LISA
Neutrino masses and Ordering via multimessenger astronomy Rencontres de Moriond VHEPU- 26th March 2017—La Thuile, Italy Aurora Meroni
K. Langæble, A. Meroni and F. Sannino Phys.Rev. D94 (2016) no.5, 053013 Not so Standard SM
What we have explained so far
• Unification of strong and electroweak interactions • Interactions: gauge, Yukawas and self-interactions • Discovery of the Higgs boson Several puzzles to solve…
• Elusive sector: Dark Matter and Neutrinos • Baryon asymmetry • Unification of the forces of Nature • Hierarchy problem • Stability of the vacuum • The flavour puzzle From Quanta Magazine • …
Aurora Meroni University of Helsinki 2 1 Motivations and Goals
neutrino masses.
I The three neutrino mixing framework
In the formalism used to construct the Standard Model (SM), the existence of a non- trivial neutrino mixing and massive neutrinos implies that the left-handed (LH) flavour neutrino fields ⌫lL(x), which enter into the expression for the lepton current in the charged current weak interaction Lagrangian, are linear combinations of the fields of three (or more)1 Motivations neutrinos ⌫ , and having Goals masses m = 0: j j 6
neutrino masses. ⌫lL(x)= Ulj ⌫jL(x),l= e, µ, ⌧, (1.1) Xj I The three neutrino mixingwhere framework⌫ (x) is the LH component of the field of ⌫ possessing a mass m 0 and U is a jL j j In the formalism used to construct the Standardunitary Model matrix (SM),1 Motivations—the the Pontecorvo-Maki-Nakagawa-Sakata existence and Goals of a non- (PMNS) neutrino mixing ma- trivial neutrino mixing and massive neutrinostrix implies [3,1 4, Motivations 9],thatU the left-handedUPMNS and. Goals Similarly (LH) flavour to the Cabibbo-Kobayashi-Maskawa (CKM) quark neutrino masses. ⌘ neutrino fields ⌫lL(x), which enter into themixing expression matrix, for the lepton leptonic current matrix inU thePMNS, is described (to a good approximation) by charged current weak interaction Lagrangian, are linear combinations of the fields of neutrino masses. I The three neutrino mixinga3 3 framework unitary mixing matrix. In the widely used standard parametrization [6], UPMNS three (or more) neutrinos ⌫ , having masses m⇥= 0: j is expressedj 6 in terms of the solar, atmospheric and reactor neutrino mixing angles ✓12, In the formalism usedNEUTRINO to construct the Standard OSCILLATION Model (SM), PROBABILITY the existence of a non- 249 I The three neutrinotrivial neutrino mixing mixing and massive framework neutrinos✓23 and implies✓13 that, respectively, the left-handed (LH) and flavour one Dirac - , and two (eventually) Majorana [21] - ↵21 neutrino fields⌫lL(⌫x)=(x), whichU enterlj ⌫j intoL(x the),l expression= e, µ, for⌧, the lepton current in the (1.1) lL and ↵31, CP violating phases: In the formalism usedcharged to construct current weak the interaction Standardj Lagrangian, Model (SM), are linear the combinations existence of of athe non- fields of coeffithreecient (or of more)νβ neutrinos, X⌫ , having masses m = 0: trivial neutrino mixing and massive| ⟩ neutrinosj implies thatj the6 left-handed (LH) flavour where ⌫ (x) is the LH component of the field of ⌫ possessing a massUPMNSm 0 andU =U Vis( a✓12, ✓23, ✓13, ) Q(↵21, ↵31) , (1.2) neutrino fieldsjL ⌫lL(x), which enter into the⌫lL(x expression)= Ulj ⌫jLj for(x),l the= e, lepton µ, ⌧, current inj theiE(1.1)kt Aνα νβ (t) νβ να(t) = Uα∗k Uβk e− ⌘ , (7.16) chargedunitary current matrix weak —the interaction Pontecorvo-Maki-Nakagawa-Sakata Lagrangian,→ areXj≡⟨ linear| combinations⟩ (PMNS) of the neutrino fields of mixing ma- Neutrino Oscillationsk threetrix (or [3, 4, more) 9], U neutrinosUwherePMNS⌫⌫j,.( havingx Similarly) is the LH masses component to themj = of Cabibbo-Kobayashi-Maskawawhere the0: field of ⌫ possessing! a mass m 0 and (CKM)U is a quark jL j j ⌘ unitary matrix —the Pontecorvo-Maki-Nakagawa-Sakata6 (PMNS) neutrino mixing ma- mixing matrix,is the the leptonic amplitude matrix of νUαPMNSν,β istransitions described (to as a a good function approximation) of time. The by transition trix [3, 4, 9], U UPMNS. Similarly to the Cabibbo-Kobayashi-Maskawa (CKM) quark i ⌫lL(x)=⌘ Ulj ⌫jL→(x),l= e, µ, ⌧, 10 0(1.1) c13 0 s13e c12 s12 0 a3 3 unitaryprobability mixingmixing matrix. matrix, is, then, the In leptonic the given widely matrix byUPMNS used, is standard described (to parametrization a good approximation) [6], by UPMNS ⇥ a3 3 unitary mixingj matrix. In the widely usedV = standard0 parametrizationc23 s23 [6], U 010 s12 c12 0 , (1.3) is expressed in terms⇥ of the solar,X atmospheric and reactor neutrino mixingPMNS angles ✓12, is expressed in terms of the solar, atmospheric2 and reactor0 neutrino mixing angles1i(E✓0, Ej )t i 1 0 1 P (t)= A (t) = U ∗ 0U Us U ∗c e− k12− s . e 0(7.17)c 001 where✓23 and⌫ (x✓)13 is, the respectively, LH✓ componentandνα✓ and,ν respectively,β of one the Dirac field andνα one ofν -⌫β Dirac ,possessing and - , and two two a (eventually) mass (eventually)αk mβk α Majorana230j Majoranaandβj23U [21]is a - ↵ [21] -13↵21 13 jL 23 13→ → j j 21 unitaryand ↵ matrix31, CP —the violating Pontecorvo-Maki-Nakagawa-Sakataand ↵31 phases:, CP violating phases: (PMNS)k,j @ neutrino mixing ma-A @ A @ A " and" we! have used the standard notation c cos ✓ , s sin ✓ , the allowed range trix [3, 4, 9], U UPMNS. Similarly toU the" Cabibbo-Kobayashi-MaskawaU = V (✓" , ✓ , ✓ , ) Q(↵ , ↵ ) , (CKM) quark(1.2) ij ij 4 ij ij ⌘For ultrarelativisticPMNS neutrinos,⌘ the12 23 dispersion13 21 relation31 in eqn (7.8) can be approxi-⌘ ⌘ mixing matrix, the leptonicUPMNS matrix UUPMNS= V,( is✓12 described, ✓for23, ✓ the13 (to, values) aQ good(↵21 ofapproximation), ↵31 the) , angles by being 0(1.2)✓ij ⇡/2, and Takaaki Kajita where ⌘ a3 3 unitary mixingmated matrix. by In the widely used standard parametrization [6], UPMNS and Arthur⇥ B. McDonald 2 TABLE I: Results of the global 3⌫ oscillation analysis, in terms of best-fiti m values for the mass-mixing parameters and associated n iswhere expressed in terms of the solar,2 102 atmospheric2 0 andc13 reactor0 s13 neutrinoe mixingc12k s12 angles0 ✓12, i↵21/2 i↵31/2 ranges (n =1, 2, 3), defined by min = n with respect toE thek separateE + minima. in each mass orderingQ = Diag(1 (NO, IO),e and(7.18) to the,e absolute) . (1.4) ✓23 and ✓13, respectively,V and= one0 Diracc23 s23 - , and2 two010 (eventually)2 Majoranas12 c12 [21]0 , - ↵21(1.3) minimum in any ordering. (Note that0 the fit to the1 0 m andi sin ✓12≃parameters1 02 E is basically1 insensitive to the mass ordering.) We recall 0 s23 c23 s13e 0 ic 13 001 thatarXiv:1703.04471and ↵m312,is CP defined violating Lisi10 herein et al. phases: as m2 0(m2 + m2)c/2,13 and that0 s13is takene in the (cyclic)c12 intervals12 0 /⇡ [0, 2]. In this case,3 @ 1 2 A @ A @ A 2 V = 0 cand23 wes have23 used the standard010 notation cTheij cos neutrino✓ij, sij sins212 oscillation✓ij, thec12 allowed0 rangedata,, accumulated(1.3) over many years, allowed to determine Parameter0 Ordering1 0 Best fit 1 range⌘ 1 0∆⌘ mkj 2 1range 3 range 0 UforsPMNS the valuesc U of= theV ( angles✓12s, ✓ beinge23i , ✓13 00,the ✓)ijQ(c frequencies↵⇡/212,, and↵31) , and001 the amplitudes(1.2) (i.e. the angles and the mass squared di↵erences) 2 5 2 23 ⌘23 13 Ek13 Ej , (7.19) m /10 eV NO, IO, Any 7.37 7.21− – 7.54≃ 2E 7.07 – 7.73 6.93 – 7.96 Q = Diag(1,ei↵21/2,ei↵31/2) . (1.4) 2 1 @ A @ which driveA @ the solar and atmosphericA neutrino oscillations, with a rather high precision wheresin ✓ /10 NO, IO, Any2 2.97 2.81 – 3.14 2.65 – 3.34 2.50 – 3.54 and12 we have usedwhere the∆m standardis the notation squared-masscij dicosfference✓ij, sij sin ✓ij, the allowed range 2 3 2 kj (see, e.g., [6]). Furthermore, there were spectacular developments in the period June m /10 eV NOThe neutrino oscillation 2.525 data, accumulatedi 2.495⌘ – over2.567 many⌘ years, allowed 2.454 to determine – 2.606 2.411 – 2.646 | for the| values10 of thethe 0 frequenciesangles being andc13 the 0 amplitudes0 ✓sij13e (i.e.⇡/2, the and anglesc12 ands the12 mass0 squared di↵erences) IO 2.505 2011 2.473 -2 – June 2.539 20122 year2 in 2.430 what – 2.582 concerns the 2.390CHOOZ – 2.624 angle ✓13. In June of 2011 the T2K V = 0 c23 whichs23 drive the solar010 and atmospheric neutrino∆mkj oscillations,s12mkc12 withm0j a rather, , high(1.3) precision (7.20) 0 (see,Any e.g.,1 [6]).0 Furthermore, 2.525i therei werecollaboration↵21 2.495/1 spectacular2 0 –i↵ 2.56731≡/2 developments− reported1 in the 2.454[22] period evidence – June 2.606 at 2.5 2.411for – a 2.646 non-zero value of ✓ . Subsequently 0 s23 c23 Qs13=e Diag(10 ,ec13 ,e 001) . (1.4) 13 2 2 2011 - June 2012 year in what concerns the CHOOZ angle ✓13. In June of 2011 the T2K sin ✓13/10 @ and NOA @ 2.15the 2.08A MINOS@ – 2.22 [23] andA Double 1.99 – Chooz 2.31 [24] collaborations 1.90 – 2.40 also reported evidence for ✓13 = collaboration reported [22] evidence at 2.5 for a non-zero value of ✓13. Subsequently and we have used the standardIO notation 2.16cij cos ✓ij 2.07, sij – 2.24sin ✓ij, the allowed 1.98 range – 2.33 1.90 – 2.42 6 The neutrino oscillationthe MINOS [23] data, and Double accumulated Chooz⌘ [24]0, collaborations although over⌘E many= also⃗p with years, reported a allowed evidence smaller for to✓ statistical13 determine= significance.(7.21) Global analysis of the neutrino for the values of the angles being 0 ✓ ⇡/2, and | | 6 the frequencies and0,Any although the amplitudes with a 2.15 smallerij (i.e. statistical the angles 2.08 significance. – 2.22 and Global the mass analysis squared of the 1.99 neutrino – di 2.31↵erences) 1.90 – 2.40 2 1 is theoscillation neutrino data, energy, including the neglecting data fromoscillation the the T2K mass and data, MINOS contribution. including experiments, performed Therefore, the data from the transition the T2K and MINOS experiments, performed sin ✓23/10 NO 4.25 4.10 – 4.46 3.95 – 4.70 3.81 – 6.15 which drive the solarin [25], and showedQ atmospheric= Diag(1 that actually,ei↵ neutrino21 sin/2✓,e13 i=↵31 0/ atoscillations,2) . 3 . In March with of 2012 a rather the first(1.4) high data of precision probabilityIO in eqn 5.89 (7.17) can 4.17 bein6 – 4.48 [25],approximated 5.67 showed – 6.05 that by 3.99 actually – 4.83 5.33 sin ✓ –13 6.21= 0 at 3.843 – 6.36. In March of 2012 the first data of the Daya Bay reactor antineutrino experiment on ✓13 were published [26]. The value 6 (see, e.g., [6]). Furthermore,2 there were spectacular developments in the period June ofAny sin 2✓13 was measured 4.25 with a ratherthe 4.10 high Daya – precision 4.46 Bay and reactor was found 3.95 – to antineutrino 4.70 be di↵erent5.75 – 6.00 experiment 3.81 – on 6.26✓13 were published [26]. The value 2011The - neutrino June 2012 oscillation yearfrom zero in data, what at 5.2 accumulated concerns: the over CHOOZ many2 years, angle allowed✓13. In to June determine of 2011 2 the T2K /⇡ NO 1.38of 1.18 sin –2 1.61✓ was measured 1.00∆m with –kj 1.90t a rather 0 high – 0.17 precision0.76 – 2 and was found to be di↵erent the frequencies and the amplitudes (i.e. thesin2 angles2✓ =0. and092 the0.016 mass13 0.005 squared. di↵erences)(1.5) collaboration reported [22] evidencePνα νβ at(t)= 2.135 forUα∗± akU non-zeroβk±UαjUβ value∗j exp of ✓13i . Subsequently. (7.22) which drive the solar andIO atmospheric 1.31 neutrino→ oscillations,from 1.12 zero – 1.62 with at a rather 5.2 : high# precision− 0.922 –E 1.88$ 0 – 0.15 0.69 – 2 the MINOS [23] and Double Chooz [24] collaborationsk,j also reported evidence for ✓13 = (see, e.g., [6]). Furthermore,Any there were 1.38 spectacular! 1.18 developments – 1.61 in the period 1.00 June – 1.902 3 6 0 – 0.17 0.76 – 2 0, although with a smaller statistical significance. Global analysis ofsin the2 neutrino✓13 =0.092 0. 016 0.005 . (1.5) 2011 - June 2012The year finalin what step concerns in the the standard CHOOZ angle derivation✓13. In of June the of neutrino 2011 the T2K oscillation probability± is ± Aurora Meronioscillation data, including the data fromUniversity the T2K of and Helsinki MINOS2 experiments, performed 3 collaborationTable I reports reportedbased best-fit [22] on values evidencethe fact and at that, parameter 2.5 infor neutrino a ranges non-zero for oscillation value separate of ✓13 experiments,. Subsequentlyminimization the in each propagation separate ordering time (NO in [25], showed that actually sin ✓ = 0 at 3 . In March of 20122 the first data of 3 andthe MINOS IO) and [23] in any and ordering; Double Chooz the latter [24]13 collaborations case takes into also account reported the evidence above for IO✓13NO= value. The known parameters 2 2 t2 is not2 measured. What6 is known is the distance L between 6 the source and the (0, them although, Daya m , Bay withsin reactor✓ a12 smaller, sin antineutrino✓13 statistical), which a significance.↵ experimentect the absolute Global on ✓ mass13 analysiswere observables published of the neutrino in [26].Eqs. (4)–(6), The value are determined with a | 2 | detector. Since ultrarelativistic neutrinos propagate almost at the speed of light, it fractionaloscillationof sin 2 1✓ data, 13accuracywas including measured (defined the data with as 1/6 from a of rather the the T2K3 high andrange) precision MINOS of (2 experiments,.3 and, 1.6, was5.8, found4 performed.0) percent, to be respectively. di↵erent For such param- is possible to approximate±t = L,leadingto 2 eters,infrom [25], it zero showed turns at out that5.2 that : actually minimization sin ✓13 = in 0 any at ordering3 . In reproduces March of 2012 the the same first allowed data of ranges as for NO. Given the m 2 6 andthe Daya m estimates Bay reactor in antineutrino Table I, Eq.2 experiment(3) becomes on ✓ were published [26]. The value sin 2✓13 =0.092 130.016 0.005 . 2 (1.5) of sin2 2✓ was measured with a rather high precision± and± was found to be di↵erent∆mkjL 13 P (L, E)= (0,U0∗.86U, 5.06)U U10∗ 2expeV (NO)i , . (7.23) (νmα ,mνβ ,m) > αk βk αj β j (10) from zero at 5.2 : →1 2 3 (4.97, 5.04, 0) ⇥ 10 2 eV# (IO)− . 2E $ 2 ⇠ k,j 3 sin 2✓13 =0.092 0.016⇢! 0.005 . ⇥ (1.5) 2 ± ± The parameterThis sin expression✓23 is less well shows known, that at the the source–detector level of 9.6%. At distance 3 , its octantL and degeneracy the neutrino is unresolved, energy and maximal mixingE isare also the allowed. quantities At lower depending significance, on the maximal experiment mixing is which disfavored determine3 in both the NO phases and IO, of and the first octant is preferred in NO. The n ranges for ✓23 for any ordering are larger than for NO (Table I), as a result of neutrino oscillations 2 2 joining the NO and IO intervals determined by the curves in the∆m right-lower2 L panel of Fig. 1 at = n . Concerning the possible CP-violating phase , our analysis strengthen the trendkj in favor of 3⇡/2 [9, 11, 42], and disfavors Φkj = . (7.24) ranges close ⇡/2 at > 3 . In any case, the parameters ✓− and2 E do not enter in⇠ the calculation of (m ,m , ⌃). ⇠ 23 A few remarks are in⇠ order about the IO-NO o↵set in Eq. (9). This value is in the ballpark of the o 2cial SK fit Of course, the phases2 are determined also by the squared-mass2 differences ∆mkj , results quoted in [46, 47], namely: IO NO =4.3 (for SK data at fixed ✓13) and IO NO =5.2 (for SK + T2K which are physical constants. The amplitude of the2 oscillations is specified only data at fixed ✓13). By excluding SK atmospheric data in our fit, we find IO NO =1.1, in qualitative accord with the o cial T2K data analysis constrained by reactor data [42]. Concerning SK atmospheric data, it has been emphasized [9, 11, 12] that the complete set of bins and systematics [46, 47] can only be handled within the collaboration, especially when ⌫/⌫ or multi-ring event features are involved. Nevertheless, we think it useful to continue updating our analysis of reproducible SK samples, namely, sub/multi-GeV single-ring (e-like and µ-like) and stopping/through-going (µ-like) distributions. These samples encode interesting (although entangled and smeared) pieces of information about subleading e↵ects driven by known and unknown oscillation parameters, see e.g. [2]; in particular, they contributed to early hints of nonzero ✓13 [48]. At present, we trace the atmospheric hint of NO to e-like events, especially multi-GeV, in qualitative agreement with [49].1 Summarizing, the SK(+T2K) o cial results in [42, 46, 47] and ours in Eq. (9) suggest, at face value, that global 3⌫ oscillation analyses may have reached an overall 2 sensitivity to the mass ordering, with a preference for NO driven by atmospheric data and corroborated by accelerator⇠ data, together with reactor constraints. This intriguing indication, although still tentative, is generally supported by cosmological data (see Sec. II C) and thus warrants a dedicated discussion in the context of absolute ⌫ mass observables (see Sec. III).
