Two Higgs doublet model with vectorlike leptons and contributions to pp → W W and H → W W
HJE
Two Higgs doublet model with vectorlike leptons and contributions to pp
Radovan Derm sek 0 1 2 3
Enrico Lunghi 0 1 3
Seodong Shin 0 1 3
0 Seoul National University , Seoul 151747 , Korea
1 Bloomington , IN 47405 , U.S.A
2 Department of Physics and Astronomy and Center for Theoretical Physics
3 Physics Department, Indiana University
We study a two Higgs doublet model extended by vectorlike leptons mixing with one family of standard model leptons. Generated heavy and light leptons can dramatically alter the decay patterns of heavier Higgs bosons.
Higgs Physics; Beyond Standard Model

We focus on pp ! H !
4
! W
, where 4 is a new neutral lepton, and study
possible e ects of this process on the measurements of pp ! W W and H ! W W since it
leads to the same
nal states. We discuss predictions for contributions to pp ! W W and
H ! W W and their correlations from the region of the parameter space that satis es all
available constraints including precision electroweak observables and from pair production
of vectorlike leptons. Large contributions, close to current limits, favor small tan
region
of the parameter space. We nd that, as a result of adopted cuts in experimental analyses,
the contribution to pp ! W W can be an order of magnitude larger than the contribution
to H ! W W . Thus, future precise measurements of pp ! W W will further constrain the
parameters of the model. In addition, we also consider possible contributions to pp ! W W
from the heavy Higgs decays into a new charged lepton e4 (H ! e4 ! W
Higgs decays, and pair production of vectorlike leptons.
), exotic SM
1 Introduction 2
Model
3 Branching ratios
2.1
Couplings of the Z and W bosons
2.2 Couplings of the Higgs bosons 4.1 4.2 4.3
and direct production
The muon lifetime
Invisible width of Z Direct production of vectorlike leptons
4 Parameter space scan and constraints from precision electroweak data
5
Main results: contributions of H ! W
6 Contributions from H ! e4
7 Contributions from SMlike Higgs boson
8 Contributions from DrellYan production of vectorlike leptons
9 Conclusions
1
Introduction
Among simple extensions of the standard model (SM) are those with extended Higgs sector
and extra vectorlike leptons near the electroweak (EW) scale. Since masses of vectorlike
leptons are not related to their Yukawa couplings, in the absence of mixing with SM leptons,
they are not strongly constrained by experiments. However, even small Yukawa couplings
between SM leptons and vectorlike leptons can signi cantly a ect a variety of processes
and can dramatically alter the decay patterns of heavier Higgs bosons.
We consider an extension of the two Higgs doublet model typeII by vectorlike pairs of
new leptons: SU(2) doublets LL;R, SU(2) singlets EL;R and SM singlets NL;R, where LL
and ER have the same hypercharges as SM leptons. We further assume that the new leptons
mix only with one family of SM leptons and we consider the mixing with the second family
as an example. The mixing of new vectorlike leptons with leptons in the SM generate
avor violating couplings of W , Z and Higgs bosons between heavy and light leptons.
These couplings can result in new decay modes for heavy CP even (or CP odd) Higgs
{ 1 {
and H ! e4 , where e4 and 4 are the lightest new charged and neutral
leptons. These decay modes, when kinematically open, can be very important, especially
when the mass of the heavy Higgs boson is below the tt threshold, about 350 GeV, and the
this case, avor violating decays H !
4
or H ! e4
compete only with H ! bb (for
su ciently heavy H also with H ! hh) and can be large or even dominant. Subsequent
, e4 ! Z , e4 ! h and 4 ! W , 4 ! Z
, 4 ! h
lead to
In this paper, we focus on pp ! H !
4
! W
and study possible e ects of
this process on the measurements of pp !
!
W W and H
W W since it leads to the
presented in terms of the Higgs mass, the mass of 4 and the product of branching ratios
predictions for contributions to pp !
W W and H
! W W and their correlations from
the region of the parameter space that satis es all available constraints including precision
electroweak observables [3] and constraints from pair production of vectorlike leptons [4].
Large contributions, close to current limits, favor small tan
region of the parameter
space. We nd that, as a result of adopted cuts in experimental analyses, the contribution
to pp ! W W can be an order of magnitude larger than the contribution to H ! W W . In
addition, we also consider possible contributions to pp ! W W from H ! e4
! W
from similar processes involving SMlike Higgs boson and from pair production of vectorlike
leptons.
Vectorlike leptons near the electroweak scale provide a very rich phenomenology and
were studied in a variety of contexts. Most of the previous studies would apply also to
the two Higgs doublet model we consider here since we assume typeII couplings of Higgs
doublets to fermions relevant for supersymmetric extensions and we also consider the limit
when the light Higgs is SMlike which is relevant for SM extensions by vectorlike fermions.
For example, analogous processes involving SMlike Higgs boson decaying into 2`2 or 4`
through a new lepton were previously studied in ref. [5] and the 4` case also in ref. [6].
Possible explanation of the muon g
2 anomaly with vectorlike leptons was studied in [7, 8].
Further extensions with vectorlike quarks and possibly Z0 are straightforward and o er
possibilities to explain anomalies in Zpole observables [9{12]. In addition, extensions
with complete vectorlike families were considered that provide an understanding of
values of gauge couplings from IR
xed point behavior and threshold e ects of vectorlike
fermions, as in insensitive uni cation [13, 14]. Many studies were also done in
supersymmetric framework, see for example refs. [15{20], and in various frameworks the constraints
from precision electroweak data have been analyzed [21{27]. Further discussion and more
references can be found in a recent review [28].
This paper is organized as follows. In section 2 we present two Higgs doublet model
typeII with vectorlike leptons mixing with one family of the SM leptons and derive formulas
for couplings of Z, W and Higgs bosons to leptons. In section 3 we discuss branching
{ 2 {
SU(2)L
U(1)Y
Z2
2
1
2
+
doublets. The electric charge is given by Q = T3 + Y , where T3 is the weak isospin, which is +1=2
for the rst component of a doublet and 1=2 for the second component.
