Charged fermions below 100 GeV
HJE
Charged fermions below 100 GeV
Daniel EganaUgrinovic 0 1 3 6 7
Matthew Low 0 1 3 4 7
Joshua T. Ruderman 0 1 2 3 5 7
Geneva, Switzerland
0 New York , NY 10003 , U.S.A
1 Einstein Drive , Princeton, NJ 08540 , U.S.A
2 Theoretical Physics Department , CERN
3 Stony Brook , NY 11794 , U.S.A
4 School of Natural Sciences, Institute for Advanced Study
5 Center for Cosmology and Particle Physics, Department of Physics, New York University , USA
6 C.N. Yang Institute for Theoretical Physics, Stony Brook University
7 We revisit the
How light can a fermion be if it has unit electric charge? lore that LEP robustly excludes charged fermions lighter than about 100 GeV. We review
Beyond Standard Model; Supersymmetric Standard Model

LEP chargino searches, and
nd them to exclude charged fermions lighter than 90 GeV,
assuming a higgsinolike cross section. However, if the charged fermion couples to a new
scalar, destructive interference among production channels can lower the LEP cross section
by a factor of 3. In this case, we nd that charged fermions as light as 75 GeV can evade
LEP bounds, while remaining consistent with constraints from the LHC. As the LHC
collects more data, charged fermions in the 75{100 GeV mass range serve as a target for
future monojet and disappearing track searches.
1 Introduction
2
3
4
5
A review of LEP limits on higgsinos
Simpli ed model for charged fermions
LEP limits on the simpli ed model
LHC limits on the simpli ed model
5.1
5.2
5.3
5.4
5.5
Invisible decays of the Higgs
Monojet searches
Disappearing track searches
Other LHC searches
Combined LEP and LHC limits
6
Conclusions
A Validation of LHC analyses
A.1
Monojet searches
A.2 Disappearing track searches
Higgs, they may also be relevant for understanding the electroweak phase transition [6{8].
The LHC is now sensitive to charginos with masses of hundreds of GeV [9{16]. As
more data are collected, heavier states will come into reach. Signi cant attention has been
devoted towards maximizing the mass reach for new electroweak fermions (see for example
refs. [17{35]). However, it is also important to be mindful of any gaps in the exclusion
limits at lower masses, to make sure that new physics is not missed during the march to
higher masses.
The conventional view is that LEP sets the strongest bounds on electroweak fermions
lighter than about 100 GeV, while the LHC probes higher masses. The clean environment
bounds on fermions lighter than half the maximum centerofmass energy, p
of LEP, plus the robust production mechanism through schannel =Z, implies powerful
s = 209 GeV.
Photons from initial state radiation (ISR) can be tagged, and therefore detection does not
{ 1 {
require energetic decay products from the new fermions. There has developed a sort of
folk bound : it is commonly believed that LEP robustly excludes fermions with unit charge
lighter than about 100 GeV. Indeed, most LHC searches for charginos only display bounds
above 100 GeV [9, 11{16, 36{45],1 and many theory studies of charginos also only consider
masses above 100 GeV.
In this work, we explore fermions with unit electric charge and masses between mZ =2
and 100 GeV. We limit ourselves to study charged fermions in the higgsino gauge
representation and call these fermions charginos, both if they are part of the MSSM or if they
arise in a more generic, possibly nonsupersymmetric, context. We critically examine the
robustness of the LEPII bounds on charginos. We do not consider the region below mZ =2,
where the Z boson can decay to the new fermions, leading to powerful constraints from
LEPI [51{54].
The LEP SUSY working group combined limits from the 4 experiments: ALEPH,
DELPHI, L3, and OPAL (\ADLO" combination). A combined limit excludes charginos
with masses below 103.5 GeV [55], however this bound relies on a restrictive set of
assumptions: (
1
) winolike production cross section, (2) gauginouni ed relation between the bino
and wino mass (implying a large splitting between the chargino and lightest neutralino),
and (3) decoupled sneutrinos. There is also a combined limit applied to the regime of
small splitting between the chargino and neutralino [56], excluding charginos lighter than
92.4 GeV (91.9 GeV) for higgsino (wino)like cross sections, respectively. In this work, we
review the LEP bounds, including newer searches not included in the LEP SUSY
working group combination, and we
nd that charginos with a higgsinolike cross section are
excluded in the range mZ =2 to approximately 90 GeV.
In
gure 1, we compare the cross section of higgsinolike charginos to two bounds
from LEP. Note that although we
nd a bound of about 90 GeV, the higgsino cross
section is always within an order one factor of the bound for all masses above mZ =2. If
the cross section can be reduced, the bound may be signi cantly weakened. We consider
a deformation of the minimal model, illustrated in
gure 2, where the cross section is
reduced. A new scalar has a Yukawa coupling with the charged fermion and the electron,
such that tchannel exchange of the scalar destructively interferes with the usual schannel
diagram. The dashed curve in
gure 1 shows how the fermion's cross section is reduced,
for a particular choice of the scalar mass and the strength of its Yukawa interaction.
As we will describe below, we nd that the tchannel scalar can reduce the LEPII
limit on charginos from about 90 GeV to about 75 GeV. We
nd that this gap survives
current searches at the LHC. A previous study identi ed a window of light charginos that
decay to leptons through displaced vertices and survive LEP searches [58], however this
gap has now been closed by LHC searches for displaced leptons [59]. Previous studies have
considered charged scalars, below 100 GeV, that are not excluded by LEP [60{62].
The rest of this paper is organized as follows. In section 2, we review LEP searches
and nd that a charged fermion, with a higgsinolike cross section, is bounded to be heavier
than about 90 GeV. In section 3, we introduce the simpli ed model that we use to study
1A few LHC searches, mainly from ps = 7 TeV, do show bounds on masses below 100 GeV [10, 46{50].
