Right-handed SneutrinoCosmology and Hadron Collider Signature

Transcription

1 Right-handed Sneutrino and Hadron Northwestern University with Andre de Gouvea ( Northwestern) & Werner Porod ( Valencia)... June 15, 2006 Susy 06, UC Irvine Right-handed Sneutrino and Hadron Collider Signature

2 Outline Motivation Sneutrino mass matrix & mixing Right-handed sneutrino (Ñ R ) dark matter Ñ R Tevatron and LHC signatures Conclusions Right-handed Sneutrino and Hadron Collider Signature

3 Motivation Neutrino has mass Old Standard Model (SM) had only left-handed ν e,µ,τ L Oscillation experiments : νl α νβ L : m ν 0.1eV A renormalizable theory for mass requires adding: Right-handed Neutrino (NR i.) OR Higgs triplet If Supersymmetry and NR i. then right-handed sneutrino Dark Matter WMAP result (2003) Ω mh 2 = ; h2 0.5 If Ñ R LSP... overclose the universe?... Dark Matter? Is it possible to test this?... Collider implications? Right-handed Sneutrino and Hadron Collider Signature

4 SUSY Sector Neutrino Mass Sneutrino Mass Most general (renormalizable) theory, with Lepton-# violation Superpotential W = N c Y N L H u + N c M N 2 N c + W MSSM SUSY Breaking terms L SUSYBr = l L m2 l l L Ñ R m2 NÑR + h.c. + Ñ T R Ñ R A N l L h u + h.c. b 2 N 2 ÑR + h.c. Right-handed Sneutrino and Hadron Collider Signature

5 Neutrino Mass Neutrino Mass Sneutrino Mass L ν mass = Nv u Y N ν N c M N 2 N + h.c. For m ν 0.1eV m ν = v 2 u Y 2 N M N If M N GeV then Y N O(1) (Seesaw) If M N 10 2 GeV then Y N 10 6 If no M N term then Y N (Dirac ν) [Asaka et al. 05] Right-handed Sneutrino and Hadron Collider Signature

6 Sneutrino mass matrix Neutrino Mass Sneutrino Mass ( L ν mass = ν L Ñ R ν T L Ñ T R ) M ν ν L Ñ R ν L Ñ R From now assume as real : m 2 LL, m2 RR, m2 RL, c l, b 2 N Redefine: ν L = ( ν 1 + i ν 2 )/ 2 Ñ R = (Ñ 1 + iñ 2 )/ 2 Right-handed Sneutrino and Hadron Collider Signature

7 Mass matrix becomes... Neutrino Mass Sneutrino Mass L ν mass = 1 2 M r ν = ` ν T 1 Ñ T 1 ν T ν 1 Ñ2 T BÑ 1 C Mr ν 2 A Ñ 2 0 mll 2 c l mrl 2 T + vuy T 1 N M N 0 0 BmRL 2 + vum N Y N mrr 2 b2 N mll 2 + c l mrl 2 T vuy C N T M A N 0 0 mrl 2 vum N Y N mrr 2 + b2 N [Hirsch et al., Grossman et al. 97] Right-handed Sneutrino and Hadron Collider Signature

8 Diagonalization Neutrino Mass Sneutrino Mass ( ) νi Ñ i ( cos θ ν = i sin θ ν i sin θ ν i cos θ ν i ) ( ) ν i ; s i sin θ ν i Mixing angle is: 2 µ v d Y N + v u A N ± v u M tan 2θ ν N Y N i = (mll 2 c l) (mrr 2 b2 N ) Assume: A N a N Y N m l ; s 1 Y N v u m l α m Ñ i Y N 10 6 ; A N a N 0.1 MeV ; s α m ; ν 0 Ñ 1 Right-handed Sneutrino and Hadron Collider Signature

9 Diagonalization Neutrino Mass Sneutrino Mass ( ) νi Ñ i ( cos θ ν = i sin θ ν i sin θ ν i cos θ ν i ) ( ) ν i ; s i sin θ ν i Mixing angle is: 2 µ v d Y N + v u A N ± v u M tan 2θ ν N Y N i = (mll 2 c l) (mrr 2 b2 N ) Assume: A N a N Y N m l ; s 1 Y N v u m l α m Ñ i Y N 10 6 ; A N a N 0.1 MeV ; s α m ; ν 0 Ñ 1 Right-handed Sneutrino and Hadron Collider Signature

