General Composite Higgs Models

Transcription

1 General Composite Higgs Models Marco Serone, SISSA, Trieste In collaboration with David Marzocca and Jing Shu, based on

2 The Higgs hunt at the LHC is quickly coming to an end A SM Higgs is ruled out everywhere below 600 GeV, except a small window around 125 GeV, where an excess has been found 2

3 We will hopefully know soon whether there is an Higgs at around 125 GeV or not Next question: is the SM Higgs or not? Naturalness arguments disfavour a SM Higgs, but non-sm Higgs, in a way or another, should come together with new physics particles, yet to be seen Broadly speaking, there are two ways to go for naturally motivated new physics: 3

4 Weakly coupled (Supersymmetry) Strongly coupled (technicolor, little Higgs, composite Higgs) Technicolor, already in trouble for tensions with LEP electroweak bounds, would be essentially ruled out by a 125 GeV Higgs (but let s wait for discovery...) Little Higgs are also Composite Higgs Models (CHM) 4

5 Little Higgs: thanks to an ingenious symmetry breaking mechanism, the Higgs mass is radiatively generated, while the quartic is not Composite Higgs: the entire Higgs potential is radiatively generated In principle little-higgs models are better, because allow for a natural separation of scales between the Higgs VEV and the Higgs compositeness scale In practice they are not, because the above ingenious mechanism becomes very cumbersome when fermions are included 5

6 Fundamental difference between Technicolor and CHM: Technicolor: the EW group is broken by the strongly coupled sector (techni-quark condensates), no Higgs at all is necessary Composite Higgs: the EW group is unbroken by the strongly coupled sector, but a Higgs-like particle appears in the spectrum and breaks the EW group via its VEV, as in the SM Thanks to this difference, LEP bounds can be successfully passed by CHM (in particular pngb CHM) 6

7 Plan Introduction on Composite Higgs Models General Set-Up Minimal Higgs Potential (MHP) Hypothesis Results for Selected Models Conclusions 7

8 Introduction on Composite Higgs Models (CHM) A Composite Higgs coming from some strongly coupled theory might resolve the hierarchy problem At some scale the Higgs compositeness appears and the quadratic divergence is naturally cut-off The Higgs field might or might not be a pseudo Nambu-Goldstone boson (pngb) of a spontaneously broken global symmetry. Models where the Higgs is a pngb are the most promising The Higgs is naturally light and naturalness and LEP bounds are improved 8

9 The global symmetry has also to be explicitly broken (by SM gauge and Yukawa couplings), otherwise the Higgs remains a massless NGB Whole Higgs potential is radiatively generated Implementations in concrete models hard (calculability, flavour problems) Recent breakthrough: the composite Higgs paradigm is closely related to theories in extra dimensions! Extra-dimensional models have allowed a tremendous progress The Higgs becomes the fifth component of a gauge field, leading to Gauge-Higgs-Unification (GHU) models Not only relatively weakly coupled description of CHM, Higgs potential fully calculable, but the key points of how to go in model building have been established in higher dimensions 9

10 Main lesson learned from extra dimensions and reinterpreted in 4D L tot = L el + L comp + L mix Elementary sector: SM particles but Higgs (and possibly RH top quark) Composite sector: unspecified strongly coupled theory with unbroken global symmetry G G SM Mixing sector: mass mixing between SM fermion and gauge fields and spin 1 or 1/2 bound states of the composite sector SM fields get mass by mixing with composite fields: the more they mix the heavier they are (partial compositeness) m L R v H Light generations are automatically screened by new physics effects Natural mechanism to suppress dangerous FCNC 10

11 Equipped with this crucial insight one can consider a bottom-up approach to build simplified 4D versions of CHM [Panico & Wulzer, 2011] Calculability of the Higgs potential is ensured by considering a collective symmetry breaking mechanism on moose-type models, deconstructed versions of 5D models Considerable progress, but models still too close to their 5D parents... Is it possible to build more general CHM, not directly related to 5D models and yet with a calculable Higgs potential? This requires either the knowledge of a UV completion or of a symmetry principle, alternative to collective symmetry breaking, to protect the Higgs potential Or we might look for the generic constraints a model like that should have 11

12 Our aim: Construct 4D pngb composite Higgs models, not directly related by deconstruction to 5D models, where the Higgs mass can at least be assumed to be calculable, and characterize the main properties these models should have in order to give rise to a Higgs mass at around 125 GeV (or 320 GeV) 12

13 General Set-Up Assume composite sector with SO(5) U(1) X SO(4) U(1) X Gauge SU(2) L U(1) Y SO(4) U(1) X Y = T 3R + X NGB matrix: U =exp i 2 h f L σg = 1 4 W al µν W alµν 1 4 B µνb µν + f 2 4 Tr ˆdµ ˆdµ 13

