Higgs Physics Alex Pomarol, UAB (Barcelona) & Englert, Brout 1 The 4th of July of 2012 marked a new milestone in particle physics A Higgs-like state discovered: LHC most relevant piece of data: m 125 GeV H ⇡ Really shook the theory community 2 What is the SM Higgs about? What makes the SM Higgs exceptional? 3 Two achievements of the Higgs mechanism I. Breaking the EW symmetry, giving masses and providing the longitudinal component of the W & Z II. Providing an excitation, the Higgs particle, that makes the theory of massive W & Z consistent up to very high-energies 4 I 5 The Weak interaction is weak because mediators W, Z are massive How to gain mass? (thinking contrary to dietitians!) 1) From compositeness (as a proton)? NO! Experiments tell us W, Z have properties of elementary gauge bosons at energies above their masses 2) From a condensate (Higgs mechanism): Already found Superconductivity in nature: Cooper’s pair <ee>≠0 responsible for making the magnetic field weak inside the SC “photon gets mass” due to the Cooper’s pair Meissner effect 6 Key points for W, Z to become massive 1) Weak Charge should not be conserved by the vacuum ➥ guarantees weak force is short-range = force-mediators get mass Q 0 = 0 W| i6 charged states can have Φ 0 0 0 Φ 0 =0 overlapping with the | i/| i!h| | i6 vacuum state charged ↓ spin=0 Non-zero charged operator condensate = Higgs condensate To avoid Noether’s theorem: Symmetry ⟺ Charge conservation ➥ Vacuum must break the electroweak symmetry SU(2) x U(1) →7 U(1)EM ! 2) To become massive (W, Z), extra states are needed: Massless gauge boson: Massive gauge boson: AT = ( A+ , A- ) AT = ( A+ , A- ) AL Must be provided by a new sector: The sector responsible for the Electroweak (EW) Symmetry Breaking 8 Non-zero charged condensate: e.g. U(1) case Mexican-hat condensate potential “Angular excitations” Massless: Goldstone ɸ hi ɸ hi Charge is not conserved interaction are short-range gauge bosons gets mass ... but where the extra state comes from? The Goldstone boson corresponds to the longitudinal component of the gauge9 boson AL Feynman-diagrammatically: the condensate change the propagator of the gauge boson x x x x G Aµ Aµ Aµ Aµ Englet & Brout, PRL 13(1964)321 10 First beauty of the Higgs mechanism: From 3 massless states, it delivers 3 massive states G = Goldstone (A+, A-) = Gauge bosons Higgs machine c Massive gauge boson 11 These new states WL , ZL (Goldstones) spoil the nice properties of gauge theories Calculability is lost! Untitled-1.nb 1 M 0.5 WL WL 0.4 a) s 0.3 0.2 / v2 0.1 WL WL 200 400 600 800 1000 ps Amplitudes diverge WL b) Loops are not finite! WL Do not allow for precision calculations as in QED 12 II 13 Extra state(s) needed to make the theory consistent! ...but there are extra states in the EWS breaking sector: condensate potential “Radial excitation” H ɸ hi ɸ hi Second beauty of the Higgs mechanism: A very particular “radial excitation”, we call it the Higgs particle, can recovered calculability in massive gauge theories 14 Not all “radial excitations” of Mexican-hat potentials can make the theory consistent: Only that of the Higgs Mexican-hat potential works: 15 Higgs mediated processes recover calculability: Untitled-1 1 3.5 L L W W WL WL 3 M 2.5 h 2 1.5 + 1 0.5 WL WL WL WL 500 1000 1500 2000 2500 3000 ps h Finite results! Massive gauge theories become as good as massless gauge theories 16 To do this job, the Higgs couplings must take a particular value: W , Z gMZ h = gMW , cos θW W , Z f gM h = f 2MW f The couplings must be exactly these ones (at tree-level) to make the SM a consistent theory All couplings predicted by the Higgs mechanism! 17 Without a Higgs With a Higgs (100 GeV <mh<170 GeV) New Physics 10¹⁹ GeV (MP) New Physics Validity of Energy the SM ? Energy Magic Where is thewith the Higgs TeV all couplings MW Validity of MW are dimensionless the SM parameters 18 Very simple Lagrangian: Higgs must couple to particles that must get masses 2 2 4 = D H†D H +(y Hf f + h.c.) µ H + λ H L µ µ f L R − | | | | { H is a 2 1 of SU(2)L ⊗ U(1)Y a a D = @ igT W ig0B µ µ − µ − µ Φ = 0 •h i6 19 Very simple Lagrangian: Higgs must couple to particles that must get masses 2 2 4 = Dµ"H #†Dµ"H #+(yf"Hf # LfR + h.c.) µ H + λ H L − | | | | { H is a 2 1 of SU(2)L ⊗ U(1)Y a a D = @ igT W ig0B µ µ − µ − µ Φ = 0 In the vacuum, fermions and h i6 gauge bosons get masses • H is a (complex field) doublet = 4 d.o.f. = 3 Goldstones to become WL and ZL + Higgs 20 Very simple Lagrangian: Higgs must couple to particles that must get masses 2 2 4 = D H†D H +(y Hf f + h.c.) µ H + λ H L µ µ f L R − | | | | a a D = @ igT W ig0B µ µ − µ − µ dimensionless couplings only grow/decrease logarithmically with the energy (due to quantum effects): ➥ remain small at high-energies that we know them from the masses: yf = mf /v from mW 2 2 λ = mh/8v 21 Very simple Lagrangian: Higgs must couple to particles that must get masses 2 2 4 = D H†D H +(y Hf f + h.c.) µ H + λ H L µ µ f L R − | | | | a a D = @ igT W ig0B µ µ − µ − µ dimensionless couplings H 6 Add extra terms, | | , and this property is gone! ⇤2 Non-renormalizable theory: Inconsistent at E>Λ ! 