The Anomalous Magnetic Moment of the Muon in the Minimal
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The Anomalous Magnetic Moment of the Muon in the Minimal Supersymmetric Standard Model for tan β = ∞ Markus Bach Institut für Kern- und Teilchenphysik Technische Universität Dresden IKTP Institute Seminar February 6, 2014 1 / 40 Outline 1 Anomalous Magnetic Moment of the Muon 2 Minimal Supersymmetric Standard Model for tan β = ∞ 3 Calculation and Approximation 4 Identification of Viable Parameter Regions 2 / 40 Outline 1 Anomalous Magnetic Moment of the Muon 2 Minimal Supersymmetric Standard Model for tan β = ∞ 3 Calculation and Approximation 4 Identification of Viable Parameter Regions 3 / 40 Definition magn. moment of a fermion: µ ~ =g Qe~ ~s 2m c (g - gyromagn. ratio) interaction with an external photon: Aρ (q) = −i Q e ū(p0 ) Λρ u(p) f (p0 ) f (p) decomposition: ū(p0 ) Λρ u(p) = ū(p0 ) γρ FE (q 2 ) − 2 m FM (q 2 ) + (p + p0 )ρ FM (q 2 ) + . . . u(p) g = 2 1 − 2 m FM (0) g−2 anomalous magnetic moment: a := = −2 m FM (0) 2 classical limit: 4 / 40 Experimental Determination muons from pion decay in a storage ring ~ relative to the momentum with spin precession in magnetic field B ~ ~ 1 β×E e ~ ω ~ = aµ B − aµ − 2 mµ γ −1 c " # vanishes for “magic” momentum p = 3,094 GeV detection of electrons from muon decay result from E821 experiment at Brookhaven National Laboratory: aµexp = (11 659 208,9 ± 6,3) · 10−10 5 / 40 Standard Model Prediction different kinds of contributions I I I QED: massless class, massive class hadronic: vacuum polarization, light-by-light scattering electroweak combined result [Davier et al., arXiv:1010.4180]: aµSM = (11 659 180,2 ± 4,9) · 10−10 discrepancy between experiment and theory: ∆aµ = aµexp − aµSM = (28,7 ± 8,0) · 10−10 new physics? 6 / 40 Contributions from New Physics aµ not only points to BSM physics but also restricts it close connection between Feynman diagrams for aµ and self energy: aµNP = O(1) × mµ MNP 2 × ∆mµ (NP) mµ ! [Czarnecki, Marciano, arXiv:hep-ph/0102122] ⇒ ∆mµ (NP) ≈ mµ is promising MSSM one-loop result for common sparticle mass MS : aµMSSM,1L ≈ 1,3 · 10−9 sgn(µM2 ) tan β 100 GeV MS 2 What happens for tan β → ∞? 