Probing New Physics at the Highest Energies

Probing New Physics at the Highest Energies OUTLINE: José I Illana CAFPE & Granada U in collaboration with: Manuel Masip and Davide Meloni 1 Ultrahigh energy cosmic rays vs New Physics 2 TeV gravity explored by cosmogenic neutrinos 3 Long-lived gluinos from UHE nucleons 4 Conclusions PRL 93, 151102 [hep-ph/0402279], PRD 72, 024003 [hep-ph/0504234] and hep-ph/0611036 JI Illana Christmas Workshop, Madrid, 18-20 December 06 1

UHE cosmic rays vs New Physics Cosmic rays interactions reach several orders of magnitude beyond the largest energies available at (even future) man-made accelerators To probe UHE, new generation of large experiments already operating or being deployed (Extensive Air Showers: Auger, ; Neutrino telescopes: AMANDA, IceCube, ) Ideal laboratory to explore New Physics Two examples considered here: Cosmogenic neutrinos [ 10 7 GeV 10 11 GeV] Never observed (but expected) Low νn cross sections in SM good opportunity for testing TeV gravity Ultrahigh energy nucleons [until GZK cutoff 5 10 11, even beyond?] Well established flux Easier to extract NP if long-lived exotic particles eg split-susy gluinos JI Illana Christmas Workshop, Madrid, 18-20 December 06 2

TeV gravity explored by cosmogenic neutrinos JI Illana Christmas Workshop, Madrid, 18-20 December 06 3

Motivation Cosmogenic neutrinos (GZK) 100 E ν dφ/de ν [km 2 sr 2 yr 1 ] Downward neutrinos [bin 1 km 2 yr 1 ] 10 3 p + γ 27K + n + π + (p + π 0 ) 10 10 2 ν, γ have access to TeV physics in interactions with terrestrial Nucleons: s = 2m N E ν > 10 TeV 1 10 7 10 9 E ν [GeV] 10 11 10 7 10 9 E ν [GeV] 10 11 10 1 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 1: A s/t Closed strings (gravity) spin 2: A 1/M 2 D s 2 /t Gravity dominates Transplanckian collisions are a direct probe of M D (model independent) JI Illana Christmas Workshop, Madrid, 18-20 December 06 4

Gravitational interactions R S 1 M D ( s M D ) 1 n+1, Planck length λp 1 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+1 θ MD n+2 b RS 1 q 2 /s = 1 n+1 b 2 (1 cos θ ) 1 Elastic process (reliable) calculation based on the eikonal approximation JI Illana Christmas Workshop, Madrid, 18-20 December 06 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 1: exponential of Born amplitude A eik (s, q) = 4πsb 2 cf n (b c q) with b c [ (4π) n 2 1 2 Partonic cross sections σ eik = ( ) n Γ 2 [n = 2] π 2 b 2 c σ BH = πr 2 S s 1 n+1 ] 1 n s MD n+2 [n > 2] 2πb 2 cγ ( 1 2 n F n (u) i ) cos π n 0 s 2 n dv v J 0 (uv)(e i 10 08 06 04 02 00 02 0 2 4 eikonal phase v n 1), v b/b c F 2 (u) Re Im Mod 6 8 10 0 2 4 F 6 (u) Re Im Mod 6 8 10 JI Illana Christmas Workshop, Madrid, 18-20 December 06 6

νn cross sections Hard processes (BH formation): initial neutrino destroyed σ νn BH = 1 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 1 S Soft processes (eikonal): neutrino loses small fraction y of its energy and keeps going dσ νn eik dy = 1 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 1, b b s = b c (n/qb c ) 1 n+1, q > b 1 c b c, q < b 1 c JI Illana Christmas Workshop, Madrid, 18-20 December 06 7

BH versus eikonal events /dy [mbarn] dσ eik νn 10 4 10 2 10 0 10 2 10 4 M D = 1 TeV n = 2 3 6 10 6 10 4 10 2 10 0 y E ν = 10 10 GeV σ soft νn [mbarn] 10 1 10 2 10 3 10 4 10 5 10 6 M D = 1 TeV 10 6 10 4 10 2 10 0 y min σbh [mbarn] eg E thres = 100 TeV y min = 10 5 JI Illana Christmas Workshop, Madrid, 18-20 December 06 8

