1. Determination of Higgs branching ratio into 𝑊 + 𝑊 − and 𝑍𝑍
Grant Riley
UTK-QFT 2012

2. Branching Ratio
Ratio of specific type of decay (channel) to total number of decays
Also called decay rate
Total decay width changes
Based on number of possible
Decay products
H ->ZZ
H ->WW

3. Branching Ratio
Differential Width is the percent of the total decay width that is made up of a certain channel
Goal of this calculation

4. Lagrangian

5. Lagrangian Rotate through an angle in B, W space
Plug into previous equation for 𝐷 𝜇
Also knowing that the coefficient needs to equal eQ

6. Lagrangian
We can set eQ equal to the coefficient
And solve

7. Symmetry breaking This Lagrangian symmetry must be broken
Choose a non zero vacuum expectation value for energy (v)
Where

8. Mass Acquisition We choose this gauge to keep the photon massless
4 degrees of freedom, 3 taken by the gauge bosons
The 4th to be taken by the Higgs particle

9. Feynman rules Branching diagrams with Feynman amplitude rules
Feynman matrix element is M
Branching ratio 𝐵= Γ ΣΓ where Γ is decay rate

10. Matrix element ZZ
Decay rate
Identical products

11. Matrix Element ZZ
After some work

12. Kinematic Restriction
p and q are the 4 momenta of the two products
By conservation of energy we can get

13. Further Development Plugging in the restriction on energy
Further reduction

14. Decay Rate
Plug this value for 𝑀 2 in the equation for the differential decay rate and take the integral
To get

15. Decay Rate WW
This decay rate is exactly the same except for a factor of due to the
Term which has n = 1 in the 𝑊 + 𝑊 − case because they are not identical products

16. Final branching ratios