Light scalars and exotic top partner decays
in composite Higgs models
Thomas Flacke
IBS CTPU, Daejeon

G. Cacciapaglia, T. Flacke, S.J. Lee, A. Parolini, H. Serodio [JHEP 1506, 085]
G. Cacciapaglia, H. Cai, A. Deandrea, T. Flacke, S.J. Lee, A. Parolini [JHEP 1511, 201]
H. Cai, T. Flacke, M. Lespinasse [arXiv:1512.04508]
A. Belyaev, G. Cacciapaglia, H. Cai, T. Flacke, H. Serodio, A. Parolini [PRD 94 (2016) no 1, 015004]
M. Backovic, T. Flacke, J. H. Kim, S. J. Lee [JHEP 1504, 082]
M. Backovic, T. Flacke, J. H. Kim, S. J. Lee [JHEP 1604, 014]
M. Backovic, T. Flacke, B. Jain, S. J. Lee [JHEP 1703, 127]
A. Belyaev, G. Cacciapaglia, H. Cai, G. Ferretti, T. Flacke, H. Serodio, A. Parolini [JHEP 1701, 094]
G. Cacciapaglia, H. Cai, A. Carvalho, A Deandrea, T. Flacke, B. Fuks, D. Majumder, H.-S. Shao [JHEP 1707, 005 ]A. Belyaev, T. Flacke, B. Jain, P.B. Schaefers [PRD98 (2018) no.3, 035019 ]G. Cacciapaglia, G. Ferretti,T. Flacke, H. Serodio [EPJC 78 (2018) no.9, 724]
N. Bizot, G. Cacciapaglia, T. Flacke [JHEP 1806, 065]

Beyond the BSM, Ikaho, Oct 2nd, 2018

Outline•

Motivation & Introduction

H

?

•

Towards UV embeddings of acomposite Higgs: Models•

Common light pseudo-Nambu
Goldstone bosons•

Top-partners and common exotic
decays / new signatures•

Conclusions

??

2/31

Motivation for a composite Higgs
An alternative solution to the hierarchy
problem:• Generate a scale ΛHC<<Mpl througha new confining gauge group.
• Interpret the Higgs as a pseudo-NambuGoldstone boson (pNGB) of a spontaneously
broken global symmetry of the new strong sector.
Kaplan, Georgi [1984]

The price to pay:
• From the generic setup, one expects additional
resonances (vectors, vector-like fermions, scalars)around ΛHC (and additional light pNGBs?).
• The non-linear realization of the Higgs yields
deviations of the Higgs couplings from their SM
values.
• … many model-building questions …
• … and potentially new signatures for LHC …

αs

Running of the newstrong couplingH(𝜓𝜓)

1019GeVeVfmhΛHC=g*f~few TV Mpl
eV

ρ, ρµ
T’

O(few TeV)𝝅’?

f > 800 GeV“Higgs”a’??

125 GeV

3/31

Composite Higgs Models: Towards an underlying
model and its low-energy phenomenology
Ferretti etal. [JHEP 1403, 077] classified candidate models which:c.f. also Gherghetta etal (2014), Vecchi (2015), Ferretti (2016) for related works on individual models

•
•
•
•
•

contain no elementary scalars (to not re-introduce a hierarchy problem),
have a simple hyper-color group,
have a Higgs candidate amongst the pNGBs of the bound states,
have a top-partner amongst its bound states (for top mass via partial compositeness),satisfy further “standard” consistency conditions (asymptotic freedom, no
anomalies),

The resulting models have several common features:• All models require two types of hyper-quarks 𝜓, 𝜒 . The Higgs is realized as a 𝜓𝜓bound state. Top partners are realized as 𝜓𝜓𝜒 or 𝜓𝜒𝜒 bound states.
• None of the models has the minimal EW coset SO(5)/SO(4) which yields only the
Higgs multiplet as pNGBs. The smallest EW cosets are instead SU(4)/Sp(4), SU(5)/SO(5), or SU(4)xSU(4)/SU(4), and all contain additional colored and uncoloredpNGBs.

4/31

Example: SU(4)/Sp(4) coset based on GHC = Sp(2Nc)
and colored pNGBs
Motivation
Phenomenology of quark partners
Towards a CH UV embedding and its phenomenology
Conclusions and Outlook

One example: SU(4)/Sp(4) coset based on GHC = Sp(2Nc )Field content of the microscopic fundamental theory and its charges w.r.t.
Field
contentof themicroscopic fundamental theory andand propertytransformation
the
gauge
group
Sp(2N)×SU(3)×SU(2)×U(1),the global
symmetries
under the gauged symmetry group Sp(2Nc ) ⇥ SU(3)c ⇥ SU(2)L ⇥ U(1)Y , andSU(4)×SU(6)×U(1):under the global symmetries SU(4) ⇥ SU(6) ⇥ U(1).
Sp(2Nc )
1
2
3
4
1
2

SU(3)c

SU(2)L

U(1)Y

1

2

0

1
1

1
1

1/2
1/2

3

1

2/3

3
4
5

3

1

SU(4)

SU(6)

U(1)

4

1

3(Nc

1

6

q

1)q

2/3

6

[JHEP1511,201]
14 / 46

5/31

Motivation
Phenomenology of quark partners
Towards a CH UV embedding and its phenomenology
Conclusions and Outlook

Bound states of the model:

ample: SU(4)/Sp(4) coset based on GHC = Sp(2Nc )Bound states of the model:
spin SU(4)⇥SU(6) Sp(4)⇥SO(6)0(6, 1)(1, 1)(5, 1)
0(1, 21)(1, 1)(1, 20)1/2(6, 6)

1/2(6, 6)

1/2
1/2(1, 6)(15, 6)µ1(15, 1)µ1(1, 35)[JHEP1511,201](1, 6)(5, 6)(1, 6)(5, 6)(1, 6)(5, 6)(10, 6)(5, 1)(10, 1)(1, 20)(1, 15)

names
⇡
c
⇡c
1
1
5
1
1
2
5
2
3
5
4
10
4

a
⇢
ac
⇢c

contains SU(2)L×SU(2)Rbidoublet “H”
form a and 𝜂’; SM singlets
20 colored pNGB:(8,1,1)0⊕(6,1,1)4/3⊕(6,1,1)-4/3

contain (3,2,2)2/3
fermions: tL-partners
contain (3,1,X)2/3
fermions: tR-partners: ⇡ transforms as 4 1 under SO(4) ! identify ⇡ ⌘ (H, ⌘).
5
5
10
tners: This(3, 2,is2)
states
(for
t
)
in
,
,
andwith SM gauge bosons and matter through:
L
2/3
1,2
4 interacts
the BSM + Higgs sector which
1
5
5
10
(3,
1,
1)
or
(3,
1,
3)
(for
t
)
in
,
,
,
,
R
3and4 mixing
2/3
1,2
1,2
4 . of the top with top partners,
SM gauge2/3
interactions, (global)
anomalycouplings,
15 / 46

6/31

Full list of "minimal" CHM UV embeddings[JHEP1701,094]

7/31

New PNGBs and their phenomenology
1. ALL models:a and η’:(one HC anomaly free, one anomalous pseudo-scalar) which couple to
SM gauge bosons through WZW couplings and to fermions with mf /f.
[JHEP1701,094, EPJC 78 (2018) no.9, 724]

2. ALL models:
𝝅8 : Color octet pseudo-scalar pNGB which couples to gg, gɣ, gZ, tt [JHEP1701,094]
3. Depending on the embedding model: Additional colored and uncolored pNGBs[JHEP1511,201]

8/31

As weSinglet
discussedpNGB
in the previous
section, andthe singlet
pseudoscalars couple to a pairsummary
phenomenology

SM gauge bosons via the WZW anomaly terms, and to a pair of top quarks. The gener
a and η’: Arise from the SSB of U(1)𝜒 ⨉ U(1)𝜓. One linear combination has a GHC anomalye↵ective Lagrangian for a SM neutral pseudo-scalar ⇡0 can be written as(η’) and is expected heavier. The orthogonal linear combination (a) is a pNGB.
1
mt
µ
2 2
L ⇡0 = @ µ ⇡ 0 @ ⇡ 0 M ⇡ 0 ⇡ 0 + i C t⇡0 t 5 t
2
f⇡
✓
◆
(4
2
2
↵s g
g2 W µ⌫⇢g1 B µ⌫⇢
µ⌫⇢
a
a
i
i
+
⇡0 ✏
Gµ⌫ G⇢ + 2✏
Wµ⌫ W⇢ + 2✏
Bµ⌫ B⇢,
8⇡ f⇡
g 3 gg 3 g•whichThe mass
ma must resultby
fromexplicit
breaking of
U(1) Msymmetries(e.g. through massis characterized
fiveparameters:
thethemass
coupling g /⇡0 , the dimension-fullterms for the underlying 𝜒). mη also obtains mass from instantons.

(coefficient of the anomalous coupling to gluons) that controls the production cross sectio• f𝝅0 results from chiral symmetry breaking.

.

and the three ratios Ct /g , B /g and W /g which dictate the branching ratios.

• The WZW coefficients 𝜅i are fully determined by the quantum numbers of 𝜒, 𝜓.

In the following, we will neglect the e↵ect of top loops to the branching ratios into a pa

• The coefficient Ct is also fixed (depends on spurion charge of dominantly mixing top-partner)2agi rationale
i
mt is that, once such e↵ects are sizeabof 1gauge
main
a
L =
@µ a@ µbosons:a m2 a2the++a✏µ⌫⇢ Gbehind
Ga this+ i Cfacta t 5t(1.3)
aa2
Phenomenology

32⇡ 2 fa

i,µ⌫

i,⇢

fa

the decay is dominated by the tt̄ final state, so that searches in diboson final states becom• 𝝅0 is produced in gluon fusion (controlled by 𝜅g/f𝝅).
irrelevant. Thus, in this large top coupling limit, the only phenomenologically relevant e↵e(1.4)
ratios.
• 𝝅0 decays to gg, W W, ZZ, Z , , tt̄, ff with fully determined branching
will be on the gluon fusion production. As shown in Appendix ??, the e↵ect on gluon fusi(controlled by 𝜅B/𝜅g, 𝜅W/𝜅g, Ct/𝜅g)
can be encoded in a M⇡0 –dependent shift of the g coupling, as in Eq.(??). Thus, o
9/31• The resonance is narrow.
analysis can be extended in a straightforward way.

Coefficients of a for sample models M1 - M12

Ct:[EPJC 78 (2018) no.9, 724]

[EPJC 78 (2018) no.9, 724]

10/31

For a given model, we can combine bounds from resonance searches to
get a bound on f .

very weak
constraints
for light a

11/31

NOTE: Low mass region has a “gap” between 15 - 65 GeV.

𝛾𝛾
[PRL113, 17801](ATLAS)[CMS-PAS-HIG-17-013]

BR(h➝BSM)<.34[JHEP1608, 045]
(ATLAS+CMS)𝜇𝜇[PRL109, 121801](CMS)[ATLAS-CONF-2011-020][EPJC 78 (2018) no.9, 724]

12/31

We studied an option to close this gap by searching for a-decays to
di-taus (!!) in OSOF leptonic decays.[EPJC 78 (2018) no.9, 724](more in backup-slides)[EPJC 78 (2018) no.9, 724]

ISR-boosted di-photons [arXiv:1710.01743] yield another option withcomplementary discovery potential.
Upshot: these light composite pNGBs are NOT ruled out and are testable.

13/31

and possible connections with the properties of the singlets.
color octet ⇡8 , which is present in all models discussed in Sec. II, can be described
B. Phenomenology of the color
As aoctet
first connection, we note that its mass can be expressed in t
↵ective Lagrangian
8
3 2 2
1 2
3 2 2
2
2
mdiscussed= m⇡ +inCgSec.
gs fII,=can bemadescribed+ Cg g s f ,
a
The
color
octet
⇡
,
which
is
presentinallmodels
8
1
1
m
t
4
⇠
4
(Dµ ⇡8a )2
m2⇡8 (⇡8a )2 + i Ct8⇡8a t̄ 5 t2
f ⇡82
by the 2e↵ective Lagrangian
 the second term0 comes from loop corrections from QCD, andEffective Lagrangian:where↵s g8 a µ⌫⇢ 1 abc b cg B8 a+⇡8 ✏d Gµ⌫ G⇢ +aGµ⌫ B⇢ , (63)(thegsloopg8 contribution is cut o↵ at a scale ⇤ ⇠ 4⇡f1
18⇡f2⇡8 a 2 order2 one
mtnumbera 2aColored PNGBs (the color octet 𝝅 )m⇡8 (⇡8 ) + i Ct8⇡8 t̄ 5 t
L⇡8 = (Dµ ⇡8 )22
2 the octet
betweenf⇡themassofthe masses8
he covariant derivative contains QCD interactions
withgluons.
modelsdis- in the singlet sector: in In theand
0
↵

1
g
B8 thats
g8a µ⌫⇢by Eq.abc
b Wec also recall
thesingletmasses(26).
expecte✏ the coefficients(63)
d Gµ⌫ G⇢are+equal Gaµ⌫ B⇠ ⇢ ⇠ ,1, asn this article (f⇡8 = f ), matching with Eq.s+(46) and⇡8(37),8⇡f⇡82
gs g8in QCD. In the limit of ma ⌧ m⌘0 , ma ⇠ ma sin ⇣, thus

where
the CHderivative
UV embeddings:
where
theincovariant
contains QCD interactions with gluons.2 In the models disma
3 2 2+ Cg gare.
s f equal2g8 =in this2c5 article
d , (f
2c
2Y
d
,
C
=
n
2c
.
(64)
B8⇡=
5
t8
5
cussed=f),matching
with
Eq.s
(46)
and
(37),
the
coefficients,4⇠ sin ⇣8pppm2⇡8 ⇠toet ⇡8 is produced
at the LHC in pairs via QCD interactions or singly via gluon fusion
Phenomenology

17
p
p
p
production
section at =the LHC
13or
TeV
are shown C
inthroughFig. 7, whereis single-produced
in5 gluon
QCD.
• 𝝅8cross2c
d for, 8 fusion
and2cpair-produced
2c
g8
B8 =
5 2Y d ,t8 = n
5.

