Testing supersymmetric neutrino mass models at the LHC

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1 Testing supersymmetric neutrino mass models at the LHC Werner Porod Universität Würzburg Vienna, 7 May W. Porod, Uni. Würzburg p.

2 Overview Neutrinos & lepton flavour violation Signals in models with Dirac neutrinos Majorana neutrinos in seesaw models How to acccess the seesaw scale(s) Conclusions Vienna, 7 May W. Porod, Uni. Würzburg p.

3 Lepton flavour violation, experimental data Neutrinos: tiny masses m atm.4 3 ev m sol ev 3 H decay: m ν < ev Neutrinos: large mixings tan θ atm tan θ sol.4 U e3 <.5 strong bounds for charged leptons BR(µ eγ) <. BR(τ eγ) <. 7 BR(τ lll ) < O( 8 ) (l, l = e, µ) BR(µ e e + e ) < BR(τ µγ) < d e < 7 e cm, d µ <.5 8 e cm, d τ <.5 6 e cm SUSY contributions to anomalous magnetic moments a e, a µ 43, a τ.58 Vienna, 7 May W. Porod, Uni. Würzburg p. 3

4 Supersymmetry, MSSM Standard Model MSSM matter: e d d d ν e u u u ẽ d d d ν e ũ ũ ũ gauge sector: γ Z W ± g γ z w ± g Higgs sector: h H A H ± h d h h u h ± assume at the moment conserved R-Parity: ( ) (3(B L)+s) ( γ, z, h d, h u) χ i, ( w±, h ± ) χ ± j Vienna, 7 May W. Porod, Uni. Würzburg p. 4

5 Dirac neutrinos analog to leptons or quarks Y ν H ν L ν R Y ν v ν L ν R = m ν ν L ν R requires Y ν Y e no impact for present or future collider experiments Exception: ν R is LSP and thus a candidate for dark matter long lived NLSP, e.g. t l + b ν R Remark: m νr hardly runs e.g. m νr m in msugra m νr in GMSB S. Gopalakrishna, A. de Gouvea and W. P., JHEP 6 (6) 5 S. K. Gupta, B. Mukhopadhyaya, S. K. Rai, PRD 75 (7) 757 D. Choudhury, S. K. Gupta, B. Mukhopadhyaya, PRD 78 (8) 53 Vienna, 7 May W. Porod, Uni. Würzburg p. 5

6 Majorana neutrinos: Seesaw mechanism Neutrino masses due to f Λ (HL)(HL) P. Minkowski, Phys. Lett. B 67 (977) 4; T. Yanagida, KEK-report 79-8 (979); M. Gell-Mann, P. Ramond, R. Slansky, in Supergravity, North Holland (979), p. 35; R.N. Mohapatra and G. Senjanovic, Phys. Rev. Lett (98); M. Magg and C.Wetterich, Phys. Lett. B 94 (98) 6; G. Lazarides, Q. Shafi and C. Wetterich, Nucl. Phys. B 8 (98) 87; J. Schechter and J. W. F. Valle, Phys. Rev. D5, 774 (98); R. Foot, H. Lew, X. G. He and G. C. Joshi, Z. Phys. C 44 (989) 44. Vienna, 7 May W. Porod, Uni. Würzburg p. 6

7 The Setup: GUT scale Relevant SU(5) invariant parts of the superpotentials at M GUT Type-I W RHN = Y I N Nc 5 M 5 H + M R N c N c Type-II W 5H = Y II N 5 M 5 5 M + λ 5 H 5 5 H + λ 5 H 5 5 H +M Type-III W 4H = 5 H 4 M YN III 5 M + 4 MM 4 4 M Vienna, 7 May W. Porod, Uni. Würzburg p. 7

