The muon g 2: the role of hadronic effects at present and in future

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1 The muon g 2: the role of hadronic effects at present and in future Fred Jegerlehner, DESY Zeuthen/Humboldt University Berlin fjeger@physik.hu-berlin.de Determination of the Fundamental Parameters of QCD International Workshop, NANYANG Technological University, Singapore 18 to 21 March, 2013 Due to probelms with validity of my passport (which was valid for 3 more month only in place of 6 as required), my F. Jegerlehner NTU Singapore, March 2013

2 Outline of Talk: Introduction Standard Model Prediction for a µ The hadronic effects and precision limitations Theory vs experiment: do we see New Physics? Implications of low and high energy measurements on SUSY Epilogue trip ended at the Berlin airport, i.e. the talk was not given. F. Jegerlehner NTU Singapore, March

3 Introduction Particle with spin s magnetic moment µ (internal current circulating) µ = g µ e 2m µ c s ; g µ = 2 (1 + a µ ) Dirac: g µ = 2, a µ = α 2π + muon anomaly γ(q) µ(p ) µ(p) Electromagnetic Lepton Vertex [ ] = ( ie) ū(p ) γ µ F 1 (q 2 ) + i σµν q ν 2m µ F 2 (q 2 ) F 1 (0) = 1 ; F 2 (0) = a µ u(p) a µ responsible for the Larmor precession F. Jegerlehner NTU Singapore, March

4 Larmor precession ω of beam of spin particles in a homogeneous magnetic field B µ spin momentum Storage Ring ω a = a µ eb mc actual precession 2 12 /circle Million Events per 149.2ns Time modulo 100µs [µs] Magic Energy: ω is directly proportional to B at magic energy 3.1 GeV ω a = e m [ a µ B ( ) E 3.1GeV a µ 1 β E] γ 2 1 at magic γ e m [ aµ B ] CERN, BNL g-2 experiments Stern, Gerlach 22: g e = 2; Kusch, Foley 48: g e = 2 ( ± ) F. Jegerlehner NTU Singapore, March

5 In a uniform magnetic field, as in muon g 2 experimental setup: a µ = ω a γ ω c = ω a /ω p µ µ /µ p ω a /ω p = R λ R ω p = (e/m p c) B free proton NMR frequency R = ω a /ω p = (20) from E-821 λ = ω L /ω p = µ µ /µ p = from hyperfine splitting of muonium value used by E (10) new value (84) CODATA 2011: [raxiv: v1] change in a µ : a exp µ = ( ± 5.4 ± 3.3[6.3]) updated F. Jegerlehner NTU Singapore, March

6 Standard Model Prediction for a µ What is new? new CODATA values for lepton mass ratios m µ /m e, m µ /m τ spectacular progress by Aoyama, Hayakawa, Kinoshita and Nio on 5 loop QED calculation (as well as improved 4 loop results) O(α 5 ) electron g 2, substantially more precise α(a e ) Complete O(α 5 ) muon g 2, settles better the QED part QED Contribution The QED contribution to a µ has been computed through 5 loops Growing coefficients in the α/π expansion reflect the presence of large ln m µ m e 5.3 terms coming from electron loops. Input: F. Jegerlehner NTU Singapore, March

7 a exp e = (28) Gabrielse et al α 1 (a e ) = (331)(68)(46)(24)[0.25 ppb] Aoyama et al 2012 a QED µ = } (0.029) {{ } (0.009) } {{ } (0.018) } {{ }} (0.007) {{ } [0.36] α inp m e /m µ α 4 The current uncertainty is well below the ± experimental error from E821 # n of loops C i [(α/π) n ] a QED µ (43) (16) (9) (32) (4) (63) (18) (1.04) (7) tot (0.036) α 5 F. Jegerlehner NTU Singapore, March

8 ❶ 1 diagram Schwinger 1948 ❷ 7 diagrams Peterman 1957, Sommerfield 1957 ❸ 72 diagrams Lautrup, Peterman, de Rafael 1974, Laporta, Remiddi 1996 ❹ 871 diagrams Kinoshita 1999, Kinoshita, Nio 2004, Ayoama et al. 2009/2012 ❺ estimates of leading terms Karshenboim 93, Czarnecki, Marciano 00, Kinoshita, Nio 05 all diagrams (fully automated numerical) Ayoama et al F. Jegerlehner NTU Singapore, March

9 Weak contributions W W ν µ + µ µ Z + γ Z W W ν µ ν µ W + + H e, u,d, Z γ + µ Brodsky, Sullivan 67,..., Bardeen, Gastmans, Lautrup 72 Higgs contribution tiny! a weak(1) µ = ( ± 0.02) Kukhto et al 92 potentially large terms G F m 2 µ α π ln M Z mµ Peris, Perrottet, de Rafael 95 quark-lepton (triangle anomaly) cancellation Czarnecki, Krause, Marciano 96 Heinemeyer, Stöckinger, Weiglein 04, Gribouk, Czarnecki 05 full 2 loop result Most recent evaluations: improved hadronic part (beyond QPM) a weak µ = (154.0 ± 1.0[had] ± 0.3[m H, m t, 3 loop]) new: m H known! (Knecht, Peris, Perrottet, de Rafael 02, Czarnecki, Marciano, Vainshtein 02) F. Jegerlehner NTU Singapore, March

