The high-energy galactic tau neutrino flux and its atmospheric background

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Digital Object Identiﬁer (DOI) 10.1140/epjcd/s2004-03-1844-9 Eur Phys J C 33, s01, s959–s961 (2004)

EPJ C direct

electronic only

The high-energy galactic tau neutrino ﬂux

and its atmospheric background

Husain Athar1, Kingman Cheung2, Guey-Lin Lin3, and Jie-Jun Tseng4

1 _{Physics Division, National Center for Theoretical Sciences, Hsinchu 300, Taiwan} 2 _{Department of Physics, National Tsing-Hua University, Hsinchu 300, Taiwan} 3 _{Institute of Physics, National Chiao-Tung University, Hsinchu 300, Taiwan} 4 _{Institute of Physics, Academia Sinica, Taipei 115, Taiwan}

Received: 7 November 2003 / Accepted: 22 November 2003 /

Published Online: 8 April 2004 – c Springer-Verlag / Societ`a Italiana di Fisica 2004

Abstract. We compare the tau neutrino ﬂux arising from the galaxy and the earth atmosphere for 103 ≤

E/GeV ≤ 1011_{. The intrinsic and oscillated tau neutrino ﬂuxes from both sources are considered. We ﬁnd}

that, forE ≥ 103GeV, the oscillatedν_τ flux along the galactic plane dominates over the maximal intrinsic atmosphericντ flux, i.e., the flux along the horizontal direction. We also briefly comment on the prospects for observing these high-energy tau neutrinos.

PACS. 95.85.Ry Neutrino, muon, pion, and other elementary particles; cosmic rays – 13.85.Tp Cosmic-ray interactions

1 Introduction

The Milky way is one of the nearby astrophysical sources producing high energy neutrinos, besides the familiar earth atmosphere [1]. Measurements of galactic neutrino and photon fluxes could provide information about the distribution of matter and cosmic rays in the galaxy. Fur-thermore, the above flux is also a background for the search of more distant high energy neutrino sources such as the AGNs and the GRBs. In this talk, we shall focus on the flux ofν_τ. It is clear that the observation of astro-physical ν_τ, with a flux comparable to the flux ofν_e and

νµ, directly conﬁrms the neutrino oscillations. In order to

observe galacticν_τ ﬂux, it is essential to study the atmo-spheric background. We shall focus on the energy range

Eν ≥ 103GeV.

We first discuss the distinction between intrinsic and oscillated neutrino fluxes arising from the Milky way and the earth atmosphere. We then present results for galactic and atmospheric tau neutrino fluxes. Finally we comment on the prospects for observing galactic tau neutrinos.

2 Intrinsic and oscillated neutrino ﬂuxes

It is well known that the relative ﬂavor ratio for astrophys-ical neutrinos at the source is approximately φ0_ν_e : φ0_ν_µ :

φ0

ντ = 1 : 2 : 0. The commonly accepted astrophysical

processes for producing electron and muon neutrinos are

(γ, p) + p → π±+X where pion further decays into

elec-tron and muon neutrinos with the ratioφ0_ν_e :φ0_ν_µ = 1 : 2. On the other hand, the production mechanism for the tau

neutrino is (γ, p) + p → D_s+X where D_s further de-cays into tau neutrinos. The production cross section for

Dsmeson is much smaller than that forπ± for

center-of-mass energy √s ∼ (1-10) GeV. Hence φ0_ν_τ is suppressed compared to φ0_ν_e andφ0_ν_µ.

Althoughν_τ flux is rather suppressed at the source, it is not negligible at the detector. As neutrinos propagate to the earth, the oscillation effect takes place and the relative neutrino flavor ratio changes as a result. Let us denote the neutrino flux reaching the earth asφ_ν_α. Then [2]

φνα =

β

Pαβφ0νβ, (1)

where P_αβ is a function of neutrino mixing matrix U_αi which connects the neutrino mass eigenstate to the ﬂavor eigenstate. The α, β run over e, µ and τ. Assuming a bi-maximal mixing for U_αi, one obtains for vanishingδ and

θ13 [3] Pαβ=    1/2 1/4 1/4 1/4 3/8 3/8 1/4 3/8 3/8    . (2)

Such a probability matrix implies φ_ν_e : φ_ν_µ : φ_ν_τ = 1 : 1 : 1. This ﬂavor ratio is applicable to galactic neutrinos since these neutrinos propagate through a distance much greater than the neutrino oscillation length. On the other hand, this ratio is not applicable to the atmospheric neu-trinos forE_ν ≥ 103 GeV considered here. At this energy, the oscillation length for the atmospheric neutrino is of the order 1010cm, which is much greater than even the earth

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960 H. Athar et al.: The high-energy galactic tau neutrino ﬂux and its atmospheric background

diameter. Hence the atmospheric ν_τ ﬂux for E_ν ≥ 103 GeV must be dominantly an intrinsic one.