H
! e4
!
W
remarks in section 9.
2
Model
ratios of the heavy Higgs boson H and neutral lepton 4 and nd approximate expressions
in section 6, from the SMlike Higgs boson in section 7 and from
pair production of vectorlike leptons in section 8. We summarize and present concluding
We consider an extension of a two Higgs doublet model by vectorlike pairs of new leptons:
SU(2) doublets LL;R, SU(2) singlets EL;R and SM singlets NL;R. The quantum numbers of
new particles are summarized in table 1. The LL and ER have the same quantum numbers
as the muon doublet
L (we use the same label for the charged component as for the
whole doublet) and the righthanded muon
R respectively. We further assume that the
new leptons mix only with one family of SM leptons and we consider the mixing with the
second family as an example. This can be achieved by requiring that the individual lepton
number is an approximate symmetry (violated only by light neutrino masses). The results
for mixing with the rst or the third family could be obtained in the same way. The mixing
of new leptons with more than one SM family simultaneously is strongly constrained by
various lepton avor violating processes and we will not pursue this direction here. Finally,
we assume that leptons couple to the two Higgs doublets as in the typeII model, namely
the down sector couples to Hd and the up sector couples to Hu. This can be achieved by
the Z2 symmetry speci ed in table 1. The generalization to the whole vectorlike family of
new leptons, including the quark sector, would be straightforward.
With these assumptions, the most general renormalizable Lagrangian containing
Yukawa and mass terms for the second generation of SM leptons and new vectorlike leptons
and couplings of the neutral leptons, and
nally mass terms for vectorlike leptons. The
components of doublets are labeled as follows:
L =
LL;R =
Hd =
Hu =
(2.2)
L0L;R
LL;R
!
;
H+ !
d
H0
d
;
Hu0 !
Hu
;
L
!
;
Higgs doublet model with qvu2 + vd2 = v = 174 GeV and we de ne tan
where the neutral Higgs components develop the vacuum expectation values hHu0i = vu
and hHd0i = vd. We assume that both are real and positive as in the CP conserving two
vu=vd.
After spontaneous symmetry breaking the resulting mass matrices in the charged and
neutral sectors can be diagonalized and we label the two new charged and neutral mass
eigenstates by e4 and e5 and 4 and 5 respectively. Couplings o
all involved particles to
the Z, W and Higgs bosons are in general modi ed because SU(2) singlets mix with SU(2)
doublets. The avor conserving couplings receive corrections and avor violating couplings
between the muon (or muon neutrino) and heavy leptons are generated. The couplings
resulting from the mixing in the charged sector were discussed in detail in ref. [8] in the
connection with the muon g
2 anomaly. Here we will focus on couplings resulting from
the mixing in the neutral sector. These are also more relevant for the discussion of the
contribution of the Higgs boson decays to pp ! W W .
The mass matrix in the neutral lepton sector is given by:
L0R
NR
C =
A
L0L NL
N vu
L0R
NR
C ;
A
where we inserted R = 0 for the righthanded neutrino which is absent in our framework
in order to keep the mass matrix 3
3 in complete analogy with the charged sector. For
the discussion of couplings it is convenient to de ne vectors
Ra
( R = 0; L0R; NR)T . The mass matrix M
transformation
La
( ; L0L; NL)T and
can be diagonalized by a biunitary
0 0 0
0 0
0
0 C ;
1
A
m 5
resulting in masses for 4 and 5 leaving the muon neutrino massless. The light neutrino
masses can be generated by a variety of ways. Once they are generated, the mixing of
light neutrinos with vectorlike leptons results in corrections to both the masses and mixing
angles controlled by Yukawa couplings in eq. (2.1).
For better understanding of corrections to gauge and Yukawa couplings discussed later,
approximate analytic formulas for diagonalization matrices are useful. These can be
obtained in analogy with those in the charged lepton sector given in ref. [8]. In the limit
N vu; vu; vu
ML; MN
{ 4 {
(2.3)
(2.4)
(2.5)
with ML and MN not close to each other, we nd
and
we nd:
VL = BBB
0
2MN2
N v2
u
MLMN
MN2
ML2
(ML +MN )2vu2
2(MN2
ML2 )2
(ML +MN )vu
MN2 ML2
0
(ML +MN )2vu2
2(MN2
ML2 )2
(ML +MN )vu
MN2 ML2
1
1
0; ML + O( 2); MN + O( 2). However, in our numerical analysis we do not use any
approx= ( N ; ; )vu=(ML; MN ). The mass eigenvalues are
2.1
Couplings of the Z and W bosons
Couplings of the muon and new heavy leptons to the Z and W bosons are modi ed from
their SM values because SU(2) singlets mix with SU(2) doublets. These couplings can be
written in terms of VL and VR, de ned in eq. (2.4), and of the analogue matrices UL and
UR that are related to the charged lepton sector and that were discussed in detail in ref. [8]
(with the replacement v ! vd due to the two Higgs doublet model). The couplings of the
Z boson to charged leptons can be found in ref. [8] and those to neutral leptons follow from
the kinetic terms:
Lkin
LaiD= a La + RaiD= a Ra
= ^La(VLy)aciD= c(VL)cb ^Lb + ^Ra(VRy)aciD= c(VR)cb ^Rb ;
where the vectors of mass eigenstates are ^La
(^ ; ^L4; ^L5)
T and similarly for ^Ra
(^R = 0; ^R4; ^R5)T . We label the components of vectors and diagonalization matrices by
2, 4 and 5 because they correspond to 2nd, 4th and 5th mass eigenstate. The covariant
derivative is given by:
i
g
cos W
Ta3Z ;
where the weak isospin Ta3 is +1=2 for neutral components of SU(2) doublets and 0 for
singlets. De ning couplings of the Z boson to leptons fa and fb as
L
fLa
gZfafb fLb + fRa
L
gZfafb fRb Z ;
R
L
neutrinos ^a and charged leptons e^b as
L
^La g
LW aebe^Lb + ^Ra g
RW aebe^Rb W + + h:c: ;
We assume a CP conserving two Higgs doublet model in the limit with the light Higgs h
being fully standard model like in its couplings to gauge bosons and the heavy CP even
Higgs H having no couplings to gauge bosons. The mass eigenstates h and H in this limit
are related to doublet components as follows (see for example ref. [29]):
h
H
!