1 Note, however, that weaker results for the IO-NO di↵erence (< 1 ), with or without atmospheric data, have been found in [11]. ⇠ Unknowns in Neutrino Physics
• Mass Ordering (Normal or Inverted) • Absolute Neutrino Mass Scale • CP violation in the leptonic sector • The nature: Dirac or Majorana
Aurora Meroni University of Helsinki 4 I The three neutrino mixing framework
Subsequently, the RENO experiment reported a 4.9 evidence for a non-zero value of ✓13 [27], compatibleI The three with neutrino the Day mixing Bay result: framework
sin2 2✓ =0.113 0.013 0.019 . (1.6) Subsequently, the RENO13 experiment± reported± a 4.9 evidence for a non-zero value of ✓13 [27], compatible with the Day Bay result: The results on ✓13 described above will have far reaching implications for the program 2 of future research in neutrino physicssin 2✓ (see,13 =0 e.g.,.113 [28]).0.013 In0 Table.019 . 1.1 we list the best(1.6) fit values of the angles parametrising the PMNS± mixing± matrix with 1 uncertainty coming formThe results two of on the✓13 latestdescribed global above fits will analysis have whichfar reaching combine implications results from for the several program experimentsof future [29, 30]. research From in the neutrino 3 allowed physics intervals (see, e.g., obtained [28]). In in Table [29] we 1.1 can we write list the the best fit values of the angles parametrising the PMNS mixing matrix with 1 uncertainty numerical expression for UPMNS : coming form two| of the latest| global fits analysis which combine results from several experiments [29, 30].0.788 From0 the.853 3 0allowed.505 intervals0.590 0 obtained.130 0.177 in [29] we can write the numerical expression for U : U = 0.474 | PMNS0.481| 0.398 0.666 0.570 0.785 . (1.7) | PMNS| 0 1 0.201 00.788.3930 0.853.549 0.5050.7030.590 0.593 0.1300.8110.177 U @ = 0.474 0.481 0.398 0.666 0.570 0.785A . (1.7) | PMNS| 0 1 0.201 0.393 0.549 0.703 0.593 0.811 Parameter@ Fogli et al. [29] Gonzalez-Garcia et al. [30] A 2 5 2 +0.26 m21[10 eV ]7.54 0.22 7.50 0.185 Parameter Fogli et al. [29] Gonzalez-Garcia± et al. [30] m2 [10 5eV22]7.43+0.06.54+0.26 2.477+0.50.069 0.185 2 3 21 2 0.10 0.22 0.067± m31[10 eV ] +0.11 +0.042 2.42 0.07 +0.06 2.43 0.065+0.069 2 3 2 2.43 0.10 2.47 0.067 m31[10 eV ] +0.11 +0.042 2 +0.0182.42 0.07 2.43 0.065 sin ✓12 0.307 0 .016 0.30 0.013 ± 2 +0.018 I The three neutrino mixing framework sin ✓12 +00..024307 0.016 0+0.30.037 0.013 2 0.386 0.021 0.41 0.025± sin ✓23 Subsequently, the RENO experiment reported a 4.9 evidence for a non-zero0.392 value+0 of0..039386+0.0240.41+0.037 0.041.59+0+0.037.021 ✓13 [27], compatible with the Day Bay result: 2 0.022 0.021 0.025 0.0250.022 sin ✓23 sin2 2✓ =0.113 0.013 0.019 . (1.6) +0.039 +0.037 +0.021 13 ± ± 0.392 0.022 0.41 0.025 0.59 0.022 0.0241 0.0025 The results on ✓13 described above willsin have2 far✓ reaching implications for the program± 0.023 0.0023 of future research in neutrino physics (see, e.g.,13 [28]). In Table 1.1 we list the0 best+0.0241.0023 0.0025 fit values of the angles parametrising the PMNS mixing matrix2 with0 1. 0244uncertainty0.0025 ± coming form two of the latest global fits analysis whichsin combine✓13 results from several ±+0.0023 0.023 0.0023 experiments [29, 30]. From the 3 allowed intervals obtained in [29] we can write the0.0244 0.0025 ± numerical expression for UPMNS : Table 1.1:| | The table summarizes two recent global fit analysis for the neutrino os- 0.788 0.853 0.505 0.590 0.130 0.177 2 2 2 UPMNS = 0Table.474 0.481 1.1: 0.398 0The.666 0. table570 0.785 summarizes. (1.7) two recent global fit analysis for the neutrino os- cillation| | 0 parameters corresponding 1 to 1 uncertainty. For m ,sin ✓23 and sin ✓13 0.201 0.393 0.549 0.703 0.593 0.811 31 2 2 2 the upper@ cillation (lower) parameters row corresponds correspondingA to normal to 1 (inverted) uncertainty. neutrino For massm31,sin ordering.✓23 and These sin ✓13 valuesParameter andthe the Fogli upper et methods al. [29] (lower) Gonzalez-Garcia to row extract et corresponds al. [30] them tofrom normal experimental (inverted) data neutrino are mass discussed ordering. in re- These 2 5 2 +0.26 m21[10 eVvalues]7.54 and0.22 the methods7.50 0.185 to extract them from experimental data are discussed in re- spectively in [29] and [30]. ± +0.06 +0.069 2 3 spectively2 2.43 0.10 in [29]2. and47 0.067 [30]. m31[10 eV ] +0.11 +0.042 comparable to that of LBNE. 2.42 0.07 2.43 0.065 European long-baseline projects (LAGUNA-LBNO) involve an intense neutrino source 2 +0.018 at CERN, a near detector, and a (phased) 100 kT underground LAr detector at Pyh¨asalmi Thesin experimental✓12 0.307 0.016 data0.30 we0.013 have summarized in Table 1.1 are compatible with dif- ± in Finland, at a baseline of 2300 km. The long baseline, large detector mass, underground The experimental data welocation, have near detector, summarized and a broad-band neutrino in beam Table from a 2 MW 1.1 proton are source make compatible with dif- 0.386+0.024 0.41+0.037 Mass Ordering 2 0.021 0.025 LAGUNA-LBNO an ultimate neutrino oscillation experiment, with outstanding sensitivity ferent neutrinosin ✓ mass patterns (see Figure 1.1): ferent23 neutrino+0.039 mass+0.037 patterns+0.021 to both (see the neutrino Figure mass hierarchy 1.1): and . However, the timescale, costs, and priority to 0.392 0.022 0.41 0.025 0.59 0.022 CP host such an experiment in Europe are not well defined at present. JUNO is a 20 kT liquid scintillator detector to be located at the solar oscillation maxi- 2 0.0241 0.0025 sin ✓13 ±+0.0023 0.023 0.0023 mum, approximately 60 km away from two nuclear power plants in China. This experiment 2 2 spectrum0 with.0244 0.0025 normal± ordering (NO), m
Cosmological Surveys Planck + EUCLID + …
β-Decay Experiments
KATRIN + Project8
Neutrinoless Double β-Decay Experiments EXO-200 + GERDA + CUORE + KamLAND-Zen + SNO+ …
Multi-Messenger astronomy
Ligo + Virgo + Super-Kamiokande + Antares + IceCube + HSK…
Aurora Meroni University of Helsinki 6 Prepared for submission to JCAP
Neutrino masses and cosmology with Lyman-alpha forest power spectrum Nathalie Palanque-Delabrouille,a Christophe Yeche,` a Julien Baur,a Christophe Magneville,a Graziano Rossi,b Julien Lesgourgues,c,d,e Arnaud Borde,a, f Etienne Burtin,a Jean-Marc LeGoff,a James Rich,a Matteo Viel,g,h David Weinbergi aCEA, Centre de Saclay, IRFU/SPP, F-91191 Gif-sur-Yvette, France bDepartment of Astronomy and Space Science, Sejong University, Seoul, 143-747, Korea cInstitut de Theorie´ des Phenom´ enes` Physiques, Ecole´ Polytechnique Fed´ erale´ de Lausanne, CH- 1015, Lausanne, Switzerland dCERN, Theory Division, CH-1211 Geneva 23, Switzerland eLAPTh, Univ. de Savoie, CNRS, B.P.110, Annecy-le-Vieux F-74941, France f DGA, 7 rue des Mathurins, 92221 Bagneux cedex, France gINAF, Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34131 Trieste, Italy hINFN/National Institute for Nuclear Physics, The Via Valerio absolute 2, I-34127 Trieste, Italymass iDepartment of Physics and Center for Cosmology and Astro-Particle Physics, Ohio State Univer- sity, Columbus, OH 43210, USA I The three neutrino mixing framework E-mail: [email protected],Cosmological [email protected], Surveys [email protected], [email protected], [email protected], Julien.Lesgourgues@cern.ch Planck temperature power spectrum with a WMAP polarization low-multipole (` 23) Abstract. We present constraints on neutrino masses,and ACT the primordial high-multipole fluctuation (` spectrum2500) from data. We refer to this CMB data combination as inflation, and1 other parameters of the ⇤CDM model, using the one-dimensional Ly↵ -forest power Planck+WP. InMeasuring this case neutrino the upper masses limit with on a the future sum galaxy of the survey neutrino mass reads: spectrum measuredPlanck by+ Palanque-DelabrouilleWP et al. [1] from the BaryonJan OscillationHamann, Steen Spectroscopic Hannestad, Yvonne Y.Y. Wong. Survey (BOSS) of the Sloan Digital Sky Survey (SDSS-III), complementedJCAP 1211 by⌃ m Planck(2012)i < 0520 2015.66 eV cosmic at 95% C.L. (Planck + WP), (1.9) 0.50 QD microwave background (CMB) data and other cosmologicalCombining probes. the latter This paper with improves the Barion on the Acoustic Oscillation data (BAO), the limit is
previous] analysis by Palanque-Delabrouille et al. [2] by using a morePlanck powerful 2013 set results. of calibrating XVI. Cosmological parameters significantly loweredAstron.Astrophys. at 571 (2014) A16 eV hydrodynamical[ Planck simulations+WP+ thatBAO reduces uncertainties associated with resolution and box size, by adoptingi a more flexible set of nuisance parameters for describing the evolution⌃ mi < of0. the23 eV intergalactic at 95% C.L. (Planck + WP + BAO). (1.10) m
medium,Σ by including additional freedom to accountThe for systematic above upper uncertainties, limits and can by be using converted Planck into limits on the absolute scale of neutrino 2015 constraintsBOSS in place Ly ofα Planck+ Planck 2013. CMB Neutrino masses and cosmology with Lyman-alpha forest masses that readpower respectively spectrum m min . 0.22 eV in the more conservative case (eq. 1.9) Fitting0.10 Ly↵ data alone leads to cosmological parameters in excellentNathalie agreement Palanque-Delabrouille with the values (IRFU, SPP, Saclay) et al.. and mmin 0.07 eV in the more stringent case (eq. 1.10). This is depicted in Figure IH . JCAP 1511 (2015)n no.11, 011 derived independently from CMB data, except for a weakKATRIN tension on the scalar index . Combining 1.2. s BOSS Ly↵ with Planck CMB constrains the sum of neutrino masses to m⌫ < 0.12 eV (95% C.L.) 0.05 NH arXiv:1506.05976v2 [astro-ph.CO] 14 Oct 2015 including all identified systematic uncertainties, tighter than our previous limit (0.15 eV) and more P 1.50 robust. Adding Ly-4↵ data to CMB data reduces the uncertainties on the optical depth to reionization 10 0.001 0.010 0.100 1 1.00 ⌧, through the correlation of ⌧ with 8. Similarly, correlations between cosmological parameters Euclid will test the sum mmin[eV] 0.70 Planck+WP help in constraining the tensor-to-scalar ratio of primordial fluctuations r. The tension on ns can be of the neutrino masses accommodated by allowing for a running dns/d ln k. Allowing running as a free parameter0.50 in the fits at the level of 0.01 eV
does not change the limit on m⌫. We discuss possible interpretations of these resultsD in the context 0.30 eV
@ Planck+WP+BAO
of slow-roll inflation. i
P m 0.20 S 0.15 An artist view of the Euclid Satellite – 0.10 Aurora Meroni University of Helsinki IH 7 KATRIN
NH
10-4 0.001 0.01 0.1 1
mmin eV
Figure 1.2: The sum of the light neutrino masses@ D plotted as function of the lightest neutrino mass considering the 3 uncertainty in the atmospheric and solar m2 given in [29]. The horizontal solid lines represent the recent Planck limits. The allowed area is indicated by the arrows.
We have to add that in addition to the Planck Collaboration also the South Pole Telescope (SPT) Collaboration released in December 2012 a fit analysis that indicated a preferred value for the sum of the light neutrino, being the latter ⌃ m =0.32 0.11 i ± eV, with a 3 detection of positive neutrino mass in the range [0.01, 0.63]eV at 99.7 % C.L. [35]. Clearly, all these bounds are not definitive and they will be improved by current or forthcoming observations. For instance, the EUCLID survey [36], approved in 2012, will be able most likely to measure the neutrino mass sum at the 0.01 eV level of precision by combining their data with measurements of the CMB anisotropies by the Planck mission [33]. Such an outstanding precision will be able to provide unique information on, and possibly determine, the absolute scale of neutrino masses [37]: the minimum of the sum compatible with current neutrino oscillation data being ⌃ =5.87 10 2 min ⇥ eV for a normal hierarchical (NH) spectrum and ⌃ =9.78 10 2 eV for an inverted min ⇥ hierarchical spectrum (IH). This information could be used in synergy with ( )0⌫- decay data to test the nature —Dirac or Majorana— of massive neutrinos.
6 1 Motivations and Goals
3 2 6 6 6 2 1 ? m21
2 2 m31 m32 2 6 2 ?1 ? m21 ?3
Figure 1.1: The two possible neutrino mass spectra: with normal ordering (NO, left) and with inverted ordering (IO, right).
inverted hierarchical (IH): m m
5
Figure 4: Dependence on endpoint energy E0 of total count rate (left), relative fraction in the last 10 eV below the endpoint (middle) and total count rate in the last 10 eV of a -emitter (right). These numbers have been calculated for a super-allowed -decay using (18) for m(⌫e) = 0 and neglecting possible final states as well as the Fermi function F .
