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UHE showers from n e : What do we know, and what don’t we know

UHE showers from n e : What do we know, and what don’t we know. Spencer Klein, LBNL. Electromagnetic Interactions & the LPM effect Photonuclear and Electronuclear Interactions Uncertainties Shower Shapes Effect on radio emission. Presented at the SalSA Workshop, Feb. 3-4, 2005, SLAC. g.

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UHE showers from n e : What do we know, and what don’t we know

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  1. UHE showers from ne: What do we know, and what don’t we know Spencer Klein, LBNL • Electromagnetic Interactions & the LPM effect • Photonuclear and Electronuclear Interactions • Uncertainties • Shower Shapes • Effect on radio emission Presented at the SalSA Workshop, Feb. 3-4, 2005, SLAC

  2. g xds/dx 1/X0 x = Eg/Ee for 10 GeV … 10 PeV in Lead 640 GeV…. 640 PeV in water 180 GeV …. 180 PeV in salt .0023 ….2300 ELPM LPM Bremsstrahlung • Cross section is reduced for • k < E(E-k)/ELPM • ELPM ~ 61.5 TeV X0 (cm) • dN/dk ~ 1/k • vs. Bethe-Heitler dN/dk ~ 1/k • When suppression is large, the mean photon emission angle increases • Broadens showers?

  3. Pair Production e- g e+ g --> e+e- • Cross section is reduced • Symmetric pairs most suppressed • Scales with X0 (in cm) • Less affected than bremsstrahlung • Due to kinematics High-mass & wide angle pairs are less suppressed • Mee >> 1 MeV • qopen >> 1/g x = e+/e- energy fraction 70 TeV (top) to 7 1019 eV (bottom) in ice 20 TeV – 2 1019 eV in rock salt

  4. e/g Energy Loss Relative Energy Loss/s g • Electron energy loss/ sgA reduced • Bigger effect for electrons • For E>> ELPM • Electrons act like muons • Photons interact hadronically e .01 1 100 104 106 Electron (photon) Energy/ELPM ELPM = 278 TeV in water ELPM = 77 TeV in `standard rock’ ELPM = 77 TeV in rock sal.

  5. Photonuclear interactions stot • Vector meson dominance • Photon fluctuates to a qq pair • qq interacts strongly, as a virtual r0 • s rises slowly with energy • At high energies, direct photon interactions become significant • gq --> gq • Faster rise in cross section • Not yet experimentally accessible • Shadowing reduces sgN for nuclei • Glauber calculation • Take ‘low-energy’ s for H2O • scale s ~ W0.16 • Energy dependence of gq --> gq & shadowing cancel sgp (mb) Direct g 1 10 1000 s (GeV) R. Engel, J. Ranft and S. Roessler, PRD 57, 6597 (’97)

  6. Electromagnetic vs. Hadronic Showers Lead Ice • LPM effect suppresses pair production • Photonuclear cross sections increase with energy g-->e+e- g-->e+e- g-->hadrons g-->hadrons Above ~ 1020 eV, in lead/ice photonuclear interactions dominate There are no electromagnetic showers Similar effect in air, above 5*10 22 eV (at sea level) SK: astro-ph/0412546

  7. Caveats • Approximations in LPM calculations • Suppression of bremsstrahlung due to pair conversion and vice-versa • Higher order reactions and corrections • All LPM calculations are lowest order • Radiation from electrons

  8. LPM calculations • Most shower studies use Migdal’s (1956) calculation • Gaussian scattering • Underestimates large angle scatters • No electron-electron interactions • No-suppression limit,  Bethe-Heitler cross section • Unclear normalization of s to modern X0 • Calculations by Zakharov (1997) and Baier and Katkov (1998) avoid these problems • Seem to agree with Migdal within ~ 20%

  9. Is there a problem at low-Z? SLAC E-146 • Uranium (& other high-Z materials) fit Migdal well • Carbon (& aluminum) poor agreement in transition region • Zakharov’s calculation seems to show similar disagreement with the E-146 data SLAC E-146 0.2 1 10 100 500 0.2 1 10 100 500 Photon energy in MeV (log scale)

  10. g e- Formation Length Suppression • Additional suppression when lf > X0 • A bremsstrahlung photon pair converts before it is fully formed. • Reduces effective coherence length • A super-simple ansatz – limit lf to X0 • Suppression for k/E ~ 10-4 when • E > Ep=15 PeV (sea level air) • E > Ep = 540 TeV (water) • Additional suppression for k/E < 0.1 for E=5 1020 eV in water Landau & Pomeranchuk, 1953 Galitsky & Gurevitch, 1964 Klein, 1999 kp kp~10-4E E2/ELPM

  11. g e- Formation Length Suppression • Couples pair production and bremsstrahlung. • When lf encompasses both reactions, they are no longer independent • Need to find cross section for complete interaction • eNN --> eNgN --> eNeeN • 2-step process – not just direct pair production • As the se-->eg and sg-->ee drop, the effective radiation length rises, slowly self-quenching the interaction • Photonuclear interactions also limit coherence • When lf > 1/rsgn • sgn rises with energy, unlike pair production • Dominates when sgn >> see • When photonuclear interactions dominate Ralston, Razzaque & Jain, 2002

  12. Higher-order corrections Water • LPM calculations are lowest order • May fail for s/s0 ~ aEM ~ 1/137 • When suppression is large, higher order processes become more important • eN --> e+e-eN • Momentum transfer equivalent to bremsstrahlung of a massive (1 MeV) photon • lf is much shorter • No LPM suppression up to at least 1020 eV g-->e+e- g-->hadrons

