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Ul a iole comple e echnicolo and Higgs physics a LHC
An ola, Ma i; Di Chia a, S e ano; Tuominen, Kimmo
An ola, M., Di Chia a, S., & Tuominen, K. (2015). Ul a iole comple e echnicolo and
Higgs physics a LHC. Nuclea Physics B, 899, 55-77.
h ps://doi.o g/10.1016/j.nuclphysb.2015.07.012
2015
A ailable online a www.sciencedi ec .com
ScienceDi ec
Nuclea Physics B 899 (2015) 55–77
www.else ie .com/loca e/nuclphysb
Ul a iole comple e echnicolo and Higgs physics
a LHC
Ma i An ola a,1, S e ano Di Chia a b,a,∗, Kimmo Tuominen c,a
aHelsinki Ins i u e o Physics, P.O. Box 64, FI-000140, Uni . o Helsinki, Finland
bDepa men o Physics, P.O. Box 35, FI-40014, Uni . o Jy äskylä, Finland
cDepa men o Physics, P.O. Box 64, FI-000140, Uni . o Helsinki, Finland
Recei ed 23 Feb ua y 2015; ecei ed in e ised o m 27 June 2015; accep ed 11 July 2015
A ailable online 23 July 2015
Edi o : Hong-Jian He
Abs ac
We conside a supe symme ic model wi h a new s ong in e ac ing sec o . The model is buil on a
s ongly in e ac ing N=4 Supe Yang Mills sec o , b oken explici ly o N=1 supe symme y by em-
bedding wi hin he Minimal Supe symme ic S anda d Model (MSSM). Due o cancella ion o global and
gauge anomalies, he model addi ionally ea u es a ou h lep on supe amily. We p opose a scena io whe e
all elemen a y scala s, gauging and higgsinos a e decoupled a an ene gy scale subs an ially highe han he
elec oweak (EW) scale, he eby a oiding he li le hie a chy p oblem o MSSM.
We cons uc a low ene gy e ec i e model, whe e EW symme y b eaking and iable mass spec um a e
p oduced dynamically. To es u he he iabili y o he model, we wo k ou he Higgs couplings as well
as he EW p ecision pa ame e s and hen pe o m a goodness o i analysis using LHC and EW p ecision
da a. The model i s he gi en expe imen al da a a a le el compa able o ha o he S anda d Model.
©2015 The Au ho s. Published by Else ie B.V. This is an open access a icle unde he CC BY license
(h p://c ea i ecommons.o g/licenses/by/4.0/). Funded by SCOAP3.
*Co esponding au ho .
E-mail add esses: [email p o ec ed] (M. An ola), [email p o ec ed] (S. Di Chia a),
[email p o ec ed] (K. Tuominen).
1Cu en ly a Eni am, Helsinki, Finland.
h p://dx.doi.o g/10.1016/j.nuclphysb.2015.07.012
0550-3213/©2015 The Au ho s. Published by Else ie B.V. This is an open access a icle unde he CC BY license
(h p://c ea i ecommons.o g/licenses/by/4.0/). Funded by SCOAP3.
56 M. An ola e al. / Nuclea Physics B 899 (2015) 55–77
1. In oduc ion
The da a collec ed a he LHC expe imen s du ing he 7 and 8TeV uns, wi h he epochal
disco e y o he Higgs boson [1,2] and he measu emen o i s couplings [3,4], seem o ha e
p o ided he expe imen al e i ica ion o he S anda d Model (SM) in i s en i e y below a TeV.
Because o his, new physics coupled wi h he Elec oweak (EW) SM cu en s mus ha e a ypical
scale o he o de o a TeV o highe . One possibili y is ha he new physics scale is much abo e
he e ascale, and hen na u ali y as a model building pa adigm should be ein e p e ed [5,6]. I
on he o he hand na u ali y is ealized in na u e, hen he new physics scale should be nea he
e ascale and he p esen LHC da a would p o ide hin s o a new spec um awai ing disco e y in
he u u e uns a he LHC. In his pape we in es iga e a model amewo k alling in o he la e
ca ego y.
In Technicolo (TC) heo ies [7,8] he new physics scale is na u ally o he o de o a TeV.
The EW symme y is b oken by a new s ong in e ac ion which gene a es a e mion condensa e,
in a way analogous o QCD. The absence o ligh elemen a y scala s in TC au oma ically sol es
he SM ine- uning p oblem. The mass o he ligh es composi e scala is usually expec ed o be
o O(TeV), well abo e he measu ed 126 GeV alue. A ligh scala can a ise as consequence o
app oxima e global symme ies, chi al symme y [9–11] o scale in a iance [12–16]. Howe e ,
only ecen ly i has been ealized ha also wi h simple QCD-like TC dynamics he scala pa icle
can become ligh because o loop co ec ions o igina ing om ex ended sec o s, which a e always
equi ed in TC models o accoun o he gene a ion o e mion masses [17–19].
The obse ed mass pa e n o ma e ields is gene a ed in TC by coupling he echni e mions
wi h he SM e mions ei he ia hea y gauge bosons o an Ex ended Technicolo (ETC) sec o
[20–23] o h ough scala ields in bosonic echnicolo (BTC) [24–28]. In case he scala media-
o s a e elemen a y, one can con ol ine- uning a scales abo e he elemen a y scala masses by
in oducing supe symme y (SUSY) [29,30]. Combining SUSY wi h TC is he e o e appealing
because o wo gene al ea u es
•The undamen al Higgs ields do no pa icipa e in elec oweak symme y b eaking, bu se e
as na u al messenge s be ween he symme y b eaking sec o and SM ma e ields.
•The s ong TC dynamics esponsible o he EW symme y b eaking alle ia es he li le
hie a chy p oblem o supe symme ic scena ios.