7 / 40 Outline 1 Anomalous Magnetic Moment of the Muon 2 Minimal Supersymmetric Standard Model for tan β = ∞ 3 Calculation and Approximation 4 Identification of Viable Parameter Regions 8 / 40 Vector Superfields keep Standard Model gauge group SU (3)c × SU (2)L × U (1)Y Component Fields Spin 21 Spin 1 Group Generators Coupling Superfields U (1)Y Ŷ g1 V0 λ0 Bµ SU (2)L Ta g2 Va λa Wµa SU (3)c Tsd g3 Vsd λds Gµd total gauge multiplet: Vg := 2g1 Ŷ V 0 + 2g2 T a V a + 2g3 Tsd Vsd 9 / 40 Chiral Superfields Superfield Li = Lνi Lei Qi = Qui Qdi ν̃iL ẽiL ũiL d̃iL q̃iL = † ũiR Di † d̃iR Hu Hu0 Hu = + Hd0 Hd− hu = hd = νiL eiL `iL = SU (3)c 1 2 1 eiR Ui Hd = `˜iL = † ẽiR Ei Component Fields Spin 0 Spin 1 uiL diL qiL = 3 uiR diR + hu hu0 hd0 hd− ψHu = + ψH u 0 ψH u ψHd = 0 ψH d − ψH d I3 1/2 −1/2 0 1/2 −1/2 Y −1/2 1 1/6 3̄ 0 −2/3 3̄ 0 1/3 1 1/2 −1/2 1/2 1 1/2 −1/2 −1/2 10 / 40 Supersymmetric Lagrangian R-parity conserving superpotential (no generation mixing): WMSSM = 3 X (yei Hd · Li Ei + yui Hu · Qi Ui + ydi Hd · Qi Di ) − µ Hd · Hu i=1 supersymmetric, gauge invariant and renormalizable Lagrangian: Z Lsusy = d4 θ Li† eVg Li + Ei† eVg Ei + Qi† eVg Qi + Ui† eVg Ui + Di† eVg Di + Hu† eVg Hu + Hd† eVg Hd Z d θ + + 2 hZ 1 1 1 d W 0α Wα0 + W aα Wαa + Wsdα Wsα + h. c. 16g12 16g22 16g32 θ̄=0 d2 θ WMSSM θ̄=0 + h. c. i 11 / 40 Soft Supersymmetry Breaking up to now: sparticles have same mass as corresponding particles supersymmetry breaking realized through additional terms: Lsoft = − − + − 3 X i=1 mh2u m`2˜i |`˜iL |2 + mẽ2i |ẽiR |2 + mq̃2i |q̃iL |2 + mũ2i |ũiR |2 + md̃2i |d̃iR |2 |hu |2 − mh2d |hd |2 1 M1 λ0 λ0 + M2 λa λa + M3 λds λds + h. c. 2 3 hX † † † Aei yei hd · `˜iL ẽiR + Aui yui hu · q̃iL ũiR + Adi ydi hd · q̃iL d̃iR i=1 − Bµ hd · hu + h. c. i 12 / 40 Electroweak Symmetry Breaking vacuum expectation values for the Higgs doublets: ! h0|hu |0i = 0 , vu h0|hd |0i = important parameter: tan β := vd 0 ! vu vd gauge boson masses: MW g q = √2 vu2 + vd2 , 2 s MZ = g12 + g22 q 2 M vu + vd2 = W 2 cW 13 / 40 Electroweak Symmetry Breaking vacuum expectation values for the Higgs doublets: ! h0|hu |0i = 0 , vu h0|hd |0i = important parameter: tan β := vd 0 ! vu vd gauge boson masses: MW g q = √2 vu2 + vd2 , 2 s MZ = √ 2 MW tan β = ∞ implies: vu = , g2 g12 + g22 q 2 M vu + vd2 = W 2 cW vd = 0 13 / 40 Fermion Masses at tree level: me0i = yei vd , mu0i = −yui vu , md0i = ydi vd usual constraint: tan β . 50 such that the Yukawa couplings remain perturbative if mass is created at tree-level tan β 50 is possible if one considers loop corrections which are tan β-enhanced [Dobrescu, Fox, arXiv:1001.3147] e.g. muon mass: mµ = mµ0 − Σµ = mµ0 (1 + ∆µ ) = yµ vd (1 + ∆µ ) 14 / 40 Fermion Masses at tree level: me0i = yei vd , mu0i = −yui vu , md0i = ydi vd usual constraint: tan β . 