Beyond the Higgs. new ideas on electroweak symmetry breaking

Transcription

1 E = mc 2 Beyond the Higgs new ideas on electroweak symmetry breaking Higgs mechanism. The Higgs as a UV moderator of EW interactions. Needs for New Physics beyond the Higgs. Dynamics of EW symmetry breaking E = hν Review of possible scenarios :Gauge-Higgs Unification, Little Higgs, Composite Higgs, (5D) Higgsless models. R µν 1 2 Rg µν = 16πG T µν Ch!"ophe Grojean CERN-TH & CEA-Saclay/SPhT ( christophe.grojean@cern.ch )

2 Summary of % 1 lecture EW interactions need a UV moderator to unitarize WW scattering amplitude at high energies the Higgs mechanism is only a description of EWSB no dynamics to explain why EW symmetry is broken new particles/symmetries are expected to populate the TeV scale to cure instabilities of the Higgs potential

3 New physics and EW prec'ion tests

4 New Particles & EW Precision Measurements We ve seen that we need new particles to stabilize the weak scale. They have to be massive to evade direct searches. They still influence SM physics and can be detected trough precision measurements. Define B in = B + B, B out = B B L = 1 2 W 3 Example: Take an extra heavy B gauge boson L = 1 2 W 3(p 2 M 2 W )W 3 + t 0 M 2 W W 3 B B(p2 t 2 0M 2 W )B + gj 3 W 3 + g J y B B (p 2 M 2 )B + g J y B t 0 = g /g and integrate out B out L =0 B out = (t2 0MW 2 M 2 )B in 2t 0 MW 2 W 3 B out 2p 2 t 2 0 M W 2 M B in ( p 2 M 2 W + t 2 0 M 4 W M 2 ) W 3 + t 0 MW 2 ( p 2 t 2 0MW 2 + p4 2t 2 0MW 2 p2 + t 4 0MW 4 +gj 3 W 3 + g J y B in + O ( 1+ p2 t 2 0M 2 W holographic method M 2 ( p 6 M 4 ) + O ( ) M 6 W M 4 ) M 2 B in ) W 3 B in

5 New Particles & EW Precision Measurements L = 1 2 W B in Mass matrix in the ( p 2 M 2 W + t 2 0 MW 4 ) M 2 W 3 + t 0 MW 2 ( p 2 t 2 0MW 2 + p4 2t 2 0MW 2 p2 + t 4 0MW 4 M 2 (W 3,B in ) basis ( 1 t 2 0 M 2 W M 2 This mass matrix is diagonalized by Z = cw 3 sb in γ = sw 3 + cb in ) with masses ( 1+ p2 t 2 0MW 2 ) M 2 W 3 B in ) B in + gj 3 W 3 + g J y B in Note: det=0, so the photon is still massless! M 2 W t 0 M 2 W t 0 M 2 W t 2 0M 2 W MZ 2 = ( 1 t 2 0 M 2 W /M 2 ) c 2 0 Mγ 2 =0 M 2 W unmodified weak mixing angle s = s 0, c = c 0 that s what you need to ensure that the photon couples to T 3L +Y Rho and T parameters ρ M 2 W M 2 Z c2 1+ s 2 0 c 2 0 M 2 W M 2 SM deviation: ρ 1+α em T T = s2 0 α em c 2 0 M 2 W M 2

6 Experimental Constraints on T T 0.2 M 1.1 TeV That s rather generic bound on new physics needed to stabilize the weak scale is at least one order of magnitude above the weak scale Particle Data Group section 10.3 Little Hierarchy Pb

7 About integrating out In the holographic approach, we have integrated out a state that is not a mass eigenstate We could have proceeded differently L = 1 2 W 3(p 2 M 2 W )W 3 + t 0 M 2 W W 3 B B(p2 t 2 0M 2 W )B + gj 3 W 3 + g J y B B (p 2 M 2 )B + g J y B L B =0 B = g J y p 2 M 2 The effective Lagrangian now contains some four Fermi interactions We can recover the previous action by a field redefinition B = a B + bw 3 + cj Y the coefficients of the transformation are chosen to reproduce the SM couplings to the fermions

8 Model Independent BSM Analysis Deviations from SM are measured by dimension 6 operators assuming flavor universality and CP, there are 20 such operators (linear case, similar results in the non-linear case) O S =(H σ a H)W a µνb µν O T = H D µ H 2 [Buchmuller, Wise 86] [Han, Skiba 04] i(h σ a D µ H)(f d γ µ σ a f d )+h.c. f d = L, Q i(h D µ H)(fγ µ f)+h.c. (Lγ µ σ a L)(Lγ µ σ a L) f = L, E, Q, U, D probed by LEP1 and SLD (Lγ µ σ a L)(Qγ µ σ a Q) (fγ µ f)(f γ µ f ) f = L, E f = L, E, Q, U, D probed by LEP2 e + e ff (actually, there is another operator, but it is poorly constrained ɛ abc Wµ aν Wν bρ Wρ cµ )

