Physics of vacuum polarization ... Lectures on the physics of vacuum polarization: from GeV to TeV scale [email protected] www-com.physik.hu-berlin.de/ fjeger/QCD-lectures.pdf ∼ F. JEGERLEHNER University of Silesia, Katowice DESY Zeuthen/Humboldt-Universität zu Berlin Lectures , November 9-13, 2009, FNL, INFN, Frascati supported by the Alexander von Humboldt Foundaion through the Foundation for Polish Science and by INFN Laboratori Nazionale di Frascati F. Jegerlehner INFN Laboratori Nazionali di Frascati, Frascati, Italy –November 9-13, 2009– Physics of vacuum polarization ... Outline of Lecture: ① Introduction, theory tools, non-perturbative and perturbative aspects ② Vacuum Polarization in Low Energy Physics: g 2 − ③ Vacuum Polarization in High Energy Physics: α(MZ ) and α at ILC scales ④ Other Applications and Problems: new physics, future prospects, the role of DAFNE-2 F. Jegerlehner INFN Laboratori Nazionali di Frascati, Frascati, Italy –November 9-13, 2009– Physics of vacuum polarization ... Memories to EURODAFNE, EURIDICE and all that F. Jegerlehner INFN Laboratori Nazionali di Frascati, Frascati, Italy –November 9-13, 2009– Physics of vacuum polarization ... ① Introduction, theory tools, non-perturbative and perturbative aspects 1. Intro SM 2. Some Basics in QFT 3. The Origin of Analyticity 4. Properties of the Form Factors 5. Dispersion Relations 6. Dispersion Relations and the Vacuum Polarization 7. Low Energies: e+e− hadrons → 8. High Energies: the electromagnetic form factor in the SM F. Jegerlehner INFN Laboratori Nazionali di Frascati, Frascati, Italy –November 9-13, 2009– Physics of vacuum polarization ... 1. Introduction Theory is the Standard Model: SU(3) SU(2) U(1) local gauge theory c ⊗ L ⊗ Y broken to SU(3) U(1) QCD ⊗ QED by the Higgs mechanism Yang Mills 1954, Glashow 1961, Weinberg 1967, Gell-Mann, Fritzsch, Leutwyler 1973, Gross, Wilczek 1973, Politzer 1973, Higgs 1964, Englert, Brout 1964, ... Nobel Prize 1999: G. ’t Hooft, M. Veltman; 2003 Politzer, Gross, Wilczek for elucidating the quantum structure of electroweak interactions in physics and for asymptotic freedom F. Jegerlehner INFN Laboratori Nazionali di Frascati, Frascati, Italy –November 9-13, 2009– Physics of vacuum polarization ... Constituents of matter: SU(3)c Spin 1/2 fermions color siglets triplets➜ anti-triplets ν u u u ¯u ¯u ¯u ➜ SU(2) 1st family eL L L L L L L L ¯ ¯ ¯ eL− dL dL dL dL dL dL weak iso-spin doublets sterile νs ➯ νeR uR uR uR ¯uR ¯uR ¯uR weak iso-spin singlets ¯ ¯ ¯ eR− dR dR dR dR dR dR ν 2nd family µL cL cL cL ¯cL ¯cL ¯cL µL− sL sL sL ¯sL ¯sL ¯sL νµR cR cR cR ¯cR ¯cR ¯cR µR− sR sR sR ¯sR ¯sR ¯sR ν ¯ ¯ ¯ 3rd family τL tL tL tL tL tL tL ¯ ¯ ¯ τL− bL bL bL bL bL bL ντR tR tR tR ¯tR ¯tR ¯tR ¯ ¯ ¯ τR− bR bR bR bR bR bR Leptons Quarks F. Jegerlehner INFN Laboratori Nazionali di Frascati, Frascati, Italy –November 9-13, 2009– Physics of vacuum polarization ... Carrier of Forces: Spin 1 Gauge Bosons Photon γ Octet of ⇔ 0 + W − Z W Gluons Vector Bosons “Cooper Pairs”: Higgs Ghosts ϕ0 + Spin 0 Higgs Boson ϕ− ϕ H Higgs Particle t X c X u Also note quark decay pattern: b X s X d Note: The u quark is stable, the