9 The Nature: Dirac or Majorana
c T i = C ¯i = i The Majorana nature of neutrinos manifests itself in the existence of processes in which the total lepton charge L changes by two units. + + + K + µ + µ + µ +(A, Z) µ +(A, Z 2) Double β-Decay
(A, Z) (A, Z + 2) + 2e (+2¯ ) e e WL WL e
¯e i
¯e W WL L
e e Double b-Decay with neutrinos Neutrinoless Double β-Decay 1935, Maria Goeppert-Mayer 1939, Wolfgang Furry
Aurora Meroni University of Helsinki 9 I Possible L =2coupligs in ( )0⌫-Decay
I.I Light Majorana Neutrino exchange mechanism
The standard scenario to allow ( )0⌫-decay is the exchange of a light Majorana left- handed neutrino, , via V A weak interactions. The following term in the S-matrix jL (or scattering matrix) gives the contribution to the matrix element of the process in second order of perturbation theory in GF :
(2) i w.i.(x)dx i S.I.(x)dx S = T e HI e HI R R 2 (2.4) ⇣( i) ⌘ S.I. 2 4 4 w.i. w.i. h h i I (x)dx GF dx1dx2N I (x1) I (x2) T j↵(x1)j (x2)e H / 2! L L R Z ⇣ ⌘ where ⇥ ⇤ w.i. =¯e ⌫ . (2.5) LI L ↵ eL We can recast the weak lepton current part using the Majorana properties T C = j † c = ⇠ , C 1 C = T and ⌫ = 3 U with U being the elements of the j j j ↵ ↵ eL j=1 ej jL ej first row of the PMNS mixing matrix. P Thus we get1:
2 T T T (¯e ⌫ )(¯e ⌫ )= (U ) e¯ P C†CP C†Ce¯ L ↵ eL L eL ej ↵ L j j L Xj = ⇠ (U )2e¯ P P Ce¯T j ej ↵ L j j L (2.6) Xj = ⇠ (U )2e¯ P S(x x )P Ce¯T j ej ↵ L |{z1} 2 L Xj where S(x x ) is the propagator: 1 2
iq(x1 x2) iq(x x ) e (/q + mk)dq e 1 2 P S(x x )P = P ( i) P = P ( i)(m ) P L 1 2 L L q2 m2 L L k q2 m2 L R k R k (2.7) ThereforeEffective one can define Majorana the e↵ective Majorana mass mass m corresponding to the con- |h i| tribution from standard (V A) charged current (CC) weak interaction as follows: 3 m (U )2 m = m U 2 + m U 2 + m U 2 , (all m 0). (2.8) |h i| ⌘ ej j | 1 e1 2 e2 3 e3| j j X One can show (appendix of [9]) that taking some approximations, that usually are made in calculating ( )0⌫-decay amplitudes, the hadron current is a symmetric operator: IGEX+HdM+GERDA IGEX+HdM+GERDA QD A↵ J↵(x1)J (x2)=J (x2)J↵(x1), (2.9) 0.100 ⌘ 0.100 therefore in the matrix element the product of the hadron part and the weak V-A IH current can be written as: ] ] 1 T eV T T eV 0.010 0.010 WP |[ |[ e¯ P Ce¯ A =¯e P Ce¯ A =¯e(g + ( ))P Ce¯ A , (2.10) ↵ L ↵ ↵ R〉 ↵ ↵ ↵ ↵ R ↵ 〉 +
2 BAO m m 〈 〈 + | | 1 NH We define theBAO chiral projectors as PL,R = (1 5)/2 WP +
⌥ Planck + WP 0.001 WP 0.001 + 20 + Planck Planck KATRIN Planck
-4 10-4 10 10-4 0.001 0.010 0.100 1 0.05 0.10 0.50 1
mmin [eV] Σ [eV]
Aurora Meroni University of Helsinki 10 Heavy neutrino contributions in ( )0⌫-decay using a multi-isotope approach and 48Ca
Heavy neutrinoAurora contributionsMeroni⇤ in ( )0⌫-decay 48 CP3-Originsusing & the a Danishmulti-isotope Institute approach for Advanced and StudyCaDanish IAS, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark. Aurora Meroni⇤ CP3-Origins & the Danish Institute for Advanced Study Danish IAS, S. T. Petcov University of Southern Denmark, Campusvej 55,† DK-5230 Odense M, Denmark. SISSA, Via Bonomea 265, 34136 Trieste, Italy & Kavli IPMU (WPI), S. T. Petcov† SISSA,The University Via Bonomea of Tokyo, 265, 34136 Kashiwa, Trieste, Japan. Italy & Kavli IPMU (WPI), The University of Tokyo, Kashiwa, Japan. +....‡ +... +....‡ We study the implications of two on-interfering+... or interfering mechanisms in ( )0⌫ -decay using a multi-isotope approach involving NMEs of 48Ca . We study the implications of two on-interfering or interfering mechanisms in ( )0⌫ -decay using a multi-isotope approach involving NMEs of 48Ca . Status of 2β0ν-decay experiments I. LIMITS I. LIMITS
GERDA T 0⌫ (76Ge) > 5.3 1025yr at 90% C.L., (1) GERDA T1/02⌫ (76Ge) > 5.3 ⇥1025yr at 90% C.L., (1) 1/2 ⇥ IGEX+HdM+GERDA QD 0.100 00⌫⌫ 136136 2626 Kamland-ZenKamland-Zen TT1/2(( Xe)Xe) > 11..11 1010 yryr at at 90% 90% C.L C.,.L., (2) (2) 1/2 ⇥⇥ IH ]
0⌫ 76 27 28 eV 0.010 48 76 0100⌫ 76 116 2713028 136 150 |[
LEGEND-200 T ( Ge) >few10 (10 laterstage)yr at 90% C.L., 〉 (3) LEGEND-200Ca, Ge,T1/12/(2 Mo,Ge) >fewCd,10 (10Te,laterstageXe,)yr at 90%Nd C.L., (3) m 〈 |
NH BAO II. CONSTRAINTS + II. CONSTRAINTS WP 0.001 WP + + 130 76 136 76 130 The most stringentCUORE upper ( Te), limits GERDA on (m Ge),were SuperNEMO, set by the EXO IGEX ( Xe), ( Ge), MAJORANA CUORICINO ( Te), 76 100 116 136 76 48 130 The most stringent100 ( Ge), MOON upper ( limitsMo), on COBRAm| (| wereCd), XMASS set by the( Xe), IGEX CANDLES (136 Ge), ( CUORICINOCa), 76 ( Te), Planck KATRIN NEMO3 ( Mo) and more recently by EXO-200 , KamLAND-ZEN ( Xe) and GERDA ( Ge) Planck 100 KamLAND-Zen (136Xe), SNO+| (150| Nd), etc. 136 76 NEMO3experiments ( Mo) (see and e.g. more [1] for recently a summary). by EXO-200 A lower limit , KamLAND-ZEN on the half-life of (76Ge,Xe) T0 and⌫ > 1 GERDA.9 1025 (yr Ge) 76 1/2 0⌫ ⇥ 10-4 25 experiments (see e.g. [1] for a summary). A lower limit76 on the half-life of Ge, T > 1.9 10 -4yr (90% C.L.), was found in the Heidelberg-Moscow Ge experiment (HdM) [2]. Further1/2 a positive⇥ 10 0.001 0.010 0.100 1 0⌫ 76 25 m [eV] (90%( C.L.),)0⌫-decay was signal found at in> 3 the , corresponding Heidelberg-Moscow to T1/2 =(0Ge.69 experiment4.18) 10 (HdM)yr (99.73% [2]. C.L.) Further and implying a positive min 0⌫ ⇥ 25 ( ) m-decay =(0 signal.1 0. at9)> eV,3 was, corresponding claimed to have to been T observed=(0.69 in [3],4.18) and10 a lateryr analysis (99.73% reported C.L.) and evidence implying |0⌫ | 1/2 ⇥ for ( ) -decay at 6 corresponding to m =0.32 0.03 eV [4]. More recently, a large number of m =(0.01⌫ 0.9) eV, was claimed to have| been | observed± in [3], and a later analysis reported evidence | projects,| or already running experiments, have aimed at a sensitivity of m (0.01 0.05) eV, i.e., for ( )0⌫-decay at 6 corresponding to m =0.32 0.03 eV [4]. More recently, a large number of | | 130⇠ 76 to probe the range of m corresponding| to| IH mass spectrum± [1]: CUORE ( Te), GERDA ( Ge), projects, or already running| | experiments, have aimed at a sensitivity of m (0.01 0.05) eV, i.e., SuperNEMO, EXO (136Xe), MAJORANA (76Ge), MOON (100Mo), COBRA| (116|Cd),⇠ XMASS (136Xe), to probe the range of m corresponding to IH mass spectrum [1]: CUORE (130Te), GERDA (76Ge), | | SuperNEMO, EXO (136Xe), MAJORANA (76Ge), MOON (100Mo), COBRA (116Cd), XMASS (136Xe), ⇤Electronic address: [email protected] †Electronic address: [email protected] Aurora Meroni University of Helsinki ‡Electronic address: +... 11 ⇤Electronic address: [email protected] †Electronic address: [email protected] ‡Electronic address: +... Multi-Messenger Astronomy
Photons, neutrinos and gravitational waves
LISA
Fermi Gamma-ray Space Telescope
Gravitational waves Observatories
Borexino
Super-Kamiokande
Antares Dayα Bay
IceCube SNEWS: SuperNova Early Warning System Aurora Meroni University of Helsinki 12 PHYSICAL REVIEW LETTERS week ending PRL 116, 061102 (2016) PHYSICAL REVIEW LETTERS 12 FEBRUARY 2016 week ending PRL 116, 061102 (2016) 12 FEBRUARY 2016 propagation time, the events have a combined signal-to- noise ratio (SNR) of 24propagation[45]. time, the events have a combined signal-to- Only the LIGO detectorsnoise ratio were (SNR) observing of 24 at[45] the. time of Only the LIGO detectors were observing at the time of GW150914. The Virgo detector was being upgraded, GW150914. The Virgo detector was being upgraded, and GEO 600, though not sufficiently sensitive to detect and GEO 600, though not sufficiently sensitive to detect this event, was operatingthis event, but was not operating in observational but not in observational mode. With only twomode. detectors With the only source two detectors position the is source position is primarily determinedprimarily by the relative determined arrival by the time relative and arrival time andweek ending Multi-MessengerPHYSICAL Astronomy REVIEW LETTERS2 PRL 116, 061102localized (2016) to an arealocalized of approximately to an area600 ofdeg approximately(90% 600 deg2 (90%12 FEBRUARY 2016 propagationObservation time,credible the of eventsGravitational region) have Waves[39,46] a combined fromcredible. a Binary signal-to- region) Black Hole[39,46] Merger . LIGO ScientificThe and Virgo basic Collaborations features (B.P. Abbott of (Caltech GW150914) et al.). point to it being PHYSICAL REVIEW LETTERSnoise ratioPhys.Rev.Lett. (SNR) of 116 24 (2016)[45]week no.6, ending. 061102 The basic features of GW150914 point to it being PRL 116, 061102 (2016) Only the LIGOproduced detectors12 FEBRUARY by were 2016 the observing coalescenceproduced at the time of by of two the coalescence black holes— ofi.e., two black holes—i.e., propagation time, the events have a combined signal-to- GW150914. Thetheir Virgo orbital detector inspiral was and beingtheir merger, orbital upgraded, and inspiral subsequent and merger, final and black subsequent final black noise ratio (SNR) of 24 [45]. and GEO 600,hole though ringdown. not sufficiently Over sensitive 0.2hole s, the ringdown. to signal detect increases Over 0.2 s, in the frequency signal increases in frequency Only the LIGO detectors were observing at the time of this event, was operating but not in observational GW150914. The Virgo detector was being upgraded, and amplitude in aboutand 8 cycles amplitude from in 35 about to 150 8 cycles Hz, where from 35 to 150 Hz, where and GEO 600, though not sufficiently sensitive to detect mode. With only two detectors the sourcethe positionamplitude is reaches a maximum. The most plausible this event, was operating but not in observational primarily determinedthe amplitude by the relative reaches arrival a maximum. time and The most plausible mode. With only two detectors the source position is localized to anexplanation area of approximately for this evolution600explanationdeg2 is(90% the for inspiral this evolution of two is orbiting the inspiral of two orbiting primarily determined by the relative arrival time and masses, m1 and m2, due to gravitational-wave emission. At localized to an area of approximately 600 deg2 (90% credible region)masses,[39,46]. m1 and m2, due to gravitational-wave emission. At credible region) [39,46]. The basic featuresthe lower of GW150914 frequencies, pointthe such to lower it evolution being frequencies, is characterized such evolution by is characterized by The basic features of GW150914 point to it being produced by the coalescence of two blackthe chirpholes— massi.e., [11] produced by the coalescence of two black holes—i.e., their orbital inspiralthe and chirp merger, mass and[11] subsequent final black their orbital inspiral and merger, and subsequent final black 3=5 3 FIG. 2. Top: Estimated gravitational-wave strain amplitude hole ringdown. Over 0.2 s, the signal increases in frequency hole ringdown. Over 0.2 s, the signal increases in frequency 3=5 3=5 3 m1m2 c3=5 5 −8=3 −FIG.11=3 2. Top: Estimated gravitational-wave strain amplitude and amplitude in about 8 cycles from 35 to 150 Hz, where and amplitude in about 8 cycles fromm m 35 to 150 Hz,Mc where5 ð Þ π f f_ ; from GW150914 projected onto H1. This shows the full M ð 1 2Þ ¼ mπ−8=3mf−111==53¼f_ G ;96 from GW150914 projected onto H1. This shows the full the amplitude reaches a maximum. The most plausible the amplitude reaches a maximum.¼ m m The1 most=5 ¼ plausibleG 96ð 1 þ 2Þ bandwidth of the waveforms, without the filtering used for Fig. 1. explanation for this evolution is the inspiral of two orbiting explanation for this evolution is the1 inspiral2 of two orbiting bandwidth of the waveforms,The inset without images theshow filtering numerical used relativity for Fig. models1. of the black masses, m and m , due to gravitational-wave emission. At ð þ Þ 1 2 where f and f_ are the observed frequencyThe and inset its images time showhole numerical horizons as relativity the black models holes coalesce. of the blackBottom: The Keplerian the lower frequencies, such evolution is characterized by masses, m1 and m2, due to gravitational-wave_ emission. At the chirp mass [11] the lower frequencies,where suchf and evolutionf are is the characterizedderivative observedobserved and by frequencyG and c are and the its gravitational time hole constant horizons and as the blackeffective holes black coalesce. hole separationBottom: The in units Keplerian of Schwarzschild radii the chirp mass [11]derivative and G and c are thefrequency gravitational constant and effective black hole( separationR 2GM=c in2) units and the of Schwarzschild effective relative radii velocity given by the 3=5 3 3=5 FIG. 2. Top: Estimated gravitational-wave strain amplitude speed of light. Estimating f and f_ from the data in Fig. 1, S m1m2 c 5 2 ¼ M ð Þ π−8=3f−11=3f_ ; from GW150914 projected onto H1. This shows the full (R 2GM=c ) and the effective relative velocity given by the3 1=3 1=5 chirp mass speed of light. Estimating f and f_ from the datatotal in Fig.mass1 , S post-Newtonian parameter v=c GMπf=c , where f is the ¼ m1 m2 ¼ G 96 bandwidth of the waveforms, without the filtering3=5 used for3 Fig. 1. we obtain3=5 a chirpFIG. mass 2. ofTop:M Estimated30M ,implyingthatthe gravitational-wave¼ strain amplitude 3 1=3 ¼ð Þ ð þ Þ m1m2 c 5 8=3 11=3 ⊙ post-Newtonian parametergravitational-wavev=c GM frequencyπf=c calculated, where f withis the numerical relativity The inset images showM numericalð relativityweÞ obtain models of a the chirp blackπ− massf− off_M ; 30M from,implyingthatthe GW150914≃ projected onto H1. This shows the full _ 1=5 total mass M m1 m2 is 70M in the detector frame. ¼ð Þ where f and f are the observed frequency and its time hole horizons as the black holes¼ m coalesce.1 mBottom:2 The¼ G Keplerian96 ≃ ¼ ⊙bandwidthþ of≳ the waveforms,⊙ withoutgravitational-wave the filtering used frequency forand Fig.M1.is calculated the total mass with (value numerical from relativity Table I). derivative and G and c are the gravitational constant and effective black hole separationð in unitstotalþ ofÞ Schwarzschild mass M radiim1 mThis2 is bounds70M thein sumthe detector of the Schwarzschild frame. radii of the 2 The inset images show numericaland relativityM is the models total of mass the black (value from Table I). _ (RS 2GM=c ) and the effective relative velocity given by¼ the þ ≳ ⊙ 2 speed of light. Estimating f and f from the data inAurora Fig. 1, Meroni¼ _ This boundsUniversity the sum of Helsinkibinary of the components Schwarzschild to 2GM=c radii of the210 km.13 To reach an post-Newtonianwhere parameterf v=cand fGMareπf=c the3 1=3 observed, where f is the frequency and its time hole horizons as the black holes coalesce. Bottom: The Keplerian we obtain a chirp mass of M 30M ,implyingthatthe ¼ð Þ 2 ≳ detector [33], a modified Michelson interferometer (see ≃ ⊙ gravitational-wavederivative frequency and calculatedG and with numericalc are the relativity gravitationalorbital constant frequency and effective of 75 black Hz (half hole separation the gravitational-wave in units of Schwarzschild radii total mass M m1 m2 is 70M in the detector frame. binary components to 2GM=c 210 km. To reach an ¼ þ ⊙ and M is the total mass (value from Table I). 2 This bounds the sum of the≳ Schwarzschild radii of the _ frequency) the≳ objects(RS must2GM=c have) and been the effective verydetector close relative and velocity[33] very, a given modifiedFig. by the3) that Michelson measures interferometer gravitational-wave (see strain as a differ- speed of light. Estimatingorbital frequencyf and f from of the 75 data Hz in (half Fig. 1, the gravitational-wave¼ binary components to 2GM=c2 210 km. To reach an post-Newtonian parameter v=c GMπf=c3 1=3, whereencef is the in length of its orthogonal arms. Each arm is formed ≳ detector [33]we, a modified obtain a Michelson chirpfrequency) mass interferometer of M the (see30 objectsM ,implyingthatthecompact; must have equal been Newtonian very close point and very massesFig. orbiting¼ð 3) that atÞ this measures gravitational-wave strain as a differ- orbital frequency of 75 Hz (half the gravitational-wave ≃ ⊙ gravitational-wave frequency calculated with numerical relativityby two mirrors, acting as test masses, separated by frequency) the objects must have been very close and very Fig. 3) that measurestotal mass gravitational-waveM m1 m strain2 is as a70 differ-M in thefrequency detector frame. would be only 350 km apart.ence A in pair length of of its orthogonal arms. Each arm is formed ¼compact;þ equal≳ ⊙ Newtonian point massesand M orbitingis the total at mass this (value from Table I). compact; equal Newtonian point masses orbiting at this ence in lengthThis of its bounds orthogonal the arms. sum Each of arm the is formed Schwarzschildneutron radii stars, of the while compact,≃ would not have the required Lx Ly L 4 km. A passing gravitational wave effec- by two mirrors, acting as testfrequency masses, separated would by be only 350 km apart. A pair of by two mirrors, acting as test masses, separated by frequency would be only 350 km apart. A pair of binary components to 2GM=c2 210 km. To reach an tively¼ alters¼ the¼ arm lengths such that the measured neutron stars, while compact,≃ would not have the required Lx Ly L 4 km. A passing gravitational wave effec- mass, while≃ a black hole neutron star binaryL L with theL 4 km. A passing gravitational wave effec- ¼ ¼ orbital¼ frequencyneutron of 75 Hzstars, (half while≳ the gravitational-wave compact, would notdetector have the[33] required, a modified Michelsonx y interferometer (see mass, while a black hole neutron star binary with the tively alters the arm lengths such that the measured ¼ ¼ ¼ difference is L t δL − δL h t L, where h is the deduced chirp massFig. would3) that havemeasures a very gravitational-wave largetively total alters mass, strain the as a arm differ- lengthsΔ such thatx the measuredy deduced chirp mass would have a very large total mass, difference