Massimo Passera INFN Padova. Symposium on Muon Physics in the LHC Era INT - Seattle October 27-30, 2008

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1 Massimo Passera INFN Padova Symposium on Muon Physics in the LHC Era INT - Seattle October 27-30, 2008

2 The present experimental values: 2

The muon g-2: experimental result July 02 January 04 Today: a μ EXP = (116592080 ± 54 stat ± 33 sys )

3 The muon g-2: experimental result July 02 January 04 Today: a μ EXP = ( ± 54 stat ± 33 sys ) [0.5ppm]. Future: a new (g-2) μ exp? See D. Hertzog s talk. Are theorists ready for this? [not yet] 3

4 The anomalous magnetic moment: the basics The Dirac theory predicts for a lepton l=e,μ, : QFT predicts deviations from the Dirac value: Study the photon lepton vertex: F 1 (0)=1 F 2 (0) = a l 4

The QED contribution to a μ QED a μ = (1/2)( / ) Schwinger 1948 + 0.765857410 (27) ( / ) 2 Sommerfield; Petermann; Suura & Wichmann 57; Elend 66; MP 04 + 24.

5 The QED contribution to a μ QED a μ = (1/2)( / ) Schwinger (27) ( / ) 2 Sommerfield; Petermann; Suura & Wichmann 57; Elend 66; MP (43) ( / ) 3 Remiddi, Laporta, Barbieri ; Czarnecki, Skrzypek; MP 04; Friot, Greynat & de Rafael (8) ( / ) 4 Kinoshita & Lindquist 81,, Kinoshita & Nio 04, 05; Aoyama, Hayakawa, Kinoshita & Nio, June & Dec (20) ( / ) 5 In progress Kinoshita et al. 90, Yelkhovsky, Milstein, Starshenko, Laporta, Karshenboim,, Kataev, Kinoshita & Nio March 06. Adding up, I get: 5

6 [ A parenthesis on the electron g-2 a e SM = (1/2)( / ) (60) ( / ) 2 Schwinger 1948 Sommerfield; Petermann; Suura & Wichmann 57; Elend 66; MP 06 A 2 (4) (m e /m μ ) = (28) x 10-7 A 2 (4) (m e /m ) = (60) x (19) ( / ) 3 Kinoshita, Barbieri, Laporta, Remiddi,, Li, Samuel; Mohr & Taylor 05; MP 06 A 2 (6) (m e /m μ ) = (29) x 10-6 A 2 (6) (m e /m ) = (19) x 10-8 A 3 (6) (m e /m μ, m e /m ) = (62) x (35) ( / ) 4 Kinoshita & Lindquist 81,, Kinoshita & Nio 05; Aoyama, Hayakawa, Kinoshita & Nio, June (4.6) ( / ) 5 In progress (12672 mass ind. diagrams!) Mohr & Taylor 05; Aoyama, Hayakawa, Kinoshita, Nio & Watanabe, June 2008 (more in progress) (20) x Hadronic Mohr,Taylor & Newell 08; Davier & Hoecker 98, Krause 97, Knecht (5) x Electroweak Mohr & Taylor 05; Czarnecki, Krause, Marciano 96 6

... and the best determination of alpha ] The new measurement of the electron g-2 is: exp a e = 1159652180.

3 (4.2) x 10-12 Van Dyck et al, PRL59 (1987) 26 Equating a SM exp e ( ) = a e best determination of alpha to date: C 4 qed C 5

7 ... and the best determination of alpha ] The new measurement of the electron g-2 is: exp a e = (28) x Hanneke et al, PRL100 (2008) vs. old (factor of 15 improvement, 1.8 difference): exp a e = (4.2) x Van Dyck et al, PRL59 (1987) 26 Equating a SM exp e ( ) = a e best determination of alpha to date: C 4 qed C 5 qed a e had a e exp (smaller than th!) Compare it with other determinations (independent of a e ): = +0.8 and -0.3 beautiful test of QED at 4-loop level! 7

8 Old and new determinations of alpha Gabrielse, Hanneke, Kinoshita, Nio & Odom, PRL99 (2007) Hanneke, Fogwell & Gabrielse, PRL100 (2008)

The Electroweak contribution One-loop term: 1972: Jackiv, Weinberg; Bars, Yoshimura; Altarelli, Cabibbo, Maiani; Bardeen, Gastmans, Lautrup; Fujikawa, Lee, Sanda.

9 The Electroweak contribution One-loop term: 1972: Jackiv, Weinberg; Bars, Yoshimura; Altarelli, Cabibbo, Maiani; Bardeen, Gastmans, Lautrup; Fujikawa, Lee, Sanda. One-loop plus higher-order terms: 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, M top error, 3-loop nonleading logs Hadronic loop uncertainties: 9

10 The hadronic leading-order (HLO) contribution Bouchiat & Michel 1961; Gourdin & de Rafael 1969 Central values Errors 2 Dec 01 Aug 03 F. Jegerlehner, PhiPsi 08, Frascati, April 2008 Hagiwara et al., PRD 69 (2004)

The HLO contribution: e + e - data a μ HLO = 6909 (39) exp (19) rad (7) qcd x 10-11 = 6894 (42) exp (18) rad x 10-11 = 6923 (60) tot x 10-11 = 6944 (48) exp (10) rad x 10-11 S. Eidelman, ICHEP06; M.