Recen ly supe symme ic TC models based on N=4supe Yang–Mills we e conside ed in
[31,32] whe e he low ene gy e ec i e heo y a scales below he TC scale, TC, was aken o be
Minimal Walking Technicolo (MWT) [14,15,33]. In his pape we s udy a simple bu s ill, as
we shall show, phenomenologically iable possibili y wi hin he UV comple e heo y o [31,32]:
we assume a la ge po ion o he supe symme ic spec um o be hea y which s ill allows he
esul ing low ene gy e ec i e heo y, ea u ing an SU(3)global symme y in he TC sec o , o
b eak co ec ly EW symme y. Due o i s global symme y and he nea con o mal TC coupling
we call his SU(3)Walking Technicolo (3WT).
The pape is s uc u ed as ollow: In Sec ion 2we e iew he pa icle con en and eno -
malizable Lag angian o MSCT, which ep esen s he elemen a y desc ip ion o 3WT. Nex we
in eg a e ou he hea y mass eigens a es o MSCT and de i e he e ec i e Lag angian a scales
below he SUSY b eaking scale, mSUSY, in Sec ion 3. In he subsequen Sec ion 4we w i e
he e ec i e Lag angian a scales below TC, whe e he TC in e ac ion becomes s ong and is
assumed o bind echni e mions and echnigluons wi hin composi e s a es. We con inue in Sec-
M. An ola e al. / Nuclea Physics B 899 (2015) 55–77 57
Table 1
Non-MSSM supe ield con en o MSCT. He e Adj and deno e he
adjoin and undamen al ep esen a ions, espec i ely. None o he ields
abo e is cha ged unde SU(3)c.
Supe ield SU(2)TC SU(2)LU(1)Y
LAdj 1/2
3Adj 1 −1
VAdj 1 0
L1−3/2
N111
E112
ion 5by wo king ou he mass eigens a es, ligh Higgs couplings, and EW p ecision pa ame e s
o he model. Then, in Sec ion 6, we es he 3WT iabili y by scanning he pa ame e space o
da a poin s sa is ying he di ec sea ch limi s on new pa icles and hen pe o ming a goodness o
i analysis o Higgs physics da a a LHC wi h he iable scanned da a poin s. The esul o his
analysis, which is ha 3WT i s he cu en expe imen al da a a a goodness le el compa able o
ha o he SM, is he main esul o he pape . Finally, we o e ou conclusions in Sec ion 7.
2. An UV comple e echnicolo model
The UV comple e supe symme ic heo y which p o ides ou s a ing poin is he same which
has been in oduced in [31,32] and called Minimal Supe symme ic Con o mal Technicolo
(MSCT). The gauge symme y g oup o MSCT ex ends he SM one by he TC gauge g oup,
SU(2)TC. The TC ec o supe ields can be ea anged wi h he chi al supe ields, con aining he
echni e mions which ans o m unde he adjoin ep esen a ion o SU(2)TC, in N=4 supe -
ields. The MSCT Lag angian can hence be exp essed in compac o m as ha o he Minimal
Supe symme ic S anda d Model (MSSM) ex ended by an N=4 Supe Yang Mills (4SYM)
sec o , which con ains he TC sec o . We u he mo e add o he supe po en ial a ou h lep on
supe amily sec o , in which he e mion componen s a e needed o cancel he Wi en opological
anomaly gene a ed by he odd numbe o le -handed echni e mions. The non-MSSM supe -
ields in oduced in MSCT and hei quan um numbe s a e summa ized in Table 1. Analogously
he MSCT supe po en ial can be exp essed in compac o m in e ms o he MSSM supe po en ial
and i s ex ension
P=PMSSM +PTC,(1)
whe e PMSSM is he MSSM supe po en ial, and PTC is exp essed by
PTC =−gTC
√2abca
L·b
Lc
3+yUa
L·Hua
3+yNL·HuN+yEL·HdE
+yREa
3a
3,(2)
wi h Hu(Hd) deno ing he Y=+1/2
(−1/2)Higgs supe ield. The do (·) indica es a con ac ion
be ween he SU(2)Ldouble s wi h he an isymme ic wo-index Le i-Ci i a enso .
To he po en ial ob ained om Eq. (1) we add he so SUSY b eaking e ms o he MSSM as
well as hose co esponding o PTC, wi h he la e exp essed by:
58 M. An ola e al. / Nuclea Physics B 899 (2015) 55–77
LTC
so =−aTCabc ˆ
Ua
Lˆ
Db
Lˆ
U∗c
R+aUˆ
Qa
L·ˆ
Huˆ
U∗a
R+aNˆ
L·ˆ
Huˆ
N∗
R
+aEˆ
L·ˆ
Hdˆ
E∗
R+aRˆ
U∗a
Rˆ
U∗a
Rˆ
E∗
R+1
2MDD†a
RD†a
R+c.c.−M2
Qˆ
Q†a
Lˆ
Qa
L
−M2
Uˆ
U∗a
Rˆ
Ua
R−M2
Lˆ
L†
Lˆ
LL−M2
Nˆ
N∗
Rˆ
NR−M2
Eˆ
E∗
Rˆ
ER,(3)
whe e we w i e a ha on op o he scala componen o he chi al supe mul iple s.
The model de ined by Eqs. (1), (2) and (3) cons i u es he undamen al desc ip ion o he
heo y we s udy in his pape . The ele an scales o he model a e he SUSY b eaking scale,
mSUSY, and he EW scale ha we iden i y wi h he low-ene gy s ongly coupled egime o he
TC heo y TC ∼4π w, which o w=246 GeV implies TC ∼3TeV. We will assume he e
ha he wo scales sa is y
mSUSY TC.(4)
Wi h his o de ing he EW symme y is b oken dynamically. Fu he mo e, we assume he mass
spec um o ea u e oughly he ollowing hie a chy:
1) All SUSY b eaking masses as well as he μpa ame e a e o O(mSUSY), he e o e all he
supe pa ne s as well as he elemen a y Higgs scala s ha e masses o he same o de .
