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