G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries

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The SEENET-MTP Workshop JW2011
Scientific and Human Legacy of Julius Wess
27-28 August 2011, Donji Milanovac, Serbia

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G. Martinelli - From the Standard Model to Dark Matter and beyond: Symmetries, Masses and Mysteries

  1. 1. From the Standard Model to DarkMatter and beyond: Symmetries,Masses and MisteriesGuido MartinelliSISSA & INFN NIS, Serbia 29/08/2011
  2. 2. Plan of the Talk1) The UT analysis within the SM2) Beyond the SM: the case of Bs3) Outlook
  3. 3. In the Standard Model the quark massmatrix, from which the CKM Matrix andCP originate, is determined by the YukawaLagrangian which couples fermions andHiggs Lquarks = Lkinetic + Lweak int + Lyukawa CP invariantCP and symmetry breaking areclosely related !
  4. 4. Two accidental symmetries:Absence of FCNC at tree level (& GIMsuppression of FCNC in quantum effects @loops)NO CP violation @tree levelFlavour Physics is extremely sensitiveto new physics
  5. 5. QUARK MASSES ARE GENERATEDBY DYNAMICAL SYMMETRYBREAKING Charge +2/3Lyukawa ≡ ∑i,k=1,N [ Yi,k (qiL HC ) UkR + Xi,k (qiL H ) DkR + h.c. ] Charge -1/3 ∑i,k=1,N [ mui,k (uiL ukR ) + mdi,k (diL dkR) + h.c. ]
  6. 6. Diagonalization of the Mass Matrix Up to singular cases, the mass matrix can always be diagonalized by 2 unitary transformations uiL  UikL ukL uiR  UikR ukR M´= U†L M UR (M´)† = U†R (M)† ULLmass ≡ mup (uL uR + uR uL ) + mch(cL cR + cR cL ) + mtop(tL tR + tR tL )
  7. 7. N(N-1)/2 angles and (N-1)(N-2) /2 phases N=3 3 angles + 1 phase KMthe phase generates complex couplings i.e. CPviolation;6 masses +3 angles +1 phase = 10 parameters Vud Vus Vub Vcd Vcs Vcb Vtb Vts Vtb
  8. 8. NO Flavour Changing Neutral Currents (FCNC) at Tree Level (FCNC processes are good candidates for observing NEW PHYSICS) CP Violation is natural with three quark generations (Kobayashi-Maskawa) With three generations all CP phenomena are related to the same unique parameter ( δ )
  9. 9. Vud Vus Vub Quark masses & GenerationVcd Vcs Vcb MixingVtd Vts Vtb β-decays e- | Vud | = 0.9735(8) W | Vus | = 0.2196(23) down νe up | Vcd | = 0.224(16) | Vcs | = 0.970(9)(70)Neutron | Vcb | = 0.0406(8) Proton | Vub | = 0.00409(25) | Vtb | = 0.99(29) | Vud | (0.999)
  10. 10. The Wolfenstein Parametrization 1 - 1/2 ! 2 ! 3 A ! (" - i #) Vub -! 1 - 1/2 ! 2 A! 2 + O(λ4) A !3 $ -A !2 1 (1- " - i #) Vtd Sin θ12 = λ Sin θ23 = A λ2λ ~ 0.2 A ~ 0.8 Sin θ13 = A λ3(ρ-i η)η ~ 0.2 ρ ~ 0.3
  11. 11. The Bjorken-Jarlskog Unitarity Triangle | Vij | is invariant under a1 b1 phase rotations a1 = V11 V12* = Vud Vus*d1 a2 b2 a2 = V21 V22* a3 = V31 V32*e1 a1 + a2 + a3 = 0 a3 b3 (b1 + b2 + b3 = 0 etc.) c3 γOnly the orientation depends a3 a2on the phase convention α a1 β
  12. 12. Physical quantities correspond to invariants under phase reparametrization i.e. |a1 |, |a2 |, … , |e3 | and the area of the Unitary Triangles J = Im (a1 a2 * ) = |a1 a2 | Sin β a precise knowledge of the moduli (angles) would fix J CP ∝ J Vud*Vub+ Vcd* Vcb+Vtd* Vtb = 0Vud*Vub α γ = δCKM Vtd*Vtb γ β Vcd*Vcb
