the passage of ultrarelativistic neutralinos through matter...the passage of ultrarelativistic...
TRANSCRIPT
The Passage of Ultrarelativistic Neutralinos throughMatter
Sascha Bornhauser
Physikalisches Institut der Rheinischen Friedrich-Wilhelms-Universität Bonn
SUSY08, Seoul
in collaboration with M. Drees
based on hep-ph/0603162 and 0704.3934
S. Bornhauser (University of Bonn) Cosmic neutralinos SUSY08 1 / 15
Outline
1 Introduction/Motivation
2 Transport equations
3 Event rates
4 Summary
S. Bornhauser (University of Bonn) Cosmic neutralinos SUSY08 2 / 15
Experiments...have shown the existence of ultra high energy (UHE) cosmic rayswith E >
∼ 1011 GeV
indicate that most UHE events are caused by protons
Protons with E >∼ 5 ·1010 GeV lose energy through inelastic scattering:
p + γ2.7K → n + π+
→ p + π◦ =⇒proton energy losslength ∼ 50 Mpc =⇒ local sources
Questions:B.-U. models: are there objects which have sufficiently large B · L?
are the arrival directions of UHE events homogeneouslydistributed? ⇒ exclusion of one or a few local point sources
are there local sources? AUGER indicates correlation betweennearby AGNs and the origin of UHE events ( arXiv: 0712.2843)
S. Bornhauser (University of Bonn) Cosmic neutralinos SUSY08 3 / 15
One possible source: Top-Down Models (TDMs)existence and decay of very massive, long-lived X-particles(MX > 1012GeV ) ⇒ UHE events
X-particles could be associated with a Grand Unified Theory
Signature for Top-Down ModelsDecay chain in the framework of R-parity conserving SUSY:
(M.Drees and C.Barbot)
Stable particles:photons
neutrinos ν
electrons
protons
neutralinos χ̃01(LSPs)
⇒“smoking gun” for TDMs:Detection of χ̃0
1
S. Bornhauser (University of Bonn) Cosmic neutralinos SUSY08 4 / 15
Discrimination between ν and χ̃01?⇒
Possible measurement method for χ̃01:
Cross section for χ̃01
interactions with matter issmaller than that of ν
⇒ Using the Earth as a filterDetector
Neutrinos
Neutralinos
Necessary tools:calculation of total & differential cross section (⇒ hep-ph/0603162)
solution of the transport equations
calculation of event ratesS. Bornhauser (University of Bonn) Cosmic neutralinos SUSY08 5 / 15
Transport equation for s−channelscattering (bino-dominated χ̃
01)
∂Fχ̃
01(E , X )
∂X= −
Fχ̃
01(E , X )
λχ̃
01(E)
︸ ︷︷ ︸
decrease
+1
λχ̃
01(E)
∫ ymax
0
dy1 − y
Ks(E , y)Fχ̃
01(Ey , X )
︸ ︷︷ ︸
increase due to χ̃01+qi→χ̃
01+qi
,
Fχ̃
01(E , X ): differential χ̃0
1 flux where
E : χ̃01 energy and
X : matter depth.λ
χ̃01(E)−1 = NAσtot
χ̃01N
(E): interaction length
Ks(E , y) = σtots (E)−1dσs(Ey )/dy : kernel
Ey : E/(1 − y)
mSUGRA scenariowith mg̃ > mq̃ =⇒
σtots (χ̃0
1 + qi → X ) ≈σtot
s (χ̃01 + qi → χ̃0
1 + qi)
S. Bornhauser (University of Bonn) Cosmic neutralinos SUSY08 6 / 15
Solution method...based on the first order Taylor expansion:
Fχ̃
01(E , X + dX ) = F
χ̃01(E , X ) + dX
∂Fχ̃
01(E , X )
∂X+ · · · where
the boundary condition Fχ̃
01(E , 0) is given by the incident χ̃0
1 flux(e.g. SHdecay: hep-ph/0211406).