50 such that the Yukawa couplings remain perturbative if mass is created at tree-level tan β 50 is possible if one considers loop corrections which are tan β-enhanced [Dobrescu, Fox, arXiv:1001.3147] e.g. muon mass: mµ = mµ0 − Σµ = mµ0 (1 + ∆µ ) = yµ vd (1 + ∆µ ) tan β = ∞ implies: mµ0 = 0 ⇒ mµ = −Σµ 14 / 40 Muon Sneutrino and Smuon Masses muon sneutrino mass: mν̃2µ = mL2 + 1 2 M cos 2β 2 Z smuon mass matrix: Mµ̃2 = 2 (mµ0 )2 + mL2 + MZ2 (sW − 12 ) cos 2β mµ0 (A∗µ − µ tan β) mµ0 (Aµ − µ∗ tan β) 2 2 (mµ0 )2 + mR − MZ2 sW cos 2β diagonalization: U µ̃ Mµ̃2 U µ̃† = diag(mµ̃21 , mµ̃22 ) 15 / 40 Muon Sneutrino and Smuon Masses muon sneutrino mass: mν̃2µ = mL2 − 1 2 M 2 Z smuon mass matrix: Mµ̃2 = diagonalization: 2 mL2 − MZ2 (sW − 12 ) mµ0 (A∗µ − µ tan β) mµ0 (Aµ − µ∗ tan β) 2 2 mR + MZ2 sW U µ̃ Mµ̃2 U µ̃† = diag(mµ̃21 , mµ̃22 ) 15 / 40 Muon Sneutrino and Smuon Masses mν̃2µ = mL2 − muon sneutrino mass: 1 2 M 2 Z smuon mass matrix: Mµ̃2 = √ − 2 yµ µ MW /g2 2 mL2 − MZ2 (sW − 12 ) √ ∗ − 2 yµ µ MW /g2 diagonalization: 2 2 mR + MZ2 sW U µ̃ Mµ̃2 U µ̃† = diag(mµ̃21 , mµ̃22 ) smuon masses: mµ̃2 1/2 = 1 2 2 mL2 + mR + ± rh 1 2 MZ 2 mL2 − 2 mR + MZ2 1 2 − 2 sW 2 i2 + 8 yµ2 M2 |µ|2 W g22 ! 15 / 40 Chargino Masses chargino mass matrix: X = diagonalization: √ √ M2 2 MW sin β 2 MW cos β ! µ U ∗ X V −1 = diag(mχ− , mχ− ) 1 † Hermitian form: V X X V −1 = 2 diag(mχ2 − , mχ2 − ) 1 2 16 / 40 Chargino Masses chargino mass matrix: X = diagonalization: √ M2 ! 2 MW µ 0 U ∗ X V −1 = diag(mχ− , mχ− ) 1 † Hermitian form: V X X V −1 = 2 diag(mχ2 − , mχ2 − ) 1 2 chargino masses: mχ2 − = 1/2 1 2 |µ|2 + |M2 |2 + 2 MW 2 ± q |µ|2 |2 + |M2 + 2 2 2 MW − 4 |µ|2 |M2 |2 16 / 40 Neutralino Masses neutralino mass matrix: M1 0 0 Y = −MZ sW cos β MZ cW cos β MZ sW sin β −MZ cW sin β diagonalization: M2 −MZ sW cos β MZ sW sin β −MZ cW sin β −µ MZ cW cos β 0 −µ 0 N ∗ Y N −1 = diag(mχ01 , mχ02 , mχ03 , mχ04 ) Hermitian form: N Y † Y N −1 = diag(mχ2 0 , mχ2 0 , mχ2 0 , mχ2 0 ) 1 2 3 4 17 / 40 Neutralino Masses neutralino mass matrix: Y = M1 0 0 MZ sW 0 M2 0 −MZ cW 0 0 0 −µ −µ 0 MZ sW diagonalization: −MZ cW N ∗ Y N −1 = diag(mχ01 , mχ02 , mχ03 , mχ04 ) Hermitian form: N Y † Y N −1 = diag(mχ2 0 , mχ2 0 , mχ2 0 , mχ2 0 ) 1 2 3 4 17 / 40 