=
cos
sin
sin cos
!
p2(Re Hd0
p2(Re Hu0
vd)
vu)
!
:
{ 6 {
we nd:
where
LY
La Y ab Rb Hu0 + h:c:
=
^La(VLy)ac Y cd (VR)db ^Rb Hu0 + h:c: ;
0
0 0 N
0
0
1
C :
A
g
g
2
2
g
g
LW aeb = p
(VLy)a2(UL)2b + (VLy)a4(UL)4b ;
RW aeb = p (VRy)a4(UR)4b :
2.2
Couplings of the Higgs bosons
As a consequence of explicit mass terms for vectorlike leptons, the usual relations between
the mass of a particle and its coupling to Higgs bosons do not apply. The couplings of
neutral Higgs bosons to neutral leptons can be obtained from the following Yukawa terms
in the Lagrangian (2.1):
(2.13)
(2.14)
(2.15)
(2.16)
(2.17)
(2.18)
(2.19)
(2.20)
(2.21)
HJEP02(16)9
The Y matrix is not proportional to the mass matrix given in eq. (2.3) and thus the Higgs
couplings are in general avor violating. De ning couplings of mass eigenstate leptons fa
and fb to CPeven Higgs bosons by
1
2
L
h
p fLa fafb fRb h
H
p fLa fafb fRb H + h:c: ;
1
2
diag(0; ML; MN ), the Higgs boson couplings can be also written as:
h
a b v = B 0 m 4
0 0 0
0 0
0 C
A
where we used vu = v sin . The rst terms in above equations represent the expected
relations between fermion masses and their couplings to Higgs bosons and the second term
represents contributions from the ML;N terms. This form of couplings makes it obvious
that in the absence of vectorlike masses the couplings of h to leptons are fully SMlike,
while couplings of H are enhanced by tan
as expected in the limit we assume.
Couplings to charged leptons follow from Hd0 terms in eq. (2.1) and can be obtained
from those in eqs. (2.23) with replacements: VL;R ! UL;R, Y
! Ye and
!
+ =2, see
also ref. [8] in the case of SM. The corresponding formulas to eqs. (2.24) would show that
couplings of h have the usual SM strength, up to contribution from ML;N , while couplings
of H to charged leptons are suppressed by tan . Finally couplings of the CPodd Higgs
boson, A, copy those of H up to the usual 5 factor.
We collect expressions for the relevant branching ratios for the process pp ! H ! 4
!
and provide several approximate formulas in the limit of small mixing between
neutral leptons discussed in the previous section. These formulas will be useful for qualitative
understanding of results. From now on, we drop the hat notation for mass eigenstates and
also label the mass eigenstates ^L2 and e^2 as
and .
Sizable decay modes of the heavy CP even Higgs boson are 4 , bb and gg for mH <
250 GeV. As discussed in the previous section we assume that H does not have direct
couplings to pairs of gauge bosons and that decay modes to other Higgs bosons are not
kinematically possible. However, our results could be straightforwardly modi ed to account
for additional sizable decay modes of H.
{ 7 {
(2.22)
(2.23)
(2.24)
where the second line is an appropriate approximate formula in the case of singletlike
lepton with mass originating from MN .
The decay width of H ! bb is given by
(H ! bb) =
(where we include both 4
m24
m2H
2
;
ML (VLy)24(VR)44 +
MN (VLy)25(VR)54
v
M N2
+
MN (ML
+ MN )
ML2
(ML
+ MN )2v2 sin2
2(M N2
ML2)2
where the second line is an approximate formula in the limit of small mixing discussed in
section 2. Note, that this limit assume the 4 is mostly the doublet with mass originating
from ML. For an approximate formula corresponding to a singletlike neutral lepton, the
5 should be used instead. This coupling is given by
;
;
nal
(3.1)
(3.2)
(3.3)
(3.4)
(3.5)
(3.6)
(3.7)
(3.8)
(3.9)
( 4 ! h ) =
16
m 4 ( h
4
)
{ 8 {
where mb(mH ) is the running bquark mass evaluated at the scale mH and the correction
factors
qq and
2H can be found in ref. [30]. The decay width of H ! gg is given by
(H ! gg) =
GF S2m3H cot2
= m2H =4mt2 and f ( ) = arcsin2 p
The branching ratio of H ! 4
is then given by
The neutral lepton 4 can decay into standard model leptons and the Higgs, W , and
Z bosons. Neglecting the muon mass, the partial decay width of 4 ! h
is given by:
where
where
where
Finally, the partial decay width of 4 ! Z
Assuming only these decay modes of 4, the branching ratio of 4 ! W
Parameter space scan and constraints from precision electroweak data
and direct production
We perform a scan over all the model parameters introduced in section 2 over the ranges
ML;N 2 [0; 500] GeV;
N ; ;
tan
We x the mass term of the SU(2) singlet charged vectorlike lepton ME = 1000 GeV.
We simplify the decay patterns of the heavy Higgs by requiring m 5 > mH (to avoid
5X channels) and m 4 > mH =2 (to avoid decays into pairs of heavy vectorlike
leptons). Moreover we include mixing exclusively in the neutral sector.
We impose constraints from precision EW data related to the muon and muon neutrino
that include the Z pole observables (Z partial width to +
, the invisible width,
forwardbackward asymmetry, leftright asymmetry), the W partial width, and the muon lifetime.
We also impose constraints from oblique corrections, namely from S and T parameters.
