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1 α QED, eff (s) for precision physics at the FCC-ee/ILC Fred Jegerlehner Zeuthen and 11th FCC-ee workshop: Theory and Experiments, 8-11 January 2019, CERN Geneva F. Jegerlehner FCCee Workshop, CERN Geneva, January 2019

2 Outline of Talk: 1. α QED,eff (MZ 2 ) in precision physics (precision physics limitations) 2. Reducing uncertainties via the Euclidean split trick: Adler function controlled pqcd 3. Prospects for future improvements 4. Need for space-like α QED,eff (t) 5. Conclusions Appendix: The coupling α 2, M W and sin 2 Θ f F. Jegerlehner FCCee Workshop, CERN Geneva, January

3 1. α(mz 2 ) in precision physics (precision physics limitations) Uncertainties of hadronic contributions to effective α are a problem for electroweak precision physics: besides top Yukawa y t and Higgs self-coupling λ α, G µ, M Z most precise input parameters precision predictions sin 2 Θ f, v f, a f, M W, Γ Z, Γ W, 50% non-perturbative α(m Z ), G µ, M Z best effective input parameters for VB physics (Z,W) etc. δα α δgµ Gµ δm Z M Z δα(m Z ) α(m Z ) (present : lost 10 5 in precision!) δα(m Z ) α(m Z ) (FCC ee/ilc requirement) LEP/SLD: sin 2 Θ eff = (1 v l /a l )/4 = ± δ α(m Z ) = δ sin 2 Θ eff = ; δm W /M W affects most precision tests and new physics searches!!! δm W M δm, H W M , H For pqcd contributions very crucial: precise QCD parameters α s, m c, m b, m t Lattice-QCD F. Jegerlehner FCCee Workshop, CERN Geneva, January δmt Mt

4 Relevance of α(m 2 Z ) The Parameters of the Standard Model in four fermion and vector boson processes µ-decay Thomson scattering e + e, ep, p ( p ) G µ α α s M Z p ( p, ) e + e Z in addition QCD coupling α s, y t vs. M t, λ H vs. M H unlike in QED and QCD in SM (SBGT) parameter interdependence only 6 independent quantities (besides fermion masses and mixing parameters) α, G µ, M Z α eff (MZ 2 ) large hadronic correction sin 2 Θ i cos 2 Θ i = π α 2 G µ M 2 Z νe, νn e + e e + e sin 2 Θ W 1 1 r i ; r i = r i ( α, G µ, M Z, m H, m f t, m t ) y t λ SU(2) L U(1) Y Higgs mechanism g 2, g 1, v y t, λ,... v f, a f e + e f f e + e e + e M W M t M H p ( p, ) e + e H p ( p, ) e + e W + W p ( p, ) e + e t t parameter relationships between very precisely measurable quantities precision tests, possible sign of new physics non-perturbative α (5) had (M2 Z ) is limiting precision predictions λ = 3 2G µ M 2 H (1 + δ H( α, )) ; y 2 t = 2 2G µ M 2 t (1 + δ t ( α, ) Note: 30 SD disagreement between SM prediction and experiment when subleading corrections are dropped! F. Jegerlehner FCCee Workshop, CERN Geneva, January

5 SM extrapolation up to Planck scale? After LHC Higgs discovery: Higgs vacuum stability issue! Need very precise SM parameters: g, g, g s, y t, λ Riesselmann, Hambye 1996 first 2-loop analysis knowing M t LHC The SM dimensionless couplings in the MS scheme as a function of the renormalization scale for M H = GeV. proper effective parameters affect early cosmology, inflation, reheating etc. F. Jegerlehner FCCee Workshop, CERN Geneva, January

6 perturbation expansion works up to the Planck scale! no Landau pole or other singularities, Higgs potential remains (meta)stable! U(1) Y screening (IR free), S U(2) L, S U(3) c antiscreening (UV free): g 1, g 2, g 3 as expected (standard wisdom) Top Yukawa y t and Higgs λ : screening if standalone (IR free, like QED) as part of SM, transmutation from IR free to UV free As SM couplings are as they are: QCD dominance in top Yukawa RG requires g 3 > 3 4 y t, top Yukawa dominance in Higgs RG requires λ < 3 ( 5 1) 2 y 2 t in the gaugeless (g 1, g 2 = 0) limit. In the focus: does Higgs self-coupling stay positive λ > 0 up to Λ Pl? the key question/problem concerns the size of the top Yukawa coupling y t decides about stability of our world! [λ = 0 would be essential singularity!] Will be decided by: more precise input parameters better established EW matching conditions direct measurements of y t and λ at future e + e -colliders F. Jegerlehner FCCee Workshop, CERN Geneva, January

