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

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

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

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?

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?

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?

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

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

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

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

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)

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: + −

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.

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

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

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

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

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

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

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

Sample Diagram g q Q W*

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

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

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

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

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

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

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

What’s Next? + one more gluon (NNNLO)

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?

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?

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+...

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

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)