{ 9 {
Unless speci ed otherwise these are obtained from ref. [3]. Finally, we impose limits from
direct searches: the LEP limits on masses of new charged leptons, 105 GeV, and the limits
on pair production of vectorlike leptons at the LHC summarized in ref. [4]. Constraints
on the production of heavy Higgs will be discussed in the following section together with
results.
Constraints on the muon couplings were already discussed in ref. [8]. Precision
electroweak measurements constrain modi cation of couplings of the muon to the Z and W
bosons at
0:1% level which, in the limit of small mixing, approximately translates into
95% C.L. bounds on
E;L couplings:
E vd
ME
. 0:03 ;
Lvd
ML
assuming only mixing (Yukawa couplings) in the charged sector.
In the neutral lepton sector the strongest limits are obtained from the muon lifetime.
In what follows we discuss this limit together with the invisible widths of the Z boson and
constraints from direct production of vectorlike leptons.
4.1
The muon lifetime
The Fermi constant GF is determined with a high precision from the measurement of muon
lifetime. In the standard model GF = (p2=8)g2=M W2 while in our model one of the g=p2
factors is replaced by gL
(VLy)22(UL)22 + (VLy)24(UL)42 :
The allowed range for g
is obtained from the uncertainty in the W mass, MW =
80:385
0:015 GeV. The relative uncertainty in M W2 is 2
the 95% C.L. upper limit on the deviation of gL
W
from g=p
2 as:
Assuming no mixing in the charged sector and using the small mixing approximation
eq. (2.6),
= p (VLy)22 ' p
and we obtain an approximate 95% C.L. upper bound on the size of N coupling:
Considering also mixing in the charged sector, the bound is shared between
N and
E :
The partial decay width of W
depends quadratically on the gL
W
coupling.
However, it is measured with about 2% precision and thus the resulting constraint on the
coupling is signi cantly weaker.
corresponding
gauge couplings.
the left panel, we show the ( N vu=MN )2{gLZ
=(gLZ
EW precision constraints. The blue, cyan, magenta and red points have singlet fraction (de ned as
j(VLy)45j2=2 + j(VRy)45j2=2) in the ranges [0; 5]%, [5; 50]%, [50; 95]%, and [95; 100]%, respectively. In
)SM plane; on the right axis we show the
exp = SZMinv ratio. In the right panel we show the o diagonal jgLW 4
Zinv
j and jgL
Z 4 j
4.2
Invisible width of Z
The partial width of Z !
where
(Z !
Z
L
g
g
=
where the second line is an appropriate approximate formula in the case of small mixing.
In this limit, the upper bound on
N obtained from muon lifetime, eq. (4.8), suggests that
) can be modi ed at most at 0.3% level (the sign of the correction is always
negative). Since we assume that only one generation of SM leptons mix with vectorlike
pairs, the invisible width of Z can be lowered at most by 0.1%. This is also visible in
gure 1 where we consider randomly generated points in the
N , , , ML and MN
parameter space for xed mH = 155 GeV and m 4 = 135 GeV (di erent choices of masses do
not sizably a ect the allowed ranges), assuming no mixing in the charged lepton sector,
and impose all EW precision constraints (including direct productions bounds discussed in
section 4.3 below). In the left and right panels of gure 1 we consider the ( N vu=MN )2{
g
)SM, ( N vu=MN )2{ eZxinpv = SZMinv and jgL
W 4 j{jgL
j planes. Both the upper
limit on
N vu=MN , eq. (4.8), and the resulting largest possible e ect in
Zinv follow closely
those obtained from the approximate formulas. Points with 4 being mostly singlet (red
points) or mostly doublet (blue points) cluster very near the line that assumes the
approximate relation in eq. (4.7) is exact and even highly mixed scenarios (cyan and magenta)
are not very far.
[R 4 4
Since the ratio of the measured value of the Zboson invisible decay width and its SM
the invisible width does not provide additional constraint to that obtained from the muon
lifetime. This however assumes that only the 2nd generation of SM leptons mixes with
vectorlike leptons. The e ect on invisible width can be larger if more generations mix with
vectorlike leptons or if one considers mixing with the 3rd generation instead of the 2nd
since the constraints on 3rd generation couplings are weaker.
In conclusion, couplings of SM gauge bosons to the second family of leptons, g
W
L
, can deviate from their SM values by less than
0:1%. Moreover, within the
explicit model we consider, these constraints imply upper limits of order
0:02 on the new
gauge couplings as we can see in the right panel of gure 1.
4.3
Direct production of vectorlike leptons
Let us rst consider constraints from DrellYan production of 4 4 or 4e4 leading to at
least 3 leptons in the nal state and Emiss. The cross section of pp !
T
to (gLZ 4 4 )2 + (gRZ 4 4 )2 where the couplings are given in eqs. (2.11){(2.12). Thus the cross
4 4 is proportional section is modi ed from the one that corresponds to fully doublet 4 by factor
At present, searches for anomalous production of multilepton events constrain only the
case when both 4s decay to W
and the limits on R 4 4
from table 2 of ref. [4]. They are summarized in our table 2 for reference values of m 4 . In
our numerical analysis we interpolate these results for other values of m 4 .
Similarly, the cross section of pp ! e4 4 is proportional to (gLW 4e4 )2 + (gRW 4e4 )2 where
the couplings are given in eqs. (2.17){(2.18). Thus the cross section is modi ed from the
BR2( 4 ! W ) can be read
one that corresponds to fully doublet 4 and e4 by factor
Re4 4
(VLy)42(UL)24 + (VLy)44(UL)44
2 +
(VRy)44(UR)44 :
2
(4.15)
The analysis in ref. [4], assuming me4 = m 4 , shows strong limits on this production cross
section. Some decay modes of e4 and 4 are consistent with data only for masses higher
than 500 GeV. In our analysis we are focusing on the case with no mixing in the charged
1
2
1
2
mixing in the neutral sector) and the limits on Re4 4
from table 2 of [4]. Other decay modes of 4 are not constrained in this case. The upper
bounds are summarized in table 2. We again interpolate these results for other values
) = 1 (the required coupling originates from
BR( 4 ! W ) can be obtained
of m 4 .
searches.