10 Boltzmann Equation Thermalization Big Bang Inflation BBN Today Thermal equilibrium if σv SI n ν0 > 3H Freeze-out Ω 0 n 0M ρ c ( GeV 2 σv [Kolb & Turner, Early Universe] ) Right-handed Sneutrino and Hadron Collider Signature

11 When is ν 0 Thermal? Thermalization σv n > 3H Self-interaction processes (a s ) ν 0 ν 0 ν L ν L W 3 ; B exchange (d s ) ν 0 ν 0 ν L ν L ; e L e L H + u ; H 0 u exchange Process Cross-section Limit ( ) s1 (a s ) 4 g 2 16π M + g 2 2 W M α m Y N > 10 3 ( B ) YN (d s ) 4 2 c4 1 me 16π M LSP Y N > M 2 H Right-handed Sneutrino and Hadron Collider Signature

12 When is ν 0 Thermal? Thermalization σv n > 3H Self-interaction processes (a s ) ν 0 ν 0 ν L ν L W 3 ; B exchange (d s ) ν 0 ν 0 ν L ν L ; e L e L H + u ; H 0 u exchange Process Cross-section Limit ( ) s1 (a s ) 4 g 2 16π M + g 2 2 W M α m Y N > 10 3 ( B ) YN (d s ) 4 2 c4 1 me 16π M LSP Y N > M 2 H Right-handed Sneutrino and Hadron Collider Signature

13 Thermalization Thermalization Thermalization conditions not met Nonthermal ν 0 Ñ R interacts only through tiny Yukawa, so Nonthermal for: Y N 10 6 i.e., ν 0 is almost pure right-handed Low Reheat temp T RH < 100 GeV ; Reheat into ν 0 + SM [S.G., Porod, de Gouvea, hep-ph/ JCAP] Right-handed Sneutrino and Hadron Collider Signature

14 Tevatron and LHC Signatures Unique features Heavier SUSY decays thro Y N (tiny?)... Disp vtx? All SUSY decays must have a lepton (charged or neutrino) Expect non-universality in e, µ, τ events 3 gens of Ñ R... Cascade decays give leptons (how soft?) At hadron colliders look for: q q / g g t t, g g,... Monte Carlo Program: Pythia 6.327: With modification to include angular dep of 3-body stop decays [Special thanks to Stephen Mrenna & Peter Skands for help with Pythia] Right-handed Sneutrino and Hadron Collider Signature

15 Tevatron and LHC Signatures Unique features Heavier SUSY decays thro Y N (tiny?)... Disp vtx? All SUSY decays must have a lepton (charged or neutrino) Expect non-universality in e, µ, τ events 3 gens of Ñ R... Cascade decays give leptons (how soft?) At hadron colliders look for: q q / g g t t, g g,... Monte Carlo Program: Pythia 6.327: With modification to include angular dep of 3-body stop decays [Special thanks to Stephen Mrenna & Peter Skands for help with Pythia] Right-handed Sneutrino and Hadron Collider Signature

16 t R production and decay q t g t g γ, Z q ( iyn P ij L ) ( iyu * 33 P R ) ~ H + u ~ t R b L e L j ~ N R i Level 1 cuts: The rapidity cuts η l < 2.5, η b < 2.5. The transverse momentum cuts p T l > 20 GeV, p T b > 10 GeV. The isolation cut R bl > 0.4, where R 2 bl (φ b φ l ) 2 + (η b η l ) 2 Right-handed Sneutrino and Hadron Collider Signature

17 t R production and decay q t g t g γ, Z q ( iyn P ij L ) ( iyu * 33 P R ) ~ H + u ~ t R b L e L j ~ N R i Level 1 cuts: The rapidity cuts η l < 2.5, η b < 2.5. The transverse momentum cuts p T l > 20 GeV, p T b > 10 GeV. The isolation cut R bl > 0.4, where R 2 bl (φ b φ l ) 2 + (η b η l ) 2 Right-handed Sneutrino and Hadron Collider Signature

18 t R production and decay : Disp Vtx stop Disp Vtx (ctau = 10 mm) stop 150 dtvx stop 300 dtvx stop Disp Vtx (ctau = 10 mm) stop 150 dtvx stop 300 dtvx dtvx (mm) dtvx (mm) Right-handed Sneutrino and Hadron Collider Signature