10 Hadronic stuff: the limitation to theory General problem in electroweak precision physics: contributions from hadrons (quark loops) at low energy scales Leptons Quarks e, µ, τ < γ γ > γ α : weak coupling pqed u, d, s, < γ g γ > α s : strong coupling pqcd (a) µ µ + γ γ(z) (b) γ γ µ (c) u,d, u,d, γ Z + µ γ + (a) Hadronic vacuum polarization O(α 2 ), O(α 3 ) (b) Hadronic light-by-light scattering O(α 3 ) (c) Hadronic effects in 2-loop EWRC O(αG F m 2 µ) Light quark loops Hadronic blobs F. Jegerlehner NTU Singapore, March

11 Evaluation of a had µ Leading non-perturbative hadronic contributions a had µ can be obtained in terms of R γ (s) σ (0) (e + e γ hadrons)/ 4πα2 3s data via dispersion integral: a had µ = ( αmµ ) 2 ( 3π E 2 cut 4m 2 π ds Rdata γ Data: CMD-2, SND, KLOE, BaBar (s) ˆK(s) + s 2 E 2 cut ds RpQCD γ (s) ˆK(s) ) s 2 Experimental error implies theoretical uncertainty! Low energy contributions enhanced: 75% come from region 4m 2 π < m 2 ππ < M 2 Φ a had(1) µ = (690.7 ± 4.7)[695.5 ± 4.1] e + e data based [incl. BaBar MD09] ρ, ω 1.0 GeV 0.0 GeV, Υ ψ 9.5 GeV 3.1 GeV φ, GeV φ,... ρ, ω 0.0 GeV, 3.1 GeV 2.0 GeV 1.0 GeV F. Jegerlehner NTU Singapore, March

12 Good old idea: use isospin symmetry to include existing high quality τ data (including isospin corrections) e + e τ ν µ γ W γ ū, d u, d isospin rotation W ū d π + π, [I = 1] π 0 π, Corrected data: large discrepancy [ 10%] persists! τ vs. e + e problem! [manifest since 2002] F. Jegerlehner NTU Singapore, March

13 Recent: τ (charged channel) vs. e + e (neutral channel) puzzle resolved F.J.& R. Szafron, ρ γ interference (absent in charged channel): µν (π) iπ γρ (q) = +. 0 (s) = r ργ (s) R IB (s) (s) τ require to be corrected for missing ρ γ mixing! results obtained from e + e data is what goes into a µ F. Jegerlehner NTU Singapore, March

14 τ decays e + e +CVC ALEPH 1997 ALEPH 2005 OPAL 1999 CLEO 2000 Belle 2008 τ combined CMD SND 2006 KLOE 2008 KLOE 2010 BABAR 2009 e + e combined ± 2.65 ± ± 4.00 ± ± 7.27 ± ± 4.11 ± ± 0.53 ± ± 1.42 ± ± 2.76 ± ± 1.40 ± ± 0.34 ± ± 0.71 ± ± 0.37 ± ± 0.87 ± 2.18 a µ [ππ], I = 1, ( ) GeV I=1 part of a had µ [ππ] F. Jegerlehner NTU Singapore, March

15 τ decays e + e +CVC ALEPH 1997 ALEPH 2005 OPAL 1999 CLEO 2000 Belle 2008 τ combined CMD SND 2006 KLOE 2008 KLOE 2010 BABAR 2009 e + e combined ± 2.65 ± ± 4.00 ± ± 7.27 ± ± 4.11 ± ± 0.53 ± ± 1.40 ± ± 2.76 ± ± 1.40 ± ± 0.34 ± ± 0.71 ± ± 0.37 ± ± 0.87 ± 2.18 a µ [ππ], I = 1, ( ) GeV I=1 part of a had µ [ππ] F. Jegerlehner NTU Singapore, March

16 F π (E) 2 in units of e + e I=1 (CMD-2 GS fit) Best proof : F. Jegerlehner NTU Singapore, March

17 F π (E) 2 in units of e + e I=1 (CMD-2 GS fit) Best proof : F. Jegerlehner NTU Singapore, March

18 Is our model viable? How photons couple to pions? This is obviously probed in reactions like γγ π + π, π 0 π 0. Data infer that below about 1 GeV photons couple to pions as point-like objects (i.e. to the charged ones overwhelmingly), at higher energies the photons see the quarks exclusively and form the prominent tensor resonance f 2 (1270). The π 0 π 0 cross section in this figure is enhanced by the isospin symmetry factor 2, by which it is reduced in reality. F. Jegerlehner NTU Singapore, March