Finally, let us comment on a single production of a new lepton. The W
4
T
coupling results in a production of 4 through the process pp ! W
!
can lead to at least 3 leptons with Emiss in the nal state. The bounds were discussed in
4
which also
ref. [31] in the context of TeV scale seesaw models with very small lepton number violating
terms, see for example ref. [32], which are not constrained from the samesign dilepton
The cross section of pp !
4 is proportional to (gLW 4 )2 + (gRW 4 )2 where the
couplings are given in eqs. (2.17){(2.18). Thus the cross section is modi ed from the one that
corresponds to full strength coupling of the two leptons to W by factor
R 4
(VLy)42(UL)22 + (VLy)44(UL)42
2 + (VRy)44(UR)42 2:
We closely follow ref. [4] to set limits from the ATLAS searches for anomalous production
of multilepton events [33] on three decay modes:
pp ! W
! 4
! W
; Z
; h
;
where h is the SM Higgs with mass 125 GeV. The obtained upper bounds on R 4
BR( 4 ! W ; Z
; h ) are shown in
gure 2 as functions of m 4 . We see that for any
combination of branching ratios the constraint on R 4 is at most of O(10 2). This limit is
much weaker than those obtained from precision EW data; in fact, for the surviving points
in gure 1 the maximum value of R 4 is of O(10 3).
(4.16)
(4.17)
In this section we explore the impact that this model has on pp ! (W W; H
! W W )
! ` `0 0 measurements.
We show detailed results for the two representative points
(mH ; m 4 ) = (155 GeV; 135 GeV) and (250 GeV; 230 GeV) in gures 3 and 4. In gures 5{7
we show how these results vary for di erent values of mH and m 4 .
In gure 3 we present the results of the scan described in section 4 for the reference point
(mH ; m 4
) = (155 GeV; 135 GeV) discussed in ref. [1]. The blue, cyan, magenta and red
points have 4 with singlet fraction (j(VLy)45j2=2+j(VRy)45j2=2) in the ranges [0; 5]%, [5; 50]%,
[50; 95]%, and [95; 100]%, respectively (note that in some of these plots blue/cyan/magenta
colors are not easily distinguishable). In the two upper plots the black contours are the
values of the e ective pp ! W W cross section as de ned in [1] for the e
e
and
([ NWPW ] ) nal states, respectively. In parenthesis we show the corresponding
e ective pp ! H ! W W cross sections ([ NHP!W W ]e ; ). These e ective cross sections1
([ NWPW ]e )
are explicitly de ned as:
) nal states and the NP and SM acceptances ANP and ASM
are calculated using the experimental W W and H ! W W cuts (for the latter we follow
ref. [34] and consider the six Higgs mass hypotheses discussed in refs. [35, 36] and show
the most constraining e ective cross section). Note that points displayed in the two upper
panels are identical and that the only di erence lies in the
crucially on the very di erent acceptances for e and
nal states as well as the factor
NP
W W contours that depend
. Note that eq. (5.1) implies
(5.1)
(5.2)
(5.3)
NHP!W W =
ANHP ASWMW
ASHM ANWPW NWPW :
The product of acceptances in this equation is the crucial parameter that controls the size
of contributions to pp ! W W that are allowed by H ! W W searches. For most (but
not all) masses that we consider, this ratio is of order 10% (typically ANHP=ASHM
O(0:1)
and ASWMW =ANWPW
large
di erence mH
W W cross sections while simultaneously surviving H ! W W bounds. When the
NP
m 4 is large and m 4 is small, Emiss and mT increase while m`` decreases
T
O(1)). The smallness of ANHP=ASHM is the reason for which we can
nd
implying a larger ANHP=ASHM ratio. For instance, for mH = 250 GeV and m 4 = 135 GeV
we nd that this ratio can be as large as 2.
The yellow shaded area is excluded by H ! W W searches. The upper bound on the
e ective
NHP!W W cross section is independent of m 4 and is given by
NHP!W W < min
H
H
95
ASHM
1
BR(W ! ` )2
;
where 9H5 is de ned in appendix A of ref. [1]. The measurement of the pp ! W W cross
section is very sensitive to NNLO QCD corrections which have not been fully implemented
1An extended discussion of the e ective cross sections is presented in section 2 of ref. [1].
magenta and red points have singlet fraction in the ranges [0; 5]%, [5; 50]%, [50; 95]%, and [95; 100]%,
respectively. In the two upper plots all constraints are imposed and we focus on the BR(H
!
W
){tan
plane for the e
e
and
nal states, respectively. The black contours are
the values of the e ective pp !
W W and pp !
H
!
W W cross sections (in pb) de ned in
eq. (5.1). The yellow shaded area is excluded by H ! W W searches. In the middleleft plot, we
consider the R 4 4
BR( 4 ! W
pp !
BR( 4 ! Z
4 4 ! W +W
+
)
BR( 4 ! W
). Here the lightshaded points do not satisfy the muon lifetime
constraint and the impact of multilepton + ETmiss searches from DrellYan pair production process
is indicated by the black curve. In the middleright plot we show the
). Here the gray points are excluded by multilepton searches. In
the two lower plots we consider the BR(H ! 4
){BR( 4 ! W ) and
H
4
{ h
4 planes.
in the experimental analysis yet. Following, for instance, the discussion around eq. (1.7) of
ref. [1], the deviation of the pp ! W W cross section with respect to the SM expectation
found by ATLAS [2] and CMS [37] are:
(
[ NWPW ]eATLAS = (12:7+65::28) pb
[ NWPW ]ATLAS = (9:9+87::03) pb
and
(
[ NWPW ]CMS = ( 0:1
e
[ NWPW ]CMS = (4:5
Since these two results adopt di erent theoretical setups, we refrain from combining them
into a weighted average. For this reason do not use pp ! W W data to constrain our model
and simply quote the allowed values.
A prominent feature of gure 3 is that for a doubletlike 4 the product of branching
ratio BR(H
!
