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Decadimenti rari del B: risultati e sfide per il futuro

Decadimenti rari del B: risultati e sfide per il futuro. Paolo Gambino INFN Torino. Any room left for New Physics in the flavor sector?. With advent of B factories B physics has entered a new precision era Presently, only Δ F=2 transitions are considered in the fits.

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Decadimenti rari del B: risultati e sfide per il futuro

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  1. Decadimenti rari del B: risultati e sfide per il futuro Paolo Gambino INFNTorino Paolo Gambino IFAE 14/4/2004

  2. Any room left for New Physics in the flavor sector? With advent of B factories B physics has entered a new precision era Presently, only ΔF=2 transitions are considered in the fits ΔF=1 could be affected by new physics in a different way B→ΦKs? Paolo Gambino IFAE 14/4/2004

  3. Why inclusive? ΛQCD«mb : inclusive decays admit systematic expansion in ΛQCD/mbNon-pert corrections are generally small and can be controlled Hadronization probability =1 because we sum over all states Approximately insensitive to details of meson structure as ΛQCD«mb Paolo Gambino IFAE 14/4/2004

  4. b -> s inclusive transitions ΛQCD«mb«MW Large L=log mb/MW must be resummed. LO: αsnLn, NLO: αsnLn-1 Tower of local ops OPE But many more operators appear adding gluons mb«MW Inclusive decays admit systematic expansion in αsand ΛQCD/mb (except charm loop contributions) Paolo Gambino IFAE 14/4/2004

  5. The main ingredients Process independent: • The Wilson coefficients Ci(encode the short distance information, initial conditions) • The Anomalous Dimension Matrix (the mixing among operators, the large logs, determines the evolution) Process dependent: the matrix elemts B→ Xsγ : NLO QCD calculation completed, all results checked, EW , power corrections B→ Xsll: NNLO & EW calculation just completed,power corrections Paolo Gambino IFAE 14/4/2004

  6. NLO ADM: a real tour de force EOM vanishing ops Physical operators Evanescent operators Gauge variant ops Paolo Gambino IFAE 14/4/2004

  7. New ADM calculation Check of Chetyrkin,Misiak,Munz & NEWADM for b->sll Gorbahn,Haisch,PG 2loop 3loop Paolo Gambino IFAE 14/4/2004

  8. The ADM for b->s: method • Rξ gauge • Anticommuting γ5: choice of basis allows it • Common mass M for all fields to distinguish UV from IR. After 1/M expansion, extract UV • Pro: allows 3 loop calculation (only tadpoles,MATAD) • Con: insertion of non-phys ops and c.t. M2G2 • Checks:locality,gauge inv,indep of external states, basis completeness, no mixing non-phys->phys Paolo Gambino IFAE 14/4/2004

  9. b quark γ s quark γ s quark The photon spectrum and its uses Motion of b quark inside B and gluon radiation smear the spike at mb/2 Belle NEW: lower cut at 1.8GeV Paolo Gambino IFAE 14/4/2004

  10. Photon spectrum & its uses (II) The photon spectrum is very insensitive to new physics, can be used to study the B meson structure <Eγ> = mb + ... var<Eγ> = μп2/12+...μп2~ <B|bD2b|B> Importance of extending to Eγ~ 1.8 GeV or less for the determination of both the BR AND the B parameters (Bigi Uraltsev) - Excellent agreement with NEW Babar fit to moments of s.l. distributions Mb(1GeV)= 4.585±0.059 GeV μп2(1GeV)=0.454±0.052 GeV2 Mb(1GeV)= 4.611±0.067 GeV μп2(1GeV)=0.447±0.052GeV2 without Belle photon moments Extremely important for inclusive Vcb, Vub Paolo Gambino IFAE 14/4/2004

  11. The charm mass problem mc enters the phase factor = 0.581±0.017 And the NLO matrix elements LO diagrams vanish: the definition of mc is a NNLO issue. Numerically important because these are large NLO contributions: mc(mc)=1.25±0.10 GeV mc(mb)=0.85±0.11 GeV mc(pole)~1.5GeV But pole mass has nothing to do with these loops Changing mc/mb from 0.29 (pole) to 0.22 (MSbar) increases BRγby 11% 0.22 ±0.04 gives DOMINANT 6% theory error Paolo Gambino IFAE 14/4/2004

  12. Electroweak effects in BRγ Almost complete calculation of O(ααsnLn) effects Haisch, PG Normalization of α : Czarnecki Marciano Other leading log effects small except in sl rate Baranowski,Misiak NLO EW effects: • Two loop matching conditions (1/sin2θW etc) • QED-QCD evolution neglecting 3loop O(ααs) ADM • QED matrix elements Total EW effects -3.6% in BRγ, of which -1.6% due to NLO Dilution due to interplay with QCD, small MHiggs dependence Paolo Gambino IFAE 14/4/2004

  13. Error anatomy of BRγ Total error 8% dominated by charm mass Can be partially resolved by NNLO Update under way Paolo Gambino IFAE 14/4/2004

  14. First steps towards the NNLO... • NNLO C7,8 matching completed Misiak, Steinhauser <2% in MSbar scheme, MW< μ < Mt • NNLO ADM of the 4quark operatorsGorbahn,Haisch used already for NNLO b->sll • Soon: NNLO mixing of Q7 Q8 (Gorbahn, Haisch) and NNLO Matrix element of Q2 in some approx (Misiak Steinhauser) Most difficult part 4loop ADM & bremstrahlung Paolo Gambino IFAE 14/4/2004