19 γ γ π + π+,π0 π π,π 0 ū, d u,d Di-pion production in γγ fusion. At low energy we have direct π + π production and by strong rescattering π + π π 0 π 0, however with very much suppressed rate. Above about 1 GeV, resolved q q couplings seen. Strong tensor meson resonance in ππ channel f 2 (1270) with photons directly probe the quarks! Photons seem to see pions below 1 GeV Photons definitely look at the quarks in f 2 (1270) resonance region We apply the sqed model up to GeV (relevant for a µ ). This should be pretty save (still we assume a 10% model uncertainty) Switching off the electromagnetic interaction of pions, is definitely not a realistic approximation in trying to describe what data we see in e + e π + π F. Jegerlehner NTU Singapore, March

20 New BaBar ISR 2π result: arxiv: v1 10 May 2012 e + e ee BaBar ee KLOE ee CMD-2 ee SND τ τ ALEPH τ CLEO τ OPAL τ Belle a 2π,LO µ γ ρ correction: not applied F. Jegerlehner NTU Singapore, March

21 New BaBar ISR 2π result: arxiv: v1 10 May 2012 e + e ee BaBar ee KLOE ee CMD-2 ee SND τ τ ALEPH τ CLEO τ OPAL τ Belle a 2π,LO µ γ ρ correction: applied F. Jegerlehner NTU Singapore, March

22 a 2π,LO µ [2m π 1.8 GeV]: (514.1 ± 3.8) [BaBar] (507.8 ± 3.2) [ee all] (508.7 ± 2.5) [ee + τ JS] a the µ : (54) [BaBar] (50) [ee all] (46) [ee + τ JS] δa µ = a exp µ a the µ : (224 ± 83) 10 11, 2.7 σ [BaBar] (287 ± 80) 10 11, 3.6 σ, [ee all] (278 ± 78) 10 11, 3.6 σ, [ee + τ JS] F. Jegerlehner NTU Singapore, March

23 The hadronic LbL: setup and problems Hadrons in 0 T{A µ (x 1 )A ν (x 2 )A ρ (x 3 )A σ (x 4 )} 0 γ(k) k ρ had Key object full rank-four hadronic vacuum polarization tensor Π µνλρ (q 1, q 2, q 3 ) = µ(p) q 3λ q 2ν d 4 x 1 d 4 x 2 d 4 x 3 e i (q 1x 1 +q 2 x 2 +q 3 x 3 ) q 1µ µ(p ) non-perturbative physics 0 T{ j µ (x 1 ) j ν (x 2 ) j λ (x 3 ) j ρ (0)} 0. general covariant decomposition involves 138 Lorentz structures of which 32 can contribute to g 2 fortunately, dominated by the pseudoscalar exchanges π 0, η, η,... described by the effective Wess-Zumino Lagrangian F. Jegerlehner NTU Singapore, March

24 generally, pqcd useful to evaluate the short distance (S.D.) tail the dominant long distance (L.D.) part must be evaluated using some low energy effective model which includes the pseudoscalar Goldstone bosons as well as the vector mesons which play a dominant role (vector meson dominance mechanism); HLS, ENJL, general RLA, large N c inspired ansätze, and others Need appropriate low energy effective theory amount to calculate the following type diagrams 83(12) (13) (3) π 0, η, η π ±, K ± q = (u, d, s,...) L.D. L.D. S.D. LD contribution requires low energy effective hadronic models: simplest case π 0 γγ vertex F. Jegerlehner NTU Singapore, March

25 Crystal Ball 1988 u, d g π 0 + π ± u, d } {{ } L.D. } {{ } S.D. Data show almost background free spikes of the PS mesons! Substantial background form quark loop is absent. Clear message from data: fully non-perturbative, evidence for PS dominance. However, no information about axial mesons (Landau-Yang theorem). Illustrates how data can tell us where we are. Low energy expansion in terms of hadronic components: theoretical models vs experimental data KLOE, KEDR, BES, BaBar, Belle,? Basic problem: (s, s 1, s 2 ) domain of F π 0 γ γ (s, s 1, s 2 ); here (0, s 1, s 2 ) plane F. Jegerlehner NTU Singapore, March

26 Two scale problem: open regions??? RLA pqcd??? Data, OPE,??? QCD factorization, Brodsky-Lepage approach One scale problem: no problem RLA pqcd Novel approach: refer to quark hadron duality of large-n c QCD, hadron spectrum known, infinite series of narrow spin 1 resonances t Hooft 79 no matching problem (resonance representation has to match quark level representation) De Rafael 94, Knecht, Nyffeler 02 Constraints for on-shell pions (pion pole approximation) General form factor F π 0 γ γ (s, s 1, s 2 ) is largely unknown F. Jegerlehner NTU Singapore, March

27 The constant e 2 F π 0 γγ(m 2 π, 0, 0) = e2 N c 12π 2 f π = α π f π GeV 1 well determined by π 0 γγ decay rate (from Wess-Zumino Lagrangian); experimental improvement needed! Information on F π 0 γ γ(m 2 π, Q 2, 0) from e + e e + e π 0 experiments e (p t ) 0.30 CELLO e (p b ) γ Q 2 > 0 π 0 Q 2 I F(Q 2 ) I (GeV) CLEO 2 f γ q 2 0 e + e CELLO and CLEO measurement of the π 0 form factor F π 0 γ γ(m 2 π, Q 2, 0) at high space like Q 2. outdated by BABAR? Belle conforms with theory expectations! 0 Q 2 (GeV 2 ) F. Jegerlehner NTU Singapore, March

