Electroweak Physics Krishna S. Kumar University of Massachusetts, Amherst Acknowledgements: M. Grunewald, C. Horowitz, W. Marciano, C. Quigg, M. Ramsey-Musolf, www.particleadventure.org
Electroweak Physics SU() L X U(1) Y Gauge Interactions QED & weak interactions: properties of W ±, Z 0 bosons and particle couplings to them Emphasis on Q <<M Z Connections to High Energy Physics What lies beyond the electroweak scale? Are forces unified at a high energy scale? Can we interpret new physics at colliders? Applications to Nuclear Physics tests of low energy QCD Electroweak probe more versatile than just the electromagnetic probe
Some Remarks Student background and preparation varies Some of you would have had nuclear or particle physics but not all of you Basic knowledge of modern physics assumed As postdoctoral researchers, you will learn to cope with imperfect knowledge Qualitative rather than quantitative understanding You wont follow everything, but if you are totally lost, you should stop me with a question I hope to communicate the big picture
Overview of Lectures I. Introduction to Electroweak Physics: Emphasis on Colliders II. Current Status of Electroweak Physics and Role of Low Energy III. Electroweak Physics at Low Q IV. Weak Neutral Current Interactions V. Anatomy of Parity-Violating Electron Scattering Experiments
Electroweak Physics Lecture I: Introduction to Electroweak Physics
Fundamental Interactions Gravity and Electromagnetic Infinite range Strong and Weak 10-15 meter Radioactivity Electricity & Magnetism Nuclei & Nucleons 60 Co 60 Ni Weak decay of 60 Co Nucleus parity transformation x, y,z x, y, z r p r p, r L L r, r s r s Parity Nonconservation
Quantum Electrodynamics Free fermions fields are solutions to the Dirac equation (iγ µ µ m)ψ = 0 Corresponding Lagrangian: L ~ ψ (iγ µ µ m)ψ Local gauge invariance: interaction with photon field: J µ A µ Conserved electromagnetic current J µ = qψ γ µ ψ 4-vector Feynman Rules: emission and absorption of virtual photons by fermion electromagnetic current current γ Feynman Diagram Matrix Element Fermi s Golden Rule Cross-section Transition probability
e-µ scattering t P 3,, s 3 p 4, s 4 p 1,, s 1 x µ - µ + 3 4 1 e + e - * Momenta and spins p and s p, s 1 g e (p 1 p 3 ) u s 3 (p 3 )γ µ us 1 (p 1 ) [ ]u s 4 (p 4 )γ µ u s (p ) [ ] Differential Cross Section dσ = 4α E' ϑ cos dω q 4 Muon pair production in e+e- annihilation M ~ M ~ g e (p 1 + p ) u (3)γ µ v(4) [ ]v ()γ µ u(1) [ ] s = (p 1 +p ) : square of the C.O.M. energy dσ dω = α 4s (1 + cos θ) Multiply by 0.389 GeV -mbarn g e = 4πα E E θ µ 4-momentum transfer θ q = 4E E sin µ + e + θ e - µ - Total σ in barn (10-4 cm )
60 Co 60 Ni γ 5 u = ( r p r Σ )u Σu =+u P L (1 γ 5 ) Weak Interactions G F [ u (Co)γ (1 γ 5 µ )u(ni)]u(e)γ µ (1 γ 5 )v(ν ) 4-Fermi Contact interaction with parity violation (1 γ 5 ) r Σ r σ 0 r 0 σ u = 0 Left- and right-handed projections P i P j = δ ij P j M ~ P L,R u u L,R For massless particles: P R (1 + γ 5 ) P i = I i r p Σ r h helicity operator [ ] Σu = u (1 γ 5 ) u = u G F [ u (Co)γ u (Ni) L µ L ]u [ L (e)γ µ v R (ν )] J µ ~ ψ γ µ ψ J µ ~ ψ γ µ γ 5 ψ e - 60 Co vector V-A Interaction ν e 60 Ni axial-vector V X A gives rise to pseudo-scalars
Handedness Important: Chirality Helicity if m 0! Helicity operator commutes with free-particle Hamiltonian Conserved but not Lorentz invariant! (Can race past a massive particle and observe it spinning the other way) Chirality operator not conserved, but Lorentz invariant! Freely propagating left-chiral projection will develop a right-chiral component
