Debasish Borah. (Based on with A. Dasgupta)

Transcription

1 & Observable LNV with Predominantly Dirac Nature of Active Neutrinos Debasish Borah IIT Guwahati (Based on with A. Dasgupta) 1 / 44

2 Outline / 44

3 Evidence of Dark Matter In 1932, Oort found that the gravitational potential provided by the visible stars was not enough to keep the stars bound to the Galactic plane. Since the galaxy is stable and not losing stars, there has to be more matter to keep the stars bound to the galaxy. The other claim that some mysterious form of matter (Dark Matter) must dominate in Galaxy clusters was made by Fritz Zwicky in He found that the radial velocities of galaxies in a cluster are almost a factor of 10 larger than expected from the summed mass of all galaxies in the cluster. 3 / 44

4 Evidence of Dark Matter 4 / 44

5 Evidence of Dark Matter Distorted images of galaxy clusters due to gravitational lensing indicates the presence of dark matter. 5 / 44

6 Evidence of Dark Matter A direct empirical proof of dark matter was given by NASA s Chandra X-ray observations of a bullet cluster: two clusters of galaxies (90% of which is intergalactic gas) passing through each other. As they passed through each other, the individual galaxies and dark matter (if exists) passed right through each other whereas the hot gas in each of them smacked into each other. The gravitational lensing maps of the event show that the gravitational potential does not trace the hot gas (plasma) distribution, the dominant baryonic mass component. But it rather approximately traces the distribution of galaxies implying the presence of an enormous amount of invisible matter. 6 / 44

7 Evidence of Dark Matter 7 / 44

8 Evidence of Dark Matter Numerical simulations incorporating dark matter agree well with the observed structure in the Universe. 8 / 44

9 Evidence of Dark Matter CMBR power spectrum is sensitive to composition of the Universe: baryons, dark matter and dark energy. 9 / 44

10 Particle Dark Matter Presence of dark matter is very well established through its gravitational effects; however, their particle origin is not yet known. In the popular WIMP (Weakly Interacting Massive Particle) paradigm, the dark matter is a weakly interacting particle which is non-relativistic (Cold) during the epoch of freeze-out, typically having masses in the GeV-TeV range. Other non-standard possibilities also exist. For example, warm dark matter (WDM), with kev scale masses. Such possibilities not only change the dark matter detection techniques, but also change the astrophysical structure formation history, making their verification/falsification possible in galaxy survey experiments. No such cold or warm dark matter candidates are there in the standard model of particle physics (ν s are Hot Dark Matter, with negligible abundance). 10 / 44

11 Particle Dark Matter: Ten Point Test 1 Does it match the appropriate relic abundance? Is it cold? Is it electromagnetic and color neutral? Is it consistent with Big Bang Nucleosynthesis? Does it leave stellar evolution unchanged? Is it compatible with constraints on self-interactions? Is it consistent with direct dark matter searches? Is it compatible with gamma-ray searches? Is it compatible with other astrophysical bounds? Can it be probed experimentally? 1 Bertone et al, / 44

12 Dark Matter Candidates 12 / 44

13 Dark matter could well be composed of more than one particle: multi-component dark matter scenarios with very interesting consequences in direct/indirect detection, cosmology/astrophysics. (Also see talks by Sahu, Majumdar..) All of them could be perfectly stable due to enhanced symmetries like Z 2 Z 2 ( , ) or some of them could be long-lived while the lightest one is perfectly stable ( , , ). A two-component WIMP dark matter with kev mass difference (or say one at GeV-TeV scale and the other at kev) can explain gamma ray as well as X-ray anomalies. Two component DM with one behaving like cold dark matter and the other as warm dark matter could have interesting implications for astrophysical structure formation at small scales ( ). 13 / 44

14 Baryon and Lepton numbers are conserved in the standard model at perturbative level. They can be violated by non-perturbative spharelon transitions ( t Hooft 1980) which are important only at very high temperature (Kuzmin et al 1985). Any observation of LNV will carry a signature of beyond the standard model physics: Neutrinoless double beta decay (0νββ) (e.g., ), muon to positron conversion (e.g., ) etc. (Also see the talk by Patra). 0νββ is a process where a heavier nucleus decays into a lighter one and two electrons (A, Z) (A, Z + 2) + 2e without any (anti) neutrinos in the final state thereby violating lepton number by two units. Any observation of 0νββ confirms the Majorana nature of neutrinos (Schechter-Valle Theorem 1982). However, the absence of any positive signal at 0νββ experiments does not necessarily rule out the Majorana nature of light neutrinos. 14 / 44