{ 2 {
HJEP05(218)
(black solid), and charged fermion
pair production cross section,
F +F , allowing for tchannel interference (black dashed). In the
tchannel diagram shown in
gure 2, the coupling is set to
= 0:5 and the singlet mass to mS =
110 GeV. The light and dark red lines are the LEP limits on the pair production cross section
+H H
from [56] and [57], respectively. The limits in this gure assume higgsinolike decays, and a
chargedneutral mass splitting of
m = 2:7 GeV.
e+
e
, Z
F +
F
pair production at LEP. The schannel production is
xed by the fermion's quantum numbers, while the tchannel production depends on the scalar's
mass and the strength of the Yukawa interaction between the charged fermions and the scalar.
the e ect of tchannel interference on the chargino bounds. In section 4, we discuss LEPII
limits in the presence of tchannel interference. Then, in section 5, we evaluate the limits
from LHC searches for monojets, multileptons, and disappearing tracks. Section 6 contains
our conclusions. We include an appendix that describes the validations of our simulations
for recasting LHC searches.
2
A review of LEP limits on higgsinos
We start by providing a brief summary of LEP limits on the pure higgsino model. The
pure higgsino model corresponds to an extension of the Standard Model with a vectorlike
pair of colorneutral, SU(2)W doublet fermions with hypercharge Y =
1=2. We assume
that discrete symmetries prevent mixing between the new doublet fermions and Standard
{ 3 {
HJEP05(218)
e+
e
, Z
+
H
H
+
fu
+
H
+
0
H
higgsinos decays (center and right). fu; fd stand for Standard Model up or down type quarks or
leptons. Both the cross section and branching ratios are xed by the higgsino's quantum numbers
and the chargino and neutralino masses.
Model leptons. At the renormalizable level, all of the new doublet fermion interactions are
set by their quantum numbers.
The spectrum of the higgsino system contains one charged and one neutral Dirac
fermion: the chargino,
, and the neutralino,
H
H
0 . At dimension ve, the masses of
H and
0H may be split by the Weinberg operator (in the MSSM this mass splitting
arises from the mixing among the higgsinos, winos, and bino). At oneloop, there is an
additional irreducible contribution to the mass splitting from infrared e ects. In the range
H
50 GeV
m
100 GeV, this radiative splitting monotonically increases from 206 MeV
to 256 MeV [63]. In this work, we assume that the neutral fermion is the lightest component
of the doublet and is stable.
At LEP, charginos are pair produced via schannel diagrams mediated by gauge bosons
and they decay through W bosons into quarks, leptons or pions, as shown in gure 3. The
decays may be two or threebody, depending on the charginoneutralino mass splitting.
Since all interactions are
xed by the higgsino's quantum numbers, the properties of the
higgsino system, including the chargino lifetime and branching ratios, are completely
determined by the chargino and neutralino masses.
LEP performed several searches for charged higgsinos heavier than half the Z boson
mass. The searches may be divided into di erent categories depending on the
charginoneutralino mass splitting
m
m
H
m 0 ;
H
(2.1)
which controls both the typical momentum of the nal state particles and the chargino
lifetime [66]. The region
m > 3 GeV is covered by conventional searches looking for
charginos promptly decaying into leptons and jets. For 320 MeV <
m < 3 GeV, the
most e ective searches require a photon from ISR as well as other detector activity from the
chargino's decay products. For m
<
m < 320 MeV the chargino lifetime is greater than
1 cm, and dedicated searches for disappearing tracks and large impact parameters set
the strongest limits. Finally, for mass splittings below the charged pion mass,
m < m
the chargino quickly becomes colliderstable and is probed by heavy stable charged particle
(HSCP) searches. According to [56], the combination of the above searches leads to a lower
limit on the chargino mass of m
> 92:4 GeV.
H
{ 4 {
Prompt decays
Displaced decays
m
m
Search
ADLO conventional
3 GeV
3 GeV
m
320 MeV
m
10 GeV (prompt)
m
m
320 MeV (displaced)
320 MeV
m
5 GeV
reference. Above, ` stands for leptons (e; ; ), j for jets, ISR for initial state radiation (of a photon),
and HSCP for heavy stable charged particles. The searches included in the ADLO combination
are speci ed in parentheses. They include a combination of the analyses using a subset of the full
dataset, up to 2001, for conventional searches and using the full dataset, up to 2002, for \low DM"
compressed searches. We further break down the ADLO compressed searches into \prompt" and
\displaced" depending on the charginoneutralino mass splitting, which
xes the chargino lifetime.
The ADLO combination also reports limits on HSCP searches for
m
m
, which we do not
use in this work. Instead, we recast the OPAL HSCP search [71], which provides stronger limits.
None of the OPAL searches in the table are included in the ADLO combination, and they are all
performed with the full luminosity. The last column indicates the chargedneutral higgsino mass
splitting covered by each reference.
To understand this limit in more detail, we reanalyze a selection of LEP results, which
we summarize in table 1. These results include the ADLO results, which are a
combination of the ALEPH, DELPHI, L3, and OPAL limits, and additionally, results published
afterwards individually by the OPAL collaboration.
The results of our analysis are shown in
gure 4.
Most regions of the
chargino
H
neutralino parameter space are excluded by more than one search, so each region is labeled
by the search that leads to the strongest limit at that point in parameter space. We nd
that charged higgsinos are excluded up to at least 100 GeV, except in two wellde ned
regions. In the rst region, the mass splitting is large,
m & 60 GeV. In this case, for
m 0 . 25 GeV, the limit on the chargino mass degrades to 96 GeV because the signal
kinematics resemble the background from W boson pair production.
The second region with weaker limits occurs when the chargino and neutralino are
compressed, but the chargino is not colliderstable, namely m
.
m . 3 GeV. This
region of parameter space is covered by ISR assisted searches and searches for large impact
parameters or disappearing tracks. In this region, the limit on the charged higgsino mass
degrades
90 GeV, as discussed in the introduction. This is the absolute lower limit
that we nd on the charged higgsino mass, and is approximately consistent with the limit
m
> 92:4 GeV reported by the ADLO combination [56].
