Constraining Neutrino Mass from Neutrinoless Double Beta Decay in TeV Scale Left-Right Model

Transcription

1 Constraining Neutrino Mass from Neutrinoless Double Beta Decay in TeV Scale Left-Right Model Manimala Mitra IPPP, Durham University, UK November 24, 2013 PASCOS 2013, Taipei, Taiwan

2 Outline Neutrinoless double beta decay-the canonical interpretation Implications of recent results of neutrinoless double beta decay and Planck Left-right symmetry and neutrinoless double beta decay Summary arxiv: , P. S. Bhupal. DeV, Srubabati Goswami, Manimala Mitra and Werner Rodejohann

3 Experimental observation ev neutrino masses m i and mixing U from oscillation and non-oscillation experiments Cosmological bound on the sum of light neutrino masses i m i < 0.23 ev Planck collaboration, 2013 m 2 21 = ( ) 10 5 ev 2 m 2 31 = ( ) 10 3 ev 2 sin 2 θ 12 = sin 2 θ 23 = sin 2 θ 13 = Schwetz et al., 2012 Also Fogli., et al., 2012 Super Kamiokande, Long Baseline T2K, MINOS, K2K Reactor DAYA BAY, RENO, Double CHOOZ,... Solar SNO, Borexino, SAGE, GALLEX...

4 Neutrinoless Double Beta Decay Neutrino Mass Dirac or Majorana? Majorana mass mν T C 1 ν Lepton number violation Neutrinoless double beta decay (0ν2β) The process is (A,Z) (A,Z +2)+2e Probing lepton number violation

5 The light neutrino contribution The half-life 1 T 0ν 1/2 = G 0ν M ν 2 m ν ee 2 m e G 0ν phase-space M ν nuclear matrix element m ν ee = Σm i U 2 ei effective mass of 0ν2β α, β Majorana phase, m i light neutrino masses m ν ee = m 1U 2 e1 +m 2U 2 e2 e2iα +m 3 U 2 e3 e2iβ Unknown neutrino mass spectra, absolute mass scale, CP phases

6 Experimental results Experimental Results for 76 Ge Heidelberg-Moscow, T 0ν 1/2 > yr, 90% C.L H. V. Klapdor-Kleingrothaus et al., 2001 GERDA, T 0ν 1/2 > yr, 90% C.L GERDA combined (IGEX+Heidelberg-Moscow) T 0ν 1/2 > yr, 90% C.L GERDA collaboration, 2013 Experimental Results for 136 Xe EXO-200, T 0ν 1/2 > yr at 90% C.L EXO collaboration, 2012 KamLAND-Zen, T 0ν 1/2 > yr at 90% C.L KamLAND-Zen combined, T 0ν 1/2 > yr at 90% C.L KamLAND-Zen collaboration, 2012

7 Positive claim The half-life for 76 Ge, T 0ν 1/2 = yr, 68% CL. Ν H. V. Klapdor-Kleingrothaus et al., 2004 The half-life for 76 Ge, T 0ν 1/2 = yr, 68% CL. H. V. Klapdor-Kleingrothaus et al., Positive claim 90 GERDA IH GERDA HDM IGEX 90 QD ev m ee NH Planck1 KATRIN Planck2 Light neutrino contribution can not saturate the limit m lightest ev Pascoli, Mitra, Wong, 2013

8 Contd Limit on m ν ee (ev) NME 76 Ge 136 Xe GERDA comb KK KLZ comb EDF(U) ISM(U) IBM pnqrpa(u) SRQRPA-B SRQRPA-A QRPA-B QRPA-A SkM-HFB-QRPA Individual bound from GERDA does not rule out the positive claim Tension between the GERDA combined and positive claim Experiments using 136 Xe A complimentary way to test the positive claim. The constraint on the effective mass from 136 Xe is stronger than 76 Ge

9 Contd The correlation between the half-lives T 0ν 1/2 (136 Xe) = GGe 0ν G Xe 0ν ( ) M0ν ( 76 Ge) 2T 0ν M 0ν ( 136 Xe) 1/2 (76 Ge) The positive claim for 76 Ge will be ruled out for T1/2 0ν (predicted) < T0ν 1/2 (exp) for 136 Xe. Ge (yr) 76 T 1/ GCM IBM NSM KamLAND-ZEN 90% CL RQRPA QRPA-2 90% CL T 1/2 Xe (yr) Heidelberg- Moscow 90% CL EXO-200 (this work) KK&K 68% CL 68% CL Ge (yr) 76 T 1/ GCM IBM (R)QRPA NSM EXO % C.L KamLAND-Zen 90% C.L T 1/2 Xe (yr) From A. Gando et al., 2012 Combined 90% C.L. KK 68% C.L