is frequency)ΔL t δLx − theδLy objectsmass,h t L must, while where haveh is a the been black very hole close neutron and very star binary with the ð Þ¼ ¼ ð Þ ð Þ¼ ¼ ð Þ and would thus merge at much lower frequency. This gravitational-wave strain amplitude projected onto the and would thus merge at much lower frequency. This gravitational-wavecompact; strain equal amplitudededuced Newtonian projected chirp pointonto the mass masses would orbiting have at this a veryence large in length total of mass, its orthogonaldifference arms. Each is Δ armL ist formedδLx − δLy h t L, where h is the leaves black holes as the only known objects compact detector. Thisfrequency differential length would variation be only alters the350 phasekm apart.leaves A blackpair of holesby as two the mirrors, only known acting objectsas test masses, compact separatedð Þ¼detector. by This differential¼ ð Þ length variation alters the phase enough to reach an orbital frequency of 75 Hz without difference between the two lightand fields would returning thus to the merge at much lower frequency. This gravitational-wave strain amplitude projected onto the neutron stars, while compact,≃ would not haveenough the required to reachL anx orbitalLy L frequency4 km. A of passing 75 Hz gravitational without wavedifference effec- between the two light fields returning to the contact. Furthermore, the decay of the waveform after it beam splitter, transmitting an opticalleaves signal proportional black holes to as the only known objects¼ ¼ compact¼ detector. This differential length variation alters the phase the gravitational-wavemass, while strain to a the black output hole photodetector. neutron star binarycontact. with Furthermore, the tively the alters decay the of arm the lengths waveform such after that it the measuredbeam splitter, transmitting an optical signal proportional to peaks is consistent with the damped oscillations of a black difference between the two light fields returning to the hole relaxing to a final stationary Kerr configuration. To achievededuced sufficient sensitivity chirp massenough to measure would to gravitational have reach a very an orbital largepeaks total is frequency consistent mass, difference of with 75 the Hz is dampedΔ withoutL t oscillationsδLx − δLy ofh at blackL, where htheis gravitational-wave the strain to the output photodetector. ð Þ¼ ¼ ð Þ Below, we present a general-relativistic analysis of waves, the detectorsand would include thus severalcontact. merge enhancements at Furthermore, much to the lower frequency. the decay This of thegravitational-wave waveform after strain it amplitudebeam splitter, projected transmitting ontoTo the achieve an optical sufficient signal sensitivity proportional to measure to gravitational GW150914; Fig. 2 shows the calculated waveform using basic Michelson interferometer. First, each arm contains a hole relaxing to a final stationary Kerr configuration. the resulting source parameters. resonant opticalleaves cavity, black formed holesbypeaks its two as test is the mass consistent only mirrors, known with objectsBelow, the damped compact we present oscillationsdetector. a general-relativistic This of differentiala black lengththe analysis gravitational-wave variation alters of thewaves, phase strain the to detectors the output include photodetector. several enhancements to the that multipliesenough the effect to of a reach gravitationalhole an orbital waverelaxing on frequency the light to a of final 75 Hz stationary without Kerrdifference configuration. between the two lightTo achieve fields returning sufficientbasic to the sensitivity Michelson to interferometer. measure gravitational First, each arm contains a phase by a factor of 300 [48]. Second, a partially trans- GW150914; Fig. 2 shows the calculated waveform using III. DETECTORS contact. Furthermore, the decay of the waveform after it beam splitter, transmitting an optical signal proportional to missive power-recycling mirror atBelow, the input provides we addi-presentthe a general-relativistic resulting source parameters. analysis of waves, the detectorsresonant include optical several cavity, enhancements formed by its to two the test mass mirrors, peaks is consistent with the damped oscillations of a black the gravitational-wave strain to the output photodetector. Gravitational-wave astronomy exploits multiple, widely tional resonant buildup of the laser light in the interferometer that multiplies the effect of a gravitational wave on the light hole relaxing toGW150914; a final stationary Fig. 2 Kerrshows configuration. the calculatedTo waveform achieve sufficient using sensitivitybasic to Michelson measure gravitational interferometer. First, each arm contains a separated detectors to distinguish gravitational waves from as a whole [49,50]: 20 W of laser input is increased to 700 W phase by a factor of 300 [48]. Second, a partially trans- local instrumental and environmental noise, to provide incident on theBelow, beam splitter, we which presentthe is resulting further a general-relativistic increased source to parameters. analysis of waves,III. DETECTORS the detectors includeresonant several enhancements optical cavity, to the formed by its two test mass mirrors, source sky localization, and to measure wave polarizations. 100 kW circulatingGW150914; in each arm Fig. cavity.2 shows Third, the a partially calculated waveform using basic Michelson interferometer.that First, multiplies each arm the contains effectmissive ofa power-recycling a gravitational wave mirror on at the the light input provides addi- The LIGO sites each operate a single Advanced LIGO transmissive signal-recycling mirror at the output optimizes the resulting source parameters. Gravitational-waveresonant astronomy optical cavity, exploits formed multiple,phase by its by two widely a test factor masstional mirrors, of 300 resonant[48]. buildup Second, of a the partially laser light trans- in the interferometer III. DETECTORS separated detectorsthat to multiplies distinguish the gravitational effect of amissive gravitational waves power-recycling from wave on theas a light whole mirror[49,50] at the: 20 input W of provideslaser input addi- is increased to 700 W 061102-3 phase by a factor of 300 [48]. Second, a partially trans- III. DETECTORS local instrumental and environmental noise, to provide incident on the beam splitter, which is further increased to Gravitational-wave astronomy exploitsmissive multiple, power-recycling widely mirrortional at the resonant input provides buildup addi- of the laser light in the interferometer separated detectors to distinguishsource sky localization, gravitational and waves to measure from waveas polarizations. a whole [49,50]:100 20 W kW of laser circulating input is in increased each arm to cavity. 700 W Third, a partially Gravitational-wave astronomy exploits multiple,The LIGO widely sites eachtional resonant operate buildup a single of the Advanced laser light in LIGO the interferometertransmissive signal-recycling mirror at the output optimizes separated detectorslocal to distinguish instrumental gravitational and environmental waves from as noise, a whole to[49,50] provide: 20 W of laserincident input is on increased the beam to 700 splitter, W which is further increased to local instrumentalsource and sky environmental localization, noise, and to to provide measureincident wave polarizations. on the beam splitter,100 which kW is further circulating increased in eachto arm cavity. Third, a partially source sky localization,The LIGO and to sites measure each wave operate polarizations. a single100 Advanced kW circulating LIGO in eachtransmissive arm cavity. Third,061102-3 signal-recycling a partially mirror at the output optimizes The LIGO sites each operate a single Advanced LIGO transmissive signal-recycling mirror at the output optimizes
061102-3 061102-3 2
CUBE [9]). The next-generation kilometer-scale 2 laser-interferometric GW detectors such as aLIGO 2 [10], aVIRGO [11], and KAGRA [12] will have GW Tg strongCUBE impact [9]). on The multi-messenger next-generation astronomy. kilometer-scale TheCUBElaser-interferometric goal [9]). of this The work next-generation is to GW investigate detectors kilometer-scale whether such as ex- aLIGO laser-interferometric[10], aVIRGO [11], GW and detectors KAGRA such [12] as aLIGO will have ⌫ GW periments, making use of GW detection in com- Tg [10],strong aVIRGO impact [11], on andmulti-messenger KAGRA [12] astronomy. will have GW T⌫ bination with associated photon and neutrino de- Tg tections,strongThe goal impact can of make this on multi-messenger work a dent is in to understanding investigate astronomy. whether the ex- ⌫ orderingTheperiments, goal of of neutrino this making work masses. is use to investigate of GW detection whether in ex- com- ⌫ T T⌫ Currentperiments,bination experiments makingwith associated use cannot of GW photon yet detection decide and neutrino on in com- the de- T⌫ neutrinobinationtections, mass with can ordering associated make while a photon dent their in and understandingabsolute neutrino mass de- the tections, can make a dent in understanding the E E E is constrainedordering of by neutrino cosmology masses. and tritium-beta de- tg t⌫ t tg t⌫ t T cayorderingCurrent experiments. of experiments neutrino Future masses. large cannot scale yet structure decide sur- on the T veysCurrentneutrino like the experiments recently mass ordering approved cannot while EUCLID yet their decide absolute [13], on will the massFigure 1. GW, neutrino and photon propagation in allowneutrino to constrain mass orderingmi whiledown their to 0. absolute01 eV when mass time. E E E is constrained byi cosmology and tritium-beta de- tg t⌫ t tg t⌫ t combinedis constrained with byPlanck cosmology data. and tritium-beta de- tE tE tE t t t cay experiments.P Future large scale structure sur- g ⌫ g ⌫ Incay theveys experiments. following like the werecently Future explore approved large the scale conditions EUCLID structure under [13], sur- willlike theFigure merging 1. GW, of a neutrino neutron and star photon binary propagation or the in whichveys like multi-messenger the recently approved astronomy EUCLID can reveal [13], will or coreFigure bounce 1. GW, of a neutrino core-collapsed and photon supernova propagation (SN) in allow to constrain i mi down to 0.01 eV when time. constrainallow to the constrain neutrinom massi down ordering to 0.01 and eV abso- when aretime. believed to follow this pattern. We will adopt combined with Plancki data. 3 lutecombined mass. with PlanckP data. and extend the notation of [14]. The di↵erence In the followingP we explore the conditions under like the merging of a neutron star binary or the Inwhich the following multi-messenger we explore astronomy the conditions can under revealof orlike the the arrival merging times of between a neutron the star GWs binary and neu- or the core bounce of a core-collapsedNormal supernova Ordering (SN) Inverted Ordering which multi-messenger astronomy can reveal or trinos,core bounce⌧obs t of⌫ at core-collapsedg, or the GW and supernova a photon, (SN) constrainII. MULTI-MESSENGER the neutrino mass ASTRONOMY ordering and abso- are believed⌘ to follow thisbfp pattern.1 We3 range will adoptbfp 1 3 range constrain the neutrino mass ordering and abso- ⌧ are believedt tg, are to follow both observables, this pattern.± which We will can adopt be ± lute mass. obs ⌘ 2 +0.013 +0.013 and extendsin the✓ notation12 0.304 of0.012 [14].0. The270 di0.↵344erence0.304 0.012 0.270 0.344 lute mass. positiveand extend or negative the notation for an of early [14]. or The late di arrival↵erence! ! The detection of GWs is a crucial test of of the arrival times2 between+0.052 the GWs and neu- +0.025 ofof a GW. the arrival Typically timessin the✓ between emission23 0.452 the time0.028 GWs of the0. and382 three neu-0.643 0.579 0.037 0.389 0.644 ! ! general relativity and, as already discussed in trinos, ⌧obs t⌫ tg, or the GW1 and a photon, signals (GW, and ⌫2) do not coincide . For in- II. MULTI-MESSENGER ASTRONOMY trinos, ⌧obs t⌫ ⌘sintg✓, or the0.0218 GW+0.0010 and0.0186 a photon,0.0250 0.0219+0.0011 0.0188 0.0251 the literatureII. MULTI-MESSENGER (see e.g. [14]), it ASTRONOMY is also important 13 0.0010 0.0010 stance ⌧ inobs thet supernova ⌘ tg , are both explosion observables, SN1987A which [16],! can be ! ⌧ t ⌘ tg, are both observables, which can be to deduce other relevant physical properties. obs m2 [10 5 eV2] 7.50+0.19 7.02 8.09 7.50+0.19 7.02 8.09 the neutrinospositive⌘ arrived or21 negative approximately for an0.17 early 2 – 3 or hours late arrival 0.17 This newThe information detection of can GWs be is derived a crucial when test ofpositive or negative for an early or late arrival! ! The detection of GWs is a crucial test of beforeof the a GW. associated Typically2 photons.3 the2 emission+0.047 time of the three +0.048 of a GW. Typically m3`[10 the eV emission] +2.457 time0.047 + of2.317 the three+2.607 2.449 0.047 2.590 2.307 comparing,general relativity for example, and, as their already propagation discussed in !1 ! general relativity and, as already discussed in Let ussignals assume (GW, now thatand a neutrino⌫) do not is coincide emitted1 at. For in- the literature (see e.g. [14]), it is also importantsignals (GW, and ⌫) do not coincide . For in- velocitythe literature with those(see e.g. of [14]),photons it is and also neutrinos important E E ⌫ tTable= t I.stance+ Three-flavor⌧ and in the detected oscillation supernova at parameters time explosiont⌫. A from relativistic the SN1987A fit to global [16], data after the NOW 2014 conference performed to deduce other relevant physical properties.2 ⌫stanceg inint the supernova explosion SN1987A [16], comingto deduce both from other the relevant same astrophysical physical properties. source. 2 Setmass byUp thethe eigenstate NuFIT neutrinos group neutrino [17]. arrived The with numbers approximately mass inm thei c 1st (2nd) 2E –( 3 column hours are obtained assuming NO (IO). Note that This new information can be derived whenthe2 neutrinos2 arrived approximately2 2 2 –⌧ 3 hours This new information can be derived when i =m13`, 2before, 3m )31 propagates> the0 for associated NO and with m a photons.3` group m32 velocity:< 0 for IO. CUBE [9]). The next-generation kilometer-scalecomparing, for example, their propagationbefore⌘ the associated photons.⌘ laser-interferometric GW detectors such ascomparing, aLIGO for example, their propagation Let us assume now that a neutrino is emitted at Let us assume now2 that4 a neutrino4 8 is emitted at velocityGW with those of photons and neutrinos E E ⌫ m c m c [10], aVIRGO [11], and KAGRA [12] willvelocity have with those of photons and neutrinos tEi witht E = respecttv⌫i+ ⌧ to aand masslessi detected particle,i at time emittedt . Aby relativisticB. Neutrino orderings: current status A. Set-upTg t = t⌫ + ⌧g =and1int detected+ at time t ., A relativistic⌫ (1) strong impact on multi-messenger astronomy.coming both from the same astrophysical source.⌫ g int 2 4 ⌫ coming both from the same astrophysical source. the samemass sourcec eigenstate at the2E same neutrino time,O 8 isE with mass2 m c2 E ( The goal of this work is to investigate whether ex- mass eigenstate neutrino with0 mass1 mi c i E ( B C ⌧ ⌧ periments, making use of GW detection in com-Let’s start⌫ by considering a potential obser- i = 1i, =2, 31, )2 propagates, 3 ) propagates with with aB group aC group velocity: velocity: T⌫ where we assumed that the@ di↵erentA species1 Motivations of and Goals bination with associated photon and neutrinovation de- of an astrophysical catastrophe. Using m2c4 2 2 2 neutrinosi haveL beenm producedic 2 E4 with aL4 common8 tections, can make a dent in understandingthe thesame notation of [14], we denote with ti = 2.v57 2 4 m c 4 8 m c s. A. Set-up Tg 2E2 cvi i meVi c iMeVmi c 50kpci ordering of neutrino masses. A. Set-up neutrino⌘ energy masses. value E.