The limits presented in gure 4 rule out most of the parameter space with charginos
below 100 GeV, but are speci c to the pure higgsino model. In the introduction we pointed
out that O(
1
) modi cations to the pure higgsino production rates may lead to considerably
weaker limits. In the following sections, we investigate quantitatively how the limits on
charginos change when the basic assumptions of the pure higgsino model are relaxed.
{ 5 {
gion (left) and in the compressed region (right). In the uncompressed region the strongest limits are
set by the OPAL multilepton search [65] and by ADLO searches for promptly decaying higgsinos [55].
H
The range m
50 GeV is not covered by the OPAL multilepton search, so we rely exclusively
on the ADLO combination. In the compressed region, the space from 3 GeV
m
10 GeV is
mainly covered by a combination of the ADLO conventional and ADLO \low DM" prompt searches,
as well as by the OPAL multilepton search. The OPAL and ADLO ISR assisted searches [56, 57],
set bounds in the regions 320 MeV
m
3 GeV and 320 MeV
m
5 GeV, respectively. In
the region m
m
320 MeV, the chargino decays within the detector, and we rely exclusively
on the ADLO combination, which contains dedicated searches for kinked tracks and large impact
parameters. The region
m
m
is covered by the OPAL HSCP search [71], which applies
to particles with a decay length
3 m. The black dashed line indicates the oneloop radiative
charginoneutralino mass splitting.
3
Simpli ed model for charged fermions
In this section, we consider a minimal extension of the pure higgsino model to illustrate
how simple deviations from this model modify the LEP phenomenology.
We add to the Standard Model a pair of colorneutral, vectorlike doublet fermions F
and F with hypercharges Y =
1=2 and Y = 1=2, respectively, as in the pure higgsino
model. The charged and neutral components of the doublets are de ned as
F =
F 0 !
F
;
F =
F + !
F 0
:
(3.1)
We refer to the fermions F
as charginos to indicate that they have unit charge and are
part of an SU(2)W doublet, even though our simpli ed model is nonsupersymmetric.
Consider now introducing a real scalar singlet S, which couples to the doublet F and
the electron doublet Le. Up to dimension ve, the Lagrangian contains the operators,
L
mF F F +
m2S S2 +
2
1
(F H)(F Hc) +
LeF S + h:c: + V (H; S):
(3.2)
{ 6 {
We require the potential, V (H; S), to be minimized at the origin of the eld space of
S, so that it does not condense. This model does not violate lepton number, as can be
seen by assigning F and F electron numbers of 1 and
1, respectively. Individual lepton
avor numbers are also preserved, implying that the model is safe from
avor constraints.
Additional renormalizable interactions beyond the ones in eq. (3.2) are easily forbidden
by imposing discrete and continuous global symmetries. Such symmetries forbid mixing
of the new doublets with Standard Model fermions and stabilize the lightest component
of the singletdoublet sector. The only dimension ve term we include is the Weinberg
operator, which is responsible for splitting the neutral and charged components of the
SU (2)W doublets at treelevel.2 The couplings
and
are generically complex, but for
simplicity we set the phases to zero and do not study the CP violating phenomenology.
Without loss of generality, we work in the basis where mF
0 and
0.
In addition to the scalar singlet with mass mS, the model contains one charged Dirac
fermion with mass mF
= mF and one neutral Dirac fermion with mass mF 0 . The mass
splitting between the charged and neutral fermions is
v
2
2
m
mF
mF 0 =
+ mrad ;
(3.3)
or mS ! 1). For mF
where the Higgs condensate is v = 246 GeV and
mrad is positive and accounts for the
radiative splitting of the doublet. We assume that mF
> mF 0 .
The model in eq. (3.2) is very similar to the pure higgsino model, but the Yukawa
interaction,
LeF S, leads to two important modi cations to LEP phenomenology. First,
the pair production rate of F
at LEP is modi ed with respect to the pure higgsino case,
since a new tchannel singletmediated contribution interferes destructively with the
schannel gaugemediated contribution. The diagrams contributing to the production cross
section are shown in gure 2. To show the e ect of this interference, in gures 5 and 6 we
plot the LEP F
pair production cross section normalized to the charged higgsino cross
section, as a function of the coupling
and the singlet mass mS for mF
= 75 GeV. We
see that over a wide range of couplings and masses, the LEP pair production cross section
is reduced with respect to the pure higgsino case (which is recovered in the limits
! 0
= 75 GeV, the absolute minimum is obtained for
= 0:5 and
mS = 81 GeV, at which point the cross section is reduced to a factor of 0:3 of the cross
section when
= 0. This minimum is indicated by the red cross in gure 6.
The second e ect of the singletdoublet Yukawa interaction is to alter the decay
branching fractions and lifetime of the charged fermion. When mS > mF , as we assume for the
rest of this work, the scalar singlet mediates a new threebody decay mode, shown in
gure 7 (right panel). In gure 8 (left panel), we show the branching fractions into quarks,
leptons, and pions as a function of the coupling , and in
gure 8 (right panel) as a
function of the chargedneutral fermion mass splitting
m. Since the new Yukawa interaction
2The Weinberg operator (F H)(F Hc) may be obtained from integrating out a heavy complex singlet
with electron number coupling to the bilinears F H and F Hc at treelevel. Note that in this case the
operator (F F )(HyH), which may not be forbidden by continuous and discrete symmetries respected by the
interactions in eq. (3.2), is not generated.
{ 7 {
F +F , at LEP within our simpli ed model,
normalized to the charged higgsino pair production cross section
. The cross section is shown
as a function of the coupling
for xed singlet mass mS = 150 GeV (left), and as a function of the
singlet mass mS for xed coupling
= 0:5 (right). In both cases, the charged fermion mass is set
+H H
to mF
= 75 GeV. Cross sections are obtained from [72].