10 Contd NME T1/2 0ν Xe) Method M 0ν ( 76 Ge) M 0ν ( 136 Xe) [10 25 yr] EDF(U) ISM(U) IBM pnqrpa(u) SRQRPA-B SRQRPA-A QRPA-B QRPA-A SkM-HFB-QRPA The positive claim is ruled out from the combined bound of KamLAND-Zen (T 0ν 1/2 > yr) for all but one NME calculation. However, is consistent with individual limits for 136 Xe

11 Additional contributions? 0ν2β light Majorana neutrinos? The effective Lagrangian llhh L eff = L SM +ξ 1 M +ξ qqql 2 M 2 +ξ (qdl) 2 3 M Weinberg, PRL 43, 1979 llhh ξ 1 M d-5 operator. Generates neutrino mass qqql ξ 2 d-6. Relevant for proton decay M 2 ξ 3 (ude) 2 M 5 d-9. Relevant for neutrinoless double beta decay Dimension 5 and Dimension 9 operators are uncorelated

12 Contd: 0Ν T1 2 yr NH IH 76 Ge Planck1 95 CL Planck2 95 CL 0Ν T1 2 yr NH IH 136 Xe Planck1 95 CL Planck2 95 CL GERDA HM IGEX 90 CL GERDA 90 CL KK 90 CL QD KLZ EXO 90 CL KLZ 90 CL QD mlightest ev mlightest ev The most stringent bound from Planck Σ i m i < 0.23 ev. The light neutrino contribution saturates the 0ν2β in quasi degenerate region Strong tension with cosmology!! (Fogli et al., 2008; Mitra et al., 2012, 2013) More than one order of magnitude improvement in half-life is required Additional contributions!!!

13 Contd: Previous and recent studies R parity violating supersymmetry, (Mohapatra 1986; Hirsch et al, 1995; Choi et al, 2002; Allanach et al, ) Left Right symmetry (Hirsch et al., PLB, 96, Tello et al., PRL, 2011, Goswami et al., JHEP, 2012, Barry et al., JHEP, 2013, Vogel et al., PRD, 2003) Quasidirac neutrinos (Petcov, Ibarra, 2010) Sterile neutrinos ( S. Pascoli et al., 2012; M. Blennow et al., 2010; Mitra, Vissani, Senjanović, 2012; Meroni et al, 2012 ) Heavy Sterile Neutrino Exchange in Type I seesaw Saturating contribution from sterile neutrino sector? Light and sterile contribution decoupled?

14 Heavy sterile neutrino exchange n h heavy Majorana neutrinos N i mixing V li mass M i. M 2 i > p2 (200) 2 MeV 2 ; p intermediate momentum Half-life 1 T 1/2 = G 0ν M ν η ν +M N η N 2 η ν = U 2 ei m i/m e, η N = V 2 ei m p/m i, M ν and M N nuclear matrix elements for light and heavy exchange

15 Bounds on active-sterile mixing Bounds on active-sterile mixing angle from meson decays, sterile neutrino decays and neutrinoless double beta decay. Heavy sterile mass M 2 > p 2 (100) 2 MeV 2 VeN PS191 NA3 K eν CHARM L3 DELPHI GERDA M N GeV Pascoli, Mitra, Wong, 2013; Atre et al., JHEP 0905, 030 (2009); Mitra et al., NPB 856, 26 (2012) 0ν2β most stringent bound

16 Contd: For light sterile m 4 < 100MeV, the half life Half-life 1 T 1/2 = G 0ν M ν η ν 2 where η ν Σ i m i U 2 ei+σ i m 4i U 2 e4 i Re 3 H 63 Ni 64 Cu U e GERDA S 20 F Ferm i 2 Bugey Borexino Π eν PS m 4 GeV Pascoli, Mitra, Wong, 2013

17 Type-I seesaw Dirac mass matrix m D m, Majorana mass matrix M m The light neutrino contribution m2 M contribution m2 M 3 1 p 2. The heavy sterile For heavy sterile M 2 > p 2. The naive dimensional analysis implies a small heavy sterile contribution Vaanishing seesaw condition M T D M 1 R M D = 0 light neutrino mass perturbation of the seesaw condition Fine tuning of the parameter ǫ? Radiative stability of the light neutrino mass matrix? The heavy sterile mass M 10 GeV Mitra, Senjanović, Vissani, NPB, 2012 Fine tuning can be avoided if sterile neutrino is embedded in Left-Right symmetry. The gauge boson W R participate in neutrinoless double beta decay.