19 p T distributions b p T stop 150 top stop stop 150 top stop 300 b pt b pt pt pt l p T stop 150 top stop stop 150 top stop 300 E pt E pt pt pt Right-handed Sneutrino and Hadron Collider Signature

20 distributions cos(θ bl ) cos(th)_be stop 150 top stop cos(th)_be stop 150 top stop cos(th) cos(th) p T miss stop 150 mpt top mpt stop 300 mpt stop 150 mpt top mpt stop 300 mpt missing pt missing pt pt miss pt miss Right-handed Sneutrino and Hadron Collider Signature

21 Tevatron and LHC Top M tr = 150 M tr = 175 M tr = 250 M tr = 500 M tr = 750 σ(pb) α # (for 1 fb 1 ) S/ B(for 1 fb 1 ) L(fb 1 for 5 σ) Tevatron LHC Tevatron LHC Tevatron LHC Tevatron LHC LHC LHC Right-handed Sneutrino and Hadron Collider Signature

22 Conclusions Pure right-handed ν investigated here When SUSY breaking, Majorana mass at weak scale; Y N 10 6 Nonthermal dark matter candidate Tevatron and LHC Signatures Look for nonuniversal lepton signature Right-handed Sneutrino and Hadron Collider Signature

23 Backup Slides Backup Slides Right-handed Sneutrino and Hadron Collider Signature

24 Sneutrino mass matrix ( L ν mass = ν L Ñ R ν T L Ñ T R ) M ν ν L Ñ R ν L m M ν = 1 LL 2 m 2 RL vu 2 c l v u Y N M N m RL 2 mrr 2 v u MN T Y N b 2 N 2 vu 2 c l v u YN T M N mll 2 mrl 2 T v u M N Y N bn 2 mrl 2 mrr 2 Ñ R m 2 LL = (m 2 l + v 2 u Y N Y N + 2 ν) ; 2 ν = (m 2 Z /2) cos 2β m 2 RR = (M N M N + m 2 N + v 2 u Y N Y N ) m 2 RL = ( µ v d Y N + v u A N ) Right-handed Sneutrino and Hadron Collider Signature

25 Real fields Mixing effects m 2 RL : ν L Ñ R mixing c l : ν L ν L mixing M N : ν L Ñ R mixing b 2 N : Ñ R Ñ R mixing From now assume as real : m 2 LL, m2 RR, m2 RL, c l, b 2 N Redefine: ν L = ( ν 1 + i ν 2 )/ 2 Ñ R = (Ñ 1 + iñ 2 )/ 2 Right-handed Sneutrino and Hadron Collider Signature

26 Mass matrix becomes ν 1 L ν mass = 1 ` ν T 2 1 Ñ1 T ν 2 T Ñ2 T BÑ 1 C Mr ν 2 A Ñ 2 0 mll 2 c l mrl 2 T + vuy T 1 N M N 0 0 M r ν = BmRL 2 + vum N Y N mrr 2 b2 N mll 2 + c l mrl 2 T vuy C N T M A N 0 0 mrl 2 vum N Y N mrr 2 + b2 N [Hirsch et al., Grossman et al. 97] c l, b N and M N split ν 1 ν 2 degeneracy, and Ñ 1 Ñ 2 degeneracy Denote LSP as ν 0 ; Heavy states as ν H Bose symmetry forbids Z ν 0 ν 0 coupling leads to acceptable relic density [Hall et al. 97] Right-handed Sneutrino and Hadron Collider Signature

27 Thermal History of the Universe Big Bang Inflation BBN Today Hubble rate: H ȧ a ; H = 1.66 g T 2 H2 = 8πG 3 ρ M Pl (Rad Dom) Right-handed Sneutrino and Hadron Collider Signature

28 Boltzmann Equation Big Bang Inflation BBN Today d dt n ν 0 = 3Hn ν0 σv SI n 2 ν 0 n 2 ν 0 eq σv CI `n ν0 n φ n ν0 eqn φ eq + CΓ Thermal equilibrium if σv SI n ν0 > 3H ; σv CI n φ > 3H Freeze-out Ω 0 n 0M ρ c [Kolb & Turner, Early Universe] GeV 2 σv Right-handed Sneutrino and Hadron Collider Signature