14 iu D µ U = ˆd µ + ʵ [CCWZ notation] ˆdµ = 2 f (D µh)+... Ê µ = g 0 A µ + i f 2 (h D µ h)+... m W = gf 2 sin h f gv 2. s h =sin h f, ξ s2 h 14

15 Theory makes sense up to energies of order Λ=4πf We assume that a given number of spin 1 and 1/2 resonances of the composite sector are lighter than Λ and hence appear in the low-energy effective action Spin 1 resonances It is known how to add spin 1 resonances in a chiral Lagrangian Consider fields in the SU(2) L SU(2) R representations ρ L :(3, 1) ρ R :(1, 3) a: (2, 2) ``Vector Resonances ``Axial Resonances 15

16 L v L = N ρl i=1 L g = L v L + L v R + L a, 1 4 ρi,2 L,µν + f 2 ρ 2 L v R = L v L, with L R, L a = N a 1 4 ai,2 µν + f a i i=1 g ρ ρ i L ÊL g a a i u i ˆd. j<i f 2 mix ij 2 ρ i L,µν = µ ρ i L,ν ν ρ i L,µ ig ρ [ρ i L,µ,ρ i L,ν], g 2 ρ 2 ρ i L ρ j L, ρ-sm gauge mass mixing terms a µν = µ a ν ν a µ, = iê m 2 ρ i L = f 2 ρ i L g 2 ρ i L m 2 ρ i R = f 2 ρ i R g 2 ρ i R m 2 a i = f 2 a i g 2 a i 2 i 16

17 Spin 1/2 resonances Fermion resonances S and Q in singlet and fundamental SO(4) representations Let us introduce explicit breaking terms, transforming in SO(5) representations N L = q L i ˆDq L + t R i ˆDt S N R + S i (i ˆ m Q is )S i + Q j (i ˆ m iq )Q j + N S i=1 i=1 i ts 2 ξr P L US i + i qs ξ L P R US i + N Q j=1 j=1 j tq 2 ξr P L UQ i + j qq ξ L P R UQ i + h.c., Spin 1/2 resonance -SM fermion mass mixing terms ξ L = 1 2 b L ib L t L it L 0, ξ R = t R

18 Example: N Q = N S =1 Q =(Q 1,Q 7 ), Y = 1 6, Y = 7 6 Before EWB, LH and RH top mix with doublet Q 1 and singlet S Degree of compositeness measured by the angles tan θ L = qq m Q, tan θ R = ts 2mS [Contino et al, 2007] m top sin θ L sin θ R 2 qs qq m Q tq ts m S s h m 0 = m S cos θ R, m 1/6 = m Q cos θ L, 18 m 7/6 = m Q

19 Minimal Higgs Potential (MHP) hypothesis Assume that the Higgs potential is saturated at one-loop by the contributions given by the SM and spin 1, 1/2 resonances, made calculable by imposing generalized Weinberg sum rules Strong, but reasonable, assumption, because any CHM (within our construction) where a symmetry mechanism is at work to have a calculable Higgs potential will fall into this class 19

20 In QCD, for Weinberg sum rules SU(2) V SU(2) A SU(2) V V a µ (q)v b ν ( q) P t µνδ ab Π VV (q 2 ) A a µ(q)a b ν( q) P t µνδ ab Π AA (q 2 ) Π LR =Π VV Π AA is such that lim Π LR ( p 2 E)=0 p 2 E First sum rule (I) lim p 2 EΠ LR ( p 2 E)=0 p 2 E Second sum rule (II) (I) consequence of symmetry restoration, (II) assumes UV asymptotically free theory The radiatively induced pion potential (analogue of Higgs potential) calculable if I and II imposed [S. Weinberg, 1967] Good theoretical prediction of pion mass difference 20

21 Generalized Weinberg sum rules in our context Analogue of Π LR in gauge sector Π 1 (p 2 )=g 2 0f 2 +2g 2 0p 2 N a i=1 lim g 2 p 2 E 0 Π 1( p 2 E)=f 2 +2 lim g 2 p 2 E 0 p2 EΠ 1 ( p 2 E)=2 N a i=1 f 2 a i (p 2 m 2 a i ) N a i=1 f 2 a i 2 f 2 a i m 2 a i 2 N ρ j=1 N ρ j=1 N ρ j=1 f 2 ρ j (p 2 m 2 ρ ) j f 2 ρ j 0. (I) f 2 ρ j m 2 ρ j 0. (II) Sum rule (I) requires at least one vector resonance. Sum rule (II) requires at least one axial resonance. 21