  13. 13. VubVud+ VcbVcd+V* Vtd = 0 * * tb 13
  14. 14. FromA. StocchiICHEP 2002
  15. 15. For details see: UTfit Collaborationhttp://www.utfit.org
  16. 16. sin 2β is measured directly from B J/ψ Ksdecays at Babar & Belle Γ(Bd0 J/ψ Ks , t) - Γ(Bd0 J/ψ Ks , t)AJ/ψ Ks = Γ(Bd0 J/ψ Ks , t) + Γ(Bd0 J/ψ Ks , t) AJ/ψ Ks = sin 2β sin (Δmd t)
  17. 17. DIFFERENT LEVELS OF THEORETICALUNCERTAINTIES (STRONG INTERACTIONS) 1) First class quantities, with reduced or negligible theor. uncertainties2) Second class quantities, with theoretical errors of O(10%) or less that can be reliably estimated 3) Third class quantities, for which theoretical predictions are model dependent (BBNS, charming, etc.) In case of discrepacies we cannot tell whether is new physics or we must blame the model
  18. 18. Unitary 2005Triangle SMsemileptonic decays K0 - K0 mixingB0d,s - B0d,s mixing Bd Asymmetry
  19. 19. Classical Quantities used in the levels @Standard UT Analysis 68% (95%) CL Vub/Vcb εK Δmd Δmd/Δms f+,F 1/2 ξ fBBB BK Inclusive vs Exclusive before Opportunity for lattice QCD only a lower bound see later
  20. 20. New Quantities used in the UT Analysis sin 2β cos 2β α γ sin (2β + γ) ( ) B→J/Ψ K0 B→J/Ψ K*0 B→ππ,ρρ B→D * K ( ) B→D * π,Dρ
  21. 21. Repeat with several fCP final states
  22. 22. THECKM
  23. 23. Global Fit within the SM SM FitIn the Consistence on anhadronicsector, over constrained fitthe SM of the CKM parametersCKM ρ = 0.132 ± 0.020patternrepresentsthe η = 0.353 ± 0.014principalpart of the α = (88 ± 3)0flavour sin2β = 0.695 ±structureand of CP 0.025??violation β = (22 ±1)0 γ= (69 ± 3)0 CKM matrix is the dominant source of flavour mixing and CP violation
  24. 24. The UT-angles fit does not depend onComparable accuracy theoretical calculations (treatement ofdue to the precise sin2β errors is not an issue)value and substantialimprovement due to UT-angles UT-latticethe new ΔmsmeasurementCrucial to improvemeasurements of theangles, in particular γ(tree level NP-freedetermination) Still imperfect agreement in η due to sin2β and Vub ρ = 0.129 ± 0.027 ρ = 0.155 ± 0.038 tension η = 0.340± 0.016 η = 0.404 ± 0.039 Vincenzo Vagnoni ANGLES 06, Moscow, 28 July 20062011 ICHEP VS LATTICE th
  25. 25. SM predictions of Δms Δms SM expectation Δms = (18.3 ± 1.3 ) ps-1 10 Prediction “era” Monitoring “era” ExpΔms = (17.77 ± 0.12 ) ps-1 Legendaagreement between the predicted values and the measurements at better than : 1σ 3σ 5σ 2σ 4σ 6σ
  26. 26. Theoretical predictions of Sin 2 β in the years predictions exist since 95 experiments sin 2 βUTA = 0.65 ± 0.12 Prediction 1995 from Ciuchini,Franco,G.M.,Reina,Silvestrini
  27. 27. Is the present picture showing a Model Standardissimo ? An evidence, an evidence, my kingdom for an evidence From Shakespeares Richard III1) Possible tensions in the present SM Fit ?2) Fit of NP-ΔF=2 parameters in a Model “independent” way3) “Scale” analysis in ΔF=2