3 The galactic and atmospheric tau

neutrino ﬂuxes

The total galactic tau neutrino ﬂux consists of intrinsic and oscillated components. Both components follow from the collisions of primary cosmic-ray proton with interstel-lar medium proton. The density of interstelinterstel-lar medium proton is taken to ben_p= 1 cm−3along the galactic plane, while the primary cosmic ray spectrum, φ_p(E_p), is taken to be [4]

φp(Ep) =

1.7 (E_p/GeV)−2.7forE_p< E₀,

174 (E_p/GeV)−3 forE_p≥ E₀, (3) where E₀ = 5· 106 GeV andφ_p(E_p) is in units of cm−2 s−1sr−1GeV−1. We assume directional isotropy inφ_p(E_p) for the above energy range. A more recent measurement of cosmic-ray ﬂux spectrum between 2· 105 GeV and 106 GeV agrees with the φ_p(E_p) given by (3) within a factor

of∼ 2 in this energy range [5]. The intrinsic galactic tau

neutrinos are produced by p + p → D_s+X, with the D_s meson decays into aτ lepton and a ν_τ, while theτ lepton further decays into the secondν_τ with other particles. We calculate the D_s production cross section by the follow-ing two approaches: (i) the perturbative QCD (PQCD) and (ii) the quark-gluon string model (QGSM) [6]. In the PQCD approach, we use the CTEQ5 parton distribution functions [7] and apply aK factor, K = 2, to account for the NLO corrections [8]. With the D_s production cross section determined, one can calculate theν_τ ﬂux using

φ0 ντ = _∞ E dE_pφ_p(E_p)f(E_p) 1 σpp(E_p) dσ_pp→ν_τ_+Y dE , (4)

wheref(E_p) =R/λ_pp(E_p) withλ_pp(E_p) thepp interaction length andR a representative distance in the galaxy along the galactic plane. We takeR to be ∼ 10 kpc, where 1 pc

 3·1018_{cm. We have focused on the intrinsic tau neutrino}

flux along the galactic plane just to obtain the maximal expected tau neutrino flux. The matter density decreases exponentially in the direction orthogonal to the galactic plane, therefore the amount of intrinsic tau neutrino flux decreases by approximately two orders of magnitude for the energy range of our interest. Another component of galactic tau neutrinos comes from the oscillation of galac-tic muon neutrinos. The flux of the latter can also be cal-culated by (4) withν_τ replaced byν_µ[9]. In this case,π± andK± are the dominant intermediate states that decay into muon neutrinos. Sinceφ0_ν_µ is few orders of magnitude greater than φ0_ν_τ while φ0_ν_e is approximately one half of

φ0

νµ, we recover the ﬂavor ratioφ0νe :φ0νµ :φ0ντ = 1 : 2 : 0

for the galactic neutrinos at the source. From the previ-ous section, we have φ_ν_τ = φ0_ν

µ/2. The ﬂux φντ can be

3 5 7 9 11 Log10(E/GeV) 10−20 10−18 10−16 10−14 10−12 10−10 10−8 dN tot ν τ /d(log 10 E) (cm −2 s −1 sr −1 ) Galactic−plane ντ flux Atmospheric ντ flux GZK ντ flux

Fig. 1. Galactic-plane, horizontal atmospheric and GZK tau neutrino ﬂuxes under the assumption of neutrino ﬂavor oscil-lations parameterized as Eφντ(E) = 1.5 · 10−5(E/GeV)−2.63forE < E₁, 9.5 · 10−4(E/GeV)−2.95forE ≥ E₁, (5)

where E₁ = 4.7 · 105 GeV. The Eφ_ντ(E) is in units of cm−2 s−1 sr−1.

Having discussed the calculation of galactic tau neu-trinos, we now turn to the atmospheric tau neutrinos. As said before, for E_ν ≥ 103 GeV, atmospheric ν_τ flux has only the intrinsic component. We have used the nonper-turbative QCD approach mentioned earlier to model the production ofD_smesons in the pA interactions. We have used theφ_p(E_p) given by (3) and theZ-moment descrip-tion for the calculadescrip-tion of intrinsic tau neutrino flux [10]. We obtain the atmospheric tau neutrino flux by solving a set of cascade equations [11, 12]

The results for galactic and atmospheric tau neutrino fluxes, along with the GZK [13] oscillated tau neutrino flux [14], are presented Fig. 1, where we have used the no-tation φ_ν_τ ≡ dN_ν_τ/d(log₁₀E) . From the figure, we note that the galactic plane oscillated ν_τ _{flux dominates over} the intrinsic atmospheric ν_τ flux for E ≤ 5 · 107 GeV, whereas the GZK oscillated tau neutrino flux dominates

for E ≥ 5 · 107 GeV. Quantitatively, the atmospheric

ντ ﬂux in the horizontal direction is ∼ 5 times smaller

than the galactic-plane ν_τ flux. Furthermore, the down-ward atmospheric ν_τ flux is factor of ∼ 8 smaller than its horizontal counterpart. Let us recall here that particle physics aspects of intrinsic tau neutrino flux calculation presented here are empirically supported only up to√s ∼ TeV, which corresponds toE_p∼ 106GeV.