Check of the results:
For s- and t-channel: χ̃01 + qi → · · · → χ̃0
1 + X
=⇒ Φχ̃
01=
∫ Emax
mχ̃
01
Fχ̃
01(E , X )dE = const.
Fχ̃
01(E , 0) = 0 for E > Emax
independent of X
S. Bornhauser (University of Bonn) Cosmic neutralinos SUSY08 7 / 15
Transport equation for s−channel scattering (bino-dominated χ̃01)
1e+06 1e+07 1e+08 1e+09 1e+10 1e+11 1e+12E χ ~1
0[GeV]
1e-73
1e-72
1e-71
1e-70
1e-69
E χ ~
1 0. F
χ ~1 0(E
χ ~1 0)[
GeV
3 ]
initial spectrum0.09.X
max0.45.X
max1.00.X
max
xmax : maximalcolumn depth ofthe Earth
XXmax
Φχ̃
01(X)
Φχ̃
01(0)
0.09 1.0000.45 1.0001.00 1.001
(integrated from103 to 1012 GeV)
S. Bornhauser (University of Bonn) Cosmic neutralinos SUSY08 8 / 15
Transport equation fort−channel scattering(higgsino-dominated χ̃
01)
1e+05 1e+06 1e+07 1e+08 1e+09 1e+10 1e+11 1e+12E χ ~1
0[GeV]
1e-73
1e-72
1e-71
1e-70
1e-69
E χ ~
1 0. F
χ ~1 0(E
χ ~1 0)[
GeV
3 ]
initial spectrum0.09.X
max0.45.X
max1.00.X
max
xmax : maximalcolumn depth ofthe Earth
XXmax
Φχ̃
01(X)
Φχ̃
01(0)
0.09 1.0020.45 1.0021.00 1.004
(integrated from105 to 1012 GeV)
S. Bornhauser (University of Bonn) Cosmic neutralinos SUSY08 9 / 15
Event rates...can be calculated with the help of F
χ̃01(E , X ). For example, the
neutralino event rates for the s-channel are given by:
N =
∫ Emax
Emin
dEvis
∫ Xmax
Xmin
dX∫ ymax
0
dyy
dσs(Evisy )
dyF
χ̃01(Evis
y, X )V
V ∝ Veffǫdc t , whereVeff: w.e. effective volume,ǫdc : duty cycle,t : measurement period.However: One will need at least teraton scale targets to detectneutralinos...
Future satellite experiments
EUSO: stay on the ISS; monitors a surface area of O(105) km2 ⇒
target volume of ≈ 2.4 teratons
OWL: two satellites; monitors a surface area of O(106) km2 ⇒
target volume of ≈ 10.0 teratonsS. Bornhauser (University of Bonn) Cosmic neutralinos SUSY08 10 / 15
Event rates for higgsino–like χ̃01
Evis ≥ 106 GeV, MX = 1012 GeV Nχ̃
01
Nντ
qq̄ 0.19 3.87qq̃ 0.58 7.04l l̃ 7.37 14.17
5 × qq̃ 4.97 45.00
Evis ≥ 109 GeV, MX = 1012 GeV Nχ̃
01
Nντ
qq̄ 0.0089 0.0001qq̃ 0.0608 0.0001l l̃ 2.5121 0.0003
5 × qq̃ 0.2624 0.0006
Evis ≥ 106 GeV, MX = 1016 GeV Nχ̃
01
Nντ
qq̄ 0.0105 0.4448qq̃ 0.0078 0.3079l l̃ 0.0063 0.2917
5 × qq̃ 0.0124 0.4940
Evis ≥ 109 GeV, MX = 1016 GeV Nχ̃
01
Nντ
qq̄ 0.000927 0.000007qq̃ 0.001258 0.000005l l̃ 0.001735 0.000005
5 × qq̃ 0.001807 0.000005
Parameters of thegiven results:
target volume:10Tt
m. period: 1y
duty cycle: 10%
Detectable if:
mass of Xparticle close toits lower bound
large ratio ofneutralino andproton fluxes
experimentmust be able todetectCerenkov light
S. Bornhauser (University of Bonn) Cosmic neutralinos SUSY08 11 / 15
1e+06 1e+07 1e+08 1e+09 1e+10 1e+11 1e+12E ν [GeV]
1e-72
1e-71
1e-70
1e-69
1e-68
E ν . F
ν (E
ν )[G
eV3 ]
initial spectrum0.09.X
max0.45.X
max1.00.X
max
Event rates for higgsino–like χ̃01
Evis ≥ 2 · 107 GeV, MX = 1012 GeV Nχ̃
01
Nντ
qq̄ 0.10 0.18qq̃ 0.35 0.03l l̃ 5.41 0.67
5 × qq̃ 2.78 1.80
Higher lower bound for Evis
leads to higher reduction ofχ̃0
1 fluxes compared to νfluxes due to the softerneutrino spectra.
