Earth Skimming VHE Neutrinos

Transcription

1 1/8/04, Ashra meeting arth Skimming VH Neutrinos G.-L.Lin National Chiao-Tung University, Taiwan

2 Outline Neutrino oscillations and Astrophysical Tau Neutrino Fluxes The Rationale for Detecting arth-skimming or Mountain-Penetrating Neutrinos The Rough stimate of Tau Lepton Fluxes Tau Lepton Fluxes from Mountain-Penetrating AGN, GRB, and GZK Tau Neutrinos Tau-Lepton nergy Fluctuations and Advantages for Detecting Mountain-Penetrating Neutrinos Conclusions

3 Neutrino oscillations and astrophysical fluxes Although flux from the source is suppressed compared to that of µ and e, the oscillation effects make the flux of each flavor comparable at the earth.

4 The idea of observing in view of neutrino oscillations, was suggested sometime ago. Learned and Pakvasa 1995 For a source in a cosmological distance, with e : µ : =1:2:0, the oscillation effects taking place as the neutrinos reach the terrestrial detector make e : µ : =1:1:1. Athar, Jezabek, Yasuda 2000

5 Tau neutrino fluxes Athar, Tseng and Lin, ICRC 2003 GZK 10 9 GeV

6 Detecting arth-skimming The Rationale

7 The idea of detecting earth-skimming neutrinos. Domokos and Kovesi-Domokos, 1998 Fargion, 1997, 2002 Bertou et al., 2001 Feng et al., 2001 Bottai and Giurgola, 2002 Tseng et al., 2003

8 N only scatters once. produced near the earth surface. effective interaction region 1 tau range! nergy losses and decays N inelasticity

9 The effective tau lepton production probability =Tau Range(R ) / N interaction length(λ ) R increases with energy, while λ decreases with energy. Hence it is favorable to detect neutrinos of higher energies!

10 Iyer Dutta, Reno, Sarcevic, & Seckel, 01 Tseng, Yeh, Athar, Huang, Lee, & Lin, 03 Log(/GeV) Tau lepton range approaches to 20 km in rock. Mountain-penetrating is sufficient!

11 Mountain-penetrating tau neutrinos/tau leptons

12 Gandhi, Quigg, Reno, Sarcevic, 1998 The N interaction length: g / cm km ρ ev 0.363, ρ = 2.65 g/cm 3 in rock

13 The effective tau lepton production probability

14 The Rough stimate of Tau Lepton Fluxes

15 A qualitative picture: d dx = α + β z L-z ρ: medium density P T P s P = 0 = exp cc λ (, x) z dzp s L (, z) p ( ) P (, L z) z = exp cc, p ( ) cc cc λ ( ) 1 βρd = 1 ( exp[ βρx] 1). ( ),

16 Let us ' is dp dr For 0 T r βρd 1 = exp cc λ take βρl ln 10 ( ) = the exiting tau lepton energy. around10 ( ) 1 exp βρd i 18 ( ) ( r 10 1 ) ( ) = ev, β 8 10 = ( ) cc( ) r ln(10) ln 10 L βρ βρλ ( L /10 km) ev 18 and define -7 g r -1 log cm 2 10, ' where

17 : initial energy, : final energy, r=log(/ ) New physics means a factor of 10 enhancement on σ N Log( /ev)

18 : initial energy, : final energy, r=log(/ ) Log( /ev)

19 The differential spectrum dp T /dr remains rather flat for ev. This causes a pile up of tau leptons at ev. The energy reconstruction for the initial neutrino energy becomes a challenge beyond ev! The enhancement on σ N generally brings enhancement on dp T /dr for L=30 km. It is not the case for L=100 km due to the medium absorption.

20 Tau Lepton Fluxes The detailed calculations

21 (A). The Tau Lepton Range

22 The tau lepton loses its energy in the rock through 4 kinds of interactions: (1). Ionization (α): the tau lepton excites the atomic electrons. H. A. Bethe 1934 (2). Bremsstrahlung (β): A (3). Pair Production (β): A. A. Petrukhin &V.V. Shestakov, 1968 A R. P. Kokoulin & A. A. Petrukhin, 1971

23 (4). Photo-nuclear interaction: γ N F 2 (x,q 2 ) Basic component X The nucleus shadowing effect is considered: A 2 2 F2 ( x, Q ) a( A, x, Q ) = N 2 AF ( x, Q ) Brodsky & Lu, 1990; Mueller & Qiu 1986; 665 Collab. Adams et al., 1992 Summarizing all these: 2

24 The energy loss: Iyer Dutta, Reno, Sarcevic, & Seckel, 01 d = α + βi, X in units of dx i α and β ' s are plotted below. i g/cm 2,

25 The Tau Lepton Range: dp(, X ) = dx Then R ( ) 0 = Note that we can parameterize β P(, X ), d ( ) ρ( X ) ( ) ( 18 = /10 ev) 0 dx P( ( ) [ ] g cm 0 d dx, X ). = α + β.

