Quarks, Gluons,
and Jets
Babar Ali
Questions
Daniel Pelikan
Can you explain the 1+cos(theta)^2 prediction (p295)
What does 3 x 3* = 1+8 mean?Why is it expressed in this form?(p293)
Henrik Öhman
Explain why the angular distribution for e^+e^- \rightarrow \mu^+\mu^- is
proportional to 1 + cos^2 \theta + sin^2 \theta cos2\phi (10.2) if the beams are
completely polarized. (p297)
What is the physical explanation for the "longitudinal crosssection" and the
"transverse cross section" for spin-0 and spin-1/2 respectively? (p297)
Andreas Brändström
How would an color octet meson and color octet and decuplet baryon look?
What would be the common properties within the multiplets? (Page 293)
Yuyan Li
What are the rules of SU(3)? (p 293)
Can you explain the 1+cos(theta)^2 prediction (p295)
Consider the process e+ + e- → µ+ + µ-
e + ( p1 , r1 ) + e − ( p2 , r2 ) → l + ( p1′, s1 ) + l − ( p2′ , s2 )
The Feynman amplitude
For the unpolarized cross-section we require
Using Hermiticity condition
Kinematics for the process in CoM system
dσ
σ / dΩ = 1 / 64π2(E1 + E2)2 P1′ / P1 (
2ml)M 2
E ≥ mµ =207me and by neglecting the terms proportional to (me)2
Differential cross-section
Total cross-section
In the extreme relative limit E>>ml
Where θ is production angle of either muon with repect to initial
electron. The cross-section for quak anti-quark pair
where
a=u,d,s by replacing the charge with of muon with the quark
charge and multiply with 3 for three colour states
Explain why the angular distribution for e+ + e- → µ+ + µis proportional to 1 + cos2θ+ sin2θcos2φ (10.2) if the beams are completely
polarized. (p297)
What is the physical explanation for the "longitudinal cross-section" and the
"transverse cross section" for spin-0 and spin-1/2 respectively? (p297)
Consider the reaction
e+ + e- → µ + + µ -
Large transverse polarizations have been obtained at SPEAR at energy 7.7 GeV
The transverse polarization are not very useful for the purpose of
exploring weak interactions or CP violation
so it is required to rotate one or both of the
beam polarizations into the longitudinal direction.
Electron beam polarized longitudinally
Where θ is polar angle and φ is Azimuthal angle measured from
horizontal plane.P is Magnitude of polarization
What are the rules of SU(3)? (p 293)
What does 3 x 3* = 1+8 mean?Why is it expressed in this form?(p293)
The quark flavour is associated with the electroweak interactions, while strong forces to be
flavour conserving and flavour independent. Also colour is charge associated with the
strong forces.So the fundamental theory of colour interactions should satisfy
1.
Exact colour symmetry GC
2.
NC = 3. Thus quarks belong to triplet representation 3 of GC
3.
Quarks and anti quarks are different states. 3 is not equal to 3*
4.
Confinement Hypothesis:hadronic states are colour singlets
5.
Asymptotic freedom
Among all the lie groups, only SU(3) fulfil the conditions.
So the well known SU(3) decomposition of the products of 3 and 3* representations
How would an color octet meson and color octet and decuplet baryon look? What would be the
common properties within the multiplets? (Page 293)
pseudoscalar nonet
vector meson nonet