Lepton magnetic moments: precision tests of the Standard Model

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1 Lepton magnetic moments: precision tests of the Standard Model Massimo Passera INFN Padova Technische Universität Dresden January

2 Outline Lepton magnetic moments: the basics The muon (and electron) g-2: an update The muon g-2 and the bounds on the Higgs mass The tau g-2: opportunities and challenges (fantasies?) 2

3 Preamble: today s values a e = (28) x parts per billion!! Hanneke et al., PRL100 (2008) a μ = (63) x parts per million!! E821 Final Report: PRD73 (2006) a τ = (17) DELPHI - EPJC35 (2004) 159 [a τ SM =117721(5)x10-8, Eidelman & MP 07] 3

4 Lepton magnetic moments: the basics 4

5 The beginning: g=2 Uhlenbeck and Goudsmit in 1926 proposed: Dirac 1928: ~µ = g e 2mc ~s g = 2 (not 1!) (i@ µ ea µ ) µ = m A Pauli term in Dirac s eq would give a deviation a e 2m µ F µ! g = 2(1 + a)...but there was no need for it! g=2 stood for ~20 yrs. 5

Theory of the g-2: Quantum Field Theory Kusch and Foley 1948: µ exp e = e~ 2mc (1.00119 ± 0.00005) Schwinger 1948 (triumph of QED!

6 Theory of the g-2: Quantum Field Theory Kusch and Foley 1948: µ exp e = e~ 2mc ( ± ) Schwinger 1948 (triumph of QED!): µ th e = e~ 1+ = e~ 2mc 2 2mc Keep studying the lepton γ vertex: F 1 (0) = 1 F 2 (0) = a l A pure quantum correction effect! 6

7 The muon (and electron) g-2: an update 7

8 The experiment E821 Homepage of E821 8

9 The experiment E821 (II) 9

Future: new muon g-2 experiments proposed at: Fermilab (E989), aiming at 0.

10 The muon g-2: the experimental result? Jan 04 July 02 Today: aμ EXP = ( ± 54 stat ± 33 sys )x10-11 [0.5ppm]. Future: new muon g-2 experiments proposed at: Fermilab (E989), aiming at 0.14ppm J-PARC aiming at 0.1 ppm Has now Stage 1 Approval! [D. Hetzog & N. Saito, U.Paris, Feb 2010; B. Lee Roberts & T. Mibe, Tau2010] Are theorists ready for this (amazing) precision? No(t yet) 10

aμ SM : the QED contribution QED a µ = (1/2)(α/π) Schwinger 1948 + 0.765857408 (27) (α/π) 2 Sommerfield; Petermann; Suura & Wichmann 57; Elend 66; MP 04 + 24.

11 aμ SM : the QED contribution QED a µ = (1/2)(α/π) Schwinger (27) (α/π) 2 Sommerfield; Petermann; Suura & Wichmann 57; Elend 66; MP (42) (α/π) 3 Remiddi, Laporta, Barbieri ; Czarnecki, Skrzypek; MP 04; Friot, Greynat & de Rafael 05, Mohr,Taylor & Newell (8) (α/π) 4 Kinoshita & Lindquist 81,, Kinoshita & Nio 04, 05; Aoyama, Hayakawa, Kinoshita & Nio, June & Dec (20) (α/π) 5 In progress... Kinoshita et al. 90, Yelkhovsky, Milstein, Starshenko, Laporta, Karshenboim,, Kataev, Kinoshita & Nio 06, Kinoshita et al Adding up, we get: QED a µ = (14)(04) x from coeffs, mainly from 5-loop unc from δα( 08) with α=1/ (51) [0.37 ppb] 11

