The muon g 2: the role of hadronic effects and first lessons from the LHC

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1 The muon g 2: the role of hadronic effects and first lessons from the LHC Fred Jegerlehner fjeger@physik.hu-berlin.de QCD History and Prospects WE-Heraeus Seminar, Oberwölz, Austria, September, 3rd 8th, 2012 F. Jegerlehner Oberwölz, September 2012

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 F. Jegerlehner Oberwölz, September

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 Oberwölz, September

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 Oberwölz, September

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 Oberwölz, September

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 Oberwölz, September

7 a exp e = (28) Gabrielse et al α 1 (a e ) = (331)(68)(46)(24)[0.25ppb] 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 Oberwölz, September

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 about 1000 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 Oberwölz, September

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 Oberwölz, September

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 Oberwölz, September

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 Oberwölz, September

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 Oberwölz, September

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 Oberwölz, September

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 Oberwölz, September

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 Oberwölz, September

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

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

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 Oberwölz, September

19 Normalization as in reality: σ(π 0 π 0 )/σ(π + π ) = 1 2 at the f 2(1270) peak (art work by Mike Pennington) F. Jegerlehner Oberwölz, September

20 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 Oberwölz, September

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: not applied F. Jegerlehner Oberwölz, September

22 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 Oberwölz, September

23 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 Oberwölz, September

24 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) had k ρ q 3λ q 2ν q 1µ Key object full rank-four hadronic vacuum polarization tensor Π µνλρ (q 1, q 2, q 3 ) = 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 ) µ(p) 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 Oberwölz, September

25 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 Oberwölz, September

26 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 Oberwölz, September

27 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 Oberwölz, September

28 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 Oberwölz, September

29 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 Oberwölz, September

30 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)! 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 Oberwölz, September

31 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 Oberwölz, September

32 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 Lattice QCD will provide an answer [take time ( yellow region only?)]! Try exploiting possible new experimental constraints from γγ hadrons F. Jegerlehner Oberwölz, September

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 Oberwölz, September

34 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 Oberwölz, September

35 with M SUSY a typical SUSY loop mass and the sign is determined by the Higgsino mass term µ ( RG improved). 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! muon g 2 in contrast requires moderately light SUSY masses and in the pre-lhc era fitted rather well with expectations from SUSY F. Jegerlehner Oberwölz, September

36 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 Oberwölz, September

37 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 Oberwölz, September

38 Kazakov et al. very recent analysis July 2012 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 Oberwölz, September

39 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 Oberwölz, September

40 likely for me we could have been missing some electromagnetic radiation effects in the relation between observed and calculated quantity! γ γ l γ l + + γ Does real radiation not affect g 2 measurement? Could yield IR finite correction to helicity flip amplitude? 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 Oberwölz, September

41 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 Oberwölz, September

42 also low energy effective RLA of QCD need be further developed. Global fit HLS resonance Lagrangian approch 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 excl. ISR DHea09 (e + e ) ± 5.8 A (e + e +τ) ± 5.3 B (e + e +τ) ± 5.3 experiment BNL-E821 (world average) ± 6.3 [3.6 σ] [2.4 σ] [3.4 σ] [3.3 σ] [3.5 σ] [4.3 σ] [4.1 σ] 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 Oberwölz, September

43 And here we are: BNL CERN III CERN II CERN I th QED 6th 8th 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 Oberwölz, September

44 Muon g 2 remains a key monitor for NP and a great challenge for theorists as well as for experimenters! Thank you for your attention! F. Jegerlehner Oberwölz, September

45 Backup Slides 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 excl. ISR DHea09 (e + e ) ± 5.8 A (e + e +τ) ± 5.3 B (e + e +τ) ± 5.3 experiment BNL-E821 (world average) ± 6.3 [3.6 σ] [2.4 σ] [3.4 σ] [3.3 σ] [3.5 σ] [4.3 σ] [4.1 σ] 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 Oberwölz, September

46 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 Oberwölz, September

47 A new representation for single particle exchange in LbL a µ does not depend on direction of muon momentum p may average in Euclidean space over the directions ˆP: = 1 2π 2 dω( ˆP) Hadronic single particle exchange amplitudes independent of p 2 integrations may be done analytically: amplitudes T i, propagators (4) (P + Q 1 ) 2 + m 2 µ and (5) (P Q 2 ) 2 + m 2 µ with P2 = m 2 µ 1 1 (4)(5) = 1 ( zx ) arctan m 2 µr 12 1 zt (P Q 1 ) 1 (5) = (Q 1 Q 2 ) (1 R m2) 2 8m 2 µ, F. Jegerlehner Oberwölz, September

48 (P Q 2 ) 1 (4) = (Q 1 Q 2 ) (1 R m1) 2 8m 2 µ 1 (4) = 1 R m1 2m 2 µ 1 (5) = 1 R m2 2m 2 µ R mi = 1 + 4m 2 µ/q 2 i, (Q 1 Q 2 ) = Q 1 Q 2 t, t = cos θ, θ= angle between Q 1 and Q 2. Denoting x = 1 t 2, we have R 12 = Q 1 Q 2 x and z = Q 1Q 2 4m 2 µ (1 R m1 ) (1 R m2 ). For any hadronic form-factor end up with 3 dimensional integral over Q 1 = Q 1, F. Jegerlehner Oberwölz, September