2) All he ligh es composi e s a es acqui e masses, which a e a mos o he o de o TC.
In he ollowing sec ion we p oceed o de i e he e ec i e Lag angian desc ibing he physics
below he SUSY b eaking scale by in eg a ing ou he hea y s a es.
3. Mesoscopic Lag angian
A e we in eg a e ou all pa icles wi h mass g ea e han mSUSY, he only echni e mions le
a e he e mionic componen s o he EW double supe ield Land EW single 3in Table 1:
Qa
L=Ua
L
Da
L,U
a
R,a=1,2,3.(5)
To de i e he e ec i e Lag angian, alid be ween he scales TC and mSUSY, one i s w i es
down he Higgs Yukawa sec o in MSCT:
−LMSCT
Yukawa =ˆ
Hu·Fu+ˆ
Hd·Fd+h.c. ,
Fu=qi
LuYi
uu†i
R+yUQLU†
R+yNLLN†
R,
Fd=qi
LdYi
dd†i
R+li
LYi
le†i
R+yELLE†
R,(6)
whe e i=1, 2, 3is he la o index and i is summed o e . The ma ices Yu, Yd, and Yla e
diagonal, and he CKM ma ix Vis con ained in he de ini ions o he ec o s
qTi
Lu =(ui
L,Vij dj
L)and qTi
Ld =(V †ij uj
L,di
L). (7)
Gi en ha he po en ial o he MSSM Higgs ields is
VMSSM =m2
SUSY +|μ|2|ˆ
Hu|2+m2
SUSY +|μ|2|ˆ
Hd|2−bˆ
Huˆ
Hd+h.c.+... (8)
by sol ing he equa ion o mo ion in e ms o he Higgs mass eigens a es and plugging he solu-
ions back in o Eq. (6), leads us o he i s line o he ollowing dimension six in e ac ion e ms
o he e mions in he in e media e scale (o mesoscopic) e ec i e Lag angian

M. An ola e al. / Nuclea Physics B 899 (2015) 55–77 59
L4- e mion =c2
θ
m2
sF†
uFu+F†
dFd−cθsθ
m2
s
(Fu·Fd+h.c.)
+g2
TC
m2
SUSY
abccdeηαa
iηb
jαη†d
i˙
βη†˙
βe
j.(9)
Simila ly, he las e m o igina es in an analogous way om he po en ial and he Yukawa sec o
o 4SYM. In Eq. (9) we ha e de ined
ηT
α=ULα,D
Lα,−iσ2
αβ U†β
R,(10)
whe e σ2is he second Pauli ma ix, and he indices iand jdeno e SU(3) la o ; he i s le e s
o he alphabe a e ese ed o he adjoin SU(2) echnicolo indices, while he G eek indices
label he spin componen , and he TC indices, unning om 1 o 3, a e w i en explici ly only in
he las e m. We supp ess summed spin indices as long as i can be done consis en ly. Finally,
we ha e de ined
m2
s=μ2+m2
SUSY(μ2+m2
SUSY)2−b2
μ2+m2
SUSY2+b2, an θ=b
μ2+m2
SUSY
.(11)
In he es o his pape we use abb e ia ions sθ≡sin θ, cθ≡cos θand θ≡ an θ.
The ou - e mion in e ac ion e ms in Eq. (9) a e ele an because hey e en ually gi e mass
o he SM e mions once he echni e mions condense. The i s line in Eq. (9) de i es om
decoupling he Higgs scala s, and b eaks he global SU(3)symme y, while he las e m in
Eq. (9), s emming om he 4SYM sec o , espec s he global SU(3)symme y o he pu e TC
sec o .
A ene gy scales below TC he TC in e ac ion becomes s ong, and physical s a es cha ged
unde TC ge bound in composi e s a es wi h ze o TC cha ge. In he nex sec ion he e o e we
de i e he e ec i e Lag angian in ol ing such s a es.
4. E ec i e Lag angian a he elec oweak scale
Simila ly o QCD, in TC a owe o composi e s a es is p edic ed o a ise a low ene gies. A
scales below TC he new physics deg ees o eedom a e he composi e s a es associa ed wi h
he s ong TC in e ac ion, and he o m o he e ec i e Lag angian is cons ained o sa is y he
app oxima e global symme ies o he undamen al Lag angian. In he ollowing we de i e he
e ec i e Lag angian in oducing i s he composi e scala s and hen he composi e ec o s.
4.1. Technicolo scala sec o
The composi e scala ma ix ield M, single unde SU(2)TC, has minimal pa icle con en
gi en by he echniqua k bilinea s:
Mij ∼ηα
iηβ
jεαβ =ηiηj,wi h i, j =1...3.(12)
The ield M ans o ms unde he ull SU(3) g oup acco ding o
M→uMuT,wi h u∈SU(3). (13)
The e ec i e linea ly ans o ming SU(3)in a ian Lag angian eads:
60 M. An ola e al. / Nuclea Physics B 899 (2015) 55–77
Table 2
T ans o ma ion p ope ies o he componen ields o he ma ix Mun-
de SU(2)L×U(1)Y. The complex scala s a e g ouped, based on hei
ans o ma ion p ope ies unde SU(2)L, in o one iple , one double ,
and one single .
