The Leptonpropagator PROPOSAL for CORSIKA Jan Soedingrekso, - - PowerPoint PPT Presentation

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lehrstuhl physik e5

The Leptonpropagator PROPOSAL for CORSIKA

Jan Soedingrekso, Alexander Sandrock Jean-Marco Alameddine, Maximilian Sackel

CORSIKA Phone Call 05.03.2019

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PROPOSAL

▶ Monte Carlo tool for charged lepton propagation through media. ▶ Used in the simulation chain of IceCube ▶ PRopagator with Optimal Precision and Optimized Speed for All Leptons

▶ Calculate energy losses ▶ Passes interaction points and decay products to further simulation programs 05.03.2019 2 / 16

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Energy cuts

▶ Distinguish between continous and stochastic energy losses ▶ Cut between continuous and stochastic loss:

cut = min(𝑓cut, 𝑤cut ⋅ 𝐹), 𝑤 ≔ relative energy loss

▶ Set energy cuts before, inside and behind the detector

Energy cuts in IceCube

▶ before: 𝑤cut = 0.05 ▶ inside: 𝑓cut = 500 MeV ▶ behind: 𝑤cut = 𝑤max

Continuous loss

Describes energy loss in the range 𝑤 ∈ [𝑤min, 𝑤cut] 𝑔(𝐹) ≔ ∑

processes

d𝐹𝜏 d𝑦 = 𝐹 ⋅ ∑

process

∑

atom in medium

𝑂𝑗 𝐵𝑗

𝑤cut

∫

𝑤min

𝑤d𝜏 d𝑤 d𝑤

Stochastic loss

Described by the interaction probability 𝑤 ∈ [𝑤cut, 𝑤max] 𝑒𝑄(𝐹) = 𝜏(𝐹)d𝑦 𝜏(𝐹) = ∑

processes

∑

atom in medium

𝑂𝑗 𝐵𝑗

𝑤max

∫

𝑤cut

d𝜏 d𝑤 d𝑤

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Basic Propagation Principle

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Determine the occurrence of a stochastic loss

• Probability to have

no stochastic loss in (𝑦𝑗, 𝑦𝑔), but at 𝑦𝑔 within d𝑦: ⎧ { { { ⎨ { { { ⎩ (1 − d𝑄(𝐹(𝑦𝑗))) ⋅ … ⋅ (1 − d𝑄(𝐹(𝑦𝑔−1))) ⋅ d𝑄(𝐹(𝑦𝑔)) ≈ exp(−d𝑄(𝐹(𝑦𝑗))) ⋅ … ⋅ exp(−d𝑄(𝐹(𝑦𝑔−1)))d𝑄(𝐹(𝑦𝑔)) ≈ exp [− ∫

𝑄(𝐹(𝑦𝑔)) 𝑄(𝐹(𝑦𝑗)) d𝑄(𝐹(𝑦))] ⋅ d𝑄(𝐹(𝑦𝑔))

= d [− exp(− ∫

𝐹𝑔 𝐹𝑗 𝜏(𝐹) −𝑔(𝐹)d𝐹)] ≕ d(−𝜊) ∈ (0, 1]

⇒ Sample𝐹𝑔 from ∫

𝐹𝑔 𝐹𝑗

𝜏(𝐹) −𝑔(𝐹)d𝐹 = − ln(𝜊)

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Basic Propagation Principle

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Advance the particle according to 𝐹𝑔

▶ Calculating the displacement

𝑦𝑔 = 𝑦𝑗 − ∫

𝐹𝑔 𝐹𝑗

d𝐹 𝑔(𝐹)

▶ the elapsed time

𝑢𝑔 = 𝑢𝑗 − ∫

𝑢𝑔 𝑢𝑗

d𝑦 𝑤(𝑦) = 𝑢𝑗 − ∫

𝐹𝑔 𝐹𝑗

d𝐹 𝑔(𝐹)𝑤(𝐹)

▶ and the deviation from the shower axis (multiple scattering)