7 JKK On-Shell vs MS parameter matching the big issue is the very delicate conspiracy between SM couplings : precision determination of parameters more important than ever the challenge for LHC and ILC/FCC: precision values for λ, y t and α s, and for low energy hadron facilities: more precise hadronic cross sections to reduce hadronic uncertainties in α(m Z ) and α 2 (M Z ) New gate to precision cosmology of the early universe! F. Jegerlehner FCCee Workshop, CERN Geneva, January

8 Shaposnikov et al., Degrassi et al. matching the big issue is the very delicate conspiracy between SM couplings : precision determination of parameters more important than ever the challenge for LHC and ILC/FCC: precision values for λ, y t and α s, and for low energy hadron facilities: more precise hadronic cross sections to reduce hadronic uncertainties in α(m Z ) and α 2 (M Z ) New gate to precision cosmology of the early universe! F. Jegerlehner FCCee Workshop, CERN Geneva, January

9 R-data Evaluation of α(m 2 Z ) Non-perturbative hadronic contributions α (5) had (s) = ( Π γ(s) Π γ(0) ) can be evaluated in terms of σ(e + e hadrons) data via dispersion integral: where γ α (5) s had (s) = α 3π had Π had γ (q 2 ) ( + P P E 2 cut 4m 2 π E 2 cut ds Rdata γ (s ) s (s s) ds RpQCD γ (s ) s (s s) R γ (s) σ(0) (e + e γ hadrons) 4πα 2 γ γ 3s had σtot had (q 2 ) hadronic vacuum polarization 2 ) 5.2 GeV 9.5 GeV Υ 13.GeV 3.1 GeV 2.0 GeV ψ φ p-qcd ρ, ω 1.0 GeV 0.0 GeV, α(s) = α 1 α(s) ; α(s) = α lep(s) + α (5) had (s) + α top(s) F. Jegerlehner FCCee Workshop, CERN Geneva, January

10 Still an issue in HVP region 1.2 to 2 GeV data; test-ground exclusive vs inclusive R measurements (more than 30 channels!) VEPP-2000 CMD-3, SND (NSK) scan, BaBar, BES III radiative return! still contributes 50% of uncertainty excl. vs incl. clash illustrating progress by BaBar and NSK exclusive channel data vs new inclusive data by KEDR. Why point at 1.84 GeV so high? F. Jegerlehner FCCee Workshop, CERN Geneva, January

11 Present situation: (after KLOE, BaBar and first BESIII results) α (5) hadrons (M2 Z ) = ± ± Adler α 1 (MZ 2 ) = ± ± Adler Possible improvements: direct dispersion integral requires reducing error of R(s) to 1% up to above Υ resonances (likely nobody will do that) Euclidean split method (Adler) requires improvement of 1 to 2 GeV exclusive region (NSK,Belle II can top what BaBar has achieved) improved pqcd Adler function massive 4-loop, better parameters m c and m b besides α s (profiting from activities going on anyway, FCC-ee/ILC further strong motivation) F. Jegerlehner FCCee Workshop, CERN Geneva, January

12 α QED,eff : time-like vs. space-like Real α Exp data Th.pred. for Re α=re α lep 0.03 Th.pred. for Re α=re α lep+had s (GeV) Im α Exp data Th.pred. for Im α=im α lep 0.03 Th.pred. for Im α=im α lep+had Energy (GeV) KLOE 2016, arxiv: α QED,eff duality: α QED,eff (s) is varying dramatically near resonances, but agrees quite well in average with space-like version. Locally ill-defined near OZI suppressed meson decays: J/ψ, ψ 1, Υ 1,2,3! Dyson series not convergent. F. Jegerlehner FCCee Workshop, CERN Geneva, January