Field SU(2)LU(1)Y
∼QLQL 1
σ∼QLU†
R−1
2
δ−− ∼U†
RU†
R1−2
LM=1
2T DμM†DμM−VM,(14)
whe e he co a ian de i a i e is gi en by
DμM=∂μM−igLGμM+MGT
μ,
wi h
Gμ=˜
Wa
μ
λa
2+ ξBμYM,a=1,2,3.(15)
In he abo e equa ion λaa e he Gell-Mann ma ices, ξ= an ξwi h ξ he EW mixing angle,
˜
Wμand Bμa e he SM EW gauge ields, and
YM=diag 1
2,1
2,−1.(16)
The mos gene al SU(3)p ese ing e ec i e po en ial, including ope a o s up o dimension ou ,
is2
VM=−m2
2T M†M+λ
4T M†M2+λT M†MM†M−2mde M+de M†,
(17)
which b eaks SU(3)spon aneously o SO(3) o posi i e m2, as we show explici ly in Ap-
pendix A. The TC gauge in e ac ion is ac ually in a ian unde U(3) ≡SU(3) ×U(1)A, a he
han jus SU(3). Howe e he U(1)Aaxial symme y is anomalous, and is he e o e b oken a
he quan um le el. This co esponds o he de M e m in Eq. (17). The componen s o he ma-
ix M∼ηTηcan be desc ibed in e ms o he ans o ma ion p ope ies o he composi e s a es
unde SU(2)L×U(1)Y. This no a ion is in oduced in Table 2.
Using his no a ion, he ma ix Mis w i en in e ms o complex scala s as
M=⎛
⎝
√2++ +σ0
+√20σ−
σ0σ−√2δ−− ⎞
⎠.(18)
This no a ion is sui able o s udy he acuum, since he la o ex ension sec o b eaks he global
symme y o he po en ial om SU(3)down o he EW gauge g oup SU(2) ×U(1). Nex , we
discuss how o consis en ly in oduce also he composi e ec o ields.
2In p inciple he highe dimensional ope a o s can play a ole and should be sys ema ically included. Fo an ini ial
in es iga ion and quali a i e accoun o he a ious cons ain s, we unca e he e ec i e heo y a he le el o dimension
ou ope a o s. This p o ides a quan i a i e baseline o possibly mo e e ined analyses in he u u e.
M. An ola e al. / Nuclea Physics B 899 (2015) 55–77 61
4.2. Vec o sec o
A minimal se o composi e ec o ields ans o ming homogeneously unde SU(3)can be
w i en, in e ms o Gell-Mann ma ices λa, as
Aμ=Aa
μ
λa
2,(19)
which ans o m unde SU(3) acco ding o
Aμ→uAμu†,wi h u∈SU(3). (20)
The elemen a y pa icle con en o Aμis exp essed by he equi alence
Aμj
i∼ηα
iσμ
α˙
βη†˙
βj −1
3δj
iηα
kσμ
α˙
βη†˙
βk =jγμi−1
3δj
ikγμk,
=¯
UL,¯
DL,¯
Uc
R,(21)
whe e he componen s o in SU(3)space a e Di ac spino s, wi h he supe sc ip con he las
en y deno ing he cha ge conjuga ion. The ec o and axial- ec o cha ge eigens a es and hei
elemen a y pa icle con en a e gi en in Appendix B.
The e ec i e Lag angian including composi e ec o ields, Aμ, has al eady been de i ed in
[33] o a heo y wi h SU(4) global symme y in he TC sec o by applying he hidden local
symme y p inciple [34,35]. Those esul s can be s aigh o wa dly used o SU(3)symme ic
TC by de ining he co esponding ec o ield and he ield s eng h enso :
Cμ=Aμ−G
μ,=gL
gTC
,F
μν =∂μAν−∂νAμ−igTC Aμ,A
ν,(22)
wi h Gμde ined in Eq. (15). The ec o ield Cμhas he same ans o ma ion law as Aμ:
Cμ→uCμu†,wi h u∈SU(3). (23)
The kine ic and mass e ms o he ec o ields can hen be w i en as
LV=−1
2T ˜
Wμν ˜
Wμν−1
4BμνBμν −1
2T FμνFμν+m2
AT CμCμ,(24)
while he scala - ec o ield in e ac ion e ms up o dimension ou ope a o s ead
LM–V=g2
TC 1T CμCμMM†+g2
TC 2T CμMCμT M†
−g2
TC
3
4T CμCμT MM†,(25)
wi h cons an s i∼O(1). A ew ema ks a e in o de : Fi s , highe dimensional ope a o s a e
supp essed by powe s o TC, and a e he e o e subleading. Second, e ms p opo ional o yU,
which explici ly b eak SU(3)global symme y, a e small compa ed o hose p opo ional o g2
TC
and can he e o e be neglec ed a leading o de . Thi d, o simpli y he phenomenological analy-
sis o 3WT, p esen ed in he nex sec ion, we neglec also a co a ian de i a i e coupling e m
(see [33] o i s p ecise de ini ion).3Finally, in he nex subsec ion, we de e mine he e ec i e
Lag angian e ms o he la o ex ension o 3WT below scale TC and hen summa ize he 3WT
ull Lag angian.
3Neglec ing his e m is simply a es ic ion on he pa ame e space: his e m could be included in mo e ho ough
u u e analyses.
62 M. An ola e al. / Nuclea Physics B 899 (2015) 55–77
4.3. Fla o ex ension sec o
The ou - e mion heo y, Eq. (9), is gi en jus below he SUSY b eaking scale and he ech-
niqua k condensa e needs o be e ol ed down o he EW scale. This is achie ed by mul iplying
he echniqua k Yukawa coupling yU, eno malized a he SUSY b eaking scale, wi h he dimen-
sionless ac o
ω=ULU†
RmSUSY
ULU†
RTC =mSUSY
TC γ
,(26)
w i en unde he assump ion ha he anomalous dimension γo he echniqua k mass ope a o
is cons an .
No e ha in he ollowing we neglec he con ibu ion o he las e m in Eq. (9) because ha
e m espec s he global SU(3)symme y, and he e o e i s e ec s should al eady be pa ame ized
by he qua ic couplings in he TC e ec i e Lag angian, Eq. (17). The masses o he SM e mions
and he ou h amily lep ons a ise om he e ms on he i s line o Eq. (9): mo e speci ically
hose masses a e gene a ed by he ollowing ou - e mion ope a o
ηTKη , (27)
wi h
Kij =yUcθω
m2
sδikcθq†k
LuY∗
uuR+y∗
NL†k
LNR
−iksθqk
LdYdd†
R+lk
LYle†
R+yELk
LE†
Rδ3j,
i, j =1,...,3;k=1,2;3k≡0,(28)
upon condensa ion o he echniqua ks. Unde SU(3)global symme y he spu ion K ans o ms
as K→u∗Ku†.
