High-energy cosmic ra ys and w eak-scale string theo ries - PDF document

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

Intro duction Detection of cosmic ra ys: � Energy sp ectrum: p o w er la w b ehaviour over a wide range of 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 of p rima ries from space � ab ove � 100 T eV sho w ers of seconda ry pa rticles can b e detected from the ground Comp osition: � muon content and depth of sho w er maximum p rovide info rmation on the chemical comp osition � rule of 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 ones

Greisen-Zatsepin -Kuzm in (GZK) cuto� 19 at energies E > 6 � 10 eV p rotons lose energy due to pion photop ro duc tion + 0 p + � � ! � � ! p + � CMB > 19 fo r nuclei at E 10 eV: photo disint egra tion in the � CMB and IR background 56 55 F e + � � ! F e + n CMB photons interact with the CMB and the geomagnetic �eld ) pair p ro duction ab ove � 200 T eV 20 Events ab ove 10 eV have b een observed: events a re consistent with nucleon p rima ries: � longitudin al sho w er p ro�le of 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 o rigin no plausibl e astrophysical sources within � 100 Mp c Could neutrinos b e the p rima ries?

All-particle spectrum Akeno [16] MSU [17] (cm -2 sr -1 s -1 GeV 1.7 ) 10 AGASA [18] Haverah Park [19] Yakutsk [20] Fly’s Eye (mono) [21] Fly’s Eye (stereo) [6] 1 E 2.7 dN/dE 0.1 α =2.25 α =2.0 Super-GZK 0.01 10 17 10 18 10 19 10 20 10 21 E (eV / nucleus)

300 Number of particles/10 9 200 100 0 0 250 500 750 1000 Depth in g/cm 2 900 850 800 X max (g/cm 2 ) 750 700 650 Fly’s Eye [6] HiRes-MIA [7] Haverah Park [8] Yakutsk [9] 600 SIBYLL 2.1 [11] QGSJET [12] 550 500 16.5 17 17.5 18 18.5 19 19.5 20 log 10 ( E(eV) )

La rge Extra Dimension s Consider a w o rld with � extra dimensions Compacti�cati on radius R Standa rd mo del �elds live on a 3-b rane ) they do not feel the extra dimensions only gravit y p ropagates in the higher dimensional space ) Gravit y is w eak due to the la rge compacti�catio n radius � 1 � � +2 G = 8 � R M N D F undamental mass scale M � 1 T eV ) R � 1 mm fo r � = 2 D Solution to the hiera rchy p roblem? 4-d Planck scale � electro w eak scale new hiera rchy p roblem: � 1 � 3 M � 1 T eV � R � 10 eV D

Astrophysical b ounds Sup ernova b ounds: SN 1987a (Hanha rt et al., astro-ph/0102063 ) energy loss due to KK emission ) sho rtening of the neutrino signal � = 2 ) M > 60 T eV D � = 3 ) M > 5 T eV D SN contributi ons to � -ra y background: (S. Hannestad et al., hep-ph/0103201 ) deca ys of KK gravitons emitted b y all SNe over the age of the universe + K K ! 2 � ; e e ; � � � � ) contribution to the di�use � -ra y background � = 2 ) M > 84 T eV D � = 3 ) M > 7 T eV D

Cosmol ogi 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 during reheating 1 GeV M AX � = 2 ) M > 170 T eV D � = 3 ) M > 20 T eV D � = 4 ) M > 5 T eV D � = 5 ) M > 2 T eV D contribution to the energy densit y of matter (M. F airbairn, hep-ph/0101131 ) ) ea rlier matter-radia tion equalit y ) lo w age of the universe T = 170 MeV and t > 12 : 8 Gyrs RE H 3 � = 2 ) M > 10 T eV D � = 3 ) M > 60 T eV D � = 4 ) M > 9 T eV D

Naturally realized in T yp e I string theo ries: � SM �elds co rresp ond to op en strings b eginnin g and ending on D-b ranes � gravitons co rresp ond to closed strings which can p ropagate in the higher dimensiona l space ) from our 4-dimensiona l p oint of view the graviton is an in�nite to w er of Kaluza-Klein excitations with masses 2 2 ~ n m = n ~ 2 R assume p 8 � g = ~ n M Pl in p ro cesses mediated b y a virtual graviton one has to sum over all KK-mo des 1 X 2 2 p � m ~ n ~ n diverges fo r � > 1 ! intro duce cuto� b y hand j ~ n j < M R st