12 [ A parenthesis on the electron g-2... a e SM = (1/2)(α/π) (60) (α/π) 2 Schwinger 1948 Sommerfield; Petermann; Suura & Wichmann 57; Elend 66; MP 06 A 2 (4) (m e /m µ ) = (26) x 10-7 A 2 (4) (m e /m τ ) = (60) x (19) (α/π) 3 Kinoshita, Barbieri, Laporta, Remiddi,, Li, Samuel; Mohr,Taylor & Newell 08, MP '06 A 2 (6) (m e /m µ ) = (27) x 10-6 A 2 (6) (m e /m τ ) = (19) x 10-8 A 3 (6) (m e /m µ, m e /m τ ) = (62) x (35) (α/π) 4 Kinoshita & Lindquist 81,, Kinoshita & Nio 05; Aoyama, Hayakawa, Kinoshita & Nio, (4.6) (α/π) 5 In progress (12672 mass ind. diagrams!) Aoyama, Hayakawa, Kinoshita, Nio 07; Aoyama, Hayakawa, Kinoshita, Nio, Jan (20) x Hadronic Krause 1997, Jegerlehner & Nyffeler (52) x Electroweak Mohr,Taylor & Newell, 08; Czarnecki, Krause, Marciano 96 12

13 ... and the best determination of alpha ] The 2008 measurement of the electron g-2 is: exp a e = (28) x Hanneke et al, PRL100 (2008) vs. old (factor of 15 improvement, 1.8σ difference): exp a e = (4.2) x Van Dyck et al, PRL59 (1987) 26 Equating a SM e (α) = a exp e best determination of alpha to date: α 1 = (12)(37)(2)(33) [0.37ppb] Hanneke et al, 08 δc 4 qed δc 5 qed δa e had δa e exp (smaller than th!) Compare it with other determinations (independent of a e ): α 1 = (110) [7.7 ppb] PRA73 (2006) (Cs) α 1 = (62) [4.6 ppb] PRL101 (2008) (Rb) α 1 = (91) [0.7 ppb] PRL106 (2011) (Rb) Excellent agreement beautiful test of QED at 4-loop level! 13

14 Old and new determinations of alpha h/m(rb) 2011 h/m(rb) 2011 Gabrielse, Hanneke, Kinoshita, Nio & Odom, PRL99 (2007) Hanneke, Fogwell & Gabrielse, PRL100 (2008) Bouchendira et al, PRL106 (2011)

aμ SM : the Electroweak contribution One-loop term: 1972: Jackiv, Weinberg; Bars, Yoshimura; Altarelli, Cabibbo, Maiani; Bardeen, Gastmans, Lautrup; Fujikawa, Lee, Sanda; Studenikin et al.

15 aμ SM : the Electroweak contribution One-loop term: 1972: Jackiv, Weinberg; Bars, Yoshimura; Altarelli, Cabibbo, Maiani; Bardeen, Gastmans, Lautrup; Fujikawa, Lee, Sanda; Studenikin et al. 80s One-loop plus higher-order terms: a µ EW = 154 (2) (1) x Kukhto et al. 92; Czarnecki, Krause, Marciano 95; Knecht, Peris, Perrottet, de Rafael 02; Czarnecki, Marciano, Vainshtein 02; Degrassi, Giudice 98; Heinemeyer, Stockinger, Weiglein 04; Gribouk, Czarnecki 05; Vainshtein 03. Higgs mass variation, M top error, 3-loop nonleading logs Hadronic loop uncertainties: 15

aμ SM : the hadronic leading-order (HLO) contribution Central values Errors 2 F. Jegerlehner and A. Nyffeler, Phys. Rept. 477 (2009) 1 a µ HLO = 6903 (53) tot x 10-11 = 6923 (42) tot x 10-11 F.

16 aμ SM : the hadronic leading-order (HLO) contribution Central values Errors 2 F. Jegerlehner and A. Nyffeler, Phys. Rept. 477 (2009) 1 a µ HLO = 6903 (53) tot x = 6923 (42) tot x F. Jegerlehner, A. Nyffeler, Phys. Rept. 477 (2009) 1 Davier et al, EPJ C71 (2011) 1515 (incl. BaBar & KLOE10 2π) = 6949 (37) exp (21) rad x Hagiwara et al. (HLMNT11), arxiv: Radiative Corrections are crucial! S.Actis et al, Eur. Phys. J. C66 (2010)

