we miss you another Minimal Composite Higgs (through LHC bumps) - PowerPoint PPT Presentation

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another Minimal Composite Higgs (through LHC bumps) Argonne BSM workshop with the Lattice Higgs Collaboration (L at HC) Zoltan Fodor, Kieran Holland, JK, Santanu Mondal, Daniel Nogradi, Chik Him Wong Julius Kuti University of California, San Diego Argonne'BSM'workshop:'Composite'Dynamics'in'2016' April 21, 2016 Argonne National Laboratory 2

The light 0++ scalar BSM lattice challenges We want to understand: 22 M N light scalar separated from 2-3 TeV resonance spectrum 5 20 M a 1 M ρ 4.5 More complex scalar spectrum close to CW? 18 what is the eta’? diphoton bump? 4 16 entangled scalar-goldstone dynamics sigma model or dilaton? 3.5 14 tuning to CW and away from CW? M / TeV 3 12 M / F bridge between UV and IR scale? scale-dependent gauge coupling - high precision 2.5 10 2 what list of predictions independent of mass generation? 8 related phenomenology a 0 scalar isovector? 1.5 6 consistent EW embedding ➞ dark matter 1 4 diphoton res? lattice: actually have to solve the theory 0.5 2 0 ++ scalar Higgs? BSM needs new lattice tools RMT and delta-regime 0 0 scaled up QCD cannot do this 3.2 β

What is our composite Higgs paradigm? ⇤ R elementary scalar? e-writing the Higgs doublet field 1 ⇤ ⇥ ⇧ M . ⇤ ⌅ 1 ⇤ 2 + i ⇤ 1 � ⌅ + i ⌦ ⇧ · ⌦ ⌦ H = ⌦ ⌅ � i ⇤ 3 2 2 ⇧ a ⇧ 3 W µ = W a D µ M = µ M � i g W µ M + i g ⌥ M B µ , with 2 , B µ = B µ µ 2 spontaneous symmetry breaking The Higgs Lagrangian is Higgs mechanism m 2 � � 1 ⌃ 2 ⇧ ⌃ ⇧ ⌃ ⇧ M D µ M † D µ M M † M M † M L = 2Tr 2 Tr 4 Tr � strongly coupled gauge theory fermions (Q) in gauge group reps: L Higgs → − 1 4 F µ ν F µ ν + i ¯ Q γ µ D µ Q + . . . light scalar separated from has to be unlike QCD 2-3 TeV resonance spectrum

composite Higgs mechanism (textbook TC paradigm) We want something different from scaled up QCD (near-conformal theory): ‣ m=0 fermion doublet SU(2) flavor QCD ▸ light scalar is the excitation of the chiral condensate ▸ Gold stone pa rticle important in composite Higgs mechanism … ▸ f π sets the EW scale ~ 250 GeV and gauge coupling g ▸ Higgs mechanism does not depend on hypercharge of fermion multiplet! ▸ 29 MeV ➛ 90 GeV scaled-up QCD ?

three lattice BSM models with light scalars and SU(3) color: sextet from haystack: SCGT Theory Space Marciano in qcd Sannino and Tuominen BSM early lattice work: DeGrand/Shamir/Svetitsky LatHC Kogut-Sinclair recent Boulder work and CP 3 QCD far from scale invariance nf = 8 and nf=12 are popular: LatKMI and LSD sextet rep near-conformal? PNGB is the opposite approach ⎡ ⎤ minimal EW u(+e/2 Nf=2 sextet rep embedding ⎢ ⎥ massless fermions ⎣ d(-e/2) ⎦ SU(2) doublet what do we do with unwanted nf=8 goldstones 3 Goldstones > weak bosons which pull away from CW when made massive? minimal realization of Higgs mechanism ⎡ ⎤ u(+2/3e adding lepton doublets is a choice ⎢ ⎥ ⎣ d(-1/3e) ⎦ adding EW singlet massive flavor Hence the tag minimal for the sextet model is also a choice its gauge group is SU(3) and predicts new QCD intuition for near-conformal Electroweak physics (gauge anomaly) compositeness is plain wrong Technicolor thought to be scaled up QCD what happens to the flavor singlet Goldstone? motivation of the project: composite Higgs-like scalar close to the aka eta’ (axial anomaly) conformal window with 2-3 TeV new physics

scale-dependent coupling of the 3 lattice BSM models without the gradient flow based method this accuracy would not have been possible 2.5 fund N f = 4 c = 3/10 s = 3/2 fund N f = 8 c = 3/10 s = 3/2 sextet N f = 2 c = 7/20 s = 3/2 fund N f = 12 c = 1/5 s = 2 2 ( g 2 (sL) - g 2 (L) ) / log(s 2 ) L at HC Nf = 4 fundamental 1.5 L at HC and Boulder Nf = 8 fundamental L at HC and Boulder Nf = 2 sextet 1 Boulder Nf = 12 fundamental sextet beta function! 0.5 New analysis ? 0 IRFP? 0 1 2 3 4 5 6 7 g 2 (L)

