TeV Gravity at Neutrino Telescopes

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1 TeV Gravity at Neutrino Telescopes OUTLINE: José I Illana CAFPE & Granada U in collaboration with: Manuel Masip and Davide Meloni Motivation: cosmogenic neutrinos and TeV gravity 2 Gravitational interactions 3 Signals at neutrino telescopes 4 Conclusions Based on: PRL 93, 502 [hep-ph/ ] and PRD 72, [hep-ph/ ] JI Illana Workshop on Exotic Physics with Neutrino Telescopes, Uppsala, September 06

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 have access to TeV physics in interactions with terrestrial Nucleons: s = 2m N E ν > 0 TeV E ν [GeV] E ν [GeV] 0 0 νn transplanckian interactions ( s > M D ) if M D TeV in D > 4 dimensions String Theory is soft in the UV: Scattering amplitudes 0 except forward (destructive interference of string excitations) In forward amplitudes only zero mode survives Open strings (gauge) spin : A s t Closed strings (gravity) spin 2: A MD 2 s 2 t Gravity dominates JI Illana Workshop on Exotic Physics with Neutrino Telescopes, Uppsala, September 06 2

3 Extra dimensions Parameters: number n of compact extra dimensions (only seen by gravity) and M D r R : F = G N m m 2 r 2 (D = 4) G N M 2 P r R : F = G D m m 2 r 2+n (D = 4 + n) G D = V n G N, G D (2π)n 8πM 2 D r = R : M 2 P = (8πR n )M 2+n D (if all equal and toroidal: V n = (2πR) n ) Size R of extra dimensions if M D TeV: 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, M R ) probes R (M D indirectly!) Collider bounds (LEP, Tevatron): M D > 4 (06) TeV if n = 2 (6) Astrophysical and cosmological: very stringent from SN cooling but indirect! In transplanckian collisions: direct probe of M D (model independent) JI Illana Workshop on Exotic Physics with Neutrino Telescopes, Uppsala, September 06 3

4 Gravitational interactions R S M D ( s M D ) n+, Planck length λp M D Transplanckian R S > λ P Short distance (b < R S ): strongly coupled (non-linear, high q 2 ) BH formation geometric cross section σ πr 2 S (estimate) Long distance (b R S ): weakly coupled (linear, low q 2 ) b λ P : classical gravity (quantum gravity acts inside event horizon) Small deflection angle (CM): ( ) s n+ θ MD n+2 b RS q 2 /s = n+ b 2 ( cos θ ) Elastic process (reliable) calculation based on the eikonal approximation JI Illana Workshop on Exotic Physics with Neutrino Telescopes, Uppsala, September 06 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 taking t/s : exponential of Born amplitude A eik (s, q) = 4πsb 2 cf n (b c q) with b c [ (4π) n 2 2 Partonic cross sections σ eik = ( ) n Γ 2 [n = 2] π 2 b 2 c σ BH = πr 2 S s n+ ] n s MD n+2 [n > 2] 2πb 2 cγ ( 2 n F n (u) i ) cos π n 0 s 2 n dv v J 0 (uv)(e i eikonal phase v n ), v b/b c F 2 (u) Re Im Mod F 6 (u) Re Im Mod JI Illana Workshop on Exotic Physics with Neutrino Telescopes, Uppsala, September 06 5

6 νn cross sections Hard processes (BH formation): initial neutrino destroyed 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, µ = R S 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 f i (x, µ), y = E ν E ν E ν σ νn soft = ymax y min dy dσνn eik dy, y max 02 (eikonal valid), y min = E thres /E ν q 2 = xys, µ = b, b b s = b c (n/qb c ) n+, q > b c b c, q < b c JI Illana Workshop on Exotic Physics with Neutrino Telescopes, Uppsala, September 06 6

7 BH versus eikonal events /dy [mbarn] dσ eik νn M D = TeV n = y E ν = 0 0 GeV σ soft νn [mbarn] M D = TeV y min σbh [mbarn] eg E thres = 00 TeV y min = 0 5 JI Illana Workshop on Exotic Physics with Neutrino Telescopes, Uppsala, September 06 7