(64)

XXXX.

• 𝝅8 decays to gg, gɣ, gZ, tt- with fully determined branching fractions into dibosons:

The octet ⇡8 is produced at the LHC in pairs via QCD interactions or singly via gluon fusion𝞆 =2/3:Y𝞆 gluon-photon=1/3: gg/gɣ/gZ
1 / .05/ .015,gg/gɣ/gZ
1 / .19 / .06.
production
throughfusion=would
requirevery Ylarge
hyperchargeof the= constituent• For
11. The production cross section at the LHC for 8 and 13 TeV are shown in Fig. 7, wherens, so we neglect it, here. Single production from tt̄ fusion is also suppressed by the need of creating•gluonThe
resonance
is narrow.
is fromwe
splittings
as well as by the additional (mt /f⇡8 )2 suppression from (63).
used
XXXX.
11

14/31
Single production through gluon-photon fusion would require very large hypercharge of the constituent
fermions, so we neglect it, here. Single production from tt̄ fusion is also suppressed by the need of creating

Colored PNGBs
Constraints from pair production:

Bounds from ATLAS and CMS 4t and dijet-pair searches at 8 and 13 TeV.
[JHEP1510,150, JHEP1508,105 ,EPJC78,2,140, 1805.10835][PLB747,98, EPJC78,3,250 ,CMS-PAS-EXO-17-021]
For (more model-dependent) single-production bounds see[JHEP1701,094] and backup slides.

15/31

Direct bounds on composite PNGBs• a and η’ : Studied in JHEP1701,094 , EPJC 78 (2018) no.9, 724:
tested in many channels: gg, 𝛾𝛾, Z𝛾, ZZ, WW, tt, bb, 𝜏𝜏, 𝜇𝜇
CH decay constants are being constrained, but no mass is excluded.
15 GeV < ma < 65 GeV is poorly covered by existing searches.
• 𝝅8 : Studied in JHEP1701,094 and work in progress:
bounds on mass (QCD pair prod., decay to tops, gg, g𝛾): ~1 TeV.
• 𝝅6 : Partially studied in JHEP1511,201:
bounds on mass (QCD pair production, decay to tops): ~1 TeV• 𝝅3 : To my knowledge not studied in detail for composite models.
• Other un-colored pNGBs: only produced through EW interactions (ifSU(2)⨉U(1) charged) or EW Wess-Zumino-Witten terms (if SM
neutral). Thus bounds on the mass are expected to be weak.
See e.g. arXiv:1808.10175 for the EW PNGB sector of SU(5)/SO(5)models.
16/31

Other CH model signatures
The model
Phenomenology of quark partners
Conclusions and Outlook

Vector-like quarks (top- partners or quark partners)
Production and decays
with charge 5/3, 2/3, -1/3, -4/3
Production mechanisms (shown here: X5/3 prod. for partners of up-type quarks)
q

q

0

Du/c

W

W
u/c

u/c

u/c
X5/3

(a) EW single production

u/c

u/c

X5/3

(b) EW pair production(c) QCD pair production

Decays:• X5/3 ! W + t (100%),• B ! W t (⇠ 100%),• Tf 1 , Tf 2 , Ts ! W b, Zt, ht (with parameter-dependent BRs)

17/31

mB [GeV]mB [GeV]Bounds on VLQ masses

Figure 3: Observed (solid line) and expected (dashed line) 95% CL upper limits on the B B̄ cross-section versus
mass for the combination and the standalone analyses for the (left) singlet and (right) (T , B) doublet scenarios [8].
The shaded bands correspond to ±1 and ±2 standard deviations around the combined expected limit. The thin redline and band show the theory prediction and [ATLAS:
corresponding
uncertainty [13], respectively.
JHEP 1381,104; CMS: PRL 112(2014), 171801]

X5/3 : Run I: MX ≳ 800 GeV,
Run II: MX ≳ 1.3 TeV,

0.7

13

Observed limit

1380
13
50

0.6
0.5

SU(2) doublet
1320

0.4

SU(2) singlet

1360
1340

0.3
0.2

1320

0.1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.8

VLQ combination

0.7

Observed limit
SU(2) (B,Y) doublet
SU(2) singlet

1100

0.5
0.4
0.3
0.1

BR(T → Wb)[ATLAS-CONF-2018-032]

1250
1200
1150
1100

0.2

1300

1350
1300

SU(2) (T,B) doublet

0.6

1400

95% CL mass limit [GeV]

75

1400

s = 13 TeV, 36.1 fb-1

0

VLQ combination

ATLAS Preliminary

0.9

130

s = 13 TeV, 36.1 fb-1

1400

0.8

1420

1

12
00

ATLAS Preliminary

0.9

BR(B → Hb)

1

Run II (examples):
95% CL mass limit [GeV]

BR(T → Ht)

T & B:[CMS PAS B2G-16-019, ATLAS: 1806.01762]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

1050
1000

BR(B → Wt)

Figure 4: Observed lower limits at 95% CL on the mass of the (left) T and (right) B as a function of branching18/31
ratio
assuming B(T!Ht) + B(T!Zt) + B(T ! W b) = 1 and B(B!Hb) + B(B!Z b) + B(B!Wt) = 1. The yellow

300 fbZ’(10%

60 fb

Z’(30%

X5/3 → tW

Bounds on VLQTmasses→ bW
0

T & B cont.:

0.3

0.6

0.9

Resonances
to heavy
Vector-likequarkquarks
single production

20 fbZ’(1.2%)→t →tt lepT→ tH cWb)=1.5
cWb=1.5

8 fb
800 fb

T → tH35 fb

t → lep
T → tH→cZt=2.5
Z’(10%)
tt
cZt=2.5

900
15fb
fb

T → tZ

25 fb

t → had
T →gKKtH cWb=1.5→ tt

Q → qW

T → bW

7 fb

B → bZ

35 fb

B → tW

8 TeV

9 fb
4 fb

X5/3 → tW

300 fbZ’(10%)→cWb
tt =1.0Y→tH c(Wb)=1.0

60 fb

Z’(30%) → tt

T → bW
0.3

0.6

0.9

1.2

1.5

b* → tW KR=1
KR=1

50 fb

250 fb100 fb

0

0.25

0.5

200 fb120 fb200 fb

1

1.5

0.75

1.25

200 fbt → lep
T → tH cZt=2.5
cZt=2.5

900 fb2

200 fb

8 TeVW’ → tb

400 fbZ’→ Tt → tZt

13 TeV

1.75

Observed limit 95%CL (TeV)⟡

800 fbb* → tW k=k=1
KL/KR=1

200 fb[CMS B2G Summary Plots]

Vector-like quark single production

b* → tW KL=1
KL=1

50 fb

gKK → tt

Observed limit 95%CL (TeV)

t* → tg S=1/2

200 fbZ’(1%) → tt
cWb=1.5
T → bW c(Wb)=1.5

13 TeVX5/3 → tW

W’

13 TeV

400 fb40 fb

cWb=1.5
T → tZ cWb=1.5
W’ → tb M!
Mν<MW’
R < MW’
T → tZ c(Zt)=1.5
cZt=1.5
W’ → tb M!
Mν>MW’
R > MW’cWt=1.5
B → bZ c(Wt)=1.5gKK⟡t* → tg Z’→
S=3/2
Tt

40600
fb fb

cWb=1.5t → hadT → tH cZt=2.5
Zt=2.5W’ → ctb

7 fb

B → bHt → lep
T → tH cWb)=1.5
cWb=1.5

1.5

Observed limit 95%CL (TeV)

Vector-like quark pair production

0

1.2

13 TeV

150 fb
0

0.5

1

1.5

2

2.5

3

3.5

4

radion → HH
W’ → WH

19/31
Z’ → ZH

…are we missing other “common”
top partner decays?
• UV embeddings of composite Higgs models come with additional pNGBs, which
are naturally lighter than the top-partners, so decays of top partners to top / bottom
and a pNGB are kinematically possible.
• To determine branching ratios to h/W/Z vs new pNGBs, can we find relations
between the top partner couplings to different pNGBs?
YES, WE CAN! [JHEP 1806, 065]
The top is supposed to obtain its mass through mixing with a top partner. But the top
partners come a full multiplets of the global symmetry groups and the Higgs comesin the Goldstone-boson matrix which includes ALL pNGBs of the model. Thus, we
can relate the coupling of a top partner to the Higgs to its couplings to other pNGBs.

Scanning through the different underlying models we looked for “common
exotic” top partner decays and found:

20/31

eacompletion, as defined in Ref. [12]. All the possible modlet
2 The
first
weand
consider
a
model
with
a
charge2/3
toppartnerT andicles simplified
areelsconsidered,
the current
bound
is
of
order
M
&
1
TeV
[41–47].
last term
can bescenario,
classified,give
precisepredictions
for
the
T
CommonexoticVLQ
decaysmter
pseudo-scalar
acandidate
light pseudo-scalara is genuinely
present
in doesmodelsproperties
ofa.theSuch
TCP
mappingout aa. Thisq. (2.1)
parameterises
thecouplingof T[15],
to thusthe pseudo-scalar
term
notof
completeof possibilities.
We[26–30],
show
that,
while
ith a gauge-fermion
underlying
description
where
it canassociatedwithificantlya↵ect thelandscape
top-partner
production,which
occursthrough
QCDbepair
production,
Candidate1:
decaystothesingletpseudo-scalar
singletaogy
somemodelsarealready
partlytested
by
the
low
mass
hroughofsingle-production
dictated byWetheparameterise
first three terms(Cf. e.g. Refs
19] forNGB
a global U (1) symmetry.
the interactionsof [18,a vector-like100
di-photonsearches,
others arecompletely
unconstrained.
1 term in Eq. (2.1)
[JHEP
1806,
065]
Effective
Lagrangian(s):partnersingleandpair
production
rates).
If
M
>
m
+
m
,
the
last
artnerwithStandard
Modelparticles
andthepseudo-scalar
a
as
a
t
T
arWe point out that searches for di-tau resonances (whichs an additional decay channel of T✓! t a. Explicit expressions for the tree-level decay
onnow start at 90 GeV invariant mass at the LHC [18, 19])
g
g
+
ths
be
found
in
Ref.
[55].
T
T
di- canL/ MTsignals/a powerful
/ Lt
give
veryTpromising
could
p be
iD
T + and
W,LTW
PL b + comT ZP
T =
Z,L
2cW
2channel,
At analogy,In
as a second
model, weintroduce
a vectorlikeplementaryprobesimplified
to the di-photon
or evenbe◆ quark partner B
hanchargethe1/3,
thesimplified
onlywithway
toTaccessthis Lagrangian
classof TCPs.
T M
T

T
hP
t
+
i
T
,
(2.1)
L
a,L aPL t + L $ R + h.c.
h,L
the
v
✓
atg
g
+
B
B
/
/
/
p
L
=
B
i
D
M
B
+

B
W
P
t
+

B
Z
PL b
(2.2)
B
B
L
W,L
Z,L
DESCRIPTION
OF
THE
MODELS
mo2cW the top partner mass
PL,R are left- and right-handed projectors,
and T denotes2◆
hlytate with mass BMTM
. BThe first three
B interaction terms dictate the partial widths of
h,LBhPL b + iwe$
R SM
+ h.c.
.
toLb + La,L BaPThe
e↵ective
Lagrangian
consideristhe
Lav th as often considered in vector-like top-partner models. In
ays into bW , tZ, andike
grangian augmented by the following
terms, up to diT
boveparametrisation,
the coefficients W/Z/h,L/R are determined by the SU (2) charge
hatmensionfive
operators:
To illustrate the relevance of the new decay channels, we consider two benchmark
hebemixing angles of the top partner with the elementary top. If only decays into SMels, “Bm1” andarisingan underlying
embedding of composite Higgs
X
1 2from
iCf mf ¯ UV
1 “Bm2”,µ25(@µ a)(@ a)ma awhich are discussed
a f more= (4)/Sp(4)f in (1)withLSUbreaking,
detail in Sec. 3. In Fig. 1
eels
followtheparametrisationofRef.[18]
forthecouplings
toSM
particles.
2
2
f
a
ouf
show the branching ratios in the two benchmarks
as a function of the a mass. Each
2
2
02
ons
gs Kong Kpartner,
g aoneWa
B aThe two
a vector-likeaµ⌫i eitheriµ⌫ T gorKµ⌫ benchmark models areario focuses
B.
+
G
G̃
+
W
W̃
+
B
B̃
.
µ⌫
eak
µ⌫
µ⌫
2
2
2
16⇡ fa16⇡
fa
16⇡ faectivelycharacterisedbythefollowing
couplings:
ggs

luA pseudo-scalar a described by–thisgeneral Lagrangian
3
–
T
T
m1
TeV example,
, T
T
=
0.06
,

=
0.24
,

T = 1 forto : M
arises,
UV , completions
ofcomposZ,R =in 0.03
a,R
a,L =
h,R
B
B
m2 : MB = 1.38 TeV , B
=
0.02
,