15 0νββ Outline n p W L ν e L W L e L n p The light neutrino contribution to 0νββ is given by = Γν NDBD ln2 A ν U2 Lei m i p 2 = G M ν 2 U 2 me 2 Leim i 2 15 / 44

16 The Schechter-Valle theorem The Schechter-Valle theorem (PRD 1982) says, any non-zero amplitude of 0νββ induces a non-zero effective Majorana mass to the electron type neutrino, irrespective of the underlying mechanism behind the 0νββ process. Although one can introduce some cancellations between different terms leading to a vanishing effective Majorana mass, one can not guarantee such cancellations to all orders of perturbation theory. In fact, there exists no continuous or discrete symmetry that can forbid such an effective Majorana mass term to all orders in perturbation theory (Takasugi 1984, Nieves 1984). 16 / 44

17 The Schechter-Valle theorem The lowest possible order such a mass term can arise is through the four loop diagram below u L u L W L d L d L W L O 0νββ e L e L ν Le ν Le 17 / 44

18 The Schechter-Valle theorem The authors in , showed all possible Lorentz invariant operators that can contribute to 0νββ and showed that one such operator contributes δm ee ν (0.74 5) ev to the Majorana mass of electro type neutrino. The above estimate which incorporates the recent bound on 0νββ amplitude confirms the qualitative validity of the Schechter-Valle theorem, though the calculated Majorana mass term is way too small compared to the neutrino mass squared differences. Therefore, it is possible that light active neutrino masses originate primarily from a mechanism which preserves lepton number whereas LNV process like 0νββ can still have a sizeable amplitude originating from other particles in the theory. 18 / 44

19 Minimal L-R Symmetric Model MLRSM is the extension of the standard model to the enlarged gauge symmetry SU(3) c SU(2) L SU(2) R U(1) B L (Pati, Salam, Mohapatra, Senjanovic). The right handed fermions which are singlets under the SU(2) L of SM, transform as doublets under SU(2) R, making the presence of right handed neutrinos natural in this model (Seesaw mechanism arises naturally). The Higgs doublet of the SM is replaced by a Higgs bidoublet to allow couplings between left and right handed fermions, both of which are doublets under SU(2) L and SU(2) R respectively. The enhanced gauge symmetry of the model SU(2) R U(1) B L is broken down to the U(1) Y of SM by the vacuum expectation value (vev) of additional Higgs scalar, transforming as triplet under SU(2) R and having non-zero U(1) B L charge. This triplet also gives rise to the Majorana masses of the right handed neutrinos through symmetry breaking. 19 / 44

20 MLRSM Outline The fermion content of the minimal LRSM is ( ) ul Q L = (3, 2, 1, 1 ( ) d L 3 ), Q ur R = (3, 1, 2, 1 d R 3 ), l L = ( νl e L ) (1, 2, 1, 1), l R = ( νr Similarly, the Higgs content of the minimal LRSM is ( φ 0 Φ = 11 φ + ) 11 φ 12 φ 0 (1, 2, 2, 0) 12 ( δ + L = L / 2 δ ++ ) L δl 0 δ + L / (1, 3, 1, 2) 2 ( δ + R = R / 2 δ ++ ) R δr 0 δ + R / (1, 1, 3, 2) 2 e R ) (1, 1, 2, 1) 20 / 44

21 MLRSM Particle Spectra The spontaneous breaking of gauge symmetry: SU(2) L SU(2) R U(1) B L R SU(2) L U(1) Y Φ U(1) em Denoting bidoublet vev s as k 1, k 2 and that of triplets L,R as v L,R and considering g L = g R, k 2 v L 0 and v R k 1, the gauge boson masses after symmetry breaking can be written as MW 2 L = g 2 4 k2 1, MW 2 R = g 2 2 v R 2 MZ 2 L = g 2 k1 2 ( 4 cos 2 1 cos2 2θ w k 2 ) 1 θ w 2 cos 4 θ w vr 2, MZ 2 R = g 2 vr 2 cos2 θ w cos 2θ w 21 / 44

22 Extension of MLRSM Particles ( ) SU(3) c SU(2) L SU(2) R U(1) B L Z 4 Z 4 ul q L = (3, 2, 1, d 1 3 ) (1, 1) ( L ) ur q R = (3, 1, 2, d 1 3 ) (1, 1) ( R ) νl l L = (1, 2, 1, 1) (1, 1) ( e L ) NR l R = (1, 2, 1, 1) (1, 1) e R U L,R (3, 1, 1, 4 3 ) (1, 1) D L,R (3, 1, 1, 2 3 ) (1, 1) E L,R (1, 1, 1, 2) (1, 1) ν R (1, 1, 1, 0) (1, i) ψ L,R (1, 1, 1, 0) (i, 1) Table: Fermion Content of the Model 22 / 44

