Supersymmetric contributions to Z decays Gennaro Corcella INFN, - PowerPoint PPT Presentation

Supersymmetric contributions to Z’ decays Gennaro Corcella INFN, Laboratori Nazionali di Frascati 1. Introduction 2. Z ′ production in U(1) ′ and Sequential Standard Model 3. MSSM features including U(1) ′ 4. Z ′ branching ratios in SM and MSSM channels 5. Cross sections and event rates at the LHC 6. Conclusions and outlook G.C. and S.Gentile, Nucl.Phys.B886 (2013) 293 and work in progress

Searches for heavy gauge bosons Z ′ among the main objectives of LHC GUT-inspired U(1)’, Kaluza–Klein gravitons, Sequential Standard Model LHC analyses focus on SM decays, e.g. high-mass dilepton resonances CMS: L = 5 fb − 1 ( e + e − ) and L =5.3 fb − 1 ( µ + µ − ), √ s = 7 TeV m ( Z ′ SSM ) > 2 . 33 TeV , m ( Z ′ GUT ) > 2 . 00 TeV, m ( Z ′ KK ) > 1 . 81 − 2 . 14 TeV ATLAS: L =5.9 fb − 1 ( e + e − ) and L =6.1 fb − 1 ( µ + µ − ), √ s = 8 TeV m ( Z ′ SSM ) > 2 . 49 TeV , m ( Z ′ GUT ) > 2.09-2.24 TeV In BSM analyses, why not BSM Z ′ decays, e.g. both SM and MSSM modes Z ′ constrains invariant masses; unexplored phase space; monojet events Lower SM branching ratios with BSM decays ⇒ lower Z ′ mass exclusion limits T. Gherghetta et al., PRD57 (1998) 3178: pioneering work on Z ′ decays in the MSSM for m Z ′ = 700 GeV and one point in the parameter space J. Kang and P. Langacker, PRD71 (2005) 035014: exotic modes vs LHC limits B − L and Z ′ slepton decays M. Baumgart et al., JHEP 0711 (2007) 084: U(1) ′ C.-F. Chang et al., JHEP09 (2011) 058: 2 sets of MSSM parameters and m Z ′ =1-2 TeV

U(1)’ gauge groups in GUT-inspired models: E 6 → SO(10) × U(1) ′ SO(10) → SU(5) × U(1) ′ ψ , χ Z ′ ( θ ) = Z ′ ψ cos θ − Z ′ χ sin θ � 5 / 8 ⇒ Z ′ E 6 → SM × U(1) η θ = arccos η Orthogonal combination to Z ′ � 5 / 8 − π/ 2 ⇒ Z ′ η : θ = arccos I √ 15 / 9) − π/ 2 ⇒ Z ′ Secluded model (singlet S ): θ = arctan( S Representations of E 6 , SO(10) and SU(5) : : 27 = ( Q, u c , e c , L, d c , ν c , H, D c , H c , D, S c ) L E 6 SU(5) : 10 = ( Q, u c , e c ) , ¯ 5 = ( L, d c ) , 1 = ( ν c ) , ¯ 5 = ( H, D c ) , 5 = ( H c , D ) , 1 = ( S c ) ‘Conventional ′ SO(10) : 16 = ( Q, u c , e c , L, d c , ν c ) , 10 = ( H, D c , H c , D ) , 1 = ( S c ) ‘Unconventional ′ SO(10) : 16 = ( Q, u c , e c , H, D c , ν c ) , 10 = ( L, d c , H c , D ) , 1 = ( S c ) √ From conventional to unconventional SO(10) (Nardi–Rizzo ’94): θ → θ + arctan 15

U(1)’ coupling and charges in the conventional assignments: √ √ √ 2 10 Q χ 2 6 Q ψ 2 15 Q η Q -1 1 2 u c -1 1 2 d c 3 1 -1 Model θ L 3 1 -1 Z ′ − π/ 2 χ e c -1 1 2 Z ′ 0 ψ ν c -5 1 5 � Z ′ e arccos 5 / 8 η H -2 -2 -1 Z ′ � arccos 5 / 8 − π/ 2 H c I √ 2 -2 -4 Z ′ arctan 15 − π/ 2 S c 0 4 5 N √ Z ′ arctan( 15 / 9) − π/ 2 D 2 -2 -4 S D c -2 -2 -1 � 5 g ′ = Q ′ (Φ) = Q ′ ψ (Φ) cos θ − Q ′ 3 g 1 ; χ (Φ) sin θ Q = ( u d ) L , L = ( e ν e ) L , D : (s)quarks , H : (s)leptons , S : singlet Assumption: D and H are exotic quarks and leptons much heavier than the Z ′ ZZ ′ mixing is also neglected (J.Erler et al., JHEP09: sin θ ZZ ′ ∼ 10 − 3 - 10 − 4 )