=
0.08
,

W,L
W,R
a,L = 0.25 ,0.07 ;
(2.3)

21/31

we show the branching ratios in the two benchmarks as a function of the a mass. Eachscenario focuses on one vector-likepartner,eitherVLQ
T or B.decays
The two benchmark models are
Commonexoticrespectively characterised by the following couplings:

Benchmark parameters (obtained as eff. parameters from UV model):Bm1 : MT = 1 TeV ,

T
Z,R =

T
0.03 , T
=
0.06
,

a,R =
h,R

B
Bm2 : MB = 1.38 TeV , B
=
0.02
,

W,L
W,R =

0.24 , Ta,L =0.08 , Ba,L =0.25 ,

0.07 ;(2.3)

while the ones that are not reported are suppressed and thus negligible. The branchingratios of T ! t a and B ! b a are model dependent. However, the benchmarks we
present in Fig.
1 clearly showthat,fully realistic
canbenchmarks:
be comparable to theBranchingratiosof inquarkpartnersmodels,
to a inthey
thesebranching ratios into SM particles, which are considered in standard searches at the LHC.
To determine new possible final states that can occur from the T ! t a (or B ! b a)
decay, we briefly review the properties of, and constraints on, the pseudo-scalar a. Theinteractions of the pseudo-scalar a with SM particles can be parameterised as 3
1
La = (@µ a)(@ µ a)
2

1 2 2
ma a
2

X iCfa mf
f

fa

2K a
2K a
g
g
s
g
a
aµ⌫
+
W
af¯ 5 f +
aG
G̃
+
aW
µ⌫
µ⌫ W̃
2
2
16⇡ fa
8⇡ fa

,µ⌫

a
2 c2 K aegc
Ke2 K a
g
W
Z
µ⌫
µ⌫
µ⌫
W Z
+
aA
Ã
+
aZ
Z̃
+
aA
Z̃
. (2.4)
µ⌫
µ⌫
µ⌫
2
2
2
16⇡ fa16⇡ fa8⇡ fa2

Bounds on MT from QCD produced T -pairs depend on the T branching ratios into bW, tZ, th. The
strongest reported bound is for 100% branching ratio T ! bW (MT & 1.3 TeV) [41, 43], while bounds
on 100% branching ratio T ! tZ or T ! th are around 1 TeV. Bounds on MT from electroweak singleproduction [48–54] are even more model-dependent as the production cross section depends on additional
22/31
BSM couplings.

Common exotic VLQ decays
Examples of diagrams:• T and B can be produced like“standard” top partners: QCD
pair production or single
production.
• New final states: MANY,
depending on ma and single- orpair-production

23/31

Decays ofto vector
bosonskinematically
can yield
t , tZ ⌘.
, tW
W ,situation is
2/3a that
does notmix (ifwiththe SM top, allowed)
and a lighter
pseudo-scalarThisor tZZ resonances.
In our benchmark
model(s),these baseda decaysdo (4)/Sp(4)not have breaking,large
realised, for example,
in composite
Higgs models
on SU
where
CommonexoticVLQ respectdecaysbranchingratios,nevertheless
the
final
statesthe couplings
kinematics
with aa boosted
top⌘ is
the additional
singletand thetop(andpartnerparity associatedwithand a di-boson
resonance)o↵er manyfor excellent⌘. A concrete
realisation
will handles
be discussed
in Sec. SM
3.2.background
The modelrejection.
is described by the
Lagrangian
Candidatea topB.
partner to the “exclusive pseudo-scalar” 𝜂.
r considerations hold2:
forDecays
the VLQof
partner
⇣
⌘
e
T e
e iD
e
/
L
=
T
M
T
i
T ⌘PLspecifict + L $ Rtop
+ h.c.
,(2.7)
ee⌘,L oneT SU(4)/Sp(4)Tbreaking,Inmodelswithpartner
coupleseExclusive pNGB, T ! t ⌘tointeractions
theCP-oddsingletpNGB
𝜂.a Botharebyoddunder𝜂-parity.
for theinvolvingTe, whichdi↵ersfromEq.(2.1)
theabsenceofcouplings𝜂toecond only
simplified
scenario,
we SM
considera modelwith
toppartner
Te withcharge
the
Forby
theEW
pseudo-scalar⌘, inprinciple,
one
can
an
e↵ectiveat doesparity
notSM
mix
with theSMtop, anomaly
and a lighter
pseudo-scalar⌘.𝜂writeThis
situation
isLagrangianisbosons.
brokencouplings,
anddecaysto WW,ZZ, Z𝛾.
similar toin thisbased
specific
not all couplingson the samed, for example,
in Eq.(2.4).
compositeHowever,Higgs models
on case,SU (4)/Sp(4)breaking,arise
wherefooting.
To start,
if theof the toprespect
respecta⌘-parity,
no couplingsof ⌘ to tops
e additional
singletand thetopcouplings
partner couplings
parity associatedwitharegeneratedwill
at leading
order [94].
The couplings
tolight isfermions
are model
dependent,
concreterealisationbediscussed
in
Sec.
3.2.
The
model
described
bytheEffective
Lagrangian:
but
they
may
also be suppressed: for instance, if they are generated by bilinear couplings,
ngian
they are absent at the leading
minimal, we will only
⇣ order [95]. Thus, to keep the scenario
⌘
Te e
e
e
considercouplings
togaugebosons:/LTe = T iD MTe Ti⌘,L T ⌘PL t + L $ R + h.c. ,
(2.7)

2K a
2K ⌘
g
1
1
g
g
s
µ
2
2
a
aµ⌫
+ of couplings,µ⌫Winteractions
involvingfrom
Eq.(2.1)
bytheabsencetoL⌘ =(@µ ⌘)(@Te,⌘)whichmdi↵ers
⌘
+
⌘G
G̃
+
⌘W
W̃
⌘
µ⌫
µ⌫
2
2
2
2
16⇡ f⌘
8⇡ f⌘
M bosons. For the pseudo-scalar ⌘, in principle, one can write
an e↵ective Lagrangian
⌘
⌘
⌘
2
2
2
egc
K
g
c
K
W
e
K
Z same µ⌫µ⌫ not allµ⌫arise on the
W couplingsZr to Eq.(2.4). However, in thiscase,
+ specific
⌘A
Ã
+
⌘Z
Z̃
+
⌘Aµ⌫ Z̃ , (2.8)
µ⌫
µ⌫
2f
2f
2f
16⇡
16⇡
8⇡
⌘ respect ⌘-parity,⌘ no couplings of ⌘⌘ to tops
g. To start, if the couplings of the top
nerated forat leading
order [94].
to light fermions are model dependent,
the interactionsof ⌘Thewithcouplings
the SM particles.
ey may also In
bethe
suppressed:
formodelinstance,
if they
are generated
by bilinear
couplings,
benchmarkwe areinterested
in, as detailedin Sec.
3.2, ⌘ arises as a⌘re absent
at thefrom
leadingorderSU[95].
Thus, tothe sector.
scenario
we willKonly
singletthe coset(4)/Sp(4)in keep
the EW
Asminimal,
a consequence,g = 0, and thecouplings
to065]
theEW bosons can be expressed in terms of two parameters, as in Eq.(2.5),
er couplings
togaugebosons:
[JHEP
1806,
⌘
⌘
with the further constraint KB= KW. Thus, the coupling to photons vanishes, and the

⌘

24/31

Common exotic VLQ decays• The 𝜂-parity top partner is only QCD-pair
produced.
• It decays 100% to t𝜂.
• 𝜂 dominantly decays to W+ W- or Z𝛾(depending on its mass).

25/31

X5/3
is therefore
an ideal 2targetXfor
at hadronSemi-leptonic
activechannel.
For pair-produced
the current
boundcolliders.
on its mass
is MX5/3 > decays
1.3
5/3 ,searches
colliders.
of 97–99],
t W + havebackgrounda higher branchingand provide
another
V [43,
whilehigher
highersensitivitybut
foralsosingle-produced
X5/3 isratio
possible,but modelwhile the channel.
one associatedto the ⇡6 couplings
tocurrent
SM particles
isCommonexoticVLQ
decaysattractiveForpair-produced
X
,
the
bound
on its massis M
X5/3 > 1.3
5/3
endent [100]. However, all these bounds assumetheabsenceof“exotic”
X
decays.
5/3⇣⌘
Coloured
pNGB,
X
!
b̄
⇡
.
The
presenceofcolouredfermionsor
scalars
in theCandidate3:(with
subsequent
𝝅
→
t
t)
6
6
5/3
TeV
[43,
97–99],
while
highersensitivity
forsingle-producedXispossible,butmodel22⇡
2c
6including the sextet,
5/3$ R reads
The e↵ective LagrangianX⇡5/3|⇡couplings,
L⇡6 = |Dµfor⇡6 |the mt⇡6 (PR t) + L+ h.c.
,
6 | + itt,R

6
underlying
theoryyields potentiallylight coloured
pNGBs.
Their
couplings
to thedependent[100].
However,alltheseboundsassumetheabsenceof“exotic”
X
decays.
5/3
In modelswith SU(6)/SO(6)breaking in the color sector.
⇣⌘
c denote
imply
additional
decay
channelsbeyondthestandard
ones.
As
an
example,we
Thebce↵ective
Lagrangian
for theconjugate
X5/3
couplings,
includingand
thesextet,
reads
⇡VLQs
where
and
t
the
chargeofthebottom
the
top
quark
fields.
Note
6
/
=
X
i
D
M
X
X5/3
5/3
5/3
Lagrangian:X5/3 Effective⇡6
considera pNGBtransforming
asasextetof
QCD
colourandwithchargeThis
that, in
the
model
we
consider,⇡isasinglet
of
SU
(2)
.
The
couplingleft handed✓◆ to4/3.
L
⇣
⌘ 6
tt,L
giD
⇡6
2 with+m2X
X
X
c/
Lis⇡X65/3
=thus
X
M
tops
are+
suppressedby/frespectto
TheR sextet
decaysas charge⇡6 ! tt,
state
presentin
someunderlying
models
[32],
and
it
can
the
exoticX
5/3 p X 5/3 W/ 5/3PLt t 5/3
W,L+⇡6i⇡6 ,L X 5/3 ⇡6 PL b tt,R
+ L. couple$+toh.c.
, (2.10)✓◆large dominancetog right-handed
tops.
5/3with
top partner
X5/32.XNote
that coloured
pNGB
can
also
modifytheproduction
rates
+
X
c
/ PL t + i⇡6 ,L X 5/3 ⇡6 PL b + L $ R + h.c.
+ arises,
W,L pX, (2.10) of
5/3 W
The
sextetforexample,
as
part
of
the
pNGB
spectruminUV
embeddings
leoftheassociatedto theSM particles
istheoneVLQs,
especiallyif ⇡thantothem[33].
6 couplings
2heavier

composite Higgs models with SU (4)/Sp(4)breaking [32] (see Sec.3.2).
⇣⌘ For illustration
2
⇡6
c
while
the
one|D
associatedto2 the⇡26+couplings
to (P
SM t)
particles
isR + h.c.
L
=
⇡
|
m
|⇡
|
i
t⇡
+
L
$
⇡6
µ 6
6
6
R
purposes,
we againuse ⇡thisunderlying
model
todefinea benchmark ,model, Bm3, in
tt,R
6
⇣
⌘
2 couplings
2are
⇡6
2
c
Sec.
3.3.
The
values
of
the
L
=
|D
⇡
|
m
|⇡
|
+
i
t⇡
(P
t)
L$
+ h.c.
, Note
c
c
⇡
µ
6
6
6
R
⇡
6
parametersaseff.tt,R
parametersfrommodel):
6
ere b Benchmark
and t denotethe charge(obtained
conjugateof thebottomand +thetopRUV
quark
fields.
XsingletX
X ⇡6 to left ⇡handed
6
–
2
–
c
t, inwhere
the model
weconsider,
⇡
is
a
of
SU
(2)
.
The
coupling
Bm3
:bc M
=
1.3
TeV
,

=
0.03
,

=
0.11
,

=
1.95
,

0.56 ,
6LX5/3
andt denote the charge
conjugateofthebottom
and
the
top
quark
fields.
tt,L
W,L
W,R
⇡6 ,L
tt,R = Note
2 /f 2 with respect to ⇡6 . The sextet decays
6 as ⇡6 ! tt,(2.11)
s arethat,
thusinsuppressedbym
the model we consider,(2)L . The coupling ⇡tt,L
to left handedt⇡6 ⇡6 is a singlet of SU
tt,R⇡6 GeV (note that f
2 /f
2 with respecth largedominance
tocouplings
right-handed
tops.
while
thethusotheraremsuppressed,
and
f
=
430
is notdirectly
tops
aresuppressed
by
to

⇡6 !
tt,
⇡
⇡6 as
6
t
⇡6
tt,R . The sextet decays
relatedtothe compositenessscale
fortops.
Higgs,
as spectrum
it comes froma di↵erent
sectorofof the
Thewithsextetarises,for example,
as
part
ofthe
the
pNGB
in UV
embeddings
large
dominance
to right-handed
theory,wearises,
usewithhere
anestimatewithrespectto(seea decay
constant= 1 TeV inofthe
mpositeHiggs
models(4)/Sp(4)breaking
Sec.3.2).
illustration
The andsextetforSU
example,as partofthe[32]
pNGB
spectrumin ForUVfembeddings
composite
Higgs
modelswith thanSU (4)/Sp(4)(seeproduction
Sec.3.2).
For[33].
illustration
6we again
poses,
use
thisis underlying
model
tobreaking
definea[32]benchmarkmodel,
Bm3,
in
If a coloured
pNGB
heavier
top
partners,
it can a↵ect
their
rates
we of
again
this underlying
model to define a benchmark model, Bm3, in. 3.3.purposes,
The values
the usecouplings
areSec. 3.3. The values of the couplings are⇡6XX
3 : MX5/3 = 1.3 TeV , X
=
0.03
,

=
0.11
,

=
1.95
,

= 0.56 ,
W,L
W,R
⇡6 ,L
tt,R
⇡6
X
X
[JHEP
1806,
065]
Bm3 : MX5/3 = 1.3 TeV , X
=
0.03
,

=
0.11
,

=
1.95
,

0.5626/31
,
W,L
W,R
⇡6 ,L
tt,R =(2.11)–9–(2.11)

Common exotic VLQ decays
Examples of diagrams:• X5/3 and B can be produced in
QCD pair production or single
production.
• 𝝅6 decays to t t.

