SUSY FCNC at the LHC

Transcription

1 SUSY FCNC at the LHC Siannah Peñaranda-Rivas Departamento de Física Teórica Universidad de Zaragoza Flavour Physics at LHC run II Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 1 / 42

2 Outline 1 Introduction Flavour Changing Neutral Currents Flavour-changing interactions in SUSY R-parity conserving and violating SUSY models 2 Approaches for probing SUSY 3 New Physics Beyond the SM at the LHC B anomalies and LFV (SUSY) 4 Other relevant flavour changing interactions in SUSY Direct FCNC LHC Higgs LHC 5 Conclusions Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 2 / 42

3 Introduction Flavour Changing Neutral Courrents (FCNC) FCNC are processes in which one up-type (or down-type) quark is converted into another one of the same type. K 0 K 0 b sγ K 0 d s s d K 0 b s γ Effect of mixing: Mass matrix ( ) m 2 K A Diagonalize mk 2 A 1,2 = mk 2 ± A m 2 K Mass difference m K m K1 m K2 : signal of FCNC Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 3 / 42

4 Standard Model FCNC absent at the tree-level Produced at one-loop by charged currents Cabibbo-Kobayashi- Maskawa mixing matrix (V ) GIM Mechanism K 0 d t, c, u s V ld V ls S. L. Glashow, J. Iliopoulos and L. Maiani, Phys. Rev. D2, (1970). Unitarity of the CKM matrix: q W W + V qs V qd = 0 V qs V qd s u, c, t d K 0 Loop induced GIM = FCNC processes have very small rates Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 4 / 42

5 New Physics (NP) New Physics = New FCNC Sources Strong constraints from low energy data Ideal place to get indirect evidence of NP So far, most of experimental results on flavor observables are consistent with SM expectations and lead to strong indirect constraints on NP models Increase the sensitivity of flavour experiments & More precision on theoretical determination Here we will focus on some SUSY contributions to flavour observables Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 5 / 42

6 New Physics (NP) New Physics = New FCNC Sources Strong constraints from low energy data Ideal place to get indirect evidence of NP So far, most of experimental results on flavor observables are consistent with SM expectations and lead to strong indirect constraints on NP models Increase the sensitivity of flavour experiments & More precision on theoretical determination Here we will focus on some SUSY contributions to flavour observables Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 5 / 42

7 New Physics: Supersymmetry Flavour-changing interactions in SUSY Minimal Flavor Violation (MFV) in the MSSM FC phenomena is analogue to the SM case supersymmetrization of the one-loop SM contributions squarks are assumed to be aligned with quarks originates from CKM matrix as the only source and proceeds via loop-contributions the size is expected to be small Non Minimal Flavor Violation (NMFV) in the MSSM Additional FC phenomena is due to misalignment between the rotations that diagonalize quark/squark sectors (beyond CKM) arise at tree level sizeable contributions are expected to occur Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 6 / 42

8 Flavour-changing interactions in SUSY Supersymmetry allows for flavour-mixing terms in the scalar-quark mass matrix Squark Mixing: ( M M 2 q 2 = Q + mq 2 + cos 2β(T 3 Q q sin θw 2 ) )M2 Z m q (A µ{cot β, tan β}) m q (A µ{cot β, tan β}) MU,D 2 + m2 q + cos 2βQ q sin θw 2 M2 Z MQ 2, A, M2 U,D are 3 3 matrices in generation space Flavour Mixing parameters M2 ij δ ij = M ii M jj induces strong FCNC interactions! q i ( b + s + d) SUSY-QCD tree-level gluino coupling g α s b Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 7 / 42

9 extra FCNC induced at one-loop and CKM by extra charged particles: H ± and χ ± V ld V qs K 0 d t, c, u H s u, c, t K 0 s H + d V ls V ld V qd V qs K 0 d t, c, ũ s χ χ + s ũ, c, t d K 0 V V ls qd Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 8 / 42