Minimal Supersymmetric Standard Model and U(1)’ The extra Z ′ requires a singlet Higgs to break U(1)’ and get mass φ + � φ 0 � � � 1 , Φ 3 = φ 0 , Q ′ i = Q ′ (Φ i ) 2 Φ 1 = , Φ 2 = φ − φ 0 3 2 1 Higgs sector after EWSB: h , H , A , H ± (MSSM) and a new scalar H ′ √ 2 � φ 0 Three vacuum expectation values v i = i � v 1 < v 2 < v 3 tan β = v 2 /v 1 Z ′ and ˜ H ′ lead to two new neutralinos, i.e. ˜ Gauginos: new ˜ χ 0 χ 0 1 , . . . ˜ 6 Chargino sector is unchanged, as the Z ′ is neutral New Z ′ decay modes besides the SM ones: Z ′ → ˜ q ∗ , ˜ ℓ + ˜ χ + χ − ℓ − , ˜ ν ∗ , ˜ χ 0 χ 0 1 , 2 , ZH , Zh , ZA , H + H − , hA , HA , WW q ˜ ν ˜ i ˜ j , ˜ 1 , 2 ˜ Tree-level gaugino masses are obtained after diagonalizing the mass matrices in terms of the MSSM parameters M 1 , M 2 , M ′ , tan β , A f , µ

Sfermion masses get D- and F-term corrections ( m 0 soft mass at the Z ′ scale): V ( φ, φ ∗ ) = F ∗ i F i + 1 2 D a D a , D a = − g a ( φ ∗ T a φ ) , F i = δW δφ i First contribution to D-term (electroweak symmetry breaking): 2 ) = ( T 3 ,a − Q a sin 2 θ W ) m 2 m 2 a = ( T 3 ,a g 2 1 − Y a g 2 2 )( v 2 1 − v 2 ∆ ˜ Z cos 2 β Second contribution driven by the new U(1)’ symmetry: a = g ′ 2 m ′ 2 2 Q ′ a ( Q ′ 1 v 2 1 + Q ′ 2 v 2 2 + Q ′ 3 v 2 ∆ ˜ 3 )   ˜ ˜ f f LL ) 2 LR ) 2  ( M ( M M 2 f = ˜ ˜ ˜  f f LR ) 2 RR ) 2 ( M ( M � 1 2 − 2 � u L ) 2 + m 2 ( M ˜ LL ) 2 u ( m 0 m 2 m ′ 2 = u + 3 x w Z cos 2 β + ∆ ˜ ˜ uL ˜ � 1 2 − 2 � uR ) 2 + m 2 ( M ˜ RR ) 2 u ( m 0 m 2 m ′ 2 = u + 3 x w Z cos 2 β + ∆ ˜ ˜ uR ˜ ( M ˜ LR ) 2 u = m u ( A u − µ cot β ) . Contributions ∼ m 2 u and mixing are inherited by the F-term

� Representative Point: 5 8 − π m Z ′ = 3 TeV , θ = θ I = arccos 2 µ = 200 , tan β = 20 , A q = A ℓ = A f = 500 GeV m 0 qL = m 0 qR = m 0 ℓL = m 0 ℓR = m 0 νL = m ˜ νR = 2 . 5 TeV ˜ ˜ ˜ ˜ ˜ M 1 = 100 GeV , M 2 = 200 GeV , M ′ = 1 TeV m ˜ m ˜ m ˜ m ˜ m ˜ m ˜ m ˜ m ˜ u 1 u 2 ν 1 ν 2 d 1 d 2 ℓ 1 ℓ 2 2499.4 2499.7 2500.7 1323.1 3279.0 2500.4 3278.1 3279.1 m ˜ m ˜ m ˜ m ˜ m ˜ m ˜ m ˜ m ˜ χ 0 χ 0 χ 0 χ 0 χ 0 χ 0 χ ± χ ∓ 1 2 3 4 5 6 1 2 94.6 156.5 212.2 260.9 2541.4 3541.4 154.8 262.1 m h m A m H m H ′ m H ± 90.7 1190.7 1190.7 3000.0 1193.4 3000 [GeV] [GeV] 4000 Squarks Sleptons ~ l 3500 1 2500 ~ ~ q ∼ ν l m / ∼ ~ l 2 ν m ∼ 1 ν 3000 2 2000 2500 1500 2000 1000 ~ u 1 ~ 1500 u ~ 2 500 d ~ 1 d 2 1000 0 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 θ θ