W
) = BR(H
!
small. This is mainly due to bounds from the multilepton plus Emiss searches in the
DrellT
Yan pair production process pp !
looking at the middleleft panel of gure 3 where we consider the R 4 4 {BR( 4 ! W )
plane. The quantity R 4 4 is de ned in eq. (4.14).
Here the light colored points are obtained without imposing any of the constraints discussed in section 4 and the darker colored points are those that survive after imposing the muon lifetime bound. Additional constraints from oblique corrections are very strong (especially from the S parameter) but
W +W
+
. This can be understood by
in the [BR(H ! W
region.
); tan ] plane they do not modify signi cantly the overall allowed
Bounds from multilepton searches exclude the region above the black contour
separatand large R 4 4
1 with low BR( 4 ! W ).2
ing the surviving points in two disconnected regions at low R 4 4 with BR( 4 ! W )
70%
At small R 4 4 the 4 is mostly singlet, the second term in eq. (3.16) is suppressed by a
factor (VLy)44 with respect to the rst and the 4
Z
coupling is controlled by the single
quantity (VLy)42 (we remind the reader that (VL)22 is very close to 1). Under the assumption
of no mixing in the charged sector, the matrix U is the identity and the 4
W
coupling
in eq. (3.13) is also controlled by the parameter (VLy)42. As a consequence the ratio of these
two couplings is the same as in the SM (i.e. independent of
avor mixing parameters),
implying an almost constant 4 ! W
mostly doublet, both terms in the 4
Z
branching ratio (
70%). At large R 4 4 the 4 is
coupling are of similar size, and the 4 ! W
branching ratio can acquire any value depending on the choice of input parameters. On
top of this one should note that the 4 ! h
channel is phase space suppressed for
the case m 4 = 135 GeV. These considerations are also illustrated in the middleright
plot of gure 3 where we show the points in the BR( 4 ! Z
){BR( 4 ! W ) plane.
Here the gray points are excluded by multilepton searches and, to a lesser extent, oblique
corrections.
The surviving region at large R 4 4 is also characterized by a very small H
4
coupling as we can see in the lowerleft panel of gure 3. In fact, an almost completely
2Note that these arguments rely strongly on the particular choice of masses ((mH ; m 4
) = (155 GeV;
135 GeV) in this case); a completely di erent situation characterizes the con guration presented in gure 4
and discussed later on.
gure 3 for further details.
doublet 4 requires very small couplings
and , implying a strong suppression of the
H
4
Yukawa coupling
given, for doublet 4, in eq. (3.3). This can be seen in the lowerright
panel of gure 3 where we show the values of the Yukawa couplings H
4
and h
4 for the
points that survive all constraints. Therefore BR(H ! 4 ), and hence BR(H ! W
are very small for doubletlike 4. If 4 is singletlike, the SMlike Higgs Yukawa coupling
),
is given, in the limit of small mixing, by
h
4
N sin , see eq. (3.5). In this case, at
xed MN , the muon lifetime limit (4.8) translates into a direct constraint on the Yukawa
coupling h
4
.
); tan ] plane of the parameter scan described in
the main text for various values of mH and m 4 . The black contours are the values of the e ective
pp ! W W and pp ! H ! W W cross sections (in pb) for the e e
in gure 3 for further details.
nal state. See the caption
In gure 4 we present the (mH ; m 4 ) = (250 GeV; 230 GeV) case. Now, the large 4
mass implies that the decay mode 4 ! h
is no more phase space suppressed and can be
dominant in large part of the parameter space as we can seen directly in the middleright
plot in
large as 60%. On top of this, the constraint from multilepton + Emiss searches is weaker
gure 4 and indirectly in the middleleft plot where BR( 4 ! W ) can only be as
(this happens generally for m 4 > 150 GeV as we can see in table 2), implying that there
is a large region of allowed parameter space in which the 4 is mostly doublet as can be
seen in the two top plots in gure 4. Even though there are many points for which the 4
T
doublet fraction is large, the corresponding values for BR(H ! W
than for typical singlet points. This is because the H
4
) are much smaller
coupling for a doubletlike
4 is suppressed compared to the singletlike 4 by vu=MN , see eqs. (3.3) and (3.5). From
the bottomright plot in gure 4 we see that the actual bounds on
h
4 and
H
4 are 0.05
and 0.17, respectively. Given that the ratio of these couplings is equal to tan , the second
bound is e ectively set by the perturbativity request tan
& 0:3.
In
gures 5 (for the e
nal state) and 6 (for the
nal state) we present
the result of similar scans for (mH ; m 4 ) = (140 GeV; 135 GeV), (250 GeV; 135 GeV),
); tan ] plane of the parameter scan described in
the main text for various values of mH and m 4 . The black contours are the values of the e ective
pp ! W W and pp ! H ! W W cross sections (in pb) for the
in gure 3 for further details.
nal state. See the caption
(155 GeV; 125 GeV) and (155 GeV; 150 GeV). The interpretation of these plots is
similar to that of gure 3. The main di erence between these plots is the maximum value
). In gure 7 we show the BR( 4 ! Z
){BR( 4 ! W ) plane
allowed for BR(H ! W
for each set of masses.
In gure 8 we show the envelopes of the allowed parameter space for a wide range of
masses; in the left plot we take m 4 = 135 GeV and mH 2 [140; 250] GeV and in the right
plot we have mH = 155 GeV and m 4 2 [125; 150] GeV. This e ect is due to change in the
phase space available for H ! 4
! W
as the masses vary.
Assuming that the acceptances ratios ANWPW =ASWMW and ANHP=ASHM remain constant
when increasing the center of mass energy from 8 to 13 TeV, the
NP
W W contours in
gures 3{6 will simply scale with pp !
mH = 250 GeV the rescaling factor is about 2.776 [38].
H production cross section. For instance, for
Finally let us comment on the reach of the next LHC run at 13 TeV with a luminosity
L = 100 fb 1
. Taking into account that (pp ! W W )t1h3 TeV= (pp ! W W )t8hTeV ' 2 [39]
and that the uncertainty on NWPW is e8xTpeV
Moreover, our new physics contributions to
' 5 pb (see eq. (5.4)), we estimate e1x3pTeV
3 pb.