The ou - echniqua k e m on he o he hand is
y2
Uc2
θ
m2
s
ω2(QLU†
R)(Q†
LUR)=K
ij kl ηα
iηjαη†
kβ η†β
l,
K
ij kl =y2
Uc2
θ
m2
s
ω2(δik1+δik2)δjl3,(29)
whe e αand βa e spin indices. Fo his e m o be in a ian unde SU(3), he spu ion Kmus
ans o m as K
ij kl →uimujnu∗
kou∗
lp K
mnop, wi h u ∈SU(3). To es ima e he e ec s o eno mal-
iza ion, we simply assume ac o iza ion, leading o a mul iplica i e ac o o ω2.
A he lowes o de in he spu ions, he SU(3)b eaking e ec i e Lag angian, ob ained om
Eqs. (28) and (29) is:
LF=c12
TCT [MK]+c24
TCK
ij kl Mij M∗
kl +h.c. ,(30)
whe e we in oduced ac o s o TC o de ine he dimensionless coe icien s ci, which
pa ame ize he couplings o he e ec i e Lag angian in e ms o hose o he unde lying heo y.
We es ima e hese coe icien s using dimensional analysis [36–38] and ind
c1=Oϒ−1,c
2=Oϒ−2,ϒ≡TC
w
.(31)
M. An ola e al. / Nuclea Physics B 899 (2015) 55–77 69
Table 3
Combined signal s eng hs om LHC and Te a on expe imen s.
ij ATLAS CMS Te a on
ZZ 1.50 ±0.40 0.91 ±0.27
γγ 1.65 ±0.32 1.11 ±0.31 6.20 ±3.30
WW 1.01 ±0.31 0.76 ±0.21 0.89 ±0.89
ττ 0.70 ±0.70 1.10 ±0.40
bb −0.40 ±1.10 1.30 ±0.70 1.54 ±0.77
Table 4
Signal s eng hs and e iciencies o Higgs decay o γγ associa ed o a dije a LHC.
ATLAS 7 TeV ATLAS 8 TeV CMS 7 TeV CMS 8 TeV
γγJJ 2.7±1.92.8±1.62.9±1.90.3±1.3
pp →h22.5% 45.0% 26.8% 46.8%
pp →qqh 76.7% 54.1% 72.5% 51.1%
pp → ¯
h 0.6% 0.8% 0.6% 1.7%
pp →Vh 0.1% 0.1% 0% 0.5%
whe e is he e iciency associa ed wi h he gi en inal s a e in an exclusi e sea ch, while
o inclusi e sea ches one simply has σ o =σpp→h0(X), he h0p oduc ion o al c oss sec ion.
The combined signal s eng hs om ATLAS, CMS,7and Te a on a e gi en in Table 3, while
he signal s eng hs and e iciencies8 o dije associa ed γγ p oduc ion a ATLAS and CMS a e
lis ed in Table 4.
Finally, he obse ed alues o he Sand Tpa ame e s a e [39]
S=0.04 ±0.09 ,T=0.07 ±0.08 , (S,T)=88% ,(62)
wi h he las quan i y de ining he co ela ion o he wo pa ame e s.
Fo a de ailed desc ip ion o he p esen i we e e he eade o [41], whe e he same s a-
is ical analysis has been pe o med o a di e en model. Gi en ha no new physics has been
de ec ed, only he con ibu ions o new cha ged pa icles a one loop o h→γγ become ele an
when compa ing he 3WT p edic ions o he da a in Tables 3, 4. Mo e explici ly one has [59]
h→γγ =α2
em3
h
256π3 2
w
i
Nie2
iFi
2
,(63)
wi h isummed o e all he cha ged pa icles, Niis he numbe o colo s, ei he cha ge in elec on
uni s, and Fia unc ion o he mass miand he coupling coe icien de ined in [41]. In he limi
o new pa icles being much hea ie han he ligh Higgs, one inds
FWi=7aWi,F
E=FN=−a
4
3,F
Si=−aSi
1
3,(64)
wi h he coupling coe icien s de ined by Eq. (52). We can he e o e mimic he con ibu ion o
he cha ged non-SM pa icles in 3WT o he obse ables in Tables 3, 4by including only he new
con ibu ion o a hea y singly cha ged ec o boson wi h coupling coe icien aVde e mined by
7We use he mass cu based esul o CMS esul on he Higgs o dipho on decay.
8We chose o include only he loose ca ego ies om he ATLAS and CMS da ase a 8 TeV.

70 M. An ola e al. / Nuclea Physics B 899 (2015) 55–77
Fig. 1. Viable da a poin s in he (aV, a )(le panel) and (aV, aV)( igh panel) planes, oge he wi h he 68% (g een),
90% (blue), and 95% (yellow) CL egion. The blue s a in each plo ma ks he op imal coupling coe icien s on he
espec i e planes. (Fo in e p e a ion o he e e ences o colo in his igu e legend, he eade is e e ed o he web
e sion o his a icle.)