8 The SU(5)-broken phase Under SU(3) SU L () U() Y The 5, and 5 H contain 5 M = ( b D c, b L), = ( b U c, b E c, b Q), 5 H = ( b H c, b H u ), 5 H = ( b H c, b H d ) The 5 decomposes as 5 = bs(6,, 3 ) + bt(,3,) + bz(3,, 6 ) The 4 decomposes as 4 M = c W M (,3, ) + b B M (,,) + b X M (3,, 5 6 ) + b X M (3,, 5 6 ) + b G M (8,,) Vienna, 7 May W. Porod, Uni. Würzburg p. 8

9 Seesaw I Postulate very heavy right-handed neutrinos yielding the following superpotential below M GUT : W I =W MSSM + W ν, W ν = b N c Y ν b L b Hu + bn c M R b N c, Neutrino mass matrix m ν = v u Y T ν M R Y ν Inverting the seesaw equation gives Y ν a la Casas & Ibarra Y ν = i q v u ˆM R R p ˆm ν U ˆm ν, ˆMR... diagonal matrices containing the corresponding eigenvalues U neutrino mixing matrix R complex orthogonal matrix. Vienna, 7 May W. Porod, Uni. Würzburg p. 9

10 Seesaw II Below M GUT the superpotential reads W II = W MSSM + (Y T b L b T b L + YS b D c b S b D c ) + Y Z b D c b Z b L + (λ b Hd b T b Hd + λ b Hu b T b Hu ) + M T b T b T + M Z b Z b Z + M S b S b S fields with index () originate from the 5-plet (5-plet). The effective mass matrix is m ν = v u λ M T Y T. Note that Ŷ T = U T Y T U, Vienna, 7 May W. Porod, Uni. Würzburg p.

11 Seesaw III In the SU(5) broken phase the superpotential becomes W III = W MSSM + b H u ( c W M Y N r 3 bb M Y B ) b L + b H u b XM Y X b D c + bb M M B bb M + bg M M G bg M + cw M M W cw M + bx M M XXM b giving m ν = v u 3 Y B T M B Y B + «Y W T M W Y W v u 4 Y T W M W Y W last step: valid if M B M W and Y B Y W Casas-Ibarra decomposition for Y W as in type-i up to factor 4/5 Vienna, 7 May W. Porod, Uni. Würzburg p.

12 Effect of heavy particles on MSSM parameters MSSM: (b, b, b 3 ) = (33/5,, 3) per 5-plet b i = 7/ type II model b i = 7 per 4-plet b i = 5 type III model b i = 5 Vienna, 7 May W. Porod, Uni. Würzburg p.

13 Effect of heavy particles on MSSM parameters MSSM: (b, b, b 3 ) = (33/5,, 3) per 5-plet b i = 7/ type II model b i = 7 per 4-plet b i = 5 type III model b i = M 3 M Q M,M,M 3 (GeV) 5 M M Q, M L, M E (GeV) M L 5 M M E M Seesaw (GeV) M Seesaw (GeV) Q = TeV, m = M / = TeV, A =, tan β = and µ > Full lines... seesaw type I, dashed lines... type II, dash-dotted lines... type III degenerate spectrum of the seesaw particles J. N. Esteves, M. Hirsch, W.P., J. C. Romao, F. Staub, Phys. Rev. D83 () 33 Vienna, 7 May W. Porod, Uni. Würzburg p.

14 Effect on heavy particles on MSSM spectrum, I 8 m χ M A M h, m χ, m χ + (GeV) 6 4 m χ M A, m χ, m χ + (GeV) m χ + m χ 4 M h M Seesaw (GeV) M Seesaw (GeV) m = M / = TeV, A =, tan β = and µ > Full lines... seesaw type I, dashed lines... type II, dash-dotted lines... type III degenerate spectrum of the seesaw particles J. N. Esteves, M. Hirsch, W.P., J. C. Romao, F. Staub, Phys. Rev. D83 () 33 Vienna, 7 May W. Porod, Uni. Würzburg p. 3