13 α had (MZ 2 ) results from ranges: for M Z = GeV in units update in terms of e + e -data and pqcd. 43% data, 57% perturbative QCD. pqcd is used between 5.2 GeV and 9.5 GeV and above 11.5 GeV. final state range (GeV) α (5) had 104 (stat) (syst) [tot] rel abs ρ ( 0.28, 1.05) ( 0.05) ( 0.18)[ 0.19] 0.6% 1.4% ω ( 0.42, 0.81) 3.10 ( 0.04) ( 0.08)[ 0.09] 3.0% 0.3% φ ( 1.00, 1.04) 4.76 ( 0.07) ( 0.11)[ 0.13] 2.7% 0.7% J/ψ ( 0.60) ( 0.67)[ 0.90] 7.2% 32.1% Υ 1.30 ( 0.05) ( 0.07)[ 0.09] 6.9% 0.3% had ( 1.05, 2.00) ( 0.06) ( 0.83)[ 0.83] 5.0% 27.4% had ( 2.00, 3.20) ( 0.08) ( 0.61)[ 0.62] 4.0% 15.2% had ( 3.10, 3.60) 4.98 ( 0.03) ( 0.09)[ 0.10] 1.9% 0.4% had ( 5.20, 5.20) ( 0.12) ( 0.21)[ 0.25] 0.0% 2.4% pqcd ( 5.20, 9.46) ( 0.12) ( 0.25)[ 0.03] 0.1% 0.0% had ( 9.46,11.50) ( 0.07) ( 0.69)[ 0.69] 6.2% 19.2% pqcd (11.50, ) ( 0.00) ( 0.05)[ 0.05] 0.0% 0.1% data ( 0.28,11.50) ( 0.63) ( 1.45)[ 1.58] 1.0% 0.0% total ( 0.63) ( 1.45)[ 1.58] 0.6% 100.0% F. Jegerlehner FCCee Workshop, CERN Geneva, January

14 Correlation between different contributions to a had had (5) µ and α a µ (δ a µ ) 2 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 contribution error 2 α had (M Z ) ( δ α had (M Z ) ) GeV 3.1 GeV ψ 2.0 GeV 1.0 GeV φ 3.1 GeV 2.0 GeV φ 9.5 GeV Υ ρ, ω 0.0 GeV, ψ ρ, ω 1.0 GeV 0.0 GeV, 13. GeV 13.GeV p-qcd Υ 5.2/9.5 GeV contribution error 2 Contributions from e + e data ranges and form pqcd to a had µ and α had (5). F. Jegerlehner FCCee Workshop, CERN Geneva, January

15 2. Reducing uncertainties via the Euclidean split trick: Adler function controlled pqcd experiment side: new more precise measurements of R(s) theory side: α em (MZ 2 ) by the Adler function controlled approach α(m 2 Z ) = αdata ( s 0 ) + [ α( M 2 Z ) α( s 0) ] pqcd + [ α(m 2 Z ) α( M 2 Z )] pqcd data pqcd Adler pqcd HVP the space-like s 0 is chosen such that pqcd is well under control for s < s 0 ; offset α data ( s 0 ) integrated R(s) data the Adler function is i) the monitor to control the applicability of pqcd and ii) pqcd part [ α( M 2 Z ) α( s 0) ] pqcd by integrated Adler function D(Q 2 ) small remainder [ α(m 2 Z ) α( M2 Z )] pqcd by calculation of VP function Π γ (s) F. Jegerlehner FCCee Workshop, CERN Geneva, January

16 α had Adler function controlled use old idea: Adler function: Monitor for comparing theory and data D( s) 3π α s d ds α had(s) = ( 12π 2) s dπ γ(s) D(Q 2 ) = Q 2 ( E2 cut 4m 2 π ds R(s)data ( s + Q 2 ) 2 + E 2 cut ds R pqcd (s) (s + Q 2 ) 2 ds ). pqcd R(s) pqcd D(Q 2 ) very difficult to obtain smooth simple function in theory in Euclidean region Conclusion: time-like approach: pqcd works well in perturbative windows GeV, GeV and Kühn,Harlander,Steinhauser space-like approach: pqcd works well for Q 2 = q 2 > 2.0 GeV (see plot) F. Jegerlehner FCCee Workshop, CERN Geneva, January

17 Experimental Adler function versus theory (pqcd + NP) Error includes statistical + systematic here (in contrast to most R-plots showing statistical errors only)! Update spring 2017 pqcd (Eidelman, F. J., Kataev, Veretin 98, FJ 08/17 updates) theory based on results by Chetyrkin, Kühn et al. F. Jegerlehner FCCee Workshop, CERN Geneva, January

18 pqcd works well controlled to predict D(Q 2 ) down to s 0 = (2.0 GeV) 2 ; use this to calculate α had ( Q 2 ) α dq 2 D(Q 2 ) 3π Q 2 α (5) had ( M2 Z ) = [ α (5) had ( M2 Z ) α(5) had ( s 0) ] pqcd + α (5) had ( s 0) data and obtain, for s 0 = (2.0 GeV) 2 : (FJ 98/17) α (5) had ( s 0) data = ± α (5) had ( M2 Z ) = ± α (5) had (M2 Z ) = ± shift from the 5-loop contribution error ± added in quadrature form perturbative part QCD parameters: α s (M Z ) = (20), m c (m c ) = 1.286(13) [M c = 1.666(17)] GeV, m b (m c ) = 4.164(25) [M b = 4.800(29)] GeV based on a complete 3 loop massive QCD analysis Kühn et al 2007 F. J., Nucl. Phys. Proc. Suppl (2008) 135 F. Jegerlehner FCCee Workshop, CERN Geneva, January