= If1 a= given1 + neutrino+ is, produced, (1) (1) 2! ✓ 2 ◆ 4 4 L/vg, T⌫i L/v⌫i and T TL /v respectively the c c 2EO O 8E (2) Current experiments cannot yet decide on the ⌘ ⌘ by a source at a distance2EL, the time-of-flight0 8E 01 1 delay neutrino mass ordering while their absolutetime mass of propagation of a GW, a given neutrino Here we do not take into accountB cosmicBC expan-C Current available neutrino oscillation data Let’sLet’s start start by by considering considering a potential a potential obser-I obser- The three neutrino mixing frameworkB BC C mass eigenstateE and photonsE E with group veloci- sionwhere sincewhere we we assumed we consider assumed that sources thethat at@B di the↵ lowerent@ diAC redshift,↵erent speciesA species of of is constrained by cosmology and tritium-beta de- tg t⌫ t tg t⌫ t Neutrinos are produced as flavour eigenstates [17] (see Table I) are compatible with two types of vationvation of of an an astrophysical astrophysical catastrophe. catastrophe. UsingIn the Using formalism1 In alternative used to theory construct of gravity the Standard the three Model particles (SM), the under existence of a non- cay experiments. Future large scale structureties sur-vg, v⌫ , and v . Following Fig. 1 a GW is emit- zneutrinos< ν0_(e,.neutrinos1. Thisμ, τ have) but causes they have been an propagate beenerror produced less produced as than mass with 5%. with a From common a commonneutrino mass spectra. These depend on the sign thethe same samei notation notation of [14], of [14], we we denote denote with withtrivialT T neutrinostudy mixing — photons, and massive gravitons neutrinos and neutrinos— implies that can the couple left-handed to (LH) flavour veys like the recently approved EUCLID [13],ted will at theFigure time 1.E GW,from neutrino a source and photon at distance propagationand ing gtheenergyeigenstates expressionenergy value value ν inE_(1,2,3). (2) IfE we a. given If observe a given neutrino that neutrino larger is produced dis- is producedof m2 (` = 1, 2) and are summarised below: tg L neutrino⌘ fieldsdi⌘↵erent⌫lL( ex↵),ective which metrics. enter into In the this expression case the Shapiro for the delaylepton current3` in the allow to constrain mi down to 0.01 eV whenL/,v ,time.T L/vandand T L/respectivelyvTgrespectivelyL/vg the the i L/vg Tg ⌫i ⌫i L/v⌫i ⌫i T L/v chargedtances current and weak small interaction neutrino Lagrangian, energies are are linear needed combinations in i) spectrumof the fields with of normal ordering (NO): combined with Planck data. detected on⌘ Earth⌘ at tg. Similarly,⌘ ⌘ we have emis- byis not aby source the a source same at a for distance at the a distance threeL signals, theL time-of-flight, the [15]. time-of-flight In this work delay delay time of propagation of a GW, a given neutrinothree (or more) neutrinos ⌫j, having masses mj = 0: 2 2 P time of propagation of a GW, a given neutrinoorder to maximise the experimental sensitivity. m1 < m2 < m3, m > 0, m > 0, In the following we explore the conditionssion under andlike detection the merging times of a neutron for photons star binary and or neu- the however we assume the same coupling6 to the metric for 31 21 2 2 1 massmass eigenstateD. eigenstate Fargion Lett.Nuovo and and Cim. photons 31 photons (1981) 499-500 with with group group veloci- veloci-Forall the distances signals. around 50 kpc (SN1987A) and an m = (m + m ) 2 ; which multi-messenger astronomy can revealtrinos. or core For bounce instance, of a astrophysicalcore-collapsed supernova catastrophes (SN) 1 1 ⌫lL(x)= Ulj ⌫jL(x),l= e, µ, ⌧, 2(3) 1(1.1) 21(31) K. Langaeble, A. Meroni & F. Sannino Phys.Rev. D94 (2016) no.5, 053013 energyIn alternativeIn of alternative10 MeV, theory a neutrino theory of gravity of with gravity the a three mass the particles three of 0.07 particles under under constrain the neutrino mass ordering andties abso-tiesvg,varevgO.⌫,i ,G.v believed and⌫ Ryazhskaya,i , andv to.v FollowingV. follow .G. FollowingRyasny this and pattern. O. Fig. Saavedra, Fig. 1 We a GWJETP 1 will a Lett. GW adopt is 56 emit- (1992) is emit- 417 j ii) spectrum with inverted ordering (IO): studystudy — photons, — photons, gravitonsX gravitons and neutrinos— and neutrinos— can couple can couple to to lute mass. J. F. Beacom andE P.E Vogel, Phys. Rev. D 58 (1998) 093012 eV (the upper current absolute mass scale inferred 2 2 tedted at attheand the time extend timetg thefromt notationfrom a source a of source [14]. at The distance at distancedi↵erenceL andL and m3 < m1 < m2, m < 0, m > 0, J. F. Beacom, R. N. gBoyd and A. Mezzacappa, Phys. Rev. D 63 (2001)where 073011⌫jL( x di) is↵erent thedi LH↵erent e↵ componentective e↵ective metrics. of the metrics. field In this of In⌫ casej possessing this the case Shapiro the a mass Shapiro delaymj 0 delay and U is a 32 21 ofN. theArnaud, arrival M. Barsuglia, times M. betweenA. Bizouard, theF. Cavalier, GWs M. and Davier, neu- P. Hello and T.from Pradier, the Planck Collaboration [8]) would arrive 2 2 1 2 2 2 1 detecteddetected on on Earth Earth at t atg.t Similarly,. Similarly, we wehave have emis-unitary emis- matrixis not —the the Pontecorvo-Maki-Nakagawa-Sakata same for the three signals [15]. (PMNS) In this neutrino workm2 = mixing(m + ma- m ) 2 , m1 = (m + m m ) 2 . Phys. Rev. D 65 (2002) 033010g 4 is not the same for the three signals [15]. In this work3 23 3 23 21 trinos,G. G. Raffelt,⌧obs Nucl. tPhys.⌫ tProc.g, or Suppl. the 110 GW (2002) and 254 a photon,trix [3, 4, 9],10U sU laterPMNS. than Similarly a massless to the Cabibbo-Kobayashi-Maskawa particle. Similar to (CKM) quark II. MULTI-MESSENGER ASTRONOMYsion and detection⌘ times for photons and neu- however⌘ however we assume we assume the same the couplingsame coupling to the tometric theIt metric for should for be kept in mind also that sion⌧ andE. Nardit detectionand J.t I., Zuluaga, are both Phys. times observables, Rev. D for69 (2004) photons which 103002 can and bemixing neu- matrix,⇠ the leptonic matrix U , is described (to a good approximation) by obs g (2) we express the time delayPMNS between the arrival 2 2 J.I.Zuluaga,astro-ph/0511771.⌘ all theall signals. the signals. ( ) = ( ) , where the notation trinos.trinos.positive For For instance, or instance, negative astrophysical for astrophysical an early or catastrophes late catastrophes arrivala3 3 unitary mixing matrix. In the widely used standard parametrizationm31 [6],NOUPMNS m32 IO The detection of GWs is a crucial test of A.Strumia and F.Vissani, hep-ph/0606054. ⇥ of two neutrino mass eigenstates as: | | ofA. aNishizawa GW. Typically and T. Nakamura, the emission Phys. Rev. D time 90, no. of 4, the044048 three is expressed in terms of the solar, atmospheric and reactor neutrino mixingis self-explanatory. angles ✓12, Depending on the value of the general relativity and, as already discussed in 1 ✓23 and ✓13, respectively, and one Dirac - , and two (eventually) Majorana [21] - ↵21 signals (GW, and ⌫) do not coincide . For in- lightest neutrino mass, mmin, the neutrino mass the literature (see e.g. [14]), it is also important and ↵ , CP violating phases: Aurora Meronistance in the supernova explosion SN1987A [16],University31 of Helsinki 14 to deduce other relevant physical properties. m2 c4 spectrum can be: the neutrinos arrived approximately 2 – 3 hours ij L UPMNS U = V (✓12, ✓23, ✓13, ) Q(↵21, ↵31) , a) Normal Hierarchical(1.2) (NH): This new information can be derived when t⌫i⌫j = ti t⌘j = T0 with T0 = , (3) before the associated photons. 2E2 c 1 2 2 3 comparing, for example, their propagation where m1 m2 < m3, m2 ( m21) 8.68 10 eV, Let us assume now that a neutrino is emitted at ⌧ 1 ⇥ velocity with those of photons and neutrinos E E ⌫ 2 2 2 t = t + ⌧ and detected at time t⌫. A relativistic i m3 ( m31) 4.97 10 eV; or coming both from the same astrophysical source. ⌫ g int 102 02 2c13 0 s13e c12 s12 0 ⇥ mass eigenstate neutrino with mass m c2 E ( with m = m m and to leading order in b) Inverted Hierarchical (IH): i V = 0 c23ij s23 i j 010 s12 c12 0 , (1.3) ⌧ 02 4 2 1 0 i 1 0 1 2 1 i = 1, 2, 3 ) propagates with a group velocity: m c 0/E .s23 In thisc23 limit thes13e time0 intervalsc13 don’t001 de- m m < m , with m m 2 3 1 2 1,2 32 @ A @ A @ A⌧ 2 | | 2 4 4 8 pend on the absolute neutrino mass scale. To 4.97 10 eV; or m c m c and we have used the standard notation cij cos ✓ij, sij sin ✓ij, the allowed range vi i i ⌘ ⌘ ⇥ A. Set-up = 1 + , (1)for the valueslearn of about the angles the sensitivity being 0 ✓ needed⇡/2, and to disentangle c) Quasi-Degenerate (QD): c 2E2 O 8E4 ij 0 1 2 2 B C di↵erent neutrino mass di↵erences we pause this m1 m2 m3 m0, m m , m0 & 0.1 eV, Let’s start by considering a potential obser- B C Q = Diag(1,ei↵21/2,ei↵31/2) . (1.4) j | 31(32)| where we assumed that the@B di↵erentAC species of discussion and resume it after having briefly re- j = 1, 2, 3. We denote solar and atmospheric vation of an astrophysical catastrophe. Using neutrinos have been produced with a common Theviewed neutrino oscillation the current data, status accumulated of neutrino over many ordering years, in allowedsquare to determine mass di↵erences respectively, m2 and the same notation of [14], we denote with Tg 21 ⌘ energy value E. If a given neutrino is producedthe frequencies and the amplitudes (i.e. the angles and the mass squared2 di↵erences) L/v , T L/v and T L/v respectively the the next subsection. m . g ⌫i ⌘ ⌫i ⌘ by a source at a distance L, the time-of-flight delaywhich drive the solar and atmospheric neutrino oscillations, with a rather high3` precision time of propagation of a GW, a given neutrino (see, e.g., [6]). Furthermore, there were spectacular developments in the period June mass eigenstate and photons with group veloci- 2011 - June 2012 year in what concerns the CHOOZ angle ✓13. In June of 2011 the T2K 1 In alternative theory of gravity the three particles under ties vg, v⌫i , and v . Following Fig. 1 a GW is emit- collaboration reported [22] evidence at 2.5 for a non-zero value of ✓ . Subsequently study — photons, gravitons and neutrinos— can couple to 13 ted at the time tE from a source at distance L and the MINOS [23] and Double Chooz [24] collaborations also reported evidence for ✓ = g di↵erent e↵ective metrics. In this case the Shapiro delay 13 6 detected on Earth at tg. Similarly, we have emis- is not the same for the three signals [15]. In this work0, although with a smaller statistical significance. Global analysis of the neutrino sion and detection times for photons and neu- however we assume the same coupling to the metric foroscillation data, including the data from the T2K and MINOS experiments, performed all the signals. in [25], showed that actually sin ✓ = 0 at 3 . In March of 2012 the first data of trinos. For instance, astrophysical catastrophes 13 6 the Daya Bay reactor antineutrino experiment on ✓13 were published [26]. The value 2 of sin 2✓13 was measured with a rather high precision and was found to be di↵erent from zero at 5.2 : sin2 2✓ =0.092 0.016 0.005 . (1.5) 13 ± ± 3 3
Normal Ordering Inverted Ordering bfp 1 3 range bfp 1 3 range ± ± 2 +0.013 +0.013 sin ✓12 0.304 0.012 0.270 0.344 0.304 0.012 0.270 0.344 ! ! 2 +0.052 +0.025 sin ✓23 0.452 0.028 0.382 0.643 0.579 0.037 0.389 0.644 ! 4 ! 2 +0.0010 +0.0011 sin ✓13 0.0218 0.0010 0.0186 0.0250 0.0219 0.0010 0.0188 0.0251 ! ! 2 5 2 +0.19 +0.19 m21[10 eV ] 7.50 0.17 7.02 8.09 7.50 0.17 7.02 8.09 ! ! 2 3 2 +0.047 +0.048 m3`[10 eV ] +2.457 0.047 +2.317 +2.607 2.449 0.047 2.590 2.307 ! ! 5
Table I. Three-flavor oscillation parameters from the fit to global data after the NOW 2014 conference performed by the NuFIT group [17]. The numbers in the 1st (2nd) column are obtained assuming NO (IO). Note that m2 m2 > 0 for NO and m2 m2 < 0 for IO. 3` ⌘ 31 3` ⌘ 32
Figure 2. The range of ti (it=i with 1,Time2, 3), respect the time to delayLapses a massless of neutrinos particle, with respect emitted to photons, by vs the lightestB. Neutrino of orderings: current status the neutrino masses, mmin, forthe a same distance source of 1 Mpc at and the 10 same Mev. time, We show is the results for NO and IO (left and right panels) considering a the 3 uncertainty in the oscillations parameters given in Table I. The dashed and dotted vertical lines correspond to the Planck limit on the sum of neutrinos masses and the perspective upper limits from the KATRIN experiment (more details in the text). 2 4 2 2 2 mi c L mic E L Figure 2. The range of ti (i = 1, 2, 3), the time delay of neutrinos with respect to photons, vs the lightest of ti 2 = 2.57 s. larger than 0.8 Mpc. We show in2 Fig.E 2c the time eVthe neutrinom MeV[eV] masses, 50kpcmmin, for t a⌫ distance[s] of 1 Mpc and 10 MeV. We show the results for NO and IO (left and ! min i ⇠ right panels)✓ considering◆ a the(2) 3 uncertainty in the oscillations parameters given in Table I. The dashed and delay (for each mass eigenstate) ti considering NO IO dotted vertical lines correspond to the Planck5 limit3 on the sum of neutrinos masses and the perspective upper NO and IO (left and rightHere panels we do respectively) not take into account cosmic0 expan-1.23 10 Current(10 ) available neutrino oscillation data limits from the KATRIN experiment7 5 (more· 5 details3 in the text). Time delayas function of neutrinos of the lightestwith respectsion neutrino since to photons mass, we setting consider sourcesL=100 kpc at3. low86(1 Mpc)10 redshift, (10 and ) 1 E=.26 1010 MeV.(10 ) · 5 3 [17]· (see Table I) are compatible with two types of for a distancethe neutrino of 400 energy Mpc to(LIGO 10 MeV event) and and the distance 1.26 10 (10 ) 0 z < 0.1. This causes an error less than· 5%.7 From5 neutrino5 3 mass spectra. These depend on the sign E=5 MeV. mmin [eV] 5.14 10 (10 t)⌫i 1[s].28 10 (10 ) time lapse di↵erences between NO and IO will of the source to 1 Mpc. The physically relevant · 7 5 · 5 2 3 the expression in (2) we observe0.01 that9.00 larger10NO (10 dis-) 1.32of10IO m(10 ()` = 1,not2) and be distinguishable. are summarised below: arrival time di↵erences between neutrino mass · 5 3 · 7 3`5 1.32 10 (10 ) 5.14 10 5 (10 3 ) �� tances and small neutrino energies are· needed0 in1.23 i)·10 spectrum (10 ) with normalHowever, ordering in addition (NO) to: the time information, eigenstates t⌫i⌫j can be readily determined from 7 5 · 5 3 � 0 3.86 10 (10 ) 1.26 10 (10 ) also the ratio2 between the amplitudes2 of the dif- Fig. 2. We also report in theorder plot to the maximise future sensi- theTable experimental II. Benchmark sensitivity.· time5 lapses3 for·m⌫11, ⌫2
Δ Planck Collaboration on the sum of the light active TableL=1 II. BenchmarkMpc (10 Mpc) time lapses and forE=⌫ 15, ⌫MeV.2 and ⌫3 re- probability1 is: 1 from the Planck Collaboration [8]) would arrive 2 2 2 2 2 2 2 ����neutrinosν� [8] i mi 0.23 eV 95% CL. From Fig. 2 spectively. We consider a distance ofm 102 kpc= (m (13 Mpc)+ m23) , m1 = (m3 + m23 m21) . 4 2 2 10 s later than a masslessmmin particle.[eV] Similar t⌫ toi [s] ����we observe that for the given distance and energy, and a neutrino energy of E = 10 MeV.It should be keptP ⌫↵ in⌫ mind= U also↵i U i that, (4) P ν ⇠ ! the NO and IO spectra� di(2)↵er we by havingexpress di the↵erent time delay between theNO arrival IO2 2 i m 3 (NO2 ) = m (IO⇣) , where⌘ X the notation 0 4.91 10 31(10 ) 32 mmin [eV] t⌫ [s] | | ����time delays i.e. di↵erentof detection two neutrino patterns. mass We eigenstates as: 4 3 i · 3 2 where ↵ and are flavour eigenstates. In fact, this ����� ����� ����� � 0 1.54 10 (10 ) 5.06is10 self-explanatory. (10 ) Depending on the value of the note that for IO the delay between the two heavi- · NO3 2 · IO expression holds true whenever the time arrival ���� [��] 5.06 10 (10 ) 03 2 · 0 4.91 lightest10 (10 ) neutrino mass, mmin, the neutrino mass est mass eigenstates is equivalent to the time lapse 2.06 10 4(10 3) 5.11· 10 3(10 2) di↵erences among the three mass eigenstates is 0 1.54 10 4(10 3) 5.06 10 3(10 2) between the first two lighter mass eigenstates for 2 4 · 4 3 spectrum· 3 2 can be: m c 0.01 3.60 · 10 3(10 2 ) 5.27· 10 (10 ) smaller than the detector time resolution. How- ij 5.06· 10 L(10 ) · 0 NO. The time lapse di↵erences for= both NO and= with5.27 · 10= 3(10, 2(3)) 2.06a)10 Normal4(10 3) Hierarchicalever, when (NH) t⌫ ⌫: is larger than the detector resolu- t⌫i⌫j ti tj 2 T0 2.06T010 4(10 3) 5.11 10 3(10 2) i j 2E · c · 2 1 3 IO will fall within reach of the next generation of · 4 3 ·m 3 m2 < mtion,, m then each( m mass) 2 eigenstates 8.68 ⌫10i can beeV, detected Table III.0.01 Benchmark3.60 10 time (10 lapses) 5.27 for101 ⌫ (10, ⌫ )and2 ⌫ 3 2 21 · 3 2 · 41⌧ 23 13 ⇥ detectors in which the time accuracy is expected to 5.27 10 (10 ) 2.06 10 (10 ) 2 independently2 and will interact with the detector Aurora Meroni University of Helsinkirespectively. We consider· a distance of·m 13 (10) ( Mpcm and) 2 4.97 1510 eV; or be around 10 4s. In Table II we produce relevant 31 with probability 5 2 2 2a neutrino energy of E = 5 MeV. ⇥ with mij = mi mj Tableand III. to Benchmark leading order time lapses in forb)⌫ Inverted1, ⌫2 and Hierarchical⌫3 (IH): benchmark neutrino time lapses considering two 2 21 2 4 2 respectively. We consider a distance of 1 (10) Mpc and P ⌫↵ ⌫ = U↵i U2 i . (5) m c /E . In this limit the time intervals don’t de- m3 m1 < m2, with m1,2 i m 2 di↵erent source-distances for di↵erent values of a neutrino energy of E = 5 MeV. ! 32 In addition to the time stamp information,⌧ 2 also | | the lightest neutrino masspend for 10 on MeV the neutrinos. absolute neutrino mass scale. To 4.97 10 eV;For or simplicity,⇣ here we⌘ do not consider matter ef- the ratio between the amplitudes of⇥ the di↵er- Table III shows the substantiallearn gain about in time-lapse the sensitivity needed to disentangle c) Quasi-Degeneratefects which (QD): could in principle take place in the mass eigenstates is equivalent to the time lapse for the distances of 1 (10) Mpc but with a neutrino ent neutrinos reaching the detector can be mea- 2 2 di↵erent neutrino massbetween di↵erences the first we two pause lighter this massm eigenstates1 m2 form3 m0, m m , m0 & 0.1 eV, mass energy of 5 MeV which is still within exper- sured. Since the distances considered here are der to obtainj a global| 31(32) time,| when comparing with other discussion and resumeveryNO. it after large, If we having consider neutrinos briefly a conservative will reach re- thej time= detector1 accuracy, 2, 3. in- Weexperiments, denote a solar higher uncertainty and atmospheric is expected. imental reach [18]. 5 4 4 We work in the regime of incoherence.2 Defining xP ( xD) coherentlyof 10 s for such the next that generation the time integrated of detectors arrival, the viewed the current status of neutrino ordering in square mass di↵aserences the spatial respectively, width of the production m21 (detection)and neu- the next subsection. m2 . trino wave packet, we work under the assumption that 4 3` This accuracy is conservative compared with an estimate (vj vk)L/c max( xP, xD) being vi and vj the two group | | based on the uncertainty on the vertex reconstruction, velocities of the two wave packets of neutrino mass eigen- which is about 3 m for Hyper-Kamiokande [34]. In or- states ⌫i and ⌫j. 3
Normal Ordering Inverted Ordering bfp 1 3 range bfp 1 3 range ± ± 2 +0.013 +0.013 sin ✓12 0.304 0.012 0.270 0.344 0.304 0.012 0.270 0.344 ! ! 2 +0.052 +0.025 sin ✓23 0.452 0.028 0.382 0.643 0.579 0.037 0.389 0.644 ! ! 2 +0.0010 +0.0011 sin ✓13 0.0218 0.0010 0.0186 0.0250 0.0219 0.0010 0.0188 0.0251 ! ! 2 5 2 +0.19 +0.19 m21[10 eV ] 7.50 0.17 7.02 8.09 7.50 0.17 7.02 8.09 ! ! 2 3 2 +0.047 +0.048 m3`[10 eV ] +2.457 0.047 +2.317 +2.607 2.449 0.047 2.590 2.307 ! !