9 Example of physical effects O T = H D µ H 2 H = v+h 2 ( 0 ), D µ H = µ H i ( ) gw 3 µ + g B µ 2gW + µ 2 2gW µ gwµ 3 + g H B µ O T = 1 16 v4 ( gw 3 µ + g B µ ) 2 = 1 16 (g2 + g 2 )v 4 Z 2 µ δm 2 Z = v2 2Λ 2 M 2 Z ρ = M 2 W M 2 Z cos2 θ W 1+ v2 2Λ 2 T = v 2 2α em Λ 2 Λ > 5 TeV

10 Facing the LEP Paradox L BSM = c i O i Λ 2 c i O(1) Λ 5 10 TeV LEP paradox: such a large cutoff will destabilize a light Higgs [Barbieri, Strumia 00] 1 Find points with reduced fine tuning improved naturalness 2 Loop induced EW corrections 3 Cancellations among various operators or a combination of the three...

11 The Structure of the Oblique Corrections Assuming heaviness of new physics, flavor universality, CP [Peskin, Takeuchi 90, 92] [Golden, Randall 90] [Holdom, Terning 90] L = W µ + Π + (p 2 ) W µ W µ 3 Π 33(p 2 ) W 3 µ + W µ 3 Π 3B(p 2 ) B µ Bµ Π BB (p 2 ) B µ 4 vacuum polarizations that we expand in powers of momentum: A priori 12 coefficients: Π V (p 2 )=Π V (0) + p 2 Π V (0) (p2 ) 2 Π V (0) + O(p 6 ) But 3 can be removed by canonically normalized the gauge bosons (g, g and v). Π + (0) =Π BB(0) = 1, Π + (0) = M 2 W = ( GeV) 2 And we need to impose the masslessness of the photon and its couplings to Q=T 3 +Y. We are left with 7 coefficients

12 The Structure of the Oblique Corrections We are left with seven coefficients [Grinstein, Wise 91] [Barbieri, Pomarol, Rattazzi, Strumia 04] Coefficients Dim. 6 Operators SU(2) c SU(2) L Ŝ = g g Π 3B (0) O WB = (H τ a H)WµνB a µν /gg + 1 T = (Π M 2 33 (0) Π + (0)) O H = H D µ H 2 W Û = Π + (0) Π 33(0) dim. 8 V = M 2 W 2 ( Π 33(0) Π + (0) ) dim. 10 X = M 2 W 2 Π 3B (0) dim. 8 + Y = M 2 W 2 Π BB (0) O BB = ( ρ B µν ) 2 /2g W = M 2 W 2 Π 33(0) O WW = (D ρ Wµν) a 2 /2g ( S =4s 2 wŝ/α em 119 Ŝ, T = T /α em 129 T ), U = 4s 2 wû/α em 119 Û For universal models (couplings of BSM to SM fermions only through SM currents) Û M 2 W Λ 2 T, V M 4 W Λ 4 T, X M 2 W Λ 2 only four oblique parameters dominate Ŝ [Barbieri, Pomarol, Rattazzi, Strumia 04] [Cacciapaglia, Csaki, Marandella, Strumia 06]

13 Tools #1: Disguising the Oblique Parameters Certain linear combinations remain poorly constrained Indeed massaging the eqs of motion, we obtain the two identities 2gscv2 α O S g v 2 α O T + g y f O Hf =2iB µν D µ H D ν H f 4g scv 2 d d O S + g(o HL + O HQ )=4iWµνD a µ H σ a D ν H α

14 Model Independent BSM Analysis Deviations from SM are measured by dimension 6 operators assuming flavor universality and CP, there are 20 such operators (linear case, similar results in the non-linear case) O S =(H σ a H)W a µνb µν O T = H D µ H 2 [Buchmuller, Wise 86] [Han, Skiba 04] OHf d i(h σ a D µ H)(f d γ µ σ a d = f d )+h.c. f d = L, Q O i(h D µ Hf = H)(fγ µ f)+h.c. f = L, E, Q, U, D (Lγ µ σ a L)(Lγ µ σ a L) probed by LEP1 and SLD (Lγ µ σ a L)(Qγ µ σ a Q) (fγ µ f)(f γ µ f ) f = L, E f = L, E, Q, U, D probed by LEP2 e + e ff (actually, there is another operator, but it is poorly constrained ɛ abc Wµ aν Wν bρ Wρ cµ )