aV≡1
7(FW+FW +4F)−aS
21 ,
aS≡−3(16FE+4FN+FH±+4Fh±± +4FH±±),(65)
whe e he ac o s o 4 accoun o he double cha ge o he co esponding s a es. Mo eo e , o
simpli y he analysis we ede ine consis en ly wi h [41]
aZ≈aW≡aV,(66)
whe e he nume ical de ia ions om he i s app oxima e equali y abo e u n ou o be negligible
o he collec ed da a poin s compa ed o he unce ain ies on he coupling coe icien s. A each
collec ed da a poin we de e mine he nume ical alues o a , aV, and aVby Eqs. (53), (65) and
(66), while we calcula e nume ically he coupling coe icien s o he cha ged scala s. In Fig. 1 we
plo he iable da a poin s on he (aV, a )(le panel) and (aV, aV)( igh panel) planes, while in
Fig. 2 we plo he da a poin s on he (aV, a )plane, oge he wi h he 68% (g een), 90% (blue),
and 95% (yellow) con idence le el (CL) egions. In bo h plo s he missing pa ame e is ixed
o he op imal alue ma ked wi h a blue s a . I is clea om Fig. 1, le panel, ha he Wand
Zcouplings a e enhanced, compa ed o hei SM alues, while he SM e mion couplings a e
supp essed. This esul o he 3WT couplings enhances he Higgs decay o dipho ons. Howe e ,
he con ibu ion o he new cha ged e mions and scala s, exp essed by Eq. (65), is la ge and
in e e es des uc i ely wi h he Wcon ibu ion o he same p ocess. As a consequence he da a
poin minimizing χ2in he (a , aV, aS)space, ob ained om a 3WT pa icle spec um wi hou
he composi e ec o esonances a low ene gy, is uled ou :
aV=1.00 ,a
=1.00 ,a
S=20.5,S=0.04 ,T=0.07 ;
χ2
min/d.o. . =3.42 ,P
χ2>χ2
min=0.0004 % ,d.o. . =16 .(67)
In calcula ing χ2
min/d.o. . in he abo e equa ions we assumed he model o allow h ee ee pa am-
e e s (a , S, T), since aVis s ongly co ela ed wi h a nea χ2
min and aSis basically cons an .
The con ibu ion o he new cha ged ec o bosons, and especially ha o he ec o ba yon , o
M. An ola e al. / Nuclea Physics B 899 (2015) 55–77 71
Fig. 2. Viable da a poin s in he (aV, a )plane passing h ough he poin wi h op imal coupling coe icien s in he
(aV, a , aV)space, ma ked by a blue s a , oge he wi h he 68% (g een), 90% (blue), and 95% (yellow) CL egion.
(Fo in e p e a ion o he e e ences o colo in his igu e legend, he eade is e e ed o he web e sion o his a icle.)
he Higgs decay in o dipho on is la ge, and o se s en i ely he nega i e con ibu ion o E,N, and
cha ged scala s in Eq. (65). Among he 1000 iable da a poin s, he one p oducing he minimum
alue o χ2is:
aV=1.01 ,a
=0.99 ,a
V=0.21 ,S=0.04 ,T=0.07 ;
χ2
min/d.o. . =0.83 ,P
χ2>χ2
min=65 % ,d.o. . =15 ,(68)
whe e he numbe o deg ees o eedom (d.o. .) has dec eased by one, since aVis a ee pa-
ame e . I is in e es ing o no ice ha he op imal alue o aVabo e is equal o he a e age aV,
calcula ed o e he 1000 da a poin s, while he a e age alues o a and aVa e, espec i ely,
0.98 and 1.03, which a e e y close o he co esponding op imal alues gi en abo e. This shows
ha s ong dynamics, which we used o de e mine he scanned ange o alues o he ee pa-
ame e s, gene a es a he na u ally he coupling s eng hs a o ed by LHC da a, a leas once he
di ec cons ain s on he mass spec um and he EW p ecision pa ame e s a e sa is ied.
The 3WT esul in Eq. (68) should be compa ed o he SM one:
χ2
min/d.o. . =0.89 ,P
χ2>χ2
min=60% ,d.o. . =19 .(69)
While he SM i is less sa is ac o y han he 3WT one, i clea ly shows ha he SM is s ill
pe ec ly iable in ligh o p esen collide da a. I is ins uc i e o no ice ha he i pe o med
wi h comple ely ee coupling coe icien s, he e o e no mo i a ed by any speci ic unde lying
heo y, p oduces a wo se i han he 3WT:
aV=0.97+0.10
−0.11 ,a
=1.02+0.25
−0.32 ,a
V=0.21+0.16
−0.18 ,
χ2
min/d.o. . =0.85 ,P
χ2>χ2
min=62% ,d.o. . =14 .(70)
This is because he unde lying s ong dynamics in oduces a la ge co ela ion be ween a and
aV, hence inc easing he numbe o d.o. . by one, while achie ing a χ2
min e y close o he co e-
sponding esul ob ained wi h ee coupling coe icien s (Fig. 2).
72 M. An ola e al. / Nuclea Physics B 899 (2015) 55–77
7. Conclusions
In his pape we de i ed he low ene gy e ec i e heo y o a supe symme ic model wi h a
new s ong in e ac ing sec o and es ed i s iabili y a he LHC. We s a ed om MSSM ex-
ended by a s ong in e ac ing N=4 Supe Yang Mills (4SYM) sec o as well as by a ou h
lep on supe amily. By in eg a ing ou all he elemen a y scala s (as well as gauginos and hig-
gsinos), which we assume o be e y hea y, we ob ained a Technicolo (TC) sec o ex ended by
ou - e mion in e ac ions be ween he (4SYM) TC e mions and he SM ones. Due o hese in e -
ac ions, he TC e mion condense gi es mass o he EW gauge bosons and o he SM e mion as
well. The ad an age o his se up is wo old: Supe symme y na u alizes he scala s which allow
ETC- ype gene a ion o e mion masses, while he s ong sec o disen angles he SUSY b eaking
scale om he elec oweak scale and sol es he li le hie a chy p oblem.