Table I. Three-flavor oscillation parameters from the fit to global data after the NOW 2014 conference performed by the NuFIT group [17]. The numbers in the 1st (2nd) column are obtained assuming NO (IO). Note that m2 m2 > 0 for NO and m2 m2 < 0 for IO. 3` ⌘ 31 3` ⌘ 32 10 14. Neutrino mixing ti with respect to a massless particle, emitted by B. Neutrino orderings: current status ′ the same source at the same time, is (l l) violating effects will be strongly suppressed. In particular,wegetACP =0,unlessall 10 14. Neutrino mixingthree ∆m2 =0,(ij)=(32), (21), (13). ij ̸ If the number of2 massive4 neutrinos2 n′ is equal to the number of neutrino flavours, violating effects will be strongly suppressed. Inm c particular,weget2 A(l l) =0,unlessall2 n =3,onehasasaconsequenceoftheunitarityoftheneutrinomi L mic CP E L ixing matrix: 2 ti 2 = 2.57 s. three ∆mij =0,(ij)=(32), (21), (13). 2E′ c eV MeV 50kpc ′ ′ ̸ l′=e,µ,τ P (νl νl )=1, l = e, µ,!τ, l=e,µ,τ P (νl νl )=1, l = e, µ, τ. If the number of massive neutrinos n is→ equal to the number of✓ neutrino◆ flavours, (2)→ !Similar “probability conservation” equations! hold for P (¯νl ν¯l′ ). If, however, the n =3,onehasasaconsequenceoftheunitarityoftheneutrinomnumber ofHere light we massive do not neutrinos take into is account biggerixing cosmic than matrix: the expan- number→ ofCurrent flavour neutrinos available as neutrino oscillation data ′ P (ν ν ′ )=1, l = e, µ, τ, P (ν ν ′ )=1, l′ = e, µ, τ. l =e,µ,τ l → l aconsequence,sion sincee.g.l,= wee,µ, ofτ a consider flavourl → neutrino sourcesl at - sterile low redshift, neutrino[17] mixing, (see Table we would I) are have compatible with two types of !Similar “probability conservation” equations! hold for P (¯ν ν¯ ′ ). If, however, the ′ P (ν ν ′ )=1 Pl (→ν l ν¯ ), l = e, µ, τ,wherewehaveassumedthe number of light massive neutrinosl =e,µ, isτ z bigger< l0.→1. than Thisl the causes number− anl error o→f flavoursL less than neutrinos 5%. as From neutrino mass spectra. These depend on the sign ′ ′ aconsequence,e.g., of a flavour!existence neutrinothe of just expression - one sterile sterile neutrino in neutrino. (2) we mixing, observe Obviously, we that would in larger have this cdis-ase l =e,µ,2τ P (νl νl ) < 1if of m3` (` = 1→, 2) and are summarised below: ′ P (ν ν ′ )=1P (Pνl(ν ν¯sLν¯) =0.Theformerinequalityisusedinthesearchesforoscilla), l = e, µ, τ,wherewehaveassumedthe ! tions between l =e,µ,τ l → l − →l →tancessL̸ and small neutrino energies are needed in i) spectrum with normal ordering (NO): active and sterile neutrinos. ′ !existence of just one sterile neutrino. Obviously, in this case l′=e,µ,τ P (νl νl ) < 1if 2 2 order to maximise the experimental→ sensitivity. m1 < m2 < m3, m > 0, m > 0, P (ν ν¯ ) =0.TheformerinequalityisusedinthesearchesforoscillaConsider next neutrino oscillations! in thetions case of between one neutrino mass squared difference31 21 l → sL ̸ For distances around 50 kpc (SN1987A) and an 2 2 1 active and sterile neutrinos.“dominance”: suppose that ∆m2 ∆m2 , j =2,...,(n 1),m2(3)∆=m(2m L/+ (2mp) ! 1and) 2 ; | j1| ≪ | n1| − | n1|1 21(31) Consider next neutrino oscillations2 energy in the case of 10 of MeV, one neutr a neutrinoino mass2 with squared a mass difference of 0.07 ii) spectrum with inverted ordering (IO): ∆mj1 L/(2p) 1, so that exp[i(∆mj1 L/(2p)] ∼= 1, j =2,...,(n 1). Under these “dominance”: suppose that| ∆m2 | eV∆ (them2≪ upper, j =2 current,...,(n absolute1), ∆m2 massL/(2 scalep) ! inferred1and m <− m < m , m2 < 0, m2 > 0, conditions| j1| ≪ | we obtainn1| from Eq.− (14.13)| andn1| Eq. (14.14), keeping only3 the oscillating1 2 terms32 21 ∆m2 L/(2p) 1, so that exp[i(∆mfrom2 L/2 the(2p)] Planck= 1, j Collaboration=2,...,(n 1). [8]) Under would these arrive 2 2 1 2 2 2 1 j1 involving ∆jm1 n1: ∼ m2 = (m + m ) 2 , m1 = (m + m m ) 2 . | | ≪ 4 − 3 23 3 23 21 conditions we obtain from Eq. (14.13) and10 Eq.s (14later.14), than keeping a massless only the particle. oscillating Similar terms to 2 It should be kept in mind also that involving ∆m : ⇠ ′ ′ ′ ′ ′ 2 ′ ′ 2 n1 (2)P we( νlTime( expressl ) νl ( thel)) ∼= timeLapsesP (¯ν delayl(l ) betweenν¯l (l)) ∼= theδll arrival2 Uln δll2 Ul n 2 → → − | | "m31(−NO| ) |=# m32(IO) , where the notation of two neutrino mass eigenstates2 2 as:2 | | P (ν ′ ν ′ ) = P (¯ν ′ ν¯ ′ ) = δ ′ 2 U δ ∆′ mnU1 ′ is self-explanatory. Depending on the value of the l(l ) → l (l) ∼ l(l ) → l (l) ∼ ll − |(1ln| cosll − | l Ln|) . (14.20) − " 2p # ∆m2 lightest neutrino mass, mmin, the neutrino mass (1 cos n1 L) . (14.20) − 2p 2 4 spectrum can be: It follows from the neutrino oscillationmijc data (SectionsL 14.4and14.5)thatinthecase a) Normal Hierarchical (NH): of 3-neutrino t⌫ mixing,i⌫j = ti one oftj = the two2 independentT0 with T0 neutrino= , (3) mass squared differences, say It follows from the neutrino oscillation data (Sections 14.4and14.5)thatinthecase2E c 2 1 3 2 m 2 m <2m , m 2( m ) 2 8.68 10 eV, ∆m21,ismuchsmallerinabsolutevaluethanthesecondone,∆1m31: ∆2 m21 3 ∆2 m 31 . 21 of 3-neutrino mixing, one of the two independent neutrino mass squared differences, say ⌧ | 1 | ≪ | | ⇥ 2 The data imply: 2 2 2 2 2 2 ∆m ,ismuchsmallerinabsolutevaluethanthesecondone,Neutrinos ∆oscillate!m : ∆ m ∆m . m3 ( m31) 4.97 10 eV; or 21 2 2 2 31 | 21| ≪ | 31| ⇥ The data imply: with m = m m and to2 leading order−5 in2 b) Inverted Hierarchical (IH): ij i j ∆m = 7.5 10 eV , 2 4 2 21 ∼ 2 1 m 2c /E . In this−5 limit2 the| time intervals| × don’t− de- m m < m , with m m 2 ∆m = 7.5 10 eV , ∆m2 = 2.5 10 3 eV2 , 3 1 2 1,2 32 21 ∼ 31 ∼ ⌧ 2 | | | | × − | | × 4.97 10 eV; or ∆pendm2 = on2.5 the10 absolute3 eV22, neutrino2 mass scale. To 31 ∼ ∆m21 / ∆m31 ∼= 0.03 . ⇥ (14.21) Normal2 Ordering| learn2 | about× the sensitivity| | | needed| to disentangleInverted Orderingc) Quasi-Degenerate (QD): ����� ∆m / ∆m = 0.03 . ����� (14.21) | 21| | 31| ∼ 2 2 2 Neglectingdi the↵erent effects neutrino due to mass∆m21 diwe↵erences get from we Eq. pause (14.20) this by settingm1 mn2 =3andchoosing, m3 m0, m m , m0 & 0.1 eV, 2 ′ ′ j | 31(32)| Neglecting the effects due toe.g.∆m,i)21 wel = getl = frome and Eq. ii) (14l .=20)e( byµ), settingl = µ(ne=3andchoosing,)[60]: ′ ����� ′ discussion and resume it after����� having briefly re- j = 1, 2, 3. We denote solar and atmospheric e.g.,i)l = l = e and ii) l = e(µ), l = µ(e)[60]: 2 ν� viewed the current status of neutrinoν� ordering in square mass2 di↵erences respectively, m and ] ] ∆m 21 � � 2 2 31 [ ����� [ �����2 2 � P (ν ν )=P (¯ν ν¯ ) = 1 2 � U 1 U 1 cos L , (14.22) e the nexte2 subsection.e 2 e ∼ ∆me313 e3 m . Δ → → − |Δ | ν� − | | & − 3 2p ' P (νe νe)=P (¯νe ν¯e) ∼= 1 2 Ue3 1 Ue3 1 cos L$ , (14.22)% ` → → − | | $ − | | % & − 2p ' ��-� ��-� ν� ν� ν� ∆m2 P (ν ν ∆)m=2 2 U 2 U 2 1 cos 31 L ��-� 2 2µ(e) e(µ) 31 ��µ-�3 e3 P (ν-� ν ) = 2 U U 1→ cos ∼ L| | -|� | & − 2p ' �� µ(e) →�����e(µ) �����∼ | µ3�����| | e3| &� − 2p ' �� ����� ����� ����� � � [��] 2 � [��] 2 ��� Uµ3 ��� Uµ3 2ν 2 2 = | | P 2ν U 2,m2= , | | 2 P Ue3 ,m31 , (14.23) (14.23) 1 U 2 | e3| 31 1 Ue3 $| | % Time− |delaye3| of neutrinos$ with %respect− | to |photons for a distance of 1 Mpc and 10 MeV using a 3σ uncertainty on neutrino oscillation parameters.
August 29, 2014 14:37 August 29, 2014 14:37 Aurora Meroni University of Helsinki 16 5
Figure 2. The range of ti (i = 1, 2, 3), the time delay of neutrinos with respect to photons, vs the lightest of the neutrino masses, mmin, for a distance of 1 Mpc and 10 MeV. We show the results for NO and IO (left and right panels) considering a the 3 uncertainty in the oscillations parameters given in Table I. The dashed and dotted vertical lines correspond to the Planck limit on the sum of neutrinos masses and the perspective upper limits from the KATRIN experiment (more details in the text).
mmin [eV] t⌫i [s] time lapse di↵erences between NO and IO will NO IO not be distinguishable. 5 3 0 1.23 10 (10 ) However, in addition to the time information, 7 5 · 5 3 0 3.86 10 (10 ) 1.26 10 (10 ) also the ratio between the amplitudes of the dif- · 5 3 · Disentangling neutrino mass ordering 1.26 10 (10 ) 0 ferent neutrinos reaching the detector can be mea- · 7 5 5 3 5.14 10 (10 ) 1.28 10 (10 ) · 7 5 · 5 3 sured. Since the distances considered here are 0.01 9.00 10 (10 ) 1.32 10 (10 ) · 5 3 · 7 5 very large, neutrinos will reach the detectordecoherence in- 1.32 10 (10 ) 5.14 10 (10 ) · · coherently such that the time integrated arrival Table II. Benchmark time lapses for ⌫1, ⌫2 and ⌫3 re- probability is: spectively. We consider a distance of 10 kpc (1 Mpc) 2 2 2 2 and a neutrino energy of E = 10 MeV. P ⌫ ⌫ = U U , (4) P (⌫↵ ⌫ ) = U↵i U i ↵ ! ↵i i ! i | | | | i Valid if⇣ the time arrival⌘ Xdifferences among When ∆tνiνj is larger than the detector m [eV] t [s] min ⌫i wherethe↵ and three are mass flavour eigenstates eigenstates. is smaller In fact, this resolution, each mass eigenstates νi can be NO IO expressionthan the holds detector true time whenever resolution the time arrival detected independently 3 2 0 4.91 10 (10 ) di↵erences among the three mass eigenstates is 4 3 · 3 2 0 1.54 10 (10 ) 5.06 10 (10 ) Schematic representation of the square root of the probability of detecting flavour state νe if the source emits · 3 2 · smallera thanshort burst the of detector νe as a function time of resolution. time. E=5 MeV. How- We assume NO and each bin corresponds to a fiducial 5.06 10 (10 ) 0 collective time of 5 ms. · 4 3 3 2 ever, when t⌫i⌫j is larger than the detector resolu- 2.06 10 (10 ) 5.11 10 (10 ) · 4 3 · 3 2 tion, then each mass eigenstates� ��� ⌫i can be detected �� ��� 0.01 3.60 10 (10 ) 5.27 10 (10 ) ��� ��� · 3 2 · 4 3 independently and will interact with the detector 5.27 10 (10 ) 2.06 10 (10 ) ν� ν� ��� ��� · · 5 ν� ν� with probability ν� ν� ��� ��� � �
Table III. Benchmark time lapses for ⌫1, ⌫2 and ⌫3 | | �� 2 2 �� � � respectively. We consider a distance of 1 (10) Mpc and | ��� P ⌫↵ ⌫ = U↵i U i . (5) | ��� ! i a neutrino energy of E = 5 MeV. ��� ��� For simplicity,⇣ here we⌘ do not consider matter ef- ��� ��� fects which-� could� in� principle�� �� take�� place in the -�� � �� �� �� �� �� �� mass eigenstates is equivalent to the time lapse � [��] � [��] between the first two lighter mass eigenstates forAurora Meronider to obtain a global time, when comparingUniversity with other of Helsinki 17 NO. If we consider a conservative time accuracy experiments, a higher uncertainty is expected. 4 4 5 We work in the regime of incoherence. Defining ( ) of 10 s for the next generation of detectors , the xP xD as the spatial width of the production (detection) neu- trino wave packet, we work under the assumption that 4 This accuracy is conservative compared with an estimate (vj vk)L/c max( xP, xD) being vi and vj the two group | | based on the uncertainty on the vertex reconstruction, velocities of the two wave packets of neutrino mass eigen- which is about 3 m for Hyper-Kamiokande [34]. In or- states ⌫i and ⌫j. What can be measured?What informa'on can we get? 30 ) ν
-1 e s 20 ν 57 e Prob. νx When t 1 can be (10 i 10
ν disentangled from int and R 1 detector timing uncertainties, ) 0 -1 we can get information on the 6 2 3 absolute mass. erg s
{
int { 53 4 Time 2 When t 13 can be (10 i
ν t1 disentangled from int and/or L 0 t12 t13 detector timing uncertainties, 20 we can get information on the Courtesy of K. Langæble hierarchy. > (MeV) i
ν 10
BLACK HOLE–NEUTRON STAR MERGERS WITH A HOT NUCLEAR EQUATION OF STATE: OUTFLOW AND NEUTRINO-COOLED DISK FOR A LOW-MASS, HIGH-SPIN CASE M. Brett Deaton et al. When Δt13 can be disentangled from τint and/or detector timing uncertainties, we can get information on the absolute mass. Aurora Meroni University of Helsinki 18 6 6 6 Figure 4. Plot of as function of the lightest neutrino mass considering ⌧⌫ 10 ms considering the (15). In g int ⇠ Left Panel we consider E⌫ = 5 MeV and L = 10 Mpc (grey region) or 100 Mpc (orange region). In the Right 6 Panel we show the same but considering the distance of the GW150914 event i.e. 400 Mpc. In the plots we 6 consider the most stringent bound for g given in (18). The dashed and dotted vertical lines correspond to the Planck limit and the perspective upper limits of KATRIN. that implies: L = 10 Mpc (grey region) and 100 Mpc⌫ (orange Figure 4. Plot of g as function of the lightest neutrino mass considering ⌧ 10 ms considering the (15). In region). In the right panel of Fig. 4 weint show⇠ the i ⌫ Left Panel we consider E⌫ = 5 MeV and L = 10 Mpc (grey region) or 100 Mpc (orange region). In the Right T⌫i g = ⌧obs ⌧intPanel, we show the(10) same but considering the distance of the GW150914 event i.e. 400 Mpc. In the plots we inequality (15) reach in the case neutrinos were ⌫ Figure 4. Plot of g as function of the lightest neutrino mass considering ⌧ 10 ms considering the (15). In consider the most stringentdetected bound for for g given the GW150914 in (18). The dashed event and [1] dotted correspond- vertical lines correspondint to⇠ the where i denotes now the i-th neutrinoPlanck mass limit and eigen- the perspective upperLeft Panel limits we of consider KATRIN.E⌫ = 5 MeV and L = 10 Mpc (grey region) or 100 Mpc (orange region). In the Right ing to aPanel distance we show of the 400 same Mpc. but considering the distance of the GW150914 event i.e. 400 Mpc. In the plots we state. The deviation from the speed of light for consider the most stringent bound for given in (18). The dashed and dotted vertical lines correspond to the Figure 4. Plot of as function of the lightest neutrino mass consideringg ⌧⌫ 10 ms considering the (15). In g Depending on the distance and the consideredint GWs and neutrinos reads: that implies: Planck limit and the perspectiveL = 10 upper Mpc limits(grey of region)⇠ KATRIN. and 100 Mpc (orange Left Panel we consider E⌫ = 5 MeV and L = 10 Mpc (grey region) or 100 Mpc (orange region). In the Right Panel we show the sameneutrino but considering energy, the distance we obtainregion). of the GW150914 di In↵erent the right event sensitivity panel i.e. 400 of Mpc. Fig. 4 In we the show plots the we c vg c v i ⌫ ⌫ Figure 4.⌫ Ploti of g as T function⌫ g = ⌧ of the⌧ lightest, neutrino(10) mass considering ⌧ 10 ms considering the (15). In , consider, the most(11) stringenti onobsm boundminintthatwhich for implies: g given are in at (18). leastinequality The an dashed order (15)and ofint dotted reach⇠ magnitude vertical in theL linescase= 10 correspond neutrinos Mpc (grey to were region) the and 100 Mpc (orange g ⌫iLeft Panel we consider E = 5 MeV and L = 10 Mpc (grey region) or 100 Mpc (orange region). In the Right ⌘ c ⌘ Planckc limit and the⌫ perspective upper limits of KATRIN.detected for the GW150914region). event [1] In correspond- the right panel of Fig. 4 we show the Panelwhere we showi denotes the same now but thelower consideringi-th neutrino than the presentmass distance eigen- T ofcosmological the= ⌧ GW150914i ⌧⌫ , limitsevent i.e. and(10) 400 Mpc. the In the plots we ⌫i g obs int inequality (15) reach in the case neutrinos were with: consider the most stringent bound for given in (18). The dasheding to a and distance dotted of vertical 400 Mpc. lines correspond to the state. The deviation fromperspective the speedg upper of light limit for from KATRIN. For exam-detected for the GW150914 event [1] correspond- Planckthat limit implies: and the perspective upperwhere limitsi denotes of KATRIN. now theLDependingi-th= 10 neutrino Mpc on (grey mass the eigen- region) distance and and 100 the Mpc considered (orange 2 4 4GWs8 and neutrinos reads: ple, forstate. 10 Mpc The deviation it is possible from the to speed probe of the light lightest for ing to a distance of 400 Mpc. mi c mi c neutrinoregion). energy,In the right we panel obtain of di Fig.↵erent 4 we sensitivity show the Absolute neutrinoc vg i massc⌫ v⌫ Depending on the distance and the considered ⌫i = + . 