Outline 1 Anomalous Magnetic Moment of the Muon 2 Minimal Supersymmetric Standard Model for tan β = ∞ 3 Calculation and Approximation 4 Identification of Viable Parameter Regions 18 / 40 Parameters and Feynman Diagrams relevant free MSSM parameters: approximation: yµ , µ, M1 , M2 , mL , mR mµ |µ|, |M1 |, |M2 |, mL , mR one-loop calculation sufficient calculation with mass eigenstates → diagonal propagators Feynman Diagrams for muon self energy: χ− l µ− µ̃− k µ− ν̃µ µ− χ0m µ− 19 / 40 Parameters and Feynman Diagrams relevant free MSSM parameters: approximation: yµ , µ, M1 , M2 , mL , mR mµ |µ|, |M1 |, |M2 |, mL , mR one-loop calculation sufficient calculation with mass eigenstates → diagonal propagators Feynman Diagrams for muon anomalous magnetic moment: χ− l µ− Aρ µ̃− k µ− ν̃µ µ− χ0m Aρ µ− 19 / 40 Auxiliary and Loop Functions expressions with sparticle mixing matrices occur: µ̃ ∗ µ̃ mχ− Ul2 Vl1 (Uk1 ) Uk1 mχ0m Nm1 Nm3 l → substitution introduces different functions auxiliary functions: −AJ q2 q3 q4 + BJ (q2 q3 + q2 q4 + q3 q4 ) − CJ (q2 + q3 + q4 ) + DJ (q1 − q2 ) (q1 − q3 ) (q1 − q4 ) q3 q4 (BJ q3 q4 − CJ (q3 + q4 ) + DJ ) = (q1 − q3 ) (q1 − q4 ) (q2 − q3 ) (q2 − q4 ) x1,J = y12,J loop function for muon self energy: I (qa , qb , qc ) = qa qb ln qa qb + qb qc ln qb qc + qc qa ln qc qa (qa − qb ) (qb − qc ) (qa − qc ) 20 / 40 Auxiliary and Loop Functions expressions with sparticle mixing matrices occur: µ̃ ∗ µ̃ mχ− Ul2 Vl1 (Uk1 ) Uk1 mχ0m Nm1 Nm3 l → substitution introduces different functions auxiliary functions: −AJ q2 q3 q4 + BJ (q2 q3 + q2 q4 + q3 q4 ) − CJ (q2 + q3 + q4 ) + DJ (q1 − q2 ) (q1 − q3 ) (q1 − q4 ) q3 q4 (BJ q3 q4 − CJ (q3 + q4 ) + DJ ) = (q1 − q3 ) (q1 − q4 ) (q2 − q3 ) (q2 − q4 ) x1,J = y12,J loop functions for muon anomalous magnetic moment: KC/N (qa , qb , qc ) = GC/N (qa , qc ) − GC/N (qa , qb ) qb − qc with: GC (qa , qb ) = GN (qa , qb ) = −3 qa2 + 4 qa qb − qb2 + 2 qa2 ln qa qb (qa − qb )3 −qa2 + qb2 + 2 qa qb ln qa qb (qa − qb )3 20 / 40 Contribution to the Muon Self Energy √ ΣMSSM µ = 2 y 2 µ 16π( g2 Re(µ M2 ) MW + 4 X I (mν̃2µ , mχ2 − , mχ2 − ) 1 2 I (mχ2 0m , mµ̃2 1 , mµ̃2 2 ) m=1 Re − µ MW + g12 x + g1 xm,12 g2 m,11 yµ2 ∗ 2 2 µ MW xm,33 + g1 xm,13 mµ̃2 2 − mR − MZ2 sW g2 1 g x + g2 xm,23 mµ̃2 1 − mL2 − MZ2 − 2 1 m,13 + 4 h X 1 n,p=1 n6=p 4 Re(g1 ynp,13 + g2 ynp,23 ) I (mµ̃2 1 , mχ2 0n , mχ2 0p ) − 2 g1 Re(ynp,13 ) I (mµ̃2 2 , mχ2 0n , mχ2 