F +F , at LEP within our simpli ed model,
normalized to the charged higgsino pair production cross section
as a function of the coupling
and singlet mass mS, for mF
= 7+H5 GHeV. The red cross indicates
. The cross section is shown
the point of maximal s and tchannel interference, at which the cross section is minimal. Cross
sections are obtained from [72].
couples the fermion doublets to electrons, larger values of this interaction increase the
branching fraction to electrons. This modi cation to the branching ratios results in more
electronrich decays, which alter the LEP search e ciencies relative to the pure higgsino
case. Moreover, the singletmediated decay mode increases the charged fermion width (for
xed masses). This e ect is particularly strong for mass splittings below the pion
threshold. For example, for
m = 100 MeV and mF
the decay length from 57 to 3 m.
= 80 GeV, increasing
from 0 to 1 lowers
F +
decays. fu; fd stand for Standard Model up
or down type quarks or leptons. The decays through a W
(left) or the two body decays into
(center) are set by the fermion's quantum numbers, while the singletmediated decay width (right)
and the scalar singlet mass mS. In the singletmediated diagram,
both F 0 e and F 0 e nal states are possible.
decay branching fractions as a function of the coupling
mF 0 = 3 GeV (left), and as a function of the mass splitting for coupling
= 0:5 (right). In both cases, the charged fermion mass is mF
= 75 GeV and the scalar singlet
mass is mS = 110 GeV. Decays into the charged pion are matched to decays into up and down
quarks at
m = 0:9 GeV. Decay widths are obtained from [63, 73].
UV completions.
We conclude this section by brie y commenting on some possible UV
completions of our simpli ed singletdoublet model. One motivation for this is the fact
that the electroweakscale mass of the scalar singlet within our simpli ed model is not
technically natural. This is easily remedied by, for instance, promoting the scalar to be
part of a chiral super eld in a supersymmetric setup.
The singletdoublet model is a simpli ed version of the winobinosneutrino system. In
the MSSM with decoupled higgsinos, the lightest chargino is winolike. At LEP, schannel
production proceeds via gaugemediated diagrams, while the interfering tchannel diagram
is mediated by the electron sneutrino.
Destructive interference due to the
sneutrinomediated diagram modi es the charged wino production rates at LEP, and weakens the
limits. As an example, consider taking the bino, wino, and higgsino masses to be M1 =
300 GeV, M2 = 95 GeV, and
= 500 GeV, with tan
= 2. In this case, the lightest
neutralino and chargino are winolike, with a chargino mass m
= 82:4 GeV and a chargino
neutralino mass splitting
m = 0:5 GeV.
With a decoupled sneutrino, the chargino
production cross section is
= 5:35 pb and the chargino is excluded by the ADLO
com
W
{ 9 {
bination [56], which sets a 2 pb limit on the cross section. Taking m~e = 85 GeV reduces
the wino production cross section by more than a factor of 6,
= 0:81 pb, so the
limits in [56] are avoided. Di erently from our simpli ed model, in this scenario there are
a plethora of additional states with electroweak charges at the electroweak scale,
including a 105 GeV lefthanded selectron and
500 GeV higgsinos. While the selectron and
higgsinos in this example are beyond LEP reach, a careful analysis of LHC multilepton
and monojet searches is required to decisively test the possibility of light charginos in
this supersymmetric context. We leave a detailed study of the winosneutrino system for
future work.
An alternative UV realization of our simpli ed model is to consider the MSSM extended
HJEP05(218)
by a complex scalar singlet charged under electron number. The scalar singlet can then
couple to the higgsinos through a superpotential interaction, LeHuS, where Hu is the
uptype Higgs super eld and S has been promoted to a super eld. In this theory, the charged
higgsinos would play the role of the fermions F
in our simpli ed model. If the fermion
partners of the singlet eld are heavy, the discussion would be similar to the one in this
work, but with a complex scalar in the e ective theory providing the tchannel interference
in gure 2 instead of a real scalar.
4
LEP limits on the simpli ed model
In the previous section, we found that a simple modi cation to the pure higgsino benchmark
scenario, namely the addition of a singlet scalar, can lead to signi cant di erences in the
production rates and decay branching fractions relevant for LEP searches for charginos.
In this section, we reanalyze LEP limits in the context of our simpli ed model. Due to
the modi ed branching ratios, the relative composition of nal states is di erent in the
simpli ed model compared to the pure higgsino model. As a result, the overall search
e ciency is di erent in the simpli ed model than in the benchmark models considered in
the experimental searches. We take a conservative approach to setting limits meaning that
we only set limits from experimental searches that can be reliably recast. When insu cient
information about a search is available we do not set limits using that search, however, we
do show the wouldbe limits under speci ed assumptions. We make use of the di erent
searches as follows.
The OPAL multilepton search [65] sets bounds on the chargino pair production cross
section times branching fraction squared into electrons, muons, and hadronicallydecaying
taus. The search assumes lepton
avor universality, which is violated in our simpli ed
model since the singlet S mediates threebody decays into electrons only (see
gure 7).
The e ciencies of electrons and muons are similar, and higher than that of
hadronicallydecaying taus [65]. Consequently, the search e ciency in our simpli ed model should be
larger than in the avor universal scenario, since decays to electrons are enhanced. There is
not enough information presented by OPAL to determine the e ciencies for separate nal
states, so we conservatively apply the OPAL limit by assuming the same overall e ciency
for leptonic nal states, despite the higher e ciency expected in our simpli ed model.
(from the simpli ed model of section 3), set by the searches in
= 0:5 and the scalar singlet mass to mS = 110 GeV. All the searches included present limits
for the pure higgsino, so we present limits for our simpli ed model by conservatively estimating
the e ciencies, as explained in section 4. For comparison, we also show in hatched regions the
excluded space that one would obtain assuming the same e ciencies as in the pure higgsino scenario.
In the uncompressed region, limits are obtained from the OPAL multilepton search [65] and the
ADLO combination with promptlydecaying higgsinos [55]. In the compressed region, limits are
obtained from the ADLO conventional combination [55], ADLO \low DM" combination [56], OPAL
multilepton, OPAL ISR assisted, and OPAL HSCP searches [57, 65, 71]. The black dashed line
indicates the oneloop radiative chargedneutral mass splitting.