S. Bornhauser (University of Bonn) Cosmic neutralinos SUSY08 12 / 15
Event rates for bino–like χ̃01
Evis ≥ 106 GeV, MX = 1012 GeV ND1 ND2 ND3
qq̄ 0.055 0.039 0.017qq̃ 0.130 0.099 0.051l l̃ 0.805 0.796 0.586
5 × qq̃ 1.294 0.944 0.434
Evis ≥ 109 GeV, MX = 1012 GeV ND1 ND2 ND3
qq̄ 0.0005 0.0034 0.0055qq̃ 0.0021 0.0142 0.0234l l̃ 0.0381 0.2551 0.4321
5 × qq̃ 0.0145 0.0992 0.1571
Evis ≥ 106 GeV, MX = 1016 GeV ND1 ND2 ND3
qq̄ 0.0026 0.0020 0.0010qq̃ 0.0020 0.0015 0.0007l l̃ 0.0018 0.0018 0.0007
5 × qq̃ 0.0032 0.0024 0.0012
Squark masses:
D1: 370 GeV
D2: 580 GeV
D3: 1000 GeV
Bino–like neutralino fluxes of many X decay scenarios remain invisible;even monitoring of the whole Earth’s surface “only” leads to Veff of5000 teratons
S. Bornhauser (University of Bonn) Cosmic neutralinos SUSY08 13 / 15
Use of the Moon as a detectorMoon’s surface covered by regolith(homogeneous dielectric medium) upto a height of 10m
UHE particles produce radio waves viaAskarayan effect and the emission ofCerenkov light, respectively(Dagkesamanskii and Zheleznyk)
Event rates for ν and χ̃01
Evis ≥ 1010 GeV, MX = 1012 GeV Nν
total Nχ̃
01
qq̄ 2.46 0.10qq̃ 4.25 1.10l l̃ 65.04 60.10
5 × qq̃ 11.29 1.22
Evis ≥ 1010 GeV, MX = 1016 GeV Nν
total Nχ̃
01
qq̄ 8.38 0.04qq̃ 5.52 0.05l l̃ 6.09 0.19
5 × qq̃ 4.97 0.07
Parameters of the givenresults:
target volume: 320 Tt
E threshold: 1010 GeV
duty cycle: 40%
S. Bornhauser (University of Bonn) Cosmic neutralinos SUSY08 14 / 15
Summary:
there are cosmic rays with E >∼ 1011 GeV
possible explanation within the scope of TDMs
detection of χ̃01’s would be a “smoking gun” for TDMs
detection of UHE χ̃01’s might be possible with aid of future satellite
experiments like EUSO or OWL if:neutralinos are higgsino–likeexperiments can detect Cerenkov lightmass of X particle is near its lower boundlarge ratio of neutralino and proton fluxes
detection of UHE ν ’s and χ̃01’s might be possible through
measurement of radio waves which are produced in the Moon’smatter via the Askarayan effect
S. Bornhauser (University of Bonn) Cosmic neutralinos SUSY08 15 / 15