Cosmic-Ray Neutrinos
from the Decay of Long-Lived Particle– Implication to the IceCube Results –Takeo Moroi (Tokyo)（向こう側からきました、お手柔らかにお願いします）
Refs:
Ema, Jinno & TM, PLB 733 (’14) 120 [arXiv:1312.3501]
Ema, Jinno & TM, JHEP 1410 (’14) 150 [arXiv:1408.1745]
Rironkon, Mitaka (Christmas Eve, 2014)

1. Introduction

Recent big news in particle physics: Discovery of Higgs boson• Higgs: the last piece of standard-model particles

The biggest issue: What’s next?

• There is no sign of new physics at colliders so far• What can we do?

Our (or my) motto:• Use whatever information available!
High-energy cosmic rays seem interesting• Many particle-physics models predict “signals” in cosmicrays• There are many on-going projects which have provided
interesting results (i.e., “anomalies”)– PAMELA– Fermi-LAT– ···– IceCubeToday, I concentrate on the recent IceCube result:First observation of sub-PeV – PeV neutrinos[IceCube 3 years result (May, ’14); Talk by Yoshida-san]IceCube found 37 high energy neutrino events• The observed flux is well-above the expected background– 8.4 ± 4.2 from cosmic-ray muons– 6.6+5.9−1.6 from atmospheric neutrinos• The flux is consistent with E −2 power-law with a cut-oﬀ⇒ 3.1 events above Eobs > 2 PeV, if no cut-oﬀ⇒ Cut-oﬀ at ∼ PeV (or softer spectrum)?
We need a new source of high-energy cosmic-ray neutrinos• ∼ E −2 power-law @ E <∼ PeV• Cut-oﬀ @ E ∼ PeV• Isotropic

What is the origin of high-energy cosmic-ray neutrinos?

• Astrophysical origin[Kalashev, Kusenko & W. Essey; Stecker; Cholis & Hooper; Murase & Ioka;
Razzaque; Winter; Fox, Kashiyama & Mszars; Liu et al.; Murase, Ahlers &Lacki; N. Gupta; Gonzalez-Garcia et al.; Ahlers & Murase; Gao et al.; Rouletet al.; Laha et al.; Anchordoqui et al.; He et al.]• Particle-physics origin[Feldstein, Kusenko, Matsumoto & Yanagida; Esmaili & Serpico; Ema, Jinno& TM; Bai, Lu & Salvado; Bhattacharya, Reno & Sarcevic; Zavala; Chen &Nomura; Higaki, Kitano & Sato; Rott, Kohri & Park]

I consider one of the possibilities of particle-physics origin⇒ PeV neutrinos from the decay of long-lived particle

Today, I will talk about:• Possibility to explain IceCube results with the neutrino
production via the decay of long-lived particle• “The early-decay scenario,” which explains the IceCube
events with a particle X with τX  tnow and mX  PeVOutline
1. Introduction
2. Scenario
3. Case with Dark-Matter Decay
4. The Early Decay Scenario
5. Summary2. The Scenario

Assumption: There exists a long-lived particle X• X is somehow produced in the early universe• Neutrinos are produced by the decay of XννWhat is the parent particle X ?

• Dark matter⇒ τX  tnow & mX ∼ O(PeV)• Something else (“early-decay scenario”)⇒ τX  tnow & mX  O(PeV) is possible
BTW, why particle-physics explanation?

• I am particle physicist• No convincing explanation so far, so we should be openminded• The observed neutrino events do not have any correlation
with known sources (like AGN, γ -ray burst, · · ·)

3. Case with Dark-Matter Decay

Neutrino flux can be classified into:• Galactic contribution Φν(Galaxy)• Cosmological contribution Φ(Cosmo)νΦν(Galaxy) depends on direction(X) ∫~l)1dN
ρ(1Xν(Galaxy)Φν(E, ˆl) =d~l
4π τX dE l.o.s.
mXBoltzmann equation for Φ(Cosmo)
ν(Cosmo)Φ̇(Cosmo)
(t,E)
=−2HΦ
(t, E) + HEνν

1 1 ρX (t) dNν(X)+4π τX mX dE∂ (Cosmo)
Φν(t, E)∂EThe present neutrino flux depends on the primary spectrum⇒ Hereafter, I consider two examples
Case 1: Monochromatic neutrino injection• X as a neutral component of SU (2)L triplet
X → νν

⇒dNν(X)= 2δ(E − mX /2)
dE

Case 2: Vector-like SU (2)L doublet L, mixed with leptons• L = ML L̄L + L̄` + yl ē`H + · · ·• L0 can play the role of X
X → νZ 0 , e± W ∓Neutrino distribution for SU (2)L doublet modelNeutrino flux for τX  tnow (with mX = 3 PeV)
Monochromatic injection

SU(2) doublet model• ρX = ρDM with τX ' 3 × 1028 sec• NFW dark matter density is used

Cut-oﬀ scale of the neutrino spectrum: Ecut ∼ mX

⇒ Mass of DM is required to be O(PeV)
Dark-matter density is enhanced at the Galactic center⇒ Flux from the direction of galactic center is enhanced◦Φ(Galaxy)(θ<90)
ν(Galaxy)Φν(θ > 90◦ )∼2Neutrino flux is proportional to τX−1

⇒ In order to explain the IceCube result, τX ∼ O(1028 sec)

4. The Early-Decay Scenario[Ema, Jinno & TM]

The early-decay scenario: τX  tnow

• X decays into neutrinos before the present epoch⇒ The energy is redshifted: E = (1 + zprod. )−1 Eprod.
Φνt ~ τxΦνt = t nowredshift

