[PDF] - High-energy cosmic ra ys and w eak-scale string theo ries PDF Document

SLIDE 1 High-energy cosmic ra ys and w eak-scale string theo ries Michael Pl umacher Universit y

f

Oxfo rd M. Kachelrie, M. P .: Phys. Rev. D 62, 103006; astro-ph/0005309 Outline

Intro

duction

La

rge extra dimension s

Neutrino-Nucleon

scattering

Conclusions

SLIDE 2 Intro duction Detection

f

cosmic ra ys:

Energy

sp ectrum: p

w

er la w b ehaviour

ver

a wide range

f

energies

p

rima ries a re shielded b y the atmosphere

fo

r energies less than

100

T eV the cosmic ra y ux is high enough to allo w direct detection

f

p rima ries from space

ab
ve
100

T eV sho w ers

f

seconda ry pa rticles can b e detected from the ground Comp

sition:
muon

content and depth

f

sho w er maximum p rovide info rmation

n

the chemical comp

sition
rule
f

thumb: heavy nuclei p ro duce air sho w ers with a higher muon content and a sho w er maximum higher up in the atmosphere than light

nes

SLIDE 3

SLIDE 4 Greisen-Zatsepin

Kuzm

in (GZK) cuto at energies E > 6

10

19 eV p rotons lose energy due to pion photop ro duc tion p +

CMB
!
+
!

p +

fo

r nuclei at E

>

10 19 eV: photo disint egra tion in the CMB and IR background 56 F e +

CMB
!

55 F e + n photons interact with the CMB and the geomagnetic eld ) pair p ro duction ab

ve
200

T eV Events ab

ve

10 20 eV have b een

bserved:

events a re consistent with nucleon p rima ries:

longitudin

al sho w er p role

f

the Fly's Ey e event b est tted b y a p roton

lateral

electron and muon distribut ion s measured b y A GASA indicate that the p rima ries a re nucleons isotropic a rrival directions ) extragalactic

rigin

no plausibl e astrophysical sources within

100

Mp c Could neutrinos b e the p rima ries?

SLIDE 5

0.01 0.1 1 10 1017 1018 1019 1020 1021 E2.7dN/dE (cm-2sr-1s-1GeV1.7) E (eV / nucleus) All-particle spectrum α=2.25 α=2.0 Super-GZK Akeno [16] MSU [17] AGASA [18] Haverah Park [19] Yakutsk [20] Fly’s Eye (mono) [21] Fly’s Eye (stereo) [6]

SLIDE 6

100 200 300 250 500 750 1000 Depth in g/cm2 Number of particles/109

500 550 600 650 700 750 800 850 900 16.5 17 17.5 18 18.5 19 19.5 20

Xmax (g/cm2)

log10 ( E(eV) ) Fly’s Eye [6] HiRes-MIA [7] Haverah Park [8] Yakutsk [9] SIBYLL 2.1 [11] QGSJET [12]

SLIDE 7 La rge Extra Dimension s Consider a w

rld

with

extra

dimensions Compacticati

n

radius R Standa rd mo del elds live

n

a 3-b rane ) they do not feel the extra dimensions

nly

gravit y p ropagates in the higher dimensional space ) Gravit y is w eak due to the la rge compacticatio n radius G 1 N = 8 R

M
+2

D F undamental mass scale M D

1

T eV ) R

1

mm fo r

=

2 Solution to the hiera rchy p roblem? 4-d Planck scale

electro

w eak scale new hiera rchy p roblem: M D

1

T eV

R

1

10

3 eV

SLIDE 8 Astrophysical b

unds

Sup ernova b

unds:

SN 1987a (Hanha rt et al., astro-ph/0102063) energy loss due to KK emission ) sho rtening

f

the neutrino signal

=

2 ) M D > 60 T eV

=

3 ) M D > 5 T eV SN contributi

ns

to

ra

y background: (S. Hannestad et al., hep-ph/0103201) deca ys

f

KK gravitons emitted b y all SNe

ver

the age

f

the universe K K ! 2 ; e + e

;
)

contribution to the diuse

ra

y background

=

2 ) M D > 84 T eV

=

3 ) M D > 7 T eV

SLIDE 9 Cosmol

gi

cal Bounds KK gravitons a re p ro duced in the ea rly universe at high temp eratur es: pair annihilat ion : 2 ; e + e

;
!

K K gravi-b remsstrahl un g gravi-Compton scattering contributio ns to

ra

y background : (S. Hannestad, hep-ph/0102290) T M AX during reheating 1 GeV

=

2 ) M D > 170 T eV

=

3 ) M D > 20 T eV

=

4 ) M D > 5 T eV

=

5 ) M D > 2 T eV contribution to the energy densit y

f

matter (M. F airbairn, hep-ph/0101131) ) ea rlier matter-radia tion equalit y ) lo w age

f

the universe T RE H = 170 MeV and t > 12:8 Gyrs

=

2 ) M D > 10 3 T eV

=

3 ) M D > 60 T eV

=

4 ) M D > 9 T eV

SLIDE 10 Naturally realized in T yp e I string theo ries:

SM

elds co rresp

nd

to

p

en strings b eginnin g and ending

n

D-b ranes

gravitons

co rresp

nd

to closed strings which can p ropagate in the higher dimensiona l space ) from

ur

4-dimensiona l p

int
f

view the graviton is an innite to w er

f

Kaluza-Klein excitations with masses m 2 ~ n = ~ n 2 R 2 assume g ~ n = p 8 M Pl in p ro cesses mediated b y a virtual graviton

ne

has to sum

ver

all KK-mo des X ~ n 1 p 2

m

2 ~ n diverges fo r

>

1 ! intro duce cuto b y hand j ~ nj < M st R

SLIDE 11 ) Neutrino-Nucl eon cross section at high energies

tot
E

10 20 eV

2
1

T eV M D

4

ba rn 4-dim eld theo ry result not valid fo r E > M D eld theo retical unita rizati

n:
tot
4

s M 4 D

E

10 20 eV

1

T eV M D

4

mba rn Right

rder
f

magnitude to explain the ultrahig h energy cosmic ra y events! Ho w ever, lo w energy eective theo ry not valid fo r E

10

20 eV nite width

f

the b ranes b ecomes imp

rtant

b rane tension supp resses the couplings

f

higher KK mo des g n = g e c(n=R) 2 = M 2 D ; where c = 1 2

M

D f

4

SLIDE 12 Neutrino-Nucleon Scattering mediated b y graviton in the t-channel Sum

ver

all KK mo des: exp

nential

supp resion

f

couplings

f

higher KK mo des p rovides a dynamical cuto P ( ^ t ) = R

P

~ n exp ( cm 2 ~ n = M 2 D ) ^ tm 2 ~ n =

=2

( ^ t )

=21

exp

c

^ t M 2 D

1
2

;

c

^ t M 2 D

Cross-section

in the lo w-energy limit, s

M

2 D Neutrino-qua rk scattering: d d xd ^ t = 1 512 ^ s 2 P 2 ( ^ t ) M 4+2 D

32

^ s 4 + 64 ^ s 3 ^ t + 42 ^ s 2 ^ t 2 + 10 ^ s ^ t 3 + ^ t 4

gluon-neutrin
scattering

d

dxd

^ t = 1 32 ^ s 2 P 2 ( ^ t) M 4+2 D

2

^ s 4 + 4 ^ s 3 ^ t + 3 ^ s 2 ^ t 2 + ^ s ^ t 3

SLIDE 13 T

tal

cross section:

1e-09 1e-08 1e-07 1e-06 1e-05 1e-04 0.001 0.01 0.1 1 10 17 17.5 18 18.5 19 19.5 20 20.5 21

log(Eν/eV) σνN/mbarn CC 6 TeV 15 TeV 30 TeV

) M D

1

T eV needed fo r

KK

N

=

1

10

mba rn energy-loss in SN 1987a due to KK graviton p ro duction M D

>

60 T eV Age

f

the universe

>

12 Gyrs ) M D

>

10 3 T eV

SLIDE 14 Energy transfer: y = (E

E
)=E
nucleon-nuc

leon collisions: y

0:6

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 3 4 5 6 7 8 9 10 11 12

log(Eν/GeV) y CC g q

) neutrinos a re deeply p enetrati ng pa rticles

SLIDE 15 Cross section in the high-energy limit s

M

2 D 1. e. 4-dim. theo ry not valid fo r s > M 2 D 2. and

KK

N

violates

unita rit y ) calculation

f
KK

N

in

string theo ry needed Conservative upp er b

und:

Unita rize the cross section:

Regge

Amplitude

eik
nal

metho d xes the energy dep enden ce

f

the cross section:

tot

/ ln 2 (s=s ) cho

se

constant as

KK

N

(s

), where s

M

D is the scale where s-w ave unita rit y is violated

tot

(s) =

KK

N

(M

2 D ) ln 2

s=

M 2 D

s=

M 2 D

0:363

SLIDE 16 String theo ry calculati

n:

(Co rnet, Illana and Masip, hep-ph/0102065) T yp e I IB

rbifold

6 la rge extra dimension s SM elds conned to N D3 b ranes V eneziano Amplitude S (s; t) = (1

s)(1
t)

(1

s
t)

gives a series

f

p

les

and zero es ) string amplitude can b e app ro ximated as a sum

ver

s-channel resonances (lepto qua rks) Neutrino-Nucle

n

total cross section: M S = 2:0 T eV M S = 0:5 T eV SM (i) (ii) (i) (ii) E

[GeV℄
N

[ m 2 ℄ 10 13 10 12 10 11 10 10 10 9 10 8 10 7 10 6 10 5 10 4 10 3 10 2 10 29 10 30 10 31 10 32 10 33 10 34 10 35 10 36 10 37

SLIDE 17 Conclusions Neutrino-nucl eon interaction s via KK gravitons in mo dels with la rge extra dimension s cannot explain the ultrahigh energy cosmic ra ys:

supp

ression

f

KK couplings due to b rane uctuations )

KK

N

is

small

energy

transfer p er interaction is small neutrinos a re deeply p enetrati ng pa rticles ) sho w ers initiated b y p rotons and neutrinos a re clea rly distinguish ab le Outlo

k:

neutrino induced ho rizontal air sho w ers ma y give interesting b

unds
n

the string scale