0p ) 1 2 − sW 2 ) i 21 / 40 Contribution to the Muon Anomalous Magnetic Moment √ a MSSM µ = 2 y mµ 2 µ 16π( g2 Re(µ M2 ) MW KC (mν̃2µ , mχ2 − , mχ2 − ) 1 + 4 X 2 KN (mχ2 0m , mµ̃2 1 , mµ̃2 2 ) m=1 Re − µ MW + g12 x + g1 xm,12 g2 m,11 yµ2 ∗ 2 2 µ MW xm,33 + g1 xm,13 mµ̃2 2 − mR − MZ2 sW g2 1 g x + g2 xm,23 mµ̃2 1 − mL2 − MZ2 − 2 1 m,13 + 4 h X 1 n,p=1 n6=p 4 1 2 − sW 2 Re(g1 ynp,13 + g2 ynp,23 ) KN (mµ̃2 1 , mχ2 0n , mχ2 0p ) − 2 g1 Re(ynp,13 ) KN (mµ̃2 2 , mχ2 0n , mχ2 0p ) ) i 22 / 40 Properties of the Results direct dependency on parameters yµ , µ, M1 , M2 , mL , mR symmetries: ΣMSSM → −ΣMSSM µ µ if yµ → −yµ and aµMSSM → −aµMSSM or µ → −µ or (M1 , M2 ) → (−M1 , −M2 ) mµ = −ΣMSSM can be used to determine yµ numerically µ ⇒ aµMSSM only depends on µ, M1 , M2 , mL , mR if yµ is eliminated from the formula via the self energy: aµMSSM invariant under µ → −µ and (M1 , M2 ) → (−M1 , −M2 ) Which sign is usual for aµMSSM ? 23 / 40 Start of the Approximation relevant MSSM mass parameters assumed to be real w.l.o.g.: µ, M1 , mL and mR positive; M2 positive or negative MZ µ, M1 , |M2 |, mL , mR approximation: sparticle masses: mν̃2µ = mµ̃21 = mL2 mχ2 − = µ2 1 mχ2 0 1 = mχ2 0 2 =µ 2 2 mµ̃22 = mR mχ2 − = M22 2 mχ2 0 3 = M12 mχ2 0 = M22 4 24 / 40 Approximation for the Self Energy I dimensionless loop function: ma mb Iˆ , mc mc ∀ va , vb : := ma mb I (ma2 , mb2 , mc2 ) 0 < Iˆ(va , vb ) < 1 25 / 40 Approximation for the Self Energy II ΣMSSM ≈ µ √ µ |M2 | 2 yµ 2 ˆ M sgn(M ) 3 g I , 2 2 32π 2 g2 W mL mL − g12 Iˆ + 2 g12 Iˆ − 2 g12 Iˆ ≈ yµ sgn(M2 ) 0,705 GeV Iˆ − 0,067 GeV Iˆ + 0,135 GeV Iˆ − 0,135 GeV Iˆ µ M1 , mL mL µ M1 , mR mR M1 mL , mR mR µ |M2 | , mL mL µ M1 , mL mL µ M1 , mR mR M1 mL , mR mR µ mL µ mL 26 / 40 Approximation for the Self Energy II ΣMSSM ≈ µ √ µ |M2 | 2 yµ 2 ˆ M sgn(M ) 3 g I , 2 2 32π 2 g2 W mL mL − g12 Iˆ + 2 g12 Iˆ − 2 g12 Iˆ µ M1 , mR mR M1 mL , mR mR µ mL H̃d− W̃ − µ− L µ M1 , mL mL H̃u− W̃ − HW1: ν̃µ µ− R 26 / 40 Approximation for the Self Energy II ΣMSSM ≈ µ √ µ |M2 | 2 yµ 2 ˆ M sgn(M ) 3 g I , 2 2 32π 2 g2 W mL mL − g12 Iˆ + 2 g12 Iˆ − 2 g12 Iˆ µ M1 , mR mR M1 mL , mR mR µ mL H̃d0 W̃ 0 µ− L µ M1 , mL mL H̃u0 W̃ 0 HW2: µ̃− L µ− R 26 / 40 Approximation for the Self Energy II ΣMSSM ≈ µ √ µ |M2 | 2 yµ 2 ˆ M sgn(M ) 3 g I , 2 2 32π 2 g2 W mL mL − g12 Iˆ + 2 g12 Iˆ − 2 g12 Iˆ µ M1 , mR mR M1 mL , mR mR µ mL H̃d0 B̃ 0 µ− L µ M1 , mL mL H̃u0 B̃ 0 HBL: µ̃− L µ− R 