Signals of TeV Gravity at Neutrino Telescopes

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1 Signals of TeV Gravity at Neutrino Telescopes OUTLINE: Motivation 2 TeV gravity José I Illana CAFPE & Granada U in collaboration with: Manuel Masip and Davide Meloni 3 BH versus eikonal events 4 Signals at neutrino telescopes 5 Conclusions Based on: PRL 93, 502 [hep-ph/ ] and PRD 72, [hep-ph/ ] JI Illana SUSY 2005, Durham, 8-23 July 05

2 Motivation Cosmogenic neutrinos (GZK) 00 E ν dφ/de ν [km 2 sr 2 yr ] Downward neutrinos [bin km 2 yr ] 0 3 p + γ 27K + n + π + (p + π 0 ) ν, γ probes of new TeV physics in interactions with terrestrial Nucleons: s = 2m N E ν > 0 TeV E ν [GeV] E ν [GeV] 0 0 Gravity dominates at transplanckian energies This is the case of cosmogenic νn interactions in models with extra dimensions if the fundamental scale M D TeV νn short-distance interactions (b R S ) produce mostly light BH ( xs M D R S ) with uncertain (geometrical) cross sections At larger distances (b > R S ) transplanckian gravitational interactions are elastic, cross sections are reliable (eikonal approximation) and independent of compactification details Neutrino telescopes are ideal experiments to detect these elastic processes JI Illana SUSY 2005, Durham, 8-23 July 05 2

3 TeV gravity Two parameters: number n of compact extra dimensions (only seen by gravity) and M D : (eg toroidal) G D (2πR) n G N = (2π)n 8πM n+2 D, G N M 2 P M 2 P = (8πR n )M n+2 D Size R of extra dims if M D TeV: (isotropic toroidal compactification) n R 0 8 km 0 mm nm fm R 0 8 ev 0 3 ev 00 ev 00 MeV In processes below M D : graviton emission (KK tower proportional to M c = R ) probes R M D is deduced given n and compactification assumptions: [Mirabelli, Perelstein, Peskin 99] [Giudice, Rattazzi, Wells 99] Collider bounds (LEP, Tevatron): M D > 4 (06) TeV if n = 2 (6) [Feruglio 04] Astrophysical and cosmological: very stringent from SN cooling but not so compelling In transplanckian collisions: direct probe of M D Extra dimensions effectively infinite JI Illana SUSY 2005, Durham, 8-23 July 05 3

4 Scales in the transplanckian and forward regimes Planck length: λ P M D (quantum gravity) Schwarzschild radius: R S M D ( s M D ) n+ (gravitational collapse) Transplanckian: gravity dominant and s > M D λ P < R S Elastic and forward: t/s = q 2 /s = ( cos 2 θ ) (eikonal approximation valid) ( ) s n+ ie deflection angle θ MD n+2 b RS R n+ S b b Classical physics: small curvature, linearized gravity (negligible non-linear couplings) A new scale emerges if n > 0: b c M D ( s M D ) 2 n R S b b c (ie q b c ): classical trajectory two scattering regions: b b c > R S (ie q b c ): quantum mechanical effects (but not quantum gravity) JI Illana SUSY 2005, Durham, 8-23 July 05 4

5 The eikonal approximation Elastic scatteing ν (q, q, g in N) exchanging D dim gravitons [ t Hooft 87, Amati, Ciafaloni, Veneziano 87, Kabat, Ortiz 92] A Born = s2 d n q T MD n+2 t qt 2 }{{} KK tower Resumming ladder and cross-ladder diagrams taking t/s : A eik (s, t) = 2s i d 2 b e iq b ( e iχ(s,b) ), χ(s, b) = 2s d 2 q (2π) 2 e iq b A Born (s, q 2 ) UV cutoff dependence Integrating q T up to an UV cutoff Λ (eg M D or M string ), the eikonal phase gets: ( ) n [ bc π χ(s, b) = b 2Λb e Λb A n (Λb) ], b nc (4π) n 2 ( ) n s Γ 2 2 MD n+2 with A n (Λb ) 2 2 n /Γ 2 (n/2) Cutoff dependence negligible as long as b Λ (b R S > M D ) JI Illana SUSY 2005, Durham, 8-23 July 05 5

6 The eikonal amplitude Although eikonal phase χ(s, b) = ( bc b ) n diverges for b 0 the eikonal amplitude finite: A eik (s, q) = 4πsb 2 cf n (b c q), F n (u) i 0 dv v J 0 (uv) ( e iv n ) (v b/b c ) Classical domain (q b c ): χ large, dominated by saddle point b s = b c (n/qb c ) n+ u : F n (u) in n+ u n+2 n+ n + e i(n+)( u n ) n n+ Quantum domain (q b c u : F n>2 (u) i 2 Γ ( 2 n ): χ, dominated by b b c (not b = as Coulomb): ) e iπ/n, F 2 (u) ln u 4 + iπ 4 Always non-perturbative: χ > JI Illana SUSY 2005, Durham, 8-23 July 05 6