  13. Uncertainties Ice • LPM Calculation • 20% ? • Formation Length Limits • Combined & photonuclear interactions • Important above 1020 eV in water • Reduces electromagnetic cross sections • Higher Order Corrections • May be important when sLPM < aEMsBH • above 1020 eV in water • Photonuclear Cross Section • Unitarity limit affects Pomeron trajectory? • Factor of 2 at 1020 eV g-->e+e- g-->hadrons None of these uncertainties change the conclusion that Photonuclear interactions dominate above 1020 eV

  14. ne Showers in ice above 1020 eV EM Shower (80%) ne e • No photonuclear interactions • Hadronic shower + Long EM shower • EM= 36 cm/sqrt(E/1015 eV) Shower length ~ 60 m (E/1019 eV)1/3 • (90% containment. Alvarez-Muniz + Zas)) Hadronic Shower (20%) EM propagator Length LEM EM --> hadronic Shower (80%) ne • Photonuclear interactions • Hadronic shower + • Delayed (by LEM) hadronic shower • H= 83 cm Shower length ~ 30LH ~ 25 m m e Hadronic Shower (20%)

  15. Shower Length Purely EM Purely Hadronic Dotted - hybrid • 3 simple models • EM (w/ LPM) • Length ~ E1/3 (Alvarez-Muniz & Zas) 1 km at 1022 eV • Hadronic • Length ~ ln(E) • Hybrid • Initially EM, but • g --> hadrons • 400 m at 1022 eV • No electronuclear interactions • May shorten hybrid ne Energy (eV)

  16. Shower Width @ low energies Electromagnetic Hadronic • 150 GeV EM and hadronic showers • Lead-scintillating fiber calorimeter • CERN LAA collaboration measured lateral profiles • Hadronic 2-4X wider, with long tails • Both lateral profiles ~ constant from 5-150 GeV Deposited Charge (pC/cm) D. Acosta et al., NIM A316, 184 (1992) Radius (cm)

  17. Shower widths @ higher energies • KASKADE measured the lateral spread of electrons, muons and hadrons from 5*1014-1017 eV showers • Fit to NKG functions with radial parameter rM free • Electrons rM ~ 20-30 m • Muons rM ~ 420 m • from p--> m decays – represent low energy hadrons • Hadrons rM ~ 10 meters • high-energy shower remnants (<E> ~ 50 GeV) • They correct for the high <E>: • rM (corr) ~ rM* 50 GeV/400 MeV ~ 1.2 km • The hadronic components of these showers spread more than the electromagnetic components T. Antoni et al., Astropart. Phys. 14, 245 (2001)

  18. Shower widths • Very high energy hadronic showers are much wider than equal energy EM showers • <pT> • CERN LAA • KASKADE • Wider showers --> lower wavelengths required for full radio coherence • Detailed calculations are required to quantify this

  19. ne from 1017-1020 eV • Showers will have a significant, but not dominant hadronic component • Electronuclear interactions (tbd) • Photonuclear Interactions • P(g-->h) = 3 - 12% for Eg = 1017-1018 eV • Some shower energy will have a larger mean radius • Muons • Mostly from charm/bottom decay • Other hadronic contributions? • Initial + delayed hadronic showers might mimic double-bang nt events

  20. Conclusions • Above 1020 eV in solids, photonuclear reactions dominate over pair production • Photoproduction speeds the shower development and widens the radiating area • Above 1016 eV, ne showers have increased muon content from heavy quark production • The basic picture is clear, but theoretical work is required to reduce the uncertainties • Higher-order LPM calculations • Studies of photonuclear interactions • Integrated LPM calculations with photonuclear interactions • Electronuclear interactions (in progress – SK+D. Chirkin) • The effect of photonuclear interactions on radio and acoustic detection should be studied. • They may push detectors toward lower frequencies.

  21. Electromagnetic vs. Hadronic Showers EM Shower (80%) ne e Hadronic Shower (20%) • Conventional Wisdom • Photons produce e+e- pairs • Photonuclear interactions are rare, and can be neglected • Reality • The LPM effect reduces the electromagnetic cross sections • Lengthens the shower • sgN rises with energy • Photonuclear interactions are important

  22. Radiation from Electrons Electron dE/dx by bremsstrahlung • Electron range increases with energy as sLPM drops • At E=5 109 ELPM • 7 1023 eVfor water • dE/dx = 10-4 dE/dxBH • Range ~ 104 X0 ~ 3000 m • Ice thickness @ South pole • Other reactions become more important. • Photonuclear interactions of virtual photons • Direct pair production • Above ~ 1024 eV, electrons may begin to look like muons. dE/dx / dE/dxBH E/ELPM 1.5 TeV – 1.5 1022 eV for water

  23. g LPM Bremsstrahlung SLAC E-146 Photon energy spectrum Logarithmic bins in k • Cross section is reduced when • k < E(E-k)/ELPM • ELPM ~ 61.5 TeV X0 (cm) • dN/dk ~ 1/k • vs. Bethe-Heitler dN/dk ~ 1/k BH xds/dx 1/X0 LPM LPM + dielectric x = Eg/Ee 500 MeV 10 MeV 200 keV for 10 GeV … 10 PeV in Lead .0023 ….2300 ELPM For Aluminum ELPM = 68 TeV Suppression for k< 9.2 MeV

  24. qC Radio Waves Shower Radio waves • Radio waves are coherent Cherenkov radiation from the particles in the shower • e+ and e- cancel; e- excess produces signal • Shower width depends on shower development • Wavelength l ~ bunch width/sin(qc) • For fixed l, radiation decreases as shower width increases • Wider showers peak at lower frequencies • Quantitative studies required detailed calculations

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