18 Left-Right symmetry Left-Right symmetric theories Pati; Salam; Mohapatra, Senjanovic, 74, 75 Enlarged gauge sector SU(2) L SU(2) R U(1) B L Parity symmetry restoration at high scale Sterile neutrino N is part of the gauge multiplet ( N e Additional gauge bosons W R participate in 0ν2β ) R

19 Contd The Lagrangian L Y = f ν LL ΦL R + f ν LL ΦLR +f L L T LCiσ 2 L L L +f R L T RCiσ 2 R L R +h.c. Bi-doublet vev Φ = v. Higgs triplet vevs L,R = v L,R Dirac mass m D = f ν v. Heavy neutrino mass M R = f R v R and m L = f L v L ( ) fl v The neutrino mass matrix L f ν v fν T v f R v R The light neutrino mass m ν m L m T D M 1 R m D = f L v L v2 f T vr 2 ν fr 1 f ν

20 contd Charged current Lagrangian L W = g 2 ( ν L V L W Le L + N R V R W Re R )+h.c.. L CC = g 2 3 α=e,µ,τ i=1 [ l αl γ µ{(u L ) αi ν Li +(T) αi N c Ri }Wµ L +l αr γ µ {(S) αi νc Li +(U R) αi N Ri}W µ R ] +h.c. S,T m D /M R active-sterile neutrino mixing The mass M WR v R. For v R TeV scale, M WR will be at TeV The experimental limits: K L K S mass difference M WR > 1.6 TeV (Beall, Bander, Soni, PRL, 1982) ATLAS and CMS M WR 2.5 TeV (CMS, ATLAS, 2012) Large contribution can be obtained from TeV scale W R and M R. (Hirsch et al., PLB, 96, Tello et al., PRL, 2011, Goswami et al., JHEP, 2012, Barry et al., JHEP, 2013, Vogel et al., PRD, 2003)

21 Additional diagrams slide courtsey: S. Goswami

22 Type-II dominance and heavy neutrinos Type-II dominance, m D is negligible m ν f L v L Heavy right handed neutrinos are heavy W R W R mode is dominant. The decay width, ( Γ 0νββ M ln2 = G ν 2 0ν m e m ee ν 2 W + L 2 ) V p2m4 ej 2 MW 4 M j R Tello et al., PRL, 2011 The effective mass for right handed neutrino contribution m N ee = p 2 M4 W L M 4 W R j V 2 ej M j The exchanged momentum p 2 = m e m p M N /M ν

23 Contd Symmetry between Left and Right sector f L = f R. M R = f R v R m ν = (v L /v R )M R light neutrino mass m i M i For normal ordering, M 1 < M 2 M 3 M i right handed neutrino mass The effective mass for the heavy neutrino exchange ( ) m N ee nor = C N m3 M3 m 1 c 2 12 c m 3 m 2 s 2 12 c2 13 e2iα 2 +s 2 13 e2iα 3 The factor C N = p 2 M 4 W L /M 4 W R

24 Contd For inverted ordering, M 2 will be the largest, ( ) m N ee inv = C N m2 M2 m 1 c 2 12 c2 13 +s2 12 c2 13 e2iα 2 + m 2 m 3 s 2 13 e2iα NH M N ee IH lightest mass (ev) From S. Goswami et al., JHEP, 2012 Tello et al., PRL, 2011

25 Total contribution: The half-life is 1 T 0ν 1/2 = G 0ν M ν 2 m (ν+n) ee me 2 The total effective mass m ee (ν+n) 2 = m ν ee 2 + m N ee 2 The sterile contribution m N ee = p2 M4 W L M 4 W R j V 2 ej M j p 2 = m e m p M N /M ν For 76 Ge the momentum exchange is p 2 = ( ) 2 MeV 2 For 136 Xe the momentum exchange is p 2 = ( ) 2 MeV 2

26 Contd 0Ν T 1 2 yr MW 3 TeV 76 R Ge M 1 TeV N IH NH GERDA HDM IGEX 90 CL KK 90 CL GERDA 90 CL Planck1 95 CL Planck2 95 CL QD MW 3 TeV R M 1 TeV N NH IH 136 Xe KLZ EXO 90 CL KLZ 90 CL Planck1 95 CL Planck2 95 CL QD m lightest ev m lightest ev The heaviest right handed neutrino M N> = 1 TeV. M i m i. The lightest right handed neutrino mass M N< > 490 MeV Even for hierarchical light neutrino mass, saturating limit can be obtained All the sterile neutrinos are heavy, m lightest = (10 5 1) ev. Lower limit on light neutrino mass For the positive claim 1-4 mev (NH) and mev (IH) For normal hierarchy, it is 2 4 mev and mev for Inverted hierarchy