15 Invariants (m Q m Ẽ )/M, (m D m L)/M (m L m Ẽ )/M, (m Q m Ũ )/M M 5 = M 4 [GeV] Seesaw I ( MSSM) m Q m E M m L m E M, m D m L M.6, m Q m U M (solution of -loop RGEs) 8.55 M. Hirsch, S. Kaneko, W. P., Phys. Rev. D 78 (8) 934 J. Esteves, M.Hirsch, J. Romão, W. P., F. Staub, Phys. Rev. D83 () 33 Vienna, 7 May W. Porod, Uni. Würzburg p. 4

16 Invariants, limits for seesaw type-iii models (m L m Ẽ )/M SPS3 m =.5, M / = TeV m =, M / = TeV (m Q m Ẽ )/M SPS3 m =.5, M / = TeV m =, M / = TeV M 4 [GeV] M 4 [GeV] blue lines... SPS3 light blue lines...m = 5 GeV and M / = TeV red lines...m = M / = TeV black line... analytical approximation full (dashed) lines... -loop (-loop) results Vienna, 7 May W. Porod, Uni. Würzburg p. 5

17 Landau Poles..8.6 ggut log(m Seesaw /GeV) m = M / = TeV, A =, tan β = and µ > M GUT = 6 GeV black lines... seesaw type-ii green lines... seesaw type-iii with three 4-plets with degenerate mass spectrum full (dashed) lines... -loop (-loop) results Vienna, 7 May W. Porod, Uni. Würzburg p. 6

18 LFV in the slepton sector: approximate formulas, I one-step integration of the RGEs assuming msugra boundary ML,ij a k `3m 8π + A 3 A l,ij a k 6π A M E,ij L ij = ln(m GUT /M i )δ ij Y e Y k, N k, YN LY N k LY k N ij ij for i j with Y e diagonal a I =, a II = 6 and a III = 9 5 Vienna, 7 May W. Porod, Uni. Würzburg p. 7

19 LFV in the slepton sector: approximate formulas, II ( M L) ij and ( A l ) ij induce l j l i γ, l i l + k l r lj l i χ s χ s l i lk Neglecting L-R mixing: Br(l i l j γ) α 3 m 5 (δm L ) ij l i em 8 Br( τ e + χ ) ( M Br( τ µ + χ ) L ) 3 ( ML ) 3 tan β Moreover, in most of the parameter space Br(l i 3l j ) Br(l i l j + γ) α 3π log( m l i m ) l 4 j Vienna, 7 May W. Porod, Uni. Würzburg p. 8

20 Seesaw I take all parameters real U = U TBM = q C A R = C A Use -loop RGEs and -loop corrections including flavour effects Vienna, 7 May W. Porod, Uni. Würzburg p. 9

21 Seesaw I 3 l j ) Br(l l γ),br(l i j i m ν = ev Br(τ µ γ) Br(µ e γ) Br(τ e γ) 4 Br(τ 3 µ ) Br(µ 3 e ) Br(τ 3 e ) M (GeV) 6 χ) Br(τ e χ), Br(τ µ m ν = ev Br( τ e χ) Br( τ µ χ) 3 4 Excluded by Br(µ e γ ) 5 M (GeV) 6 degenerate ν R SPSa (M = 7 GeV, M / = 5 GeV, A = 3 GeV, tan β =, µ > ) M. Hirsch et al. Phys. Rev. D 78 (8) 36 Vienna, 7 May W. Porod, Uni. Würzburg p.

22 Seesaw I χ) Br(τ e χ), Br(τ µ m ν = ev Br( τ e χ) Br( τ µ χ) Excluded by Br(µ e γ ) χ) Br(τ e χ), Br(τ µ m ν = ev Br( τ e χ) Br( τ µ χ) Excluded by Br(µ e γ ) M (GeV) M (GeV) 6 degenerate ν R hierarchical ν R (M = M 3 = GeV) SPS3 (M = 9 GeV, M / = 4 GeV, A = GeV, tan β =, µ > ) M. Hirsch et al. Phys. Rev. D 78 (8) 36 Vienna, 7 May W. Porod, Uni. Würzburg p.