W W scale with the pp ! H cross section and
NP
Figure 7.
Projection onto the [BR( 4 !
Z ); BR( 4 !
W )] plane of the parameter
scan described in the main text for (mH ; m 4
) = (140 GeV; 135 GeV), (250 GeV; 135 GeV),
(155 GeV; 125 GeV) and (155 GeV; 150 GeV). See the caption in gure 3 for further details.
and mH 2 [140; 250] GeV. In the right plot we take mH = 155 GeV and m 4 2 [125; 150] GeV.
increase by a factor
2:5 [38] at 13 TeV. Taking these considerations into account, direct
inspection of gures 3{6 shows that most of the presently allowed parameter space will be
tested. For instance, with respect to the topleft panel of gure 3, LHC8 with 20 fb 1 is
BR(H ! e4 )
BR(e4 ! W
and
nal state (right).
) = 1 (this de nition applies only here) for the e
nal state (left)
sensitive to points below the 5 pb contour while LHC13 with 100 fb 1 will be sensitive to
points roughly below the 1.2 pb one (that will correspond to [ NWPW ]13 TeV ' 3 pb).
6
Contributions from H
! e4
In this section we discuss contributions to pp ! ``0 ` `0 stemming from heavy Higgs
production and decay into a charged vectorlike lepton and a muon:
pp ! H ! e4
! W
!
`
` :
(6.1)
We begin our analysis with a model independent study of this channel along the lines of the
analysis presented in ref. [1]. Our main results are summarized for the e
and
modes
in the two panels of gure 9. These
gures are very similar to
blue contours are the values of the e ective W W cross section
)). The yellow contours are the upper bounds on
gure 1 of ref. [1]. The
NP
W W that we obtain for
NP
W W (in pb) implied
)
BR(H !
are labelled with the value of BR(H ! W
) cot2
that leads to
NP
W W = 1 pb.
by the H ! W W limits and are controlled by the dependence of our signal acceptances
(for the W W and H ! W W analyses) on the H and e4 masses. The red dashed contours
Focusing on the e case (for which there is a larger statistics), we see that in the bulk
of the parameter space we consider the maximum allowed W W e ective cross sections are
smaller than 10 pb and well within the allowed 2 experimental ranges (see eq. (5.4)). This
is in contrast to what happens for H ! 4
as one can see from
gure 1 of ref. [1] where
H
! W W constraints allow for very large e ective W W cross sections in most of the
parameter space.
This feature is due to the di erent behavior of the ratio of acceptances ANWPW =ANHP for
the H ! 4
and H ! e4 channels. This ratio controls the upper limit on the e ective
W W cross section (as we explain in appendix A of ref. [1], the larger the ratio, the larger
the allowed cross section). Both channels have similar ANWPW =ANHP ratio at moderately large
mH and small m 4;e4 ; this implies that the 10 pb yellow contours for the 4 and e4 cases are
close to each other. As we explain below, when moving to smaller mH and larger m 4;e4
the 4 ratio increases while the e4 one decreases. Because of this behavior, in the bulk of
the parameter space in which we are interested (smaller mH and larger m 4;e4 ), we nd
large allowed
W W values for the H ! 4
NP
channel but not for the H ! e4
one.
The behavior of the acceptances ratio is essentially controlled by the di erence mH
m 4;e4 . This di erence determines the transverse mass mT in the 4 case and the dilepton
invariant mass m`` in the e4 one. The H ! W W acceptance decreases for channels with
lower mT and increases for channels with lower m`` (because the CMS Higgs cuts include
a range for mT and an upper bound on m``). The W W acceptance, on the other hand,
is controlled by a m`` > 10(15) GeV cut (for e
and
nal states): for the e4 case it
decreases at low mH
me4 , while, for the 4 one, the dilepton invariant mass is controlled by
m 4 and tends to always pass the cut implying a mild dependence of the W W acceptance
on the choice of masses. In conclusion, small mH
m 4;e4 implies a small acceptances ratio
for e4 and a large one for 4
.
The discussion of the
mode is similar. The main di erences are that the
experimental H ! W W cuts are much tighter in order to suppress DrellYan backgrounds and
that the e ective cross section is enhanced by a combinatorial factor of 2 with respect to
the e case (see eq. (5.1)). Note that in order to obtain similar e ective cross sections for
the e
and
modes one needs to include a second vectorlike lepton family as discussed
in section 4 of ref. [1].
charged lepton sector.
Since the W W e ective cross sections that we nd in the H ! e4 channel are typically
smaller than 10 pb, we refrain from performing a detailed scan that includes mixing in the
7
Contributions from SMlike Higgs boson
In this section we consider exotic decays of the SMlike Higgs into vectorlike leptons. We
begin by considering the h !
4
! W
cross sections
W W as a function of m 4 2 [95; 125] GeV for the e
NP
process. In
gure 10 we show the e ective
and
modes. Here
h
we set BR( 4 ! W ) = 1 and consider two representative values of the avor violating
Yukawa couplings j
4 j = 0:02 and 0:03. These values are close to the largest possible
as one can see from the parameter scan presented in
gure 11 where we show the j
h
4 j
{
BR( 4 !
W ) plane for m 4 = 120 GeV. The thick solid red line in
gure 10 is the
95% C.L. upper bound from the SM h ! W W ATLAS search [40].
We see that, for the e
mode, Higgs searches are not constraining while in the
mode they require m 4 & 105 GeV. In both cases, the e ective W W cross section cannot
exceed 2{3 pb. These cross sections are far from the ranges allowed by ATLAS (blue shaded
region) and the CMS upper bound (purple line) for the e
nal state but are close to the
allowed ATLAS region for the
case (see eq. (5.4) and the related discussion).
