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Slow muon production at Project X energies

This outline discusses particle production models and experimental data at Project X energies, including Mu2eX and simple models for beam properties. Conclusions are drawn regarding particle production models in the Project X energy range.

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Slow muon production at Project X energies

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  1. Slow muon production at Project X energies Sergei Striganov Fermilab 2011 Fall Project X Collaboration Meeting October 26, 2011

  2. Outline • Particle production models and experimental data at Project X energies • Mu2eX • Simple model – beam properties • Simple model – yield dependence on target material, radius, length, geometry ... • Conclusions

  3. Particle production models in Project X energy range • There are no solid theoretical base for models of multiple particle production in hadron-nucleon (hN) interaction. Hadron-nucleus interaction is more complicated because properties of hN are different from interaction with free nucleon. Many particle interactions could play important role. • Intra-nuclear cascade models: range of applicability < few GeV. They are needed cross section of baryon resonance production and baryon resonance-nucleon interaction – most of them were never measured. To extrapolate to few GeV energy range “formation length” of secondary particle should be introduced based on experimental data. • Quark-parton models: range of applicability > 10 GeV. Quark-parton structure at low momentum transfer was never measured, fragmentation partons to hadrons inside nucleus and vacuum are different. To extrapolate to few GeV energy range “formation length” of secondary partons/hadrons should be introduced based on experimental data. • So, predictive quality of current models totally depends on existing set of experimental data.

  4. Particle production models in Project X energy range-II • There are a lot of experimental data on charged pion production at low angles (< 10 degree). Some data has problems with absolute normalization. • Charged pion, kaon, proton cross section were systematically studied at large angles (>90 degree) and large momentum (> 300 MeV/c) • Negative pion production were measured at wide angular range in few experiments (JINR, KEK) • Recently, HARP collaboration partially closed gap between low and large angles region and reduced minimal measured momentum to 100 MeV/c • Two HARP groups have published different results based on same measurements

  5. HARP results – light nuclei

  6. HARP result – heavy nuclei

  7. HARP-CDP vs G4 models

  8. HARP results vs FLUKA and LAQGSM-large angles

  9. HARP results vs FLUKA and LAQGSM – intermediate angles

  10. Mu2e acceptance simulation procedure • Pion production point inside target is simulated according proton cross section along target and gaussian distributions in transverse directions with σ=0.1 cm. • Pion momentum – uniform distribution from 0 to 1 GeV/c. Pion angle – uniform distribution from 0 to 180 degree. • All materials are considered as black hole (except target) • Ionization energy losses in target are important - most of pions with kinetic energy < 30 MeV are stopped in target

  11. Acceptance is defined to be the number of negative muons, as a fraction of the number of negative pions produced in the target, that reach the end of transport solenoid channel.

  12. Convolution of pion production distribution and acceptance function Integral of acceptance multiplied by probability to create negative pion with given momentum and angle provides a number of negative muons at the end of transport solenoid at 8 GeV/c – 7.93 10-3 per proton on target. Using same acceptance function and fit of HARP data at 3 GeV/c one can get number of negative muons at the end of transport solenoid at 3 GeV/c - 2.73 10-3 per proton on target. So, muon yields rises nearly linearly from 3 GeV/c (2.205 GeV) to 8 GeV/c (7.117 GeV) with kinetic energy of proton.

  13. Simple model:cylinder rin=19.5 cm, rout=20cm, 40 cm length graphite or 16 cm tantalum, tilted on some angle to magnetic field - 2.5 Tesla, σ=0.1 cm.

  14. HARP results vs LAQGSM and two-fireball fit for 3 GeV/c proton on carbon

  15. Simple model - simulation procedure 200 mrad angle, 20.5 cm beam center, 10 m decay length • Muon distribution as function of beam center(x0), optimal beam momentum (popt) and β at some distance from cylinder center were simulated. Muons with momentum in [0.85popt1.15popt] range, radius < 10cm and Ɛ < 3 cm were included into “beam” • Maximum of this distribution in 3 dimensional space was determined • For fixed muon momentum maximum of two dimensional distribution x0vspoptwas found

  16. Beam properties:angle - 200 mrad, carbon target, 10 m decay channel, 2.5 Tesla9.6e-5 muon/POT, popt=105 MeV/c, β=27 cm, Ɛ=3 cm

  17. Beam properties:angle - 200 mrad, carbon target, 10 m decay channel, 2.5 Tesla9.6e-5 muon/POT, popt=105 MeV/c, β=27 cm, Ɛ=3 cm

  18. 10 m decay channel, 2.5 Tesla, Ɛ=3 cm,backward popt~100 MeV/c, β=20-30 cm, forward popt~200 MeV/c, β=30-35 cm

  19. 10 m decay channel, 2.5 Tesla, Ɛ=3 cm,backward popt=50 MeV/c, β=15-20 cm

  20. 10 m decay channel, 2.5 Tesla, Ɛ=3 cm, 300 mrad angle,backward direction. Dependence on target “radius”. Current model does not take into account scattering of primary proton beam in target. Could multiple Coulomb scattering (MCS) of primary beam reduce dependence on target radius?

