Lecture 16-22 Flashcards
What is Running Coupling and how does Renormalisation enter?
We cannot just consider the lowest-order diagram for QED, need to include higher order “corrections” from internal loops. Summing the infinite series is equivalent to keeping the lowest order and changing coupling strength and making it q^2 dependent.
Absorb all effects into an effective “running coupling” - process known as renormalisation.
QED coupling gets stronger as the scale gets stronger.
How is renormalisation different in QCD?
In QCD, there are now boson loops as well as fermion loops that enter the equation. These have opposite sign to fermion loops, expressed in the scale factor beta_0 = 1/108pi(2*N_f - 11N_c).
We see that the effective QCD coupling gets weaker as scale increases.
This leads to profound physical effects. As Q^2 increases, alpha goes to zero. The quarks are quasi-free, leading to “asymptotic freedom”. At small Q^2, we have “infrared slavery”.
At the Landau Pole, denominator goes to zero, and alpha_s goes to infinity. Known as “confinement”.
Describe the process of hadronisation with quarks
Initially quarks separate at high speeds.
Colour flux tube forms between quarks, potential energy increases.
V(r) ~ lambda*r
Eventually eneough energy stored to break string, produces more qq_bar.
“Fragmentation” continues until initial energy used up.
Quarks combine into mesons and baryons - known as hadronisation.
Directions of initial energetic quarks and gluons - produce collimated jets of hadrons observed in detector.
What are some of the key differences between the neutral current and charged current couplings?
W allows flavour changing at vertex
coupling g_w/g_z both of same order of magnitue but g_w is universal for quarks and leptons - g_z depends on type of fermion. Both violate parity. However, not maximal parity violation in the case of the W boson
What is the theory behind the Weak Neutral Current Interaction?
We expect a “weak neutral current particle W^0 to avoid “violation of unitarity, so the cross-section remains finite.
In Electroweak Theory,, 2 neutral gauge spin-1 bosons called the W_0 and B_0. Through mixing through a rotation matrix, for two physical neutral vector gauge bosons Z_0 and photon. theta_W is the weak mixing angle.
Require a link between weak & EM couplings. Learn the equations.
How were the W and Z bosons discovered?
They were discovered by the UA1 and UA2 experiments in the 1980’s.
Protons anti-protons together with experiments done in CM frame. I.e. beam particles have equal and opposite momenta. Effectively the quarks colided rather than the whole proton.
Cross-sections were very low for W/Z production ~ 0.6nb. 1 in 100 million interactions contained a W or Z.
For Z, no missing energy/momentum from neutrinos, so can measure full mass of Z_0.
For W, have to infer the neutrino’s momentum from overall momentum balance. Imbalance perpendicular to initial proton-antiproton collision axis implies unmeasured neutrino in final state. Momentum parallel to pp axis cannot be measured entirely.
What is Electroweak Symmetry Breaking?
EW SB is the process by which a rotation causes the weak eigenstates of EW theory to produce a massless and mass bosons.
If explicit mass terms were included for gauge bosons, this would break fundamental gauge symmetry.
BEH mechanism allows W&Z_0 to gain mass by adding a scalar Higgs field (spin-0) with non-zero vacuum expectation value.
Strength of coupling to the Higgs field determines the mass of the particle
What predictions can be made with the BEH mechanism?
If you know any out of alpha_EM, G_f, m_W, m_Z and sin(theta_W), can predict others.
Using this, we measure a Weak Boson mass that is slightly less than m_W. This is because higher order corrections invoilving quark (t-b_bar) loops and Higgs loops increases W mass slightly.
Doing this has allowed to predict the mass of the top quark before its discovery, and allowed good constraints on m_H to be placed.