49 Q 2 = Q 2 and t = cos θ: a µ (LbL; π 0 ) = 2α3 3π dq 1 dq 2 dt 1 t 2 Q 3 1 Q3 2 1 (F 1 P 6 I 1 (Q 1, Q 2, t) + F 2 P 7 I 2 (Q 1, Q 2, t)) where P 6 = 1/(Q m2 π), and P 7 = 1/(Q m2 π) denote the Euclidean single particle exchange propagators. I 1 and I 2 known integration kernels. The non-perturbative factors are F 1 = F π 0 γ γ (q2 2, q2 1, q2 3 ) F π 0 γ γ(q 2 2, q2 2, 0), F 2 = F π 0 γ γ (q2 3, q2 1, q2 2 ) F π 0 γ γ(q 2 3, q2 3, 0). F. Jegerlehner Oberwölz, September

50 Note: SU(3) flavor decomposition of em current weight factors ( Tr [λa ˆQ 2 ] ) 2 W (a) = Tr [λ 2 a]tr [ ˆQ 4 ] ; W(3) = 1 4, W(8) = 1 12, W(0) = 2 3. where Tr [ ˆQ 4 ] = 2/9 is the overall normalization such that a W (a) = 1. Note (W (8) + W (0) )/W (3) = 3, higher states enhanced in coupling by factor 3! [Melnikov&Vainshtein] overlooked by previous analyzes [HKS,HK,BPP]. Such representations I worked out for axial exchanges as well as for scalar ones. Missing is tensor state, could play similar role as ρ exchange vs scalar QED ππ contribution. F. Jegerlehner Oberwölz, September

51 SUSY and global fits A good SUSY sensitive observable is the W mass given by M 2 W 1 M2 W = MZ 2 πα 2GF (1 + r) ; r = f (α, G F, M Z, m t, ) r model-dependent radiative corrections in SUSY models M W is sensitive to the top/stop sector parameters while sin 2 Θ eff = 1 4 ( 1 Re ) eff a eff remains much less affected Buchmueller et al., Heinemeyer et al. F. Jegerlehner Oberwölz, September

52 for M W SUSY looks favored by data! F. Jegerlehner Oberwölz, September

53 Explanation: Precision predictions M W : sin 2 Θ W = 1 M2 W M 2 Z g 2 : sin 2 Θ g = e 2 /g 2 2 = πα 2 Gµ M 2 W a f : sin 2 1 Θ f = 4 Q f 1 a f : ρ f = 1 ρ ( 1 v f a f ), f ν, independent on α where sin 2 Θ i cos 2 Θ i = πα 2 Gµ M 2 Z 1 1 r i r i = r i (α, G µ, M Z, m H, m f t, m t ) quantum corrections from gauge boson self-energies, vertex and F. Jegerlehner Oberwölz, September

54 box corrections. for the most important cases and the general form of r i reads r i = α f i (sin 2 Θ i ) ρ + r i remainder with a universal term α which affects the predictions for M W, A LR, A f FB, Γ f, etc. while ρ is very process dependent: f W (sin 2 Θ W ) = cos2 Θ W sin 2 Θ W 3.3 ; f g (sin 2 Θ g ) = 1. sensitivity to top/stop sector strongly enhances in M W General: MSSM results merge into SM results for larger SUSY masses, as decoupling is at work. F. Jegerlehner Oberwölz, September

55 SUSY does not yield better global fit! F. Jegerlehner Oberwölz, September

56 Other strong constraints Data on the penguin loop induced B X s γ transition SM prediction B(b sγ) NNLL = (3.15 ± 0.23) 10 4 is consistent within 1.2 σ with the experimental result (HFAG) B(b sγ) = (3.55 ± 0.24 ± 0.09) it implies that SUSY requires heavier m 1/2 and/or m 0 in order not to spoil the good agreement. Data on dark matter relict density Ω CDM h 2 = ± SUSY+R-parity scenarios represent a tough constraint for the relic density of neutralinos produced in the early universe. A DM neutralino is a WIMP DM candidate. The density predicted is Ωh pb ( σ 0.1 MWIMP ) 2, 100GeV F. Jegerlehner Oberwölz, September

57 where σ is the relativistic thermally averaged annihilation cross-section. in most scenarios the dominating neutralino annihilation process is χ + χ A b b and the observed relict density requires the cross section to be tuned to σ cm 3 /s. The cross section is of the form σ tan 2 β m2 b M 2 Z M 4 χ (4M 2 χ M 2 A )2 + M 2 A Γ2 A and has to be adjusted to M χ 1.8 M A to 2.2 M A. On resonance the cross section would be too big, too far off resonance too small. Note that except from Ω CDM all observables prefer heavier SUSY masses such that effects are small by decoupling. F. Jegerlehner Oberwölz, September

