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
e-
Landau & Pomeranchuk, 1953Galitsky & Gurevitch, 1964Klein, 1999
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 --> eNN --> 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
Photonuclear interactions also limit coherence When lf > 1/n
n rises with energy, unlike pair production
Dominates when n >> ee
When photonuclear interactions dominate
e-
Ralston, Razzaque & Jain, 2002
Higher-order corrections
LPM calculations are lowest order May fail for /0 ~ EM ~ 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
Water
-->e +e -
-->hadrons
Uncertainties
Ice
-->e +e -
-->hadrons
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 LPM < EM BH
above 1020 eV in water Photonuclear Cross Section
Unitarity limit affects Pomeron trajectory? Factor of 2 at 1020 eV
None of these uncertainties change the conclusion thatPhotonuclear interactions dominate above 1020 eV
e Showers in ice above 1020 eV
e
Hadronic Shower (20%)
EM Shower (80%)
eNo photonuclear interactionsHadronic 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))
e
Hadronic Shower (20%)
e Photonuclear interactionsHadronic shower +Delayed (by EM) hadronic shower
H= 83 cmShower length ~ 30H ~ 25 m
EM --> hadronic
Shower (80%)
EM propagatorLengthEM
Shower Length 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 --> hadrons
• 400 m at 1022 eV
No electronuclear interactions May shorten hybrid
Purely EMPurely HadronicDotted - hybrid
e Energy (eV)
Shower Width @ low energies
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
Radius (cm)
Dep
osi
ted
Ch
arg
e (p
C/c
m)
ElectromagneticHadronic
D. A
costa et al., NIM
A316, 184 (1992)
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 --> 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
Shower widths @ higher energies
T. Antoni et al., Astropart. Phys. 14, 245 (2001)
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
e from 1017-1020 eV
Showers will have a significant, but not dominant hadronic component Electronuclear interactions (tbd) Photonuclear Interactions
P(-->h) = 3 - 12% for E = 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 events
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, e 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.
Electromagnetic vs. Hadronic
Showers 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
N rises with energy Photonuclear interactions are important
e
Hadronic Shower (20%)
EM Shower (80%)
e
Radiation from Electrons Electron range increases with energy as
LPM drops
At E=5 109 ELPM
7 1023 eV for 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.
Electron dE/dx by bremsstrahlung
E/ELPM
1.5 TeV – 1.5 1022 eV for water
dE
/dx
/ dE
/dx B
H
x = E/Ee
LPM Bremsstrahlung 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
500 MeV
xd/
dx 1
/X0
SLAC E-146Photon energy spectrum
Logarithmic bins in k
10 MeV200 keV
LPM
LPM + dielectric
BH
for 10 GeV … 10 PeV in Lead.0023 ….2300 ELPM
For Aluminum ELPM = 68 TeVSuppression for k< 9.2 MeV
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 ~ bunch width/sin(c) For fixed , radiation decreases as shower width
increases Wider showers peak at lower frequencies
Quantitative studies required detailed calculations
C
Radio waves
Shower