Lecture 03 The Standard Model of Particle Physics Part II The Higgs Boson Properties of the SM
The Standard Model So far we talked about all the particles except the Higgs If we know what the particles are and how they interact, we know (almost) everything about physics 2
Unification of Forces 3
Electroweak Unification E&M and Weak interaction are unified at high energy This means that they behave the same, or are indistinguishable, at that energy How does this work, if the W, Z are massive but the photon is massless? At high enough energy, E > 100 GeV there is no need to borrow energy for these bosons Challenges of unification: The QFT treatment of Aμ for E&M does not work for massive bosons No way to satisfy special relativity with massive bosons But special relativity is observed! Answer: Solve the problem with massless particles Introduce a new mechanism that gives mass as a side effect This is the Higgs mechanism What are the boundary conditions? Massless photon Massive W, Z A valid theory must satisfy these! 4
Electroweak Symmetry Gauge symmetry Special Relativity Treats the four gauge bosons (photon, W+, W-, Z) the same Masseless bosons obeying special relativity Symmetric under gauge transformations (Lorentz Transformations) A single coupling can't distinguish E&M and Weak Charge at rest in one frame No B field Moving in another frame Does have B field Maxwell's equations are consistent with this 5
The Higgs Mechanism Write the rest of the SM in as massless particles This includes both the bosons and the fermions Recall, the photon was massless, so we already know how to solve this problem Quantize A μ This means the W and Z would be massless, and behave like the photon (hint hint, unification) Consequences of Φ Any particles associated with this field would be spin 0 Remember we only had spin ½ and 1 so far The quartic potential gives 4 degrees of freedom Quantization yields 4 states Higgs doublet (2 pairs, charged and neutral) Add a quartic potential to the SM A QFT treatment of this lets us define a scalar (spin 0) field Φ to quantize this potential (via second quantization) 6
Vacuum Expectation Value (vev) A vev is the expectation value of a field (QFT version of a potential) at its minimum value, e.g. the bottom of the potential For the potential we introduced, the vev is zero Spontaneous symmetry breaking breaks the degenerecy of the potential: This has a non-zero vev If vev is negative (only if x is complex) then vev is lower after symmetry breaking 7
Mexican Hat Potential Since the Higgs field is complex, the quartic potential makes a Mexican Hat False vacuum (at origin) is not the minimum in potential A ring at potential minimum Azimuthal symmetry Infinite positions around circle at minimum Nature has to select one Breaks symmetry 8
Spontaneous Symmetry Breaking The fact that the Higgs spontaneously chooses some value for the minimum breaks gauge symmetry E&M and Weak interaction are no longer the same Happens below electroweak unification scale Couplings become distinct 9
The Higgs Doublet Revisited What are the consequences of spontaneous symmetry breaking? Three of the Higgs doublet states become mass terms for the Weak bosons: But the fourth state is leftover (called a Goldstone boson) Interactions of fermions with the Higgs field (not the boson, the field) give mass terms to the fermions Mass is a property, not a force The coupling to the Higgs field is mass Heavier particles couple more strongly to the field 10
What does the Higgs do? The mass of fermions and W/Z bosons comes from interactions with Higgs field The coupling is the particle's mass No longer the same for every particle (like α in E&M) Gives effective drag to particles as they propagate Heavier particles couple more strongly than lighter particles The origin of mass 11
Predictions of the Higgs Mechanism Introduced to particle physics in 1962 following work done in superconductivity Before the discovery of W, Z, H Predicted a very precise relationship between W and Z mass The Weinberg angle is a calculated quantity in the Higgs mechanism After discovering and measuring the W mass, the Z mass was precisely predicted The Z was discovered exactly where it should be at 91.2 GeV Higgs Boson Massive spin zero particle It's a boson, so it transmits a force Not a new force, a 5th component of the electroweak force (unified E&M with Weak) It HAD to exist for the mechanism to work Discovered in 2013 Higgs and Englert awarded 2013 Nobel Prize Exceptionally successful mechanism! 12
Discovery of the Higgs Large Hadron Collider (LHC) Located at Cern in the Swiss/French Alps 4 Experiments on the LHC ALICE: Discovered and studies quark gluon plasma LHCb: Studies b-meson physics ATLAS and CMS: Higgs and new particle searches 14 TeV center of mass energy Proton proton collisions Composite objects, so only part of the 14 TeV is available in collisions High luminosity high statistics Hadronic interactions lots of top quarks Since Higgs couples to mass, look for rare production of Higgs boson through heavy intermediate states (e.g. top) 13
Symmetry in the SM Symmetry is at the core of the SM Noether's theorem: For every symmetry, there is a corresponding conserved quantity Translational symmetry conservation of momentum Rotational symmetry conservation of angular momentum Gauge symmetry (special relativity) conservation of electric charge SU(2) symmetry of QCD conservation of color charge And so on... Emmy Noether: Referred to as the most important woman in the history of mathematics 14
Fundamental Rule of Particle Physics Anything not expressly forbidden is possible! Conserved quantities in the SM: Globally conserved Energy, momentum, angular momentum Electric charge Color charge Lepton number (and lepton flavor number) Baryon number Conserved by strong interaction Quark generation number For each of these quantities, there is a symmetry in the SM to describe it Other quantities were naively expected to be conserved Parity (mirror symmetry), Charge conjugation times parity There is no symmetry in the SM to conserve them, so they are found to NOT be conserved Exception: CP violation in strong interactions IS conserved, but there is no symmetry to protect it 15
Helicity (handedness) Recall particle spin: Fermions (spin ½) Two spin states Can be aligned or antialigned with momentum Right or Left handed helicity Sometimes called handedness or chirality The same can be said for the spin 1 bosons (e.g. right, left polarized light) 16
Handedness in Weak Interactions Observational curiosity: The weak interaction only couples to left handed fermions and right handed antifermions Every Weak decay observed obeys this rule! No good explanation for this Always left handed! 17
Helicity and Special Relativity Consider a weak decay of a particle at rest in the laboratory The fermions in the decay products will always be left handed. But Special Relativity says I can boost (Lorentz Transformation) into a frame where the momentum changes sign (spin stays the same) How does this decay take place in that frame? This is an open question Helicity is not a Lorentz invariant quantity! Not a good quantum number for special relativity Yet it is a conserved quantity in the Weak Interaction 18
SM Neutrinos and Helicity In the standard model, neutrinos have zero mass They move at the speed of light Then, helicity is a good quantum number This solves at least part of the mystery of the handedness of the weak interaction Neutrinos are always left handed and antineutrinos are always right handed in every frame 19