Naturalness & Compositeness Riccardo Rattazzi, EPFL

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1 Naturalness & Compositeness 2014 Riccardo Rattazzi, EPFL

2 In QM whatever is possible is also compulsory selection rules O = i O i O i = c i λ n 1i 1...λ n ki k dim = dim = If O exp max O i it seems we are missing something Un-Naturalness = failure of dimensional analysis and selection rules

3 Mass Hierarchies Λ UV scale invariant dynamics L fixed point of RG Λ IR Naturalness of Λ IR Λ UV stability of fixed point 3 options

4 1. Marginality Λ UV the fixed point theory does not possess scalar operators with dimension strictly less than 4 Λ IR L mass = c Λ UV O 4 Λ IR = c Λ UV Λ IR = c 1/ Λ UV algebraica"y small c and is enough to produce hierarchy see Strassler arxiv:hep-th/ Ex: Yang-Mills, TechniColor, Randall-Sundrum model

5 2. Symmetry Λ UV L mass = Λ 2 UV O 2 Λ IR small parameter protected by symmetry Λ IR = Λ UV ϵ must be hierarchica"y small how does this smallness originate? Ex: QCD, Supersymmetry

6 3. Sequestering Λ UV Λ IR

7 3. Sequestering Λ UV Λ IR

8 SFT1 3. Sequestering O() SFT2 Λ UV Λ IR

9 SFT1 3. Sequestering O() SFT2 Λ UV Dilations D 1 D 2 D 1+2 by small coupling Λ IR Λ IR Λ UV technically natural Ex. a-gravity by a-strumia Salvio, Strumia 2012 SFT2 = UV completion of gravity not clearly compatible with basic principles = Λ UV /M P but imagine we find a gorgeous candidate for SFT1?

10 The Standard Model Λ UV L SM L free fixed point H H relevant and unprotected Λ IR m W but tuning comes with a bonus L SM = L (d 4) + 1 Λ UV L (5) + 1 Λ 2 UV L (6) +... Accidenta"y possesses all the symmetries we observe in Nature: B, L, Flavor,... Not the case in any natural completion of the SM

11 Composite Higgs Scenario E Λ UV new dynamics CFT TeV Higgs dynamics h, W ±,Z L q,, γ, W T, Z T, g

12 Weak scale structure CFT TeV 100 GeV W ± L,Z L,h H = h1 + ih 2 h + ih 3 must be a pseudo-golstone multiplet Ex.: H SO(5)/SO(4) Georgi, Kaplan 84 Banks 84 Arkani-Hamed, Cohen, Katz, Nelson 02 Agashe, Contino, Pomarol 04

13 EWSB is broadly described by mass one mass scale m m one coupling g Ex.: g 4π N g ΨΨΦ g 2 m 2 (π π) 2 h π = pseudo-ng g m 1 f

14 Flavor

15 The two ways to Flavor Bilinear: ETC, conformaltc Dimopoulos, Susskind Holdom... Luty, Okui Linear: partial compositeness D.B. Kaplan... Huber RS with bulk fermions

16 The two ways to Flavor Bilinear: ETC, conformaltc Dimopoulos, Susskind Holdom... Luty, Okui disfavored by CFT theorems Rychkov, Rattazzi, Tonni, Vichi 2008 Poland, Simmons-Duffin, Vichi 2011 Linear: partial compositeness D.B. Kaplan... Huber RS with bulk fermions

17 Flavor from partial compositeness D.B. Kaplan Huber, Shafi 00 RS with bulk fermions L Yukawa = i qq i LΨ i q + i uu i LΨ i u + i dd i LΨ i d H Y ij u Y ij d i q j ug i q j d g Ψ = composite with dimension 5 2 i q, i u, i d = dimensionless Hypothesis seems a bit wishful, but no other option is in sight Problems of minimal technicolor greatly alleviated, but not eliminated

18 Flavor transitions controlled by selection rules ( accidental non-compact U(1) 9 flavor symmetry ) ΔF=2 i q j d k q d g2 m 2 ( q i γ µ d j )( q l γ µ d ) ΔF=1 i q j ug v m 2 g2 16π 2 q i σ µν u j G µν

19 Flavor and CP bounds Keren-Zur et al., 2012 ΔF=2 ΔF=1 edms µ eγ ( K,...) ( c D CP, /,,b sγ) m > (TeV) 15 g 4π (10 15) g 4π (50 200) g 4π 200 Partial compositeness is likely not the full story Flavor and CP symmetry must be assumed U(1) e x U(1) μ x (1) Range of possibilities SU(3) x SU(3) x... Redi, Weiler 11 Barbieri et al. 12

20 The most clever set up SU(3) comp SU(3) Q SU(3) D SU(2) U Redi 2012 g ˆλ D ˆλ U ˆλ t g ˆ1 D Q i D j L R Q i L U R,C R g g ˆ1 U Q i L g g tr t R Ŷ D = ˆλ D D Ŷ U = ˆλ U U + ˆλ t tr U,D sufficiently small to satisfy bounds from light quark compositeness sufficiently large to avoid sizeable flavor violation from ˆλ U,D tr sufficiently large to confortably account for top Yukawa y t = ˆλ t tr

