New Cross Section for Muon-Proton-BremsstrahlungThorben Menne 10.10.2014

IceCube Simulation

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detection spectrum

flux

energy

⌫

IceCube Simulation

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simulations machine learning and unfolding

detection spectrum

flux

energy

⌫

IceCube Simulation

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generators: - NuGen - CORSIKA

lepton propagator PROPOSAL

µ

�

e+, e�X

photon propagators: - photonics - PPC - clsim

µ

⌫

N

detector components: - electrics - trigger - …

X

PROPOSAL PRopagator with Optimal Precision and Optimized Speed for All Leptons

‣ … Optimal Precision … ‣ aiming for exact simulation ‣ small errors in cross sections necessary

‣ systematic errors higher than statistical ones ‣ cross sections for different interactions

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ionisation pair production bremsstrahlung photo nuclear

multiple models to choose from

µA ! µA+e� µA ! µAe+e� µA ! µA� µN ! µNX

Bremsstrahlung Cross Sections in PROPOSAL

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‣ 4 different parametrizations ‣ based on Bethe-Heitler formula, QED ‣ various corrections

Bremsstrahlung Cross Sections in PROPOSAL

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d�

dv=

4↵Z2e4

m2µ

1

v

✓(2� 2v + v2)�1(�)�

2

3(1� v)�2(�)

◆

� =m2µk

2E0(E0 � k)

‣ 4 different parametrizations ‣ based on Bethe-Heitler formula ‣ various corrections ‣ finite nucleus size ‣ screening ‣ nucleus excitation ‣ coulomb correction

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divergence due to ! ! 0

New Cross Section

‣ static field ‣ not Lorentz-invariant !

!

‣ valid for very high energies only

‣ Thomas-Fermi form-factors

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‣ dynamic field with recoil ‣ explicit Lorentz-invariant ‣ semi automatic calculation

possible

‣ no kinematical approximations

‣ proton form-factors from 2013 measurements

new c.s.existing c.s.

New Cross Section

‣ effective proton-vertex function

‣ tree level QED calculation ‣ find best working phase

space

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�µ = F1(q2)�µ +

i�µ⌫q⌫

2MF2(q

2)

Computer Aided Calculation

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FeynArts - topologies - particles - amplitude

FormCalc - process

amplitude - indices, fermion

chains, …

u↵�⌫↵� ū�

Mathematica

Fortran

numerical calculation of cross section

Phase Space First Approach

‣ recursively build up phase space

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R3 =1

2ps

ZdM2 ⌦2

p32

Zd⌦1

p22

Results First Approach

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Problems

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Phase Space Second Approach

‣ two energies and two angles

‣ better suited for bremsstrahlung

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R3 =⇡

4

ZdE5 dE3 dcos ✓ d⌘

Results Second Approach

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Results Second Approach

‣ better than first approach ‣ similar behavior to existing cross sections But:

‣ both calculations in center of mass system ‣ not comparable to existing cross sections

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Phase Space Third Approach

‣ 4 kinematic invariants ‣ complicated border functions ‣ comparison to existing cross

sections possible

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R3 =⇡

16p�(s,m21,m

22)

Zdt25 ds34

Zds45 dt13

1p��4

Results Third Approach

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Summary

‣ need for more precise cross sections ‣ systematic errors higher than statistical ones

‣ new muon-proton-bremsstrahlung cross section ‣ numerical calculation problematic ‣ instable even for small energies ‣ optimal phase space not found yet !

‣ further studies only make sense if numerical integration problem is solved

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