BH versus eikonal events /dy [mbarn] dσ eik νn 10 4 10 2 10 0 10 2 10 4 M D = 3 TeV n = 2 3 6 10 6 10 4 10 2 10 0 y E ν = 10 10 GeV σ soft νn [mbarn] 10 1 10 2 10 3 10 4 10 5 10 6 M D = 3 TeV 10 6 10 4 10 2 10 0 y min σbh [mbarn] eg E thres = 100 TeV y min = 10 5 JI Illana Christmas Workshop, Madrid, 18-20 December 06 9

Example (I) One UHE neutrino of E ν = 10 10 GeV with E thres = 100 TeV and M D = 1 TeV Number of eikonal interactions before the neutrino gets destroyed: L BH /L eik = σ soft /σ BH L σ = (ρn A σ) 1 is the mean free path [L SM = 440 km] n = 2 n = 6 σ BH 982 10 4 mbarn 407 10 3 mbarn σ soft 194 10 2 mbarn 688 10 3 mbarn L BH in ice 17 km 4 km L BH /L eik 198 169 E loss eik in L BH 10 10 9 GeV 50 10 8 GeV E loss rad in L BH 16 10 9 GeV 49 10 8 GeV E loss eik in 1 km 59 10 7 GeV 12 10 8 GeV E loss rad in 1 km 92 10 7 GeV 12 10 8 GeV JI Illana Christmas Workshop, Madrid, 18-20 December 06 10

Signals at neutrino telescopes Cosmogenic neutrinos per flavour (consistent with p and γ at AGASA /HiRes and EGRET ) 100 E ν dφ/de ν [km 2 sr 2 yr 1 ] Downward neutrinos [bin 1 km 2 yr 1 ] 10 3 10 10 2 1 10 1 10 7 10 9 10 11 10 7 10 9 10 11 E ν [GeV] E ν [GeV] Higher : 100 % EGRET 820 km 2 yr 1 in [10 8, 10 11 ] GeV Lower : 20 % EGRET 370 km 2 yr 1 [Semikoz, Sigl 04] Minimal : No protons above E GZK 35 km 2 yr 1 [Fodor, Katz, Ringwald 03] JI Illana Christmas Workshop, Madrid, 18-20 December 06 11

N events = 2πAT Signals at neutrino telescopes 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 ) 1 e Lρ icen A σint νn 1 P surv P int 1 with longitudinal detector size L P surv P int eik P event P event 01 n = 2 01 n = 6 001 05 1 BH 15 2 M D [TeV] 25 3 001 05 IceCube ( ) E ν = 10 10 GeV [P event = P surv P int ] 1 15 2 M D [TeV] JI Illana Christmas Workshop, Madrid, 18-20 December 06 12 25 3

Signals at neutrino telescopes Multiple-bang events: When detector L larger than interaction length L 0 = (ρn A σ eik ) 1 1 01 001 05 [P N event = P surv P N ] IceCube ( ) E ν = 10 10 GeV 1 n = 2 n = 6 15 2 M D [TeV] P 1 event Pevent 2 P event >2 25 3 Probability of N > 1 bangs: P N (L) = e L/L 0 (L/L 0) N N! Average (and most probable) # of bangs: N = N=1 NP N = L/L 0 In a SM CC interaction (or in BH evaporation) a double-bang ν τ event may occur only if 25 10 6 < E τ /GeV < 10 7 in IceCube [125 m < cτ < 1 km] Prob is just 68 10 5 JI Illana Christmas Workshop, Madrid, 18-20 December 06 13

Example (II) Again one UHE neutrino of E ν = 10 10 GeV with E thres = 100 TeV M D = 1 TeV IceCube/AMANDA 0 deg [18 km] 64 deg [4 km] BH (n=6) 84 deg [17 km] BH (n=2) 92 deg [440 km] SM Interaction probability P SM int = 00022 P BH int = 006 (022) P eik 1 = 036 (027) [L = 1 km, M D = 1 TeV, n = 2 (6)] P eik 2 = 015 (006) P eik >2 = 005 (0008) JI Illana Christmas Workshop, Madrid, 18-20 December 06 14