27/31

when X5/3 is pair-produced and both decay into this exotic cha
CommonexoticVLQ
decayson the two legs
produce
final
states similar to four tops, i.e.
through + and one standard) or ttb̄b̄W W (for one decay).
Charged pNGB, X through
!t +

2.4
5/3
Charged pNGB, X5/3 ! t +++++W
As Candidatea second
exampleof X
a charge
5/3
top !
partner,
we+consider
ChargedpNGB,!
t decaysThe
channel!
bbW
leads toa amodel
signature s
4: Xfor5/3•exotic
and5/3
a second
example for exotic
decays chargedof a charge
5/3 +top
partner,considera modelwith a colour-neutral,electricallyscalar. The
latter wearisesfor example
as part+XdecaystW(withsubsequent
top decay
toconsider
bWcharged), butwith di5/3 ! scalar+ . TheInmodelswith
SU(5)/SO(5)breaking
intheEW
sector,wehaveexampleforexoticofacharge5/3
toppartner,weamodel
hsecondaofcolour-neutral,electricallychargedlatterarisesforexampleaspart
the pNGB spectrum in composite Higgs models with SU (5)/SO(5) breaking [2] (see+ . SU(anddoublycharged)pNGBs.
thepNGB
incomposite
Higgs
modelswithbreaking[2](see as parta colour-neutral,chargedscalarThe(5)/SO(5)latterarisesforexampleSec.
3.4),spectrum
where itelectricallyis accompaniedbyadoubly-charged
scalar.
Thee↵ective
Lagrangians
Finally, let us remark thatthe charged
pNGBs
couple in gen.e 3.4),
where
it X
isLagrangian:accompanied
by a doubly-charged
scalar.
Thee↵ectivefor Effective
the
VLQ
the
chargedscalarcouplings,
respectively
read Lagrangians
pNGB
spectruminpartners.
composite
Higgs
modelswithSU(5)/SO(5)breaking in[2] more(see de
5/3 and
The resulting new decay modes are discussed✓
the VLQ
X5/3itandthe charged
couplings,
respectively
read The e↵ective Lagrangians⇣ scalar
⌘
3.4),
where
is accompaniedbyadoubly-charged
scalar.
gwant to mention+
interesting
final
state
that
we
is due to(2.12)
decays of a
X
✓
/ M
/
p
LX5/3 = ⇣X 5/3 iD
X
+

X
W
P
t
⌘ X5/3
L
5/3
5/3
gW,L
+ + read +he VLQX
andthechargedscalarcouplings,
respectively
X2
5/3/ charged/ bPL t ! bW
scalarT !
, ◆which
LX5/3 = X 5/3 itheD
MX5/3 X
W,L p to
X 5/3
W(2.12) is similar to
5/3 + leading✓ 2 ++⇣⌘
X+
X◆ h.c. ,theadditiona i
hard
photon.
+i
X 5/3 Pof
XX5/3 g PL b + L $
+ ,L
++ ,L
Lt +
+ R+
/ +P
/+ P
p
X
++
LX5/3 = +i
XX5/3
i
D
M
X
+

X
W
(2.12)
X
Lt ,
5/3
5/3
W,L
5/3
X
t
+
i
X
P
b
+
L
$
R
h.c.
+ ,L
++
L
L
5/3
5/3
,L
2
◆
and
+
X
++
✓
d
⌘
2 c$
+iX+⇣,L X 5/3
P
t
+
i
X
P
b
+
L
+ +h.c. ,µ⌫
X
++
egK
L
L
5/3
g
KR
,L
w
W
2
2
2
+
µ⌫
W
Z
L X
=
|Dµ |
m⌘ | |✓ egK+Wµ⌫ B̃ 2 +Wµ⌫ B̃
⇣
2
2
g
c
K
w W8⇡
W 8⇡ +f
2
2
2
µ⌫
µ⌫
Z– f+
+
++
12
–
L =
|D
|
m
|
|
+
W
B̃
+
W
B̃
= , µ
µ⌫
µ⌫
2f
2f
8⇡
8⇡
◆
= + , ++
2
g KW ++
mt +
µ⌫, ✓
◆K
⇣
⌘
2 c+
Wµ⌫ W̃
+itb,L
t
P
b
+
L
$
R
h.c. .
(2.13)
X g 2 K+ 22
egK
L
g
w
W
m
2
µ⌫
WZ +
f m2 |µ⌫,| +f + W B̃ µ⌫ +t+
W 8⇡|++
L =
W
B̃
+ |D
W
W̃
+
i
t
P
b
+
L
$
R
+
h.c.
.
(2.13)
µ⌫
µ⌫
L
µ⌫
2f
2f
tb,L8⇡
2 fµ8⇡8⇡f+ , ++
Note=that
we have defined a unique decay constant, f , for both charged scalars, as theyte thatwe originate
have defineda theuniquedecay
constant,
f , forbothoncharged
scalars,as◆theyusuallyfromsamecoset.
In
modelsbased
theSU(5)/SO(5)breaking
2[JHEP 1806, g065]
28/31
KW ++
mt +
µ⌫,
±
ally
originatemodelsSUL(5)/SO(5)breaking
pattern(minimalcosetsamewithchargedthe charged
to .SU (2)L(2.13)+from theWcoset.
W̃ In pNGBs),+itb,Lbasedt onPthe+$ Rbelongs+ h.c.
L bscalarµ⌫2

Figure 5. Branching ratios of X5/3 as a function of the mass of the charged pNGBs m = m + =m ++ for the benchmark model Bm4 introduced in Sec. 3.4.

Common exotic VLQ decays

To illustrate these exotic decay modes, we define another benchmark model, Bm4, inSec. Benchmark
3.4. The corresponding
valuesof the couplings
given by from UV model):parameters(obtained
as eff.areparameters
Bm4 : MX5/3 = 1.3 TeV ,

X
X
X
X
=
0.03
,

=
0.13
,

=
0.49
,

+
+ ,R = 0.12 ,
W,L
W,R
,L

X++ ,L =0.69 , tb,L = 0.53 ,(2.14)– 11 –

Production of X5/3:
Single- or pair-production.

Decays of the pNGBs:
𝜙++ → W+ W+
𝜙+ → tb, W+ Z, W+ 𝜸

29/31

Common exotic VLQ decays
Examples of processes:

30/31

Conclusions• Composite Higgs Models provide a viable solution to the hierarchy
problem but — being strongly coupled theories — they still provide many
challenges and room for exploration.
• EFT descriptions of composite Higgs models are only part of the story.
UV embeddings need to be studied in more detail, and they lead to novel(as well as already well-known) BSM LHC signatures.
• We showed that additional pNGBs are present in CH UV embeddings(colored as well as uncolored ones) and summarized constraints for the
SM singlet and the color octet pNGB.
• Decays of top partners to t/b + pNGBs rather than to t/b + W/Z/h occur
commonly in CH UV embeddings. These decays lead to many final states
which are not targeted by current LHC searches. (Recasts of existing
searches can provide some coverage).

There is lots to do!

31/31

Backupthe SU (2)L doublet Q of Eq. (3.1). The Sp(4) singlet representation,
having hypercharge
7such aastop
partner easily arises as a “chimera baryon” in underlying models with two
reandlabelledfollows:
2/3, is trivially identified with the singlet S that couples linearly to the right-handed top.
! of Relating! [20,
speciesfermions
21].
Under theSU (2)L ⇥U(1)Y symmetry,the pNGBs
5-plet decomposes as
toppartner
couplings
to Higgs
and otherThevarious
top
partners
arelabelledasfollows:
X25/3 + 2 +T1 . Itethus contains an
doublet! additional
7/6 Example:
2/3 ,[JHEP, 1/6
T5 ; 1806, 065]singlet! !Te1 exotic.
(3.10)and a singlet together withXthe
X5/3 The Sp(4)T singlet
2/3 SU (2)L B
doubletQofEq.
(3.1).
having5-plet !
,, Te5 ; representation,
singlet !
Te1 .hypercharge(3.10)For
modelswith
EW
breaking
patternSU(4)/Sp(4),top-partners
comein
X2/3singlet SBthat couples linearly to the right-handed top.
2/3,
istrivially
identified
withther mixing of the left-handed top (and bottom) with the doublet
Sp(4) representations,e.g. 5 (forthe tL partner) and 1 (for the tR partner).
Thevarious
top
partners
arelabelledasfollows:We
thenintroducealinearmixingofthetop (andof the right-handed top with the singlet: theyleft-handed
are the sourcesof bottom) with the doublet!
!
contained
inthe
5-pletandoftheright-handed
top with
the[7].
singlet: they are the sources of
introduced in the e↵ective Lagrangian
in
way
X5/3
T the standard
5-plete↵ect! can be introduced,
Te5e↵ective;
singlet !in the
Te1 standard.
(3.10)
PC, and theirin,theLagrangianway[7].
the same procedure and notations
as
in
Ref.
[32]
to
obtainthe
X2/3
B
In this work, we will follow the same procedure and notations as in Ref. [32] to obtain the
o the top partners and the elementary fermions. As we study
We thenintroduce
a linear mixing
thepartners
left-handed
topelementary(and tobottom)with
thedoubletmass
matrices
associatedto theoftop
andthefermions.
As in
we studyThe“massmatrix”(pNGB
interactions,
expandedleadingorder
Bs other than the Higgs doublet, we will keep them explicitly incontained
in the 5-pletandof theotherright-handed
withthe singlet:
the explicitly
sources ofin
the couplings
to thepNGBs
than the top
Higgs
doublet,we willthey
keeparethemeechargefermions,
inFor
theintroduced
basis=in {t,T,e↵ective
X2/3 ,in
T1Lagrangian, T }, we
s2/3
reads
in
the
basis
θ=v/f)
themass e↵ectmatrix.
charget 2/3
fermions,
the5 basis tin=the{t, T,
X2/3 , Te1way, Te5 },[7].
wePC, andtheir
canbe thethestandard
x: In thisobtainmatrix:work,thewefollowing
will follow
the same procedure andnotations as in Ref. [32] to obtain the1a
0 y5R i⇠5 fa
1aaai⇠5 fa
i⇠
yp
1
5R
i⇠
i⇠
i⇠
f
y
y
5
5
1
p
a
a
a
mass
matrices
associated
to
the
top
partners
andtheelementary
fermions.
As we study
5R
5R ⌘
e
f
s
e
f
s
y
e
f
iy
c
facf
fa f s yfa f c iy
p
p
1R
5R
✓
✓
✓
✓
0
e
s
e
e
c
⌘
1R
5R
✓
✓
✓
✓
2
2
2
2 C
B
Cexplicitly inathecouplings
to
the
pNGBs
other
than
the
Higgs
doublet,
we
will
keep
them
i⇠
5
2
C
B y5L e 0 fa f c
M5
0M5
0 C
0
0
0 C
✓/2
B
Ce e
a
the mass
matrix.
For
thecharge2/3
fermions,
in
the
basis
=
{t,
T,
X
, T1 , T5 }, we
C
B
t
i⇠5 f
2/3C
2
¯
a
0
0 C tL , (3.11)
0
M5 f s✓/200
0 M
C5 tL , (3.11)
tR B y5L eCCobtain the B
followinga
yp1L i⇠1matrix:
BC
fa f s
C
e
0
0
M
0
1
1
✓
0 0 @
0
M
0
A
2
i⇠5 fa1i⇠5 faAi⇠1 faypy
5R
5R
0 i yp5L s ⌘e a0f s✓ p2 e a0f s✓ y1R e a0f c✓ iy5R M
c✓ ⌘
2
5C
✓
0 B
0
M5
a 02
i⇠
B y5L e 5 fa f c2
C
M
0
0
0
5
✓/2
B7 The name a“chimera baryon” was first coined in Ref. [103].
C
B
C couplingsi⇠
5 fRef. 2
” was
first
coinedin[103].
Diagonalizing
themassmatrix(and
expanding
in
a
and
𝜂)
yields¯tRaf s✓/20
M5
0
0 C tL , (3.11)
B y5L eB y i⇠ aC1
B
C y1,5 .
1L
of
top
and
partners
to
the
pNGB
in
terms
of
the
pre-Yukawas
fatop
p e
f
s
0
0
M
0
1
✓
@
A
2
i yp5L s✓ ⌘
0
0
0
M5
2

A. usChiral
Lagrangian
irrep. To allow
to writea common8 pexpression for all cases, we introduce the quantity< 82p for real ,< 2 infordetailrealhow, an e↵ective Lagrangian formalism (3)In this section cwe
will describe
can
5 =
c:
(3)
5 =1
elsewhere .
:1 ofelsewhere.
used to describe the properties
the singlets
associated to the global U(1)’s. A ch

Chiral Lagrangian for the pNGBs[JHEP1701,094]