19 α had ( M0 2 ) results from ranges: for M 0 = 2 GeV in units update in terms of e + e -data and pqcd. 94% data, 6% perturbative QCD. pqcd is used between 5.2 GeV and 9.5 GeV and above 11.5 GeV. final state range (GeV) α (5) had ( M2 0 ) 104 (stat) (syst) [tot] rel abs ρ ( 0.28, 1.05) ( 0.04) ( 0.16)[ 0.16] 0.5% 6.6% ω ( 0.42, 0.81) 2.69 ( 0.03) ( 0.07)[ 0.08] 3.0% 1.6% φ ( 1.00, 1.04) 3.78 ( 0.05) ( 0.09)[ 0.10] 2.7% 2.6% J/ψ 3.21 ( 0.15) ( 0.15)[ 0.21] 6.7% 11.4% Υ 0.05 ( 0.00) ( 0.00)[ 0.00] 6.8% 0.0% had ( 1.05, 2.00) ( 0.04) ( 0.49)[ 0.49] 4.8% 61.2% had ( 2.00, 3.20) 6.06 ( 0.03) ( 0.25)[ 0.25] 4.2% 16.1% had ( 3.10, 3.60) 1.31 ( 0.01) ( 0.02)[ 0.03] 1.9% 0.2% had ( 5.20, 5.20) 2.90 ( 0.02) ( 0.02)[ 0.03] 0.0% 0.2% pqcd ( 5.20, 9.46) 2.66 ( 0.02) ( 0.02)[ 0.00] 0.1% 0.0% had ( 9.46,11.50) 0.39 ( 0.00) ( 0.02)[ 0.02] 5.7% 0.1% pqcd (11.50, ) 0.90 ( 0.00) ( 0.00)[ 0.00] 0.0% 0.0% data ( 0.28,11.50) ( 0.18) ( 0.61)[ 0.63] 1.0% 0.0% total ( 0.18) ( 0.61)[ 0.63] 1.0% 100.0% F. Jegerlehner FCCee Workshop, CERN Geneva, January

20 Of α (5) had (M2 Z ) 22% data, 78% pqcd! α had ( 2 GeV) ( δ α had ( 2 GeV) ) GeV φ ρ, ω ψ Υ 0.0 GeV, 13.GeV 9.5 GeV 5.2 GeV φ ρ, ω ψ 1.0 GeV 0.0 GeV, 5.2 GeV 3.1 GeV 2.0 GeV 3.1 GeV 2.0 GeV contribution error 2 α had (M Z ) ( δ α had (M Z ) ) GeV 3.1 GeV ψ 2.0 GeV 1.0 GeV φ 3.1 GeV 2.0 GeV φ 9.5 GeV Υ ρ, ω 0.0 GeV, ψ ρ, ω 1.0 GeV 0.0 GeV, 13. GeV 13.GeV p-qcd Υ 5.2/9.5 GeV contribution error 2 Contributions from e + e data ranges and form pqcd to α (5) had ( M2 0 ) vs. α(5) had (M2 Z ). F. Jegerlehner FCCee Workshop, CERN Geneva, January

21 [86%,13%] [52%,47%] [57%,42%] [18%,81%] [84%,15%] [84%,15%] [56%,43%] [16%,83%] [84%,15%] [29%,70%] [20%,79%] [20%,79%] [56%,43%] [54%,45%] [38%,41%] [26%,73%] [50%,49%] [29%,70%] [45%,54%] [21%,77%] % [ αhad data/ αtot had, αpqcd had / α tot How much pqcd? had ] in % Jegerlehner 1985 Lynn et al Burkhardt et al Martin, Zeppenfeld 1994 Swartz 1995 Eidelman, Jegerlehner 1995 Burkhardt, Pietrzyk 1995 Adel, Yndurain 1995 Alemany, Davier, Höcker 1997 Kühn, Steinhauser 1998 Davier, Höcker 1998 Erler 1998 Burkhardt, Pietrzyk 2001 Hagiwara et al 2004 Jegerlehner 2006 direct Jegerlehner 2006 Adler Hagiwara et al Davier et al Jegerlehner 2016 direct Jegerlehner 2016 Adler data-driven theory-driven fifty-fifty low energy weighted data Note: the Adler function monitored Euclidean data vs pqcd split approach is only moderately more pqcd-driven, than the time-like approach adopted by Davier et al. and others. F. Jegerlehner FCCee Workshop, CERN Geneva, January