Shower energy distribution at IceCube 10 Higher Flux n = 2 Higher Flux n = 6 Number SM 1 (ν l + ν l ) CC NC SM 2-bang HF 910 094 038 132 0008 01 LF 410 036 014 050 0003 10 Lower Flux n = 2 Lower Flux n = 6 Events/bin/year, n = 2 (6) [M D = 2 TeV]: 1 Number BH Eikonal HF 343 (122) 391 (185) 01 10 6 10 8 10 10 10 12 10 6 10 8 10 10 10 12 LF 107 (425) 106 (620) E sh [GeV] E sh [GeV] JI Illana Christmas Workshop, Madrid, 18-20 December 06 15

Contained events at IceCube and AMANDA 100 10 IceCube n = 2 IceCube n = 6 IceCube: L = 1 km A = 1 km 2 AMANDA: L = 07 km A = 003 km 2 1 Contained events per year: 01 10 AMANDA n = 2 AMANDA n = 6 Higher Flux Lower Flux (thick) (thin) 1 Eikonal (solid) Multi-bang (dashed-dotted) 01 1 2 3 4 M D [TeV] 5 1 2 3 4 M D [TeV] 5 6 BH (dashed) JI Illana Christmas Workshop, Madrid, 18-20 December 06 16

Long-lived gluinos from UHE nucleons JI Illana Christmas Workshop, Madrid, 18-20 December 06 17

Motivation Nucleon primaries of E < 10 11 GeV collide with atm nucleons s < 500 TeV And many secondary hadrons generated with enough energy to produce TeV physics Exotic particles hidden inside the shower unless they are long-lived gluino in split-susy models good candidate Our study 1 Find the flux of primary and secondary hadrons 2 Calculate the flux of long-lived gluinos 3 Discuss the detectability of gluinos: signals JI Illana Christmas Workshop, Madrid, 18-20 December 06 18

Flux of hadrons Flux of primary nucleons: dφ N de E α (90% p, 10% n; free or bound in nuclei) CR leg by Markus Ahlers α = 27 α = 30 α = 27 JI Illana Christmas Workshop, Madrid, 18-20 December 06 19

Flux of hadrons The flux of secondary hadrons (N, π ±, K ± ) generating showers with corsika 10 19 E 27 dφ/de [km 2 yr 1 sr 1 GeV 17 ] 10 18 10 17 10 16 10 15 primary N total N π K 10 14 10 4 10 5 10 6 10 7 10 8 E [GeV] 10 9 10 10 10 11 eg for E = 10 7 GeV ( s 5 TeV): secondary N (π ±, K ± ) are 50% (15%) of primary N JI Illana Christmas Workshop, Madrid, 18-20 December 06 20

Flux of long-lived gluinos The probability that a hadron h produces a gluino pair is P h g g(e) = AσhN g g with σt hair σt hair = C0 h + C1 h log(e) + C2 h log 2 (E) σ hn g g = [PDFs] σ q q,gg g g since decay length interaction length A 07 14 + 03 16 = 146 nucleons in a nucleus of air 10 3 10 2 10 1 10 0 10 1 10 2 10 3 10 4 10 5 σ hn g g N π, K [nb] M g = 200 GeV M g = 300 GeV 10 6 10 5 10 6 10 7 10 8 E [GeV] 10 9 10 10 10 11 JI Illana Christmas Workshop, Madrid, 18-20 December 06 21

Flux of long-lived gluinos Φ g g = h E min de dφ h de P h g g(e) 10 0 10 1 10 2 Φ g g [km 2 yr 1 sr 1 ] total from N π 10 3 K 10 4 10 5 10 6 150 200 250 300 M g [GeV] 350 400 450 2π sterad < 1 g g yr 1 km 2 (downgoing) if M > 160 GeV from primary N (64%), secondary N (16%), π (16%), K (4%) JI Illana Christmas Workshop, Madrid, 18-20 December 06 22

