objective: minimal realization of light composite Higgs USQCD 2015 - PowerPoint PPT Presentation

objective: minimal realization of light composite Higgs USQCD 2015 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 USQCD Collaboration Meeting May 1-2, 2015, Fermilab 1

What is our composite Higgs terminology? ⇤ R e-writing the Higgs doublet field ⇤ ⌅ 1 1 ⇤ 2 + i ⇤ 1 ⇤ ⇥ ⇧ M . � ⌅ + 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 N f fermions in gauge group reps L Higgs → − 1 4 F µ ν F µ ν + i ¯ Q γ µ D µ Q + . . . needle in the haystack? or, just one of the haystacks?

Outline SCGT Theory Space Near-conformal SCGT? haystack light scalar close to conformal window effective theory? scale setting and spectroscopy systematics and mixed action QCD far from scale Chiral Higgs condensate invariance GMOR and mode number sextet rep near-conformal? epsilon regime and RMT large mass anomalous dimension? close to scale invariance? Scale dependent renormalized coupling ⎡ ⎤ nf=2 sextet rep u(+e/2 matching scale dependent coupling from minimal EW ⎢ ⎥ massless fermions embedding ⎣ d(-e/2) ⎦ form UV to IR with chiSB SU(2) doublet 3 Goldstones morph into weak bosons Early universe minimal realization EW phase transition, sextet baryon, and dark matter QCD intuition for near-conformal compositeness is just plain wrong Summary Technicolor thought to be scaled up QCD motivation of the project: composite Higgs-like scalar close to the conformal window

− − − − light 0++ scalar and spectrum 2013-14 testing N f =12 test of scalar technology: Lowest non-singlet scalar from connected correlator N f =12 Lowest 0++ scalar state from singlet correlator − 5 − 7 x 10 x 10 9 3 C singlet (t) ~ exp(-M 0++ · t) fitting function: C non-singlet (t): L at HC and L at KMI 8 2.5 Nf=12 + 7 fundamental rep 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 6 8 10 12 14 16 18 20 22 24 26 0 5 10 15 20 25 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

light 0++ scalar and spectrum sextet model L at HC near-conformal resonance spectrum separated from light scalar B 3 TeV a 1 moving up to 2-3 TeV with refined scale setting rho a 0 within reach of LHC Run 2 ? 1 TeV light scalar at few hundred GeV? W Z EW self-energy shift t observed Higgs-like? � κ 2 r 2 t (600 GeV) 2 . then δ M 2 H ⌅ � 12 κ 2 r 2 t m 2 t ⌅ ++ correlators Triplet and singlet masses from 0 From the composite Higgs mechanism: 0.6 triplet and singlet masses Goldstone decay constant F is setting the EWSB scale 0.5 L at HC M H /F ~ 1 − 3 range circa Lattice 2013 0.4 0 ++ triplet state (connected) 0.3 0.2 β =3.20 28 3 x56, 32 3 x64 0.1 0 ++ singlet state m fit range 0.003 - 0.008 (disconnected) 0 0 0.005 0.01 0.015 fermion mass m

light 0++ scalar and spectrum sextet model L at HC near-conformal resonance spectrum separated � =3.20 (with PCA analysis) 48 3 x96 m=0.002 from light scalar B 0.25 3 TeV a 1 L at HC moving up to 2-3 TeV with refined scale setting � 2 = 0.019 Q = 1 rho effective mass of D(t) − D(T/2) 0.2 a 0 within reach of LHC Run 2 ? number of blocks = 16 block size = 4 0.15 eigenvalue threshold of PCA = 0.004 1 TeV error threshold of PCA = 2 0.1 light scalar at few hundred GeV? W Z EW self-energy shift 0.05 t observed Higgs-like? fitted range = 5 − 10 0 � κ 2 r 2 t (600 GeV) 2 . M Higgs = 0.0548 ± 0.0175 then δ M 2 H ⌅ � 12 κ 2 r 2 t m 2 t ⌅ new, preliminary − 0.05 ++ correlators Triplet and singlet masses from 0 − 0.1 2 4 6 8 10 12 14 t From the composite Higgs mechanism: 0.6 � =3.20 (with PCA analysis) 40 3 x80 m=0.002 � triplet and singlet masses Goldstone decay constant F is setting the EWSB scale 0.3 L at HC − − − − − − � � � 2 = 0.11 Q = 0.99 0.5 L at HC effective mass of D(t) − D(T/2) M H /F ~ 1 − 3 range 0.25 number of blocks = 17 block size = 5 circa Lattice 2013 0.2 0.4 eigenvalue threshold of PCA = 0.004 − 0.15 0 ++ triplet state error threshold of PCA = 2 (connected) 0.3 0.1 0.05 0.2 fitted range = 4 − 10 − − 0 β =3.20 M Higgs = 0.0494 ! 0.0147 28 3 x56, 32 3 x64 new, preliminary 0.1 0 ++ singlet state − 0.05 m fit range 0.003 - 0.008 − (disconnected) − 0.1 0 − 2 4 6 8 10 12 14 16 0 0.005 0.01 0.015 t fermion mass m � � − − − − −