17 aμ SM : the HLO contribution from e + e - data The overall agreement of all e + e - data looks reasonably good, but discrepancies exist. Energy Scan: Agreement between the CMD2 & SND π + π - data at VEPP-2M. First preliminary results presented in Sep 2011 by the CMD3 & SND exp. at the new VEPP-2000 collider in Novosibirsk. Initial State Radiation Method (ISR): Collider operates at fixed energy but sπ can vary continuously. Important independent method made possible by strong th & exp interplay. KLOE: The small angle (2008) and large angle (2010) π + π - ISR analyses agree. July 2011(EPS): new preliminary measure by the ππγ/μμγ ratio presented. It confirms their earlier results. Reasonable agreement between KLOE and CMD2-SND (especially below the ρ). The contributions to aμ HLO agree. BaBar: ISR π + π - result from 0.3 to 3 GeV! (2009). Discrepancy between the results of BaBar and KLOE. 17

18 Results at the VEPP-2M collider in Novosibirsk Overview of VEPP-2M results 1-5% systematic error for major channels E. Solodov at PhiPsi2011 workshop - Novosibirsk, Sep

19 aμ SM : the HLO contribution from e + e - data The overall agreement of all e + e - data looks reasonably good, but discrepancies exist. Energy scan: Agreement between the CMD2 & SND π + π - data at VEPP-2M. First preliminary results presented in Sep 2011 by the CMD3 & SND exp. at the new VEPP-2000 collider in Novosibirsk. Initial State Radiation Method (ISR): Collider operates at fixed energy but sπ can vary continuously. Important independent method made possible by strong th & exp interplay. KLOE: The small angle (2008) and large angle (2010) π + π - ISR analyses agree. July 2011(EPS): new preliminary measure by the ππγ/μμγ ratio presented. It confirms their earlier results. Reasonable agreement between KLOE and CMD2-SND (especially below the ρ). The contributions to aμ HLO agree. BaBar: ISR π + π - result from 0.3 to 3 GeV! (2009). Discrepancy between the results of BaBar and KLOE. 19

20 The two-pion channel: comparison of e + e - data Relative deviations from local average of all experiments (HVPTools) given by band Cross section(exp) / Average - 1 Cross section(exp) / Average Average BABAR s [GeV] Most data points dominated by systematic uncertainties that are correlated between data points -0.1 Average KLOE08 KLOE s [GeV] new preliminary KLOE results using ππ/µµ ratio not included Cross section(exp) / Average - 1 Cross section(exp) / Average Average CMD2 06 CMD Average s [GeV] 0.15 SND Davier et al., EPJ C 71, 1515 (2011) s [GeV] M. Davier at ICFA CERN, October 4th

21 aμ SM : the HLO contribution from tau-decay data The isospin symmetry is the symm. of the Lagrangian of strong int. under rotation in flavor space of u & d quarks. This global symm. implies the existence of 3 conserved currents: Vμ ± and Vμ 3. The current Vμ 3 = Jμ em,i=1 enters the evaluation of σ(e + +e - π + π - ), while Vμ - = đϒμu enters that of the decays τ - ντ + π 0 + π -. In the limit of exact isospin symmetry, at leading order we have: (e + e! + )= 4 2 s v 0 (s) d ds! 0 = V ud 2 G2 F M s M s M 2 v (s) with v0(s) = v-(s). But the isospin symmetry is not exact... 21

22 aμ SM : the HLO contribution from tau-decay data The tau data of ALEPH, CLEO & OPAL are higher than the CMD2/SND/KLOE ones, particularly above the ρ.the 2008 aμ ππ tau data result of Belle agrees with Aleph-Cleo-Opal (some deviations from Aleph s spectral functions). Revisited analysis: (Davier et al, EPJ C71 (2011) 1515) a µ HLO = 7015 (47) x Belle s data included + IB corrections revisited & updated (Marciano & Sirlin 88; Cirigliano, Ecker, Neufeld 01-02, Flores-Baez et al. 06& 07) The discrepancy with e + e - data has decreased. Are there inconsistencies in e + e - or τ data? All possible isospinbreaking (IB) effects taken into account? Claims exist that tau data are actually consistent with e + e - ones after IB effects & vector meson mixings considered! (Benayoun et al., 2007, 2009 and arxiv: , Jegerlehner & Szafron 2011). 22