Gi en ha a low ene gy he s ong in e ac ing s a es o m bound s a es, we cons uc ed he
e ec i e Lag angian a he EW scale exp essed in e ms o composi e scala and ec o ields, in
addi ion o he SM ields. Because he TC po en ial ea u es an SU(3)global symme y and he
TC coupling is nea con o mal, we called his model SU(3)walking echnicolo (3WT). To es
he iabili y o he model, we wo ked ou he Higgs couplings o he e mion and ec o mass
eigens a es, as well as he Sand TEW pa ame e s. We hen scanned he model pa ame e space
o da a poin s ea u ing a iable mass spec um, ensu ing ha he couplings emain pe u ba i e
a la ge scales. By pe o ming a goodness o i analysis using Higgs physics da a om LHC as
well as he expe imen al alues o he EW p ecision pa ame e s, we showed ha 3WT i s he
expe imen al da a wi h a le el o goodness compa able o ha o he SM. Rema kably, he ole
played by hea y composi e ec o esonances u ned ou o be c i ical, as hei con ibu ion o
he dipho on decay o he ligh Higgs is absolu ely necessa y o b ing he co esponding 3WT
p edic ion wi hin he expe imen al cons ain s. These composi e ec o esonances, ha ing mass
o O(TeV), should in p inciple be obse able a LHC.
To conclude, we highligh ha SU(3) Walking Technicolo is an UV comple e model, which,
by a oiding any scala s a he EW scale, in p inciple sol es ine uning p oblem. This model,
mo eo e , is a o ed by Higgs physics and EW p ecision da a a a le el compa able o ha o
he SM.
Acknowledgemen s
We hank R. Foadi o p o iding he code o e alua e he EW oblique co ec ions and o
discussions. This wo k was inancially suppo ed by he Academy o Finland p ojec 267842.
Appendix A. EW symme y b eaking in global SU(3)in a ian echnicolo
The SU(3)symme y o he mic oscopic TC Lag angian is spon aneously b oken o he
maximal diagonal subg oup, SO(3). The symme y b eaking pa e n lea es us wi h i e b oken
gene a o s wi h associa ed Golds one bosons. Such a b eaking is d i en by he condensa e
ηα
iηβ
jαβ Eij =2U†
RUL+DLDL,(A.1)
whe e he indices i, j=1, ..., 3 deno e he componen s o he iple o η, and he G eek indices
indica e he o dina y spin. The ma ix Eis a 3 ×3ma ix de ined as
M. An ola e al. / Nuclea Physics B 899 (2015) 55–77 73
E=⎛
⎝
001
010
100
⎞
⎠.(A.2)
The abo e condensa e is in a ian unde an SO(3)symme y. I is con enien o sepa a e he
eigh gene a o s o SU(3) in o he h ee ha lea e he acuum in a ian , Sa, and he emaining
i e ha do no , Xa. Then he Sagene a o s o he SO(3) subg oup sa is y he ela ion
SaE+ESaT=0,wi h a=1,...,3,(A.3)
so ha uEuT=E, o u ∈SO(3). An explici ealiza ion o he gene a o s is shown in Ap-
pendix B.
The scala and pseudoscala deg ees o eedom, necessa y o model he Golds one bosons
and spon aneous symme y b eaking, consis o a composi e Higgs and i s pseudoscala pa ne ,
as well as i e pseudoscala Golds one bosons and hei scala pa ne s. These can be assembled
in he ma ix
M=σ+i
√3I3+√2(ia+
a)XaE, (A.4)
which ans o ms unde he ull SU(3) g oup acco ding o
M→uMuT,wi h u ∈SU(3). (A.5)
The Xa’s, a=1, ..., 5a e he gene a o s o he SU(3) g oup which do no lea e he acuum
expec a ion alue (VEV) o Min a ian
M=
√3E. (A.6)
Appendix B. SU(3)gene a o s
The gene a o s Sio SO(3)sa is y SiE+ESiT =0. The o he gene a o s o SU(3)a e
w i en as Xi. The gene a o s a e no malized as
T [SiSj]=δij /2T [XiXj]=δij /2T [XiSj]=0(B.1)
and gi en in e ms o he Gell-Mann ma ices λiby
S1=1
2√2λ1−λ6(B.2)
S2=1
2√2λ2−λ7(B.3)
S3=1
4λ3+√3λ8(B.4)
X1=1
2√2λ1+λ6(B.5)
X2=1
2√2λ2+λ7(B.6)
X3=1
4√3λ3−λ8(B.7)
74 M. An ola e al. / Nuclea Physics B 899 (2015) 55–77
X4=1
2λ4(B.8)
X5=1
2λ5(B.9)
Using he gene a o s abo e, i is s aigh o wa d o ob ain he ec o and axial- ec o cha ge
eigens a es and hei elemen a y pa icle con en om Eqs. (19), (21). Fi s no e ha he cha ge
ope a o is Q =S3. We ind i s he linea combina ions o he gene a o s co esponding o
cha ge eigen alues 0, ±1 and ±2. Then we p ojec he co esponding ec o s a es, e.g. 0
μ=
2T (S3Aμ), and ob ain:
0
μ≡A3
μ+√3A8
μ
2∼¯
ULγμUL+¯
URγμUR,
+
μ≡A1
μ−A6
μ
2−iA2
μ−A7
μ
2∼¯
DLγμUL+¯
Dc
LγμUR,
−
μ≡A1
μ−A6
μ
2+iA2
μ−A7
μ
2∼¯
ULγμDL+¯
URγμDc
L,
a0
μ≡√3A3
μ−A8
μ
2∼¯
ULγμUL−¯
URγμUR−2¯
DLγμDL,
a+
μ≡A1
μ+A6
μ
2−iA2
μ+A7
μ
2∼¯
DLγμUL−¯
Dc
LγμUR,
a−
μ≡A1
μ+A6
μ
2+iA2
μ+A7
μ
2∼¯
ULγμDL−¯
URγμDc
L,
++
μ≡A4
μ−iA5
μ
√2∼¯
Uc
RγμUL,
−−
μ≡A4
μ+iA5
μ
√2∼¯
ULγμUc
R.(B.10)
The pa icle con en s gi en abo e ep oduce he co esponding esul s in [33] i one applies he e
he subs i u ion DR→Dc
L.