27 LHC searches Collider search same sign dilepton+jets Keung, Senjanovic, PRL, 83 S. P. Das, F.F. Deppisch, O. Kittel, J. W. F. Valle, PRD, 2012 From S. P. Das, F.F. Deppisch, O. Kittel, J. W. F. Valle, PRD, 2012 Bound from LHC on W R mass M WR 2.5 TeV (CMS, ATLAS, 2012)

28 Complementarity to LHC The contour is M N< = p2 Φ(oscillationparameters) MW 4 m ν R exp m ν ee The band is due to the 3σ oscillation uncertainty m lightest ev. Most stringent limit from Planck

29 Contd: Complementary to LHC For Inverted hierarchy no additional constraint For Normal hierarchy part of parameter space is restricted

30 Summary The updated positive claim is consistent with GERDA individual limit. Although strong tension with the combined GERDA+HM+IGEX limit KamLAND-Zen+EXO-200 combined limit rules out the positive claim for most of the NME calculations A positive signal in 0ν2β-decay from the 3 light neutrino conflict with the most stringent limit from PLANCK TeV scale Left Right Model with lower gauge boson and right handed neutrino mass In the heavy sterile neutrino regime, large effective mass can be obtained even for hierarchical light neutrino mass A lower bound on light neutrino mass TeV scale Left-Right model accessible at LHC Normal hierarchy can give more constraint in the M N M WR plane as compared to Inverted hierarchy Correlated constraints in the right handed sector: complementarity to LHC

31 Thank You

32 Left-Right symmetry Left-Right symmetric theories Pati; Salam; Mohapatra, Senjanovic, 74, 75 Enlarged gauge sector SU(2) L SU(2) R U(1) B L Parity symmetry restoration at high scale Two Higgs triplet L = (3,1,2), R = (1,3,2) ( ) N Sterile neutrino N is part of the gauge multiplet e R The vacuum expectation value of R breaks the symmetry Additional gauge bosons W R and Z. M WR R Natural way to embedd the sterile neutrinos

33 Future predictions Implications for GERDA phase-ii (T 0ν 1/2 (76 Ge) = yr) The half-life of 136 Xe T 0ν 1/2 = yr The lower value is incompatible with the combined limit from KamLAND-Zen T 0ν 1/2 > yr The range will be incomtible with the future EXO-1T limit T 0ν 1/2 (136 Xe) >

34 Contd The effective mass m N ee 1 M 4 W R The effective mass m N ee 1 M N The range is sensitive to the right handed gauge boson and sterile neutrino masses M WR and M N

35 Contd: n p n p W L e L W R e R L R W L e L W R e R n p n p Lepton flavor violation l i l j l k l p M > M N in most of the parameter space. (Tello et al., PRL, 2011) Small contribution in 0ν2β

36 Contd SRQRPA Limit on M 4 j V ej 2/M j (TeV 5 ) NME 76 Ge 136 Xe method GERDA comb KK KLZ comb Argonne intm Argonne large CD-Bonn intm CD-Bonn large W R The positive claim is consistent with the individual bounds of 136 Xe Inconsistent with the combined bound

37 Contd: n p n p W R WR e R e R ν i N i e R e R W R W R n p n p (a) (b) n p n p W L WL e L e L ν i N i e R e R W R W R n p n p (a) (b)

38 Contd: n p n p W L e L W R e R L R W L e L W R e R n p n p

39 Contd: Nuclear matrix element Simkovic et al., Phys. Rev. D82, (2010), Meroni et al., 2012 Heidelberg-Moscow, EX0-200,KamLAND-Zen and EXO-200+KamLAND-Zen bound Active-sterile mixing V 2 ei M i (4 7) 10 9 GeV 1

40 Perturbations In Dirac diagonal basis Case A M D = m ǫ ;M 1 R = M 1 The light neutrino mass matrix in Dirac diagonal basis M ν m2 M ǫ 2 ǫ 0 ǫ ǫ ǫ ǫ is the perturbing element In the limit ǫ 0, M ν 0 The above generates one massless and two massive light neutrinos

41 Contd: The sterile contribution in flavor basis is For normal hierarchy For inverted hierarchy (MD T M 3 R M D) F.l ee = ξ m2 M 3 (U e2 m2 +Ue3 m3 ) 2 m 2 +m 3 (MD T M 3 R M D) F.l ee = ξ m2 M 3 (U e2 m2 +Ue1 m1 ) 2 m 1 +m 2 Numerator and denominator depend same way on light neutrino mass Sterile contribution is not suppressed by the light neutrino mass scale.