23 Seesaw I Texture models, hierarchical ν R real textures complexification of one texture SPSa (M = 7 GeV, M / = 5 GeV, A = 3 GeV, tan β =, µ > ) F. Deppisch, F. Plentinger, G. Seidl, JHEP () 4 Vienna, 7 May W. Porod, Uni. Würzburg p.

24 Seesaw II with a pair of 5-plets 4 Br li lj Γ Br Τ ΜΓ Br Μ eγ Br Τ eγ Br Τ Χ e, Br Τ Χ Μ Br Τ Χ e Br Τ Χ Μ Excluded by Br Μ eγ M 5 M T GeV M 5 M T GeV λ = λ =.5 SPS3 (M = 9 GeV, M / = 4 GeV, A = GeV, tan β =, µ > ) M. Hirsch, S. Kaneko, W. P., Phys. Rev. D 78 (8) 934. Vienna, 7 May W. Porod, Uni. Würzburg p. 3

25 Seesaw III in comparison Br(µ e γ) m =M / = (GeV), tanβ=, A = (GeV) III II I Br(µ e γ) m =M / = (GeV), tanβ=, A = (GeV) III, δ Dirac = III, δ Dirac = π I, δ Dirac = I, δ Dirac = π M Seesaw (GeV) s 3 degenerate spectrum of the seesaw particles, M seesaw = 4 GeV J. Esteves, M.Hirsch, J. Romão, W.P., F. Staub, Phys. Rev. D83 () 33 Vienna, 7 May W. Porod, Uni. Würzburg p. 4

26 ~q ~ Masses at LHC G. Polesello 5 q l near l far Events/ GeV/ fb - 5 ~ l R ~ m(ll) (GeV) 5 kinematical observables depending on 4 SUSY masses e.g.: m(ll) = 77. ±.5 ±.8 mass determination within -5% For background suppression N(e + e ) + N(µ + µ ) N(e + µ ) N(µ + e ) Vienna, 7 May W. Porod, Uni. Würzburg p. 5

27 Seesaw I + II, signal at LHC σ(χ ) BR [fb] m = GeV m = GeV m =3 GeV m =5 GeV M / [GeV] σ(χ ) BR [fb] m = GeV m = GeV m =3 GeV m =5 GeV M / [GeV] σ(pp χ ) BR(χ P i,j l i l j µ ± τ χ ) A =, tan β =, µ > (Seesaw II: λ =., λ =.5) J.N. Esteves et al., JHEP 95, 3 (9) Vienna, 7 May W. Porod, Uni. Würzburg p. 6

28 How to measure the see-saw scale Exp. input: MEG, BELLE,... : BR(µ eγ),... LHC: mass differences, edge variables (including LFV signals) ILC/CLIC: mass spectrum, LFV branching ratios, cross sections Theo. input High scale model, e.g. msugra, GMSB Seesaw type Vienna, 7 May W. Porod, Uni. Würzburg p. 7

29 Expected experimental accuaracies Mass, ideal LHC LC LHC+LC h H χ m = 7 GeV χ m / = 5 GeV χ A = 3 GeV χ ± tan β = ẽ R sign(µ) = + ẽ L τ q R q L t b g G. Weiglein et al., Phys. Rept. 46 (6) 47; J.A. Aguilar-Saavedra et al., EPJC 46 (6) 43 Vienna, 7 May W. Porod, Uni. Würzburg p. 8