  28. 28. Compatibility plotsThey are a procedure to ``measure” the agreement of a singlemeasurement with the indirect determination from the fit αexp = (91 ± 6)0 γexp = (76 ± 11)0
  29. 29. Three “news” ingredientsεΚ 1) Buras&Guadagnoli BG&Isidori corrections (6) i"! % Im M 12 & ! K = sin "! e + $# ( * )mK +  Decrease the SM prediction by 6% 2) Improved value for BK  BK=0.731±0.07±0.35 3) Brod&Gorbhan charm-top contribution at NNLO  enhancement of 3% (not included yet) -1.5 σ devation
  30. 30. VUB PUZZLE Inclusive: uses non perturbative parameters most not from lattice QCD (fitted from the lepton spectrum)Exclusive: uses non perturbative form factorsfrom LQCD and QCDSR
  31. 31. Vcb & Vub AFTER EPS-HEP2011Vub (excl) = (3.26 ± 0.30) 10-3 ~2σ differenceVub (inc) = (4.40 ± 0.31) 10-3Vub (com) = (3.83 ± 0.57) 10-3 15% uncertaintyVcb (excl) = (39.5 ± 1.0) 10-3Vcb (inc) = (41.7 ± 0.7) 10-3Vcb (com) = (41.0 ± 1.0) 10-3 2.4% uncertainty
  32. 32. sin2β(excl) = 0.740 ± 0.0411.6 σ from direct measurementsin2β(incl) = 0.809 ± 0.0363.2 σ from direct measurement no B → τν
  33. 33. Summary Table of the Pulls Prediction Measurement σ γ (69 ±3)° (79 ±10)° 0.9 α (85 ± 4)° (91 ± 6)° 0.7 sin2β 0.795±0.051 0.667±0.021 2.3 Vub [103] 3.63±0.15 3.83 ±0.57 0.3Br(Bll ) 10-9 3.55 ±0.28 18 ±11 +1.3 ΒK [103] 0.88 ±0.09 0.731 ±0.036 1.4Br(Bτ ν) 10-4 0.83±0.08 1.64±0.34 2.3 Δms (ps-1) 19.1±1.5 17.70±0.08 1.0
  34. 34. What for a ``standardissimo” CKM which agrees so well with the experimental observations?New Physics at the EW New Physics introduces newscale is “flavor blind” sources of flavour, the-> MINIMAL FLAVOR contribution of which, atVIOLATION, namely flavour most < 20 % , should beoriginates only from the found in the present data,Yukawa couplings of the SM e.g. in the asymmetries of Bs decays
  35. 35. INCLUSIVE Vub = (43.1 ± 3.9) 10-4Model dependent in the threshold region(BLNP, DGE, BLL)But with a different modelling ofthe threshold region [U.Aglietti et al.,0711.0860] Vub = (36.9 ± 1.3 ± 3.9) 10-4EXCLUSIVE Vub = (34.0 ± 4.0) 10-4Form factors from LQCD and QCDSR
  36. 36. …. beyondthe Standard Model
  37. 37. Only tree level processes Vub/Vcb and B-> DK(*)CP VIOLATION PROVEN IN THESM !!degeneracy of γbroken by ASL
  38. 38. In general the mixing mass matrix of the SQuarks(SMM) is not diagonal in flavour space analogouslyto the quark case We may eitherDiagonalize the SMM z , γ, gFCNC qjL QjLor Rotate by the same matrices the SUSY partners of the u- and d- like quarks g UiL dk UjL (QjL )´ = UijL QjL L
  39. 39. In the latter case the Squark Mass Matrix is not diagonal(m2Q )ij = m2average 1ij + Δmij2 δij = Δmij2 / m2average
  40. 40. New local four-fermion operators are generated Q1 = (bLA γµ dLA) (bLBγµ dLB) SM Q2 = (bRA dLA) (bRB dLB) Q3 = (bRA dLB) (bRB dLA) Similarly for the s quark e.g. A d A) (b B d B) Q4 = (bR L (sRA dLA) (sRB dLB) L R Q5 = (bRA dLB) (bLB dRA) + those obtained by L ↔ R
