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New Cross Section for Muon-Proton-BremsstrahlungThorben Menne 10.10.2014
IceCube Simulation
2
detection spectrum
flux
energy
⌫
IceCube Simulation
3
simulations machine learning and unfolding
detection spectrum
flux
energy
⌫
IceCube Simulation
4
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
19
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
20