28 Brodsky Lepage interpolating formula gives an acceptable fit. F π 0 γ γ(m 2 π, Q 2, 0) 1 1 4π 2 f π 1 + (Q 2 /8π 2 fπ 2 ) 2 f π Q 2 Inspired by pion pole dominance idea this FF has been used mostly (HKS,BPP,KN) in the past, but has been criticized recently (MV and FJ07). Melnikov, Vainshtein: in chiral limit vertex with external photon must be non-dressed! i.e. use F π 0 γ γ(0, 0, 0), which avoids eventual kinematic inconsistency, thus no VMD damping result increases by 30%! In g 2 external photon at zero momentum only F π 0 γ γ( Q 2, Q 2, 0) not F π 0 γ γ(m 2 π, Q 2, 0) is consistent with kinematics. Unfortunately, this off shell form factor is not known and in fact not measurable and CELLO/CLEO constraint does not apply!. Obsolete far off-shell pion (in space-like region). F. Jegerlehner NTU Singapore, March

29 e a) (p t ) b) e (p b ) hard µ µ Q 2 γ Q 2 > 0 π soft 0 hard γ hard π 0 hard γ q 2 0 soft γ q 2 0 e + e + Measured is F π 0 γ γ(m 2 π, Q 2, 0) at high space like Q 2, needed at external vertex is F π 0 γ γ( Q 2, Q 2, 0). I still claim using F π 0 γ γ(0, 0, 0) in this case is not a reliable approximation! Need realistic model for off shell form factor F π 0 γ γ( Q 2, Q 2, 0)! Note: F π 0 γ γ( Q 2, Q 2, 0) is a one-scale problem. Self-energy type of problem can get it via dispersion relation from appropriate data Is it really to be identified with F π 0 γ γ(0, 0, 0)? Can we check such questions experimentally or in lattice QCD? F. Jegerlehner NTU Singapore, March

30 Evaluation of a LbL µ in the large-n c framework Knecht & Nyffeler and Melnikov & Vainshtein were using pion-pole approximation together with large-n c π 0 γγ form-factor FJ & A. Nyffeler: relax from pole approximation, using KN off-shell LDM+V formfactor F π 0 γ γ (p2 π, q 2 1, q2 2 ) = F π 3 P(q 2 1, q2 2, p2 π) Q(q 2 1, q2 2 ) P(q 2 1, q2 2, p2 π) = h 7 + h 6 p 2 π + h 5 (q q2 1 ) + h 4 p 4 π + h 3 (q q2 1 ) p2 π +h 2 q 2 1 q2 2 + h 1 (q q2 1 )2 + q 2 1 q2 2 (p2 π + q q2 1 )) Q(q 2 1, q2 2 ) = (q2 1 M2 1 ) (q2 1 M2 2 ) (q2 2 M2 1 ) (q2 2 M2 2 ) all constants are constraint by SD expansion (OPE). Again, need data to fix parameters! F. Jegerlehner NTU Singapore, March

31 Looking for new ideas to get ride of model dependence Need better constrained effective resonance Lagrangian (e.g. HSL and ENJL models vs. RLA of Ecker et al). Global effort needed! recent: HLS global fit available Benayoun et al 2010/12 Lattice QCD will provide an answer [take time ( yellow region only?)]! Try exploiting possible new experimental constraints from γγ hadrons e + e γ γ P, V, S q q π π, K K, T, S qq q q mostly single-tag events: KLOE, KEDR (taggers), BaBar, Belle, BES III (high luminosity) F. Jegerlehner NTU Singapore, March

32 e + e γ V γ P e + e γ V P γ e + e Dalitz-decays: ρ, ω, φ π 0 (η)e + e Novosibirsk, NA60,JLab, Mainz, Bonn, Jülich, BES e + e γ γ P γ γ would be interesting, but is buried in the background F. Jegerlehner NTU Singapore, March

33 Theory vs experiment: do we see New Physics? Contribution Value Error Reference QED incl. 4-loops+5-loops Remiddi, Kinoshita... Leading hadronic vac. pol update Subleading hadronic vac. pol update Hadronic light by light evaluation (J&N 09) Weak incl. 2-loops CMV06 Theory Experiment BNL Updated Exp.- The. 3.3 standard deviations Standard model theory and experiment comparison [in units ]. What represents the 3 σ deviation: new physics? a statistical fluctuation? underestimating uncertainties (experimental, theoretical)? do experiments measure what theoreticians calculate? F. Jegerlehner NTU Singapore, March

34 Most natural New Physics contributions: (examples) a) γ b) c) d) M M f f m µ M 0 [S,P] m µ M 0 [V,A] H X 0 H + X X + X 0 neutral boson exchange: a) scalar or pseudoscalar and c) vector or axialvector, flavor changing or not, new charged bosons: b) scalars or pseudoscalars, d) vector or axialvector Left: m µ = M M 0 Right: m µ M 0 = M F. Jegerlehner NTU Singapore, March