The pseudo-Goldstones
are parameterized
byof theGoldstone
boson
perturbation
theory
for
the
class
modelsunderinterest has been recently presented
n termsmatrices
ofwhichof whichin terms

Ref. [27], however only including the singlet associated with the non-anomalous U(1). Heppa a /fi2rT
2c ⇡ a2c
T a5 ⇡/f
rr r

ic5a
arr/f
i2
ic
/faarrlow
5 r r
5
⌃
=
e
·
⌃
,
=
e
, , energy Lagrangian, (4)r0,rr
we want⌃tobemore
general
and
keep
both
statesintheas them· ⌃0,r ,
(4)
r = e
r = e

generated for the anomalous current may be not very large.
are, thenon-abelian
generatorsin the Tfundamental
rep normalized
so thata are
a are the corresponding
awherer = 𝜓,𝝌
where
𝝅
the
non-abelianGoldstones,
brokenwhere Tr are the As
non-abelian
generatorsin thefundamental
repLagrangian
normalized
so describ
that
the model contains
two fermion
condensates,
the chiralcan bea babTr[Tr Tr ] =𝚺0,r is/2,thefrEW
andpreserving
far are thevacuum,
decay constants
for
the
non
abelian pions and thegenerators,
and
𝑎
are
the
U(1)
Goldstones
in termsof f
twoof thepNGBmatrix ⌃fortwononsinglets= , the. Tr andr , where
Tr[Tra Trb ] = ab /2,
fr andare thedecay
constants
theabelianpionsr andar copies
singlets respectively.
matrix boson⌃0,r is matrices.
the EW-preserving
vacuum.
parameterized
via the The
Goldstone(c5 is √2 forreal reps and 1 otherwise).
⌃r ’s contain the pNGBs from the non-abeliancosets,while r ’s contain the singlets. F
2
2
singlets
respectively.
Thematrix⌃isthe
EW-preserving
vacuum.
can therefore Following
be describeda single meson
matrix0,r lowestr (thethis byconvention,
theorderr ⌃chiralLagrangianr comes can be written as:
The lowestthermore,order chiralis the normalization of the decay constants fr ’s in such a w
we Lagrangianwant to choose
theFollowing
condensatethis
has convention,
charge 2). The
chiralLagrangian,then, Lagrangianlooks
2 like2
theorder chiralcan be written as:Xfflowestarr†µ†that themass(andµ ⌃
Z)r )bosons
canL pt= of the 2WTr[(D(D ⌃r )]+ be 2written(@µ r )as(@ µ r ) .
(5)
2c
X f2
5
25
2†, 8cX 2 r=rµ 2
ffar
L pt =
Tr[(Dµ r ⌃rr) (D r ⌃r )] , † µ(6) † µ
g
2pt =
L
Tr[(D
⌃
)
(D
⌃
)]
+
(@
. vacuum(5)µsuch
r that mrW = f 2sin ✓µ, wherer ) (@ 𝜃 isr )the
8c
where
we
chose
the
normalization2
5
r= , that we chose the8c2cNoticesame
normalization(drivenby5the nature of the irrep) for both2
5
r= ,misalignment angle.
pcosets,inorder
tosimplify
thenotationnt with In
thetheabove
formulation
if fadescribing=
Nrfor
fr ,.theNrabelianbeing pNGBs
thedi-later.
largewhereN
limit,✓ is expect
an angle
themisalignmentof thevacuum (thus, sin ✓ = 1 represer
Notice that we chose the same normalization (driven by the nature of the irrep) for bothcomments
areSU(4)/Sp(4)in orderat thethisstage:
for thefsinglets,
lowestorder
avour matrixA⌃few= 4 forandtheory,
SU(4)⇥SU(4)/SU(4),r (Nthe“Technicolor”
limit ofwhere
= v the= 246
GeV).
In operator
this way, we cTra

SM sigma model.
Upshot: - The pNGBs are described in a non-linear
cosets, insimply
order to simplify
thenotation
fornottheabelianpNGBs
later.
akinetic
term
which
does
dependonf.
However,theconstants
couplings of ar willaThe
different
pNGBs
can
have
differentdecayr)/SO(5), N = 6givesforSU(6)/Sp(6)andSU(6)/SO(6),
and
N
=
3
for
define the ratio(ratios
estimated,butin theend
only
calculatedcomments
atbe
this
for
the
singlets,thelowestorderwhich
operatorbe generated
byorderthe cancouplings
ofstage:thelikeU(1)currents
totheunderlying
fermions,3)).AInfew
thealways
following,
weare
willinbe
interested
in casesthelarge-N
limit
2
c
TH
vSM
on the Lattice.
✏=depends
on ansoterm
arbitraryparameter,
i.e.parameters
the charge
the fermions
the global
simplygives
does notdependon fQ
However,the under
couplings
of ar will
fr2r. ofh singlets
can abekinetic
light,
that which
we introducetheaSources of masses and couplings of the pseudo Goldstone bosons:[JHEP1701,094]

1. The SM gauge group is weakly gauged, which explicitly breaks theglobal symmetry. This yields mass contributions for SM charged
pNGBs. As the underlying fermions are SM charged, it also yields
anomaly couplings of pNGBs to SM gauge bosons.
2. The elementary quarks (in particular tops) need to obtain masses. Thiscan be achieved through linear mixing with composite fermionicoperators (“top partners”), which explicitly break the global symmetries.
3. Mass terms for the underlying fermions explicitly break the global
symmetries and give (correlated) mass contributions to all pseudo
Goldstones.
Weak gauging and partial compositeness is commonly used in composite Higgs
models to explain the generation of a potential for the Higgs (aka EW pNGBs).
On the level of the underlying fermions, such mixing requires 4-fermion
operators.
What are the implications of the above points for the SM singlet, and the coloroctet pNGB?

TH

Wess-Zumino-Witten
terms
erators
depends on the
global group the gauge interactions are a,b
embedded in, so that

Couplings of pNGBs to SM gauge bosons:

where dr is the dimension of the rep r of hypercolor, and S

in the trace correspond t

r trace is not the same as for the generators of the flavor
group. Specifically, we note2

thegenerators
with
gauge
coupling↵A =bygAthe/(4⇡).
The
normalizationof the gauge
e couplingsof gauged
the singlets
to the SM
gauge
bosons,generated
WZW
term,
can

The underlying fermions are charged under the SM gauge fields, and thus ABJt, in thecasesof wayinterest
mputedina similar
as couplings
in QCD[29].
Following
thethenormalisation
adoptedthisembedded
generators
depends
on thegroup
gaugeinteractions
anomalies
induceof global
theGoldstonebosonsto theSMfieldsinarewhich
are fully in, so tha
determined
the underlying
numbers.
[JHEP1701,094]
the couplings
beby
writtenas same quantum
theircantrace
is not theas for the generators of the flavor group. Specifically,
we notTr[S a S↵b ] =C rab ,for SU(5) ( ) and SU(6) ( ) ;that, in thecases ofA interest
Singlets:
LWZW
c5 A ab ar "µ⌫↵ Aaµ⌫ Ab↵ ,8⇡ a Sfba]r = 1 ab ,
Tr[S
2

where

r

a b
Tr[S
S ]=
coset

(34)

for all other cases .

ab, CWforCSU(5)( coset) and SU(6)CG( )C; B
B

r comparison,abb2dcompleteness andtermfor SU(3)⇥SU(3)/SU(3)thenon-abelian dpionsisCcomplex= 2drSU(4)⇥SU(4)/SU(4)Tr[S a Sthe
] , WZW
forreps,
1 ab dd
6Y
a bcomplex
A
Tr[S S ] = 2 , for all other cases .
p] , for real/pseudo-realrrealdd repsSU(6)/SO(6)d (35)
6Y 2 dCAr ab= dr Tr[S a S bSU(5)/SO(5),↵A ↵A0 CAA
0 abc
a µ⌫↵
a
0b
p
L
c
c
⇡
"
A
A
, d 6Y 2 dpions is
WZW and comparison,5
r/2 termµ⌫ the↵ non-abelian
For completeness
the
WZW
for
pseudo-realSU(4)/Sp(4)d/2d
SU(6)/Sp(6)
fr
4 2⇡

re

18

(36)

p

r
0
↵
↵
C
A
A
b
AA0 anomalous
TABLE
II:
Coefficientsofthecouplings.
Non-abelian pNGBs:
p
LWZW
c5
cabc ⇡ra "µ⌫↵Aaµ⌫ A0 ↵ ,
fr
4 2⇡

r
abc
CAA
= dr Tr[T⇡a {S b , S c }]
0c

where
where

where dr is the dimension of the rep r of hypercolor, and S

a,b

in the trace correspond to

(36

(37)

2
the gauged generators with gauge couplingr
abc ↵A = gA /(4⇡).
abThec normalization of the gauged=, S }]0cr Tr[T
complex r, and there is an additionalCAA
factorof d1/2
forreal/pseudo-realrepresentations. (37
⇡ {S

1.

generatorsUpshot:
depends- on
global groupgauge interactions
are embeddedin, so that
Thethecouplings
CrA theof pNGBs
to gauge bosons
are fully

theirtrace is r,
notandthefixed
samebyas
for additional
thegeneratorsof thegroup.
notethequantum
numbersof 𝝌forand𝜓. Specifically, werepresentations
forcomplexthere
is anfactorof flavor
1/2
real/pseudo-realmodel ⇔ one set of Branching ratios.
that, in the cases of- Oneinterest
Singlets
TH- Only unknown parameters are decay constants fr.

1.

Singlets

Tr[S a S b ] =ab,for SU(5) ( ) and SU(6) ( ) ;class of models we want to investigate, implements partial compositeness to generate a mass
[JHEP1701,094]
be realisedin theclassmodels underIf both of
pre-Yukawas
involvefermions
the same
for the top,where the
mass
is of
proportional
toconsideration.
two linear mixings
the elementary

Couplings to tops and top mass:

operatorin terms of fundamental states, then the charges are the same as the U(1)’s areto composite
states:We want to realize top masses through partial compositeness, i.e.
axial. The charge assignments depend on the structure of the fermionic bound states: if thebe realised
the class ofL,models
bothpre-Yukawas
sameyunderq̄L consideration.
yR ¯ tRoftIf+ h.c.
(16)mix
L possible
qL +charges
Rthe
fermion incontains
then◆thespurions
and of involve
the topthe
mass
are:

operator
in areterms
fundamental
states, thenthe charges
aremodelthe sameas𝜓𝜓𝝌
the U(1)’swhere 𝛙the ofcomposite
top partners,
dependingon theeitheror 𝜓𝝌𝝌areyL ,assignmentsyR ⇠(±2, 1), (0,1) ,the)
mtop
⇠ of
(±4,
, (0,quantum±2)bound, (±2,
0) , ifas
whereaxial.
arecharge
fermionic
composite
operators
that
have
the
same
numbers
qL /tRThe
dependon
structurethe2)
fermionic
states:thethebound states. The spurions yL,R thus carry charges under the U(1)𝝌,𝜓 .
left-handed
right-handed
tops
andofwhichcontains
thetoptoppartners
at low
The andtop
mass
in partial
compositenessis proportionaltoyL* yandthus
also
has are:definite
fermioncontains, thenthe respectively,
possible charges
the spurionsof themass
R fandalthough not all the possible cases are generated in all the models. For, it suffices to𝝌,𝜓 charges n𝜓,𝝌 . For 𝜓𝜓𝝌:energy. U(1)As suchoperators are made of 3 fermions, they carry charge under the two U(1): theexchangey thetwo charges. We see that
no ⇠
case
the
of ,the(±2,top0)masscan be zero
) in
mtop
(±4,
2) charge, (0, ±2),
L , yR ⇠ (±2, 1) , (0, 1) ,couplingsforof boththe pions
canThethenbe recoveredby assigning
chargeto thebepre-Yukawas
singlets.
couplingsof the singlets
to topsa cantherefore
written as yL/R
The singlet-to-top coupling Lagrangian can be written as
althoughcasesoperators.
are generated
in all✓loss
the models.
For◆ each, it spurion
suffices tothat match thenot
oneallofthe
thenpossible
composite
Withoutofgenerality,
can
a
a
n
5
Ltop
=two
mtopcharges. t̄We
+ h.c.
=inmno+ icn+nthe top mt +be. . zero
. (18)
L tRsee
top t̄t
5 charge
top t̄ canexchange
the
that
case
the
of
mass
fa
fa
be associated with a combination of pion matrices
NOTE:
for
both singlets. The couplingsof the singlets to tops can therefore be written as
0
Changing
basis
to
ã
and
⌘
˜
,
the
couplings
read couplings of the pNGBs to tops.
• The term that generates the top massalso
nLgenerates
✓
◆
nL
y
!
y
,
L
L
✓ depend on the model✓ and topapartner embedding,a ◆ ◆ with• The possible topn couplings
a discrete(17)set ofn
5
f
f
Ltop = mtop
+n a
m0 top t̄5 t + . . . (18)
mtopt̄L tR + h.c. = mtop t̄t + ic5 na
choices.
fa n q fa ⌘˜ t̄ t ,ic5(n q + n q ) ã + n q(19)
fa the coupling never vanishes asfain no casefna𝜓 = 0 = n𝝌ForthesingletpNGBs,•and similarly for yR . As mtop 0 ⇠ yL yR , the singlets decouple from the top .quark as long as
Changing basis to ã and ⌘˜ , the couplings read
𝝌 = 0.
where
we recognise
thatyields
the couplingsof theã ifis nproportional
to the charge underanalogous
argument
zero couplingof 𝝅pNGB• The
8 to tops✓✓◆◆
the charges of the two pre-Yukawas are opposite [19, 31]. However, this situation can neverfafa
mtop U(1).
05the non-anomalous
ic
(n
q
+
n
q
)
ã
+
n
q
n
q
⌘
˜
t̄
t,
(19)
5
Upshot:pNGBs
coupletotop-pairs.
fa
fa
fa
TH
In this class of-composite
Higgs
models,themattercontentoftheconfining
sectorcannotthere is a discrete13
set of possible couplings per model.
where we recognise that the couplings of the pNGB ã is proportional to the charge under