10 Constraints Limits from Low Energy Data F. Gabbiani et. al. Nucl. Phys B 477, 321 (1996) - K 0 K 0 (d s ds): m K = δ d 12 - D 0 D 0 (cū cu): m D = δ u 12 - B 0 B 0 (b d bd): m B = δ d 13 δ 12 <.1 mũ m c /500 GeV δ 13 <.098 mũ m t /500 GeV δ 23 < 8.2 m c m t /(500 GeV)2 New B-data from Belle, Babar, LHC: additional constraints The Flavour-Changing terms are communicated from the up- to the down-sector by CKM e.g. M.Misiak et. al., hep-ph/ Due to SU(2) L gauge invariance (M d LL )2 = CKM (M u LL )2 CKM (M d LL )2 DIAG 1 M 2 the bounds are transfered to the up-quark sector top-charm FCNC are constrained by b-sector measurements. Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 9 / 42

11 Flavour-changing interactions in SUSY R-parity conserving SUSY models: MFV and NMFV Provides elegant solutions to the dark matter and hierarchy problems. Leads to natural GUT R-parity violating (RPV) SUSY: RPV terms are allowed in the superpotential: W = W MSSM + λ ijk L i L j Ē k + λ ijkl i Q j Dk + k i L i H u + λ ijkūi D j Dk Lepton number violating Baryon number viol. Resonant/associated single SUSY particle production is possible Could explain large mixing angles and hierarchical masses of neutrinos The lightest SUSY particle (LSP) is no longer stable No dark matter candidate :-( Other non-minimal extensions exist, e.g. one extra Higgs (NMSSM), extra U(1) groups (Z ), extra neutrinos (see-saw models), etc. Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 10 / 42

12 Approaches for probing SUSY Most common approaches for probing SUSY: Concrete models: e.g. msugra/cmssm, GMSB: easy interpretability as a full theory but, rigid relationships of parameters, not necessarily realistic: all masses related to few parameters: m 0, m 1 2, µ Simplified models: very reduced, accessible spectrum focus on decay chains to which LHC is sensitive, easier to reinterpret not a full SUSY model

13 SUSY searches in simplified models Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 12 / 42

14 pmssm: 19 parameters (R p -conserving) MSUGRA pmssm m g > 1.85 TeV 50% of models with m g > 1.4 TeV allowed m q > 1.85 TeV 50% of models with m q > 0.6 TeV allowed m χ + > 0.71 TeV 50% of models with m χ + > 0.1 TeV allowed 1 1 pmssm scans provide powerful way to reinterpret existing searches in context of full SUSY models Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 13 / 42

15 New Physics Beyond the SM at the LHC There are few anomalies show in data hinting the need of new physics B s µ + µ 2σ B D ( ) τν 4σ B s K l + l (R K ) σ h µτ 2σ (Run1) - No excess any more (B anomalies See talks by Mescia, Martinez-Vidal, Kosnik and Capdevila on Wednesday, May 24) (LFV See talk by Fiorini on Monday, May 22) How SUSY could accomodate these results? Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 14 / 42

16 ) B s µ + µ ATLAS, Eur. Phys. J. C 76 (2016) 513, arxiv: ] 9 [10 µ µ + 0 B(B % 95.45% 68.27% ATLAS CMS & LHCb SM ATLAS 1 s = 7 TeV, 4.9 fb 1 s = 8 TeV, 20 fb Contours for 2 ln(l) = 2.3, 6.2, 11.8 from maximum of L B(B s µ + µ ) [10 ] ATLAS is consistent with the LHCb and CMS ATLAS consistency with SM is 2.0 Room for NP destructively interfering with the SM CMS and LHCb observation: BR(B 0 d µ+ µ ) = ( ) 10 10, BR(B 0 s µ + µ ) = ( ) 10 9 ATLAS: BR(B 0 d µ+ µ ) < , 95%C.L., BR(B 0 s µ + µ ) < , 95%C.L., BR(B 0 s µ + µ ) = ( ) 10 9 Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 15 / 42

