Precision observables of compositeness Roman Pasechnik Dept. of - PowerPoint PPT Presentation


 Precision observables of compositeness Roman Pasechnik Dept. of Astronomy and Theoretical physics, 
 Lund University HP2, September 5 th , 2014

Dynamical electroweak symmetry breaking Many attractive features ✓ EWSB is triggered by a new strongly-coupled dynamics more than one confinement scale in Nature? Higgs mechanism is effective? � ✓ No fundamental scalars 
 composite Higgs? Higgs “partners”? � ✓ No hierarchy problem, no fine-tuning a best alternative to SUSY with fewer free parameters? � ✓ A plenty of new hadron-like objects, difficult to find/treat though composite Dark Matter? LHC phenomenology? ..etc Evolutions of DEWSB ideas/realizations Technicolor Extended TC Walking TC Bosonic TC Composite Higgs EFT’s Hill & Simmons, Phys. Rept. 381, 235 (2003) Sannino, Acta Phys. Polon. B40, 3533 (2009), etc e.g. MCHM SO(5)/SO(4) ??? No consistent UV completion has yet been proposed…. 2

A new energy scale from confinement? Well-known example: QCD at low momentum scales QCD Static properties of light hadrons can be completely determined by two dimensionful vacuum parameters: gluon condensate: light quark condensate: Simplistic approach: one employs a direct analogy with QCD Spectrum of light composites (incl. Higgs) is governed by “T-QCD” The energy scale of both EW theory ( SM ) and working new strongly - coupled dynamics has a common hypothesis: origin: the Tquark - Tgluon condensate 3

Issues of Technicolor: oblique corrections should not disturb EW obs too much! New Physics must come in loops 1 − � α ( M Z ) T Peskin&Takeuchi PRL’90 M 2 Z = M 2 � Z 0 √ 1 − G F M 2 Z 0 S/ 2 2 π − Generic parameterization 1 M 2 W = M 2 of NP effects is EW observables √ W 0 1 − G F M 2 W 0 ( S + U ) / 2 2 π in terms of S,T,U parameters M 3 Z β Z Γ Z = α ( M Z ) T , 1 − � PDG’13 Extra chiral heavy family doublet brings up � � 2 � EW precision constraints on New Physics S = C , = 4 e 2 / 3 π t 3 L ( i ) − t 3 R ( i ) 3 π S = 0 . 00 +0 . 11 i T = 0 . 02 +0 . 11 − 0 . 10 , − 0 . 12 , U = 0 . 08 ± 0 . 11 , ] S ∼ 0 . 45 Standard QCD - like TC axial SU ( 2 ) vector SU ( 2 ) Non - QCD - like ( Walking ) TC still breaking breaking survives but has other issues… • Flavour-Changing neutral-currents � Is a new QCD - like dynamics • Too-light quarks � completely dead? • Too many unobserved pseudo-Goldstone states 4

Vector-like weak interactions Which confined symmetry enables to transform a chiral UV completion into a vector-like one? RP et al, arXiv:1407.2392 � � � 0 , if N TC = 2 , U ˜ y SU ( N TC ) TC Q = , Y ˜ Q = D 1 / 3 , if N TC = 3 . start with new R-handed WEAK L ( A ) + i two generations Q a α ′ ˜ L ( A ) = ˜ k ˜ DOUBLET Q a α 2 g W θ k τ ab Q b α of CHIRAL fields L ( A ) ) of left-handed T-qua + i R (2) ≡ ε ab ε αβ Q Cb β 2 g T C ϕ k τ αβ Q a β ˜ Q a α L ( A ) , e SU (2) W ⊗ SU (2) TC L (2) k ( A = 1 , 2) We end up Dirac WEAK ˆ C Q a α L (2) = Q Ca α L (2) , DOUBLET charge conjugation L (2) − i Q Ca α ′ L (2) = Q Ca α 2 g W θ k ( τ ab k ) ∗ Q Cb α of the SECOND L (2) Q a α = Q a α L (1) + Q a α generation − i R (2) 2 g T C ϕ k ( τ αβ k ) ∗ Q Ca β L (2) . At the fundamental level, we arrive at the simplest possible VLTC Lagrangian: 5

