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

The Leptonpropagator PROPOSAL for CORSIKA Jan Soedingrekso, Alexander Sandrock Jean-Marco Alameddine, Maximilian Sackel CORSIKA Phone Call 05.03.2019 lehrstuhl - + physik e5

05.03.2019 PROPOSAL 2 / 16 lehrstuhl - + physik e5 ▶ Monte Carlo tool for charged lepton propagation through media. ▶ Used in the simulation chain of IceCube ▶ PR opagator with O ptimal P recision and O ptimized S peed for A ll L eptons ▶ Calculate energy losses ▶ Passes interaction points and decay products to further simulation programs

3 / 16 processes 𝑤 cut ∫ 𝑤 min 𝑤d𝜏 Stochastic loss Described by the interaction probability 𝑤 ∈ [𝑤 cut , 𝑤 max ] 𝑒𝑄(𝐹) = 𝜏(𝐹)d𝑦 𝜏(𝐹) = ∑ ∑ in medium atom in medium 𝑂 𝑗 𝐵 𝑗 𝑤 max ∫ 𝑤 cut d𝜏 05.03.2019 Basic Propagation Principle 𝐵 𝑗 𝑂 𝑗 atom Energy cuts in IceCube ∑ process = 𝐹 ⋅ ∑ d𝑦 d𝐹 𝜏 processes ∑ 𝑔(𝐹) ≔ 𝑤 ∈ [𝑤 min , 𝑤 cut ] Describes energy loss in the range Continuous loss Energy cuts 𝑤 ≔ relative energy loss lehrstuhl - + physik e5 ▶ Distinguish between continous and stochastic energy losses ▶ before: 𝑤 cut = 0.05 ▶ inside: 𝑓 cut = 500 MeV ▶ Cut between continuous and stochastic loss: ▶ behind: 𝑤 cut = 𝑤 max cut = min(𝑓 cut , 𝑤 cut ⋅ 𝐹), ▶ Set energy cuts before, inside and behind the detector d𝑤 d𝑤 d𝑤 d𝑤

4 / 16 𝐹 𝑗 { { { ⎩ (1 − d𝑄(𝐹(𝑦 𝑗 ))) ⋅ … ⋅ (1 − d𝑄(𝐹(𝑦 𝑔−1 ))) ⋅ d𝑄(𝐹(𝑦 𝑔 )) ≈ exp(−d𝑄(𝐹(𝑦 𝑗 ))) ⋅ … ⋅ exp(−d𝑄(𝐹(𝑦 𝑔−1 )))d𝑄(𝐹(𝑦 𝑔 )) 𝑄(𝐹(𝑦 𝑔 )) 𝐹 𝑔 𝜏(𝐹) { −𝑔(𝐹) d𝐹)] ≕ d(−𝜊) ∈ (0, 1] ∫ 𝐹 𝑔 𝐹 𝑗 𝜏(𝐹) −𝑔(𝐹)d𝐹 = − ln(𝜊) 05.03.2019 Basic Propagation Principle { ⎨ { ⎧ Determine the occurrence of a stochastic loss ��������� ��� ��������� �� � ���������� ���� ����������� �� ���� �� ���������� ���� �� � ��� �� ������ � ������ ���� ����� ������ � ��������� ����� ����������� ��������� � Probability to have no stochastic loss in (𝑦 𝑗 , 𝑦 𝑔 ) , but at 𝑦 𝑔 within d𝑦 : lehrstuhl - + physik e5 ≈ exp [− ∫ 𝑄(𝐹(𝑦 𝑗 )) d𝑄(𝐹(𝑦))] ⋅ d𝑄(𝐹(𝑦 𝑔 )) = d [− exp(− ∫ ⇒ Sample 𝐹 𝑔 from