8 BH versus eikonal events /dy [mbarn] dσ eik νn M D = 3 TeV n = y E ν = 0 0 GeV σ soft νn [mbarn] M D = 3 TeV y min σbh [mbarn] eg E thres = 00 TeV y min = 0 5 JI Illana Workshop on Exotic Physics with Neutrino Telescopes, Uppsala, September 06 8

9 Example (I) 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 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 in ice 7 km 4 km L BH /L eik 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 Workshop on Exotic Physics with Neutrino Telescopes, Uppsala, September 06 9

10 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 Workshop on Exotic Physics with Neutrino Telescopes, Uppsala, September 06 0

11 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 Survival probability: P surv (E ν, θ z ) = e x(θ z)n A (σ SM +σ BH ) with x the column density Interaction probability: P int (E ν ) e Lρ icen A σint νn with longitudinal detector size L P surv P int P surv P int eik P event P event 0 n = 2 0 n = 6 BH IceCube ( ) E ν = 0 0 GeV [P event = P surv P int ] M D [TeV] M D [TeV] 25 3 JI Illana Workshop on Exotic Physics with Neutrino Telescopes, Uppsala, September 06

12 Multiple-bang events When detector L larger than interaction length L 0 = (ρn A σ eik ) 0 [P N event = P surv P N ] IceCube ( ) E ν = 0 0 GeV n = 2 P event Pevent 2 P event >2 Probability of N > bangs: P N (L) = e L/L (L/L 0) N 0 N! Average (and most probable) # of bangs: n = 6 N = N= NP N = L/L M D [TeV] 25 3 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 Workshop on Exotic Physics with Neutrino Telescopes, Uppsala, September 06 2

13 Example (II) Again one UHE neutrino of E ν = 0 0 GeV with E thres = 00 TeV M D = TeV IceCube/AMANDA 0 deg [8 km] 64 deg [4 km] BH (n=6) 84 deg [7 km] BH (n=2) 92 deg [440 km] SM Interaction probability P SM int = P BH int = 006 (022) P eik = 036 (027) [L = km, M D = TeV, n = 2 (6)] P eik 2 = 05 (006) P eik >2 = 005 (0008) JI Illana Workshop on Exotic Physics with Neutrino Telescopes, Uppsala, September 06 3

14 Shower energy distribution at IceCube 0 Higher Flux n = 2 Higher Flux n = 6 Number SM (ν l + ν l ) CC NC SM 2-bang HF LF Lower Flux n = 2 Lower Flux n = 6 Events/bin/year, n = 2 (6) [M D = 2 TeV]: Number BH Eikonal HF 343 (22) 39 (85) LF 07 (425) 06 (620) E sh [GeV] E sh [GeV] JI Illana Workshop on Exotic Physics with Neutrino Telescopes, Uppsala, September 06 4

15 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 Workshop on Exotic Physics with Neutrino Telescopes, Uppsala, September 06 5

16 Conclusions Cosmogenic neutrinos directly probe TeV gravity in transplanckian νn collisions Hard interactions (b < R S ): light BH (theoretical uncertainties), subdominant Soft interactions (b > R S ): elastic, small energy fraction lost to a hadronic shower No theoretical uncertainties (eikonal approx): compactification-detail independent, UV-cutoff insensitive, suppressed non-linear corrections, negligible graviton radiation Clear signal in large neutrino telescopes: contained hadronic shower, no l ± 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 Workshop on Exotic Physics with Neutrino Telescopes, Uppsala, September 06 6

17 UV cutoff dependence 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 M n+2 D d n q T 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 ) Integrating q T up to an UV cutoff Λ (eg M D or M string ), the eikonal phase gets: χ(s, b) = ( bc b ) n [ π 2Λb e Λb A n (Λb) ], b nc (4π) n 2 ( ) n Γ 2 2 with A n (Λb ) 2 2 n /Γ 2 (n/2) Cutoff dependence negligible as long as b Λ s M n+2 D (b R S > M D ) JI Illana Workshop on Exotic Physics with Neutrino Telescopes, Uppsala, September 06 7

18 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 Workshop on Exotic Physics with Neutrino Telescopes, Uppsala, September 06 8

19 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 Workshop on Exotic Physics with Neutrino Telescopes, Uppsala, September 06 9