15 Tools #1: Disguising the Oblique Parameters Certain linear combinations remain poorly constrained Indeed massaging the eqs of motion, we obtain the two identities 2gscv2 α O S g v 2 α O T + g y f O Hf =2iB µν D µ H D ν H f 4g scv 2 d d O S + g(o HL + O HQ )=4iWµνD a µ H σ a D ν H α [Grojean, Skiba, Terning 06] The RHS terms only affect the triple gauge boson couplings... which are poorly measured So it is possible to disguise oblique corrections into yet unconstrained operators It is important to measure triple gauge boson vertices to fully identify new physics in the EWSB sector

16 Tools #2: T-parity for Loop Induced Corrections heavy particles = odd light particles = even at each vertex, an even number of heavy fields are required no effective operator for light fields are generated by tree-level exchange of heavy fields [Cheng, Low 03] tree-level exchange forbidden loop exchange allowed c i α 4π Λ 500 GeV

17 ools #3: The Benefits of the Custodial Symmetry Custodial symmetry and the T parameter V (H) =λ (H H v2 2 ) 2 [Weinberg 79] [Sikivie, Susskind, Voloshin, Zakharov 80] SU(2) R is invariant under SO(4) SU(2) L SU(2) R SU(2) L ( iσ 2 H H ) =Φ if New Physics respects SU(2) R, then it won t generate the operator O T = H D µ H 2 Custodial symmetry and new SU(2) L xsu(2) R embedding Q L = t2/3 L t 5/3 L b 1/3 L b 2/3 L Z bl bl [Agashe, Contino, Da Rold, Pomarol 06] then b L is an eigenstate of L R and this ensures that δz bl bl =0 but we expect Zt L t deviations in L Wt L bl Zb R br (good for?) (2, 2) 2/3 t R (1, 1) 2/3 b R (1, 1) 2/3 (H D µ H)(b L γ µ b L ) A b FB

18 Custodial symmetry and Zb L b L g ( Q L cos θ 3 Q sin 2 θ W )Z µ bγ µ b W [Agashe, Contino, Da Rold, Pomarol 06] can receive corrections from new physics protected by gauge invariance experimental constraint: δz bl bl Z SM b L bl.25% L R invariance: δq L 3 = δq R 3 δz bl bl =0 SU(2) D invariance: 0=δQ D 3 = δq R 3 + δq R 3

19 Dynamics of EW phase transition

20 Symmetry Restoration at High T V T 1-loop(h, T )= V 0 1-loop(h) = i=h,χ,w,z,t i=h,χ,w,z,t n i T 4 2π 2 n i 2 0 d 4 k E (2π) 4 log [ k 2 E + m 2 i (h) ]. dkk 2 log [ ] k 1 e 2 +m 2 i (h)/t 2. High T expansion V T 1-loop(h, T ) 1 32 (4m2 h/v g 2 + g 2 +4y 2 t ) T 2 h 2 thermal mass that will compensate the T=0 tachyonic mass at the origin T=0 high T

21 EW Phase Transition in the Standard Model V 2 nd order V 1 st order or In the SM, a 1 st order phase transition could occur due to thermally generated cubic Higgs interactions: V (φ, T ) 1 2 In the SM: ( µ 2 h + ct 2) φ 2 + λ 4 φ4 ETφ 3 T i W,Z φ(t c ) not enough φ(t c ) T c = 2 Ev2 0 λv 2 0 = 4 Ev2 0 m 2 h 12π bosons E = 4m3 W +2m3 Z 12πv 3 0 T c 1 m h 47 GeV m 3 (φ)

22 How to strengthen the EW phase transition? add extra bosonic degrees of freedom that couple to the Higgs: e.g., susy (MSSM, NMSSM), scalars of a hidden valley... 1-loop effect add higher dimensional operators that can modify the shape of the Higgs potential: e.g., little Higgs models, composite Higgs models tree-level effect V (H) =m 2 H 2 λ H Λ 2 H 6 Can induce a strong 1 st order phase transition for large Higgs mass if Λ 1 TeV Grojean, Servant, Wells 04 Delaunay, Grojean, Wells 04

23 A strongly 1 st order PT at large Higgs mass The blue region corresponds to a first order phase transition

24 Testing the dynamics of EW colliders The H 6 interaction generates large deviations in the Higgs self-couplings L = m2 h 2 h2 + µ 3! h3 + η 4! h where µ =3 m2 H v 0 η =3 m2 H v v3 0 Λ v3 0 Λ 2 This is generic strong 1st order transition large deviations in Higgs self-couplings good example of complementarity collider-cosmo! The blue region delineates the region for a strong 1 st order phase transition

25 Why do we like 1st order phase transition? necessary ingredient for electroweak baryogenesis can create a stochastic gravitational background = picture of the universe s after the Big-Bang! Studying the dynamics of the EW phase transition can help us identify the degrees of freedom that populate the TeV scale