Some remarks on Higgs physics The Higgs mechanism Triviality and vacuum stability: Higgs bounds The no-Higgs option: strong WW scattering These are just quick remarks on an essential LHC topic! Textbook ‘Quarks & Leptons’ by Halzen and Martin Yellow report: ‘Reflections on the Higgs system’ by Veltman PhD thesis “search for Higgs at LEP” by Ivo van Vulpen Articles “The No Higgs signal”, Chanowitz, hep-ph/ FOM projectruimte, Ronald Kleiss & SB, ‘Higgs or no Higgs at the LHC

Fundamental interactions Photon Electro-magnetic Electric charge Photon exchange Gravity Not included in Standard Model SU(3)  SU(2)  U(1) Gauge theories Strong Color Gluon exchange Gluon Weak Weak isospin W ± and Z 0 exchange Charged current Neutral current

Noble history Early ‘Electroweak model’ of quarks and leptons Weinberg, Glashow & Salam (late sixties) – Nobel prize 1979 Problem: Electroweak SU(2)  U(1) model not renormalizable! Serious calculations (loop level) produced infinities. Useless?   Renormalisation of massless Yang-Mills gauge theories Veltman & ‘t Hooft (~1972) One believer left: Veltman Nobel prize 1999 Elucidating the quantum structure of electroweak interactions in physics How to give the vector bosons (W +,W -,Z 0 ) mass without destroying renormalization? ‘t Hooft: Symmetry breaking with Higgs-mechanism, and apply it to the Standard Model Mechanism preserves renormalization: it works! Veltman: ‘verrek, dat is het!’ No experimental clue that this is the correct description for EW symmetry breaking

ElectroWeak symmetry breaking SU W (2)  U Y (1) symmetry 3 massless SU W (2) vector bosons 1 massless U Y (1) vector boson 1 complex doublet self-interacting Higgs fields (=4 real scalar fields) Interaction between Higgs doublet and massless quarks & leptons U Q (1) symmetry 3 massive vector bosons: W +, W -, Z 0 1 massless U Q (1) boson:  1 real scalar Higgs field +3 Goldstone Bosons ‘eaten’ by the massive vector bosons Mass terms for quarks & leptons Unbroken Higgs potential Broken in vacuum at scale v=246 GeV Broken Higgs potential

Higgs in the vacuum Empty vacuum (unbroken phase) Massless particles traverse with speed of light. All particles are massless and move with same speed. Higgs vacuum (broken phase) Massless particles interact with constant background `Higgs’ field and slow down. Effectively they acquire a mass. Speed (=mass) of particle depends on interaction strength with Higgs field. Higgs particle Quantum mechanical fluctuations of the background itself: the Higgs particle. A necessary consequence of the Higgs background field. The syrup argument

Triviality and vacuum stability Radiative corrections Modify the value of the parameter as function of the resolution scale Q 2. Equivalent principle as the running of the couplings: These are obtained from the RGE:

Triviality The running of goes like: Upper bound on Higgs mass: Occurs for very big: And grows as function of Q2 and becomes even infinite at Landau pole

Triviality Maximum value for ; becomes infinite at the point: In order to ‘reach’ the scale Λ 2 you have to start at small values (v 2 ) [smaller than a maximum] But you have to start from a value of >0! For =0 you loose the Higgs self-coupling This translates in maximum value Higgs mass, as function of ‘new physics scale’ Λ

Vacuum stability Lower Higgs mass bound: For very small values of the Yukawa coupling with top- quark dominates: For these small values the sign is opposite, and evolving to higher values of Q2 makes at certain point <0 Potential is then unbounded below: unstable

Limits of Higgs mass Standard Model good approximation (effective theory) of ultimate theory at electro-weak energy scale O(200) GeV Ultimate theory includes quantum gravity: Planck scale M PL ~10 19 GeV Possibility that model breaks down at lower scale, . What is minimum scale  at which new physics becomes important? Behavior of Higgs self coupling Upper bound (Triviality): Lower bound (Vacuum stability): M H < 130 GeV:  < M PL 130 < M H < 180 GeV  = M PL, M H > 180 GeV  < M PL Consistent with supersymmetry

‘Fit’ all observables in Standard Model, with Higgs-mass as a free parameter Top mass fixed at  5 GeV Higgs radiative corrections ‘Radiative corrections’ to observables at LEP: Quantummechanical corrections to W-mass, denoted by  r: Corrections contain (among others) Higgs. Hence sensitivity to Higgs mass:

‘Direct’ search: Higgs at LEP Major contribution from Bjorken-Higgsstrahlung Kinematical reach to Higgs-mass m H >~  s-M Z LEP-2 (  s=200 GeV): m H ~115 WW and ZZ fusion less important: The Wall

Higgs production at the LHC Production mechanism and cross sections

‘No loose’ theorem for LHC We have two options: We find the Higgs at the LHC Its existence, mass and other properties gives deep knowledge on the realization of Electro-Weak symmetry breaking mechanism We do not find the Higgs at the LHC There is something serious wrong with our understanding of the Standard Model and it is observable at LHC In the absence of Higgs, the WW scattering amplitude violates unitarity (this happens at WW cm energy ~1.5 TeV ) New (strongly interacting) dynamics has to cure this behavior, e.g. Technicolor. They lead to observable effects at LHC