The Lunar ASKAryan project

Neutrino interactions &

the Landau-Pomeranchuk-Migdal (LPM) effect

Jaime Alvarez-MuñizDept. Física de Partículas

Universidade Santiago de CompostelaSpain

SKA sensitivity to Extremely High-Energy neutrinos

J.D. Bray et al. SKA Lunar Science Chapter arXiv:1408.6069v2

Calculations based on detailed MC simulations by C.W. James, J.D. Bray, R. Protheroe

SKA-LOW100 – 350 MHz

SKA-MID 1350 – 1050 MHz

SKA-MID 2950 – 1760 MHz

Neutrino – induced showers

Hadronic showers E ≈ 20% E @

EeV

“Mixed” showers Eelectromagnetic ≈ 80% E @ EeV

Ehadronic ≈ 20% E @ EeVElectromagnetic

or

Hadronic

Neutrino – nucleon Deep Inelastic Scattering (DIS)

(x 3)

10-6

10-5

10-4

10-3

1016 1017 1018 1019 1020 1021 1022

Cro

ss s

ectio

n [m

b]

E [GeV]

pQCD - x (=0.4)Sarkar 2011

Saturation ASW

– nucleon CC cross-section

Large uncertaintyeven within the Standard Model

Currently assuming ~20% uncertainty in x-section at 1020 eV

Effective area to neutrino detection proportional to x-section

SKA1-LOW

Relative contribution to aperture in SKA-LOW at E = 1021 eV

Type of shower/interaction Relative contribution

Primary hadronic & CC & all NC ~ 93%

Primary electromagnetic e CC ~ 1%

Tau photonuclear CC ~ 5%

Other (muon, tau bremss, etc…) ~ 1%C.W. James, R.J. Protheroe, Astropart. Phys. 30 (2009) 318

(x 3)

The Landau-Pomeranchuk-Migdal (LPM) effect

• Quantum mechanical effect that suppresses:- bremsstrahlung by electrons or positrons- pair production by photons

• Interactions do not occur at a point, but along a distance (formation length) Lint ~ 1/q|| (q|| = parallel momentum transfer) that increases with Energy

• Typically if E > ELPM ~ 1015 eV then Lint >> interatomic distance => interactions along formation length scatter electron & suppress bremsstrahlung emission.

S.R. Klein, Revs. Modern Phys. 71, No. 5, 1999

suppressed emission of bremss. photon

L. Landau and I. Pomeranchuk, Dokl. Akad. Nauk SSSR 92, 535, 1953A.B. Migdal, Phys. Rev. 103,1811, 1956

LPM effect: Cross sections

Pair production by photons Bremsstrahlung by electrons

~ 1015 eV

T.Stanev & H.P.Vankov, PRD 25 (1982)

- Significant reduction of pair-production and bremsstrahlung cross sections with respect to Bethe-Heitler predictions

- Also suppression of “soft” bremsstrahlung

LPM effect & showersElectromagnetic showers

having E > ELPM

(~ 1015 eV regolith):

• strongly affected by LPM effect

• more penetrating than those with E < ELPM.

• Width of long. profile (shower length L) increases faster than ~ log E, typically as E1/3

• Energy deposition is clumpy

J.A-M & E.Zas, Phys. Lett. B 411 (1997) 218J.A-M & E.Zas, Phys. Lett. B 434 (1998) 396J.A-M, R.A. Vazquez & E.Zas, Phys. Rev. D 61 (1999) 023001

105

106

107

108

109

1010

0 20 40 60 80 100 120 140 160 180

N (e

- + e

+ )

Depth in ice [m]

E=1019 eV, Ice

Electrom. - LPM OnElectrom. - LPM OnElectrom. - LPM OfHadronic - LPM On

Hadronic showers

• much less affected by LPM effect

10-3

10-2

10-1

101 102 103 104

R x

E-fi

eld(

,)

[V

/MH

z]

Frequency [MHz]

CherenkovCher - 1

o

Cher - 5o

0.02

0.04

0.06

0.08

0.1

0.12

50 55 60 65

R x

E-fi

eld(

,)

[V

/MH

z]

Observation angle [deg]

= 1 GHz = 300 MHz = 100 MHz

Properties of signal (freq.-domain)

Electron shower

1018 eV in ice

Δθ ~ 1/

Frequency spectrum

Angular distributionshower

far-fieldobserver

θ

E-field

- Radiation emitted in a cone around Cherenkov angle.

- Width proportional to inverse of frequency.

- Broad-band frequency spectrum. - Field increases with frequency up

to a cut-off depending on observation angle.