42 Contd However, Small neutrino mass ǫ m2 M < 0.1 ev demands ǫ = 10 9 Extreme fine-tuning condition Simple scaling of M, m and ǫ by α < 1 M α M; m α 3/2 m; ǫ α 2 ǫ Light neutrino mass ǫ m2 M remains unchanged and the sterile contribution m2 M 3 ǫ can be relatively large fine-tuning reduces With lower value of sterile neutrino mass scale M, the fine tuning reduces

43 Radiative stability The light neutrino mass M ν ǫ m2 M For M < M ew δm ν g2 m 2 (4π) 2 M M 2 M 2 ew For M > M ew δm ν g2 (4π) 2 m 2 M log(m 1/M 2 ) From radiative stability, ǫ > (M/1 TeV) 2 for M < M ew ǫ > 10 2 for M > M ew

44 Contd: Figure: One loop correction to the ν L mass

45 Upper bound T 1/2 = yr Saturating sterile contribution κm 2 /M 3 = GeV 1 Small neutrino mass, ǫm2 M < 0.1 ev Upper bound on ǫ ǫ < κ( 100 MeV M Including radiative stability M < κ 1/4 10 GeV Satisfies small neutrino mass constraint, radiative stability 0ν2β provides stringent bound ) 2

46 Perturbations Preferred choice of basis Dirac diagonal basis M D = m ǫ ;M 1 R = M ǫ M D = mdiag(ǫ,ǫ,1);m 1 R = M ǫ M ν m2 M M ν = m2 M ǫ 2 ǫ 0 ǫ ǫ ǫ2 ǫ 2 ǫ ǫ 2 ǫ 2 ǫ ǫ ǫ ǫ In the limit ǫ 0, M ν 0 For the first case, one massless and two massive light neutrinos Elements are O(ǫ), determinant is O(ǫ 4 ) Lightest neutrino mass O(ǫ 2 )

47 Two flavor Simple two flavor example M R = M basis ( ǫ ) ( ǫ 0 ; M D = m 0 1 ) = Dirac diagonal Light neutrino mass and contact term, M ν = ǫm2 M ( ) ; M D M 3 R M D = m2 M 3 ( ) M ν depends on ǫ, while the contact term is ǫ independent

48 Contd: Rotation by tanθ = m1 m 2 From Dirac diagonal basis mass basis Flavor basis Light neutrino contribution, (M ν ) ee = sin 2 θ m 2 cos 2 θ m 1 e i2φ The contact term in flavor basis, (MD TM 3 R M D) (Fl.) ee = ξ m2 (sinθ m2 +cosθ m1 e iφ ) 2 M 3 m 1 +m 2 Numerator and denominator depend same way on light neutrino mass = independent of the light neutrino mass scale ξ is a combination of order 1 coefficients in M 1 R

49 Contd: For φ=0 or π, light neutrino contribution vanishes, for cos m 2 = 2 θ sin ; m 1 = 2 θ cos2θ m 2 m 2 cos2θ Contact term is unsuppressed for φ = 0 0ν2β transition is entirely due to heavy neutrino exchange Schechter-Valle theorem?

50 Three flavor scenario The contact term in Dirac diagonal basis, M T DM 3 R M D = ξ m2 M 3 Contact term in flavor basis, Contact term in flavor basis (MD T M 3 R M D) (Fl.) ee (U O T MD T M 3 R M DOU ) ee O and U are two mixing matrices Dirac diagonal mass flavor Contact term (M T D M 3 R M D) ee = κ m2 M 3 κ is κ = ξ ϕ 2, with ϕ = 3 i=1 U ei O 3i

51 Contd: For case A and B, the contact term in flavor basis, For normal hierarchy For inverted hierarchy (MD T M 3 R M D) F.l ee = ξ m2 M 3 (U e2 m2 +Ue3 m3 ) 2 m 2 +m 3 (MD T M 3 R M D) F.l ee = ξ m2 M 3 (U e2 m2 +Ue1 m1 ) 2 m 1 +m 2 For normal and inverted mass hierarchy, (M ν) ee = m 3 U 2 e3 m 2U 2 e2 ; (Mν)ee = m 2U 2 e2 m 1U 2 e1

52 Contd: m 2 M GeV 1 to saturate 0ν2β bound m 2 12 = ev 2, m 2 23 = ev 2, θ 12 = 34, θ 23 = 42 and θ 13 = 8 ϕ for normal hierarchy; ϕ for inverted hierarchy