s and b quarks are metastable. Flavor changing neutral currents (FCNC) at tree level X are forbidden by the GIM–mechanism. Flavor changing neutral current transitions are allowed, however, as second (or higher) order transitions: e.g. b s is in fact b (u∗, c∗,t∗) s, where the → → → asterix indicates “virtual transition”. F. Jegerlehner INFN Laboratori Nazionali di Frascati, Frascati, Italy –November 9-13, 2009– Physics of vacuum polarization ... Most mysterious SM mass spectrum. Fermions: Quark mass hierarchy: Ø t X c X u × b X s X d Ù Lepton-neutrino mass hierarchy: ντ νµ νe X X e τ X µ X e e Hierarchy of quark (right top) and lepton masses (right bottom) [ log m in arbitrary units] ∼ f F. Jegerlehner INFN Laboratori Nazionali di Frascati, Frascati, Italy –November 9-13, 2009– Physics of vacuum polarization ... SM tests: ❏ High Energy Frontier, e.g top discovery, triple gauge couplings [LEP,HERA,Tevatron,LHC] ❏ Rare Processes, e.g. µ eγ ( L ), neutrino physics [PSI,BNL,Tevatron,Kamiokande,Homestake,SNO] → 6 µ ❏ High Precision Frontier, e.g. m and m bound from LEP, g 2 [LEP,BNL,Harvard,ILC] t H − Many open questions in the Standard Model Standard Model very good description – Less satisfactory explanations ✗ Why 3 families of fundamental fermions ? ✗ Why P, C and CP violations? Why not more CP ? 6 ✗ Why us ? Origin of matter–antimatter asymmetry ? ✗ What Dark Matter ? Why the Cosmological Constant ? F. Jegerlehner INFN Laboratori Nazionali di Frascati, Frascati, Italy –November 9-13, 2009– Physics of vacuum polarization ... ❏ However: most extensions of the SM run into serious problems (FVNC’s, CP): if not tuned!!! (R–parity etc.) impose MFV scheme! (Isidori et al.) ❏ another as serious issue: accidental??? custodial symmetry ρ–parameter constraint! (Veltman,Lynn+Nardi,FJ,Czakon et al.) Cries for new physics but, please, don’t touch at all what we have! In general, SM instable against perturbations! F. Jegerlehner INFN Laboratori Nazionali di Frascati, Frascati, Italy –November 9-13, 2009– Physics of vacuum polarization ... The Parameters of the Standard Model Thomson scattering in four fermion and vector boson processes − − α µ–decay pp,¯ e+e− Gµ MW SU(2) U(1) L ⊗ Y Higgs mechanism unlike in QED and QCD in SM (SBGT) g2, g1, v parameter interdependence 2 sin Θ MZ ☞ W νe, νN pp,¯ e+e− only 3 independent quantities vf , af (besides fermion masses and mixing parameters) e+e− ff¯ α, Gµ, MZ → e+e− e+e− → ⇓ parameter relationships between very precisely measurable quantities precision tests, possible sign of new physics F. Jegerlehner INFN Laboratori Nazionali di Frascati, Frascati, Italy –November 9-13, 2009– Physics of vacuum polarization ... Low Energy Parametrization and VB masses QED and four fermion processes at low energy − − Finestructure constant: e.g. Thomson scattering • 1 α = ( 137.0359895(61) )− Fermi constant: µ–decay • 5 2 G = 1.166389(22) 10− GeV− µ × Higgs mechanism: √ 1 ➤ √ GeV 2Gµ = v2 v = 1/ 2Gµ = 246.22 q Existence of the Higgs condensate verified! γ Z mixing parameter: νN–scattering • − sin2 Θ = 0.231 0.006 W ± ➤ Masses of vector bosons determined F. Jegerlehner INFN Laboratori Nazionali