𝑣𝑦,𝑧 = 1 2 ( 1 √ 3𝜊(1)

𝑦,𝑧 + 𝜊(2) 𝑦,𝑧) ,

𝜊(1,2)

𝑦,𝑧

∼ 𝒪(0, 𝜄2

0)

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Basic Propagation Principle

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Calculate the stochastic loss

▶ Calculate the interaction probability for each process

𝜏𝑗 = ∑

atom in medium

𝑂𝑗 𝐵𝑗

𝑤max

∫

𝑤cut

d𝜏 d𝑤 d𝑤

▶ Calculate the amount of stochastic loss for each atom in the medium

1 𝜏 ∫

𝑤(𝜊) 𝑤cut

d𝜏 d𝑤 d𝑤 = 𝜊 𝐹stochastic loss = 𝑤(𝜊) ⋅ 𝐹particle

▶ Choose the Component, at which the energy loss takes place

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Basic Propagation Principle

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Summary of the algorithm Basic loop

Do: Calculate the energy until a stochastic loss ↓ Advance the particle according to 𝐹𝑔 ↓ Calculate the amount of the stochastic loss Until: The particle decays

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Basic Propagation Principle

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Hadronic Decay

▶ Calculate 𝑂-body decay phase space ▶ Not consider the matrix element

𝛥 = (2𝜌)4 2𝑁 ∫

𝑜

∏

𝑗=1

d3𝑞𝑗 2𝐹𝑗 𝜀4 (𝑞 −

𝑜

∑

𝑗=1

𝑞𝑗) ⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

𝑂-body phase space set to 1

⏞ ⏞ ⏞ ⏞ ⏞ |⟨𝑁(p𝑗)⟩|2 Raubold-Lynch algorithm

▶ Iterative integration over intermediate

two-body phase spaces

▶ Exact calculable 0.0 0.2 0.4 0.6 0.8 1.0 Ehadrons/Eτ 100 101 102 103 104 count

π−K0ν π−π0π0π0ν K−π+π−ν π−π0ν π−ν π−π0π0ν π−π−π+π0ν π−π−π+ν sum

Mn R2 Mn°1 R2 M3 pn,mn R2 M2 pn°1,mn°1 R2 m1 p3,m3 p1,m1 p2,m2

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Decay

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Effects of constant Matrix Element

Leptonic decay: known decay width and known matrix element |⟨𝑁⟩|2 = 1

10000 20000 30000 40000 50000 60000 count decay width phase space non uniform 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Eµ/mτ 0.5 1.0 1.5 ratio

|⟨𝑁⟩|2 ≠ 1

5000 10000 15000 20000 25000 30000 35000 40000 count decay width phase space 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Eµ/mτ 0.5 1.0 ratio 05.03.2019

Decay

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Leptonic Decay

▶ Muon decay and electronic tau decay

(𝑛2

𝑚 /𝑁 2 ≈ 0)

d𝛥 d𝑦 = 𝐻2

F𝑁 5

192𝜌3 (3 − 2𝑦)𝑦2, 𝑦 = 𝐹𝑚 𝐹max

▶ muonic tau decay (𝑛𝜈/𝑛𝜐 ≈ 1/17)

d𝛥 d𝑦 = 𝐻2

F

12𝜌3 𝐹max√𝐹2

𝑚 − 𝑛2 𝑚 [𝑁𝐹𝑚(3𝑁 − 4𝐹𝑚) + 𝑛2 𝑚 (3𝐹𝑚 − 2𝑁)] 1 2 3 4 counts exact (theory) approx (theory) exact approx 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Eµ/mτ 0.5 1.0 ratio exact / approx

Outlook: matrix elements for hadronic modes (was not necessary for IceCube, only requiring a smooth spectrum)

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Decay

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Propagation Improvements

▶ Continuous Randomization ▶ Multiple parametrizations for cross sections ▶ Multiple parametrizations for multiple scattering ▶ Interpolation tables ▶ Further parameter for the trade-off between performance and precision