  41. 41. Bs mixing , a road to New Physics (NP) ?The Standard Model contribution to CP violation in Bs mixing is well predicted and rather small 2009 The phase of the mixing amplitudes can be extracted from Bs ->J/Ψ φ with a relatively small th. uncertainty. A phase very different from 0.04 implies NP in Bs mixing
  42. 42. Main Ingredients and General Parametrizations Neutral Kaon Mixing
  43. 43. Bd and Bs mixingCqPen and φqPen parametrize possible NP contributions toΓq12 from b -> s penguins
  44. 44. Physical observables
  45. 45. Experimental measurements
  46. 46. NP model independent Fit ΔF=2 EXP SM md = CBd md f ( " ,# , CBd , QCD..) ACP ( J / ( , K 0 ) = sin(2 $ + 2%Bd ) f ( " ,# , %Bd )Parametrizing NP physics in ΔF=2 processes & EXP = & SM ) %Bd f ( " ,# , %Bd ) | ! K |EXP = C! | ! K |SM f ( " ,# , C! , QCD..) NP SM A +ACBqCq2iφiBq e e2ö d = !B = 2 SM !B = 2 msEXP = CBs msSM ACP ( J / ( , % ) = sin(2 $ s ) 2%Bs ) f ( " ,# , CBs , QCD..) f ( " ,# , %Bs ) A!B = 2 ... ρ,η Cd ϕd Cs ϕs CεK γ (DΚ) X Tree Vub/Vcb X processes Δmd X X ACP (J/Ψ Κ) X X ACP (Dπ(ρ),DKπ) X X 1↔3 family ASL X X α (ρρ,ρπ,ππ) X X ACH X X X X τ(Βs), ΔΓs/Γs X X 2↔3 Δms X family ASL(Bs) X X 1↔2 ACP (J/Ψ φ) ~X X familiy εK X X
  47. 47. 5 new free parameters Today : Cs,ϕs Bs mixing fit is overcontrained Cd,ϕd Bd mixing Possible to fit 7 free parameters CεK K mixing (ρ, η, Cd,ϕd ,Cs,ϕs, CεK) SM analysis NP-ΔF=2 analysis ρ = 0.129 ± 0.022 ρ = 0.145 ± 0.045 η = 0.346 ± 0.015 η = 0.389 ± 0.054 ρ,η fit quite precisely in NP-ΔF=2 analysis and consistent with the one obtained on the SM analysis [error double] (main contributors tree-level γ and Vub)Please consider these numbers when you want to get CKM parameters in presence of NP in ΔF=2 amplitudes (all sectors 1-2,1-3,2-3)
  48. 48. Effective Theory Analysis ΔF=2Effective Hamiltonian in the mixing amplitudes LFj LF j C j (") = !"= "2 C j (") C(Λ) coefficients are extracted from data L is loop factor and should be : L=1 tree/strong int. NP L=α2s or α2W for stron/weak perturb. NP F1=FSM=(VtqVtb*)2 Fj=1=0 MFV |Fj | =FSM arbitrary phases NMFV |Fj | =1 Flavour generic arbitrary phases
  49. 49. Main contribution to present lower bound on NP scale come fromΔΦ=2 chirality-flipping operators ( Q4) which are RG enhanced From Kaon sector @ 95% [TeV] Scenario Strong/tree αs loop αW loop MFV NMFV 107 11 3.2 Generic ~470000 ~47000 ~14000 From Bd&Bs sector @ 95% [TeV] Scenario Strong/tree αs loop αW loop MFV NMFV 8 0.8 0.25 Generic 3300 330 100
  50. 50. b  s & τ µγ in SUSY GUTS Limits from Belle and Babar < 4.5 & 6.8 10-8 Φs ΔMs msq=500 GeV
  51. 51. We can consider simultaneously LFV, g-2e EDM,e.g. Isidori, Mescia, Paradisi, Temes in MSSM
  52. 52. FCNC in rare K decays
  53. 53. CONCLUSIONS1) CKM matrix is the dominant source of flavour mixing and CP violation σ(ρ)~15% & σ(η) ~4%2) There are tensions that should be understood : sin2β, εK , Br(B τ ν)3) Estraction of SM predictions with different possibilities: inclusive vs exclusive4) The suggestion of a large Bs mixing phase has survived for more than two years but could be killed by LHCb measurements.

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