35 In general: a NP µ = α NP m2 µ M 2 NP NP searches (LEP, Tevatron, LHC): typically M NP >> M W, then a exp the µ = a NP µ requires α NP 1 spoiling perturbative arguments. Exception: 2HDM, SUSY tan β enhanced coupling! Note: NP sensitivity enhanced for muon by relative to electron, while a e is only 2250 times more precise than a µ. F. Jegerlehner NTU Singapore, March

36 Implications of low and high energy measurements on SUSY models Most promising New Physics scenario: SUSY a) b) χ χ µ µ ν χ 0 Leading SUSY contributions to g 2 in supersymmetric extension of the SM. m lightest SUSY particle; SUSY requires two Higgs doublets tan β = 1 2, i =< H i > ; i = 1, 2 ; tan β m t /m b 40 [4 40] ( ) a SUSY µ sign(µm 2) α(m Z ) 5 + tan 2 Θ W m 2 ( µ tan β 1 4α 8π sin 2 Θ W 6 π ln M ) SUSY m µ M 2 SUSY F. Jegerlehner NTU Singapore, March

37 with M SUSY a typical SUSY loop mass and the sign is determined by the Higgsino mass term µ ( RG improved). muon g 2 in contrast requires moderately light SUSY masses and in the pre-lhc era fitted rather well with expectations from SUSY a particular role is played by the mass of the light Higgs At tree level in the MSSM m h M Z. This bound receives large radiative corrections from the t/ t sector, which changes the upper bound to (Haber & Hempfling 1990) m 2 h M2 Z cos2 2β + 3 2G µ m 4 t 2π 2 sin 2 β ln ( m t 1 m t 2 m 2 t ) + which in any case is well below 200 GeV. A given value of m h fixes the value of m 1/2 represented by {m t 1, m t 2 } F. Jegerlehner NTU Singapore, March

38 if Higgs is established at 125 GeV (LHC/CERN) we must have m 1/2 > 800GeV or higher! Constraint on large tan β SUSY contributions as a function of M SUSY. The horizontal band shows a NP µ = δa µ. The region left of M SUSY 500 GeV is excluded by LHC searches. If m h 125 ± 1.5 GeV actually M SUSY > 800 GeV depending on details of the stop sector ({ t 1, t 2 } mixing and mass splitting) and weakly on tan β. F. Jegerlehner NTU Singapore, March

39 constraints from LEP, B-physics, g-2, cosmic relict density [plots Olive 09]. m 0 scalar mass m 1/2 gaugino mass F. Jegerlehner NTU Singapore, March

40 After first LHC results: J. Ellis et al. CMSSM F. Jegerlehner NTU Singapore, March

41 J. Ellis et al. [arxiv: ]: The NUHM1,2 and sub-gut models are examples to illustrate that there is no general conflict between the LHC constraints and supersymmetry, even within the MSSM framework. It suffices to relax the constraint of universality of the soft supersymmetry-breaking parameters at the GUT scale, as we have demonstrated in a few types of scenarios. However, it is worth noting that the surviving models in these particular scenarios tend to have quite large sparticle masses, and do not provide a supersymmetric resolution of the g µ 2 discrepancy. with the Higgs found at 125 GeV muon g 2 looks to me in possible trouble. If δa µ is not SUSY, what else? Most other NP scenarios give likely even smaller contributions! At least GUT-SUSY scenarios likely cannot explain it! for m H 125 GeV, to me g 2 looks to be in trouble. If δa µ is not SUSY, what else? most other NP scenarios give likely even smaller contributions! F. Jegerlehner NTU Singapore, March

42 Most MSSM scenarios assume universal scalar masses (sfermions) m 1/2 and universal majorana masses (gauginos) m 0 at GUT scale. To be precise: a µ depends on masses of sneutrino, chargino, smuon and neutralino, only direct constraints on them are unambiguous (less constraint models)! F. Jegerlehner NTU Singapore, March

43 likely for me we could have been missing some electromagnetic radiation effects in the relation between observed and calculated quantity! γ γ γ l γ l Does soft real radiation affect g 2 measurement? Could yield IR finite correction to helicity flip amplitude? No effect in LO Steinmann 2002 equation of motion of a charged Dirac particle in an external field A ext µ (x): ( i γ µ e µ + Q l c γµ (A µ (x) + A ext µ (x)) m l c ) ψ l (x) = 0 ( g µν ( 1 ξ 1) µ ν) A ν (x) = Q l e ψ l (x)γ µ ψ l (x). Dirac equation (1st eq.) solved as a relativistic one particle problem with A µ (x) 0! Need a calculation of such possible effects! F. Jegerlehner NTU Singapore, March

44 Future The big challenge: two complementary experiments: Fermilab with ultra hot muons and KEK with ultra cold muons (very different radiation) to come Provided deviation is real 3σ 9σ possible? Provided theory and needed cross section data improves the same as the muon g 2 experiments! Key: need substantial progress in non-perturbative QCD For muon g 2: main obstacle: hadronic light-by-light progress in evaluating HVP: more data (BaBar, Belle, VEPP 2000, BESIII,...), lattice QCD in reach (recent progress Jansen et al, Wittig et al, Blum et al) in both cases lattice QCD will be the answer one day, F. Jegerlehner NTU Singapore, March

