Ultraviolet complete technicolor and Higgs physics at LHC

This is an elec onic ep in o he o iginal a icle. This ep in may di e om he o iginal in pagina ion and ypog aphic de ail. Au ho (s): Ti le: Yea : Ve sion: Please ci e he o iginal e sion: All ma e ial supplied ia JYX is p o ec ed by copy igh and o he in ellec ual p ope y igh s, and duplica ion o sale o all o pa o any o he eposi o y collec ions is no pe mi ed, excep ha ma e ial may be duplica ed by you o you esea ch use o educa ional pu poses in elec onic o p in o m. You mus ob ain pe mission o any o he use. Elec onic o p in copies may no be o e ed, whe he o sale o o he wise o anyone who is no an au ho ised use . 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). Re e ences [1] G. Aad, e al., ATLAS Collabo a ion, Phys. Le . B 716 (2012) 1, a Xi :1207.7214. [2] S. Cha chyan, e al., CMS Collabo a ion, Phys. Le . 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