23 aμ SM : the hadronic higher-order (HHO) contributions - VP HHO: Vacuum Polarization Already included in aμ HLO O(α 3 ) contributions of diagrams containing hadronic vacuum polarization insertions: a µ HHO (vp) = -98 (1) x Krause 96, Alemany et al. 98, Hagiwara et al Only tiny shifts if τ data are used instead of the e + e - ones Davier & Marciano

24 aμ SM : the hadronic higher-order (HHO) contributions - LBL HHO: Light-by-light contribution Unlike the HLO term, for the hadronic l-b-l term we must rely on theoretical approaches. This term had a troubled life! Recent values: a HHO µ (lbl) = + 80 (40) x Knecht & Nyffeler 02 a HHO µ (lbl) = +136 (25) x Melnikov & Vainshtein 03 a HHO µ (lbl) = +105 (26) x Prades, de Rafael, Vainshtein 09 a HHO µ (lbl) = (39) x Jegerlehner & Nyffeler 09 Results based also on Hayakawa, Kinoshita 98 & 02; Bijnens, Pallante, Prades 96 & 02 Bound aμ HHO (lbl) < ~ 160 x Erler&Sanchez 06, Pivovarov 02 (Boughezal&Melnikov 11) Lattice? Very hard, in progress. Recent larger value: 217 (91) x Fischer, Goecke, Williams, PRD83 (2011) Had lbl is likely to become the ultimate limitation of the SM prediction 24

25 The muon g-2: Standard Model vs. Experiment Adding up all contributions, we get the following SM predictions and comparisons with the measured value: EXP -11 a µ = (63) x 10 E821 Final Report: PRD73 (2006) 072 with latest value of λ=μμ/μp (CODATA 06) a SM µ ( a µ = a EXP µ a SM µ ) [1] (59) 307 (86) 3.6 [2] (49) 287 (80) 3.6 [3] (50) 261 (80) 3.2 [4] (54) 195 (83) 2.4 with a μ HHO (lbl) = 105 (26) x [1] F. Jegerlehner, A. Nyffeler, Phys. Rept. 477 (2009) 1 [2] Davier et al, EPJ C71 (2011) 1515 (includes BaBar and KLOE10 2π) [3] HLMNT11: Hagiwara et al, JPG38 (2011) (incl BaBar and KLOE10 2π) [4] Davier et al, Eur.PJ C71 (2011) 1515, τ data. Note that the th. error is now about the same as the exp. one 25

26 The muon g-2 and the bounds on the Higgs mass W.J. Marciano, A. Sirlin, MP PRD78 (2008) [updated in Chin. Phys. C34 (2010) 735] 26

27 The EW Bounds on the SM Higgs mass The Higgs is the last missing particle of the SM: comparing SM predictions (that depend on its mass MH via loops) with precise experiment we get indirect information on MH: clear preference for a light Higgs (below ~160 GeV) 27

The Hadronic Contribution to α(m Z ) The effective fine-structure constant at the scale Mz is given by: (M Z )= 1 (MZ ) with = lep + (5) had + top The light-quark part is given by: (5) had (M Z)= M 2

28 The Hadronic Contribution to α(m Z ) The effective fine-structure constant at the scale Mz is given by: (M Z )= 1 (MZ ) with = lep + (5) had + top The light-quark part is given by: (5) had (M Z)= M 2 Z 4 2 P 4m 2 ds Progress due to significant data improvement (in particular BES): Δα had (5) (M z ) = (s) s M 2 Z (70) Eidelman, Jegerlehner (17) Kuhn, Steinhauser (12) Troconiz, Yndurain (35) Burkhardt, Pietrzyk (23) F. Jegerlehner (14) Hagiwara et al,jpg38 (2011) (10) Davier et al, EPJ C71 (2011) (33) Burkhardt, Pietrzyk arxiv: Hagiwara et al, JPG38 (2011)