Charge and Handedness Electric charge determines strength of electric force Electrons and protons have same charge magnitude: same strength observed Neutrinos are charge neutral : do not feel the electric force not observed Weak charge determines strength of weak force Left-handed particles (Right-handed antiparticles) have weak charge 60 Co 60 Ni 60 Co Right-handed particles (left-handed antiparticles) are weak charge neutral 60 Ni observed L R right-handed anti-neutrino not observed R L left-handed anti-neutrino
e - µ ν e ν µ M ~ µ Decay G F [ u (ν )γ (1 γ 5 µ µ )u(µ)]u(e)γ µ (1 γ 5 )v(ν e ) using Fermi s Golden Rule [ ] Lifetime Each decay mode provides a partial width Γ i τ = 1 Γ i Partial width has units of energy Conversion factor: 197 MeV-fm Γ µ = G 5 Fm µ Muon lifetime in vacuum:. µs 19π Gedanken Experiments: The luxury of being a theorist Consider ν e + e ν µ + µ Can use same M σ = G F E 3π For E ~ 1 TeV, probability > 1! i More particles going out than coming in
Massive Vector Bosons: W ± µ ν µ + ν e + e e - ν e µ ν µ ν e + e ν µ + µ G F = g W 8M W µ ν µ W - W - Mass of the W between 10 and 100 GeV ν e e - V = 1 4πε 0 q σ g 4 W 4E 3π 4(E m W ) [ ]r mc r e h Short range Real W production u + d W + e + + ν e Fixed target: M new ~ ME Collider: M new ~ 4E p(e) = Γ π Very short lifetime 1 (E m W ) + (Γ /) A + B W + C + D Large width σ peak 4π 3m W Γ AB Γ tot Γ CD Γ tot
Γ AB Γ tot Collider Physics Relative probability of A+B decay w.r.t. total probability: Branching Ratio Count possibilities: Few nbarn e + ν e,µ + ν µ,τ + ν τ,ud,cs 1 1 1 3 3 Need ppbar collider with luminosity L ~ 10 7 /cm /s N ~ LσT = 10 7 x 10-9 x 10-4 x 10 7 Challenge: QCD background: 40 mbarn! e + e - or p-pbar or p-p hermetic detector Collision at heart of detector Engineering and technological challenges Few events! W signal: highly energetic lepton with energy imbalance
The Z Boson and Unification More gedanken experiments e + e + ν e W + γ Electron-positron collisions W - W - W - e * W + W + W + + γ* Z 0 e - e + e - e + e - Need WWγ vertex: same charge as electron! Need a new, neutral massive weak boson: the Z 0 One free parameter: θ W, the weak mixing angle e + e W + W Unitarity violation forces important constraints W - W + Scattering of longitudinal vector bosons (m=0) + H 0 Z 0 Z 0 eez couplings depend on sin θ W m W = cosθ W m Z
W and Z Charges Left-handed particles in isodoublets Right-handed particles iso-singlets No right-handed neutrino γ Charge W Charge Z Charge Left- q = 0,±1,± 1 3,± 3 T =± 1 T qsin θ W Right- q = 0,±1,± 1 3,± 3 T = 0 qsin θ W Ws have no couplings to right-handed particles Zs couple to both: introduce g L and g R Also use g V and g A : g V = g L + g R g A = g L g R Vector and Axial-vector couplings
e + e - Collider Data
dσ dω = α 4s (1 + cos θ) R and the Heavy Quarks R = e+ e q q e + e µ + µ = i Q i 3 colors for each quark! 10/3 11/3
The Z Resonance e + e Z 0 l + l,qq Count possibilities: 6(e + e ) + 6(uu ) + 9(dd ) Γ ff g L + g R σ Z hadrons 1π m Z (0.033 0.7) B.R.(leptons): 3.3% each, B.R.(quarks):70% 40 nbarn! 00 times larger than QED σ(e) = Γ ee Γ ff (E m Z ) + (Γ /) Can measure total width without identifying all final states!
Stanford Linear Accelerator Center
Summary Introduction to electromagnetic and weak interactions Motivation for Electroweak Unification Tests of Electroweak theory at colliders Introduced nomenclature for electroweak studies Continue precision studies of electroweak theory next time