7 A eik (s, q) = 4πsb 2 cf n (b c q) 4 F 2 (u) Re Im Mod F 6 (u) Re Im Mod The (partonic) cross sections Eikonal: dσ eik dˆt = 6πŝ 2 A eik(ŝ, ˆt) 2 = πb 4 c F n (b c t) 2 Optical theorem: σ eik σ tot = ImA eik(ŝ, 0) ŝ = π 2 b 2 c/2, for n = 2 2πb 2 cγ ( ) 2 n cos π, for n > 2 n One can see that: σ tot = σ eik if Imχ = 0 σ BH modelled by large Imχ ŝ 2 n Black Hole: σ BH = πr 2 S ŝ n+ < σ eik JI Illana SUSY 2005, Durham, 8-23 July 05 7

8 Non-linear corrections and soft graviton emission Non-linear corrections (H diagrams) strong gravitational coupling when: ˆt = q 2 ŝ = xs b b s R S (black hole formation) (Soft) graviton emission Im(χ H ) negligible if y = q 2 /ŝ : [Giudice, Rattazzi, Wells 02] [Amati, Ciafaloni, Veneziano 90] ( ) 3n+2 b r (b n c RS 2n+2 ) br 3n+2, Nsoft = Im(χ H ) y 3n+2 2n+2 b ( ŝ M 2 D ) n+2 2n+2 with transverse momentum: Q N soft b, b s M D ( ym 2 D ŝ ) n+2 Radiated energy in lab frame (νn, N at rest): E rad = γq, γ = Eν 2xm N JI Illana SUSY 2005, Durham, 8-23 July 05 8

9 νn cross sections Hard processes (BH formation): initial neutrino destroyed (b < R S ) σ νn BH = M 2 D /s dx πr 2 S(ŝ) i=q, q,g f i (x, µ), ŝ = xs, s = 2m N E ν Soft processes (eikonal): neutrino loses small fraction y of its energy and keeps going dσ νn eik dy = M 2 D /s dx ŝ πb 4 c F n (b c q) 2 i=q, q,g q = xys, µ = b, b f i (x, µ), b s, q > b c b c, q < b c y = E ν E ν E ν σ νn soft = ymax y min dy dσνn eik dy, y max 02 (eik: b > R S ), y min = E thres /E ν JI Illana SUSY 2005, Durham, 8-23 July 05 9

10 BH versus eikonal events /dy [mbarn] dσ eik νn M D = TeV n = σ soft νn [mbarn] M D = TeV σbh [mbarn] y y min Upper lines: E ν = 0 0 GeV Lower lines: E ν = 0 8 GeV JI Illana SUSY 2005, Durham, 8-23 July 05 0

11 BH versus eikonal events /dy [mbarn] dσ eik νn M D = 3 TeV n = σ soft νn [mbarn] M D = 3 TeV σbh [mbarn] y y min Upper lines: E ν = 0 0 GeV Lower lines: E ν = 0 8 GeV JI Illana SUSY 2005, Durham, 8-23 July 05

12 Example One UHE neutrino of E ν = 0 0 GeV with E thres = 00 TeV and M D = TeV Number of eikonal interactions before the neutrino gets destroyed: L BH /L eik = σ soft /σ BH where L σ = (ρn A σ) is the mean free path [L SM = 440 km] n = 2 n = 6 σ BH mbarn mbarn σ soft mbarn mbarn L BH /L eik L BH in ice 7 km 4 km E loss eik in L BH GeV GeV E loss rad in L BH GeV GeV E loss eik in km GeV GeV E loss rad in km GeV GeV JI Illana SUSY 2005, Durham, 8-23 July 05 2

13 Signals at neutrino telescopes Cosmogenic neutrinos per flavour (consistent with p and γ at AGASA/HiRes and EGRET) 00 E ν dφ/de ν [km 2 sr 2 yr ] Downward neutrinos [bin km 2 yr ] E ν [GeV] E ν [GeV] Higher : 00 % EGRET 820 km 2 yr in [0 8, 0 ] GeV Lower : 20 % EGRET 370 km 2 yr [Semikoz, Sigl 04] Minimal : No protons above E GZK 35 km 2 yr [Fodor, Katz, Ringwald 03] JI Illana SUSY 2005, Durham, 8-23 July 05 3