29 The EW Bounds on the SM Higgs mass The dependence of SM predictions on the Higgs mass, via loops, provides a powerful tool to set bounds on its value. Comparing the theoretical predictions of M W and [convenient formulae in terms of M H, M top, Δα had (5) (M Z ) and α s (M Z ) by Degrassi, Gambino, MP, Sirlin 98; Degrassi, Gambino 00; Ferroglia, Ossola, MP, Sirlin 02; Awramik, Czakon, Freitas, Weiglein 04 & 06] with M W = (23) GeV [LEP+Tevatron] and we get = (16) [LEP+SLC] Δα had (5) (M Z ) = (15) [HLMNT09, now (14)] M top = (1.3) GeV [CDF-D0 09, now 173.2(9)] α s (M Z ) = (2) [PDG 2008, now (7)] M H = GeV & M H < 153 GeV 95%CL The value of Δα had (5) (M Z ) is a key input of these EW fits 29

30 How do we explain Δaμ? Δa µ can be explained in many ways: errors in LBL, QED, EW, HHO-VP, g-2 EXP, HLO; or, we hope, New Physics (ask Dominik!) Can Δa μ be due to hypothetical mistakes in the hadronic σ(s)? An upward shift of σ(s) also induces an increase of Δα had (5) (M Z ). Consider: a µ HLO Δα had (5) and the increase (ε>0), in the range: (s) = (s) p s 2 [ p s0 /2, p s 0 + /2] 30

31 Shifts of aμ HLO and Δαhad (5) (M Z ) If this shift Δσ(s) in is adjusted to bridge the g-2 discrepancy, the value of Δα (5) had (M Z ) increases by: b( s 0, )= a µ s0 + /2 s0 /2 g(t2 ) (t 2 ) tdt s0 + /2 s0 /2 f(t2 ) (t 2 ) tdt Adding this shift to Δα had (5) (M Z ) = (15) [HLMNT09], with Δa μ = 316(79) x [HLMNT09], we obtain: (s) = (s 0 ) (s) = (s s 0 ) 31

32 The muon g-2: connection with the SM Higgs mass How much does the M H upper bound change when we shift σ(s) by Δσ(s) [and thus Δα had (5) (M Z ) by Δb] to accommodate Δaμ? τ data Δα had (5) (M Z ) = (15) Δa µ = 316(79) x

33 The muon g-2: connection with the SM Higgs mass How much does the M H upper bound change when we shift σ(s) by Δσ(s) [and thus Δα had (5) (M Z ) by Δb] to accommodate Δaμ? LHC excluded (Dec 2011) τ data Δα had (5) (M Z ) = (15) Δa µ = 316(79) x

34 The muon g-2: connection with the SM Higgs mass (II) The LEP-ATLAS direct-search lower bound is MH LB = GeV (95%CL) and CMS-ATLAS now exclude it between 127 & 600 GeV We showed that the hypothetical shifts Δσ = εσ(s) that bridge the muon g-2 discrepancy are in conflict with the LEP lower limit when s0 > ~1.2GeV While the use of τ data in the calculation of aμ HLO reduces the muon g-2 discrepancy, it increases Δαhad (5) (MZ), lowering the MH upper bound. Near-conflict with the MH lower bound if one tries to overcome the full Δaμ (2.4σ) by further Δσ increase In a scenario where τ data agree with e + e - ones below ~1GeV after isospin viol. effects & vector meson mixings (Benayoun et al., 2007, 2009 and arxiv: , Jegerlehner & Szafron 2011), we could assume that Δaμ is bridged by hypothetical errors above ~1GeV. If so, MH UB falls below MH LB!! 34

35 The muon g-2: connection with the SM Higgs mass - Conclusions As the quoted exp. uncertainty of σ(s) below 1 GeV is ~ a few per cent (or less), with a detailed analysis we concluded that the possibility to explain the muon g-2 with these shifts Δσ(s) appears to be unlikely If, however, we allow variations of σ(s) up to ~6% (7%), MH UB is reduced to less than ~137 GeV (138 GeV). E.g., the ~6% shift in [0.6, 1.2] GeV, required to fix Δaμ, lowers MH UB to 133 GeV. Some tension with the MH >~120GeV vacuum stability bound. Scenarios where Δaμ is accommodated without affecting MH UB are possible, but considerably more unlikely. Reminder: the above MH upper bounds, like the LEP-EWWG ones, depend on the value of sin 2 lept e : usual problems. They also depend on Mt & δmt: we made simple formulae to translate the MH upper bounds above into new values corresponding to Mt & δmt inputs different from those employed here. 35