22 3. Prospects for future improvements Note: new muon g 2 experiments at Fermilab and JPARC trigger continuation of e + e hadrons cross section measurements in low energy region by VEPP 2000 at Novosibirsk, BES III Beijing, Belle II at KEK. This automatically helps improving split trick approach (Adler function controlled) direct DR approach requires precise data up to much higher energies or heavy reliance on pqcd calculation of time-like R(s)! Mandatory pqcd improvements required are: 4 loop massive pqcd calculation of Adler function; required are a number of terms in the low and high momentum series expansions which allow for the appropriate Padé improvements [essentially equivalent to a massive 4 loop calculation of R(s)]; m c, m b improvements by sum rule and/or lattice QCD evaluations; improved α s in low Q 2 region above the τ mass. Theory: (QCD parameters) has to improve by factor 10! ±0.20 F. Jegerlehner FCCee Workshop, CERN Geneva, January

23 Settling the HVP issue for a µ settles it largely for α( M 2 0 ) Error profiles (standard approach): % a had µ GeV % α (5) had ( M2 0) GeV % α (5) 30 had (M2 Z ) GeV Contributions to the total error from different energy regions to the hadronic lowest order vacuum polarization contribution to a µ, α(m 2 Z ) and α( M2 0 ) for M 0 = 2 GeV in percent. These errors are to be added in quadrature to get the total uncertainty. The graph illustrates where experimental effort is needed in order to get a better precision. F. Jegerlehner FCCee Workshop, CERN Geneva, January

24 The virtues of Adler function approach are obvious: no problems with physical threshold and resonances pqcd is used only where we can check it to work (Euclidean, Q 2 > 2.0 GeV). no manipulation of data, no assumptions about global or local duality. non perturbative remainder α (5) had ( s 0) is mainly sensitive to low energy data!!! α( M0 2 ) would be directly accessible in MUonE experiment (project) and lattice QCD. What can we achieve: F. Jegerlehner FCCee Workshop, CERN Geneva, January

25 direct ± 0.90 e + e Davier et al ± 1.11 e + e Keshavarzi et al ± 1.57 e + e my update 2017? ± 0.85 e + e δσ < 1% < 11 GeV space-like split ± 1.27 e + e M 0 = 2.5 GeV Adler ± 1.20 e + e M 0 = 2.0 GeV Adler??? ± 1.06 e + e δσ < 1% < 2 GeV ± 0.54 e + e + pqcd error 0.2% ± 0.40 e + e + pqcd error 0.1% α (5) had (M Z 2 ) in units 10 4 Davier et al. 2011: use pqcd above 1.8 GeV no improvement by remeasuring cross sections above 1.8 GeV no proof that pqcd works at 0.04% precision as adopted My analysis is data driven: pqcd and > 11.5 GeV pqcd at 0.2% Adler function: pqcd error = ½ present error pqcd at 0.1% Adler function: pqcd error = data error ±0.28 F. Jegerlehner FCCee Workshop, CERN Geneva, January

26 Note: theory-driven standard analyses (R(s) integral) using pqcd above 1.8 GeV cannot be improved by improved cross-section measurements above 2 GeV!!! precision in α: present direct Adler future Adler QCD 0.2% Adler QCD 0.1% future via A µµ FB off Z Adler function method is competitive with Patrick Janot s direct near Z pole determination via forward backward asymmetry in e + e µ + µ A µµ FB = Aµµ FB,0 + 3 a2 I 4 v 2 Z + G where γ Z interference term I α(s) G µ Z alone Z G 2 µ γ only G α 2 (s) v vector Z coupling also depends on α(s MZ 2) and sin2 Θ f (s MZ 2) a axial Z coupling sensitive to ρ-parameter (strong M t dependence) using v, a as measured at Z-peak F. Jegerlehner FCCee Workshop, CERN Geneva, January

27 Challenges for direct measurement: radiative corrections needs dedicated off-z peak running under way see e.g. Gluza et al. arxiv: Adler function method is much cheaper to get, I think! Requirement look to be realistic: pin down experimental errors to 1% level in all non-perturbative regions up to 2.0 GeV switch to Euclidean approach, monitored by the Adler function improve on QCD parameters, mainly on m c and m b F. Jegerlehner FCCee Workshop, CERN Geneva, January