30 Dependence of LHC observables obs(mss)/obs( 6 ) [GeV] Kinks Seesaw II (m : 7, M / : 4, tanβ :, A : 3) m SS [GeV] (m ee ) edge m g m b m g m b m qr m χ m ll m χ 5 6 obs(mss)/obs( 6 ) [GeV] (m lq ) edge high = max[(m max l near q ),(m max l far q ) ] Seesaw II (m : 7, M / : 4, tanβ :, A : 3) m SS [GeV] 5 (m ee ) edge (m llq ) edge (m llq ) thres (m lq ) edge low (m lq ) edge high (m lq ) edge low = min[(m max l near q ),(m q m χ )(m lr m χ )/(m lr m χ )] M. Hirsch, W.P., L. Reichert, arxiv:.4 [hep-ph] 6 7 Vienna, 7 May W. Porod, Uni. Würzburg p. 9

31 Results of a MC random walk, LHC+ILC, without Yukawas Seesaw II (m : 7, M / : 4, tanβ :, A : 3) 75 Seesaw II (m : 7, M / : 4, tanβ :, A : 3) 4 m [GeV] M [GeV] m SS [GeV] m SS [GeV] Seesaw II (m : 7, M / : 4, tanβ :, A : 3) Seesaw II (m : 7, M / : 4, tanβ :, A : 3) -7 tanβ [GeV] A [GeV] m SS [GeV] m SS [GeV] original scale 5 3 GeV; M. Hirsch, W.P., L. Reichert, arxiv:.4 [hep-ph] Vienna, 7 May W. Porod, Uni. Würzburg p. 3

32 Results of MC random walk, LHC + ILC observables Seesaw II (M : 7, M / : 4, tanβ :, A : 3) mss [GeV] Seesaw II (M : 7, M / : 4, tanβ :, A : 3) σ 3σ σ m [GeV] σ 3σ σ m SS [GeV] m SS [GeV] Seesaw II (M : 7, M / : 4, tanβ :, A : 3) Seesaw II (M : 7, M / : 4, tanβ :, A : 3) M/ [GeV] σ 3σ σ tanβ [GeV] 9 5σ 3σ σ m SS [GeV] m SS [GeV] Vienna, 7 May W. Porod, Uni. Würzburg p. 3

33 Results of MC random walk, LHC observables only Seesaw II (m :, M / : 7, tanβ :, A : ) Seesaw II (m :, M / : 7, tanβ :, A : ) 6 mss [GeV] m [GeV] m SS [GeV] m SS [GeV] Seesaw II (m :, M / : 7, tanβ :, A : ) 8 M/ [GeV] m SS [GeV] Vienna, 7 May W. Porod, Uni. Würzburg p. 3

34 Results of MC random walk, varying assumptions Seesaw II (m : 7, M / : 4, tanβ :, A : 3) Seesaw II (m : 7, M / : 4, tanβ :, A : 3) mss [GeV] m SS for m SS = 3 6 mss [GeV] all LHC obs. \m h \ Edges \(m g m b/ ) Factor for errors of (m g m bi ) 5 m SS [GeV] 3 6 Seesaw II (m : 7, M / : 4, tanβ :, A : 3) Seesaw II (m : 7, M / : 4, tanβ :, A : 3) Yukawas small Yukawas fitted mss [GeV] 5 4 only χ, ẽ R \ ( l L, t ) \ l L \ t all ILC obs mss [GeV] m SS [GeV] m SS [GeV] 4 4 Vienna, 7 May W. Porod, Uni. Würzburg p. 33

35 Conclusions Dirac neutrinos: displaced vertices if ν R LSP, e.g. t lb ν R (but NMSSM: t lbν χ ) Seesaw models: in case of seesaw II, III: different mass ratios promosing: τ decays LFV signals difficult to test at LHC, of O( fb) or below Model reconstruction for seesaw II, III LHC: possible in favourable parts of parameter space; might improve if additional observables can be used, e.g. lepton and jet spectra LHC+ILC: possible for large part of parameter space, however still some model dependence to disthinguish between type II and III: need in addition LFV signals Vienna, 7 May W. Porod, Uni. Würzburg p. 34