36 The tau g-2: opportunities and challenges Work in progress in collaboration with S. Eidelman, D. Epifanov, M. Fael, L. Mercolli & C. Ng 36

37 The SM prediction of the tau (g-2) The Standard Model prediction of the tau g-2 is: SM a τ = (2) x 10-8 QED (0.5) x 10-8 EW (3.7) x 10-8 HLO (0.2) x 10-8 HHO (vac) + 5 (3) x 10-8 HHO (lbl) a τ SM = (5) x 10-8 Eidelman & MP 2007 (mτ/mμ) 2 ~ 280: great opportunity to look for New Physics, and a clean NP test too Electron Muon Tau a EW /a HAD 1/56 1/45 1/7 a EW /δa HAD if only we could measure it!! 37

38 The tau (g-2): experimental bounds The very short lifetime of the tau makes it very difficult to determine aτ measuring its spin precession in a magnetic field. DELPHI s result, from e + e - e + e - τ + τ - total cross-section measurements at LEP 2 (the PDG value): a τ = (17) PDG 2011 With an effective Lagrangian approach, using data on tau lepton production at LEP1, SLC, and LEP2: < a τ NP < (95% CL) < a τ NP < (95% CL) Escribano & Massó 1997 Gonzáles-Sprinberg et al 2000 Bernabéu et al, propose the measurement of F2(q 2 =Mϒ 2 ) from e + e - τ + τ - production at B factories. NPB 790 (2008)

µ µ ) total E >10MeV E >10MeV = 1.823% vs 1.75(18)% CLEO 2000 = 0.364% vs 0.

39 The tau (g-2) via its radiative leptonic decays: a proposal Tau radiative leptonic decays at LO: d 3 dx dy d cos = M5 G 2 F y p x 2 4r 2 2 (4 ) 6 G 0 (x, y, cos, r) Kinoshita & Sirlin PRL2(1959)177; Kuno & Okada, RMP73(2001)151 (! e e ) total (! µ µ ) total E >10MeV E >10MeV = 1.823% vs 1.75(18)% CLEO 2000 = 0.364% vs 0.361(38)% x = 2E l M,y= 2E M,r= m l M Add the contribution of the effective coupling and the QED corrections: G 0! G 0 +ã G a + G RC Measure d 3 Γ precisely and get ãτ! [see also Laursen, Samuel, Sen, PRD29 (1984) 2652] 39

Conclusions The lepton (g-2) provide beautiful examples of interplay between theory and experiment: ge probed at <ppt! α and great test of QED (&SM?) s validity gμ probed at <ppb!

40 Conclusions The lepton (g-2) provide beautiful examples of interplay between theory and experiment: ge probed at <ppt! α and great test of QED (&SM?) s validity gμ probed at <ppb! tests full SM great to unveil New Physics gτ theory is ready! (Lots of) room for exp. improvement... The discrepancy Δaμ is ~3.5σ (if e + e - data are used; with tau data the deviation is 2.4σ). QED-EW ready for new g-2 exp! Hadronic? Could Δaμ be due to mistakes in the hadronic σ(s)? Unlikely, in view of current exp. error estimates of σ(s). But if this turns out to be the solution, then the indirect upper bound on MHiggs drops to ~ 130GeV, which is still compatible with the direct searches. The tau (g-2) is essentially unknown: proposal to measure it at new Super B factories via its radiative leptonic decays. 40

41 The End 41

The muon g-2 discrepancy: new physics or a relatively light Higgs?

The muon g-2 discrepancy: new physics or a relatively light Higgs? Massimo Passera INFN Padova 4th International Symposium on Lepton Moments Centerville, Cape Cod, MA -- July 19-22 2010 Work in collaboration