The decay rate Lorentz Invariant Phase Space The decay rate The decay rate Decay amplitude Describes the interactions during the decay The Feynman diagrams The Feynman diagrams ID: 687521
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Slide1
Slide2
The decay rate
Slide3
The decay rate
Slide4
The decay rate
Lorentz Invariant Phase SpaceSlide5
The decay rate
Slide6
The decay rate
Decay amplitude. Describes the interactions during the decay.Slide7
The Feynman diagramsSlide8
The Feynman diagrams
Gluons are massless. They don’t interact with the Higgs!Slide9
The Feynman diagrams
Interaction occurs through a fermion (quark) loopSlide10
From the Feynman diagram to the decay amplitude
Slide11
From the Feynman diagram to the decay amplitude
Slide12
From the Feynman diagram to the decay amplitude
l + p
l - k
lSlide13
From the Feynman diagram to the decay amplitude
l + p
l - k
lSlide14
From the Feynman diagram to the decay amplitude
l + p
l - k
lSlide15
From the Feynman diagram to the decay amplitude
l + p
l - k
lSlide16
From the Feynman diagram to the decay amplitude
l + p
l - k
lSlide17
From the Feynman diagram to the decay amplitude
l + p
l - k
lSlide18
From the Feynman diagram to the decay amplitude
l + p
l - k
lSlide19
From the Feynman diagram to the decay amplitude
l + p
l - k
lSlide20
From the Feynman diagram to the decay amplitude
l + p
l - k
lSlide21
Calculating the decay amplitude
The numerator:Slide22
Calculating the decay amplitude
Contains
terms
The numerator:Slide23
Calculating the decay amplitude
Numerator algebra (trace technology)Tr[] = 0
+
The numerator:
Slide24
Calculating the decay amplitude
The denominator:Slide25
Calculating the decay amplitude
The denominator:Slide26
Calculating the decay amplitude
The denominator:We would like it to be in the form
Slide27
Feynman Parameterization
observe that:
This generalizes to:
Slide28
Feynman Parameterization
Slide29
Feynman Parameterization
The loop integral becomes:
}
Slide30
Feynman Parameterization
The loop integral becomes:
}
Slide31
The loop integral becomes:
Dimensional RegularizationSlide32
The loop integral becomes:
Wick Rotation
:
Dimensional RegularizationSlide33
The loop integral becomes:
Wick Rotation
:
Dimensional RegularizationSlide34
Dimensional Regularization
The loop integral becomes:
Wick Rotation
:
Slide35
Calculation of M
The loop integral :
}
Slide36
Calculation of M
The loop integral :
}
Is part of M:Slide37
Calculation of M
The loop integral :
}
Is part of M:Slide38
Calculation of M
The loop integral :
}
Is part of M:Slide39
Calculation of M
The loop integral :
}
Is part of M:
Many terms vanish!
and
Slide40
Calculation of M
The loop integral :
}
Is part of M:
Many terms vanish!Slide41
Calculation of M
The loop integral :
}
Is part of M:
Many terms vanish!Slide42
Final expression for M
Slide43
Final expression for M
For a specific polarization
of the k gluon and
of the p gluon
Slide44
Final expression for M
For a specific polarization
of the k gluon and
of the p gluon
For specific gluon colors
a
and b Slide45
Final expression for M
For a specific polarization
of the k gluon and
of the p gluon
For specific gluon colors a
and bFor a specific quark q Slide46
For the decay rate
Remembering the decay rate:
We need to sum over all different polarizations , over all different colors and over different quark species!
Slide47
For the decay rate
Slide48
For the decay rate
Useful identity:
Slide49
For the decay rate
Useful identity:
Slide50
For the decay rate
Useful identity:
Slide51
For the decay rate
Slide52
For the decay rate
The form factor
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For the decay rate
The form factor