Electron shower1018 eV in ice

E. Zas, F. Halzen, T. Stanev, PRD 45, 162 (1992), J. A-M & E. Zas, PLB 411, 218 (1997)J.A-M, C.W. James, R.J. Protheroe, E. Zas, APP 32, 100 (2009)

Diffraction by a slit

L

Angular distribution of E-field

θc

Optics analogy to understand radio emission: diffraction by a single slit

• The shower plays the role of the slit in elementary optics.• Electric-field can be obtained Fourier-transforming the

longitudinal profile Q(z) of excess charge (Fraunhofer diffraction)

Shower

slit

J. A-M, R.A. Vazquez, E. Zas, PRD 61, 023001 (1999). J. A-M & E. Zas, PRD 62, 063001 (2000)

10-3

10-2

10-1

100

40 45 50 55 60 65 70R

x E

-fiel

d [V

/MH

z]

Observation angle [deg]

e CC, Ee = 8 x 1018 eV, Ehad = 2 x 1018 eV

NC, Ehad = 2 x 1018 eV

105

106

107

108

109

1010

0 20 40 60 80 100 120 140

N (e

- + e

+ )

Depth in ice [m]

e CC, Ee=8 x 1018 eV, Ehad = 2 x 1018 eV

NC, Ehad=2 x 1018 eV

Radioemission & LPM effect in neutrino-induced showers

J.A-M, R.A. Vazquez & E.Zas, Phys. Rev. D 61 (1999) 023001

Longitudinal profile of shower θ distr. of E-field

- LPM effect “stretches” electron-induced showers in ne CC => Cherenkov cone “shrinks”

- Reduced solid angle: ~ 1º @ 10 EeV & 100 MHz

L

= 100 MHz

L

LPM effect vs electronuclear interactions

- LPM effect suppresses electron bremsstrahlung above 1015 eV - Suppression of energy loss to electromagnetic showers is so large above ~ 1020

eV that electron starts to lose energy to hadronic showers (little affected by LPM !)

L. Gerhardt, S.R. Klein, Phys. Rev. D 82 (2010) 074017

electromagnetic E-loss (LPM)

electronuclear => hadronic shower(no LPM ! )

direct pair productione- N e+ e- e- N

Shower length L vs energy

LPM only

LPM + direct pp + electronuclear

• Moderate rise in electron neutrino-induced shower length, ameliorating the dramatic shower stretching due to LPM effect.

• Should increase relative contribution to exposure from electron neutrinos.

L. Gerhardt, S.R. Klein, Phys. Rev. D 82 (2010) 074017

Full simulations of -induced showers in regolith/megaregolith/etc…

Depth (g cm-2)

Exc

ess

charg

e

e + N → e + jetE(e) = 10 EeVE(electron) = 8 EeVE(hadronic jet) = 2 EeV

Depth profile

θc -10 deg.θc + 10 deg.

Time (ns)

hadronic shower

electronshower

Electric field

Full simulations of -induced showers in (almost any) dense dielectric media now possible with ZHAireS: hadronic, mixed, tau decay-shower,…

Scaling of radiopulse from ice to regolith probably accurate enough but could be improved if needed.

J. A-M, W.R. Carvalho, M. Tueros, E. Zas, Astroparticle Physics 35 (2012) 287–299

R x

E (

V) ICE

Improvements in modeling

1. Take into account, in calculations of exposure to EHE neutrinos, the hadronic behaviour of electron above 1020 eV => increase in exposure

1. Include larger uncertainty in the neutrino cross-section

1. New parameterization of showers in regolith/megaregolith ? 10-6

10-5

10-4

10-3

1016 1017 1018 1019 1020 1021 1022

Cros

s se

ctio

n [m

b]

E [GeV]

pQCD - x (=0.4)Sarkar 2011

Saturation ASW

Backup

θC

θC -

10o

θC -

20o

Frequency spectrum in LPM showers

• Elongated profiles at EeV induce smaller cut-off frequencies at θ≠θc

• Cut-off frequency at Cherenkov angle unaffected.

Field

norm

aliz

ed

to p

rim

ary

en

erg

y

SKA-LOW SKA-MID1

18/36

LPM effect: Cross sectionsPair production cross sections Bremsstrahlung cross sections

Total

Differential

e-e+ pair asymmetric in energy Suppression of emission of low K photons

energy fraction carried by e- energy fraction carried by

Kγ=1012 eV

Kγ=1018 eV

Ee=1011 eV

Ee=1018 eV

(Ice)

(Lead)

~ PeV

T.Stanev & H.P.Vankov, PRD 25 (1982)

Radioemission & LPM effect

J.A-M, R.A. Vázquez & E.Zas PRD 61 (1999)

Δθ ~ 1/L (L = width of the longitudinal shower development).(Power @ θC still ~ Eshower

)

ZHS sims.

Long. profile θ distr. of E-field

Cone shrinks

Peak field at Cherenkov angle unchanged

~ 2 mrad @ 20 EeV & 1 GHzupdate value using new params.