21 CP conserving strong dynamics phase alignment controls edms U constrainst from compositeness and ˆλ U subdominant Uneliminable effect via the top doublet V ti V tj V ti V tj K, m Bd,B s m g > 5 TeV 2 t R 5 TeV

22 Higgs s mass versus top-partners t L t R V (h) = T T g 2 2 t L g 2 2 t R y t tl tr g tr =1 best option t R is fully composite SO(5) singlet tl g = y t Mrazek et al, 11 Panico, Wulzer 11 Pomarol, Riva 12 V (h) = m4 g 2 y2 t 16π 2 F (h/f)

23 Higgs s mass versus top-partners t L t R V (h) = T T g 2 2 t L g 2 2 t R y t tl tr g tr =1 best option t R is fully composite SO(5) singlet tl g = y t Mrazek et al, 11 Panico, Wulzer 11 Pomarol, Riva 12 V (h) = m4 g 2 y2 t 16π 2 F (h/f)

24 The connection between g,m,m t and m h V = 3y2 t m 2 16π 2 ah 2 + bh 4 /f b a b < ξ ξ v2 f 2 = a b m 2 h = b 3g2 2π 2 m2 t (125 GeV) 2 g2 b 4 m h < 125 GeV a Total tuning area = ab = 430 GeV m 2 4 g 2 De Simone, Matsedonskyi, RR, Wulzer 2012

25 Notice impact of 125 GeV Higgs m h = 125 GeV ab = 430 GeV m 2 4 g 2 weakly strong EWSB sector and light resonances preferred m h = 250 GeV ab = 860 GeV m 2 16 g 2 moderately strong and heavy EWSB sector

26 Higgs couplings a 2m2 V v b = a 2 =1 v2 f 2 1 ξ < 1 robust consequence of coset structure b m2 V v 2 c i m i v c i 1+O( v2 f 2 ) < 1 generic but not theorem m i f 2 New! No other parameter at leading order in g 2 SM/g 2 c a

27 EWPT 3 = O(1) m2 W m 2 + g2 96π 2 v 2 f 2 ln(m /m h ) m > 2 TeV 1 = δρ SM m2 t m 2 3g2 tan θw 2 v 2 32π 2 f 2 ln(m /m h ) in principle very strong bound : ξ v2 f 2 < 0.05 in practice it could be relaxed by short distance contribution

28 M W Γ Z Λ [TeV] 4 Pol Pτ 3 A l 2 0,b A FB a a =1 ξ a Franco, Mishima, Silvestrini 2013

29 Direct searches (LHC 8TeV) Top partners (Q=-1/3, 2/3, 5/3) m > 1 TeV Vector resonances W L q q V = g2 W g <g W V = g W L CMS data Pappadopulo, Thamm, Torre, Wulzer 2014 g =1 g =3 m > 3 TeV m > 2 TeV

30 m 2 ξ = g 2 v 2 A. Thamm 2014 &'!'(!'" )*!!'!!&!!!!!'&!'!( )*!!'!&!'!" )*!!'&!!!#!'!&!!!&!!!"! " # $ % &!!!!" #$%

31 m 2 ξ = g 2 v 2 A. Thamm 2014 Higgs couplings &'!'(!'" )*!!'!!&!!!!!'&!'!( )*!!'!&!'!" )*!!'&!!!#!'!&!!!&!!!"! " # $ % &!!!!" #$% direct searches

32 A. Thamm 2014 &'!'( +,-. "!&/&! "!!'"!!!!!'&!'!(!'!" )*!!'!#!!!" +,-. "!!!'!&! " # $ % &!!!!" #$%

33 A. Thamm 2014 &'!'( +,-. "!&/&! "!!'"!!!!!'&!'!(!'!" )*!!'!#!!!" +,-. "!!!'!&! " # $ % &!!!!" #$%

34 Top partners LHC8 A. Thamm 2014 &'!'( +,-. "!&/&! "!!'"!!!!!'&!'!(!'!" )*!!'!#!!!" +,-. "!!!'!&! " # $ % &!!!!" #$%

35 Top partners LHC13 A. Thamm 2014 &'!'( +,-. "!&/&! "!!'"!!!!!'&!'!(!'!" )*!!'!#!!!" +,-. "!!!'!&! " # $ % &!!!!" #$%

36 Top partners LHC13 A. Thamm 2014 &'!'( +,-. "!&/&! "!!'"!!!!!'&!'!(!'!" )*!!'!#!!!" +,-. "!!!'!&! " # $ % &!!!!" #$%

37 A. Thamm 2014 &'!'( +,-. "!&/&! "!!'"!!!!!'&!'!(!'!" )*!!'!#!!!" +,-. "!!!'!&! " # $ % &!!!!" #$% Vectors LHC8 Pappadopulo, Thamm, Torre, Wulzer 14

38 A. Thamm 2014 &'!'(!'" +,-. "!&/&! "!!!!!!!!!!'&!'!(!'!" )*!!'!# )*!!'!# )*!!'!!#!!!"!!!" +,-. "!!!'!&! " # $ % &!!!!" #$% Vectors LHC13 Pappadopulo, Thamm, Torre, Wulzer 14

39 In my opinion Compositeness remains a comparatively viable option to solve the hierarchy problem. It also forces us to think more and better about QFT Flavor is its major structural drawback Flavor and EWPT make the outcome of LHC8 unsurprising LHC13 and HL-LHC will definitely break new grounds