5 / 16 d𝑦 Basic Propagation Principle 05.03.2019 0 ) ∼ 𝒪(0, 𝜄 2 𝑦,𝑧 𝜊 (1,2) 𝑦,𝑧 ) , 3𝜊 (1) √ 𝑔(𝐹)𝑤(𝐹) d𝐹 𝐹 𝑗 𝐹 𝑔 𝑢 𝑗 𝑔(𝐹) Advance the particle according to 𝐹 𝑔 𝐹 𝑔 𝐹 𝑗 d𝐹 𝑢 𝑔 lehrstuhl - + physik e5 ▶ Calculating the displacement 𝑦 𝑔 = 𝑦 𝑗 − ∫ ▶ the elapsed time 𝑢 𝑔 = 𝑢 𝑗 − ∫ 𝑤(𝑦) = 𝑢 𝑗 − ∫ ▶ and the deviation from the shower axis (multiple scattering) 𝑣 𝑦,𝑧 = 1 2 ( 1 𝑦,𝑧 + 𝜊 (2)

6 / 16 𝑤 max Basic Propagation Principle 05.03.2019 d𝜏 𝑤 cut 𝑤(𝜊) 1 d𝜏 ∫ 𝑤 cut 𝐵 𝑗 ∑ in medium atom Calculate the stochastic loss 𝑂 𝑗 lehrstuhl - + physik e5 ▶ Calculate the interaction probability for each process 𝜏 𝑗 = d𝑤 d𝑤 ▶ Calculate the amount of stochastic loss for each atom in the medium 𝜏 ∫ d𝑤 d𝑤 = 𝜊 𝐹 stochastic loss = 𝑤(𝜊) ⋅ 𝐹 particle ▶ Choose the Component, at which the energy loss takes place

Summary of the algorithm Basic loop Do: Calculate the energy until a stochastic loss ↓ Advance the particle according to 𝐹 𝑔 ↓ Calculate the amount of the stochastic loss Until: The particle decays 05.03.2019 Basic Propagation Principle 7 / 16 lehrstuhl - + physik e5

8 / 16 2𝐹 𝑗 ⏞ set to 1 𝑂 -body phase space ⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟ 𝑞 𝑗 ) 𝑗=1 ∑ 𝑜 ⏞ d 3 𝑞 𝑗 ⏞ 𝑗=1 ∏ 𝑜 ⏞ Raubold-Lynch algorithm two-body phase spaces 05.03.2019 Hadronic Decay Decay ⏞ lehrstuhl - + physik e5 π − K 0 ν K − π + π − ν π − π − π + π 0 ν π − ν sum ▶ Calculate 𝑂 -body decay phase space π − π 0 π 0 π 0 ν π − π 0 ν π − π 0 π 0 ν π − π − π + ν ▶ Not consider the matrix element 10 4 𝛥 = (2𝜌) 4 10 3 |⟨𝑁( p 𝑗 )⟩| 2 𝜀 4 (𝑞 − 2𝑁 ∫ count 10 2 10 1 10 0 ▶ Iterative integration over intermediate 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 � E hadrons /E τ ▶ Exact calculable p n , m n p n ° 1 , m n ° 1 p 3 , m 3 p 2 , m 2 p 1 , m 1 R 2 R 2 R 2 R 2 m 1 M n M n ° 1 M 3 M 2

9 / 16 05.03.2019 Decay Effects of constant Matrix Element Leptonic decay: known decay width and known matrix element lehrstuhl - + physik e5 |⟨𝑁⟩| 2 = 1 |⟨𝑁⟩| 2 ≠ 1 60000 decay width decay width 40000 phase space phase space non uniform 50000 35000 30000 40000 25000 count count 30000 20000 15000 20000 10000 10000 5000 0 0 1 . 0 1 . 5 ratio ratio 0 . 5 1 . 0 0 . 5 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 E µ /m τ E µ /m τ

10 / 16 d𝛥 Decay Leptonic Decay 05.03.2019 ( 𝑛 2 spectrum) d𝛥 Outlook: matrix elements for hadronic modes (was not necessary for IceCube, only requiring a smooth F 𝐻 2 𝑦 = 𝐹 𝑚 𝐹 max lehrstuhl - + physik e5 4 exact (theory) approx (theory) exact 3 approx ▶ Muon decay and electronic tau decay counts 𝑚 /𝑁 2 ≈ 0 ) 2 F 𝑁 5 d𝑦 = 𝐻 2 1 192𝜌 3 (3 − 2𝑦)𝑦 2 , 0 ▶ muonic tau decay ( 𝑛 𝜈 /𝑛 𝜐 ≈ 1/17 ) 1 . 0 ratio d𝑦 = 12𝜌 3 𝐹 max √𝐹 2 𝑚 − 𝑛 2 𝑚 [𝑁𝐹 𝑚 (3𝑁 − 4𝐹 𝑚 ) + 𝑛 2 𝑚 (3𝐹 𝑚 − 2𝑁)] exact / approx 0 . 5 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 E µ /m τ