The OPAL ISR assisted search [57] and ADLO combination with prompt decays [55, 56]
set limits on the charged fermion pair production cross section assuming three body decays
through a W ( ) or two body decays into a charged pion, with rates xed by the higgsino
quantum numbers. Due to Smediated decays into electrons, in our simpli ed model the
W ( ) and
decay modes are diluted with respect to the pure higgsino case by a common
factor, so we simply dilute the reported limits on the cross section by this common factor
squared. This choice is again conservative, since it does not take into account the gain in
e ciency due to the additional electrons in the nal state.
In the case of the ADLO combination with searches for kinked tracks or for large impact
parameters [56], estimating the e ciencies is more challenging, since they depend on both
the decay branching fractions and the chargino lifetime. For these searches, we only present
for reference the limits that one would obtain by (crudely) assuming the same e ciencies
as in the pure higgsino case. In section 5, we recast LHC searches for disappearing tracks
to provide a more reliable bound in the case of displaced decays.
Finally, the OPAL HSCP search [71] covers the very small mass splitting region with
colliderstable charginos. In this case, we simply use the reported pure higgsino cross
section limits by rescaling by the fraction of events where both charged fermions have a
ight distance longer than 3 m, as required by the search.
The resulting limits, for coupling
= 0:5 and singlet mass mS = 110 GeV, are
presented in gure 9, where di erent colors represent the searches leading to the strongest
limit on the pair production cross section at each point. The hatched regions show the
wouldbe limits by assuming that the e ciencies are unchanged between the pure higgsino
model and the simpli ed model.
From
gure 9 (left panel), we see that in the uncompressed region,
m
10 GeV, the
absolute LEP limit on the charged fermion mass is mF
77 GeV. The weakest end of
the limit is achieved for mF 0 . 5 GeV. In this region, multilepton searches lose sensitivity
due similarity between the kinematics of the signal and the W +W
background.
In gure 9 (right panel), we show the limits in the compressed region,
m
First, we note that we cannot set reliable bounds in the region m
m
due to our inability to reliably recast kinked track and large impact parameter searches
at LEP. The hatched region indicates the wouldbe limit (crudely assuming higgsinolike
e ciencies) and rules out charginos up to
75 GeV. In the highly compressed region,
which is covered by HSCP searches,
m
m
, the limit on charginos is mF
& 92 GeV,
which is weaker than in the pure higgsino case due to the smaller charged fermion lifetime,
as discussed in the previous section.
For promptly decaying fermions,
m & 300 MeV, we see from
gure 9 (right panel)
that there are a couple of small gaps in coverage in the range mZ =2
mF
These gaps are at the interface between the region of validity of di erent searches. They
occur due to unphysical discrete jumps due coarse binning in the excluded cross section
reported by the corresponding LEP references, and we expect them to be excluded if more
negrained limits were provided. In addition, these gaps will be covered by LHC searches
(see section 5). Disregarding these small gaps, we nd that the absolute limit on charginos
within our simpli ed model is mF
& 73 GeV. The weakest end of the limit is achieved
for
m
2
3 GeV, a mass splitting region which is covered by ISR assisted searches.
Note that including the hatched regions does not change our conclusions.
Finally, we brie y comment on electroweak precision tests. In the renormalizable
theory, since the fermion doublets do not couple to the Higgs, there is no oneloop contribution
to the S, T , and U parameters [63]. On the other hand, at the renormalizable level the
extended oblique parameters, V , W , and X, are
nite at one loop [74]. To set limits,
we obtain the oneloop V , W , and X parameters using PackageX [75, 76] and
perform an electroweak t as in [58]. We nd a 95% CL limit on the charged fermion mass
mF
54 GeV, which is independent of coupling
and singlet mass mS at oneloop.
In addition to the oblique analysis, we also check nonoblique precision electroweak
limits. First, we check the impact on the Bhabha scattering, e+e
! e+e , cross section
at LEP. In our model, the Bhabha scattering cross section is modi ed at oneloop by
box diagrams with F and S in the loop. To set limits, we calculate the amplitudes with
FeynCalc [77, 78] and the oneloop integrals with PackageX. We then perform a full
t to the measured Bhabha scattering cross section for 7 LEP center of mass energies and
15 scattering angle bins including full correlations reported in [79]. Additional limits are
set by Zpole observables, namely by the Z decay width to electrons and the leptonic
e ective weak mixing angle. In our model, these observables are also modi ed at oneloop
by diagrams with charged fermions F
and a scalar singlet S in the loop. We obtain
the amplitudes as above and we set limits by directly comparing with [80] and [81]. The
Bhabha scattering and Zpole nonoblique limits depend strongly on the singletdoublet
Yukawa coupling and the doublet fermion and scalar singlet masses. We
nd that all of
the parameter space presented in
gure 9 is allowed. For reference,
xing the fermion
doublet masses at mF
= 75 GeV and scalar singlet mass mS = 110 GeV, we
nd that
couplings of
1:5 are excluded by the precision Bhabha scattering analysis at 95% CL,
while the strongest limit from Zpole observables comes from the leptonic e ective weak
mixing angle, which excludes
improve on the current limit on the leptonic e ective weak mixing angle by at least one
HJEP05(218)
order of magnitude [82{84] which is enough to decisively probe all the parameter space for
our charged fermions up to mF
= 100 GeV.
5
LHC limits on the simpli ed model
In the previous section, we concluded that LEP rules out charginos within our simpli ed
model with mass mF
mass mF
the impact of searches from the LHC.
77 GeV in the uncompressed region,
m
10 GeV, and with
73 GeV in the compressed region,
m
10 GeV. In this section, we discuss
There are a number of searches that can be used to probe charginos at the LHC.