scale-dependent coupling of the 3 lattice BSM models bridge between UV scale and IR scale renormalized gauge coupling in chiral limit t 0 scale of selected g 2 series in m=0 chiral limit 16 10 2 = 3.25 6/g 0 cubic spline interpolation 14 9 m=0.003 − 0.006,0.008 fitted 8 running coupling at fixed β 6/g 2 t 0 scale of g 2 in chiral limit 0 =3.25 t 0 scale of g 2 in chiral limit 12 Chiral PT fits 7 excellent χ 2 fits 6 10 5 6/g 2 0 =3.20 4 8 scale change at fixed 3 renormalized g 2 a → 0 needed 2 6 1 4 0 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 M 2 π 2 6.6 6.8 7 7.2 7.4 7.6 7.8 8 the two scale dependent couplings to be renormalized gauge coupling g 2 matched to leave no room for further 2 is linear leading dependence of g 2 (t,m) on M π speculations on conformal fixed points based on gradient flow chiPT B !! ar and Golterman works better than expected topic: how to do this right in ChiPT chiral logs are not detectable with low lying scalar coupled to Goldstone dynamics? decoupling of the scalar has to be better understood nstructed at flow time 0 depend on t

scale-dependent coupling mass dependent tuning? sextet running coupling from mass dependent β function in 1+2 freeze-out scenario anything to learn about strong coupling dynamics of single one massless flavor 0.6 massless flavor? two flavors with mass m α (m 2 / µ 2 ) runs with scale µ 0.5 Similarly, in 2+1 freeze-out α (m 2 / µ 2 ) scenario anything to learn about 0.4 sextet running coupling from mass dependent β function strong coupling dynamics of 0.6 doublet massless flavor? 0.5 0.3 α (m 2 / µ 2 ) 0.4 two massive 0.3 flavors freeze out Not clear that light scalar mass 0.2 0.2 0.1 can be tuned effectively 0 − 20 − 15 − 10 − 5 0 5 10 15 20 − log(m 2 / µ 2 ) LSD 4+8 model 0.1 walking very close to weak coupling Nf=3 IRFP topic: reverse pulling from IRFP with 4-fermion operator? 0 − 1000 0 1000 2000 3000 4000 5000 6000 − log(m 2 / µ 2 )

scale-dependent coupling of the 3 lattice BSM models without the gradient flow based method this accuracy would not have been possible 2.5 fund N f = 4 c = 3/10 s = 3/2 fund N f = 8 c = 3/10 s = 3/2 sextet N f = 2 c = 7/20 s = 3/2 fund N f = 12 c = 1/5 s = 2 2 ( g 2 (sL) - g 2 (L) ) / log(s 2 ) L at HC Nf = 4 fundamental 1.5 L at HC and Boulder Nf = 8 fundamental L at HC and Boulder Nf = 2 sextet 1 Boulder Nf = 12 fundamental sextet beta function! 0.5 New analysis ? 0 IRFP? 0 1 2 3 4 5 6 7 g 2 (L)

The light 0++ scalar nf= 2 4 higgs-less the failure of old Higgs-less technicolor: 0 ++ scalar in QCD (bad Higgs impostor) sources of uncertainty and are an order of m ate √ s σ = (400 - 1200) - i (250 - 500) MeV q estimate in Particle Data Book e dispersive representation of the S-matrix ele π - π phase shift in 0 ++ “Higgs” channel 0 o < δ o Roy solutions with 78.3 0 (s A ) < 92.3 Bugg 2006 200 broad M σ ~ 1.5 TeV in old technicolor, based Achasov & Kiselev 2007 Kaminski, Pelaez & Yndurain 2008 on scaled up QCD, hence the tag “Higgs-less” Albaladejo & Oller 2008 150 0 δ This is expected to be different in near- 0 conformal strongly coupled gauge theories 100 Low scalar mass renormalizes F! 50 Will require new low energy effective action 0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 GeV Leutwyler: √ s σ = 441 + 16 − 8 − i 272 + 9 − 12 . 5 MeV dispersion theory combined with ChiPT nt for all sources of uncertainty and a

The light 0++ scalar nf=2-4 QCD higgs-less Bernard et al. first lattice result QCD 2+1 flavor f 0 mass ( σ particle) 750(150) MeV heavy pion lattice BSM 0++ scalar has to be very different

scale-dependent coupling of the 3 lattice BSM models without the gradient flow based method this accuracy would not have been possible 2.5 fund N f = 4 c = 3/10 s = 3/2 fund N f = 8 c = 3/10 s = 3/2 sextet N f = 2 c = 7/20 s = 3/2 fund N f = 12 c = 1/5 s = 2 2 ( g 2 (sL) - g 2 (L) ) / log(s 2 ) L at HC Nf = 4 fundamental 1.5 L at HC and Boulder Nf = 8 fundamental L at HC and Boulder Nf = 2 sextet 1 Boulder Nf = 12 fundamental sextet beta function! 0.5 New analysis ? 0 IRFP? 0 1 2 3 4 5 6 7 g 2 (L)

− − − light 0++ scalar nf=12 LatKMI and L at HC − N f =12 test of technology: Lowest non-singlet scalar from connected correlator N f =12 Lowest 0++ scalar state from singlet correlator − 7 − 5 x 10 x 10 3 9 C singlet (t) ~ exp(-M 0++ · t) fitting function: LatKMI and LatHC C non-singlet (t): 8 2.5 early 2013 game begins + 7 2 aM non-singlet = 0.420(2) 6 aM 0++ =0.304(18) ! =2.2 am=0.025 1.5 5 24 3 x48 lattice simulation 4 N f =12 200 gauge configs 1 3 β =2.2 am=0.025 0.5 2 0 1 0 t − 0.5 t − 1 0 5 10 15 20 25 6 8 10 12 14 16 18 20 22 24 26 staggered correlator A n e − m n ( Γ S ⊗ Γ T )t + ( − 1) t B n e − m n ( γ 4 γ 5 Γ S ⊗ γ 4 γ 5 Γ T )t ⇥ ⇤ � C(t) = n similar analysis in sextet model with N f =2