Appendix C. Squa ed mass ma ices
Fo he neu al scala and pseudoscala s a es, he cha ged and doubly cha ged s a es, he
squa ed mass ma ices a e, espec i ely
M2
¯
h0=2 2
σλ+2λ2  σλ−2λ
2  σλ−2λ2 2
σλ + 2
λ+4λ,(C.1)
in he 
σ0, 
0basis,
M2
¯π0=8 2
λ 4  σλ
4  σλ 2 2
σλ ,(C.2)
in he 
σ0, 
0basis,
M2
¯
h±=2 2
σλ +λ2√2  σλ +λ
2√2  σλ +λ4 2
λ +λ,(C.3)
in he ±, σ±basis,

M. An ola e al. / Nuclea Physics B 899 (2015) 55–77 75
M2
¯
h±± =2 2
σλ −4 2
− 2
σλ4 2
λ +2 2
σλ
4 2
λ +2 2
σλ2 2
σλ −4 2
− 2
σλ,(C.4)
in he ±±, δ±± basis.
We de ine, besides in Eq. (22), he ollowing dimensionless pa ame e s:
x=gL w
2mA
,
ρ=√2 
σ
,z
i=gTC w
2mA2
i,i=1,2,3.(C.5)
Then he non-ze o e ms o he cha ged ec o boson squa ed mass ma ix (which by de ini ion
is symme ic) a e
M2¯
W1,1=m2
Ax2+21+z1−z3
21+c2
ρ,
M2¯
W2,2=m2
A1+z1+z2s2ρ−z3
21+c2
ρ,M2¯
W1,2=− 
√2M2¯
W2,2,
M2¯
W3,3=m2
A1+z1−z2s2ρ−z3
21+c2
ρ,M2¯
W1,3=− 
√2M2¯
W3,3,
(C.6)
in he ˜
W±
μ, V±
μ, A±
μbasis, wi h u he mo e he squa ed mass o he doubly cha ged ec o boson
gi en by
m2
=m2
A1+2c2
ρ(z1+z2)−z3
21+c2
ρ.(C.7)
Finally, he non-ze o e ms o he neu al ec o boson squa ed mass ma ix in he ˜
W3
μ, Bμ, V3
μ,
A3
μbasis a e
M2
¯
Z1,1=m2
Ax21+s2
ρ+21+z1−1
21+c2
ρz3+z2s2
ρ,
M2
¯
Z1,2=−m2
Ax21+s2
ρ+2z1−c2
ρ(2z1−z2)+z2 ξ,
M2
¯
Z2,2=m2
Ax21+s2
ρ+23+z1+c2
ρ(4z1−5z2)+z2−3
21+c2
ρz3 2
ξ,
M2
¯
Z3,3=m2
A1+2c2
ρ(z1−z2)−z3
21+c2
ρ,
M2
¯
Z1,3=−
2M2
¯
Z3,3,M2
¯
Z2,3=−3
2
ξM2
¯
Z3,3,
M2
¯
Z4,4=m2
A1+z1−z2s2ρ−z3
21+c2
ρ,
M2
¯
Z1,4=−√3
2M2
¯
Z4,4,M2
¯
Z2,4=√3
2
ξM2
¯
Z4,4.(C.8)
Appendix D. Sand Tpa ame e s o gene al neu ino mass ma ix
The mos gene al mass e ms o a pai o igh - and le -handed neu inos is de ined by
L⊃−mE¯
EREL−1
2nT
LMnL+h.c.,M=MLmD
mDMR,n
L=(NL,¯
NR)T(D.1)
76 M. An ola e al. / Nuclea Physics B 899 (2015) 55–77
wi h eigen alues
λ1,2=1
2(ML+MR)±(ML−MR)2+4m2
D.(D.2)
The con ibu ions o he co esponding hea y neu inos mass eigens a es and o he hea y elec-
on E o he Sand Tpa ame e s ha e been de i ed in e ms o in eg al unc ions in [46]. F om
hose, we de i ed he co esponding explici esul s:
S=1
12π1+2c4
ζ1+log ν2
1−2logν2
E+2s4
ζ1+log ν2
2
+s2
2ζ
36π
91−log ν2
1ν4
1ν2
2−91−log ν2
2ν2
1ν4
2−1−3logν2
1ν6
1+1−3logν2
2ν6
2
ν2
1−ν2
23
−(−1)βs2
2ζ
8π
ν1ν2ν4
1−2ν2
1ν2
2log ν2
1
ν2
2−ν4
2
ν2
1−ν2
23,(D.3)
T=2
NP
64πc2
ξs2
ξm2
Z16c4
ζν2
1log ν2
1+16s4
ζν2
2log ν2
2+8ν2
Elog ν2
E
−s2
2ζ1−2logν2
1ν4
1−1−2logν2
2ν4
2
ν2
1−ν2
2
+4(−1)βs2
2ζ1−log ν2
1ν3
1ν2−1−log ν2
2ν1ν3
2
ν2
1−ν2
2
+4c2
ζ1−2logν2
1ν4
1−1−2logν2
Eν4
E
ν2
1−ν2
E
+4s2
ζ1−2logν2
2ν4
2−1−2logν2
Eν4
E
ν2
2−ν2
E,(D.4)
whe e NP is he gi en eno maliza ion scale, ξis he EW mixing angle, and
ν1=λ1
NP
,ν
2=λ2
NP
,ν
E=mE
NP
,
2ζ=2mD
MR−ML
,
β=1
2⎡
⎢
⎣1+⎛
⎝λ1
|λ1|
∗λ2
|λ2|⎞
⎠
2⎤
⎥
⎦.(D.5)
In he limi MR→∞, and ML=mE≡mU, one eco e s he esul s in Eqs. (56).
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