28 4. Need for space-like α QED,eff (t) FCC-ee luminometer: small angle Bhabha scattering e + e γ e + + t e e + γ e + e s e VP dressed tree level Bhabha scattering in QED for small angle Bhabha scattering δ HVP σ/σ = 2 δα( t)/α( t), for FCC-ee luminometer t 3.5 GeV near Z peak and 13 GeV at 350 GeV. F. Jegerlehner FCCee Workshop, CERN Geneva, January

29 Hadronic uncertainty δ α had ( t) Progress lot of newer low energy data ππ etc. Jadach et al. arxiv: Talks B. Ward, C. M. Carloni Calame s t 1996 present FCC ee expected M Z 3.5 GeV 0.040% 0.013% GeV 13 GeV F. Jegerlehner FCCee Workshop, CERN Geneva, January

30 New project: measuring directly low energy α QED (t) very different paradigm: no VP subtraction issue! no exclusive channel collection even 1% level measurement can provide important independent information use µ e scattering MUonE projects G. Abbiendi et al., arxiv: µ γ µ t dσ unpol. µ e µ e ( dt = 4π α(t) 2 1 s m 2 µ m 2 2 e) λ(s,m 2 e,m2 µ ) t 2 + s t e e The primary goal determining a had µ in an alternative way where Q 2 (x) x2 1 x m2 µ a had µ = α 1 ( π dx (1 x) α had Q 2 (x) ) 0 is the space like square momentum transfer F. Jegerlehner FCCee Workshop, CERN Geneva, January

31 α had ( Q 2 ) = α α( Q 2 ) + αlep ( Q 2 ) 1 directly compares with lattice QCD data My proposal here: determine very accurately α had ( Q 2 ) at Q 2.5 GeV by this method (one single number!) as the non-perturbative part of α had ( M 2 Z ) as in Adler function approach. direct useful for small angle Bhabha luminometer! F. Jegerlehner FCCee Workshop, CERN Geneva, January

32 5. Conclusions Muon g 2 theory uncertainty remains the key issue and strongly motivates more precise measurements of low energy e + e hadrons cross sections (Novosibirsk VEPP 2000/CMD3,SND, Beijing BEPCII/BESIII, Tsukuba SuperKEKB/BelleII). helps to improve α QED (t) in region relevant for small angle Bhabha process and in calculating α QED (s) at FCC-ee/ILC energies via Euclidean split trick (Adler function controlled data vs pqcd split) the latter method requires pqcd prediction of the Adler-function to improve by a factor 2 (improved parameters mainly m c and m b ) Are presently estimated (essentially agreed) evaluations in terms of R-data reliable? Alternative methods important! Patrick Janot s approach certainly is an important alternative method directly accessing α QED (MZ 2 ) with very different systematics. A challenging project. F. Jegerlehner FCCee Workshop, CERN Geneva, January

33 Another interesting option is an improved radiative return measurement of σ(e + e hadrons) at the GigaZ (directly improves dispersion integral incl all resonances and thresholds in one experiment!) In any case on paper e µ + e µ + looks to be the ideal process to perform an unambiguous measurement of α( Q 2 ), which determines the LO HVP to a µ as well as the non-perturbative part of α QED (s)! Lattice QCD results are very close to become competitive here as well. at the end we have alternatives available allowing for important crosschecks. Let s do it! Thanks you for your attention! F. Jegerlehner FCCee Workshop, CERN Geneva, January

34 The coupling α 2, M W and sin 2 Θ f How to measure α 2 : see also Talk A. Vicini charged current channel M W (g g 2 ): M 2 W = g2 2 4 = π α 2 2 G µ neutral current channel sin 2 Θ f In fact here running sin 2 Θ f (E): LEP scale low energy ν e e scattering sin 2 Θ e = { } 1 α2 1 α + νµe,vertex+box + κ e,vertex sin 2 Θ ν µe The first correction from the running coupling ratio is largely compensated by the ν µ charge radius which dominates the second term. The ratio sin 2 Θ ν µe/ sin 2 Θ e is close to 1.002, independent of top and Higgs mass. Note that errors in the ratio 1 α 2 1 α can be taken to be 100% correlated and thus largely cancel F. Jegerlehner FCCee Workshop, CERN Geneva, January

