Probing New Physics at the Highest Energies

Transcription

1 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, [hep-ph/ ], PRD 72, [hep-ph/ ] and hep-ph/ JI Illana Christmas Workshop, Madrid, December 06 1

2 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 GeV] Never observed (but expected) Low νn cross sections in SM good opportunity for testing TeV gravity Ultrahigh energy nucleons [until GZK cutoff , even beyond?] Well established flux Easier to extract NP if long-lived exotic particles eg split-susy gluinos JI Illana Christmas Workshop, Madrid, December 06 2

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

4 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 ) ν, γ have access to TeV physics in interactions with terrestrial Nucleons: s = 2m N E ν > 10 TeV E ν [GeV] E ν [GeV] 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, December 06 4

5 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, December 06 5

6 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 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 eikonal phase v n 1), v b/b c F 2 (u) Re Im Mod F 6 (u) Re Im Mod JI Illana Christmas Workshop, Madrid, December 06 6

7 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, December 06 7

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

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

10 Example (I) One UHE neutrino of E ν = 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 mbarn mbarn σ soft mbarn mbarn L BH in ice 17 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 1 km GeV GeV E loss rad in 1 km GeV GeV JI Illana Christmas Workshop, Madrid, December 06 10

11 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 ] E ν [GeV] E ν [GeV] Higher : 100 % EGRET 820 km 2 yr 1 in [10 8, ] 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, December 06 11

12 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 = BH 15 2 M D [TeV] IceCube ( ) E ν = GeV [P event = P surv P int ] M D [TeV] JI Illana Christmas Workshop, Madrid, December

13 Signals at neutrino telescopes Multiple-bang events: When detector L larger than interaction length L 0 = (ρn A σ eik ) [P N event = P surv P N ] IceCube ( ) E ν = GeV 1 n = 2 n = M D [TeV] P 1 event Pevent 2 P event > 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 < E τ /GeV < 10 7 in IceCube [125 m < cτ < 1 km] Prob is just JI Illana Christmas Workshop, Madrid, December 06 13

14 Example (II) Again one UHE neutrino of E ν = 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 = 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, December 06 14

15 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 LF 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) LF 107 (425) 106 (620) E sh [GeV] E sh [GeV] JI Illana Christmas Workshop, Madrid, December 06 15

16 Contained events at IceCube and AMANDA 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: AMANDA n = 2 AMANDA n = 6 Higher Flux Lower Flux (thick) (thin) 1 Eikonal (solid) Multi-bang (dashed-dotted) M D [TeV] M D [TeV] 5 6 BH (dashed) JI Illana Christmas Workshop, Madrid, December 06 16

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

18 Motivation Nucleon primaries of E < 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, December 06 18

19 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, December 06 19

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

21 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 = 146 nucleons in a nucleus of air σ hn g g N π, K [nb] M g = 200 GeV M g = 300 GeV E [GeV] JI Illana Christmas Workshop, Madrid, December 06 21

22 Flux of long-lived gluinos Φ g g = h E min de dφ h de P h g g(e) Φ g g [km 2 yr 1 sr 1 ] total from N π 10 3 K M g [GeV] π 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, December 06 22

23 Gluino pairs in one shower? Energy [GeV] N π K N π K eg E sh = GeV Two types of showers: [left] high elasticity (a) leading hadron [right] low elasticity (b) more hadrons at lower energies JI Illana Christmas Workshop, Madrid, December 06 23

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

25 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 GeV shower have an average energy E 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/ % of their energy How can we distinguish the gluino pair(s) inside the shower? JI Illana Christmas Workshop, Madrid, December 06 25

26 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 ] 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 E sh [GeV] JI Illana Christmas Workshop, Madrid, December

27 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 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, December 06 27

28 Conclusions JI Illana Christmas Workshop, Madrid, December 06 28

29 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, December 06 29