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
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
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 = 0.135 +0.008 0.009 ; 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
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
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 10 14 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 10 12 (Dirac ν) [Asaka et al. 05] Right-handed Sneutrino and Hadron Collider Signature
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
Mass matrix becomes... Neutrino Mass Sneutrino Mass L ν mass = 1 2 M r ν = ` ν T 1 Ñ T 1 ν T 2 0 1 ν 1 Ñ2 T BÑ 1 C Mr ν @ 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 0 0 @ 0 0 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
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 1 10 6 α m ; ν 0 Ñ 1 Right-handed Sneutrino and Hadron Collider Signature
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 1 10 6 α m ; ν 0 Ñ 1 Right-handed Sneutrino and Hadron Collider Signature
Boltzmann Equation Thermalization Big Bang Inflation BBN Today Thermal equilibrium if σv SI n ν0 > 3H Freeze-out 0.01 0.001 0.0001 1 10 100 1000 Ω 0 n 0M ρ c 4 10 10 ( GeV 2 σv [Kolb & Turner, Early Universe] ) Right-handed Sneutrino and Hadron Collider Signature
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 > 10 3 1 M 2 H Right-handed Sneutrino and Hadron Collider Signature
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 > 10 3 1 M 2 H Right-handed Sneutrino and Hadron Collider Signature
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/0602027 - JCAP] Right-handed Sneutrino and Hadron Collider Signature
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
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
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
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
t R production and decay : Disp Vtx 0.16 0.14 stop Disp Vtx (ctau = 10 mm) stop 150 dtvx stop 300 dtvx 0.14 0.12 stop Disp Vtx (ctau = 10 mm) stop 150 dtvx stop 300 dtvx 0.12 0.1 0.1 0.08 0.06 0.08 0.06 0.04 0.04 0.02 0.02 0 0 5 10 15 20 25 dtvx (mm) 0 0 5 10 15 20 25 dtvx (mm) Right-handed Sneutrino and Hadron Collider Signature
p T distributions b p T 0.045 0.04 0.035 stop 150 top stop 300 0.05 0.045 0.04 stop 150 top stop 300 b pt b pt 0.03 0.025 0.02 0.015 0.035 0.03 0.025 0.02 0.015 0.01 0.01 0.005 0.005 0 0 0 50 100 150 200 250 300 0 50 100 150 200 250 300 pt pt l p T 0.045 0.04 0.035 stop 150 top stop 300 0.05 0.045 0.04 stop 150 top stop 300 E pt E pt 0.03 0.025 0.02 0.015 0.035 0.03 0.025 0.02 0.015 0.01 0.01 0.005 0.005 0 0 0 50 100 150 200 250 300 0 50 100 150 200 250 300 pt pt Right-handed Sneutrino and Hadron Collider Signature
distributions cos(θ bl ) 3 2.5 cos(th)_be stop 150 top stop 300 3.5 3 cos(th)_be stop 150 top stop 300 2 2.5 2 1.5 1.5 1 1 0.5 0.5 0 0-1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1-1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1 cos(th) cos(th) p T miss 0.02 0.018 0.016 stop 150 mpt top mpt stop 300 mpt 0.018 0.016 0.014 stop 150 mpt top mpt stop 300 mpt missing pt missing pt 0.014 0.012 0.01 0.008 0.006 0.012 0.01 0.008 0.006 0.004 0.004 0.002 0.002 0 0 0 50 100 150 200 250 300 0 50 100 150 200 250 300 pt miss pt miss Right-handed Sneutrino and Hadron Collider Signature
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 5.6 0.79 8 - - LHC 488 0.7 484 - - Tevatron 1.04 0.29 17 6 0.7 LHC 167 0.24 1947 88 0.003 Tevatron 0.42 0.47 18 6.6 0.57 LHC 81.8 0.43 3062 139 0.001 Tevatron 0.04 0.71 4 1.4 12.7 LHC 14.65 0.66 1292 58 0.007 LHC 0.37 0.81 49 2.22 5.1 LHC 0.03 0.85 4.3 0.19 692 Right-handed Sneutrino and Hadron Collider Signature
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
Backup Slides Backup Slides Right-handed Sneutrino and Hadron Collider Signature
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
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
Mass matrix becomes... 0 1 ν 1 L ν mass = 1 ` ν T 2 1 Ñ1 T ν 2 T Ñ2 T BÑ 1 C Mr ν @ 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 0 0 @ 0 0 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
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
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 0.01 0.001 0.0001 1 10 100 1000 Ω 0 n 0M ρ c [Kolb & Turner, Early Universe] 4 10 10 GeV 2 σv Right-handed Sneutrino and Hadron Collider Signature
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 :!!# 9 2 1 100 GeV + g 2 100 GeV = M W M B ; s 1 0.2 results in observed relic density Right-handed Sneutrino and Hadron Collider Signature
Relic from Decays Contribution from C Γ n χ Γ (χ ν 0 X ) H u ν 0 L Ω 0 (ad )h 2 10 26 c1 2Y N 2 MLSP M f 2 H PS ν H ν 0 ψψ h u exchange Ω 0 (bd )h 2 = 10 24 (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 10 13 ; A N 10 ev ; s 1 10 12 (Decays just before BBN!) Dirac case [Asaka et al. 05] Right-handed Sneutrino and Hadron Collider Signature
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 > 10 3 1 M 2 H Right-handed Sneutrino and Hadron Collider Signature
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 > 10 3 1 M 2 H Right-handed Sneutrino and Hadron Collider Signature
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 2 1 16π (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 > 10 6.5 ( ) 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
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 2 1 16π f 2 Mhu 4 PS YN 2Y t 2 1 16π 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
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
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