58 Is SUSY found? m H = 125 GeV CMS Preliminary s = 7 TeV, L = 5.1 fb s = 8 TeV, L = 5.3 fb -1-1 H bb H ττ H γγ H WW H ZZ Best fit σ/σ SMH Data/SM excess of H γγ while ZZ, WW in accord with SM at both ALTAS and CMS Last weeks paper by Guidice, Paradisi, Strumia arxiv: v1 [hep-ph] F. Jegerlehner Oberwölz, September

59 light maximally mixed stau-loop can accomodate for it (stau in range GeV) peculiar technically unnatural choice of parameters allows to explain δa µ by SUSY. requires higginos above 1 TeV and a light bino as the LSP F. Jegerlehner Oberwölz, September

60 Higgs decay in the MSSM: f = t, b, τ and f = t 1,2, b 1,2, τ 1,2 g h τ1 τ 1 = T τ 3 cos2 θ τ Q τ sin 2 θ W cos 2θ τ m tau 2 M 2 Z g h τ2 τ 2 = T τ 3 sin2 θ τ + Q τ sin 2 θ W cos 2θ τ m tau 2 M 2 Z m τ (A l µ tan β) 2M 2 Z + m τ (A l µ tan β) 2M 2 Z sin 2θ τ sin 2θ τ F. Jegerlehner Oberwölz, September

61 For m τ2 m τ1 and large tan β cos 2θ τ = m2 L m2 R m 2 τ 1 m 2 τ 2 ; sin 2θ τ = 2m τ (A l µ tan β) m 2 τ 1 m 2 τ 2 m 2 τ 1,2 = 1 2 [m 2L + m2r (m 2L m2r ) + 4m2τ (A l µ tan β) 2 ] Γ(h γγ) MSSM Γ(h γγ) SM tau m τµ tan β sin 2θ m 2 τ 1 2 µ m L,R, M 1,2 common slepton/gaugino mass m = m L,R = M 1,2 9 tan β δa µ ( 300 GeV m ) 2 [ µ/ m ] µ/ m + 10 F. Jegerlehner Oberwölz, September

62 Do we need new physics? Stability bound of Higgs potential in SM: Riesselmann, Hambye 1996 SM Higgs remains perturbative up to scale Λ if it is light enough (upper bound=avoiding Landau pole) and Higgs potential remains stable (λ > 0) if Higgs mass is not too light [parameters used: m t = 175[ ] GeV ; α s = 0.118] F. Jegerlehner Oberwölz, September

63 M min = [ M t GeV 1.1 GeV 2.2 α s ] 0.56 GeV [Shapovnikov et al ] for m H 129 GeV vacuum is stable up to the Planck scale, i.e. no new physics need enter Note: The Standard Model (SM), although doing surprisingly well in describing most of the precision data at the quantum level, is incomplete as it does not incorporate dark matter (DM) for example and it has fine tuning problems most notably it predicts a vacuum energy contribution induced by the Higgs condensate which is 50 orders of magnitude too large 1 and also the Higgs mass is not 1 With the Higgs vacuum expectation value = GeV and a Higgs mass of about 125 GeV the contribution from the Higgs mechanism to the vacuum density is ρ vac H = 8 1 m2 H GeV 4 [Dreitlein 1974 ]. With κ = 8πG N /c 2 the contribution to the cosmological constant is given by Λ H = κ ρ vac H cm 2. This compares to the observed value Λ obs = κ ρ crit Ω Λ cm 2. F. Jegerlehner Oberwölz, September

64 protected from being much heavier than other SM particles. As we know all SM states are protected either by chiral or by gauge symmetries, except from the Higgs. Supersymmetry (SUSY) imposing an invariance under the exchange of bosons/fermions with fermions/bosons in a field theory in principle is able to cure these problems. Exact SUSY would not only predict a vanishing cosmological constant, as H = 0 for a supersymmetric Hamiltonian [Haag, Lopuszanski, Sohnius 1974 ], but also vanishing anomalous magnetic moments like a µ exactsusy = 0, or ( B X s γ)exact SUSY = 0 [Ferrara, Remiddi 1974 ]. Another fact: matter in the universe (galaxies, stars, we) are made of 99% srong interaction binding energy! How could we know without knowing QCD? Going to chiral limit would not change much the matter content of the universe though its structure. Has dramatic consequences for evolution of the early universe (quarks and gluons in place of hadrons). Could it be that dark matter is some other type of binding energy e.g. uncharged S U(4) confined singlet states, bosons (would not form star-like objects). F. Jegerlehner Oberwölz, September

65 Upcoming Experiments F. Jegerlehner Oberwölz, September

66 The adventure: F. Jegerlehner Oberwölz, September

67 F. Jegerlehner Oberwölz, September

68 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 Oberwölz, September

69 Muon g 2/EDM at J-PARC: very different concept, working with slow muons F. Jegerlehner Oberwölz, September

70 From: N. Saito KEK F. Jegerlehner Oberwölz, September