35 Above result allow us to calculate non-perturbative hadronic correction in γγ, γz, ZZ and WW self energies, as Π γγ = e 2 ˆΠ γγ Π Zγ = Π ZZ = eg c Θ g 2 c 2 Θ Π WW = g 2 ˆΠ + V A ˆΠ 3γ V e2 s Θ c Θ ˆΠ 33 V A 2 e2 c 2 Θ ˆΠ γγ V ˆΠ 3γ V + e2 s 2 Θ c 2 Θ with ˆΠ(s) = ˆΠ(0) + sˆπ(s). Leading hadronic contributions: α (5) had (s) = [ e2 Re ˆπ γγ (s) ˆπ γγ (0) ] α (5) e2 2 had (s) = s 2 Θ [ Re ˆπ 3γ (s) ˆπ 3γ (0) ] which exhibit the leading hadronic non-perturbative parts, i.e. the ones involving the photon field via mixing. α (5) had (s) and α(5) 2 had (s) via e+ e -data and isospin arguments ˆΠ γγ V F. Jegerlehner FCCee Workshop, CERN Geneva, January

36 (u, d), s flavor separation: Π 3γ ud = 1 2 Πγγ ud ; Π3γ s = 3 4 Πγγ s Π γγ = Π (ρ) + Π (ω) + Π (φ) + Π 3γ = 1 2 Π(ρ) Π(φ) + F. J., Z. Phys. C 32 (1986) 195, Nuovo Cim. C 034S1 (2011) 31 Note: gauge boson SE potentially very sensitive to New Physics (oblique corrections) new physics may be obscured by non-perturbative hadronic effects; need to fix this! Flavor separation assuming OZI violating terms to be small perturbative rewighting disagrees with lattice QCD results!!! Note that the wrong perturbative weighting Π 3γ ud = 9 20 Πγγ ud ; Π3γ s = 3 4 Πγγ s has been proven to clearly mismatch lattice results, while the correction is in good agreement. This also means the OZI suppressed contributions should be at the 5% level and not negligibly small. F. Jegerlehner FCCee Workshop, CERN Geneva, January

37 α hvp 2 (Q 2 ) lattice data linearly extrapolated to m π in CL α 2 from alphaqed, SU(3) flavour separation α 2 from alphaqed, SU(2) flavour separation 2 4 Q 2 [ GeV 2] 6 Testing flavor separation in lattice QCD H. Meyer et al. [l], arxiv: ,arxiv: , K. Jansen et al. arxiv: [r] disproves pqcd reweighting! and pqcd prediction based on effective quark masses. F. Jegerlehner FCCee Workshop, CERN Geneva, January

38 α em (E) and α 2 (E) as functions of energy E in the time-like and space-like domain. The smooth space-like correction (dashed line) agrees rather well with the non-resonant background above the φ-resonance (kind of duality). In resonance regions as expected agreement is observed in the mean, with huge local deviations. F. Jegerlehner FCCee Workshop, CERN Geneva, January

39 sin 2 Θ W (Q) as a function of Q in the space-like region. Hadronic uncertainties are included but barely visible. Uncertainties from the input parameter sin 2 θ W (0) = (100) or sin 2 θ W (MZ 2 ) = (16) are not shown. Future ILC/FCC measurements at 1 TeV would be sensitive to Z, H etc. Except from the LEP and SLD points (which deviate by 1.8 σ), all existing measurements at lower energies are of rather limited accuracy unfortunately! F. Jegerlehner FCCee Workshop, CERN Geneva, January

40 sin 2 Θ W (E) as a function of E in the time-like region. Note that sin 2 θ W (0)/ sin 2 θ W (MZ 2 ) = a 3% correction established at 6.5 σ. sin 2 Θ eff exhibiting a specific dependence on the gauge boson SEs is an excellent monitor for New Physics F. Jegerlehner FCCee Workshop, CERN Geneva, January

41 Details about possible future progress Goal: ILC/FCC-ee requirement: improve by factor 10 in accuracy (5) data direct integration of data: 46% from data 54% p-qcd, α had 10 4 = ± 1.78 (1.4%) 1% overall accuracy ±1.27 1% accuracy for each region (divided up as in table) added in quadrature: ±0.40 (5) pqcd Data: [1.78] vs. [0.40] improvement factor 4.5, α had 10 4 = ± 0.05 (0.0%) Theory: no improvement needed! integration via Adler function: 22% from data 78% p-qcd (5) data α had 10 4 = ± 0.66 (1.1%) 1% overall accuracy ±0.60 1% accuracy in region 1.0 to 2.5 GeV added in quadrature: ±0.28 Data: [1.19] vs. [1.03,0.57,0.37] improvement factor (Adler vs Adler) [1.78] vs. [1.03,0.57,0.37] improvement factor (Standard vs F. Jegerlehner FCCee Workshop, CERN Geneva, January

42 Adler) (5) pqcd α had 10 4 = ± 1.00 (0.05%) Theory: massive 4-loop needed and more accurate m c, m b and α s! direct measurement (near/off Z peak) Patrick Janot s approach F. Jegerlehner FCCee Workshop, CERN Geneva, January