26 / 40 Approximation for the Self Energy II ΣMSSM ≈ µ √ µ |M2 | 2 yµ 2 ˆ M sgn(M ) 3 g I , 2 2 32π 2 g2 W mL mL − g12 Iˆ + 2 g12 Iˆ − 2 g12 Iˆ H̃u0 HBR: µ M1 , mL mL µ M1 , mR mR M1 mL , mR mR µ mL B̃ 0 B̃ 0 H̃d0 µ− L µ̃− R µ− R 26 / 40 Approximation for the Self Energy II ΣMSSM ≈ µ √ µ |M2 | 2 yµ 2 ˆ M sgn(M ) 3 g I , 2 2 32π 2 g2 W mL mL − g12 Iˆ + 2 g12 Iˆ − 2 g12 Iˆ µ M1 , mL mL µ M1 , mR mR M1 mL , mR mR B̃ 0 µ mL B̃ 0 BLR: µ− L µ̃− L µ̃− R µ− R 26 / 40 Approximation for the Anomalous Magnetic Moment I dimensionless loop function: K̂ N ∀ wa , wb : qa qb , qc qc := −qa qb KN (qc , qa , qb ) 0 < K̂ N (wa , wb ) < 1 27 / 40 Approximation for the Anomalous Magnetic Moment I dimensionless loop function: K̂ W ∀ wa , wb : qa qb , qc qc := qa qb [ 2 KC (qc , qa , qb ) + KN (qc , qa , qb ) ] 0 < K̂ W (wa , wb ) < 1,155 27 / 40 Approximation for the Anomalous Magnetic Moment II 2 √ 1 2 yµ µ M22 2 m M sgn(M ) g K̂ , µ W 2 W 2 32π 2 g2 µ |M2 | mL2 mL2 aµMSSM ≈ + g12 1 K̂ N µ M1 µ2 M12 , mL2 mL2 − 2 g12 1 K̂ N µ M1 µ2 M12 , 2 2 mR mR + 2 g12 µ M1 K̂ N 2 mL2 mR 2 mL2 mR , 2 2 M1 M1 µ2 M22 , mL2 mL2 µ2 M12 , mL2 mL2 µ2 M12 , 2 2 mR mR 2 mL2 mR , 2 2 M1 M1 ≈ yµ sgn(M2 ) 2,483 · 10−8 (1000 GeV)2 µ |M2 | K̂ W + 0,712 · 10−8 (1000 GeV)2 µ M1 K̂ N − 1,425 · 10−8 (1000 GeV)2 µ M1 K̂ N + 1,425 · 10−8 µ M1 (1000 GeV)2 K̂ N 2 mL2 mR 28 / 40 Result for Common Sparticle Mass special case: µ = M1 = |M2 | = mL = mR = MS MZ approximation for ΣMSSM is linear in yµ µ ⇒ yµ ≈ √ 2 · 32π 2 mµ g2 g12 − sgn(M2 ) 3 g22 MW insertion yields: aµMSSM ≈ 1 mµ2 g12 + sgn(M2 ) 5 g22 3 MS2 g12 − sgn(M2 ) 3 g22 (1000 GeV)2 ≈ MS2 ( −7,25 · 10−9 −5,34 · 10−9 für M2 > 0 für M2 < 0 How can a positive sign be achieved? 29 / 40 Outline 1 Anomalous Magnetic Moment of the Muon 2 Minimal Supersymmetric Standard Model for tan β = ∞ 3 Calculation and Approximation 4 Identification of Viable Parameter Regions 30 / 40 Scaling Behavior rescaling of the mass parameters by common factor k > 0 leads to: yµ (k µ, k M1 , k M2 , k mL , k mR ) ≈ yµ (µ, M1 , M2 , mL , mR ) aµMSSM (k µ, k M1 , k M2 , k mL , k mR ) ≈ ⇒ 1 MSSM a (µ, M1 , M2 , mL , mR ) k2 µ main task: generate a positive aµMSSM 31 / 40 Possible Parameter Scenarios √ reminder: aµMSSM ≈ 2 yµ mµ MW 32π 2 g2 sgn(M2 ) g22 1 µ2 M22 , K̂ W µ |M2 | mL2 mL2 + g12 1 K̂ N µ M1 µ2 M12 , mL2 mL2 − 2 g12 1 K̂ N µ M1 µ2 M12 , 2 2 mR mR + 2 g12 µ M1 K̂ N 2 mL2 mR 2 mL2 mR , 2 2 