Lm =

r= ,

8c25

r Tr[Xr ⌃r ] + h.c. =
r= ,

4c25

cos 2c5

ReTr[Xr ⌃r ]

f ar
✓
◆
ar
[JHEP1701,094]
sin 2c5
ImTr[Xr† ⌃r ] . (10)f ar

Underlying fermion mass terms:

The spurions Xr are related to the the fermion masses linearly

The SM singlet pNGBs cannot obtain mass through the weak gauging. To makefermions
is added,
however,itcarriesthechargeof breakthe specific
Xrnecessarily= 2B
rin=principle, U(1),(11)
them
massive,we addmass terms
forr m𝝌 r(and𝜓)which
the fermion.
Following[27], weaddyieldthe fermion
masses in the Lagrangian as follows:chiralsymmetry.
They
mass terms
where Br is a dimensional constant (that can, in principle,be◆calculated on the Lattice).
✓
X f2
X f2
ar
r
r
2
†
†
Tr[X
⌃
]
+
h.c.
=
cos
2c
ReTr[X⌃rflavour]
NoteLthat,lossofgenerality,
m
is
a
real
matrixinthenon-abelian
space ofm = without
r
5
r
r
r
r
2
2
8c
4c
f
ar
5
5
r= ,
r= ,
◆
the fermion specie r. From the above expressions, we can read ✓o↵ the massesof the singlets
ar
†
sin
2c
ImTr[X
5r ⌃r ] . (10)and non-abelian pions:
f ar
2

r
The spurionsmX
to
the
the
fermionmasseslinearly
2 r are frelated
2 ab
a b
=
2
B
Tr[⌃
m
]
,
m
=
4B
Tr[T
T ⌃0,r mr ] .
r
0,r
r
r
ar
⇡r
fa2r

(12)

Xr = 2Br mr
r= , ,(11)†
In the limit where the condensates are aligned with the mass matrices mr = µr ⌃0,r , whichcorresponds
to atheEW preserving
vacuumand
whereµr is a common
mass for on
all theunderlying
where Br isdimensional
constant(that
can,in principle,
be calculated
Lattice).
If mr is a common mass for all underlying fermions of species r, we get
fermions,
thewithoutmasses simplify
toNote that,loss of generality,
mr is a real matrix in the non-abelian flavour space ofthe fermion specie r. 2From the above expressions,fr2 we can read o↵2
2 the masses of the singletsm⇡r = 2Br µr , mar = 2Nr 2 Br µr = ⇠r m⇡r ,
(13)
f ar
and non-abelian pions:- masses2ofofthe
singletand
pNGBs
where NrUpshot:is the dimension
matrix⌃r .non-abelian
We recovertheresult are
thatrelated.
in the large-Nc limit,
f
ab
r
2
2
a b
be estimated,butthemma-rratios= 2 2 canBr Tr[⌃
m= 4Br Tr[TT ⌃needs(12)0,r mr ] ,0,r mr ] .the⇡r calculatingfthe masses of all mesons
arear equal as ⇠r = 1.
LatticeTH

We also note that Eq. (10) contains linear couplings of the singlets to the non-abelian†which should be equal to 1 in the large-Nc limit. Note that corrections to this relation will
ed by loop corrections in the chiral Lagrangian [29, 30].
ongenerated
the singletbypions,which comes
exponentials,
vanishes.
beloop corrections
in intheviachiralLagrangian[29, 30].As discussed above, mixing
require that theof thefermion because
mass wereitsmall,i.e. m⇡ [JHEP1701,094]⌧ f . Thisthe 2 singletswould
we introduced,
onlycontribution
one remains
a pNGBis associatedto Outsinglets
in 2thesets thatofnonabelian only
pions,
specificallyfromtheEWi.e.coset,
canf also
beof thesinglets
we
introduced,one
remainsapNGB
becauseitisassociatedwouldrequirethecontributionofthefermionmass
weresmall,
m⌧.
This⇡
situation contrasts
with Iftheq cosetby charges: here, coloredpNGBstoaremaly-free combinationof U(1).
andgenerated
q are theassociatedtheexpected and𝜓andstatesa𝜓masses
mix
due
to an
anomalyw.r.t.
the
hyper
color
group
which
breaksU(1)thex U(1)𝝌
generated
ifthe
thestrongof theunderlying
fermionsarenotalignedwith
theEW
preserving,𝝌contrasts
situation
with
the
coset
generatedbyhere,
coloredpNGBs
areexpectedtotheTheanomaly-freecombinationofU(1).
Ifatq0 theandq :requirearethecharges
associatedconstraints
fromsearches
LHC
theirmassestobeclose
tototheTeV
ee current,
thepNGB ã and the anomalous ⌘˜ can be defined as
to
U(1)
.
a
the
strongconstraints
fromsearches
at
the
LHCm
requiretheirmassestocloseweto thevacuum and
they
will
suppressed
by
the
Higgs
VEV
In theweTeV
will
anomaly-freecurrent,theã andtheexpectanomalous⌘˜0 canbe
as befollowing
scale
[41].
Itbe
ispNGBthus
naturaltothat⌧squared.
m
In thefollowing,
will
work
⇡
⇡ . defined
The anomaly
freeandanomalous
combinationsarequnderf[41].
+
q
f
a
q
f
a
q
a m⇡ . In the following, we will work
scale
It
is
thus
naturaltoexpect
that
m
a a
a
a
⇡fa ⌧
0such terms, which
thisassumption.
simplifyã thediscussion
andneglectareother (8)sectors of the= q, q ⌘˜fa=a q 0 q fa a .notq fa a +q faa↵ectinga2 ã 2=
2˜ =
2f2
2 +q
2f2
q
,
⌘
. terms in Eq. (22).(8)WeunderWe
thisassumption.
q
f
+
q
q
f
q
will
first
diagonalise
themassmatrixkeeping
all
the
mass
a
a
a
a
theory like the Higgs potential.
q2 f 2 + q2 f 2
q2 f 2 + q2 f 2Singlets: masses and mixingaaaa
We willdefinethefirst
massdiagonaliseeigenstate theas mass matrix keeping all the mass terms in Eq. (22). We
The mass
matrixfor thesinglets,
therefore,
can be written
fromonvenience,wecandefineasingledimensionlessparameter
describing
mixing,
0
1
0
1
0
1 the
The singlet
mass
terms
(including
contributions from underlying
fermionmasses) is thus
definethemasseigenstateas
For later convenience, we can define a single dimensionless parameter describing the mixing,↵ sin ↵1 0 a 1
A@Ale ⇣, and a single scale fa : 1 2 20@ 1a1A2 =02@ cos
1 2
(23)
2
= m
a
+
m
a
+
M
(cos
⇣a
sin
⇣a
)
(22)
0
i.e. an angle ⇣, andLmassa single
scale
f
:
a
cos
↵
sin
↵
a
a ⌘ a
sin
2 a @ q2A = @
2 ↵A cos ↵A @ a A
(23)
0
q fa
⌘
sin2↵ 2cos ↵aq
2a mass
2
q
f
where
and
M
is
contribution
generatedby instanton
tan
⇣
=
,
f
=
q
f
+
q
f
.
(9) effects.
a aA
a
2a 2
2 with22tan, fa =e↵ects,
q faproportional+ q fa . to the topological suscepti(9)where MA is the mass qgenerated
fa ⇣ = by instantonqwith⇣ q fa⌘12
2
2
2
0 M 4 + m4 + 2M 2
2 cos 2⇣The
massesof the
pNGBs
are
m
=
M
+
m
+
m
⌥
m
,
(24)
bilityofthehypercolourforthesinglet⌘˜
associatedwiththeanomalous
combination
0 group,Aaaa always
a/⌘
a
A
A
q
⇣
⌘
observables do not dependonthenormalisationofthecharges,
we
can
2
1
2
2 on the2
As physics observables
normalisation
the2 charges,
canalways44 of
2 cos wem2a/⌘0do= notMdepend
+
m
+
m
⌥
M
+
m
+
2M
m
2⇣
,
(24)
A
a
a
a
a
A
A
of
it
as
a
free
parameter,eventhoughthetopologicalmass
2 U(1)’s. For now, we will2 consider
2 /q for2
2 various models areqchose= 1q 2without
lossofgenerality.
Thevalues
of
q
the
for
short
notation,wedefine
m
=
m
m
>
0.
The
mixingangle
can2where,+ q = 1 without loss of generality. The avalues aof q /qa for the various models are be222
where,
forshort
notation,wedefinem=m
m
The
mixingangle into
can thebe a,η’is,inprinciple,
calculable
once
theunderlying
dynamics
isspecified.
andtheinteractions
in
the
mass
eigenbasis
areobtainedbyrotatingfroma𝜓,𝝌 basisaaa > 0. ⇣expressed
in
terms
of
the
mass
eigenvalues
andtheparameteras theable
I.
listed in Table I.
qand the parameter ⇣ as
0to
1
with
expressed
inwe
terms
theentertain
mass2 eigenvalues
In basis
the following,
wantof
the
case
where
the
topologicalmay
2
2 be small,2
2 mass222m⌘ 0 + ma q ( m⌘ 0
ma )4 m⌘0 ma tan ⇣
0@
1A
tan
↵
=
tan
⇣
1
, (25)
2
2
2
2
2
2
2
2
2)
+
m
(
m
m
4
m
m
tan
⇣
as it happens in large-Nc QCD.mIn
fact,
in
many
of
the
modelsweconsiderthenumber00
0
2 ma⌘0aa⌘⌘⌘uplings@A , (25)tan ↵ = tan ⇣ 1
B. Couplings
22 m⌘ 0of colours is large and/or the representation of the underlying
fermions is large. Anotherwhere,
again forshort⟨𝝌𝝌⟩
notation,definethe masses
after subtractionof the contribution
Upshot:- The
and we⟨𝜓𝜓⟩pNGBs
mix throughan anomaly

physicalconsideration
allowsus
thestructure:
them
mass
of⌧
the
pNGBs
2to simplify
2 define
2 mixing
plingsthesingletscan
only
generatedbyterms
explicitly
breaking
theglobalwhere,
again
for
short
notation,wethemassesafter
subtraction
thecontribution
0 of
Theofcouplingsofthesinglets
can
only
be
generatedbyterms
explicitly
breaking
theglobalofthemasses,
as be
m
=
m
m
.
Note
that
for
m
⌧
(m
M
), then TH
0
0
a
⌘
a
A
term
and
throughtheirmassterms.
a
a/⌘
a/⌘
2
2
2
the
masses,asm=mm. Noteforma ⌧manomalous
(m
Mjob,
then
inThe
thepartial
EWof↵
sector,due
tothecondensationof’s,thatalso
contributes
mass
00⌘ 0 toatheA ), of
⇠
⇣
and
the
mass
eigenstates
coincide
with
the
pNGB
and
the
combination,s.symmetries.
gaugingof
thenon-abelian
globalsymmetries
cannotdocannot
the
job,
as
athe
a/⌘
The partial gauging a/⌘of the non-abelian
globalsymmetries
do⌧
the
asthe

As weSinglet
discussedpNGB
in the previous
section, andthe singlet
pseudoscalars couple to a pairsummary
phenomenology

SM gauge bosons via the WZW anomaly terms, and to a pair of top quarks. The gener
a and η’: Arise from the SSB of U(1)𝜒 ⨉ U(1)𝜓. One linear combination has a GHC anomalye↵ective Lagrangian for a SM neutral pseudo-scalar ⇡0 can be written as(η’) and is expected heavier. The orthogonal linear combination (a) is a pNGB.
1
mt
µ
2 2
L ⇡0 = @ µ ⇡ 0 @ ⇡ 0 M ⇡ 0 ⇡ 0 + i C t⇡0 t 5 t
2
f⇡
✓
◆
(4
2
2
↵s g
g2 W µ⌫⇢g1 B µ⌫⇢
µ⌫⇢
a
a
i
i
+
⇡0 ✏
Gµ⌫ G⇢ + 2✏
Wµ⌫ W⇢ + 2✏
Bµ⌫ B⇢,
8⇡ f⇡
g 3 gg 3 g•whichThe mass
ma must resultby
fromexplicit
breaking of
U(1) Msymmetries(e.g. through massis characterized
fiveparameters:
thethemass
coupling g /⇡0 , the dimension-fullterms for the underlying 𝜒). mη also obtains mass from instantons.

(coefficient of the anomalous coupling to gluons) that controls the production cross sectio• f𝝅0 results from chiral symmetry breaking.

.

and the three ratios Ct /g , B /g and W /g which dictate the branching ratios.

• The WZW coefficients 𝜅i are fully determined by the quantum numbers of 𝜒, 𝜓.