di Frascati, Frascati, Italy –November 9-13, 2009– Physics of vacuum polarization ... A0 MW πα MW = , MZ = ; A0 = sinΘW cosΘW √2Gµ M = 77.570 1.010 GeV M = 88.390q0.810 GeV W ± Z ± Born level prediction! M = 80.403 0.029 GeV M = 91.1876 0.0021 GeV W ± Z ± (UA2, CDF, LEP) (LEP, SLC) Experimental result MW MZ 76 78 80 82 84 86 88 90 92 94 GeV Born approximation “contradicts” data! ➤ Radiative corrections very important! F. Jegerlehner INFN Laboratori Nazionali di Frascati, Frascati, Italy –November 9-13, 2009– Physics of vacuum polarization ... Test of quantum effects Prototype QED: µ γγ γ γ µ form factors vacuum polarization anomalous magnetic Lamb shift → → moment LEP/SLC version of g 2: − 2 2 2 √2GµMZ sin Θcos Θ = πα (1 + δ) SM: renormalizable theory (’t Hooft 1971) ➤ δ uniquely calculable F. Jegerlehner INFN Laboratori Nazionali di Frascati, Frascati, Italy –November 9-13, 2009– Physics of vacuum polarization ... in principle depends on unverified part of theory (couplings and masses) Gauge self couplings: (measured at LEP2) + W γ,Z W + γ,Z γ,Z W − W − Top quark: (discovered at Tevatron some time ago) ¯b t¯ W W γ,Z γ,Z t t Higgs boson: (the hunting is going on) H W, Z W, Z H W, Z W, Z δ ∆r =∆r( α,G , M , M ,m ,m , ) ≡ µ Z H t b ··· very precisely known | {z } F. Jegerlehner INFN Laboratori Nazionali di Frascati, Frascati, Italy –November 9-13, 2009– Physics of vacuum polarization ... ❖ MH unknown, bounds, free parameter (114 GeV < M < 186 GeV and / [160, 170] GeV) H ∈ ❖ mt rather precisely known now (m = 171.3 1.6 GeV) t ± Precision measurement of ∆r ➤ severe restrictions for “unknown physics” ➤ bounds on ∆rnew physics ? Important fact: subleading radiative corrections (beyond running ∆α and ∆ρtop ) are 10 σ effects 2 f e.g. on precision observables like sin Θeff !!! Impact for ∆α: F. Jegerlehner INFN Laboratori Nazionali di Frascati, Frascati, Italy –November 9-13, 2009– Physics of vacuum polarization ... Interference between precision test, new physics contribution and hadronic uncertainty: ❖ ∆α = ∆αlep + ∆αhad ❖ ∆αhad has substantial non-perturbative part from low energy hadrons ❖ Uncertainty δ∆αhad does seriously limit precision of predictions! ❖ Mandatory goal for all kinds of precision tests: precise determination of effective fine structure “constant” ➠ Reduction of hadronic uncertainty crucial! ➧ Some remarkable achievements: F. Jegerlehner INFN Laboratori Nazionali di Frascati, Frascati, Italy –November 9-13, 2009– Physics of vacuum polarization ... TOP mass bound ind +17 mt = 170 10 19 GeV LEP 1995 ± − with 60 GeV <mH < 1000 GeV assumed 2θlept sin eff ± AFB leptons 0.23068 0.00055 Aτ 0.23240 ± 0.00085 ± Ae 0.23264 0.00096 ± AFB b-quark 0.23235 0.00040 ± AFB c-quark 0.23155 0.00111 < > ± QFB 0.23220 0.00100 ± ALR (SLD) 0.23055 0.00041 LEP + SLD 0.23151 ± 0.00022 250 χ2/dof = 15/6 ] 200 ± mZ = 91 186 2 MeV GeV [ t m 150 mH = 70 - 1000 GeV α-1 = 128.90 ± 0.09 100 0.228 0.23 0.232 0.234 2θlept sin eff TOP discovery at Tevatron 1995 mdir = 171.3 1.6 GeV CDF/D0 2009 ⇒ t ± F. Jegerlehner INFN Laboratori Nazionali di Frascati, Frascati, Italy –November 9-13, 2009– Physics of vacuum polarization ..