26 Iyer Dutta, Reno, Sarcevic, & Seckel, 01 Tseng, Yeh, Athar, Huang, Lee, & Lin, 03 Log(/GeV) cc important for > 10 9 GeV

27 (B). The Tau Lepton Fluxes

28 The transport equations: ( ) ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) + = = + = + + = X T T y Y N y y y A T X T X m c dt T T X dtg X F X F dx d y dy d X F y dy N X G X G X F d X F X X F ; ; exp, ;, to obtain, One can solve for. and,,, 1, with,,,,, lepton : For the ' ' ' 0 ' 0 max min γ ρ β α γ σ γ ρ

29 For the resonant scattering at the W boson peak, we set G dy 1 y ymax ( ) ( ) e v,, ( e X N A F y X = y, y ). e y min dσ dy

30 For neutrinos, F (, X ) F (, X ) whereσ σ ( N Y ) For, F Note X e e 1,2,3. we have (, X ) F (, X ) X F i = (, X ) areσ = ( N Y ), Γ( Y ) e d λ λ e dn ( log ) i N N A 3 A i= 1 y y max min y y i max i min is in units dy Fi 1 y dy F 1 y of e cm ( ), X ( y, ) / c, and ( ) e, X ( y, ) e -2 y s 1 y sr -1 dσ. i dσ dy dy y, y.

31 AGN flux inferred from Kalashev, Kuzmin, Semikoz, and Sigl, 03 Log(/GeV) Tseng et al., 03

32 GRB flux inferred from Waxman and Bahcall 1997 Log(/GeV) Tseng et al., 03

33 GZK flux inferred from ngel, Seckel, and Stanev, 01 Log(/GeV) Tseng et al., 03

34 W boson contribution Glashow resonance 1960 ( ) ( ) the resonant scattering length is 60 kmwe the resonant energy; GeV is where, exp ,0, = = = R e W R R R R R e L m m L X F x F W e e

35 Integrated tau lepton flux in units of km -2 yr -1 sr -1 nergy & flux AGN GRB GZK ev ev ev ev W resonance (AGN) 0.08

36 ffective aperture (AΩ) eff required for 1 event/yr, assuming a 10% duty cycle. nergy & Aperture (km 2 sr) AGN GRB GZK ev ev ev ev 290

37 Can we identify the source of neutrinos?

38 Sensitive to spectral indices Log(/GeV) Tseng et al., 03

39 Sensitive to spectral indices Log(/GeV) Tseng et al., 03

40 Tau lepton energy fluctuations

41 ( ) = C(, ) ( ) N ( ) (, ), = N ( ) φ φ C nergy losses and decays N inelasticity

42 Assume averaged energy loss for each step. Huang, Tseng and Lin, ICRC 2003 Full simulation (take into account stochastic nature of tau-lepton energy loss) is in progress Huang, Iong, Lin and Tseng

43 Huang, Tseng and Lin, ICRC 2003

44 Huang, Tseng and Lin ICRC 2003 Conservative estimate!

45 This is essentially the pileup of tau lepton events at ev as seen before! In other words, the tau lepton energy resolution gets worse for > ev!

46 Advantages for Detecting Mountain-Penetrating Neutrinos over the arth-skimming Ones

47 Comparison of solid-angle coverage of earth-skimming and mountain-penetrating tau-neutrino experiment: R l ξ arth-skimming l = 2Rsinξ Ω = 2πξ = 0.05 max 2π 100 km km

48 For the mountain-penetrating case: w = 20 km l (distance from mountain to detector) = 20 km h (height of the mountain) = 2 km The solid angle is ( ) 20 2 km 2 ( ) 20 2 km 2 = 0.1 Both cases are comparable if 100 km is acceptable for energy resolution. But the latter is preferred if better energy resolution is required!

49 For a smaller medium depth, say L about few tens of kilometer, the enhancement on σ N also brings an enhancement on the tau lepton flux. p. 16, 17

50 Conclusions We have presented the essential features of detecting arth-skimming or mountain-penetrating. The tau lepton flux resulting from mountainpenetrating is calculated. The flux shows rather weak dependence on the traveling distance of / inside the mountain. It is controlled by the tau lepton range inside the earth.

51 The tau lepton flux already reaches its maximum for 20 km of medium depth. Larger medium depth results in poorer energy resolutions. This justifies the observations of mountain-penetrating neutrinos. We give effective aperture required for detecting 1 event/yr assuming a 10% duty cycle. The tau lepton flux resulting from mountain-penetrating neutrinos could be enhanced by anomalously large neutrino-nucleon scattering cross section at high energies.