UHE showers from e : What do we know, and what don’t we know Electromagnetic Interactions & the LPM effect Photonuclear and Electronuclear Interactions Uncertainties Shower Shapes Effect on radio emission Spencer Klein, LBNL Presented at the SalSA Workshop, Feb. 3-4, 2005, SLAC
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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. - PowerPoint PPT Presentation
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UHE showers from e: What do we know, and what don’t we know
Electromagnetic Interactions & the LPM effect Photonuclear and Electronuclear Interactions Uncertainties Shower Shapes
Effect on radio emission
Spencer Klein, LBNL
Presented at the SalSA Workshop,Feb. 3-4, 2005, SLAC
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?
x = E/Eexd
/dx
1/X
0for 10 GeV … 10 PeV in Lead640 GeV…. 640 PeV in water180 GeV …. 180 PeV in salt
.0023 ….2300 ELPM
Pair Production
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
open >> 1/
e-
e+
70 TeV (top) to 7 1019 eV (bottom) in ice20 TeV – 2 1019 eV in rock salt
--> e+e-
x = e+/e- energy fraction
e/ Energy Loss
Electron energy loss/ reduced
Bigger effect for electrons
For E>> ELPM
Electrons act like muons
Photons interact hadronically
Electron (photon) Energy/ELPM
ELPM = 278 TeV in waterELPM = 77 TeV in `standard rock’ELPM = 77 TeV in rock sal.
.01 1 100 104 106R
elat
ive
En
erg
y L
oss
/
e
Photonuclear interactions
R. Engel, J. Ranft and S. Roessler, PRD 57, 6597 (’97)
1000101 s (GeV)
Direct
tot
p (b
)
Vector meson dominance Photon fluctuates to a qq pair
qq interacts strongly, as a virtual 0
rises slowly with energy At high energies, direct photon interactions become
significant q --> gq Faster rise in cross section
Not yet experimentally accessible
Shadowing reduces N for nuclei Glauber calculation
Take ‘low-energy’for H2O scale ~ W0.16
Energy dependence of q --> gq & shadowing cancel
Lead Ice
-->e+e
-
-->e +e --->hadrons
--
>hadrons
Electromagnetic vs. Hadronic Showers
LPM effect suppresses pair production
Photonuclear cross sections increase with energy
Above ~ 1020 eV, in lead/ice photonuclear interactions dominateThere are no electromagnetic showersSimilar effect in air, above 5*10 22 eV (at sea level)
SK: astro-ph/0412546
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
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 to modern X0
Calculations by Zakharov (1997) and Baier and Katkov (1998) avoid these problems Seem to agree with Migdal within ~ 20%
Is there a problem at low-Z?
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
SLAC E-146
Photon energy in MeV (log scale)
0.2 1 10 100 500 0.2 1 10 100 500
Formation Length Suppression
kp
kp~10-4E E2/ELPM
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