36 Seesaw II with 5-plets 4 Br li lj Γ Br Τ ΜΓ Br Μ eγ Br Τ eγ Br Τ Χ e, Br Τ Χ Μ Br Τ Χ e Br Τ Χ Μ Excluded by Br Μ eγ M 5 M T GeV M 5 M T GeV λ = λ =.5 SPS3 (M = 9 GeV, M / = 4 GeV, A = GeV, tan β = ), µ > M. Hirsch, S. Kaneko, W. P., Phys. Rev. D 78 (8) 934. Vienna, 7 May W. Porod, Uni. Würzburg p. 35

37 Seesaw II with 5-plets 4 Br li lj Γ Br Τ ΜΓ Br Μ eγ Br Τ eγ Br Τ Χ e, Br Τ Χ Μ Br Τ Χ e Br Τ Χ Μ Excluded by Br Μ eγ M 5 M T GeV M 5 M T GeV λ = λ =.5 SPSa (M = 7 GeV, M / = 5 GeV, A = 3 GeV, tan β = ), µ > M. Hirsch, S. Kaneko, W. P., Phys. Rev. D 78 (8) 934. Vienna, 7 May W. Porod, Uni. Würzburg p. 36

38 Seesaw II, signal at LHC σ(χ ) BR [fb] λ =.5 λ =. λ = M / [GeV] σ(pp χ ) BR(χ P i,j l i l j µ ± τ χ ) m = GeV A =, tan β =, µ >, λ =. J.N. Esteves et al., JHEP 95, 3 (9) Vienna, 7 May W. Porod, Uni. Würzburg p. 37

39 SUSY masses at LHC talk by I. Borjanovic at Flavour in the era of LHC, Nov. 5, CERN L= fb - Fit results Mass reconstruction 5 endpoints measurements, 4 unknown masses m( ) = 96 GeV m(l R ) = 43 GeV m( ) = 77 GeV m(q L ) = 54 GeV m( )= 4.8 GeV, m( )= 4.7 GeV, m(l R ) = 4.8 GeV, m(q L )= 8.7 GeV Gjelsten, Lytken, Miller, Osland, Polesello, ATL-PHYS-4-7 Vienna, 7 May W. Porod, Uni. Würzburg p. 38

40 arbitrary M E,ij, M L,ij, A l,ij: χ l i l j l k l j χ BR( χ χ e± τ ) BR( χ χ µ± τ ) BR(τ eγ) BR(τ µγ) Variations around SPSa (M = GeV, M / = 5 GeV, A = GeV, tan β = ) Vienna, 7 May W. Porod, Uni. Würzburg p. 39

41 Flavour mixing and edge variables ± d Γ( χ l i l j χ ) Γ tot d m(l ± i l j ) d Γ( χ l+ l χ ) Γ tot d m(l + l ).8 e ± τ.5 e + e (= µ + µ ) [LFC] µ + µ µ ± τ. e + e. e ± µ m(l ± i l j ) [GeV] m(l + l ) [GeV] A. Bartl et al., Eur. Phys. J. C 46 (6) 783 Vienna, 7 May W. Porod, Uni. Würzburg p. 4

42 Mass measurements, ILC e + e χ + χ e + e µ + R µ R µ+ µ χ χ U. Martyn Vienna, 7 May W. Porod, Uni. Würzburg p. 4

43 Results of a MC random walk, LHC+ILC Seesaw II (m : 7, M / : 4, tanβ :, A : 3) Seesaw II (m : 7, M / : 4, tanβ :, A : 3) χ χ m [GeV] m [GeV] Seesaw II (m : 7, M / : 4, tanβ :, A : 3) Seesaw II (m : 7, M / : 4, tanβ :, A : 3) χ χ m SS [GeV] m SS [GeV] original scale 5 GeV original scale.3 5 GeV Vienna, 7 May W. Porod, Uni. Würzburg p. 4