Dependence of neutralino and chargino spectra on MSSM parameters [GeV] [GeV] 2000 260 Light neutralinos Light neutralinos 1800 240 0 0 ∼ ∼ χ χ m m 1600 220 1400 200 1200 180 1000 160 ∼ 800 χ 0 ∼ χ 0 ∼ 1 χ 0 140 600 ∼ 1 χ 0 ∼ 2 0 χ ∼ 2 0 120 χ 400 ∼ 3 χ 0 ∼ 3 χ 0 4 200 100 4 0 0 5 10 15 20 25 30 -2000 -1500 -1000 -500 0 500 1000 1500 2000 µ β tan [GeV] [GeV] 2000 260 Charginos Charginos 1800 ∼ ± ± χ ± ∼ χ ∼ χ m m 1 1600 240 ∼ ± χ 2 1400 220 1200 1000 200 800 600 180 ∼ ± χ 400 1 ∼ ± χ 2 160 200 0 0 5 10 15 20 25 30 -2000 -1500 -1000 -500 0 500 1000 1500 2000 µ β tan Comparison with ISAJET: good agreement for Representative Point Model m ˜ m ˜ m ˜ m ˜ m h m H m A m H ± m ˜ m ˜ χ 0 χ 0 χ 0 χ 0 χ ± χ ± 1 2 3 4 1 2 U(1)’/MSSM 94.6 156.6 212.2 261.0 90.7 1190.0 1190.0 1190.0 155.0 263.0 MSSM 91.3 152.2 210.2 266.7 114.1 1190.0 1197.9 1200.7 147.5 266.8

Lagrangian for Z ′ coupling with fermions L f = g ′ ¯ fγ µ ( v f − a f γ 5 ) fZ ′ µ v f = 1 = 1 � � � � Q ′ ( f L ) + Q ′ ( f R ) ( Q ′ ψ ( f L ) + Q ′ ψ ( f R )) cos θ − ( Q ′ χ ( f L ) + Q ′ χ ( f R )) sin θ 2 2 a f = 1 = 1 � � � � Q ′ ( f L ) − Q ′ ( f R ) ( Q ′ ψ ( f L ) − Q ′ ψ ( f R )) cos θ − ( Q ′ χ ( f L ) − Q ′ χ ( f R )) sin θ 2 2 Z ′ rate into fermions: � 1 / 2 � � � � �� � m 2 m 2 m 2 g ′ 2 Γ( Z ′ → f ¯ f f f v 2 + a 2 f ) = C f 12 πm Z ′ 1 + 2 1 − 4 1 − 4 f f m 2 m 2 m 2 Z ′ Z ′ Z ′ Lagrangian for Z ′ coupling with sfermions f = g ′ ( v f ± a f )[ ˜ L,R ( ∂ µ ˜ f L,R ) − ( ∂ µ ˜ L,R ) ˜ f ∗ f ∗ f L,R ] Z ′ µ L ˜ Z ′ rate into sfermions: � 1 / 2 m 2 � g ′ 2 ˜ Γ( Z ′ → ˜ f f L,R ˜ f ∗ 48 πm Z ′ ( v f ± a f ) 2 L,R ) = C f 1 − 4 m 2 Z ′ I couplings to ˜ f R ˜ Zero rates into sfermions if v f = ± a f , e.g. Z ′ N and Z ′ f ∗ R

Branching ratios in the Representative Point Final state BR (%) Final State BR (%) χ 0 χ 0 � i u i ¯ u i 0.00 ˜ 1 ˜ 0.07 1 i d i ¯ χ 0 χ 0 � d i 40.67 ˜ 1 ˜ 0.43 2 i ℓ + i ℓ − χ 0 χ 0 � 13.56 ˜ 1 ˜ 0.71 3 i χ 0 χ 0 � i ν i ¯ ν i 27.11 ˜ 1 ˜ 0.27 4 u ∗ χ 0 χ 0 ∼ 10 − 6 � i,j ˜ u i ˜ 0.00 ˜ 1 ˜ j 5 i,j ˜ d i ˜ d ∗ χ 0 χ 0 � 9.58 ˜ 2 ˜ 0.65 j 2 i,j ˜ ℓ i ˜ ℓ ∗ χ 0 χ 0 � 0.00 ˜ 2 ˜ 2.13 3 j ν ∗ χ 0 χ 0 � i,j ˜ ν i ˜ 0.00 ˜ 2 ˜ 0.80 j 4 H + H − χ 0 χ 0 0.50 ˜ 3 ˜ 1.75 3 ∼ 10 − 3 χ 0 χ 0 hA ˜ 3 ˜ 1.31 4 χ 0 χ 0 ∼ 10 − 6 HA 0.51 ˜ 3 ˜ 5 ∼ 10 − 3 χ 0 χ 0 ZH ˜ 4 ˜ 0.25 4 χ ± χ ∓ ZH ′ 0.00 ˜ 1 ˜ 1.95 2 χ ± χ ∓ H ′ A 0.00 ˜ 2 ˜ 0.54 2 χ ± χ ∓ W ± H ∓ ∼ 10 − 3 ˜ 1 ˜ 1.76 1