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

LPM Bremsstrahlung n Cross section is reduced for u k < E(E-k)/E LPM u E LPM ~ 61.5 TeV X 0 (cm) n dN/dk ~ 1/  k u vs. Bethe-Heitler dN/dk ~ 1/k n When suppression is large, the mean photon emission angle increases u Broadens showers? x = E  /E e xd  /dx 1/X 0 for 10 GeV … 10 PeV in Lead 640 GeV…. 640 PeV in water 180 GeV …. 180 PeV in salt.0023 ….2300 E LPM 

Pair Production n Cross section is reduced u Symmetric pairs most suppressed n Scales with X 0 (in cm) n Less affected than bremsstrahlung u Due to kinematics High-mass & wide angle pairs are less suppressed u M ee >> 1 MeV   open >> 1/   e-e- e+e+ 70 TeV (top) to eV (bottom) in ice 20 TeV – eV in rock salt  --> e + e - x = e +/ e - energy fraction

e/  Energy Loss Electron energy loss/   reduced n Bigger effect for electrons n For E>> E LPM u Electrons act like muons u Photons interact hadronically Electron (photon) Energy/E LPM E LPM = 278 TeV in water E LPM = 77 TeV in `standard rock’ E LPM = 77 TeV in rock sal Relative Energy Loss/   e

Photonuclear interactions R. Engel, J. Ranft and S. Roessler, PRD 57, 6597 (’97)  s (GeV) Direct   tot   p (  b) n Vector meson dominance u Photon fluctuates to a qq pair  qq interacts strongly, as a virtual  0   rises slowly with energy n At high energies, direct photon interactions become significant   q --> gq u Faster rise in cross section F Not yet experimentally accessible Shadowing reduces   N for nuclei u Glauber calculation Take ‘low-energy’  for H 2 O  scale  ~ W 0.16  Energy dependence of  q --> gq & shadowing cancel

Lead Ice  -->e + e -  -->hadrons Electromagnetic vs. Hadronic Showers n LPM effect suppresses pair production n Photonuclear cross sections increase with energy Above ~ 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/

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

LPM calculations n Most shower studies use Migdal’s (1956) calculation u Gaussian scattering F Underestimates large angle scatters u No electron-electron interactions u No-suppression limit,  Bethe-Heitler cross section  Unclear normalization of  to modern X 0 n Calculations by Zakharov (1997) and Baier and Katkov (1998) avoid these problems u Seem to agree with Migdal within ~ 20%

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

Formation Length Suppression kpkp k p ~10 -4 E E 2 /E LPM n Additional suppression when l f > X 0 u A bremsstrahlung photon pair converts before it is fully formed. F Reduces effective coherence length n A super-simple ansatz – limit l f to X 0 u Suppression for k/E ~ when F E > E p =15 PeV (sea level air) F E > E p = 540 TeV (water) u Additional suppression for k/E < 0.1 for E= eV in water e-e-  Landau & Pomeranchuk, 1953 Galitsky & Gurevitch, 1964 Klein, 1999

Formation Length Suppression n Couples pair production and bremsstrahlung. u When l f encompasses both reactions, they are no longer independent F Need to find cross section for complete interaction eNN --> eN  N --> eNeeN 2-step process – not just direct pair production  As the  e-->e  and   -->ee drop, the effective radiation length rises, slowly self-quenching the interaction n Photonuclear interactions also limit coherence  When l f > 1/   n    n rises with energy, unlike pair production  Dominates when   n >>  ee F When photonuclear interactions dominate e-e-  Ralston, Razzaque & Jain, 2002

Higher-order corrections n LPM calculations are lowest order  May fail for  /  0 ~  EM ~ 1/137 n When suppression is large, higher order processes become more important u eN --> e + e - eN F Momentum transfer equivalent to bremsstrahlung of a massive (1 MeV) photon u l f is much shorter F No LPM suppression up to at least eV Water  -->e + e -  -->hadrons