43 α had (s 0 ) 10 4 : present s 0 M 2 Z (2.5 GeV) 2 (2.0 GeV) 2 data ± 1.78 [1.4%] ± 0.79 [1.1%] ± 0.66 [1.1%] pqcd ± 0.05 [0.0%] ± 0.99 [0.5%] ± 1.04 [0.5%] α had (MZ 2 ) ± ± ± α 1 (MZ 2 ) ± ± ± accuracy in improvement F. Jegerlehner FCCee Workshop, CERN Geneva, January

44 α had (s 0 ) Future I: improving data only a) direct δσ< 1% above φ to 11.5 GeV, b) low energy space-like cut at s 0, δσ< 1% above φ to 2.5 GeV s 0 M 2 Z (2.5 GeV) 2 (2.0 GeV) 2 data ± 0.41 [0.3%] ± 0.33 [0.4%] ± 0.28 [0.4%] pqcd ± 0.05 [0.0%] ± 1.03 [0.5%] ± 1.04 [0.5%] α had (MZ 2 ) ± ± ± α 1 (MZ 2 ) ± ± ± accuracy in improvement F. Jegerlehner FCCee Workshop, CERN Geneva, January

45 α had (s 0 ) Future II: improving data as above plus pqcd to 0.2% in case b) s 0 M 2 Z (2.5 GeV) 2 (2.0 GeV) 2 data ± 0.41 [0.3%] ± 0.33 [0.4%] ± 0.28 [0.4%] pqcd ± 0.05 [0.0%] ± 0.40 [0.2%] ± 0.42 [0.2%] α had (MZ 2 ) ± ± ± α 1 (MZ 2 ) ± ± ± accuracy in improvement F. Jegerlehner FCCee Workshop, CERN Geneva, January

46 α had (s 0 ) Future III: improving data as above plus pqcd to 0.1% in case b) s 0 M 2 Z (2.5 GeV) 2 (2.0 GeV) 2 data ± 0.41 [0.3%] ± 0.33 [0.4%] ± 0.28 [0.4%] pqcd ± 0.05 [0.0%] ± 0.20 [0.1%] ± 0.21 [0.1%] α had (MZ 2 ) ± ± ± α 1 (MZ 2 ) ± ± ± accuracy in improvement F. Jegerlehner FCCee Workshop, CERN Geneva, January

47 a) contributions to the Adler function Adler=pQCD = α (5) had ( M2 Z ) α(5) had ( s 0) up to three loops all have the same sign and are substantial. Four and higher orders could still add up to non-negligible contribution. An error for missing higher order terms is not included. b) the link between space like and time-like region is the difference = α (5) had (M2 Z ) α(5) had ( M2 Z ) = ± which can be calculated in pqcd. It accounts for the iπ terms from the logs ln( q 2 /µ 2 ) = ln( q 2 /µ 2 ) + iπ Since the term is small we can get it as well from direct data integration α had ( MZ 2 ) = ± 0.64 ± 1.78 F. Jegerlehner FCCee Workshop, CERN Geneva, January

48 α had ( MZ 2 ) = ± 0.64 ± 1.90 and taking into account that errors are almost 100% correlated we have α had (MZ 2) α had( MZ 2 ) = 0.40 ± 0.12 F. Jegerlehner FCCee Workshop, CERN Geneva, January

49 ILC/FCC-ee community should actively support these activities as integral part of e + e -collider precision physics!!! Remember: tremendous progress since middle of 90 s Novosibirsk VEPP-2M: MD-1, CMD2, SND, KEDR; VEPP-2000: CMD3,SND Frascati DAFNE: KLOE Beijing BEPC: BES II, BESIII Cornell CESR: CLEO Stanford SLAC PEP-II: BaBar; KEK Tsukuba: Belle Many analyzes exploiting these results: Davier et al, Hagiwara et al., Burkhardt, Pietrzyk, Yndurain et al... Indispensable for Muon g 2, indirect vs direct LEP Higgs mass etc. and future precision test at ILC/FCC-ee and new physics signals in precision observables. Impact for cosmology! F. Jegerlehner FCCee Workshop, CERN Geneva, January

50 My R(s) compilation vs. pqcd. Only stat errors shown. F. Jegerlehner FCCee Workshop, CERN Geneva, January

51 pqcd 4-loops incl mass-effects Harlander,Steinhauser F. Jegerlehner FCCee Workshop, CERN Geneva, January

52 Compilation by Davier et al. F. Jegerlehner FCCee Workshop, CERN Geneva, January