14 Survival probability: P surv (E ν, θ z ) = e x(θ z)n A (σ SM +σ BH ) Column density: x(θ z ) = Interaction probability: P int (E ν ) e LρN Aσint νn θ z dl ρ(l, θ z ) ρ ice d(θ z, d v, R ) (atmosphere negligible) with longitudinal detector size L 0 P surv Pint BH P eik int P BH event P eik event n = 2 0 P surv Pint BH P eik int P BH event P eik event n = 6 IceCube ( ) E ν = 0 0 GeV [P event = P surv P int ] M D [TeV] M D [TeV] 25 3 N events = 2πAT de ν dφ νi ν i, ν i de ν d cos θ z P surv P int in time T for detector area A JI Illana SUSY 2005, Durham, 8-23 July 05 4

15 Multiple-bang events If detector L larger than interaction length L 0 = (ρn A σ eik ), prob of N > bangs: 0 [P N event = P surv P N ] IceCube ( ) E ν = 0 0 GeV n = 2 P event Pevent 2 P event >2 P N (L) = e L/L (L/L 0) N 0 N! Probability of at least one interaction: P int = N= P N = e L/L 0 Probability of more than one interaction: n = M D [TeV] P mult = P > = e L/L 0 ( + L/L 0 ) Average (and most probable) # of bangs: N = N= NP N = L/L 0 In a SM CC interaction (or in BH evaporation) a double-bang ν τ event may occur only if < E τ /GeV < 0 7 in IceCube [25 m < cτ < km] Prob is just JI Illana SUSY 2005, Durham, 8-23 July 05 5

16 Example Again one UHE neutrino of E ν = 0 0 GeV with E thres = 00 TeV M D = TeV 0 P int n = 2 n = 6 IceCube/AMANDA 0 deg [8 km] deg [4 km] BH (n=6) 84 deg [7 km] BH (n=2) 92 deg [440 km] SM M D = 2 TeV E ν = 0 0 GeV E sh [GeV] L = km M D = TeV n = 2 (6) P SM int = P BH int = 006 (022) P eik = 036 (027) P eik 2 = 05 (006) P eik >2 = 005 (0008) JI Illana SUSY 2005, Durham, 8-23 July 05 6

17 Bounds from air shower experiments Hadronic shower energy (in air or ice): BH evaporation: E sh 08E ν (around 80% to hadrons) Eikonal events: E sh = ye ν (typically y ) Air shower experiments sensitive to E sh > 0 9 GeV Exposures [km 3 we sr yr] Auger ( yr) AGASA had Fly s Eye EνdΦ/dEν [km 2 sr yr ] Limits on M D from eikonal events similar to those from BH production: M D > (5) TeV for n = 2 (6) E sh [GeV] JI Illana SUSY 2005, Durham, 8-23 July 05 7

18 Shower energy distribution at IceCube 0 Higher Flux n = 2 Higher Flux n = 6 Number SM (dotted) CC NC SM 2-bang HF LF Lower Flux n = 2 Lower Flux n = 6 Events per bin and year for M D = 2 TeV for n = 2 (6): Number BH (dashed) Eikonal (solid) HF 343 (22) 39 (85) LF 07 (425) 06 (620) E sh [GeV] E sh [GeV] JI Illana SUSY 2005, Durham, 8-23 July 05 8

19 Contained events at IceCube and AMANDA 00 0 IceCube n = 2 IceCube n = 6 IceCube: L = km A = km 2 AMANDA: L = 07 km A = 003 km 2 Contained events per year: 0 0 AMANDA n = 2 AMANDA n = 6 Higher Flux Lower Flux (thick) (thin) Eikonal (solid) Multi-bang (dashed-dotted) M D [TeV] M D [TeV] 5 6 BH (dashed) JI Illana SUSY 2005, Durham, 8-23 July 05 9

20 Conclusions Cosmogenic neutrinos (E ν > 0 8 GeV) probe TeV physics, in particular suffer transplanckian νn scattering if gravity is at TeV Hard interactions (b < R S ): geometrical cross section has uncertainties for light BH, and they are subdominant Soft interactions (b > R S ): elastic processes described by the eikonal approximation, where the neutrino loses a small fraction of energy producing a hadronic shower No theoretical uncertainties: compactification-detail independent, UV-cutoff insensitive, negligible graviton radiation and suppressed non-linear corrections Clear signal in large neutrino telescopes: contained hadronic shower above threshold (E sh = ye ν > 0 5 GeV) and no charged leptons TeV gravity signals cannot be confused with ordinary SM events with higher ν flux Absence of muons interaction accompanied by muons in 24% of SM interactions Multiple bangs rare double-bang tau events in SM IceCube could explore up to M D 5 TeV JI Illana SUSY 2005, Durham, 8-23 July 05 20