29 Mixed ν 0 Dark Matter ~ N 1 ~ N 1 (ig s 2 1P R ) W ~ 3 c W ~ 3 (ig s 2 1P R ) ν ν Ω 0 h 2 = 10 4 s 4 1 8" < g 2 :!!# GeV + g GeV = M W M B ; s results in observed relic density Right-handed Sneutrino and Hadron Collider Signature

30 Relic from Decays Contribution from C Γ n χ Γ (χ ν 0 X ) H u ν 0 L Ω 0 (ad )h c1 2Y N 2 MLSP M f 2 H PS ν H ν 0 ψψ h u exchange Ω 0 (bd )h 2 = (c 2 1 s2 1 )2 Y 2 c A 2 N M ν H MLSP f 2 Mhu 4 3PS Does not overclose if Y N ; A N 10 ev ; s (Decays just before BBN!) Dirac case [Asaka et al. 05] Right-handed Sneutrino and Hadron Collider Signature

31 When is ν 0 Thermal? σv n > 3H Self-interaction processes (a s ) ν 0 ν 0 ν L ν L W 3 ; B exchange (d s ) ν 0 ν 0 ν L ν L ; e L e L H + u ; H 0 u exchange Process Cross-section Limit ( ) s1 (a s ) 4 g 2 16π M + g 2 2 W M α m Y N > 10 3 ( B ) YN (d s ) 4 2 c4 1 me 16π M LSP Y N > M 2 H Right-handed Sneutrino and Hadron Collider Signature

32 When is ν 0 Thermal? σv n > 3H Self-interaction processes (a s ) ν 0 ν 0 ν L ν L W 3 ; B exchange (d s ) ν 0 ν 0 ν L ν L ; e L e L H + u ; H 0 u exchange Process Cross-section Limit ( ) s1 (a s ) 4 g 2 16π M + g 2 2 W M α m Y N > 10 3 ( B ) YN (d s ) 4 2 c4 1 me 16π M LSP Y N > M 2 H Right-handed Sneutrino and Hadron Collider Signature

33 When is ν 0 Thermal? Co-interaction processes with other SUSY particles Boltzmann suppressed by β φ e ( M φ/t ) ; M φ (M φ M LSP ) Co-interaction with SUSY (b c ) ν 0 s ẽ L s W ± exchange (e c ) ν 0 ν H cc ; tt h u exchange Process Cross-section Limit (b c ) (e c ) g 4 s π (c 2 1 s2 1 )2 Y 2 u 16π 2 M LSP MZ 4 1 M 2 hu fps 2 β s α m f PS Y N > ( ) 2 AN M hu f 2 PS Y u β νh α m f PS Y N > 10 7 Right-handed Sneutrino and Hadron Collider Signature

34 When is ν 0 Thermal? Co-interaction with SM (a M ) ν 0 t R,L ν L t L,R h u exchange (b M ) ν 0 t L ν L t R H u exchange Process Cross-section Limit (a M ) (b M ) A 2 N Y t π f 2 Mhu 4 PS YN 2Y t π f 2 M 2 H PS β t α m f PS Y N > 10 7 β t f PS Y N > 10 7 Right-handed Sneutrino and Hadron Collider Signature

35 Nonthermal ν 0 Thermalization conditions not met Nonthermal ν 0 Happens when : Y N 10 6 i.e., ν 0 is almost pure right-handed Low Reheat temp T RH < 100 GeV ; Reheat into ν 0 + SM No Relic-from-decay of heavier SUSY particles No ν 0 thermalization from co-interaction with SUSY or Top Ñ Relic density depends on Inflaton coupling to SM and Ñ Work in progress Right-handed Sneutrino and Hadron Collider Signature

36 Nonthermal ν 0 Thermalization conditions not met Nonthermal ν 0 Happens when : Y N 10 6 i.e., ν 0 is almost pure right-handed Low Reheat temp T RH < 100 GeV ; Reheat into ν 0 + SM No Relic-from-decay of heavier SUSY particles No ν 0 thermalization from co-interaction with SUSY or Top Ñ Relic density depends on Inflaton coupling to SM and Ñ Work in progress Right-handed Sneutrino and Hadron Collider Signature