The thick solid red line in search [40].
as a function of m 4 2 [95; 125] GeV for the e
and
to the e ective cross section NWPW
modes. We set BR( 4 ! W
) = 1 and
h
consider two representative values of the avor violating Yukawa couplings j
gure 10 is the 95% C.L. upper bound from the SM h ! W W ATLAS
4 {BR( 4 ! W ) plane for m 4 = 120 GeV.
Similar results are obtained for other choices of m 4 < 125 GeV. See the caption in gure 3 for
further details on the scan.
We do not discuss in detail the h ! e4
! W
process because we found that it
does not lead to appreciably large e ective cross sections (typically smaller than 1 pb) and
it is severely constrained by h ! W W searches.
8
Contributions from DrellYan production of vectorlike leptons
In this section we discuss contributions to the e ective cross section
the following vectorlike lepton DrellYan production processes (` = e; ):
NP
W W that stem from
pp ! ( ; Z) ! e4 e4 ! W
W
pp ! Z ! 4
! W
! ` 2 :
! 2`4 ;
(8.1)
(8.2)
Z 4 j . 0:02. Similar bounds are found for di erent 4 masses.
and gLZ 4 for m 4 = 110 GeV. We see that R 4
. 1:5 10 3
Note that there are many more processes (involving up to four light leptons in the nal
state) that one can consider and the two modes we consider in eqs. (8.1) and (8.2) are the
two most promising ones.3
The e4e4 pair production channel is avor diagonal and the Z
e4 e4 coupling can be
as large as the corresponding Z
` ` SM one. On the other hand, in the channel (8.2) the
production of a single 4 is constrained by the values of the o diagonal coupling g
allowed by EW precision data. To quantify this e ect we de ne
R 4
(gLZ 4 )
2
g2=(4 cos2 W )
;
(8.3)
SM process pp ! Z !
m 4 = 110 GeV.
which shows how the production of 4
through Z boson is suppressed compared to the
. In gure 12 we see that R 4
can be at most 1:5
10 3 for
gure 13 we show the most optimistic values of e ective cross sections for the
processes in eqs. (8.1) and (8.2). For the latter case we set R 4
Consequently one can see that allowed values of
W W for the pp ! ( ; Z) ! e4e4 and
NP
BR( 4 ! W ) = 10 3.
channels are at most of order 1 pb and 0:1 pb respectively.
We studied decay modes of a heavy CP even Higgs boson, H ! 4
and H ! e4 followed
by 4 ! W
and e4 ! W
, where e4 and 4 are the lightest charged and neutral mass
eigenstates originating from vectorlike pairs of SU(2) doublet and singlet new leptons. We
showed that, with Yukawa couplings as in two Higgs doublet model typeII, these decay
modes, when kinematically open, can be large or even dominant. After imposing all the
3If more than two light charged leptons are present, the third hardest lepton must have pT < 7 GeV in
order to avoid detection and this requirement suppresses the acceptance.
NWPW [pb] for DrellYan processes. In the left panel we
consider the channel pp ! ( ; Z) ! e4 e4 ! W
W
! 2`4
assuming SMlike strength of
the Z
e4 vertex, BR(e4 ! W
! W
! ` 2 for R 4
) = 1 and me4 = 105{250 GeV. In the right panel we show
BR( 4 ! W ) = 10 3 and m 4 = 95{250 GeV.
experimental constraints, the H ! 4
about 35%.
decay channel can have branching ratio of up to
As we discussed in sections 4 and 5, electroweak precision data impose very strong
bounds on various gauge and Yukawa couplings: the new
avor violating gauge couplings
W 4 and gL
Z 4
have to be smaller than O(10 2), the couplings of SM gauge bosons to
, can deviate from their SM values by less
4
and
H
4 are constrained to
the second family of leptons, gL
W
and gL
Z
than
0:1%, and the avor violating Yukawa couplings h
be smaller than
0:05 and
0:17, respectively.
Focusing on pp ! H
we studied possible e ects of this process
on the measurements of pp ! W W and H ! W W . Contributions from this process to
2`2
nal states can be very large since only one W has to decay to leptons unlike in
the case of pp ! W W and H
! W W . We present predictions of the model in terms
of e ective cross sections for pp ! W W and H ! W W in
e2
2 2
nal states from
the region of the parameter space that satis es all available constraints including precision
electroweak observables and constraints from pair production of vectorlike leptons. Parts
of the parameter space are already excluded by these measurements and thus possible
contributions to these processes can be as large as current experimental limits. Large
contributions, close to current limits, favor small tan
region of the parameter space.
In addition, we studied correlation of the contributions to pp ! W W and H ! W W .
We showed that, as a result of adopted cuts in experimental analyses, the contribution
to pp ! W W can be more than an order of magnitude larger than the contribution to
H
! W W . Thus more precise measurement of pp ! W W in future will signi cantly
constrain the parameter space of the model.
W
Furthermore, we also considered possible contributions to pp ! W W from H ! e4
, from similar processes involving SMlike Higgs boson and from pair production of
vectorlike leptons. These however lead to much smaller contribution to the e ective cross
section for pp ! W W while satisfying limits from H ! W W and h ! W W in rst two
cases. In the case of pair production of vectorlike leptons, the cross sections are very small,
and the contribution to the e ective pp ! W W is at most of order 1 pb.
Finally, as we discussed at the end of section 5, the next LHC run at 13 TeV with
100 fb 1 of integrated luminosity will be able to explore most of the parameter space
currently allowed by electroweak precision data and H ! W W constraints.
Acknowledgments
RD thanks Hyung Do Kim and Seoul National University for kind hospitality during nal
stages of this project. The work of RD was supported in part by the U.S. Department
of Energy under grant number DESC0010120, by the Munich Institute for Astro and
Particle Physics (MIAPP) of the DFG cluster of excellence \Origin and Structure of the
Universe" and by the Ministry of Science, ICT and Planning (MSIP), South Korea, through
the Brain Pool Program.
Open Access.
Attribution License (CCBY 4.0), which permits any use, distribution and reproduction in
any medium, provided the original author(s) and source are credited.
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