  15. Exp: B(B→Xs γ)=(3.34±0.38)x10-4 SM: B(B→Xs γ)=(3.70±0.30)x10-4 Gambino-Misiak B->Xsγ: a new physics killer It is the best measured rare decay Good agreement with SM strongly constrains most new models But don’t expect surprises... charged Higgs mass bounds in typeII 2HDM Does not carry over to MSSM! But very strong bounds there too Degrassi, Giudice,PG... Main obstacle to explain ACP(B->ΦKS) in MSSM NEW Belle 3.59±0.32±0.31±0.11 Paolo Gambino IFAE 14/4/2004

  16. CP asymmetry Belle: ACP(Xsγ)=-0.004±0.051±0.038 ACP(K* γ)=-0.015±0.044±0.012 Ab->sγ strongly suppressed in SM (<1%), Ab->dγ less so ACP(Xsγ+Xdγ) =0 (unitarity!) Very clean SM test Hurth,Lunghi,Porod Paolo Gambino IFAE 14/4/2004

  17. b->sl+l- : a more complicated case This decay mode is sensitive to different operators, hence to different new physics Here large logs are generated even without QCD: LO αsnLn+1, NLO αsnLn,... However, numerically the leading log is subdominant, yielding an awkward series: in BR 1+ 0.7 (αs)+ 5.5 (αs2)+ ... Paolo Gambino IFAE 14/4/2004

  18. Completing the NNLO calculation Two missing ingredients: 3 loop ADM mixing O2 into O9Gorbahn,Haisch,PG 3 loop ADM 4q operators Gorbahn,Haisch 2loop Matrix element of O9 Using calculations for sl Czarnecki,Melnikov,Steinhauser Paolo Gambino IFAE 14/4/2004

  19. Lowest order diagrams Two sources of large QED logs: running of α and of operators Electroweak corrections to b→sl+l- This decay is suppressed by two e.w. couplings wrt bsγ : BR ~ α(μ)2 μ= mb or MW ? Difference is 8%! LO and NLO EW effects New O(α),O(ααs) and O(αs) ADM required Paolo Gambino IFAE 14/4/2004

  20. Results for the low q2 region Bobeth,Gorbahn,Haisch,PG Charmonium resonances Safe low q2 region Normalization to sl rate introduces 8% uncertainty from mc We use b->u and evaluate C apart, expand BR in αs to minimize higher orders (pole mass), and reduce considerably error Paolo Gambino IFAE 14/4/2004

  21. Results for the low q2 region what is the best scale for α(µ)2 ? due to cancellations,close to mb New O(α),O(ααs) and O(αs) ADM required Total shift due to new corrections (EW and NNLO): -4.5% Paolo Gambino IFAE 14/4/2004

  22. Error Anatomy for BRll • Mtop dominant error 7% • scale uncertainty 5% • mbpole = 4.80±0.15 GeV →5% • phase space factor 3% • No mc issue as charm enters at LO • TOTAL ERROR ~10% • BUT: mb uncertainty is not • a fundamental limitation • δmbshort distance≈ 30-50 MeV • simply change scheme! EXP: only inclusive rate, WA: (6.2±1.1 ±1.6)x10-6 Ali et al (6.9±1.0)x10-6, Ghinculov et al (4.8±0.8)x10-6 Paolo Gambino IFAE 14/4/2004

  23. The high-q2 tail Now also at NNLO, but more sensitive to power corrections Ghinculov,Hurth,Isidori,Yao Paolo Gambino IFAE 14/4/2004

  24. Model independent contraints on new physics From a combined analysis of inclusive and exclusive b->s transitions 90%CL EMFV susy models Ali et al Paolo Gambino IFAE 14/4/2004

  25. The FB asymmetry ≈ Very sensitive to the way one treats formally NNNLO effects EW effects +3% Paolo Gambino IFAE 14/4/2004

  26. Summary • The study of the flavor problem requires precise tests of the SM flavor structure in rare decays: inclusive modes guarantee the best theory control • Radiative decays have reached maturity. NLO QCD, EW, and non-perturbative effects are routinely included. Theoretically, the challenge is NNLO, which seems to be needed because of charm mass problem. At last we have a lower cut on the photon energy. • Rare semileptonic decays are just developing. More complicated, richer structure. We have completed NNLO and introduced dominant EW effects,reducing th error as in radiative modes. Now we need progress in experiment • Exclusive modes: interesting too, especially ργ/K*γ Paolo Gambino IFAE 14/4/2004

  27. Why are QCD corr. so large? QCD corrections enhance BRγ =BR(B→Xsγ ) by almost factor 4! NLO adds ~30% to LO! Split charm and top contributions to C7: C7(MW)=Kc-Kt Kc= 0.64; Kt=0.45 → BRγ≈1x10-4 NO QCD Resumming Leading Logs makes Kc and Kt run Kt(mb)=0.32 The b mass associated to top loops is a high mass scale The b mass associated to charm loops is low virtuality Once r=mb(MW)/mb is factored out in front of Kt QCD corrections are small, convergence good Paolo Gambino IFAE 14/4/2004

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