Since the fermion doublets F; F couple to the Higgs via the Weinberg operator, invisible
Higgs decays set constraints which we discuss in section 5.1. In the compressed region,
the charged fermions may decay leaving littletono activity in the detector, and can be
probed by monojet searches, presented in section 5.2. For even smaller mass splittings, the
charged fermions may lead to kinked or disappearing tracks, as discussed in section 5.3.
Other LHC searches leading to weaker limits are mentioned in section 5.4. Finally, the
combination of LEP and LHC searches is shown in section 5.5.
5.1
Invisible decays of the Higgs
The Weinberg operator in eq. (3.2) leads to an e ective dimension ve coupling between
the Higgs and the neutral fermions F 0; F 0
where the second equality uses eq. (3.3) at treelevel. The charged fermion does not couple
to the Higgs. The invisible decay width of the Higgs to the neutral fermion is
ghF 0F 0 =
v
=
2 m
v
;
=
mh 2
8
ghF 0F 0 1
4m2F 0
m2
h
3=2
:
(5.1)
(5.2)
The current limit on the Higgs invisible width is BRh!inv
0:24 [85, 86], and rules out most
of the parameter space with mF 0
mh=2, except when mF
and mF 0 are very compressed
(since the compression also suppresses the couplings to the Higgs). The corresponding
limits are shown in gure 10.
5.2
In the compressed region of 300 MeV
m
10 GeV, the decay products of the charged
fermion are soft and therefore challenging to detect at the LHC. In this region, fermion
pair production (F +F , F +F 0, F
F 0, and F 0F 0) results in a signal with missing energy
and littletono hadronic or leptonic activity in the detector. This topology is constrained
by LHC searches that look for large missing energy along with an ISR jet, namely monojet
searches. For splittings below
300 MeV the decays are no longer prompt, and dedicated
searches for displaced objects become e ective.
There are 13 TeV monojet searches from both ATLAS [87] and CMS [88] with about
36 fb 1 of data. Here, for simplicity, we just recast the CMS search, which is representative
of both (but sets stronger limits due to an apparent downward
uctuation). This search
selects events by de ning 22 exclusive E= T regions, from E= T = 250 to 1400 GeV. The leading
jet is required to have a transverse momentum of pT
100 GeV and a pseudorapidity of
2:5. A pT cut on leptons, taus, photons, and bjets is imposed, and minimum angles
are required between the four leading jets.
In order to recast the CMS monojet search, we perform a Monte Carlo Simulation.
We implement our simpli ed model with FeynRules [89] and simulate events at leading
order with Madgraph5 aMC@NLO [90], using the nn23lo1 PDF dataset [91]. We use
Pythia8 [92] to simulate the parton shower, and Delphes 3 to perform the detector
simulation using the CMS detector card [93]. Jets are clustered using the antikT
algorithm [94] with jet radius R = 0:4. We match up to three jets using the MLM matching
scheme [95] with a matching scale of 50 GeV. In appendix A, we describe the validation
of our simulaton.
For the signal, we generate a sample of fermion pair production events. We set limits
using the CLs method [96], and combine the limits from the di erent missing energy bins
by making use of the bin with the best expected limit at each point in the model parameter
space. The resulting limits for coupling
= 0:5 and singlet mass mS = 110 GeV are
presented in gure 10. The limits are mostly driven by the low missing transverse energy bins,
E= T
590 GeV, for which the errors are already close to being dominated by systematics.
We note that the limits are roughly independent of
in the compressed region. This is
because monojets searches are sensitive to prompt decays, and therefore the only e ect of
the Yukawa coupling is to change fermion branching ratios, to which the monojet searches
are not sensitive.
5.3
Disappearing track searches
As the chargedneutral splitting goes below
300 MeV, the decay length of the charged
fermion becomes macroscopic. At the LHC, there are a number of searches that target
various decays lengths. Roughly speaking, decay lengths of O(mm) are probed by searches
for displaced vertices, O(cm) are probed by searches for kinked or disappearing tracks,
and O(m) are probed by searches for heavy stable particles. Displaced vertex searches do
not set the dominant limit anywhere in our parameter space, because they tend to require
energetic particles originating from the displaced vertex [97], and are therefore not relevant
when the charged and neutral fermions are compressed. Heavy stable particle searches will
be discussed in section 5.4.
The most recent search for disappearing tracks was performed by ATLAS at 13 TeV
with 36:1 fb 1 of data [98]. (The most recent disappearing track search from CMS was at
8 TeV [99].) The search looks for the partial track of a chargino, which decays mid ight
to 0
. The outgoing pion or lepton is very soft, since its momentum is set by
m, and is typically not seen, which means the chargino track appears to end abruptly.
In addition to the disappearing track, this search requires an ISR jet for triggering.
We recast the disappearing tracks search using the following procedure. Using
Madgraph5 aMC@NLO, we simulate pair production events at leading order and compute
the e ciency to select an event with a disappearing track as a function of the lifetime of the
charged fermion and its mass (see appendix A for a more detailed description). We then
compute the expected number of events as a function of lifetime and mass and compare to
the 95% CL excluded number from ATLAS. The results are shown in gure 10.
The disappearing tracks search excludes chargino masses below 100 GeV for mass
splittings between 100 and 300 MeV, for our benchmark point of mS = 110 GeV and
For splittings smaller than 100 MeV, the charged fermion decay length becomes long enough
that the majority of charged fermions do not decay within the tracker. For splittings larger
than 300 MeV, most of the charged fermions decay before they reach the tracker. Note
that
m = 300 MeV corresponds to c
1 cm for our benchmark point, which is naively
too short to leave a particle track. However, the large production cross section and sizable
= 0:5.3
2
5, imply that limits can be set using the exponential tail
relevant boost factor,
of the decay distribution.
5.4
Other LHC searches
As can be seen in gure 10, in the uncompressed region, the invisible Higgs limits close the
parameter space left open by LEP while in the compressed region monojet searches, and
disappearing track searches work together to constrain some of the parameter space. There
are a number of other searches at the LHC that can be used to constrain the simpli ed
model for chargino masses below 100 GeV. We mention them brie y in this section.