45 also low energy effective RLA of QCD need be further developed. Global fit HLS resonance Lagrangian approach Benayoun et al incl. ISR DHMZ10 (e + e ) ± 4.9 DHMZ10 (e + e +τ) ± 5.4 JS11 (e + e +τ) ± 6.0 HLMNT11 (e + e ) ± 4.9 DHMZ10/JS11 (e + e +τ) ± 4.6 BDDJ13 (e + e +τ) ± 4.9 excl. ISR DHea09 (e + e ) ± 5.8 BDDJ12 (e + e +τ) ± 5.3 experiment BNL-E821 (world average) ± 6.3 [3.6 σ] [2.4 σ] [3.4 σ] [3.3 σ] [3.6 σ] [4.1 σ] [3.5 σ] [4.1 σ] HLS fits a µ Data below E 0 = 1.05 GeV (just above the φ) constrain effective Lagrangian couplings, using 45 different data sets (6 annihilation channels and 10 partial width decays). F. Jegerlehner NTU Singapore, March

46 And here we are: FNAL BNL CERN III CERN II CERN I th QED 6th 8th 10th hadronic VP hadronic LBL weak New Physics??? SM precision a µ uncertainty [ppm] Sensitivity of g 2 experiments to various contributions. The increase in precision with the BNL g 2 experiment is shown as a cyan vertical band. New Physics is illustrated by the deviation (a exp µ a the µ )/a exp µ F. Jegerlehner NTU Singapore, March

47 The challenge: a had,vp µ [LO] (6923 ± 42) ±0.36 ppm a had,vp µ [NLO] ( 98 ± 1) a EW µ (154 ± 1) a had,lbl µ [( ) ± (26 40)] ±0.22 ppm δa exp µ present ±0.54 ppm δa exp µ future ±0.14 ppm Next generation experiments require a factor 4 reduction of the uncertainty optimistically feasible is factor 2 we hope F. Jegerlehner NTU Singapore, March

48 Addendum: Issue and role of QCD and the R data In the focus are the leading hadronic effects in precision observable: the photon VP and the related hadron-production in e + e annihilation encoded in the ratio R(s) = σ tot(e + e γ hadrons) σ(e + e γ µ + µ ) Unitarity predicts a decrease of the total cross section 1/s up to logs at high energies In Germany: plans to construct DORIS e + e storage ring at DESY, leading German theorist try to prevent it as a waste of money, there is nothing to be seen! Experimentalists win, 1969 construction begin, 1974 operation begins. At the dawn of QCD, in 1974 hadron physics looked to be in a deep crisis. F. Jegerlehner NTU Singapore, March

49 The ratio R as of July Cross section measurements at the e + e storage ring ADONE at Frascati, had been measuring hadronic cross sections since 1969, much too high for theoretical expectations at that time. F. Jegerlehner NTU Singapore, March

50 In 1973 two important measurements of R were made at the CEA at Harvard: find R 5 at 4 GeV and R 6 at 5 GeV. Early SLAC SPEAR results show that ADONE and CEA results consistent: showing that previous results were consistent (see Figure). At the London Conference in 1974, the conclusion was that R(s) was raising smoothly form about 2 at 2 GeV to about 6 at 5 GeV. On the theory side confusing situation, about 22 different models were proposed, among them also QCD (Fritzsch&Leutwyler), as a solution of the unitarity crisis. Only talk not mentioned by John Ellis in summary talk. The solution was QCD, providing a factor 3 from color degrees of freedom, and a new species of quark charm, which completed the 2nd family of SM fermions. QCD the Color Octet Picture Fritzsch, Gell-Mann, Leutwyler 1973 F. Jegerlehner NTU Singapore, March

51 Data today vs. QCD prediction F. Jegerlehner NTU Singapore, March

52 Ideal monitor to control the applicability of pqcd is the Adler function D(Q 2 = s) = (12π 2 ) s dπ γ(s) ds = Q 2 4m 2 π R(s) (s + Q 2 ) 2 which on the one hand for, Q 2 not too small, can be calculated in pqcd on the other hand it can be evaluated non-perturbatively in the standard manner using data at lower energies plus pqcd for perturbative regions and the perturbative tail. Application: leading hadronic contribution to muon anomaly a had µ = α 1 π m2 µ 0 dx x (2 x) ( D(Q 2 (x))/q 2 (x) ) where Q 2 (x) x2 1 x m2 µ is the space like square momentum transfer. F. Jegerlehner NTU Singapore, March

53 Experimental Adler function versus theory (pqcd + NP) Experimental data obtained by integrating R had (s). Error includes statistical + systematic here (in contrast to most R-plots showing statistical errors only)! Plots based on pqcd in BF-MOM scheme cut at 1 GeV: Curvature (in perturbative region) almost entirely due to mass effects. Very sensitive to precise values of m c and m b! F. Jegerlehner NTU Singapore, March