17 Rare decays: B s µ + µ SM SUSY SM prediction accurate: Bobeth, arxiv: BR(B 0 s µ + µ ) = (3.65 ± 0.23) 10 9 SUSY Enhancement by a factor of order tan 6 β Implications on the viability of SUSY (constrained and unconstrained models): Arbey, Battaglia, et al. - BR in the MSSM does not deviate from its SM prediction - LHC results remove 10% of the scan points in the CMSSM and a few % in the pmssm Room for NP (SUSY) opened Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 16 / 42

18 B D ( ) τν R(D) = BR( B 0 D + τ ν τ ) BR( B 0 D + l ν l ), R(D ) = BR( B 0 D + τ ν τ ) BR( B 0 D + l ν l ) PRL 115, (2015) The combined results disagree with the SM expectations at 4σ In the SM, the only difference between the numerator and the denominator is the lepton mass Sensitive test to NP at tree level Inconsistent with Type II THDM... SUSY has the potential to explain recent data Boubaa et al, Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 17 / 42

19 B D ( ) τν SUSY What needed to solve the anomaly? (Xiao-Gang He, SUSY 2016) Exp: More precise measurements! Theor: New Physics modify charged current interaction... in a way that a) The first two and third generations interact differently; b) Have P-parity conserving and violating ones differently! THDM-II cannot explain both SUSY OK (clear signal), Boubaa et al, This is a striking hint of violation of the lepton flavour universality which clearly needs also to be checked in other modes. Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 18 / 42

20 B K l + l (R K ) Experimental: At present no serious problems at colliders Deviations 2 3σ appear from time to time: LHCb: CERN seminar 18/04/2017: R K 0 = B(B0 K 0 µ + µ ) B(B 0 K 0 e + e ) = { ± low q2 ± central q SM prediction: 1 (Lepton Flavour Universality) Papers explanation: NP: Z, leptoquarks? SUSY with RPV: R p -violation superpotential: W =... + λ ijk L iq j Dk +...???... sfermions behave as leptoquarks... (Work in progress) Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 19 / 42

21 LFV Higgs decay h µτ? The CMS and ATLAS collaborations reported the first signal of LFV Higgs h µτ (Run1) BR(h µτ) = (CMS) BR(h µτ) = (7.7 ± 6.2) 10 3 (ATLAS) The SM predicts no tree-level LFV Higgs coupling MSSM: loop processes mediated by charginos or neutralinos. However, SUSY models with non-zero family mixing in the sleptons also result in enhancement in other LFV processes such as µ eγ, τ eγ, and τ µγ Important correlation between observables Run2: The limits can be used to constrain the corresponding flavour violating Yukawa couplings, absent in the standard model. Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 20 / 42

22 Other relevant flavour changing interactions in SUSY Model Setup Generic Minimal Supersymmetric Standard Model Scan over the parameters space: works done some years ago similar to present pmssm scenarious updated Flavour violation terms only in the Left-Left sector Naturally generated by Renormalization Group Equations (results similar with Right-Right and Left-Right mixing) Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 21 / 42

23 B(b sγ) Borzumati ZPC63 (1994) 291, hep-ph/ ; Borzumati, Greub, Hurt, Wyler, PRD62 (2000) , hep-ph/ [True for Left-Left mixing only!] FCNC SUSY-QCD contribution: m b (A b µ tan β) δ 23 b L b R s L m b b L δ 23 s L b R m g s L b R b L g s L Leading, Double insertion The Feynman Amplitude: A SUSY QCD (b sγ) δ 23 m b (A b µ tan β) M 2 SUSY Sub-Leading, Single insertion 1 m g Similar coupling structure in pp t c ( m t (A t µ/ tan β)) but different in Hqq ( µ) Relevant interplay between observables Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 22 / 42