Before we move on, it is instructive to compare the at-mosphericν_τ andν_µ ﬂuxes. We plot these two ﬂuxes for

Eν ≥ 103GeV in Fig. 2. The atmosphericν_µflux is taken from [15]. The atmospheric ν_µ flux has two components: conventional and prompt components. The former com-ponent is due to decays of π± and K±, while the latter component is due to decays of charm hadrons. Although produced more copiously than charm hadrons,π or K me-son does not decay efficiently in the air at sufficiently high energy. This effect disfavors the resulting neutrino flux.

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H. Athar et al.: The high-energy galactic tau neutrino ﬂux and its atmospheric background 961 3 4 5 6 7 8 9 10 11 1x10-30 1x10-25 1x10-20 1x10-15 1x10-10 1x10-5

The intrinsic atmospheric νµ & ντ flux

ντ νµ conventional νµ prompt dN ν /d (Log 10 E) (cm -2s -1sr -1) Log₁₀(E / GeV)

Fig. 2. The comparison of downward atmospheric νµandντ

ﬂuxes

Indeed, in Fig. 2, the two components of ν_µ flux cross roughly at E_ν = 106 GeV [15]. We also observe that the atmosphericν_µandν_τfluxes are comparable forE_ν > 106 GeV, since both fluxes are due to charm production in this energy range.

4 The prospects of observations

For downward going or near horizontal high-energy tau neutrinos, the deep inelastic neutrino nucleon scattering, occurring near or inside the detector, produces two show-ers [16]. The ﬁrst shower is due to a charged current neu-trino nucleon deep inelastic scattering, whereas the second shower is due to the (hadronic) decay of the associated

τ lepton produced in the ﬁrst shower. It might be

pos-sible for the proposed large neutrino telescopes such as the IceCube to constrain the two showers simultaneously for 106 ≤ E/GeV ≤ 107, depending on the achievable shower separation capabilities [17]. Here, the two showers develop mainly in ice. With such a detection strategy, we estimate the event rate for observing the galactic tau neu-trinos. In the above energy range for the tau neutrinos, the event rate in 1 km3 water/ice Cherenkov detector is rather small, about∼ 5 · 10−3yr−1sr−1. Such a low event rate implies that one can only search for galactic tau neu-trinos in the lower energy. Alternatively, one should con-sider other detection strategies. Since Fig. 1 shows that galactic tau neutrino flux dominates over its atmospheric counterpart forE_ν ≥ 103 GeV, it is desirable to develop strategies for identifying tau neutrinos at TeV energies or even lower because of relatively large absoluteν_τflux. The present AMANDA search for all flavor neutrino-induced cascades is not tight enough to constrain/observe our pre-dictedφ_ν_τ [18].

We point out that the persistent dominance of galactic tau neutrino flux over its atmospheric background is a unique phenomenon among all neutrino flavors. Such a dominance does not occur forν_eandν_µ. For example, the result in Sect. 2 tells us that φ_ν_µ =φ_ν_τ for the galactic neutrinos. On the other hand, the atmospheric ν_µ flux is much greater than the atmosphericν_τ flux forE_ν < 105 GeV, as can be seen from Fig. 2. Hence the galactic ν_µ flux no longer dominates over the atmosphericν_µ flux for

Eν < 105GeV.

In conclusion, we have presented our calculations of both the galactic and atmospheric tau neutrino ﬂuxes for

Eν ≥ 103GeV. The former ﬂux is shown to dominate over

the latter. Such a dominance is unique to tau neutrinos. The event rate for galactic tau neutrinos by observing the double showers (with 106≤ E_ν/GeV ≤ 107) is rather sup-pressed. Therefore, to observe the galactic tau neutrinos, it is desirable to develop techniques for identifying tau neutrinos at lower energies.

H.A. and K.C. are supported in part by the Physics Division of National Center for Theoretical Sciences un-der a grant from the National Science Council of Taiwan. G.L.L. and J.J.T. are supported by the National Science Council of Taiwan under the grant numbers NSC91-2112-M-009-019 and NSC91-2112-M-001-024.

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