) Neutrino-Nucl eon cross section at high energies 2 4 � E � � 1 T eV � � � � ba rn tot 20 10 eV M D 4-dim �eld theo ry result not valid fo r E > M D �eld theo retical unita rizati on: 4 4 � s � E � � 1 T eV � � � � mba rn tot 4 20 M 10 eV M D D Right o rder of magnitude to explain the ultrahig h energy cosmic ra y events! Ho w ever, lo w energy e�ective theo ry not valid fo r 20 E � 10 eV �nite width of the b ranes b ecomes imp o rtant b rane tension supp resses the couplings of higher KK mo des 4 � � 2 2 M 1 � c ( n=R ) = M g = g e ; where c = D D n 2 f

Neutrino-Nucleon Scattering mediated b y graviton in the t -channel Sum over all KK mo des: exp onential supp resion of couplings of higher KK mo des p rovides a dynamical cuto� 2 2 ( ) exp � cm = M ^ � � ~ n D P ( t ) = R P ^ 2 t � m ~ n n ~ � � � � ^ ^ ^ c t � c t � = 2 � = 2 � 1 = � � ( � t ) exp � � 1 � ; � 2 2 2 M M D D 2 Cross-section in the lo w-energy limit, s � M D Neutrino-qua rk scattering: ^ 2 d � 1 P ( t ) = � ^ 4+2 � 2 512 � s ^ d x d t M D 4 3 ^ 2 ^ 2 ^ 3 ^ 4 � � 32 s ^ + 64 s ^ t + 42 s ^ t + 10 s ^ t + t gluon-neutrin o scattering ^ 2 d � 1 P ( t ) 4 3 ^ 2 ^ 2 ^ 3 � � = 2 s ^ + 4 s ^ t + 3 ^ s t + s ^ t ^ 4+2 � 2 32 � s ^ d x d t M D

T otal cross section: 10 1 0.1 0.01 0.001 σ νN /mbarn 1e-04 CC 1e-05 6 TeV 15 TeV 30 TeV 1e-06 1e-07 1e-08 1e-09 17 17.5 18 18.5 19 19.5 20 20.5 21 log( E ν / eV) KK ) M � 1 T eV needed fo r � = 1 � 10 mba rn D N � energy-loss in SN 1987a due to KK graviton p ro duction > M 60 T eV � D > > 3 Age of the universe 12 Gyrs ) M 10 T eV � � D

Energy transfer: y = ( E � E 0 ) =E � � � nucleon-nuc leon collisions: y � 0 : 6 0.5 0.45 0.4 0.35 0.3 CC y 0.25 0.2 g 0.15 0.1 q 0.05 0 3 4 5 6 7 8 9 10 11 12 log( E ν / GeV) ) neutrinos a re deeply p enetrati ng pa rticles

2 Cross section in the high-energy limit s � M D 2 1. e�. 4-dim. theo ry not valid fo r s > M D KK 2. and � violates unita rit y N � KK ) calculation of � in string theo ry needed N � Conservative upp er b ound: Unita rize the cross section: � Regge Amplitude � eik onal metho d �xes the energy dep enden ce of the cross section: 2 � / ln ( s=s ) tot 0 KK cho ose constant as � ( s 0 ) , where s 0 � M is the D N � scale where s -w ave unita rit y is violated 0 : 363 2 KK 2 2 2 � � � � � ( s ) = � ( M ) ln s= M s= M tot N � D D D

String theo ry calculati on: (Co rnet, Illana and Masip, hep-ph/0102065) T yp e I IB o rbifold 6 la rge extra dimension s SM �elds con�ned to N D3 b ranes V eneziano Amplitude �(1 � � 0 s )�(1 � � 0 t ) S ( s; t ) = �(1 � � s � � t ) 0 0 gives a series of p oles and zero es ) string amplitude can b e app ro ximated as a sum over s -channel resonances (lepto qua rks) Neutrino-Nucle on total cross section: � 29 10 � 30 10 (ii) SM (i) = 0 : 5 T eV M S � 31 10 = 2 : 0 T eV M S � 32 10 ℄ 2 [ m (ii) � 33 10 (i) N � � � 34 10 � 35 10 10 � 36 10 � 37 2 3 4 5 6 7 8 9 10 11 12 13 10 10 10 10 10 10 10 10 10 10 10 10 [GeV℄ E �