24 Direct FCNC LHC pp[gg] tc q i q i g t q i g t g q i t q i c q i c g c Some previous works J.J. Lui et al., Nucl. Phys. B 705 (2005) 3, hep-ph/ G. Eilam, M. Frank, I. Turan, Phys.Rev.D74 (2006) , hep-ph/ J. Guasch, W. Hollik, S.P., J. Sola, Nucl. Phys. Proc. Suppl. 157 (2006) 152, hep-ph/ Leading terms from Left-Left sector: similar structure to b sγ m t (A t µ/ tan β) A(gg t c) δ 23 MSUSY 2 1 m g Large rates = Large δ 23 and Large (A t µ/ tan β) high sensitivity to A t Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 23 / 42

25 pp[gg] t c σ(pp[gg] t c) (δ 23 ) 2 m2 t (A t µ/ tan β) 2 1 MSUSY 4 m 2 g σ [pb] σ( pp[gg] -> t c ) δ 23 LL =0.68 M g =200 GeV M SUSY =746 GeV µ=400 GeV A b =2000 GeV A t =2238 GeV 1e tanβ BR exp (b sγ) ( ) 10 4 (within 3σ) events/100 fb -1 For small tan β there are no restrictions from b sγ and σ increases as A 2 t σ max (pp[gg] t c + tc) 1 pb and 10 5 events for 100 fb 1 Cross-section decay significantly with M SUSY and very fast with M g For M g 500 GeV: σ max (pp[gg] tc) 0.04 pb Cross-sections 0.5 pb possible 100, 000 events/100 fb 1 for t c + tc processes σ SM (pp[gg] t c) pb 6 orders of magnitude larger than SM! Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 24 / 42

26 Comparison with Higgs FCNC Take parameters of maximum σ(pp h t c): Large M SUSY and m g M SUSY m g 880 GeV, µ 700 GeV, δ σ(pp H 0 t c + tc) pb [tan β = 5] σ(pp[gg] t c) pb Same order of magnitude as Higgs-mediated FCNC!? Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 25 / 42

27 Higgs LHC σ(pp h q q ) σ(pp hx)b(h q q ) σ(pp hx) Γ(h q q + q q ) i Γ(h X i ) (qq bs or tc). Computation: σ(pp hx): HIGLU and HQQ packages M. Spira, hep-ph/ ; spira/higlu/, and... spira/hqq/. Γ(h X): FCNC FCHDECAY S. Béjar, J. Guasch; Γ(h q q ): SUSY-QCD contributions Don t assume alignment Exact diagonalization of 6 6 squark mass matrix Assume mixing only in the LL sector SM values: BR(H SM b s) 10 7 (m H < 2M W ) BR(H SM t c) (m H > m t ) Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 26 / 42

28 Leading contributions Diagrams with a chirality flip are enhanced by m g : mass-insertion approximation H tc m t (A t / tan β + µ) h t δ 23 t R t L c L c m g m t (A t µ/ tan β) δ 23 t L t R c L m g t c The terms proportional to A t cancel in the sum. J.Guasch, P.Häfliger, M.Spira PRD , 2003, hep-ph/ Equivalent structure for bs-channel Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 27 / 42

29 Leading contributions We can write an effective Lagrangian: G Hqq δ 23 m g µ M 2 SUSY D. A. Demir, Phys. Lett. B571, (2003), hep-ph/ cos(β α eff ) (h 0 ) M A 0 M Z 0 (h 0 ) sin(β α eff ) (H 0 ) = = = = 1 (H 0 ) 1 (A 0 ) α eff β π/2 1 (A 0 ) Different coupling structure in Hqq ( µ) and bsγ ( A b µ tan β) Possibility of small contribution to A(b sγ) and large contribution to BR(H qq ) Numerical results BR(h qq ) Find the maximum BR: MSSM parameter space scan: BR(h bs) 10 3 BR(h tc) 10 3 = several orders of magnitude larger than in the SM!! Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 28 / 42