Gluino pairs in one shower? Energy [GeV] N π K N π K 10 4 21 10 4 7539 54585 10092 9873 70692 13026 21 10 4 46 10 4 3907 27558 5196 4802 35700 6757 eg E sh = 10 10 GeV Two types of showers: [left] high elasticity (a) leading hadron [right] low elasticity (b) more hadrons at lower energies 46 10 4 10 5 2015 13628 2524 2476 17644 3360 10 5 21 10 5 909 6771 1323 1269 8415 1634 21 10 5 46 10 5 469 3352 608 600 4314 817 46 10 5 10 6 254 1695 318 300 2065 390 10 6 21 10 6 116 860 154 168 1010 200 21 10 6 46 10 6 58 421 71 66 488 97 46 10 6 10 7 24 197 32 23 230 39 10 7 21 10 7 11 89 14 27 120 20 21 10 7 46 10 7 6 36 14 13 60 9 46 10 7 10 8 4 23 3 8 31 10 10 8 21 10 8 0 17 2 2 16 2 21 10 8 46 10 8 2 8 0 1 1 0 46 10 8 10 9 0 1 2 0 0 0 10 9 21 10 9 2 1 1 0 0 0 21 10 9 46 10 9 1 0 0 0 0 0 46 10 9 10 10 1 0 0 1 0 0 JI Illana Christmas Workshop, Madrid, 18-20 December 06 23

Gluino pairs in one shower? Probability to produce a gluino pair with M = 200 (300) GeV by these two showers: P a = 54 10 5 (97 10 6 ), P b = 43 10 5 (66 10 6 ) both effects compete Probability to produce a gluino pair by an average shower of arbitrary energy: 10 2 10 3 Probability to produce g g 10 4 10 5 10 6 10 7 upper: secundary h lower: primary N Interactions of (secondary) pions main source of gluinos if E sh > 10 8 GeV in a single shower 10 8 10 9 10 8 10 9 M g = 200 GeV M g = 300 GeV 10 10 E sh [GeV] 10 11 JI Illana Christmas Workshop, Madrid, 18-20 December 06 24

Detectability of gluino pairs A gluino rapidly fragments into an R-hadron We assume a neutral gluino-gluon state G Present bound: M G > 170 GeV [Tevatron] Interaction length quite small: λ G (16/9)λ π (at the same velocity) but it loses very little energy per interaction: E/E k/m with k 02 GeV Very penetrating!! eg gluinos of M = 200 GeV produced by a 10 10 GeV shower have an average energy E 5 10 5 GeV and a λ G 160 g/cm 2, loosing E/E 10 3 per interaction In two vertical atmospheres (2000 g/cm 2 ) a proton deposits most of its energy but these gluinos give away 2000/160 10 3 12% of their energy How can we distinguish the gluino pair(s) inside the shower? JI Illana Christmas Workshop, Madrid, 18-20 December 06 25

Detectability of gluino pairs 1 We need enough events: Not in IceCube (1 km 2 ) since N g g < 1 yr 1 for M > 160 GeV But Auger has 3000 km 2!! although with a threshold at about 10 8 GeV 10 2 E sh dφ g g /de sh [km 2 yr 1 sr 1 ] 10 3 10 4 M g = 300 GeV M g = 200 GeV Auger: N g g 330 (20) yr 1 N g g 20 (2) yr 1 above threshold for M = 200 (300) GeV 10 5 10 5 10 6 10 7 10 8 10 9 E sh [GeV] JI Illana Christmas Workshop, Madrid, 18-20 December 06 26 10 10

Detectability of gluino pairs 2 We need inclined showers: (25% have zenith angle θ > 60 ) After a certain depth most of hadrons in the shower are absorbed by the atmosphere, whereas the gluino starts a series of hadronic mini-showers (trace of constant energy) Gluinos come in pairs separated by a distance Dθ g g with θ g g 5 10 4 rad, enhanced in quasi-horizontal showers, D 2HR T 250 m if H = 20 km The standard shower gets distorted by the accumulation of muons from pions produced by gluino interactions (shower profile with more pronounced curvature) JI Illana Christmas Workshop, Madrid, 18-20 December 06 27

Conclusions JI Illana Christmas Workshop, Madrid, 18-20 December 06 28

TeV gravity 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 cascade Eikonal approx (clean theoretical environment) 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 (24% of SM interactions have), multiple bangs IceCube could explore M D < 5 TeV Long-lived gluinos Inclined EAS may contain well separated, penetrating gluino pairs, distorting profile Auger would detect 20 (2) gluino pairs per year if M = 200 (300) GeV JI Illana Christmas Workshop, Madrid, 18-20 December 06 29