05.03.2019 Propagation Improvements Propagation Improvements 11 / 16 lehrstuhl - + physik e5 ▶ Continuous Randomization ▶ Multiple parametrizations for cross sections ▶ Multiple parametrizations for multiple scattering ▶ Interpolation tables ▶ Further parameter for the trade-off between performance and precision

12 / 16 till next stochastic loss ∫ 𝑓 0 d𝐹 −𝑔(𝐹) ⎛ ⎜ ⎝ 𝑓 cut ∫ 0 ⟹ continuous randomization of the muon energy ⟨(𝛦(𝛦𝐹))⟩ ≈ the same ⎟ artifacts in fjnal muon energy spectrum ⎠ with more calculation time and secondaries to deal 05.03.2019 Continuous Randomization of the 𝐹 𝑔 Propagation Improvements 𝑓 cut lehrstuhl - + physik e5 v cut = 0 . 05 v cut = 10 − 4 v cut = 0 . 05 w/ cont. 10 4 ▶ lower energy cut means higher precision, but 10 3 Number of muons 10 2 ▶ higher energy cut results in less precision and 10 1 ▶ muons without a stochastic loss are all treated 10 0 10 − 1 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 × 10 8 Muon Energy after propagation / MeV 𝑓 2 d𝜏 d𝑤 d𝑓⎞

13 / 16 also consider LPM and TM Effect Propagation Improvements 05.03.2019 with shadowing with hard and soft component and LPM Effect Parametrizations Nuclear inelastic Interaction cross section parametrizations Bremsstrahlung Parametrizations lehrstuhl - + physik e5 ▶ real photon assumption ▶ KelnerKokoulinPetrukhin ▶ Kokoulin ▶ AndreevBezrukovBugaev ▶ Rhode ▶ BezrukovBugaev ▶ PetrukhinShestakov ▶ Zeus ▶ CompleteScreening ▶ SandrockSoedingreksoRhode ▶ Regge Theory ▶ AbramowiczLevinLevyMaor91 ▶ AbramowiczLevinLevyMaor97 𝑓 + 𝑓 − Pair Production ▶ ButkevichMikheyev ▶ RenoSarcevicSu ▶ KelnerKokoulinPetrukhin ▶ ButkevichMikheyev ▶ SandrockSoedingreksoRhode ▶ DuttaRenoSarcevicSeckel

14 / 16 default Propagation Improvements New Cross Sections 05.03.2019 on current standard parametrizations for bremsstrahlung and pair production lehrstuhl - + physik e5 KKP 1 cm 2 SSR -1/E dEdx / g 10 6 ▶ improved tree-level cross sections based 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 1.10 SSR / KKP ▶ radiative corrections for bremsstrahlung 1.05 ▶ corrections of several percent ratio 1.00 ▶ current used parametrizations are still the 0.95 0.90 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 E / MeV

15 / 16 components in medium Propagation Improvements Multiple Scattering 05.03.2019 without continuous losses (default) and one lehrstuhl - + physik e5 ▶ Molière Akimenko et al. (1984) MC: Molière ▶ analytic, precise MC: Highland 10 3 MC: HighlandIntegral counted muons N ▶ slow, depending on number of 10 2 ▶ Highland 10 1 ▶ gaussian approximation to Molière ▶ two types available: one including 10 0 − 20 − 10 0 10 total scattering angle θ/ mrad ▶ no scattering

15 / 16 components in medium Propagation Improvements Multiple Scattering 05.03.2019 without continuous losses (default) and one lehrstuhl - + physik e5 ▶ Molière 0 ▶ analytic, precise performance loss / % − 50 ▶ slow, depending on number of Molière − 100 Highland HighlandIntegral ▶ Highland − 150 ▶ gaussian approximation to Molière − 200 ▶ two types available: one including − 250 10 4 10 6 10 8 10 10 10 12 E/ MeV ▶ no scattering