22 Similar sum rules in fermion sector N S i=1 i ts 2 N Q j=1 j tq 2 =0 N S i=1 i qs 2 N Q j=1 j qq 2 =0. (III) N S i=1 m 2 is i ts 2 i qs 2 N Q j=1 m 2 jq j tq 2 j qq 2 =0. (IV) Typically in moose-models one has N S = N Q i ts = i tq i qs = i qq Much more constrained choice 22

23 Higgs Potential Calculable Higgs potential is a crucial portal for new physics. Within the MHP hypothesis, Higgs mass related to new resonances masses For s h 1 V (h) =V g (h)+v f (h) V g (h) = γ g s 2 h + β g s 4 h V f (h) = γ f s 2 h + β f s 4 h Non-trivial minimum at s 2 h = ξ = γ 2β m 2 h = 8β ξ (1 ξ). f 2 Notice that we might also relax the second sum rule. In this way EWSB no longer calculable, but Higgs mass still predicted 23

24 Consider N ρ = N a = N Q = N S =1 When the sum rules (I-IV) are imposed one mass scale in gauge sector: m ρ three mass scales in gauge sector: m Q, m S and We can trade two mass scales for the angles θ L and θ R γ g g2 f 2 m 2 ρ 16π 2, β g g4 f 4 g 2 16π 2 γ g γg. g ρ m 2 top k t (θ L,θ R )m 2 Lξ, γ f N cm 4 L 16π 2 k γ(θ L,θ R ), β f N cm 4 L 16π 2 k β(θ L,θ R ) m L =min(m 0,m 1/6,m 7/6 ) Lightest fermion resonance 24

25 m 2 ρ m 2 H 4π2 γ g g 2 γ γ = γ g + γ f 0 (Fine-tuning) All mass scales parametrically determined in terms of m top, m W, ξ and the angles θ L,R m 2 ρ N cm 2 top 4m 2 W k γ k 2 t ξ m2 top, m 2 H g2 N c m 2 top 8π 2 m 2 W k β k 2 t m 2 top, m 2 L = m2 top k t ξ, For any θ L,R, k t k β m L 2πf Nc m top m H m ρ πf 2mW m H Direct relation between Higgs and resonance masses 25

26 In particular, fermion resonances lighter than vector ones by Nc factor and a light Higgs implies light fermion resonances For a 125 GeV Higgs, vector resonances not heavy enough to get sizable S parameter With more vector and/or fermion resonances, parameter space greatly enlarged The implication light Higgs The tree level S can be accommodated either by heavier vector resonances or mild tuning light fermion resonances continue to hold, with one exception only, based on a chiral composite sector Notice that the converse [A. Wulzer, talk at ICTP workshop, Jan 2012] [Matsedonskyi, Panico and Wulzer, , Redi and Tesi, ] light fermion resonances light Higgs does not always hold 26

27 Results for Selected Models In addition to the implications for a 125 GeV Higgs, we have considered ElectroWeak Precision Tests (EWPT) and computed the leading contribution to S and T (from fermion loops) and to (from W loops) and one direct search bound for Q=5/3 particles, adapted from b searches at CMS δg b [A. Wulzer, talk at ICTP workshop, Jan 2012] m 5/3 > 611 GeV. [CMS, ] Similar bounds for top partners with Q=2/3 are more model-dependent and have not been imposed We have also studied the region of a 320 GeV Higgs, yet allowed by current data 27

28 A 320 GeV composite Higgs yet not excluded MCHM5: 95 CL Exclusions Ξ LEP LHC Favored by EWPT m h Taken from Azatov, Contino and Galloway,

29 N ρ =2,N a = N Q = N S =1-ξ = m H m L (a) N ρ =2,N a = N Q = N S =1-ξ = m H m L (b) Figure 2: Mass of the lightest composite fermion (in GeV), before EWSB, as a function of the Higgs mass (in GeV). The green circles represent the singlet while the purple triangles represent the exotic doublet with Y =7/6. The masses m Q,m ρ1 and m ρ2 are taken in the range [0, 8f], a ρ1,a ρ2 [1/2, 2 and a mix [0, 5]; and m S have been obtained by fixing m top and ξ. EWPT and the bound (5.1) have not been imposed. an SO(4) singlet, however, has three different decay channels: t bw +, t tz and t th where only the first one has a significant bound. The constraints on t largely depend on its decay branching ratio and are weak. For instance, if Br(t bw + < 35%), we find that the Mass of the lightest composite fermion (in GeV), before EWSB, as a function of the Higgs mass (in GeV). The green circles represent the singlet while the purple triangles represent the Q=5/3 state 29