E

1PeVmxE

1PeVmx• PeV neutrino at present is realized due to the redshift⇒ Mass of X can be much higher than PeV scaleImportant quantities:• Mass: mXanow• Lifetime: τX ⇒ z∗ = z(t = τX ) ≡−1a(t = τX )[]nX
• Abundance: YX ≡s tτXdNν(X)• Neutrino distribution from the decay of X :dEThe case of decaying dark matter (for comparison):• mX ∼ O(1 PeV)
• Neutrino flux from the galactic center is enhanced

In the early-decay scenario:• Neutrino with higher energy is produced at later epoch⇒ (Number density of X ) ∝ e−t/τX−1⇒ For E >(1+z)
mX , flux is exponentially suppressed∗∼• Scattering processes of neutrinos may be important– ν + ν̄BG → ν + ν̄ 0 , ` + `¯0 , q + q̄
0– ν + ν̄BG→ ν + ν̄ 0 , ` + `¯0– ν + νBG → ν + ν0– ν + νBG→ ν + ν0

Neutrinos from cosmological distance: Φ(Cosmo)
ν(Cosmo)Φ̇(Cosmo)
(t,E)
=−2HΦ
(t, E) + HEν
ν∂ (Cosmo)
Φν(t, E)∂E−γν (t; E)Φ(Cosmo)(t, E)ν(eﬀ)0∫dγ(t;E, E)
ν00 (Cosmo)+ dE Φν
(t, E )
dE+ (Source Term)γν : Scattering rate
Optical depth: τν (z) ≡∫ tnowt(z)dt0 γν (t0 ; (1 + z(t0 ))−1 Ēν )• “Survival probability” ∼ e−τν
• If τν >∼ 1, the scattering processes become importantOptical depth: τν (z) ≡∫ tnowt(z)dt0 γν (t0 ; (1 + z(t0 ))−1 Ēν )4⇒ To explain IceCube result, 1 + z∗ <O(10) is necessary∼

Neutrino spectrum: (1) Relatively long lifetime
10-7-710

310-8

10-914

τX = 5 ×10E2Φν [GeVcm-2s-1sr-1]

E2Φν [GeVcm-2s-1sr-1]

21+z*=1×10

sec10-10
10-11
41010510

6E [GeV]

7101+z*=2×10-81012τX = 4 ×10sec-91010-1010-11410510106710E [GeV]• Monochromatic neutrino injection: Ēν = 1 PeV × (1 + z∗ )• YX = [nX /s]tτX = 10−26
3⇒ If z∗ <∼ (a few) × 10 , spectrum is (almost) unaﬀected by thescatteringsNeutrino spectrum: (2) Short lifetime
10-7-710410-810-910-1010-111011τX = 2 ×10

410E2Φν [GeVcm-2s-1sr-1]

E2Φν [GeVcm-2s-1sr-1]

41+z*=1×10

sec5106E [GeV]

7101+z*=5×109-8

τX = 9 ×10 sec

10-91010-1010-11104510106710E [GeV]• Monochromatic neutrino injection: Ēν = 1 PeV × (1 + z∗ )• YX = [nX /s]tτX = 10−26
3⇒ If z∗ >∼ (a few) × 10 , eﬀect of the scattering becomes important

Can we realize E −2 power-law flux with a cut-oﬀ?

⇒ Case with monochromatic neutrino injection
10-7-710410-810-9E2Φν [GeVcm-2s-1sr-1]

E2Φν [GeVcm-2s-1sr-1]

21+z*=1×1010-1010-1141010510E [GeV]6710

1+z*=1.3×10-810-91010-1010-11410510106710E [GeV]⇒ With monochromatic injection, E −2 power-law flux requires 1 + z∗ ∼ (1 − 1.5) × 104

Non-monochromatic neutrino injection (preliminary)SU(2) doublet

SU(2) doublet

Monochromatic

Monochromatic⇒ Neutrino flux at E  Ecut is enhanced⇒ Neutrino flux with ∼ E −2 behavior with cut-oﬀ is possible

One interesting check point: CMB distortion• In the early decay scenario, sizable amount of EM energy
may be injected due to the scattering process• CMB spectrum may deviate from black-bodyµ- or y -distortion may occur, if τν ∼ 1⇒ y ∼ O(10−9 ), µ ∼ O(10−9 )Current constraint from COBE-FIRAS|y| < 1.5 × 10−5 , |µ| < 9 × 10−5
In the future, distortion of O(10−9 ) may be within the reach• PRISM• PIXIE

Early-decay scenario vs. dark-matter-decay scenarioz∗ = z(τX )mXτX
YX = [nX /s]tτXDirection

Early-decay scenario< 104∼< 1010 GeV∼> 1011 sec∼∼ 10−26

Dark-matter decayIsotropic∼ Galactic center—∼ 1 PeV∼ 1028 sec∼ 10−16

41 + z∗ <10is required to avoid:∼• Too much deformation of the spectrum via scatterings• BBN constraints & CMB distortion5. Summary

I discussed “early-decay scenario” for IceCube events
4> 1010 sec• z∗ <O(10),whichcorrespondstoτX∼∼
10• mX ∼ (1 + z∗ ) × 1 PeV <O(10GeV)∼• The neutrino spectrum is isotropic• The scenario may be tested by future observations ofCMB distortion (like PIXIE / PRISM)• The direct-detection constraints on X are irrelevant
Issues:• Primordial abundance of X : non-thermal production• Models (PQ model, messengers in GMSB, · · ·)