Uncertainties Ice  -->e + e -  -->hadrons n LPM Calculation u 20% ? n Formation Length Limits u Combined & photonuclear interactions u Important above eV in water u Reduces electromagnetic cross sections n Higher Order Corrections  May be important when  LPM <  EM  BH F above eV in water n Photonuclear Cross Section u Unitarity limit affects Pomeron trajectory? u Factor of 2 at eV None of these uncertainties change the conclusion that Photonuclear interactions dominate above 1020 eV

e Showers in ice above eV e Hadronic Shower (20%) EM Shower (80%) e No photonuclear interactions Hadronic shower + Long EM shower  EM = 36 cm/sqrt(E/10 15 eV) Shower length ~ 60 m (E/10 19 eV) 1/3 (90% containment. Alvarez-Muniz + Zas)) e Hadronic Shower (20%) e Photonuclear interactions Hadronic shower + Delayed (by  EM ) hadronic shower  H = 83 cm Shower length ~ 30  H ~ 25 m  EM --> hadronic Shower (80%) EM propagator Length  EM

Shower Length n 3 simple models u EM (w/ LPM) F Length ~ E 1/3 (Alvarez-Muniz & Zas) 1 km at eV u Hadronic F Length ~ ln(E) u Hybrid F Initially EM, but   --> hadrons 400 m at eV n No electronuclear interactions u May shorten hybrid Purely EM Purely Hadronic Dotted - hybrid e Energy (eV)

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

n KASKADE measured the lateral spread of electrons, muons and hadrons from 5* eV showers u Fit to NKG functions with radial parameter r M free u Electrons r M ~ m u Muons r M ~ 420 m  from  -->  decays – represent low energy hadrons u Hadrons r M ~ 10 meters F high-energy shower remnants ( ~ 50 GeV) They correct for the high : F r M (corr) ~ r M * 50 GeV/400 MeV ~ 1.2 km n The hadronic components of these showers spread more than the electromagnetic components Shower higher energies T. Antoni et al., Astropart. Phys. 14, 245 (2001)

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

e from eV n Showers will have a significant, but not dominant hadronic component u Electronuclear interactions (tbd) u Photonuclear Interactions  P(  -->h) = % for E  = eV n Some shower energy will have a larger mean radius n Muons u Mostly from charm/bottom decay u Other hadronic contributions? Initial + delayed hadronic showers might mimic double-bang  events

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

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

Radiation from Electrons Electron range increases with energy as  LPM drops n At E= E LPM u eV for water u dE/dx = dE/dx BH F Range ~ 10 4 X 0 ~ 3000 m F Ice South pole n Other reactions become more important. u Photonuclear interactions of virtual photons u Direct pair production n Above ~ eV, electrons may begin to look like muons. Electron dE/dx by bremsstrahlung E/E LPM 1.5 TeV – eV for water dE/dx / dE/dx BH

x = E  /E e LPM Bremsstrahlung n Cross section is reduced when u k < E(E-k)/E LPM u E LPM ~ 61.5 TeV X 0 (cm) n dN/dk ~ 1/  k u vs. Bethe-Heitler dN/dk ~ 1/k 500 MeV xd  /dx 1/X 0 SLAC E-146 Photon energy spectrum Logarithmic bins in k 10 MeV 200 keV LPM LPM + dielectric BH for 10 GeV … 10 PeV in Lead.0023 ….2300 E LPM  For Aluminum E LPM = 68 TeV Suppression for k< 9.2 MeV

Radio Waves n Radio waves are coherent Cherenkov radiation from the particles in the shower u e + and e - cancel; e - excess produces signal F Shower width depends on shower development Wavelength ~ bunch width/sin(  c )  For fixed, radiation decreases as shower width increases u Wider showers peak at lower frequencies n Quantitative studies required detailed calculations CC Radio waves Shower