we concentrate on the W-associated production depicted in Fig. 1,
especially in the following dilepton mode,
W± (W+W−) (l±ν)((l±ν)(jj)) (same sign),
pp W±Z′ → (14)
→ → W± (W+W−) (jj)((l±ν)(l∓ν)) (opposite sign),
(cid:26) →
because the large SM backgrounds can be reduced in the dilepton modes. In particular, it is
shown that the tt¯background is significantly reduced for the same sign dilepton mode [14].
In the signal mode, there are three W bosons; two W bosons decay leptonically and one
W decays hadronically. In order to reconstruct the hadronically decaying W, we require the
following cuts:
at least two and less than three hard jets with p > 20 GeV,
T
•
65 GeV < m < 95 GeV,
jj
•
where the m is the invariant mass of two hard jets. We also impose b-jet veto to reduce tt¯
jj
events.
To reconstruct the two W bosons which decay leptonically, we use neutrino MAOS
momenta which are defined by a M valuable using two leptons and missing momenta.
T2
In the same (opposite) sign charge mode, we require the following:
two leptons with the same (opposite) charge with p > 10 GeV,
T
•
p/ > 50 GeV.
T
•
In the same sign dilepton mode, the requirement of the same charge lepton reduce the tt¯
events significantly. On the other hand, huge tt¯ events still remain for the opposite sign
7
Signal 461
top BG 10216
-1b
0f
0
1
V /
e
G
0
1
nts /
e
v
E
Mjj [GeV]
T2
jj
Figure 2: The M distribution in the opposite sign dilepton mode for m = 380 GeV
T2 Z′
(white) and the tt backgrounds (hatched). Here the integrated luminosity is 100 fb−1 and
the mass of the missing particle is set to m .
W
dilepton mode. To reduce the tt¯events, we also define another M valuable, Mjj, in which
T2 T2
we definethe ”effective missingp ”, P/eff = p/ +p +p andthe mass of missingparticle,
T T T Tl1 Tl2
jj
m = m , in the opposite charge mode. The M valuable should have a maximum value
X W T2
at thetop quarkmasstaking themissingparticle mass, m = m , becausewedeal withtwo
X W
jj
W bosonsdecaying leptonically as missingparticles. InFig. 2, weshow theM (m = m )
T2 X W
distributions for the signal with m = 380 GeV and the tt events after the jet and lepton
Z′
cuts. We can see a sharp endpoint around the top quark mass for the tt events while the
jj jj
signal events give larger M . Therefore, we impose M (m = m ) > 200 GeV to cut
T2 T2 X W
the tt¯events. The procedure reduces the combinatorial ambiguity of the jets and the leptons
jljl
than a procedure using M which should have a maximum value at the top quark mass
T2
taking the missing particle mass, m = 0 GeV.
X
In addition, we also impose other cuts, the value of M , which is defined as a scalar sum
eff
of the visible and the missing momenta [31], and invariant mass of two leptons, m , listed in
ll
Table 3. The m cuts reduce the Z boson and tt¯backgrounds because a lepton from a top
ll
quark decay is softer than a lepton in the signal events. In Table 4 (5), we show the number
of events after the selection cuts for the same (opposite) sign mode.
From the MAOS momenta, we can reconstruct the invariant mass of the Z′ as follows:
(p+kMAOS +p +p )2 (same sign),
m2 = j1 j2 (15)
Z′ (p+kMAOS +p′+k′MAOS)2 (opposite sign).
(cid:26)
In both modes, there is a two-fold ambiguity to reconstruct the Z′ invariant mass from two
8
m = 380 GeV m = 500 GeV
Z′ Z′
same M > 500 GeV and m > 130 GeV M > 500 GeV and m > 130 GeV
eff ll eff ll
opposite M > 600 GeV and m > 110 GeV M > 700 GeV and m > 110 GeV
eff ll eff ll
Table 3: Cuts used in the analysis for the same and the opposite sign lepton modes.
W bosons. In the same sign mode, there are two choices to combine the lepton momenta
with the hadron momenta. We choose the combination which gives the smaller m in our
Z′
analysis. On the other hand, we reconstruct Z′ invariant mass from two W bosons which
decay leptonically in order to confirm the charge of the Z′ in the opposite sign mode.
In Figs. 3 and 4, we show the invariant mass distributions of Z′ in the same and opposite
sign dilepton mode for m = 380 GeV, respectively. The hatched histograms are the SM
Z′
backgrounds. Although the MAOS momenta become equal to the true neutrino momenta
only at the M endpoint, M 80 GeV, we use the MAOS momenta in wide M regions
T2 T2 T2
≃
and plot the invariant mass distributions of Z′ for M > 60,40,20,0 GeV. ‡ In Fig. 3 we
T2
can see the peaks around the true Z′ mass regions for all the cases. The shape becomes
sharper when we use the MAOS momenta in the higher M regions. However, the number
T2
jj
of the events becomes smaller. Thanks to the M cut, we can see clear signal peaks around
T2
the true m value even in the opposite sign mode. Although the shapes of the invariant
Z′
distributions are slightly irregular compared with the same sign mode, we can determine the
Z′ mass from the peak.
In Figs. 5 and 6, we show the invariant mass distributions of Z′ in the same and opposite
sign dilepton mode for m = 500 GeV, respectively. Since the production cross section
Z′
is smaller compared with the m = 380 GeV case, the numbers of events are limited if
Z′
we use the tight M cut. In the opposite sign mode, we cannot see clear peaks for the
T2
M > 20,40,60 GeV cases. However, we can see the peaks around the true m region even
T2 Z′
for m = 500 GeV in the both modes.
Z′
5 Summary and Discussion
In this paper, we have studied the search for the neutral vector resonance, focusing on
a fermiophobic case at the LHC. Such fermiophobic vector bosons are predicted by per-
turbative TeV scale scenarios without the Higgs boson, and can be produced in the W-
‡ When the Z′ is heavy enough to decay to two on-shell W bosons, there is the other definition of the
MAOS momenta [15]. Even if we take the MAOS momenta, the distributions are not drastically changed in
our studywith 100 fb−1.
9
Selection cut Signal top BG W boson BG
(380, 500 GeV)
jet # of jets (P > 20 GeV)=2 (4844, 1451) 774624 5862
T
65 GeV < m < 95 GeV (1116, 313) 124142 1485
jj
b veto (1069, 299) 44009 1410
lepton 2 same charge leptons (P > 10 GeV) (284, 96) 1234 91
T
p/ > 50 GeV (257, 90) 777 64
T
other M > 500 GeV (207, 85) 21 9
eff
m > 130 GeV (167, 74) 0 5
ll
Table 4: Number of events after selection cuts for the same sign mode with an integrated
luminosity = 100−1 fb.
L
Selection cut Signal top BG W boson BG
(380, 500 GeV)
jet # of jets (P > 20 GeV)=2 (4844, 1451) 774624 5862
T
65 GeV < m < 95 GeV (1116, 313) 124142 1485
jj
b veto (1069, 299) 44009 1410
lepton 2 opposite charge leptons (P > 10 GeV) (508, 141) 15845 993
T
p/ > 50 GeV (461, 130) 10216 533
T
jj jj
M M (289, 99) 125 44
T2 T2
other M > (600,700) GeV (254, 83) (25, 9) (16, 12)
eff
m > 110 GeV (206, 67) (9, 1) (11, 8)
ll
Table 5: Number of events after selection cuts for the opposite sign mode with an integrated
luminosity = 100−1 fb.
L
10