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 - δ, 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, δ) 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 iδ ⌫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 iδ 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 Diracδ,possessing and - δ, 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 (✓" , ✓ , ✓ , δ) 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, δ 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-fitiδ m values for the mass-mixing parameters and associated nσ 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 χ χmin = 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 - δ, and2 two010 (eventually)2 Majoranas12 c12 [21]0 , - ↵21(1.3) minimum in any ordering. (Note that0 the fit to the1 0δm andiδ sin ✓12≃parameters1 02−E is basically1 insensitive to the mass ordering.) We recall 0 s23 c23 s13e 0 icδ13 001 thatarXiv:1703.04471and∆↵m312,is CP defined violating Lisi10 herein et al. phases: as m2 0(m2−+ m2)c/2,13 and− that0 δs13is takene− in the (cyclic)c12 intervals12 0δ/⇡ [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 1σ range⌘ 1 0∆⌘−mkj 2σ 1range 3σ range 0 UforsPMNS the valuesc U of= theV ( angles✓12s, ✓ beinge23iδ, ✓13 00,theδ✓)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) δm /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, accumulatediδ 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, 2.525iδ 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 2.5σ 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 2.5σ 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.