Multilepton searches look for one or more charged leptons. Dedicated searches in the
compressed region using an ISR jet have been performed by both ATLAS and CMS [10,
16, 41], but still the minimal lepton pT required in these searches is at least 3:5 GeV
(for muons at CMS) and more typically
5
10 GeV. For this reason, these searches
do not outperform LEP searches for chargino masses below 100 GeV and mass splittings
below
3 GeV. This expectation is con rmed by the latest ATLAS results [10], which
do not improve on the
90 GeV LEP charged higgsino bound at small mass splittings.
Multilepton searches at LHC are most e ective when the leptons are hard and they set
limits in the uncompressed region
m
10 GeV, but as discussed above, the only space
3The limits do depend on , but only very weakly. Increasing
leads to a shorter decay length, leading
to an overall shift of the limits towards lower mass splittings. From
= 0 to 1, the limits on
m only
change by . 40 MeV.
uncovered by LEP searches in the uncompressed region is already excluded by invisible
Higgs searches.
For O(cm) decay lengths, the disappearing track searches are the most sensitive, while
for longer decay lengths, HSCP searches become the most sensitive. The HSCP searches
performed by LEP constrain cross sections at the
0:01 pb 1 level, which is far below
the cross section in our simpli ed model within the range of masses that we consider.
Since HSCP searches at the LHC cover approximately the same range of
m as the LEP
searches, we do not recast HSCP searches from the LHC.
Finally, as pointed out in section 5.1, note that the charged fermions in our simpli ed
model do not couple to the Higgs at treelevel. As a consequence, there is no oneloop
diagram with charged fermions F
modifying the h !
rate, and no signi cant limits
on our simpli ed model may be set with current measurements of the Higgs to diphoton
branching fraction.
The combined LEP and LHC limits are shown in gure 10, where we indicate with colors
the LHC limits, while the LEP limits discussed in section 4 are shown in gray.
From the left panel in
gure 10 we see that the uncompressed region,
m
10 GeV,
is completely excluded up to mF
= 100 GeV by a combination of LEP results and the
constraint on the Higgs invisible width, where in the plot we highlight in red the region
which is exclusively ruled out by the Higgs invisible width constraint.
In the right panel of gure 10 we present the limits in the compressed region,
m
10 GeV. In red, blue, and green we show LHC constraints from the Higgs invisible width,
monojet, and disappearing track searches, respectively. Some parts of parameter space are
excluded by both LHC and LEP, and here we simply overlap LHC constraints on top of
LEP constraints. In the uncompressed region, the Higgs invisible width constraints do not
lead to any signi cant improvement with respect to LEP limits, since the couplings of the
Higgs to the neutral fermion are suppressed by the small chargedneutral mass splitting
(see eq. (5.1)). On the other hand, the combination of LHC monojet and disappearing
track searches cover the region m
m
300 MeV, which is hard to exclude reliably
with published data from LEP displaced searches as discussed in section 4. In addition,
for
m
300 MeV, monojet searches at LHC cover most of the small gaps for charged
fermion masses mF
. 63 GeV left out by our LEP exclusion in gure 9.
From
gure 10 we conclude that the absolute limit on the chargino mass within our
simpli ed model is mF
73 GeV, and is not improved with respect to the absolute
LEP limit. The lower end of this limit is obtained in the compressed region, with mass
splittings of a couple of GeV. In the uncompressed region,
m
10 GeV, the combination
of available LEP and LHC limits rule out charginos in our simpli ed model up to at least
mF
= 100 GeV. The limits are summarized in table 2.
We conclude the discussion by brie y commenting on the future projected
sensitivity from the LHC (with 300 fb 1). As shown in
gure 10, the remaining window is in
the compressed region, where disappearing tracks searches and monojet searches are the
most constraining. The existing disappearing track search already excludes masses up to
(from the simpli ed model of section 3), set by LEP and by
the LHC, in the uncompressed region (left) and in the compressed region (right). The coupling is
set to
= 0:5 and the scalar singlet mass to mS = 110 GeV. The LEP limits are the same as in
gure 9 but here are indicated in gray, while LHC limits are colored. In the uncompressed region,
the strongest limits are obtained from LEP and from LHC constraints on invisible Higgs decays.
In the compressed region, the strongest limits are obtained from LEP and from LHC monojet and
disappearing track searches. The black dashed line indicates the oneloop radiative chargedneutral
mass splitting.
LEP
LEP+LHC
m
m
10 GeV
10 GeV
mF
mF
76 GeV
73 GeV
mF
mF
for the simpli ed model of section 3. LEP limits are obtained from the searches in table 1, while
LHC limits consider constraints on the Higgs invisible width [85, 86], disappearing track [98], and
monojet [88] searches.
100 GeV, but in a limited range of
m. The limits from these searches lose sensitivity
steeply as a function of decay length, as discussed in section 5.3. Near
m
the decay length scales like
( m)3, so that an eightfold improvement on the lifetime
only improves the
m reach by a factor of about 2. Consequently, extrapolating current
searches to 300 fb 1, we estimate that the limit will improve moderately, by
Other projections have also been made [28, 32].
Monojet searches, on the other hand, cover a wide range of
m values, but only extend
to
65{78 GeV in charged fermion mass (depending on
m). A number of projections
have been performed [19{23, 26, 30{32, 100] and typically estimate the reach for higgsinos
to extend to
100{200 GeV. These estimates, however, are strongly dependent on the
assumed systematics, making it hard to say conclusively whether or not monojet searches,
with the high luminosity data, will be su cient to cover the remaining parameter space
below 100 GeV.
In this work, we surveyed the limits on charginos with masses ranging from mZ =2 to
100 GeV. We reviewed LEP limits on chargino pair production, and found that charged
higgsinos with masses below
90 GeV are excluded. To study limits on fermions with unit
charge in a more general scenario, we introduced small modi cations to the pure higgsino
case in the context of a simpli ed model. If a singlet scalar couples to the charged fermions
and electrons, then the production cross section is reduced, due to destructive interference,
and decay branching fractions are modi ed. We showed that for our simpli ed model, LEP
only excludes fermions with unit charge belonging to an SU(2)W doublet up to 73 GeV.
