1. WEAK DECAYS: ALL DRESSED UP
Ian Blokland
Augustana Campus
University of Alberta

2. Title-to-English translation
“WEAK DECAYS: ALL DRESSED UP”
Title-to-English translation
light particles
heavy particle
weak interaction

3. Title-to-English translation
“WEAK DECAYS: ALL DRESSED UP”
Title-to-English translation
gauge boson (e.g. QED photon or QCD gluon)
light particles
heavy particle
weak interaction

4. Part 1: What is perturbative quantum field theory and why use it?
OUTLINE
Part 1: What is perturbative quantum field theory and why use it?

5. OUTLINE
Part 1: What is perturbative quantum field theory and why use it?
Part 2: What sorts of particles are involved in these weak decays?

6. OUTLINE
Part 1: What is perturbative quantum field theory and why use it?
Part 2: What sorts of particles are involved in these weak decays?
Part 3: What are the specific technical obstacles involved in this work?

7. Perturbative QFT Experimental depiction of the process
incoming particle(s)
outgoing particles
interaction
Experimental depiction of the process

8. Perturbative QFT Theoretical depiction of the process
incoming particle(s)
outgoing particles
(virtual) gauge boson exchange
Theoretical depiction of the process

9. Perturbative QFT Theoretical depiction of the process
incoming particle(s)
outgoing particles
(virtual) gauge boson exchanges
Theoretical depiction of the process

10. Perturbative QFT Infinitely many possible diagrams but… Factor of α
If α<<1 then the simplest diagrams
provide a good approximation

11. The 3 Forces of the Standard Model
# 1: Electromagnetism
(mediated by massless photons)
# 2: Weak Force
(mediated by the massive W and Z bosons)
# 3: Strong Force
(mediated by massless gluons)

12. Electromagnetism: QED
At low energies, α≈0.007, therefore QED is extremely well-suited to perturbative calculations.
At very high energies, α≈0.008, due to the “screening” effects of virtual particles: + −

13. Weak Force
The weak force is also perturbative, especially due to the large masses of the W and Z bosons.
As a result, very few calculations require the precision afforded by higher-order weak interactions.

14. Strong Force: QCD
At low energies, α is O(1), therefore QCD is not amenable to perturbative calculations.
At higher energies, the “screening” effects of virtual particles causes α to decrease! q g g g
screening
anti-screening q g

15. Motivation # 1: Standard Model parameters
# 2: Indirect evidence for “New Physics”
# 3: Mathematical and computational advances

16. Weakly Decaying Particles
Top quark: t→b+W
Bottom quark: b→c+W*
Charm quark: c→s+W*
Strange quark:
Muon: μ→e+neutrinos
Tau:
QCD
QED

17. Represent a general weak decay as: Q→q+W*
Generalization
Represent a general weak decay as:
Q→q+W*
mass m2
mass M
mass m1

18. Kinematics
m2/M 1
“zero recoil line”
m1/M 1

19. Various decays correspond to various mass parameters
t→b+W
m2/M
b→c+l+ν 1
μ→e+ν+ν
m1/M 1

20. Results are most easily expressed as series
(“asymptotic expansions”) in mass ratios.
m2/M
Complementary expansions
can be “matched” together for
faster convergence and a
consistency check. 1
m1/M 1

21. Sample Diagram g q Q W*

22. O(α2) calculations involve 3-loop diagrams
OPTICAL THEOREM: The decay rate of a heavy
particle is related to the imaginary parts of the
particle’s self-energy diagrams.
“cuts”
O(α2) calculations involve 3-loop diagrams

23. FEYNMAN RULES: Every diagram specifies
a mathematical expression to be computed.
LOOP INTEGRALS: Virtual particle momenta
are to be integrated over all possible values.

24. DIMENSIONAL
REGULARIZATION:
4→4−2ε
ARBITRARY EXPONENTS:
MULTIPLE MASS SCALES

25. SAMPLE RESULT: Loop integrals are
expressed as analytic series in the
dimensional regularization parameter ε.

26. SAMPLE RESULT: Particle decay rates are finite
series involving ratios of mass parameters.
many
pages

27. SAMPLE RESULT: Expansions can be graphed
as functions of the mass ratio parameters.
Expansion in ρ
pieces of X2
Expansion in (1−ρ) ρ

28. What’s Next? b→c+l+ν m2/M 1 Results will be needed for
two simultaneous non-trivial
mass ratios
m1/M 1

29. What’s Next?
+ one more gluon (NNNLO)

30. OUTLINE
Part 1: What is perturbative quantum field theory and why use it?
Part 2: What sorts of particles are involved in these weak decays?
Part 3: What are the specific technical obstacles involved in this work?

31. SUMMARY
OUTLINE
Part 1: What is perturbative quantum field theory and why use it?
Part 2: What sorts of particles are involved in these weak decays?
Part 3: What are the specific technical obstacles involved in this work?

32. SUMMARY OUTLINE E↔T0+T1+...
Part 1: What is perturbative quantum field theory and why use it?
Part 2: What sorts of particles are involved in these weak decays?
Part 3: What are the specific technical obstacles involved in this work?
E↔T0+T1+...

33. SUMMARY OUTLINE E↔T0+T1+... t, b, μ
Part 1: What is perturbative quantum field theory and why use it?
Part 2: What sorts of particles are involved in these weak decays?
Part 3: What are the specific technical obstacles involved in this work?
E↔T0+T1+...
t, b, μ

34. SUMMARY OUTLINE E↔T0+T1+... t, b, μ math (loop integrals)
Part 1: What is perturbative quantum field theory and why use it?
Part 2: What sorts of particles are involved in these weak decays?
Part 3: What are the specific technical obstacles involved in this work?
E↔T0+T1+...
t, b, μ
math (loop integrals)