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Propagation Improvements

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Continuous Randomization of the 𝐹𝑔

▶ lower energy cut means higher precision, but

more calculation time and secondaries to deal with

▶ higher energy cut results in less precision and

artifacts in fjnal muon energy spectrum

▶ muons without a stochastic loss are all treated

the same ⟹ continuous randomization of the muon energy till next stochastic loss

0.0 0.2 0.4 0.6 0.8 1.0 Muon Energy after propagation / MeV ×108 10−1 100 101 102 103 104 Number of muons vcut = 0.05 vcut = 10−4 vcut = 0.05 w/ cont.

⟨(𝛦(𝛦𝐹))⟩ ≈

𝑓cut

∫

𝑓0

d𝐹 −𝑔(𝐹) ⎛ ⎜ ⎝

𝑓cut

∫ 𝑓2 d𝜏 d𝑤 d𝑓⎞ ⎟ ⎠

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Propagation Improvements

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cross section parametrizations Bremsstrahlung

Parametrizations

▶ KelnerKokoulinPetrukhin ▶ AndreevBezrukovBugaev ▶ PetrukhinShestakov ▶ CompleteScreening ▶ SandrockSoedingreksoRhode

also consider LPM and TM Effect

𝑓+𝑓− Pair Production

Parametrizations

▶ KelnerKokoulinPetrukhin ▶ SandrockSoedingreksoRhode

and LPM Effect

Nuclear inelastic Interaction

▶ real photon assumption

▶ Kokoulin ▶ Rhode ▶ BezrukovBugaev ▶ Zeus

with hard and soft component

▶ Regge Theory

▶ AbramowiczLevinLevyMaor91 ▶ AbramowiczLevinLevyMaor97 ▶ ButkevichMikheyev ▶ RenoSarcevicSu

with shadowing

▶ ButkevichMikheyev ▶ DuttaRenoSarcevicSeckel 05.03.2019

Propagation Improvements

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New Cross Sections

▶ improved tree-level cross sections based

• n current standard parametrizations for

bremsstrahlung and pair production

▶ radiative corrections for bremsstrahlung ▶ corrections of several percent ▶ current used parametrizations are still the

default

102 103 104 105 106 107 108 109 10

6

• 1/E dEdx / g

1cm2

KKP SSR 102 103 104 105 106 107 108 109 E / MeV 0.90 0.95 1.00 1.05 1.10 ratio SSR / KKP

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Propagation Improvements

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Multiple Scattering

▶ Molière

▶ analytic, precise ▶ slow, depending on number of

components in medium

▶ Highland

▶ gaussian approximation to Molière ▶ two types available: one including

continuous losses (default) and one without

▶ no scattering −20 −10 10 total scattering angle θ/mrad 100 101 102 103 counted muons N

Akimenko et al. (1984) MC: Molière MC: Highland MC: HighlandIntegral

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Propagation Improvements

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Multiple Scattering

▶ Molière

▶ analytic, precise ▶ slow, depending on number of

components in medium

▶ Highland

▶ gaussian approximation to Molière ▶ two types available: one including

continuous losses (default) and one without

▶ no scattering 104 106 108 1010 1012 E/MeV −250 −200 −150 −100 −50 performance loss / % Molière Highland HighlandIntegral

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Propagation Improvements

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Desiderata

▶ Density currently part of medium

▶ each medium has its own interpolation tables ▶ Maximilian currently investigates how large the non-linear effects of the density are

(interpolation)

▶ Magnetic fjeld defmection

▶ We have basically worked out how to implement this ▶ Jean-Marco will take care of that

▶ Propagation of electrons/positrons

▶ Was taken care of in IceCube by other MC ▶ Some processes need to be added (Annihilation; Bhabha and Møller scattering compared to 𝜈𝑓

scattering)

▶ Propagation of photons

▶ in principle similar to propagation of charged particles, but without continuous losses ▶ Jan and Alexander have discussed how to do this and will take care of it 05.03.2019

Desiderata

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