We also discussed LHC limits on such low mass \charginos". We discussed a
combination of searches, including Higgs precision measurements, monojet, multilepton, displaced
decay, and HSCP searches. For our simpli ed model, we found that the LHC, with current
statistics, is unable to improve on the overall LEP limit on the mass of charginos. The most
challenging topology to probe at the LHC corresponds to the compressed region, where
charginos decay leaving littletono energy deposition in the detector and limits rely mostly
on monojet searches.
Our results lead to several questions which remain to be addressed. First, it would
be interesting to identify the broader class of models with light fermions with unit charge
which are consistent with current data. In this work, we explored charged fermions as part
of an SU(2)W doublet, but a similar analysis may be carried out for other representations.
In the case of SU(2)W singlets, fermions with unit charge may evade LEP bounds due to
tchannel interference in the production cross section, as in this work. In the case of SU(2)W
triplets, LEP bounds may also be relaxed with tchannel interference, but we point out that
the increased pair production cross section at LHC with respect to the SU(2)W doublet
case should lead to stronger limits from monojet and multilepton searches. It would be
interesting to study the embedding of these models into full UV completions. The case of
SU(2)W triplets is particularly interesting, since it corresponds to the case of the charged
wino in the MSSM, where interference in LEP pair production arises through an electron
sneutrino. Finally, a careful analysis of the systematics and limit projections at both the
LHC and future colliders targeting the low mass region is needed. Future e+e
colliders,
such as FCCee, could de nitively test the existence of fermions with unit charge below
100 GeV.
As more data are collected, LHC searches will tend to be optimized for higher mass
signals that come into reach. It is important to be mindful of gaps in exclusion limits, and
to identify light particles that are still allowed. Light particles can serve as a target for
future searches, but often require a careful analysis in order to separate from backgrounds.
We have found that charged fermions as light as 75 GeV may have evaded both LEP and
the LHC, so far, and therefore serve as a target for future LHC searches.
Acknowledgments
The authors would like to thank Kyle Cranmer, Jared Evans, Ayres Freitas, Andy Haas,
Philip Harris, Patrick Meade, Carlos Wagner and Jose Zurita and for useful discussions.
E= T (GeV)
250
280
310
340
370
280
310
340
370
400
NCMS
79700
45800
27480
17020
10560
0:68
0:64
0:73
0:64
0:72
MC
0:016
0:02
0:027
0:033
0:044
NCMS
49200
24950
13380
7610
4361
0:70
0:76
0:72
0:83
0:88
MC
0:03
0:43
0:57
0:082
0:11
our simulation, MC. The reported uncertainties are statistical uncertainties from our simulation.
The work of D.E.U. is supported by PHY1620628, M.L. acknowledges support from the
Institute for Advanced Study, and J.R. is supported by NSF CAREER grant PHY1554858.
M.L. would like to acknowledge the Mainz Institute for Theoretical Physics (MITP) and the
Aspen Center for Physics, which is supported by National Science Foundation grant
PHY1607611, for their hospitality and support while part of this work was being completed.
A
A.1
Validation of LHC analyses
Monojet searches
We validate our monojet analysis by generating events, applying a detector simulation,
implementing the monojet selection, and comparing the resulting number of events to the
number of events reported by CMS [88]. The CMS search was performed at 13 TeV and
used an integrated luminosity of 35:9 fb 1
. We compare a sample of Z( ) + j events and
a sample of W
) + j events which have similar kinematics to our signal. The events
are generated at leading order using Madgraph5 aMC@NLO [90] with MLM matching
up to 3 jets, showered with Pythia8 [92], and processed through Delphes 3 [93].
The ratio between the number of events predicted by our simulation and the number
of events found by CMS is de ned to be
MC =
NMC :
NCMS
(A.1)
The estimation given by CMS, NCMS, is datadriven and therefore accounts for
contributions beyond leading order. In table 3 we report the values of MC found using the ve
lowest E= T bins. Across these bins we nd a variation of 8% in Z(
) + j and 18% in
W
) + j. The deviation of MC from unity by several tens of percent is expected
since we generate our events at leading order while the CMS estimation is datadriven so
automatically includes contributions from all orders.
A.2
Disappearing track searches
The ATLAS disappearing track search that we recast was performed at 13 TeV with an
integrated luminosity of 36:1 fb 1 [98]. We parametrize the e ciency to select an event
containing a disappearing track by event which we factorize, roughly following the parametrization
.
χ ± [
]
ATLAS 13 TeV result [98] (blue) and from our simulated events with e ciencies applied according
to eq. (A.2) (red).
of ATLAS, as
event = track
selection;
(A.2)
where track, the track e ciency, indicates the e ciency to reconstruct a chargino as a
disappearing track and selection, the selection e ciency, indicates the e ciency for the
event to be selected.
We compute the track e ciency in Monte Carlo. The events are generated with
Madgraph5 aMC@NLO for a range of charged fermion masses. The distribution of decay
lengths of the charged fermion is speci ed by the kinematics of the event and by the charged
fermion's lifetime. In each event, the charged fermions are decayed and assigned a track
e ciency taken from
gure 4 of [98]. Our calculation of track is thus a function of charged
fermion mass and lifetime.
The event e ciency can be found by comparing the number of signal events produced
in our Monte Carlo with the number of signal events needed to produce the limits in gure
8 of [98].
With event and track we use eq. (A.2) to nd selection, which will also be a
function of charged fermion mass and lifetime.
To compute event in our simpli ed model, we assume that selection is the same as in the
ATLAS search and compute track in simulated simpli ed model events. The result of our
procedure, applied to chargino events, and the ATLAS result are compared in gure 11.
Open Access.
This article is distributed under the terms of the Creative Commons
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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