Toy-model of DEWSB: SU(2) L xSU(2) R L σ M L σ M in QCD hadron physics: a model for constituent quark - meson interactions the source term � � − g TC ¯ ⟨ ¯ QQ ⟩ S + ¯ Q ( S + i γ 5 P a ) Q → − g TC Q ( S + i γ 5 P a τ a ) Q QQ → ⟨ ¯ ¯ QQ ⟩ + ¯ QQ pseudoscalar T-pions scalar T-sigma QGC formation (adjoint rep.) (singlet rep.) S = u + σ lightest � collective excitation � T-glueball of T-quark condensate T - pion mass global chiral SSB = − g TC ⟨ ¯ Q ˜ ˜ Q ⟩ f µ S , H � m ˜ SU (2) L ⊗ SU (2) R → SU (2) V ≡ L+R m Q � m π = π u 1 H H 2 − 1 S ( S 2 + P 2 ) + µ 2 4 λ TC ( S 2 + P 2 ) 2 − λ H H 4 + λ H 2 ( S 2 + P 2 ) 2 µ 2 Potential � 1 / 3 � 1 / 2 � λ H � 1 / 3 � λ H � ξλ ⟨ H ⟩ = 1 � � 0 g 1 / 3 g 1 / 3 √ u = ¯ v = ¯ TC , v TC 2 δ λ H δ ms: • Both chiral and EW SSB are dynamically linked to T-quark condensate � • T-pion gets mass via T-sigma interaction with T-quark condensate � Spontaneous • T-pions remain physical, the Higgs-like mechanism becomes effective EWSB 6

SU(2) L xSU(2) R : parameter space RP et al, o m ˜ π = 150 , 250 , 350 GeV, PRD88, 075009 √ (2013) √ it M ˜ σ → 3 m ˜ π , w bsolute value of sine o √ of ∆ m ˜ σ ≡ m ˜ 3 m ˜ σ − π 1 ~ mixing v/u ratio h σ 1 |sin θ | v/u 0.1 0.1 only gauge interactions m π ~ = 80 GeV m π ~ = 80 GeV m π ~ = 150 GeV m π ~ = 150 GeV of light T - pions remain… m π ~ = 300 GeV m π ~ = 300 GeV 0.01 0.01 -40 -20 0 20 40 -40 -20 0 20 40 7 ∆ m σ ~ (GeV) ∆ m σ ~ (GeV)

SU(2) L xSU(2) R : oblique corrections NEW! Modified SM + T-sigma! NEW! 8

T-pion and Dirac T-quark contributions RP et al, PRD88, 075009 (2013) give vanishing contributions can be large in to all oblique corrections the T-parameter only! for any VLTC parameters! T-pion/T-quark loops Vector-like weak interactions of the UV completion preserve Technicolor! 9

T-parameter: constraint on σ h-mixing and σ -mass RP et al, PRD88, 075009 (2013) a small mixing angle and/or small σ -mass are preferable! Given by scalar contribution ONLY 10

SU(2) L xSU(2) R : Higgs signal rates γ γ γ f, ˜ Q W W h, ˜ h, ˜ h, ˜ σ σ σ f, ˜ + Q + W W f, ˜ Q W γ γ γ ( a ) ( b ) ( c ) π + π + γ ˜ γ π + ˜ h, ˜ h, ˜ σ + σ ˜ π − ˜ γ π − γ ( d ) ( e ) res res t) m ˜ π = 350 GeV, ) g TC = 8, res Μ ΓΓ Μ ΓΓ ) m ˜ π = 350 GeV, M ˜ Q = 500 GeV, 2.0 d M ˜ Q = 400 , 500 , 700 GeV, 2.0 d g TC = 2 , 8 , 15, 1.5 1.5 1.0 1.0 0.5 0.5 � , GeV M Σ � , GeV M Σ 500 600 700 800 500 600 700 800 11 res

SU(2) L xSU(2) R : search for T-pions T-pion branching ratios γγ γ Z T - pion decay ZZ γ W ZW 1 γ , Z, W ± γ , Z, W ± ~ -> VV) ˜ ˜ Q Q π 0 , ± π 0 , ± ˜ ˜ BR( π ˜ Q 0.1 e Y Q = 0 ˜ f Y Q ̸ = 0, ˜ Q Q 0.01 150 200 250 300 350 400 450 500 RP et al, m π ~ (GeV) NP881, 288 (2014) Signal Background p 1 p ′ 1 u, d q 1 γ γ γ γ π 0 π 0 ˜ ˜ γ γ U, D U, D q 0 γ γ q 2 γ γ γ γ p ′ p 2 2 1 (fb/GeV) 10 1 (fb) T-pion production cross section γ and Z ∼ 0 pp → p γ γ p pp → pp π γ only -1 10 s = 14 TeV E pp =14 TeV σ s = 14 TeV | η | < 2.5 γ γ fusion via gg γ ~ 0 ) (pb) γ -2 10 γ 1 /dM σ (pp -> X + jj + π no Sudakov ff’s -3 σ 10 0.1 d -4 -1 10 10 via γ γ g = 10 -5 10 TC M = 100, 200 GeV M Q ~ = 300 GeV, g TC = 10, CTEQ5L quark PDFs ∼ 0 π -2 0.01 10 -6 10 200 300 400 500 160 180 200 220 240 260 280 300 0 200 400 m (GeV) ~ m π ~ (GeV) 12 Q M (GeV) γ γ