light 0++ scalar and spectrum sextet model L at HC near-conformal resonance spectrum separated � =3.20 (with PCA analysis) 48 3 x96 m=0.002 from light scalar B 0.25 3 TeV a 1 L at HC moving up to 2-3 TeV with refined scale setting � 2 = 0.019 Q = 1 rho effective mass of D(t) − D(T/2) 0.2 a 0 within reach of LHC Run 2 ? number of blocks = 16 block size = 4 0.15 eigenvalue threshold of PCA = 0.004 1 TeV error threshold of PCA = 2 0.1 light scalar at few hundred GeV? W Z EW self-energy shift 0.05 t observed Higgs-like? fitted range = 5 − 10 0 � κ 2 r 2 t (600 GeV) 2 . M Higgs = 0.0548 ± 0.0175 then δ M 2 H ⌅ � 12 κ 2 r 2 t m 2 t ⌅ new, preliminary − 0.05 ++ correlators Triplet and singlet masses from 0 − 0.1 2 4 6 8 10 12 14 t From the composite Higgs mechanism: 0.6 � =3.20 (with PCA analysis) 40 3 x80 m=0.002 � triplet and singlet masses Goldstone decay constant F is setting the EWSB scale 0.3 L at HC − − − − − − � � � 2 = 0.11 Q = 0.99 0.5 L at HC effective mass of D(t) − D(T/2) M H /F ~ 1 − 3 range 0.25 − number of blocks = 17 block size = 5 circa Lattice 2013 0.2 0.4 eigenvalue threshold of PCA = 0.004 − 0.15 0 ++ triplet state error threshold of PCA = 2 (connected) 0.3 0.1 0.05 0.2 fitted range = 4 − 10 − − 0 β =3.20 M Higgs = 0.0494 ! 0.0147 28 3 x56, 32 3 x64 new, preliminary 0.1 0 ++ singlet state − 0.05 m fit range 0.003 - 0.008 − (disconnected) − 0.1 0 − 2 4 6 8 10 12 14 16 0 0.005 0.01 0.015 t fermion mass m � � − − − − −

light 0++ scalar and spectrum sextet model L at HC near-conformal resonance spectrum separated � =3.20 (with PCA analysis) 48 3 x96 m=0.002 from light scalar B 0.25 3 TeV a 1 L at HC moving up to 2-3 TeV with refined scale setting � 2 = 0.019 Q = 1 rho effective mass of D(t) − D(T/2) 0.2 a 0 within reach of LHC Run 2 ? number of blocks = 16 block size = 4 0.15 eigenvalue threshold of PCA = 0.004 1 TeV error threshold of PCA = 2 0.1 light scalar at few hundred GeV? W Z EW self-energy shift 0.05 t observed Higgs-like? fitted range = 5 − 10 0 � κ 2 r 2 t (600 GeV) 2 . M Higgs = 0.0548 ± 0.0175 then δ M 2 H ⌅ � 12 κ 2 r 2 t m 2 t ⌅ new, preliminary − 0.05 ++ correlators Triplet and singlet masses from 0 − 0.1 2 4 6 8 10 12 14 t From the composite Higgs mechanism: 0.6 � =3.20 (with PCA analysis) 40 3 x80 m=0.002 � triplet and singlet masses Goldstone decay constant F is setting the EWSB scale 0.3 L at HC − − − − − − � � � 2 = 0.11 Q = 0.99 0.5 L at HC effective mass of D(t) − D(T/2) M H /F ~ 1 − 3 range 0.25 − number of blocks = 17 block size = 5 circa Lattice 2013 0.2 0.4 eigenvalue threshold of PCA = 0.004 − 0.15 0 ++ triplet state error threshold of PCA = 2 (connected) 0.3 0.1 0.05 0.2 fitted range = 4 − 10 − − 0 β =3.20 M Higgs = 0.0494 ! 0.0147 28 3 x56, 32 3 x64 new, preliminary 0.1 0 ++ singlet state − 0.05 m fit range 0.003 - 0.008 − (disconnected) − 0.1 0 − 2 4 6 8 10 12 14 16 0 0.005 0.01 0.015 t fermion mass m running large volumes m fit range 0.001 - 0.002 � � − − − − −

light 0++ scalar and spectrum sextet model L at HC 22 M N 5 20 M a 1 strong gauge dynamics coupling to SM? M ρ 4.5 18 4 16 3.5 14 M / TeV 3 12 M / F 2.5 10 2 8 a 0 scalar isovector? 1.5 6 1 4 0 ++ scalar Higgs? 0.5 2 0 0 3.2 β

light 0++ scalar and spectrum sextet model L at HC 22 M N 5 20 M a 1 strong gauge dynamics coupling to SM? M ρ 4.5 18 4 ETC 16 partial compositeness 3.5 14 ? M / TeV 3 12 M / F 2.5 10 2 8 a 0 scalar isovector? 1.5 6 1 4 0 ++ scalar Higgs? 0.5 2 0 0 3.2 β

light 0++ scalar and spectrum sextet model L at HC 22 M N 5 20 M a 1 strong gauge dynamics coupling to SM? M ρ 4.5 18 4 ETC 16 partial compositeness 3.5 14 ? M / TeV 3 12 M / F 2.5 10 2 8 a 0 scalar isovector? } extended linear sigma model 1.5 6 effective theories dilaton 1 4 0 ++ scalar Higgs? 0.5 2 0 0 3.2 β