22 Keystone state Z W Higgs G e u d c, s top Graviton Standard Model bottom of particles Either the Higgs or something else playing its role had to be discovered at the LHC (for consistency, as antimatter in 1932) 23 Although consistent, we think (and hope) the SM is not the full story New Physics 10¹⁹ GeV (MP) Not understandable the origin of such a small EW scale Validity of as compared to the the SM ? Planck scale Energy The problem is transferred MW to the Higgs condensate 24Is this a stable situation? Although consistent, we think (and hope) the SM is not the full story How can we keep the Higgs “light” New Physics in front of “fatty” states ? 10¹⁹ GeV Heavy states (MP) Strings/GUT Validity of the SM ? Energy MW Higgs = Scalar 25 Here is where the simplicity of the Higgs mechanism puts it into trouble Since not always simplicity is good: SIMPLICITY falls under quantum fluctuations! stable stable unstable “Vector” “fermion” “scalar” s=1 s=1/2 s=0 No spin, no “structure” to keep it light 26 The hierarchy problem in a nutshell Massless Massive Vector 2 dof 3 dof 2≠3 ✔ Massless vector Aµ (+,$) (+,0,$) are save Fermion 2 dof 4 dof 2≠4 ✔ Massless Ψ ΨL Ψ L , Ψ R fermions are save Scalar 1 dof 1 dof 1=1 Problem! h Massless (or light) scalars are not save! 27 Possibilities that theorists envisage to tackle this problem: 1) Keep the Higgs elementary, but protect it by symmetries: Supersymmetry Higss (boson) Higssino (fermion) 2) The Higgs is not elementary: Composite Higgs Higss made of fermions (as a pion in strong interactions) 28 Supersymmetry Composite Higgs New Physics New Physics 10¹⁹ GeV 10¹⁹ GeV (MP) (MP) Supersymmetric New strong SM sector (new dof) Energy Energy new fermions (Higgsino,...) TeV and scalars (stops,...) TeV MW SM MW SM Higgs potential predicted in these theories ➥ Both imply changes in the Higgs sector 29 3) Possibility gaining supporters everyday among theorists mH~MP mH~0.3MP mH~MP mH~0.1MP mH~MP Only few mHH~100 GeV H where we mH~MP m ~MP can “live” mH~MP No new physics Multiverse at the LHC! 30 Supersymmetry = MSSM For consistency, an extra Higgs (doublet) is needed, sharing the “duties” of the SM Higgs Untitled-1 1 3.5 L L W W WL WL 3 M 2.5 h, H 2 1.5 + 1 0.5 WL WL WL WL 500 1000 1500 2000 2500 3000 ps Different couplings from the SM Higgs SM e.g. ghWW, gHWW < g hWW hVV couplings smaller than in the SM 31 Composite Higgs inspired by QCD where one observes that the (pseudo) scalar are the lightest states Spectrum of mesons: ρ GeV 100 MeV π Are Pseudo-Goldstone bosons (PGB) Mass protected by the global QCD symmetry! ⇥ ⇥ + α 32 → Can the light Higgs be a kind of a pion from a new strong sector? We’d like the spectrum of the new strong sector to be: TeV ρ 100 GeV h Pseudo-Goldstone bosons (PGB) We do not know what the Higgs could be made of ! h = ? but we could study its properties at the LHC as in the 60s when pions, kaons, ... were discovered 33 Being Composite, the Higgs couplings are different from the SM values WL WL WL WL h + ● ● WL WL WL WL Untitled-1 1 partly-unitarize! different 3.5 from the SM Higgs M 3 2.5 2 1.5 A Composite Higgs 1 only partly 0.5 500 1000 1500 2000 2500 3000 ps does the job of a true Higgs 34 Being Composite, the Higgs couplings are different from the SM values WL WL WL WL h + ● ● WL WL WL WL Untitled-1 1 partly-unitarize! different 3.5 from the SM Higgs M 3 2.5 The rest of the new strong 2 1.5 sector (states of spin=0,1,2,...) 1 0.5 takes care of the fully 500 1000 1500 2000 2500 3000 ps unitarization: L WL W W (n) 35 WL WL After the 4th of July 2012 Plenty of new data on the “radial” excitation around the EWSB vacuum: CMS Preliminary s = 7 TeV, L = 5.05 fb-1 ; s = 8 TeV, L = 5.26 fb-1 12 7 TeV 4e, 4µ, 2e2µ Data 8 TeV 4e, 4µ, 2e2µ 10 Z+X In%summary% Z*,ZZ 8 mH=126 GeV Events / 3 GeV 6 4 2 H Combined results: consistency Characterization%of%the%excess:%0 mass%% of the global picture m4l [GeV] Evolution of the excess with time 80 100 120 140 160 180 Are the 4l and γγ observations m [GeV] consistent ? ! Likelihood%scan%for%mass%and%%4l signal%strength%in%three%high%% From 2-dim likelihood fit to signal Combined results: sharing of the excessmass and between strength years curves … show mass%resolution%channels% approximate 68% (full) and 95% SM (dashed) CL contours Energy-scale systematics Similar expected significances in both years not included ! results%are%selfVconsistent%and%%%%%%%%%%%% (more luminosity and larger