In the following, we will neglect the e↵ect of top loops to the branching ratios into a pa

• The coefficient Ct is also fixed (depends on spurion charge of dominantly mixing top-partner)2agi rationale
i
mt is that, once such e↵ects are sizeabof 1gauge
main
a
L =
@µ a@ µbosons:a m2 a2the++a✏µ⌫⇢ Gbehind
Ga this+ i Cfacta t 5t(1.3)
aa2
Phenomenology

32⇡ 2 fa

i,µ⌫

i,⇢

fa

the decay is dominated by the tt̄ final state, so that searches in diboson final states becom• 𝝅0 is produced in gluon fusion (controlled by 𝜅g/f𝝅).
irrelevant. Thus, in this large top coupling limit, the only phenomenologically relevant e↵e(1.4)
ratios.
• 𝝅0 decays to gg, W W, ZZ, Z , , tt̄, ff with fully determined branching
will be on the gluon fusion production. As shown in Appendix ??, the e↵ect on gluon fusi(controlled by 𝜅B/𝜅g, 𝜅W/𝜅g, Ct/𝜅g)
TCP
can be encoded in a M⇡0 –dependent shift of the g coupling, as in Eq.(??).
Thus, o• The resonance is narrow.
analysis can be extended in a straightforward way.

Production cross section for a pseudo-scalar

Production cross section of a pseudo scalar[JHEP1701,094]

TCP
with coupling g /f

. In the figure, the coupling to gluon is fixed to g /f⇡ to 1 TeV , however the production
cross section scales like (g /f⇡ )2 .

Partial widths

The singlet pseudoscalars decay to either di-boson via the WZW interactions or to tt̄.

tree-level
expressions;in analysis
weLagrangianuse full 1-loop
results)
The (here,
partial widths
are related
to the parametersin thein Eq.(45)as [25]↵s2 2g M⇡30(⇡0 ! gg) =
,
3
2
8⇡ f⇡
(⇡0 ! W W ) =(⇡0 ! ZZ) =(⇡0 ! Z ) =
(⇡0 !

) =

(⇡0 ! tt̄) =2↵W
2W M⇡30
32⇡ 3 f⇡2

(46)
✓

1

m2W
4 2
M ⇡0

◆ 32

,

2
2
4
4
3 ✓
↵W cos ✓W (W + B tan ✓W ) M⇡0
1
3
2
64⇡ f⇡
2
2
2
3 ✓↵↵W cos ✓W (W B tan ✓W ) M⇡0
1
3
2
32⇡ f⇡↵2 (W + B )2 M⇡30,
3
2
64⇡ f⇡✓◆1/2
2
2
2
3Ct M⇡0 mt
mt
1 4 2
,
2
8⇡
f⇡
M ⇡0

(47)
m2Z
4 2
M ⇡0
m2Z
M⇡20

◆ 32

◆3

,

(48)

,

(49)
(50)
(51)

where ✓W is the Weinberg angle and ↵W = ↵/ sin2 ✓W . Decays into other SM fermions are
negligible, as suppressed by the fermion masses. It is instructive to split the decay modes
into the final state tt̄ and into diboson final states. Furthermore, we will use ratios of

TCP

10

Experimental constraints at “high mass”:(37 studies, 44 “bounds’’ included),ATLAS and CMS @ 8 TeV and 13 TeV(see JHEP 1701 (2017) 094 for full refs)

TCPCoefficients of a for sample models M1 - M12

Ct:[arXiv:1710.01730][arXiv:1710.01730]

TCP

For a given model, we can combine all channels to get a bound on fa .

[JHEP 1806, 065]

[JHEP 1806, 065]

TCP

NOTE: Low mass region has a “gap” between 15 - 65 GeV.

𝛾𝛾
[PRL113, 17801](ATLAS)[CMS-PAS-HIG-17-013]

BR(h➝BSM)<.34[JHEP1608, 045]
(ATLAS+CMS)𝜇𝜇[PRL109, 121801](CMS)[ATLAS-CONF-2011-020][arXiv:1710.11142]

TCPLight pNGB: How can we search the gap at low mass?

[arXiv:1710.11142]

The models are poorly constrained in the mass range 15 - 65 GeV.
• Weak indirect bounds from h➝aa (BSM) which will not
dramatically increase as the bound on fa scales with Br(h➝aa)1/4 .
• h➝aa➝ 4𝛾 , bb𝜇𝜇, bb𝜏𝜏, etc. have very low signal rate due to small
haa coupling and small a➝𝛾𝛾,ff branching ratios.
• same applies to h➝Za.
• b-associated production is small.
• t-associated production could yield bounds in future searches.
[EPJC 75, 498]

• Extending high resolution 𝜇𝜇 resonance searches to higher mass?
• Extending 𝛾𝛾 resonance searches to even lower mass?
• …or looking for other decay channels: 𝜏𝜏!

TCPHow can we search the gap at low mass? 𝜏𝜏!

The gluon-fusion production
cross section for light a is large…

[arXiv:1710.11142]… and the 𝜏𝜏 branching ratio is(for most models) not small.

TCPHow can we search the gap at low mass? 𝜏𝜏!
Soft 𝜏lep or 𝜏had cannot be used to trigger on, but initial state radiation can boost the gg ➝ a➝ 𝜏𝜏 system (at the cost of production cross section, but we have enough).
As a very naive proof of principle analysis we look for a j 𝜏𝜇 𝜏e final state (jet + opposite
sign, opposite flavor leptons) with cuts:• pT𝜇 > 42 GeV (for triggering)• pTe > 10 GeV• ΔR𝜇j > 0.5, ΔRej > 0.5,
• ΔR𝜇e < 1.0• no lower cut on ΔR𝜇e !
• m𝜇e > 100 GeV
Main background:Z/𝛾*+jets: 35 fb,
tt+jets: 70 fb, Wt+jets:
7.4 fb, VV+jets: 13 fb.

[arXiv:1710.11142]

TCP

How can we search the gap at low mass? 𝜏𝜏!
Resulting projected reach for 300 fb-1

[arXiv:1710.11142]

TCP

How can we search the gap at low mass? 𝜏𝜏!
Note: This first proof ofprinciple study is highly nonoptimized.
• Cutting harder on ΔR𝜇e cansubstantially increase
background suppression forthe lighter mass range.
• We did not use any 𝜏 ID or
triggers.

[arXiv:1710.11142]• We only used the OSOF lepton channel. 𝜏𝜇𝜏𝜇, 𝜏𝜇𝜏had, 𝜏had𝜏had havelarger branching ratios but require a more careful background
analysis.
[And needs tagging efficiencies for boosted 𝜏𝜇𝜏had, 𝜏had𝜏had systems
which are beyond our capabilities, but possible for experimentalists.]

TCPand possible connections with the properties of the singlets.
color octet ⇡8 , which is present in all models discussed in Sec. II, can be described
B. Phenomenology of the color
As aoctet
first connection, we note that its mass can be expressed in t
↵ective Lagrangian
8
3 2 2
1 2
3 2 2
2
2
mdiscussed= m⇡ +inCgSec.
gs fII,=can bemadescribed+ Cg g s f ,
a
The
color
octet
⇡
,
which
is
presentinallmodels
8
1
1
m
t
4
⇠
4
(Dµ ⇡8a )2
m2⇡8 (⇡8a )2 + i Ct8⇡8a t̄ 5 t2
f ⇡82
by the 2e↵ective Lagrangian
 the second term0 comes from loop corrections from QCD, andEffective Lagrangian:where↵s g8 a µ⌫⇢ 1 abc b cg B8 a+⇡8 ✏d Gµ⌫ G⇢ +aGµ⌫ B⇢ , (63)(thegsloopg8 contribution is cut o↵ at a scale ⇤ ⇠ 4⇡f1
18⇡f2⇡8 a 2 order2 one
mtnumbera 2aColored PNGBs (the color octet 𝝅 )m⇡8 (⇡8 ) + i Ct8⇡8 t̄ 5 t
L⇡8 = (Dµ ⇡8 )22
2 the octet
betweenf⇡themassofthe masses8
he covariant derivative contains QCD interactions
withgluons.
modelsdis- in the singlet sector: in In theand
0
↵

1
g
B8 thats
g8a µ⌫⇢by Eq.abc
b Wec also recall
thesingletmasses(26).
expecte✏ the coefficients(63)
d Gµ⌫ G⇢are+equal Gaµ⌫ B⇠ ⇢ ⇠ ,1, asn this article (f⇡8 = f ), matching with Eq.s+(46) and⇡8(37),8⇡f⇡82
gs g8in QCD. In the limit of ma ⌧ m⌘0 , ma ⇠ ma sin ⇣, thus

where
the CHderivative
UV embeddings:
where
theincovariant
contains QCD interactions with gluons.2 In the models disma
3 2 2+ Cg gare.
s f equal2g8 =in this2c5 article
d , (f
2c
2Y
d
,
C
=
n
2c
.
(64)
B8⇡=
5
t8
5
cussed=f),matching
with
Eq.s
(46)
and
(37),
the
coefficients,4⇠ sin ⇣8pppm2⇡8 ⇠toet ⇡8 is produced
at the LHC in pairs via QCD interactions or singly via gluon fusion
Phenomenology

17
p
p
p
production
section at =the LHC
13or
TeV
are shown C
inthroughFig. 7, whereis single-produced
in5 gluon
QCD.
• 𝝅8cross2c
d for, 8 fusion
and2cpair-produced
2c
g8
B8 =
5 2Y d ,t8 = n
5.

(64)

XXXX.

• 𝝅8 decays to gg, gɣ, gZ, tt- with fully determined branching fractions into dibosons:

The octet ⇡8 is produced at the LHC in pairs via QCD interactions or singly via gluon fusion𝞆 =2/3:Y𝞆 gluon-photon=1/3: gg/gɣ/gZ
1 / .05/ .015,gg/gɣ/gZ
1 / .19 / .06.
production
throughfusion=would
requirevery Ylarge
hyperchargeof the= constituent• For
11. The production cross section at the LHC for 8 and 13 TeV are shown in Fig. 7, wherens, so we neglect it, here. Single production from tt̄ fusion is also suppressed by the need of creating•gluonThe
resonance
is narrow.
is fromwe
splittings
as well as by the additional (mt /f⇡8 )2 suppression from (63).
used
XXXX.
11

CPNGB

Single production through gluon-photon fusion would require very large hypercharge of the constituent
fermions, so we neglect it, here. Single production from tt̄ fusion is also suppressed by the need of creating

Colored PNGBs
Constraints from pair production: [JHEP1701,094]
Right: Pair production crosssection and bounds from pair
produced di-jet searches [CMS,
PLB747, 98] and 4t searches[ATLAS, JHEP 08 (2015),105
and JHEP10 (2015), 150]. Alldata from LHC @ 8 TeV, still.

Left: Implied bounds on the Ct8/
𝜅g vs. M𝝅8 parameter space.
13 TeV bound from ICHEP on
di-jet pairs [ATLASCONF-2016-084]

CPNGB

Colored PNGBs Constraints from single production:(see JHEP 1701 (2017) 094 for studies included; pre-Moriond 2017)

CPNGB

Colored PNGBs
Constraints from single and pair production:
Channels with the strongest
bound: gg (red), gɣ (cyan), tt(gray).
Contours give bounds on the 𝝅8
production cross section in pb.

Disclaimer: These plots do notinclude experimental bounds
after Oct 2016.

CPNGB

T’ single production, exclusion and discovery reach study[M. Backovic, TF, J.H. Kim, S.J. Lee; JHEP 1604, 014]

Charge 2/3 3rd family partners can decay to ht, Zt, Wb⇒ many potential final states (leptonic/hadronic decays of t,Z,W,h …).
We performed a survey study for exclusion and discovery potential in many singleproduction channels.
One example: T→Zt→thad Zll vs. thad ZMET :Kinematical features / cuts which can be
exploited:• high HT cut (500 (750) GeV for 1.0 (1.5)
TeV MT’ target mass)• Jet-substructure techniques to tag theboosted top (we used template-overlap
method)• forward-jet-tag• typical Zll reconstruction for lep. channel• high MET cut ( 500 (750) GeV for 1.0(1.5) TeV MT’ target mass) for ZMETVLQConclusions and Outlook
Complex Cuts

boosted Higgs
Rll < 1.0 ,Prospects for composite quark partners:N charge
2/3 partner(s)1,T’ single production, exclusion and discovery reach study
fwd

fat jetb-tag.014][M. Backovic, TF, J.H. Kim, S.J. Lee; JHEP
1604,
Table XVI: Summary of Complex Cuts for T 0 ! Zll thad channel. Ov3t refers to the top tagging score with Template Overlap
Method, mll is a reconstructed mass out of two hardest leptons ( Rll is an angular distance between them), N fwd is themultiplicity of forward jets (pfwd> 25 GeV and 2.5 < fwd < 4.5), and b-tag refers to presence of at least one b-tagged r =130.4
T
jet inside the fat jet which is tagged as a top.