30 Combination with production Combined analysis σ(pp h tc) Only H 0 /A 0 possible Large at small tan β differences at small M A 0: Near threshold for H 0 q 1 q 1 not possible for A σ(pp -> H 0 -> t c) 10-2 σ(pp -> A 0 -> t c) m A 0 = 300 GeV σ[pb] events/100fb -1 σ[pb] events/100fb tanβ σ(pp -> H 0 -> t c) 1 σ(pp -> A 0 -> t c) tanβ = m 0 A [GeV] Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 29 / 42

31 The best situation Maximum at maximal δ 23 σ[pb] σ[pb] σ(pp -> H 0 -> t c) σ(pp -> A 0 -> t c) tanβ = 5 m A 0 = 300 GeV log δ σ(pp -> H 0 -> t c) σ(pp -> A 0 -> t c) tanβ = 5 m 0 A = 300 GeV M SUSY [GeV] events/100fb -1 events/100fb -1 Maximum at maximal M SUSY M A 0 = 300 GeV, tan β = 5 h H 0 A 0 σ(pp h t c) pb pb events/100 fb B(h tc) Γ(h X) 0.41 GeV 0.39 GeV δ m q 880 GeV 850 GeV A t 2590 GeV 2410 GeV µ 700 GeV 930 GeV B(b sγ) tan β σ(pp H 0 tc) 5 fb 9 fb 20 fb events/100 fb increases fast at low tan β several thousand events could be produced Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 30 / 42

32 Comparison with direct FCNC production Not taking parameters of maximum σ(pp h t c): small m g m g 200 GeV, M SUSY 800 GeV, µ 700 GeV, δ σ(pp H 0 t c + tc) 10 3 pb [tan β = 5] σ(pp[gg] t c) 0.5 pb 2-3 orders of magnitude larger than Higgs-mediated FCNC Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 31 / 42

33 SUSY FCNC at the LHC Effects at LHC: σ(pp[gg] t c), σ(pp h t c) Direct production is competitive to Higgs-mediated processes Direct process can give much larger rates Parameter Higgs-mediated Direct production tan β Decreases fast insensitive M A 0 Decreases fast insensitive M SUSY Prefers large Decreases fast A t insensitive very sensitive δ 23 Moderate Moderate Left-Left flavour mixing gives large rates Experimental issues: Signal: single top-quark + light c-jet Evidence of new physics Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 32 / 42

34 CONCLUSIONS FCNC processes can be a helpful signature of SUSY physics at the LHC FCNCs are part of SUSY Constrained by low energy data Constrained by B-anomalies and LFV at the LHC The results remove ONLY between 10% 2% of the scan points in general SUSY models Room for NP (SUSY) opened Run II data expected to increase precisions... Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 33 / 42

35 ... Some works H bs, H tc MSSM A. M. Curiel, M. J. Herrero, W. Hollik, F. Merz, S. P., Phys. Rev. D 69 (2004) [hep-ph/ ]. A. M. Curiel, M. J. Herrero, D. Temes, Phys. Rev. D 67 (2003) [hep-ph/ ]. H bs + b sγ S. Béjar, F. Dilmé, J. Guasch and J. Solà, JHEP 0408 (2004) 018 [hep-ph/ ]. T. Hahn, W. Hollik, J.I. Illana, S. P., hep-ph/ pp H + H bs + H tc + b sγ S. Béjar, J. Guasch, J. Solà, JHEP 0510 (2005) 113, hep-ph/ Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 34 / 42

36 Leading terms Typical behavior of the cross-section ``stop mass matrix: Amplitude: Joan Solà (UB) (RADCOR 05 ) Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 35 / 42

37 only the presence of new physics could be an explanation for these events, if they are ever detected SM!! (Not even a single event in the SM for the entire lifetime of the LHC!!) Joan Solà (UB) (RADCOR 05 )