SU(3) L xSU(3) R composite Higgs model: content e accounts for the d Q R = ( U, D, S ) R chiral Dirac T-quarks in SU(2) TC s Q L = ( U, D, S ) L ing groups � � L T C = − 1 ∂ µ − i µ τ A − i n + i ¯ Q − m Q ¯ 4 T n µ ν T µ ν Q γ µ 2 g T C T n A µ τ n QQ + 2 g W W Fundamental Lagrangian � � ∂ µ + i 2 g 1 B µ − i + i ¯ S − m S ¯ S γ µ 2 g T C T n µ τ n SS ⎟ ⎟ ⎟ ⎟ K + , K 0 , ¯ π + , π 0 , π − ; K 0 , K − ; η pseudo-Goldstones: ⎠ ⎠ + 3 σ 3 η ′ H + , H 0 , ¯ a + , a 0 , a − ; H 0 , H − ; f , their chiral partners: 2 a 0 + 1 1 1 a + H + ⎛ 6 f + ⎞ 3 σ √ √ √ Φ = 1 2 a 0 + − 1 1 1 H 0 ˆ a − 6 f + 3 σ ⎜ ⎟ √ √ √ √ ⎠ − ⎜ ⎟ 2 ⎝ � ¯ 2 1 H 0 3 f + H − 3 σ − √ components of the 2 π 0 + bi-fundamental rep: 1 1 1 π + K + ⎛ 6 η + 3 η ′ ⎞ √ √ √ − i 2 π 0 + − 1 1 1 K 0 π − 6 η + 3 η ′ ⎜ ⎟ √ √ √ √ ⎜ ⎟ 2 ⎝ � ⎠ ¯ 2 1 K 0 3 η + K − 3 η ′ − √ √ Φ + · ∂ µ ˆ L σ = i ¯ 6 κ ( ¯ Q L Φ Q R + ¯ Q R Φ + Q L ) + ∂ µ ˆ Q γ µ ∂ µ Q − Φ + Generic global L σ M √ Lagrangian: Φ + ˆ Φ + ˆ Φ + ˆ Φ + ˆ + µ 2 ˆ Φ − λ 1 (ˆ Φ ) 2 − 3 λ 2 ˆ Φ ˆ Φ + 2 6 Λ 3 Re det Φ . 13

SU(3) L xSU(3) R CHM: EW interactions of composites Additional EW-invariant piece to the Higgs-less SM Lagrangian: � ∂ µ − i � � ∂ µ + i � √ L σ = i ¯ Q + i ¯ 6 κ ( ¯ Q L Φ Q R + ¯ Q R Φ + Q L )+ Q γ µ 2 g W W a S γ µ 2 g 1 B µ S − µ τ a 1 2( D µ π a · D µ π a + D µ a a · D µ a a ) + ( D µ K ) + · D µ K + ( D µ H ) + · D µ H + composite Higgs - like kinetic terms 1 2( ∂ µ η · ∂ µ η + ∂ µ η 0 · ∂ µ η 0 + ∂ µ f · ∂ µ f + ∂ µ σ · ∂ µ σ )+ √ Φ + ˆ Φ + ˆ Φ + ˆ Φ + ˆ µ 2 ˆ Φ − λ 1 (ˆ Φ ) 2 − 3 λ 2 ˆ Φ ˆ Φ + 2 6 Λ 3 Re det Φ − replaces Higgs potential mn ¯ mn ¯ mn ¯ Q m ˜ ( Y l L m HE n + Y d Q m HD n + Y u HU n + h.c. ) − to be l d u mn ¯ mn ¯ mn ¯ Q m ˜ ( Y L m KE n + Y Q m KD n + Y KU n + h.c. ) , constrained by FCNC etc where D µ π a = ∂ µ π a + g W e abc W b D µ a a = ∂ µ a a + g W e abc W b µ π c , µ a c , D µ K = ∂ µ K − i 2 g 1 B µ − i D µ H = ∂ µ H − i 2 g 1 B µ − i 2 g W W a 2 g W W a µ τ a K, µ τ a H . Structure of the theory has certain similarities to the class of THDMs! 14