54 Plots as above with BF-MOM couplings replaced by APT couplings. (Eidelman, F.J., Kataev, Veretin 98, FJ 12 update (BESII, CMD-2, KLOE, BABAR)) theory based on results by Chetyrkin, Kühn et al., Analytic Perturbation Theory (APT), Shirkov, Solovstov et al. full 3-loop massive pqcd (supplemented with 4- and 5-loop massless contributions [helps mainly at larger momenta]) works very well for scales µ 2 GeV. F. Jegerlehner NTU Singapore, March

55 Some observations: quark-hadron duality is an exact property of large N c QCD, likely realized approximately for appropriate observables in real QCD (but large N c QCD not known quantitatively). quark-hadron duality prefect in space-like region for scales µ 2 GeV. quark-hadron duality σ(e + e hadrons)(s) q σ(e + e q q)(s), only is useful for scales where pqcd works, quark production cross-section not known and probably ill-defined below 2 GeV. quark-hadron duality looks to work fine in charm and bottom resonance regions (non-perturbative windows in between perturbative regions) non-perturbative effects accessible to OPE are too small in regions where pqcd works (i.e. effects become relevant only where pqcd stops to converge) APT does not improve the region of validity of pqcd. F. Jegerlehner NTU Singapore, March

56 quark-hadron duality in data only to the extend that non-qed effects are small, e.g. γ ρ mixing inherent in experimental e + e data note: even if quark-hadron duality is at work it usually does not apply to weighted integrals appearing in dispersion relations (a had µ, αhad,...). Adler function monitored QCD best way to use pqcd in a controlled way. Be aware: not knowing QCD would make precise predictions like the one for the muon g 2 impossible! QCD which is encoding physics in terms of field describing the stuff in the early universe (quarks and gluons) rather than the very different interpolating fields of physical states (nucleons, mesons,...) is as revolutionary in particle physics as BCS theory was in condensed matter physics! After 40 years still the challenge for theory: quantify strong interaction physics in terms of the QCD Lagrangian. pqcd, CHPT, lattice QCD, CHRLA,... F. Jegerlehner NTU Singapore, March

57 The role of QCD in high precision physics: α from a e Example: the electron g 2: a exp e = (28) Gabrielse et al α 1 (a e ) = (331)(68)(46)(24)[0.25 ppb] Aoyama et al 2012 Most precise non-a e determination α 1 (Rb11) = (91)[0.66 ppb] yields (QED-test!) a exp e a the e = 1.13(0.82) Total hadronic contribution: a had e a had e = a (4) e (vap, had) + a (6) e (vap, had) + a e (LbL, had) (1.834 ± ± 0.005) a had e = 1.652(13) relevant now, save only due to the fact the high energy tail of the dispersion integral is controlled by QCD (AF). F. Jegerlehner NTU Singapore, March

58 Best determination of fine structure constant: a QED e (α) = N n=1 C n (α/π) n ; N = 5 a exp e = a QED e (α) + a had e result α(a e ) given above At present precision weak contributions a weak e = not relevant. so QCD plays role in the determination of the most fundamental constant α em but even more in the running α em (s) = α em (0)/(1 α(s)) α (5) had (M2 Z ) = ± [ ± ], α 1 (MZ 2 ) = ± [ ± 0.030], evaluated in Adler function approach [in braces standard evaluation]. F. Jegerlehner NTU Singapore, March

59 Related problem high energy vs early universe before QCD: Broniowski et al How many hadrons? Density of hadron mass states dn/dm increases exponentially: dn dm Ma exp M/T H (T H 2 K = 170 MeV) F. Jegerlehner NTU Singapore, March

60 QCD: replace hadrons (numerous messy) by quarks and gluons (few simple) QCD asymptotic freedom high energy limit under control Politzer, Gross & Wilczek 1972 Cosmological phase transition... hadrons melt to quark-gluon plasma...when the universe cools down below 175 MeV, 10 5 seconds after the big bang... Quarks and gluons form baryons and mesons that s what theoreticians still try to understand and to quantify. Before [QCD] we could not go back further than 200,000 years after the Big Bang. Today since QCD simplifies at high energy, we can extrapolate to very early times when nucleons melted to form a quark-gluon plasma. David Gross F. Jegerlehner NTU Singapore, March

61 FIN Muon g 2 remains a key monitor for NP and a great challenge for theorists as well as for experimenters! QCD plays a key role in the prediction of high precision observables like the muon g 2 pqcd tells us unambiguously the high energy tails (beyond accessibility to experiments) non-perturbative low energy QCD regime still is one of the biggest challenges to theory F. Jegerlehner NTU Singapore, March

62 High precision experimental data, like R(s), are very difficult to get (extracting experimental results also depend on status of theory; also requires improved high precision radiative corrections) photon radiation from hadrons remains a building lot lattice QCD is on the way to solve many problems in future. Can unambiguously isolate strong interaction effects, from the electroweak ones, which cannot be switched off in experiments. Thank you for your attention! F. Jegerlehner NTU Singapore, March