23 Extension of MLRSM Particles ( ) SU(3) c SU(2) L SU(2) R U(1) B L Z 4 Z 4 H + H L = L HL 0 (1, 2, 1, 1) (1, 1) ( ) H + H R = R HR 0 (1, 1, 2, 1) (1, 1) ( ) η + η L = L ηl 0 (1, 2, 1, 1) ( i, 1) ( ) η + η R = R (1, 1, 2, 1) ( i, 1) η 0 R R (1, 1, 3, 2) (1, 1) L (1, 3, 1, 2) (1, 1) χ 1 (1, 1, 1, 0) ( i, i) χ 2 (1, 1, 1, 0) (1, i) χ 3 (1, 1, 1, 0) ( 1, 1) Table: Scalar content of the Model 23 / 44

24 The Lagrangian The Lagrangian for fermions can be written as L Y U (q L H L U L + q R H R U R ) + Y D (q L H L D L + q R H R D R) + M U U L U R + M D D L D R + Y E (l L H L E L + l R H R E R) + M E E L E R + Y νl L η L ψ R + M ψ ψ L ψ R + Y r ν R χ 1ψ L + f R l T R C iσ 2 R l R + h.c. The relevant part of the scalar Lagrangian is L µ 2 LH L H L + λ L (H L H L) 2 µ 2 RH R H R + λ R (H R H R) 2 + µ 2 η L η L η L + λ ηl (η L η L) 2 + µ 2 η R η R η R + λ ηr (η R η R) 2 µ 2 L L L + λ L ( L L) 2 µ 2 R R R + λ R ( R R) 2 + µ 2 1χ 1 χ1 + λ1(χ 1 χ1)2 µ 2 2χ 2 χ2 + λ2(χ 2 χ2)2 + µ 3H R H R R + λ 3η L H Lχ 1χ 2 + λ 4η L η L L χ 3 + µ 4χ 1χ 1χ 3 24 / 44

25 Gauge Boson Masses The mass matrix squared for charged gauge bosons in the basis W ± L, W ± R is M± 2 = 1 ( g 2 L (vl 2 + 2v ) δ 2 L ) gr 2(v R 2 + 2v δ 2 R ) Similarly, the neutral gauge boson mass matrix in the basis (W L3, W R3, B) is M0 2 = 1 gl 2(v L 2 + 4v δ 2 L ) 0 g 1 g L (vl 2 + 4v 2 δ L ) 0 gr 2 4 (v R 2 + 2v δ 2 R ) g 1 g R (vr 2 + 4v δ 2 R ) g 1 g L (vl 2 + 4v δ 2 L ) g 1 g R (vr 2 + 4v δ 2 R ) g1 2(v L 2 + v R 2 + 4v δ 2 L + 4vδ 2 R ) 25 / 44

26 Fermion Masses After integrating out the heavy fermions, the charged fermions of the standard model develop Yukawa couplings to the scalar doublet H L as follows y u = Y U v R M U Y T U, y d = Y D v R M D Y T D, y e = Y E v R M E Y T E The dominant contribution to active neutrino mass comes from the one-loop diagram H 0 L χ 2 η 0 L χ 1 ν Li ψ R ψ L ν Rj 26 / 44

27 es at one-loop One-loop Dirac neutrino mass can be written as (m ν ) ij = (m ν ) Rij + (m ν ) Iij where the terms with subscript R, I correspond to the contribution from real and imaginary parts of the internal scalar fields respectively. The contribution of the real sector Re(ηL 0), Re(χ 1) to one loop Dirac neutrino mass can be written as ( mξ 2 (m ν) Rij = (Y ν) ik (Y r ) kj M 1 mξ 2 2 ψk sin θ1 cos θ1 32π 2 k m 2 ξ 1 M 2 ψk ln m2 ξ 1 Mψk 2 m 2 ξ 2 M 2 ψk ln m2 ξ 2 M 2 ψk ) where λ 3v L u tan 2θ 1 = m 2 Re(χ 1 ) m2 Re(η L 0) with ξ 1,2 being the physical mass eigenstates of the Re(η 0 L), Re(χ 1) 27 / 44

28 es at two-loop The active neutrinos ν L can also acquire a Dirac mass through mixing with the neutral lepton in the right handed lepton doublet N R at two loop level through the following diagram (Babu & He 1989, Ma & Popov ) t L t R W + L b L br W + R ν L l L l R N R 28 / 44