2 (12) T⌫i g neutrino= ⌧ ⌧GWsint mass, andi neutrinos up to(10) reads:0.02 eV, while events such 2 4 g , obs ⌫ , (11) oninequalitymmin which (15) are reach at least in the an case order neutrinos of magnitude were 2E O that8E implies: ⌘ c i ⌘ c ⇠L = 10 Mpc (grey region) andneutrino 100 Mpc energy, (orange we obtain di↵erent sensitivity 0 1 c vg c v where i denotes now theasi GW150914,-th neutrino mass could eigen- probelowerdetected masses than for present the⌫ ofi anGW150914 cosmological orderon of event [1]which limits correspond- are and at the least an order of magnitude CUBE [9]). The next-generation kilometer-scale B C g region)., ⌫ Ini the right, panel(11) of Fig.mmin 4 we show the B with:C i ⌫ ⌘ c ⌘ c laser-interferometric GW detectors suchFrom as aLIGO the definition (9) follows:B C T = ⌧ ⌧ , (10) perspectiveing to a distance upper of limit 400 from Mpc. KATRIN. For exam- @ state.A The deviation⌫i g obsmagnitude fromint the speed less. of light forinequality (15) reach in the caselower neutrinos than present were cosmological limits and the [10], aVIRGO [11], and KAGRA [12] will have GW 2 4 4with:8 ple,Depending for 10 Mpc on it the is possible distance to and probe the the considered lightest Tg GWs and neutrinosm c reads:Last,m wec notice that limits on v can also be ob-perspective upper limit from KATRIN. For exam- strong impact on multi-messenger astronomy. i i detected for theg GW150914 event [1] correspond- T⌫i g ⌫i whereg i denotes now ⌫i = the i-th+ neutrino mass. eigen-(12) 2 neutrino4neutrino4 mass8 energy, up to we obtain0.02ple, eV, di for while↵erent 10 Mpc events sensitivity it is such possible to probe the lightest The goal of this work is to investigate whether ex- c v 2 4 m c m c = , (13)2Eg tainedO 8E fromc v high⌫i energeticingi to a events distancei or of from 400 Mpc.⇠ the re- ⌫ state. The deviation from , the speed0 1 of light, for ⌫ =(11) on+ m which. are at(12) least an order of magnitude periments, making use of GW detection in com- T0 (1 g)(1 ⌫ ) g ⌫i i 2as GW150914,min 4 could probeneutrino masses ofmass an up order to of0.02 eV, while events such T⌫ i ⌘ c B ⌘ C c 2DependingE O 8E on the distance and the considered⇠ bination with associated photon and neutrino de- GWs From and the neutrinos definition reads: (9)quirement follows:B C of Lorentz invariance.magnitudelower0 than1 less. present In fact, cosmological if theas GW150914, limits could and theprobe masses of an order of @ A B C tections, can make a dent in understanding the with: From the definitionneutrino (9)perspective follows:B energy,C upper we obtain limit from dimagnitude↵ KATRIN.erent sensitivity less. For exam- where, as already defined earlier, T0 = cL/cv.g If GW velocityc v⌫ is subluminal,Last, then we@ notice cosmicA that rays limits lose on vg can also be ob- ordering of neutrino masses. T⌫ ⌫ i T i g, 2 4 i g 4 8, (11) on mmin which are at least an order of magnitude Current experiments cannot yet decide on the g =m c ⌫i m c , (13) ple, for 10 Mpc it is possibleLast, to probe we notice the that lightest limits on vg can also be ob- in (13) we consider an uncertainty in the⌘ timec of i their⌘ energyc i via gravitationalT⌫i g tained ⌫i from g Cherenkov high energetic radia- events or from the re- T 0 = (1 +g)(1 ⌫ ) . (12)lower than present cosmological limits and the neutrino mass ordering while their absolute mass ⌫i 2 4 i = neutrino mass, up to (13)0.02tained eV, while from events high energetic such events or from7 the re- ⌫ 2E O 8E T0 (1quirement g)(1 ⌫ of) Lorentz invariance. In fact, if the is constrained by cosmology and tritium-betaemission de- of neutrinos,tE tE tE ⌧ , inwith:t ordert t to detect the tion and cannot reach the Earth.i The fact⇠ that g ⌫ int g ⌫ 0 1 perspectiveas GW150914, upper couldlimit from probe KATRIN.quirement masses of For of an Lorentz exam- order of invariance. In fact, if the cay experiments. Future large scale structure sur- where, as already defined earlier,B CT0 = L/c. If GW velocity is subluminal, then cosmic rays lose GW and the neutrino signal, we mustFrom have: the definition2 4 ��- (9)��ultra-high-energy follows:4 8B where,C as already cosmicple, definedmagnitude for rays 10 earlier, Mpc are less. itT0 is observed= possibleL/c. If toGW on probe velocity the islightest subluminal, then cosmic rays lose veys like the recently approved EUCLID [13], will Figure 1. GW, neutrino and photon propagationin (13) we in considermi c an uncertaintymi c@ A in the time of their energy viarecasts gravitational the limits Cherenkov in eqs. (13) and radia- (14) one obtains: time. = + in. (13) we consider(12) an uncertainty in the time of their energy via gravitational Cherenkov radia- allow to constrain i mi down to 0.01 eV when ⌫i 2 ⌫ 4 neutrinoLast, mass we notice up to that0. limits02 eV, on whilevg can events also such be ob- emission of neutrinos, 2TE⌫ g OEarth⌧ 8, E⌫ in limits order g to the detect GW the propagationtion⌫ and cannot speed reach to be the Earth. The fact that combined with Planck data. ⌫ i -�� int i emission of neutrinos, ⌧ , in order to detect⇠ the 17 15 19 T > ⌧ , (14)��= 0 1 , (13) int 10tion and< cannot< 2 10 reach(10 the Earth.). (15) The fact that P ⌫i g int B C as GW150914,tained from could high probe energetic masses events ofg or an from order the of re- In the following we explore the conditions under like the merging| of a neutron| star binaryGW or and the the neutrinoT0 signal,(1B g we)(1CGW must ⌫ andi ) have: the neutrinoultra-high-energy signal, we must have: cosmic rays are observed⇥ on From the definition (9) follows:B C magnitudequirement15 less.19 of Lorentz invariance.ultra-high-energy In fact, if cosmic the rays are observed on which multi-messenger astronomy can reveal or core bounce of a core-collapsed supernova (SN) @ A c vg < 2 Earth10 limits(10 the)c, GW propagation(16) speed to be � -�� ⌫ IndependentEarth bounds limits on the g GWare propagation important, speed since to be constrain the neutrino mass orderingand and usingabso- are (13) believed to to the follow first this pattern. oder We in willwhere, adopt⌫ and as alreadyg one δ ��T defined> ⌧ earlier,, T0 = L/(14)c.Last, If⇥ GW we velocity⌫ notice that is subluminal, limits on v thencan cosmic also be rays ob- lose ⌫i g int T⌫i g > ⌧int, (14) g lute mass. τν ∼ 10 ms and L = 1 Mpc. HK and JUNO T⌫i g | ⌫i | g | | they allow for a more precise interpretation of and extendint the notation of [14]. The diin↵erence (13) we consider= an uncertainty, in the(13) timetained of their from energy high via energetic gravitational events15 Cherenkovor19 from the radia- re- 15 19 finds: Planck of theenergy arrival thresholds, times between Eν = 7 MeV the GWs(grey region) and neu- and -�� KATRIN c vg < 2 10 (10 )c, c vg < (16)2 10 (10 )c, (16) and usingT (13)0 to(1 the�� firstassumingg)(1⌫ oder ⌫iand) in that usingand the (13)one tocosmic the first rays oder have in ⌫ Fig.and galactic 4 g inone terms ori- of mmin. ⇥ Eν = 1.806 MeV (orange region) respectively.emission of neutrinos, ⌧ , in order ⌫ to detect g the tion and cannot reach⇥ the Earth. The fact that trinos, ⌧obs t⌫ tg, or the GW and a photon, int quirement of Lorentz invariance. In fact, if the II. MULTI-MESSENGER ASTRONOMY ⌘ ⌫ finds: We discussed so far the time di↵erence mea- ⌧ t tg, are both observables, whichfinds:GW can and be the neutrinogin signal, (extra-galactic) we must have: [19]. ultra-high-energy cosmicassuming rays are that observed the cosmic on rays have galactic ori- obs T &where,⌧ . as already defined(15) -�� earlier, T0 = L/c. If GWassuming velocity is that subluminal, the cosmic then rays cosmic have galactic rays lose ori- ⌘ ⌫i g 0 int �� surement between a neutrino and a GW. Simi- positive or| negative for| an early or late arrival ���� ���� ���� Earth limits⌫ the GW propagationgin (extra-galactic) speed to be [19]. The detection of GWs is a crucial test of in (13) we consider an uncertaintyFurther⌫⌫ in independent the time of their constraints ginT energy (extra-galactic)& ⌧ . via on gravitational Lorentz [19].(15) vio- Cherenkov radia- of a GW. Typically the emission time of the three T T >&⌧⌧ ,. [ ](15)(14)⌫i g 0 int general relativity and, as already discussed in ⌫ ⌫i ⌫ g⌫i g 0 intint ���� �� | | larly one canFurther imagine independent a time di↵erence constraints to emerge on Lorentz vio- signals (GW, and ⌫) do not coincideemission1. For of in- neutrinos,| ⌧ | ,| in| order to detect the tionFurther and cannot independent reach the constraints Earth. The on Lorentz fact that vio- Using the inequality above and assuming ⌧ int lation have been set by combining the observation⌫ 15 19 the literature (see e.g. [14]), it is also important intFigure 4. Plot of g as function of the lightest neutrinoc ifv rather< 2 than10 a GW,(10 one)c, were to detect(16) a photon. If stance in the supernova explosion SN1987A [16], ⇠ Using the inequality⌫ above and assumingg ⌧int lation have been set by combining the observation to deduce other relevant physical properties.Aurora Meroni GWUsing andand the using theUniversity neutrino inequality (13) of toHelsinki signal, the above first we andoder must⌫ assuming in have: ⌫ and ⌧ g oneultra-high-energylation have been19 cosmic set by⇥ combining⇠ rays are observed the observation on 10 ms (typicalthe neutrinos time arrived for a approximately SN burst) 2 –and 3 hoursE⌫ = 5 MeVmass consideringof the event10⌧ ms10 (typical GW150914 ms considering timeint for in a SN the GWs burst) eq. (12). with and Eall the= messengers5 observa- MeV of thewere event simultaneously GW150914 in detected GWs with and the observa- This new information can be derived when int ⇠ ⇠ ⌫ before the associated photons. 10finds: ms (typical timeWe considerfor a SN burst)of the HK and andE⌫ = JUNO5 MeV energyEarthof thresholds,the limits event the GW150914 GW propagation in GWs speed with the to be observa- comparing, for example, theirwe propagation show in Fig. 4 the g dependence on the light- tion⌫ madewe show by the in Fig. Fermi 4 the Gamma-Raygassumingdependence that onassuming the Burstthe cosmic light- Mon- a uniquetion rays made have source by galactic the by Fermi using ori- Gamma-Ray (2), within ex- Burst Mon- Let us assume now that a neutrino is emitted at T⌫i g > ⌧int, (14) velocity with those of photons and neutrinos we show in Fig.| E 4⌫ the= 7| MeV g dependence (greyest region)⌫ neutrino on and theE mass⌫ light-= 1.806 fortion twoMeVgin made (extra-galactic) benchmark (orange by the distances, Fermi [19]. Gamma-Rayitor [20] of a Burst transient Mon- photon source in apparent tE = tE + ⌧⌫ and detected at time t . A relativistic ⌫ T0 & ⌧ . (15) perimental15 resolution,19 the following consistency est neutrino⌫ g massint for two benchmark⌫ distances,i itorg [20]int of a transient photon sourcec v < in2 apparent10 (10 )c, (16) coming both from the same astrophysical source. est2 neutrino massregion),| for two respectively,| benchmark for L distances,= 1 Mpc. Theitor dashed [20] of and a transientg photon source in apparent mass eigenstate neutrino with massandm usingi c E (13)( to the first oder in ⌫ and g one Further independent condition⇥ constraints must hold: on Lorentz vio- ⌧ i = 1, 2, 3 ) propagates with a group velocity: dotted vertical lines correspond to⌫ the Planck limit, finds: Using the inequality above and assuming ⌧int lation have been set by combining the observation i mi < 0.23 eV, and the perspectiveassuming⇠ upper limits that of the cosmic rays have galactic ori- 2 4 4 8 t ⌫ t ⌫ = t⌫ ⌫ = tg⌫ tg⌫ . (16) v m c m c 10 ms (typical time for a SN burst) and E⌫ = 5 MeV of the event GW150914i in GWsj withj thei observa-i j A. Set-up i = 1 i + i , (1) KATRIN, 0.2⌫ eV. gin (extra-galactic) [19]. c 2 O 4 we show in Fig.⌫ P 4g theT0 & ⌧dependence. on the(15) light- tion made by the Fermi Gamma-Ray Burst Mon- 2E 0 8E 1 | i | g int B C Further independent constraints on Lorentz vio- Let’s start by considering a potential obser- B C est neutrino mass for two benchmark distances, itor [20] of a transient photon source in apparent where we assumed that the@B di↵erentAC species of ⌫ IV. CONCLUDING WITH A PRELIMINARY vation of an astrophysical catastrophe. Using Using the inequalityand above could and probe assuming neutrino⌧ mass uplation to have0.02 been eV set by combining the observation neutrinos have been produced with a common int ⇠ ⇠ FEASIBILITY STUDY the same notation of [14], we denote with T g ⌘ energy value E. If a given neutrino10 ms is produced (typical time forfor a distances SN burst) around and E⌫ = 15 Mpc, MeV whichof the are event at least GW150914 in GWs with the observa- L/v , T L/v and T L/v respectively the g ⌫i ⌘ ⌫i ⌘ by a source at a distance L, the time-of-flightwe show delay in Fig. 4 thean orderdependence of magnitude on the lower light- thantion present made by cos- the Fermi Gamma-Ray Burst Mon- time of propagation of a GW, a given neutrino g So far we have been concerned with the theo- mass eigenstate and photons with group veloci- est neutrino mass formological two benchmark limits and distances, the perspectiveitor [20] upper of limit a transient photon source in apparent 1 In alternative theory of gravity the three particles under retical setup, and since the framework presented ties vg, v⌫i , and v . Following Fig. 1 a GW is emit- from KATRIN, see orange region in Fig. 4. E study — photons, gravitons and neutrinos— can couple to ted at the time tg from a source at distance L and here relies on distant sources, we will now per- di↵erent e↵ective metrics. In this case the Shapiro delay Last, we notice that limits on vg can also be ob- detected on Earth at tg. Similarly, we have emis- is not the same for the three signals [15]. In this work form a preliminary study of the actual experi- sion and detection times for photons and neu- however we assume the same coupling to the metric for tained from high energetic events or from the re- mental feasibility. In the following, we will not trinos. For instance, astrophysical catastrophes all the signals. quirement of Lorentz invariance. In fact, if the discuss the distribution and the expected num- GW velocity is subluminal, then cosmic rays lose ber of various kinds of astrophysical events, but their energy via gravitational Cherenkov radia- focus on the number of detected neutrinos assum- tion and cannot reach the Earth. The fact that ing a specific source at a given distance. From the ultra-high-energy cosmic rays are observed on analysis above it is clear, that three parameters Earth limits the GW propagation speed to be are vital to increase the time lapse between mass 15 19 c v < 2 10 (10 )c, (13) eigenstates: the distance from the source L, the g ⇥ energy of the emitted neutrino, E⌫, and the abso- assuming that the cosmic rays have galactic ori- lute neutrino mass mmin. Conversely, the larger gin (extra-galactic) [35]. the distance is, the smaller is the rate. As a con- Further independent constraints on Lorentz vio- sequence, if the neutrino counterparts of events lation can therefore be set when observing pho- like GW150914 would be emitted by the source, it ton and gravitational waves. An attempt of do- would be hard, if not impossible, to detect them ing so appeared in [36] by combining the event on Earth. GW150914 in GWs with the observation made by As a benchmark investigation we will concen- the Fermi Gamma-Ray Burst Monitor [37] of a trate on the next generation of neutrino detection transient photon source in apparent coincidence experiments such as 1 Mton Hyper-Kamiokande [36] (HK) in Japan [34] that has already sparkled inter- 17 ests in the astrophysical community. Astrophysi- vg c < 10 c. (14) cal catastrophes like the merging of a neutron star There are serious concerns about the true correla- black hole binary or the core bounce of a core- tion between the two events. Nevertheless if one collapsed supernova are expected to produce a 8 total neutrino output carrying an overall energy actual detection probability as function of the of circa 1053 erg. For such an event one expects on distance from the source. To assess this, we Earth an integrated time flux per squared meter use the Poisson probability to detect n events as 11 2 2 n of about 3 10 d/Mpc m . Despite the fact P = e /n! where is the expected number of ⇥ n that a large number of neutrinos will reach Earth events, given in eq. (18) or eq. (19). In Fig. 5 we because of their low cross