63 How much pqcd? Backup Slides Method range [GeV] pqcd Standard approach: (0.02) My choice (0.04) (0.06) Standard approach: (0.07) Davier et al (0.05) (0.12) Adler function controlled: (0.00) (0.00) (1.03) M Z M Z 0.38(0.00) (1.03) F. Jegerlehner NTU Singapore, March

64 Summary concerning the role of ρ γ mixing VMD+sQED EFT understood as the tail of the more appropriate resonance Lagrangian approach (Ecker et al. 1989) in low energy ππ production yields proper ρ propagator self-energy effects for GS form factor (ρ ππ) pion-loop effects in ρ γ mixing contributes sizable interferences Note: so far PDG parameters masses, widths, branching fractions etc. of resonances like ρ 0 all extracted from data assuming GS like form factors (model dependent!) Pattern: moderate positive interference (up to +5%) below ρ, substantial negative interference (-10% and more) above the ρ (must vanish at s = 0 and s = M 2 ρ ) F. Jegerlehner NTU Singapore, March

65 remarkable agreement with pattern of e + e vs τ discrepancy shift of the τ data to lie perfectly within the ballpark of the e + e data Lesson: effective field theory the basic tool (not ad hoc pheno. ansätze) ρ γ correction function r ργ (s) entirely fixed from neutral channel τ data provide independent information What does it mean for the muon g 2? it looks we have fairly reliable model to include τ data to improve a had µ there is no τ vs. e + e alternative of a had µ For the lowest order hadronic vacuum polarization (VP) contribution to a µ we find a had,lo µ [e, τ] = (1.06)(4.63) (e + τ) F. Jegerlehner NTU Singapore, March

66 a the µ = (60) a exp µ = (54)(33) a exp µ a the µ = (283 ± 87) σ Höcker 2010 (theory-driven analysis) a had,lo a had,lo µ [e] = (692.3 ± 1.4 ± 3.1 ± 2.4 ± 0.2 ± 0.3) (e + e based), µ [e, τ] = (701.5 ± 3.5 ± 1.9 ± 2.4 ± 0.2 ± 0.3) (e + e +τ based), Note: ratio F 0 (s)/f (s) could be measured within lattice QCD, without reference to sqed or other hadronic models. Do it! Including ω, φ, ρ, ρ, requires to go to appropriate Resonance Lagrangian extension (e.g HLS model Benayoun et al.) F. Jegerlehner NTU Singapore, March

67 M. Benayoun et al. HLS effective resonance Lagrangian model global fits incl. ISR DHMZ10 (e + e ) ± 4.9 DHMZ10 (e + e +τ) ± 5.4 JS11 (e + e +τ) ± 6.0 HLMNT11 (e + e ) ± 4.9 DHMZ10/JS11 (e + e +τ) ± 4.6 BDDJ13 (e + e +τ) ± 4.9 excl. ISR DHea09 (e + e ) ± 5.8 BDDJ12 (e + e +τ) ± 5.3 experiment BNL-E821 (world average) ± 6.3 [3.6 σ] [2.4 σ] [3.4 σ] [3.3 σ] [3.6 σ] [4.1 σ] [3.5 σ] [4.1 σ] HLS fits a µ Data below E 0 = 1.05 GeV (just above the φ) constrain effective Lagrangian couplings, using 45 different data sets (6 annihilation channels and 10 partial width decays). F. Jegerlehner NTU Singapore, March

68 Effective theory predicts cross sections: π + π, π 0 γ, ηγ, η γ, π 0 π + π, K + K, K 0 K 0 (83.4%), Missing part: 4π, 5π, 6π, ηππ, ωπ and regime E > E 0 evaluated using data directly and pqcd for perturbative region and tail Including self-energy effects is mandatory (γρ-mixing, ρω-mixing..., decays with proper phase space, energy dependent width etc) Method works in reducing uncertainties by using indirect constraints Able to reveal inconsistencies in data. In our case in region [1.00,1.05] GeV tension between KK and 3π data sets. All data: Solution A 71.2% CL; excluding 3π above 1 GeV: Solution B 97.0% CL. Conflict in data?, model? Singling out effective resonance Lagrangian by global fit is expected to help in improving EFT calculations of hadronic light-by-light scattering (such concept so far missing) F. Jegerlehner NTU Singapore, March

69 Upcoming Experiments F. Jegerlehner NTU Singapore, March

70 The adventure: F. Jegerlehner NTU Singapore, March

71 F. Jegerlehner NTU Singapore, March

72 δa µ = by 2015 The new muon g 2: Fermilab E989 Magnetic field: δ B µ B µ Requires 10% error on HLbL HLbL white paper in progress Present: a exp µ = (63) ; a SM µ = ± E989: statistics 21 ; total error factor 4 } more precise σ stat = 0.1 ppm σ σ syst = 0.1 ppm tot = 0.14 ppm a exp µ = x xxx(16) F. Jegerlehner NTU Singapore, March

73 Muon g 2/EDM at J-PARC: very different concept, working with slow muons F. Jegerlehner NTU Singapore, March

74 From: N. Saito KEK F. Jegerlehner NTU Singapore, March