29 es at two-loop This two-loop Dirac neutrino mass can be calculated as M LR = αm l sin 2θ L R (f (x 4π sin 2 l,wr ) f (x l,wl )) θ W 2 sin 2θ L R = f (x i,j ) = 1 16π 2 2W LR ( M 2 W R M 2 W L ) 2 + 4W 2 LR W LR = 4πα m um sin 2 d V u,d Vu,df (x u,d ); θ W u,d [ x i,j ln(x i,j ) + 1 x i,j + ln 1 x i,j ( µ 2 m 2 j x i,j = m2 i Such a Dirac mass term generates a type I seesaw mass matrix in the (ν L, N R ) basis, given by ( ) 0 MLR M ν =, M T LR M RR )] m 2 j 29 / 44

30 es at two-loop Using the approximation M RR M LR, the light neutrino mass is given by the type I seesaw formula M I ν = M LR M 1 RR MT LR where M RR = f R v δr is the Majorana mass matrix of N R. Therefore, even if we consider a minimal mass of 1 GeV for N R, the corresponding Majorana mass term for active neutrinos is of the order of 10 9 ev. Therefore, the active neutrino masses are dominantly of Dirac type with tiny signature of lepton number violation. However, there can be observable signatures of lepton number violation through neutrinoless double beta decay due to the existence of additional gauge and scalar bosons as well as neutral leptons. 30 / 44

31 0νββ Outline n p n p W R W R e R e R R N R W R e R e R W R n p n p 31 / 44

32 0νββ Outline T 0 1/2 (yr) Ge Xe KamLAND-Zen GERDA r = m N /m Δ Figure: Half-life of 0νββ as a function of heavy neutrino to triplet scalar mass ratio 32 / 44

33 0νββ Outline m eff N R + Δ R (ev) m e Majorana (ev) Figure: Effective Majorana mass responsible for 0νββ versus Majorana mass of electron type neutrino. 33 / 44

34 CLFV Outline γ γ γ W R W R R R l + R l + R µ R NR e R µ R l + R e R µ R R e R Figure: New physics contribution to LFV decays 34 / 44

35 CLFV Outline γ e R η L R e R µ R µ L ψ e L e + R Figure: New physics contribution to LFV decays 35 / 44

36 CLFV Outline SINDRUM MEG BR(µ -> 3e) BR(µ -> e γ) r = m N /m Δ r = m N /m Δ Figure: Scalar triplet and heavy neutrino contribution to LFV decays 36 / 44

37 CLFV Outline Y m Η GeV Figure: Contribution from the charged component of the left handed dark matter doublet η L to LFV decay 37 / 44

38 Dark Matter Outline We consider scalar doublet dark matter that includes the neutral components of the doublets namely, ηl 0, η0 R in our model. Due to the absence of scalar bidoublet in this model (unlike in MLRSM), both of them are stable, giving rise to multi-component dark matter scenario. Scalar doublet extension of MLRSM (Garcia-Cely, Heeck 2016), the scalar coupling η T L Φη R with Φ being the scalar bidoublet, leads to the decay of the heavier DM into the lighter one and SM fermions mediated by the Higgs. We calculate the individual relic abundances of ηl 0, η0 R by assuming zero left-right mixing and considering only the gauge interactions for ηr 0 while keeping both scalar/gauge interactions for η0 L 38 / 44

39 Dark Matter Outline Ω h η L, λ = 0.1 η L, λ = 0.01 η R Planck m η (GeV) Figure: Relic abundance of η L and η R dark matter as a function of their masses 39 / 44

40 Other constraints on η L DM BR h DM DM 22 LUX 2016 Planck / 44

41 Dark Matter Outline Figure: Relative contribution of η L and η R dark matter when total relic abundance falls within the range given by the Planck experiment 41 / 44

42 Dark Matter Outline Figure: Masses of η L and η R dark matter when total relic abundance falls within the range given by the Planck experiment 42 / 44

43 Results and We have proposed a model where one can have observable lepton number violation even if the light neutrino masses are predominantly Dirac (at one-loop level) with a negligible Majorana component (at two-loop level). Such a possibility was suggested a few years back through the study of the quantitative implications of the Schechter-Valle theorem. However, concrete model building work was missing in that direction. The results of this work suggest that a positive observation of 0νββ does not necessarily suggest the light neutrinos to be dominantly of Majorana type. The model also has new physics sources of charged lepton flavour violation within the reach of ongoing and near future experiments. The model also predicts multi-component dark matter than can have very rich phenomenology. It can also have interesting implications for leptogenesis (Dirac leptogenesis is viable) and cosmology, in general. 43 / 44

44 THANK YOU 44 / 44