section only a tiny frac- show, as an illustrative example, the detection tion will be detected. Previous studies [38] indi- probability for IBD resulting from requiring at cate that HK can detect 1-2 neutrino events per least one, two, and 10 events per burst, indicated year from supernovae in the range up to 10 Mpc. respectively with blue, red and black curves. We However, our theoretical analysis made use only use in our estimates the energy range 7 30 MeV. of the neutrinos emitted during the initial burst The plot shows the HK detection probability for from the source which can be determined by inte- ⌫¯e for a NS-BH merger (solid line), as well as the grating the following neutrino detection rate over one for a hypothetical 5 Mton detector (dashed the relevant time interval: line), e.g. [40]. We observe that even for 1 Mpc ⇠ and a 7 30 MeV energy range one can still dN = np dEe dE⌫ (E⌫, t) 0(Ee, E⌫) ✏, observe 1 event. These estimates show that it is dt th th F ZEe ZE⌫ ⇠ (17) possible to reach phenomenologically interesting neutrino mass di↵erences from sources at 1 where np is the number of protons in the target, ⇠ Mpc provided one can combine more than one E⌫,e are respectively the (anti)neutrino and the (electron) positron energy of the event, (E , t) Mton experiment. In order to compute the F ⌫ is the flux per unit time, area and energy and ✏ is expected annual rate of detected neutrino events, one has to combine the above analysis with the the detector e ciency. Finally 0(Ee, E⌫) = d /dEe is the di↵erential cross section of the process un- annual rate of relevant astrophysical events. The 8 1 der study. We will assume the e ciency of the annual rate of SNs is expected to be 1/3 yr detector to be 100% for energies larger than the within 4 Mpc [38], while the rate for NS-BH th mergers is more uncertain with an expected rate total neutrino output carryingenergy an threshold overall of energy the detector,actualE⌫ > detectionE⌫ . probability as function of the 2 3 1 53 of 10 10 yr within 1 Gpc. This rate will in of circa 10 erg. For suchOur an event estimates one assume expects a on typicaldistance energy from in neutri- the source. To assess this, we the future be constrained by LIGO [41]. Earth an integrated timenos flux emitted per squared from astrophysical meter use sources the Poisson within the probability to detect n events as 51 11 initial2 burst2 to be of the order of 10n erg as well We stress that we have used conservative esti- of about 3 10 d/Mpc m . Despite the fact Pn =⇠ e /n! where is the expected number of ⇥ as a mean neutrino energy E 12 MeV. From mates, for example, in the total energy emitted that a large number of neutrinos will reach Earth events,⌫¯e given in eq. (18) or eq. (19). In Fig. 5 we h i⇠ th with the neutrino burst. Another parameter a SN at a distance d, HK (0.74 Mton, E⌫ =7 MeV, because of their low cross sectionth only a tiny frac- show, as an illustrativethat example, can be played the detection with is the time resolution Ee =4.5 MeV) would expect the following num- tion will be detected. Previous studies [38] indi- probability for IBDin resulting neutrino from detection requiring that can, at in the future, be ber of detected neutrinos (indicated by ES) via cate that HK can detectneutrino-electron 1-2 neutrino events elastic per scatteringleast one, (ES) processes: two, and 10expected events per to go burst, below indicated one millisecond. If this is year from supernovae in the range up to 10 Mpc. respectively with blue,the red case and it would black curves. allow sources We as close as 100 2 However, our theoretical analysis made use only 3 used in our estimates thekpc energy to become range relevant 7 30 for MeV. our analysis. In this ES = 1.8 10 (18) ⇥ Mpc case the neutrino flux increases by two orders of of the neutrinos emitted during the initial burst The plot! shows the HK detection probability for magnitude. from the source which canwhere be determined the initial burstby inte- is primarily⌫¯e for a NS-BH⌫e from merger the (solid line), as well as the gratingFirst the followingfeasibility neutrinoneutronization detection study process. rate over Similarly,one for from a a hypothetical neutron 5 Mton detector (dashed To conclude, we derived the theoretical the relevant time interval:star black hole (NS-BH) merger,line), where e.g. [40]. the burst We observe that even for 1 Mpc and phenomenological⇠ conditions under which consists mostly of ⌫¯e, we get viaand inverse a 7 beta30 decay MeV energy range8 one can still dN multi-messenger astronomy can disentangle or = np dEe dE(IBD)⌫ ( [39]E⌫, t a) number0(Ee, E⌫) of✏, neutrinosobserve of 1 event. These estimates show that it is dt th th F further constrain the neutrino mass ordering. ZEe ZE⌫ ⇠ total neutrino output carrying an overall energy actual(17) detectionpossible probability2 to reach phenomenologically asWe function have also of the argued interesting that it can provide salient 1 d Detection probability for anti-53νe for a NS-BH merger IBD = 1.6 10 neutrino9. mass(19) di↵erences from sources at 1 of circa 10 whereerg. Fornp suchis the an number event one of expects protons on in thedistance target,⇥ fromMpc the source. Toinformation assess this, on we the absolute⇠ neutrino masses. Mpc! provided one can combine more than one Earth an integratedE⌫,e are respectively time flux per the squared (anti)neutrino meter use and the the Poisson probability to detectWe addedn events a aspreliminary feasibility study to ��� 11 2 the2 cosmological bounds on neutrinon Mton absolute experiment. In order to compute the of about 3 (electron)10 d/Mpc positron m energy. DespiteFor of such the fact low event, ratesPn =( itE ⌫ is,et ) useful/n! where to estimate is the the expectedsubstantiate number and of further motivate our theoretical ⇥ masses. However, this requiresF highexpected resolution annual rate of detected neutrino events, that a largeis number theP1 flux(n⩾1 of) per neutrinos unit time,timing will area and reach and a significant Earth energyevents, and increase✏ givenis in the in com-eq. (18) or eq. (19). In Fig. 5 we ��� one has to combine the above analysis with the because of theirthe detectorP2 low(n⩾2 cross) e sectionciency.bined only Finally fiducial aLow tiny volume0number( frac-Ee, E⌫ of) comparedshow,= eventsd /dE asat toerequired an the illustrative current distances example, the detection P (n⩾10) annual rate of relevant astrophysical events. The tion will beis detected. the10 di↵erential Previous crossCherenkov studies sectionWhat [38] water of can indi- the detectors. improve processprobability the un-number for of events: IBD resulting from requiring at ��� 1 cate that HKder can study. detect We 1-2 will neutrino assumeConversely events the one e perciency canleast use of one, future the two,annual results and on 10 rate events of SNs per burst, is expected indicated to be 1/3 yr ����������� neutrino properties to provide detailedwithin infor- 4 Mpc [38], while the rate for NS-BH year from supernovaedetector to in be the 100% range for up energies• toLarger 10 Mpc. larger detectorrespectively than (Linear the) with blue, red and black curves. We ��� mation about astrophysical sources emitting th mergers is more uncertain with an expected rate However, ourenergy theoretical threshold analysis ofsimultaneously the made detector,• useLessE onlyGWs, uncertainty⌫ > E photons⌫use. on in τ our_int and estimates(Quadratic) neutrinos, the energy range 7 30 MeV. ��������� 2 3 1 of 10 10 yr within 1 Gpc. This rate will in of the neutrinosOur estimates emitted during assumeand the a possibly typical initial• lower energy burst uncertainties inThe neutri- plot in shows the emitted the HK detection probability for ��� Better time resolution (Quadratic) from the sourcenos emitted which can from be astrophysical determinedmulti-messenger by sources inte- signal within from⌫¯e for the a the source. NS-BHthe future merger be (solid constrained line), as by well LIGO as the [41]. grating theinitial following burst neutrino to be of detection the order rate of over1051 ergone as for well a hypotheticalWe stress that 5 Mton we have detector used (dashed conservative esti- ��� Detection⇠ probability for IBD resulting from requiring at ���� ���� the relevant���� � time interval:� �� line), e.g. [40].mates, We for observe example, that even in the for total1 Mpc energy emitted as a mean neutrino energyleastE⌫ ¯one,e two,12 MeV.and 10 From events per burst, indicated �[���] h i⇠ ⇠ a SN at a distance d, HK (0.74respectivelyNOTE Mton, ADDED withEth andblue,=7 IN MeV, PROOFred a 7and black30with MeV curves. the energy neutrino We use rangein burst. one can Another still parameter Figure 5. DetectiondN probability of neutrinos ver- ⌫ = np th=4.5dEe MeV)dE would⌫ (E⌫, expectt) 0our(Ee , theestimatesE⌫) following✏, theobserve energy num- range1that event.7 − 30 can MeV. These be played estimates with show is that the timeit is resolution sus distance from thedt source toEe Hyper-Kamiokandeth th F While our work was under review related pa- Hyper/Kamiokande (solid line)Z Ee ZE⌫ ⇠ in neutrino detection that can, in the future, be (solid5 Mton lines) detector and to (dashed a hypothetical line)ber future of detected 5 Mton ex- neutrinospers on the (indicated propagation(17) bypossible time ES) of via ultra-relativistic to reach phenomenologically interesting periment (dotted lines) [40] using a 7 30 MeV energy neutrino-electron elasticparticles scattering appeared (ES) in the processes:neutrino literature [42, massexpected 43], which di↵erences to go below from sourcesone millisecond. at 1 If this is range. Blue, red andwhere blackn curvesp is the represent number the detec- of protons in the target, ⇠ provide relevant detailsMpc for a high provided precisionthe one case ap- can it would combine allow more sources than one as close as 100 Aurora Meronition probability resultingE⌫,e are in respectively requiring observation theUniversity (anti)neutrino of of Helsinki and the 20 plication of the presented2 framework. at least one, two, and ten events per burst, respectively. 3 d Mton experiment.kpc to become In order relevant to compute for our analysis. the In this (electron) positron energy ES = of1. the8 event,10 (E⌫, t) (18) ⇥ MpcACKNOWLEDGMENTSF case the neutrino flux increases by two orders of is the flux per unit time, area and energy and !✏ is expected annual rate of detected neutrino events, The CP3-Origins centreone is partially has to combinemagnitude. funded by the above analysis with the the detectorwhere e ciency. the initial Finally burst 0(Ee is, E⌫ primarily) = d /dEe⌫e from the analysis. We haveis the seen di↵ thaterentialneutronization future cross experiments section process.the of Danishthe Similarly, process National from un- Research aannual neutron Foundation, rate of relevant grant astrophysical events. The can be useful also in testing independently number DNRF90. To conclude, we derived the1 theoretical der study.star We black will assume hole (NS-BH) the e ciency merger, of where the annual the burst rate of SNs is expected to be 1/3 yr within 4 Mpcand [38], phenomenological while the rate conditions for NS-BH under which detector toconsists be 100% mostly for energies of ⌫¯e, we larger get via than inverse the beta decay th mergers is moremulti-messenger uncertain with astronomy an expected can rate disentangle or energy threshold(IBD) [39] of the a number detector, ofE neutrinos⌫ > E⌫ . of 2 3further1 constrain the neutrino mass ordering. [1] B. P. AbbottOuret al. [LIGO estimates Scientific assume and Virgo a typical Col- energy(2015) in neutri- doi:10.1103of 10/PhysRevD.92.05200510 yr within 1 Gpc. This rate will in laborations], Phys. Rev. Lett. 116, no. 6, 061102 [arXiv:1507.043282 [hep-ex]]. We have also argued that it can provide salient nos emitted from astrophysical sources1 withind the the future be constrained by LIGO [41]. (2016) doi:10.1103/PhysRevLett.116.061102 IBD = 1.6[8] K.10 A. Olive et al.. [Particle(19) Data Group Col- ⇥ 51 Mpc We stress thatinformation we have on used the conservative absolute neutrino esti- masses. [arXiv:1602.03837initial [gr-qc]]. burst to be of the order of 10laboration],erg as Chin. well! Phys. C 38, 090001 (2014). [2] S. M. Bilenky, S. Pascoli and S. T. Pet- ⇠ doi:10.1088/1674-1137/38/9/090001 We added a preliminary feasibility study to as a mean neutrino energy E⌫¯ 12 MeV. From mates, for example, in the total energy emitted cov, Phys. Rev. D 64, 053010 (2001) e [9] P. A. R. Ade et al. [Planck Collaboration], Astron. h i⇠ th with the neutrinosubstantiate burst. and furtherAnother motivate parameter our theoretical doi:10.1103/aPhysRevD.64.053010 SN at a distanceFor suchd, HK low [hep- (0.74 rates Mton, itAstrophys. isE useful⌫ =7 MeV,571 to, estimate A16 (2014) the doi:10.1051/0004- th that can be played with is the time resolution ph/0102265].Ee =4.5 MeV) would expect the following6361/201321591 num- [arXiv:1303.5076 [astro-ph.CO]]. [3] S. M. Bilenky and S. T. Petcov, Rev. Mod. Phys. [10] N. Palanque-Delabrouillein neutrinoet al., JCAP detection1511, no. that can, in the future, be ber of detected neutrinos (indicated by ES) via 59, 671 (1987) Erratum: [Rev. Mod. Phys. 61, 169 11, 011 (2015) doi:10.1088expected/1475-7516 to/2015 go/ below11/011 one millisecond. If this is (1989)] Erratum:neutrino-electron [Rev. Mod. Phys. 60 elastic, 575 (1988)]. scattering[arXiv:1506.05976 (ES) processes: [astro-ph.CO]]. doi:10.1103/RevModPhys.59.671 [11] R. Laureijs et al. the[EUCLID case Collaboration],it would allow sources as close as 100 [4] W. Rodejohann, Int. J. Mod. Phys. E 20, arXiv:1110.31932 [astro-ph.CO]. 3 d kpc to become relevant for our analysis. In this 1833 (2011) doi:10.1142 ES/S0218301311020186= 1.8 10 [12] P. Minkowski,(18)Phys. Lett. B67:421, (1977); M. Gell- ⇥ Mpc case the neutrino flux increases by two orders of [arXiv:1106.1334 [hep-ph]]. !Mann, P. Ramond, and R. Slansky, in Supergrav- [5] L. M. Krauss and S. Tremaine, Phys. Rev. Lett. 60, ity, edited by F. Nieuwenhuizenmagnitude. and D. Fried- 176 (1988). doi:10.1103where the/PhysRevLett.60.176 initial burst is primarilyman,⌫e Northfrom Holland, the Amsterdam, (1979), p. 315; [6] M. J. Longo,neutronization Phys. Rev. Lett. process.60, 173 (1988). Similarly, fromT. Yanagida, a neutron Proc. of the Workshop on Unified To conclude, we derived the theoretical doi:10.1103/starPhysRevLett.60.173 black hole (NS-BH) merger, whereTheories the and burst the Baryon Number of the Uni- [7] P. Adamson et al. [MINOS Collabora- verse, edited by O. Sawadaand phenomenological and A. Sugamoto, conditions under which consists mostly of ⌫¯e, we get via inverse beta decay tion], Phys. Rev. D 92, no. 5, 052005 KEK, Japan 1979; R.N.multi-messenger Mohapatra and G. Sen- astronomy can disentangle or (IBD) [39] a number of neutrinos of further constrain the neutrino mass ordering. 2 We have also argued that it can provide salient 1 d = 1.6 10 . (19) IBD ⇥ Mpc information on the absolute neutrino masses. ! We added a preliminary feasibility study to For such low rates it is useful to estimate the substantiate and further motivate our theoretical Conclusions Fundamental unknowns in Neutrino Physics: • The absolute neutrino mass, • Ordering (Normal or Inverted), • CP violation in the leptonic sector, • The nature: Dirac or Majorana. Μulti-messenger astronomy can: • disentangle or further constrain the neutrino mass ordering. • provide salient information on the absolute neutrino masses. Future experiments can be useful also in testing independently the cosmological bounds on neutrino absolute masses. However, this requires high resolution timing and a significant increase in the combined fiducial volume compared to the current Cherenkov water detectors. Conversely one can use future results on neutrino properties to provide detailed information about astrophysical sources emitting simultaneously GWs, photons and neutrinos, and possibly lower uncertainties in the emitted multi-messenger signal from the source. Aurora Meroni University of Helsinki 21 Thanks for your attention