  21. 2.5 Tesla, Ɛ=3 cm, 200 mrad angle,backward direction. Decay pipe length

  22. 2.5 Tesla, Ɛ=3 cm, 200 mrad angle,backward direction. Dependence on shape of target

  23. 2.5 Tesla, Ɛ=3 cm, 200 mrad angle,popt=105 MeV/c,backward direction. Acceptance Distribution of production point of accepted muons inside target Distribution of parents of accepted muons on momentum and angle

  24. Data on negative pion production at 730 MeV and LAQGSM

  25. 1 GeV proton on carbon target 1 GeV proton on carbon target, 10 m decay channel, 2.5 Tesla, Ɛ=3 cm, 200 mradangle. Backward direction:Maximal yield at 120 MeV/c and β=27 cm – 3.6e-5 muon/POT.Muon momentum 50 MeV/c+-15% and β=12 cm - 9.0e-6 muon/POT Forward direction:Maximal yield at 180 MeV/c and β=36 cm – 4.6e-5 muon/POT

  26. Conclusion • Negative muon signal is simulated using MARS model of Mu2e and fit of HARP data. Number of negative muon at the detector solenoid entrance rises nearly linearly with kinetic energy of incoming protons between 3 and 8 GeV/c • To perform more detailed simulation MARS inclusive model of particle production should be extended up to few GeV energies • Using 3 GeV/c proton on 40 cm carbon cylinder (5 mm thickness) and 2.5 Tesla magnetic field it is possible to get about 1e-4 muon per POT at 100 MeV/c and 4e-5 at 50 MeV/c with Ɛ=3 cm and ∆p/p=15% . • Dependence of yield on target material is rather week • Decay pipe length is about 5 m at 50 MeV/c and 10 m at 100 MeV/c • Muon yield rises linearly with magnetic field, ∆p/p and even faster with emittance (Ɛ1.5). Number of muon could be also increased by optimization target shape and effective radius.

  27. Simulation setup:3 GeV/c proton on 1.6 λin target. 2.5 Tesla solenoidal field.Target tilted 14 degrees. Two detector (20 cm radius) at one and two meters from center of target.

  28. Target property

  29. 3 GeV/c protons, 300 kW, 8.5 1014 p/s,6 105 bunches/s, 1.42 109 p/bunch, σ=1 mm.Target radius – 3 mm, 14 degree to solenoidal field (2.5 Tesla).Two detectors, 20 cm radius, at 1m and 2 m from target center. Emax – maximal energy deposition in target, Etot – total energy deposition in target

  30. Momentum distribution of negative pion in proton-nucleus interaction at 3 GeV/c (angle > 1 radian)

  31. Spectra of pi-/mu- at 1 m from center of target (r < 20 cm)

  32. Spectra of pi-/mu- at 2 m from center of target ( r < 20 cm)

  33. Horizontal distribution of pi-/mu- at 1 m from center of target ( all momentum)

  34. Horizontal distribution of pi-/mu- at 2 m from center of target ( all momentum)

  35. Thick target effects - I • Mu2e target is long (16 cm of gold) . It is about 1.6 nuclear interaction length • Low energy pions could be produced in secondary, tertiary … interactions • Pion with kinetic energies < 100 MeV are mostly produced in primary proton interactions and near elastic scattering of low energy negative pion • Results obtained using MARS- default and MARS-LAQGSM are similar • Low energy negative pion yield from thick target with about 10% precision is proportional to low energy pion yield in proton-nucleus interactions

  36. Thick target effects - II • Mu2e target - gold, length is 16 cm, radius 0.3 cm. Gaussian beam with σx= σy=0.1 cm. • Mu2e mostly collects pion with kinetic energies < 100 MeV • Distribution of track length of negative pion inside target has maximum near target radius • Distributions obtained using MARS-LAQGSM and default version are similar • Due to ionization energy losses energy of pion at target surface is lower than at production vertex

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