38 Combination with production At large tan β the main production channel for h 0 is associated production: σ(pp > h 0 b b) b h b h 0 BR(h 0 bs) enhanced b b suppressed σ(pp h 0 ) suppressed!!! Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 37 / 42

39 Combined analysis σ(pp h qq ) σ(pp h bs) σ[pb], Γ[GeV] Γ(h 0 -> X) σ(pp -> h 0 -> b s) 10 6 Γ(h 0 -> X) tree-higgs σ(pp -> h 0 -> b s) tree-higgs 10 5 tanβ = events/100fb -1 σ[pb] σ(qq,gg -> h 0 bb) σ(gg -> h 0 ) σ(qq,gg -> h 0 tt) tanβ = m 0 A [GeV] m 0 A [GeV] Maximized production rates for h 0 M A 0 < 300 GeV: enhancement of σ(pp h 0 ) dominates M A 0 > 300 GeV: supression of Γ(h 0 X) dominates Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 38 / 42

40 Combined analysis σ(pp h bs) σ[pb] σ(pp -> H 0 -> b s) σ(pp -> h 0 -> b s) σ(pp -> A 0 -> b s) tanβ = 50 m 0 A = 200 GeV log δ 23 events/100fb -1 σ[pb] σ(pp -> H 0 -> b s) σ(pp -> h 0 -> b s) σ(pp -> A 0 -> b s) 10 tanβ = 50 m 0 A = 200 GeV M SUSY [GeV] events/100fb -1 h 0 : Maximum attained for small δ 23, M SUSY 700 GeV Larger δ 23 smaller µ (b sγ) Small M SUSY small δ 23 (b sγ) H 0 /A 0 : Maximum at large M SUSY Large M SUSY = small B(b sγ) = larger δ 23 allowed - Large δ 23 µ has to decrease to obtain acceptable B(b sγ) BR(H 0 /A 0 bs) can not grow. Maximun values: σ(pp h bs) 0.4pb and 10 4 events/100fb 1

41 Finding the maximum Define: δ33 LR = m t (A t µ/ tan β) MSUSY 2 σ = (δ 23 ) 2 (δ33 LR)2 =constant defines an hyperbola in the δ 23 δ33 LR plane Mass (approximation): lightest mass: m 2 q = M2 SUSY m 2 q = M 2 SUSY c L t L t R c L 1 δ 23 0 t L δ 23 1 δ LR 33 t R 0 δ LR 33 1 ( ) 1 (δ 23 ) 2 + (δ33 LR)2 > Mlimit 2. Experimental limit defines a circle in δ 23 δ33 LR plane: ( ) 2 (δ 23 ) 2 + (δ33 LR )2 < 1 M2 l MSUSY 2 R 2

42 2 1 σ Maximum at: δ 23 = δ33 LR = R = 2 1 (1 M2 l 2 MSUSY 2 M SUSY ) 1 2. δ 23 0 M limit -1 M SUSY LR δ 33 Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 41 / 42

43 2 M SUSY non-colour breaking vacua: A t < 3M SUSY 1 σ δ LR 33 < 3m t M SUSY δ M limit M SUSY LR δ 33 The maximum is obtained when: the diagonal: δ 23 = δ LR 33 the limit mass circle the limit from A t cross in a single point Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 41 / 42

44 Exact equations δ 23 = δ LR 33 (δ 23 ) 2 + (δ LR 33 )2 = δ LR 33 = m t (3M SUSY µ/ tan β) ( MSUSY 2 ) 2 1 M2 l M 2 SUSY setting: m t = 175 GeV, M l = 150 GeV, µ = 400 GeV, tan β = 5 (by b sγ) δ LR 33 = δ 23 = M SUSY = GeV A t = GeV Siannah Peñaranda-Rivas (Univ.Zaragoza) LHC Flavour Physics at LHC run II 42 / 42