30 N ρ =2,N a = N Q = N S =1-ξ = S T (a) N ρ =2,N a = N Q = N S =1-ξ = S T (b) Figure 3: S and T parameters for the points of the numerical scan with a light Higgs: m H [100, 150] GeV. The ellipses are the 99% and 90% C.L., for a mean value of m H = 125 GeV. The green circles are the points which pass both EWPT and the bound (5.1), the blue triangles pass EWPT but are ruled out by the bound (5.1) and the red squares don t pass EWPT. The range of the input parameters is as indicated in fig.2. As explained in section 4, adding a second vector resonance allows for a higher overall mass The green circles are the points which pass both EWPT and the direct bound, the blue triangles pass EWPT but are ruled out by the direct bound and the red squares don't pass EWPT. 30

31 N ρ =2,N a = N Q = N S =1-HeavyHiggs-ξ = T S m H [300, 350] GeV nd T parameters for the points of the numerical scan for a heavy Higgs (m H [300, The ellipses are the 99% and 90% C.L., for a mean value of m H = 325 GeV. re the points which pass the EWPT (and the bound (5.1)) while the red squares are 31 on t pass EWPT. The ranges of the input parameters is as indicated in fig.2.

32 N ρ = N a = N Q =1,N S =2-ξ = m H m L (a) N ρ = N a = N Q =1,N S =2-ξ = m H m L (b) Figure 5: Mass of the lightest composite fermion (in GeV), before EWSB, as a function of the Hig mass (in GeV). The green circles represent the singlet while the purple triangles represent the exot doublet with Y =7/6. All the fermion masses are taken in the range [0, 6f], the angles θ q, θ t [0, 2 and a ρ [1/ 2, 2]. The mixing t and the mass m ρ have been obtained by fixing m top and ξ respectivel EWPT and the bound (5.1) have not been imposed. respect to δg b (as done in Figs.4, 6 and 7). 19 The χ and t fields are respectively the lighte states (with m 7/6 500 GeV and m GeV) in the region of positive and sizable T an Mass of the lightest composite fermion (in GeV), before EWSB, as a function of the Higgs mass (in GeV). The green circles represent the singlet while the purple triangles represent the Q=5/3 state 32

33 N ρ = N a = N Q =1,N S =2-ξ = S T (a) N ρ = N a = N Q =1,N S =2-ξ = S T (b) Figure 6: S and T parameters for the points of the numerical scan with a light Higgs: m H [100, 150] GeV. The ellipses are the 99% and 90% C.L., for a mean value of m H = 125 GeV. The green circles are the points which pass EWPT (and the bound (5.1)) and the red squares don t. The ranges of the input parameters is as indicated in fig Two-singlet model Adding a second composite fermion, singlet of SO(4), is the minimal choice to go beyond the The green circles are the points which pass both EWPT and the direct bound, the blue triangles pass EWPT but are ruled out by the direct bound and the red squares don't pass EWPT. 33

34 N ρ = N a = N Q =1,N S =2-HeavyHiggs-ξ = S T d T parameter for the points of the numerical scan, for a heavy Higgs (m H [ The ellipses are the 99% and 90% C.L., for a mean value of m H = 325 Ge e the points which pass the EWPT (and the bound (5.1)) while the red squares m H [300, 350] GeV 34

35 Counter-example: a Light Higgs and Heavy Resonances The RH top is fully composite and arises as a chiral massless bound state In principle the simplest model of all: N ρ = N Q = 1, N a = N S = 0! L = q L i ˆDq L + t R i ˆ t R + Q(i ˆ m Q )Q + qs ξl UP S t R + qq ξl UP Q Q R + h.c. m H Nc m 2 top 2π 2 v Sum rule (III) requires qs = qq = Sum rule (IV) would require =0 Relax (IV) and keep a log. div. Higgs potential log m2 1/6 m 2 top 1 36 log m2 1/6 m 2 top 1GeV. Light Higgs (too light, below LEP bounds) and heavy fermion resonances 35

36 Conclusions We constructed general composite Higgs models, with SO(5)/SO(4) coset structure, that lead to a calculable Higgs potential, based on the MHP hypothesis For generic non-chiral composite sectors, a light Higgs seems to imply the presence of light, sub TeV, colored fermion resonances Light fermion states are welcome from EWPT considerations, because of possible sizable and positive contributions to the T parameter LHC puts severe constraints to the models where the lightest fermion resonance is an exotic particle with Q=5/3 36

37 There are obvious generalizations to our approach, other SO(4) representations, more general cosets,... It would be very interesting to find new symmetry principles leading to new UV realizations of some of our models More phenomenologically, it is important to perform a detailed analysis of the direct search bounds for top partners that can significantly constrain Composite Higgs Models 37

38 Hopefully we will soon see whether the Higgs is there or not at around 125 GeV If it s there, some more time will be needed to understand whether it is an elementary or a composite particle Searches for heavy colored fermions might play a crucial role 38

39 Hopefully we will soon see whether the Higgs is there or not at around 125 GeV If it s there, some more time will be needed to understand whether it is an elementary or a composite particle Searches for heavy colored fermions might play a crucial role The end 38