Search for top quark singlet partners in the jbtZ final state:

MT 0 = 1.0 TeV search
MT 0 = 1.5 TeV searchppsignal tt̄ Z + X Z + t S/B S/ B (100 fb 1 ) signal tt̄ Z + X Z + t S/B S/ B (100 fb 1 )comparable to the sensitivity we obtain in the Zinv thad channel (see Table V), the performance of di-lepton channels
preselection
4.9 26000 21000 44 0.00011
0.23
1.3 5200 5300
12 0.00012
0.12
in searches for a 1.5 TeV partner is clearly inferior compared to the invisible Z channel. The decrease in sensitivity is
Basic Cuts
900 Br(Z6100 l110.42 times smaller
1.0 than
140 Br(Z1200 2.4 ¯),0.00074
0.27limits+
primarily
due to the 3.5
fact thatl )0.00050
is roughly threewhich severely
Ov3t > 0.6 cross section
2.7510
6.5 channel
0.0020 and hence
0.75 the sensitivity
0.87 81 at fixed
230 luminosity.
1.6 0.0028Nonetheless,0.49 thethe observablein the840
di-lepton
300
4.1 0.0055
1.042
6.7 the0.9
0.010 mass 0.72
Zll thadb-tag
channel has a1.8
strongvirtue28of offering
one of the cleanest
ways0.51
to reconstruct
top partner
and will/hencealwaysimportantsearches
T partners. 2.6
In addition,0.39
the combination
the di-lepton
and2.5
missing
E(600) remain
GeV 1.2
13 in8.3
0.84for0.055
0.95
1.4 of
0.13
0.16
T > 400
energychannelsin searches
for T 1.2 Zt 0.25
has goodof enhancing
the 0.19
signal 0.23
sensitivity
the 1 - 1.5 TeV
Nfwd
1
0.75 2.5
0.19prospects 3.8
0.26
0.039 in 0.58
3.9 mass
range.
| E/ T ,j | > 1.0
0.62 0.89 0.91 0.21
0.31
4.4
0.21 0.072 0.17 0.031 0.78
4.1
T 0 ! Zinv thad

0

T bW
0 =M
MT 0for= c1.0MTand
1.5T 0TeV
searchTable V: Example cutflow
for signal (simulated= search
0.3 with MT 0 = 1.0 TeV= 1.5
TeV) and background
0
L TeV
p
p
p
T ! Zll thad0
events in the T ! Zinv thad channel for
s
=
14
TeV
LHC.
The
entriesshow
cross
sections
aftertherespective
cuts
signal
Z
+
X
Z
+
t
S/B
S/
B
signal
Z
+
X
Z
+
t
S/B
S/
B for signalp1
0 = 1.0 TeV
4and background channels
in fb. The S/1.6B values
a luminosity
100 fb1300
for theand MT 0 = 1.5
preselection
4800 are13given
3.3for 10
0.23 of0.42
3.5MT3.3
10 4 0.12
TeV searches. The label E/ T > 400(600) GeV refers to 1 (1.5) TeV partners respectively. Efficiencies for b-tagging are included
Basic Cuts
1.1
750
1.3
0.00140.39
0.30
170 0.36
0.00180.23
in the results.
Ov3t > 0.6
0.71
71
0.61
0.010
0.85
0.24
19
0.14
0.012
0.54
b-tag
0.49
2.6
0.40
0.16
2.8
0.14 0.64 0.082
0.19
1.7
However, because ofRall larger
Z
boost
in
the
signalevents,andhence
ahigherexpected
E
/
,
we
are
able
< 1.0
0.49
2.6
0.39
0.16
2.8
0.14 0.64 0.081 T 0.20
1.7to suppress
the tt̄ backgroundmore efficiently at higher
top0.35
partner0.16
masses byincreasing
the cut on missing
energy.
The final|mll mZ | < 10 GeV 0.44
2.4
2.7
0.13 0.58 0.074
0.19
1.6
background composition in the case of a 1.5 TeV partner appears quite different compared to searches for T of
Nfwd 10.28 0.38 0.10
0.58
4.0
0.084 0.098 0.018
0.72
2.5

lower masses. Upon the/ T ,j cut, the Z + X background contributes twice as much compared to SM tt̄, while tt̄
Epcontribution to the total backgroundM.wascomparable
Z +S.XJ. Lee
in theof a 014]
1 TeV partner.
The effect is mainly
0 caseTF, J. H.to
Kim,
Table XVII: Example-cutflow for signal Backović,and background
eventsin the T[JHEP!p
Z1604,
s = 14 TeV. Cross sections
ll thad channel fordue to the tighter E/ cut we apply in case of the 1.5 TeV T search, which results in an increase in tt̄ rejection power
after the respective Tcuts for signal and backgrounds are given in fb. The S/ B values are given for a luminosity of 100 fb 1
offor
roughlya factorboth theMT 0 =of1.02.TeV and MT 0 = 1.5 TeV searches.
Comparison of these results with the results for T
Zll thad presented in Appendix A show that the T
Zinv thadis a viable discovery channel for singly produced T which in our sample study performs comparable (slightly better)
than the dilepton channel already for MT 0 = 1 TeV and gains more advantage at higher MT 0 .

VLQ11 / 160

Phenomenology of quark partners
Conclusions and Outlook

Top partners with charge 2/3
boosted Higgs

T’ singleforproduction,
exclusionand discovery
study
Prospects
composite quark
partners:
charge 2/3reachpartner(s)[M. Backovic, TF, J.H. Kim, S.J. Lee; JHEP 1604, 014]

We also did detailed analyses of the Wlep b, Whad b, hbb thad , and hbb tlep channels,
We also studied Wb and ht channels and found Wlepb and hbbthad to be most promising.
andfound best results for Zinv thad , Wlep b and hbb thad .
Combined results:
BRHbWLŸ L‚t = 100.0 fb-1

1

MT' = 1 TeV¯

Ÿ L‚t = 100.0 fb-1

1

sT' + sT'
@fbD
140

s = 14 TeV

0

BRHbWLsT' + sT'
@fbD

s = 14 TeV
MT' = 1.5 TeV

120
0

0

¯

60

0

50

100
40
80
1

BRHtZL

01

BRHthL

1

BRHtZL

01

BRHthL

Expected discovery reach for a T 0 with mass of 1 TeV (left) and 1.5 TeV (right) in terms of T 0 production cross section for the LHC at 14 TeV with
100 fb1 of data. The yellow star marks the branching ratios at the sample model point used for simulation.

12 / 16

VLQ

t
Thetagged
model with a Existingfromsearches
to tt̄ events, the signal events almost never gethigh Ovbounds
as topit ispartner
difficultfor a proper Higgs fat
3 score,tof quark
partners
Top partners
with charge
2/3
jet to fake a top. Hence,Phenomenology
an upper cut on
Ov3 (solidline) efficiently
eliminatesa significant
fraction of tt̄ events, at ahhConclusions
OutlookHiggs
minor cost of signal efficiency. Notethat theandpeakat Ov2 Ovboosted
0 in
the signal distributions corresponds to events
3
where the hardest/second hardest fat jet is likely a light jet.
Figure 4 illustrates
theBackovic,
effects of Ov
on Kim,the mass
the two082]
highest pT jets. Note that the[M.
TF,cuts
J.H.
S.J.distribution
Lee; JHEPof 1504,
intrinsic mass filtering property of TOM can be clearly seen in the results. The mass resolution of the Higgs fat jets
improves upon the cut on the overlap, while the contributions from both high mass and low mass background regions
is significantly diminished.
In TF,
addition
to jetsubstructure
requirements
for Higgs tagging, we require both Higgs candidate jets to contain at
M. Backović,J. H. Kim,
S. J.
Lee [JHEP 1504,
082]
least one b-tagged r = 0.4 jet within the fat jet, as prescribed in Section III C.

An unconventional di-Higgs final state from light quark partners

Prospects for quark partners at LHC run II: boosted Higgs(es)Search for light quark singlet partners in the hhjj final state with h ! bb decays.
b

Signal Cross Sectionsb̄

In order to pick out the light jets, we re-cluster each event with r = p0.4 (also necessary for b-tagging) and selecthu
the 10two highest pT jets which pass the requirement of[fb]

pr=0.4> 25 GeV,T|y r=0.4 | < 2.5,

Ruh > 1.1 ,

g

(26)

Uh

1

whereDifficult
Ruhstands for the plain distance in , between the r = 0.4 jet (i.e. the up type quark) and each of theto probe at-1
Higgs candidate
LHC Run II w/fat
35 fbjets. We declare these jets to be the u quark candidates.
Ū
Since we expect two Higgs fat jets in the final state, a comparison between the masses of the htwo hardest fat jets
0.1 pass the overlap criteria provides a useful handle on the background channels. In order to exploit this feature,
which
ū
h
we construct a mass asymmetry
p

0.01

1000

1200

1400

1600

MUh [GeV]

1800hmh1 mh2,m2000
h1 + mh2

b

(27)

b̄

Demand at least four fat jets (R = 0.7) withpT > 300 GeV, | | < 2.5
Declare the two highest pT fat jets
Basic Cuts
satisfying Ov2h > 0.4 and Ov3t < 0.4
Cut Scheme
to be Higgs candidate jets.
At least 1b-tag on both Higgs candidate jets.
Select the two highest pT light jets (r = 0.4), with pT > 25 GeV
to be the u quark candidates.
| h | < 0.1| Uh | < 0.1
Complex Cuts
mUh1,2 > 800 GeV
Table III: Summary of the Event Selection Cut Scheme.
13 / 16

VLQ
11

Searchfor light quark singlet
partners
the hhjj
finallightstatequarkwith hpartners! bb decays.
An unconventional
di-Higgs
finalin statefrom
Out M. Backović, TF, J. H. Kim,[M.
S. J.Backovic,
Lee [JHEP 1504,
082] Kim, S.J. Lee; JHEP 1504, 082]
TF, J.H.
s [fb]tt̄ [fb]2bb̄ [fb]
3

Preselection Cuts
6.8
4.6 108.4 10
Basic Cuts
1.2
4.6
16.0
| mh | < 0.1
8.2 10 1
1.7
6.5| mU | < 0.1
5.6 10 1 5.5 10 1
2.0
mUh1,2 > 800 GeV 5.0 10 1 3.6 10 1
1.6
b-tag
3.4 10 1 4.4 10 2 1.1 10 2
Table IV: MUh = 1 TeV ,tt̄ [fb]
2s [fb]

2.8 10
6.8 102
2.8 10287.0
67.0
1.5 10 2

p

S/B
S/ B
2.4 10 5 7.5 10 2
1.7 10 3 2.7 10 1
2.9 10 3 2.9 10 1
6.3 10 3 3.5 10 1
7.3 10 3 3.6 10 1
4.8
7.5
1

s = 6.8 fb , L = 35 fb
bb̄ [fb]
3

Preselection Cuts
2.4
4.6 108.4 10
Basic Cuts
6.0 10 1
4.6
16.0| mh | < 0.1
3.9 10 1
1.7
6.5| mU | < 0.1
2.7 10 1 5.5 10 1
2.0
mUh1,2 > 1000 GeV 2.2 10 1 1.9 10 1
1.0
b-tag
1.34 10 1 2.2 10 2 8.5 10 3
Table V: MUh = 1.2 TeV ,multi jet [fb]5

multi jet [fb]5

2.8 10
6.8 102
2.8 10287.0
45.0
1.2 10 2

14

p

S/B
S/ B
8.15 10 6 2.6 10 2
8.6 10 4 1.4 10 1
1.4 10 3 1.4 10 1
3.0 10 3 1.7 10 1
4.8 10 3 1.9 10 1
3.1
3.8

s = 2.4 fb , L = 35 fb

1

Our results show that boosted jet techniques combined with fat jet b-tagging and kinematic constraints14of/ 16pai
oduced heavy particles can achieve S/B > 1 with signal significance of
7 at 35 fb 1 , assuming light quark
artners of MUh = 1 TeV. The significance we obtain is sufficient to claim a discovery of 1 TeV light quark partners
addition, we find that probing masses higher than 1 TeV will require more luminosity and will be challenging a

VLQ

1Unconventional (di-)Higgs final states from light quark partners
facing ATLAS / CMS-like di-Higgs search strategies[G. Cacciapaglia, H. Cai, A. Carvalho, A Deandrea, T. Flacke, B. Fuks, D. Majumder, H.-S. Shao [[JHEP 1707 (2017), 005 ]]VLQ quark partners coupling to q and h offer
more exotic (di-) Higgs production channels.
To study them in more detail (and lay groundwork for future studies), we set up a full
Madgraph implementation at NLO…
Figure 2. Sample LO Feynman diagrams for each of the five production channels described in the text
and giving rise a VLQ-induced di-Higgs final states, with the decay Q ! hq not explicitly indicated.

As this redefinition only involves right-handed fields that are not sensitive to the weakinteractions, no o↵-diagonal gauge interactions are generated. However, an o↵-diagonal
coupling to the Higgs boson arises from the fact that the elementary right-handed up-quark
couples to the composite object non-linearly, i.e. via a cosine function. The corresponding
interaction term is in this case given by2L¯ ũ = MT sin ✏ sin 2'1 h T̄ u + · · · + h.c.
yR sin ✏ h ŨL R
L R
vSM cos ✏2(2.11)

Typically, the value of sin ✏ is bounded to be small by EW precision tests, so that we
consider a generic bound of sin2 ✏ . 0.1 [23]. In the notations of Eq. (2.2) and Eq. (2.7),
the coupling strength of the VLQ to the Higgs boson has therefore a natural upper boundofMT̂TR .
· 0.05 ) T . 0.035 .
(2.12)vSM
In the limit where the singlet field decouples from the spectrum, one can design analternative composite realisation with the mixing of a bi-doublet to the SM elementary
quark field. This can be mapped to the example introduced at the beginning of thissection, with the equalities M1 = M2 and y1 = y2 being naturally enforced as the two
doublets of the first example are now the components of a single multiplet of the custodial
SO(4) symmetry [30].

VLQ

2.3

Di-Higgs production at the LHC

Unconventional (di-)Higgs final states from light quark partners
facing ATLAS / CMS-like di-Higgs search strategies[G. Cacciapaglia, H. Cai, A. Carvalho, A Deandrea, T. Flacke, B. Fuks, D. Majumder, H.-S. Shao [[JHEP 1707 (2017), 005 ]]…and determined
efficiencies of ATLAS
and CMS-like di-Higgs
resolved and boosted cutsettings, oriented at:[ATLAS-CONF-2016-049][CMS-PAS-B2G-16-008]

We also provide
numerous kinematical
distributions (at LO and
NLO) which can be used
to optimize cut-schemes if
desired.

VLQ