M 1 M1 yµ > 0 yµ < 0 M2 < 0 scenario 1 scenario 2 M2 > 0 scenario 4 scenario 3 32 / 40 Benchmark Point for Scenario 1 µ M1 , mL , mR for dominance of BLR contribution mL = mR for symmetry reasons (µ, M1 , M2 , mL , mR ) = (3000, 600, −3000, 600, 600) GeV aµMSSM (P1b) ≈ 3,23 · 10−9 yµ (P1b) ≈ 0,11 , with 4 × 10-9 2 × 10-9 a ΜMSSM P1b : 0 -2 × 10-9 BLR HW HBL & HBR total -4 × 10-9 500 1000 1500 2000 2500 3000 ΜGeV 33 / 40 Restrictions from the Tau Sector requirement for non tachyonic staus: yτ2 < g22 2 2 µ2 M W ⇒ 0 < 0,397 Iˆ 2 + MZ2 mL,τ µ |M2 | , mL,τ mL,τ 1 2 − sW 2 + 0,038 Iˆ + µ mL,τ 2 2 + MZ2 sW mR,τ M1 µ , mL,τ mL,τ 0,076 Iˆ ≈ 2 m2 mL,τ R,τ (174,1 GeV)2 µ2 − 0,076 Iˆ M1 mL,τ , mR,τ mR,τ − µ mR,τ , M1 mR,τ 174,1 GeV mR,τ 34 / 40 Restrictions from the Tau Sector requirement for perturbation theory: yτ2 < 4 π ⇒ 0 < 1,407 Iˆ µ |M2 | , mL,τ mL,τ + 0,134 Iˆ M1 µ , mL,τ mL,τ + 0,269 − 0,269 Iˆ µ ˆ I mL,τ µ mR,τ M1 mL,τ , mR,τ mR,τ , M1 mR,τ −1 34 / 40 Parameter Dependency: µ-M1 -Plane aµMSSM regions for M2 = −3000 GeV, mL = mR mL = 600 GeV : 35 / 40 Parameter Dependency: µ-mL -Plane aµMSSM regions for M2 = −3000 GeV, mL = mR M1 = 600 GeV : 36 / 40 Parameter Dependency: M1 -mL -Plane aµMSSM regions for M2 = −3000 GeV, mL = mR µ = 3000 GeV : 37 / 40 Maximization of Sparticle Masses limit case: µ → ∞ while M1 = mL = mR ⇒ aµMSSM ≈ 2 1 mµ2 −9 (1000 GeV) ≈ 3,72 · 10 3 mL2 mL2 benchmark point: P1c : (µ, M1 , M2 , mL , mR ) = (40 000, 1000, −40 000, 1000, 1000) GeV 38 / 40 Benchmark Points for All Scenarios µ/GeV M1 /GeV M2 /GeV mL /GeV mR /GeV P1a 2 000 200 −8 000 200 2 000 0,18 P1b 3 000 600 −3 000 600 600 0,11 P1c 40 000 1 000 −40 000 1 000 1 000 0,03 P2 2 000 2 000 −2 000 18 000 1 000 −1,86 P3 2 400 400 2 400 10 000 400 −0,75 P4a 30 000 2 000 30 000 2 000 2 000 0,32 yµ large mass splittings large masses compared to the normal MSSM huge yµ values compared to the Standard Model 39 / 40 Conclusion and Outlook MSSM for tan β = ∞ is capable of explaining the aµ discrepancy large Yukawa couplings → diagrams with Higgs boson loops relevant? analysis of other observables to further constrain or exclude this model 40 / 40 Conclusion and Outlook MSSM for tan β = ∞ is capable of explaining the aµ discrepancy large Yukawa couplings → diagrams with Higgs boson loops relevant? analysis of other observables to further constrain or exclude this model Thanks for your attention! 40 / 40