11 The HLO contribution: e + e - data a μ HLO = 6909 (39) exp (19) rad (7) qcd x = 6894 (42) exp (18) rad x = 6923 (60) tot x = 6944 (48) exp (10) rad x S. Eidelman, ICHEP06; M. Davier, TAU06 Hagiwara, Martin, Nomura, Teubner, PLB649(2007)173 F. Jegerlehner, PhiPsi 08, Frascati, April 2008 de Troconiz & Yndurain, PRD71 (2005) Radiative Corrections (Luminosity, ISR, Vacuum Polarization, FSR) are a very delicate issue! Are they all under control? CMD2 s data in the energy range, published in 2007, agree well with their earlier 1995 ones. SND s data reanalysis appears to be in good agreement with CMD2. 11

12 The HLO contribution: e + e - data (ISR Method) The RADIATIVE RETURN (ISR) Method: KLOE & BaBar. Collider operates at fixed energy but s can vary continuously. Important independent method made possible by beautiful interplay between theory and experiment. KLOE: at Tau08 (Novosibirsk, Sep 2008) KLOE presented an update of their analysis & a new measurement (arxiv: ). The 2008 analysis supersedes the 2005 one. Agreement between KLOE (2008) and CMD2-SND below the, some discrepancies above. Their contributions to a μ HLO agree. News from BaBar. + preliminary results (from 0.5 to 3 GeV) presented at Tau08. Disagreement with CMD2, SND and KLOE. Better agreement with results, especially with Belle. 12

13 CMD2 & SND vs KLOE G. Venanzoni, Tau08, Novosibirsk, September

14 CMD-2, SND & KLOE vs BABAR M. Davier, Tau08, Novosibirsk, September

The HLO contribution: Tau-decay data (Aleph, Opal, Cleo & now Belle) The data of ALEPH and CLEO are significantly higher than the CMD2-SND-KLOE ones, particularly above the.

15 The HLO contribution: Tau-decay data (Aleph, Opal, Cleo & now Belle) The data of ALEPH and CLEO are significantly higher than the CMD2-SND-KLOE ones, particularly above the. The recent a μ result of BELLE agrees with Aleph-Cleo- Opal. Some deviations from Aleph s spectral functions. Value: by Davier, Eidelman, Hoecker, Zhang, EPJC31 (2003) 503. NB: Davier & Eidelman chose not to include data in their updates of this article until the discrepancy is understood. Inconsistencies in e + e - or data? All possible isospinbreaking (IB) effects taken into account? Further recent IB corrections somewhat reduce the diff. with e + e - data. Recent claims that e + e - & data are consistent after IB effects & vector meson mixings considered (Marciano & Sirlin 88; Cirigliano, Ecker, Neufeld 01-02, Flores-Baez et al. 06 & 07, Benayoun et al. 07). 15

16 Fujikawa, Hayashii, Eidelman [for the Belle Collab.], arxiv: , May 08 16

The hadronic higher-order (HHO) contributions: VP HHO: Vacuum Polarization Already included in a μ HLO O( 3 ) contributions of diagrams containing hadronic vacuum

17 The hadronic higher-order (HHO) contributions: VP HHO: Vacuum Polarization Already included in a μ HLO O( 3 ) contributions of diagrams containing hadronic vacuum polarization insertions: Krause 96, Alemany et al. 98, Hagiwara et al. 03 & 06 Shifts by ~ -3 x if data are used instead of the e + e - ones Davier & Marciano 04 17

The hadronic higher-order (HHO) contributions: LBL HHO: Light-by-light contribution Unlike the HLO term, no direct exp. input for the had lbl term. Must rely on theory. This term had a troubled life!

18 The hadronic higher-order (HHO) contributions: LBL HHO: Light-by-light contribution Unlike the HLO term, no direct exp. input for the had lbl term. Must rely on theory. This term had a troubled life! Its recent determinations vary between: based also on Hayakawa, Kinoshita 98 & 02; Bijnens, Pallante, Prades 96 & 02; Estimate by Prades, de Rafael, Vainshtein out soon ( g-2 white paper ). Erler & Sanchez upper bound: a HHO μ (lbl) < ~ 159 x Lattice? In progress: Rakow et al (QCDSF), Hayakawa et al. Likely to become the ultimate limitation of the SM prediction. 18

19 The muon g-2: Standard Model vs. Experiment Adding up all the above contribution we get the following SM p predictions for a μ and comparisons with the measured value: a SM μ Δa μ σ [1] (60) 287 (87) 3.3 [2] (61) 302 (88) 3.4 [3] (72) 273 (96) 2.8 [4] (63) 252 (89) 2.8 [5] (70) 89 (95) 0.9 with a μ HHO (lbl) = 110 (40) x a μ = a μ EXP - a μ SM. [1] Eidelman at ICHEP06 & Davier at TAU06 (update of ref. [5]). [2] Hagiwara, Martin, Nomura, Teubner, PLB649 (2007) 173. [3] F. Jegerlehner, PhiPsi 08, Frascati, April [4] J.F. de Troconiz and F.J. Yndurain, PRD71 (2005) [5] Davier, Eidelman, Hoecker and Zhang, EPJC31 (2003) 503 ( data). The th error is now the same (or even smaller) as the exp. one! If BaBar s prelim. results are used instead, a μ drops to ~1.7! 19

20 20

21 How do we explain a μ? a μ can be explained in many ways: errors in HHO-LBL, QED, EW, HHO-VP, g-2 EXP, HLO; or New Physics. Can a μ be due to hypothetical mistakes in the hadronic (s)? An upward shift of (s) also induces an increase of had (5) (M Z ). Consider: a μ HLO : had (5) : and the increase ( >0), in the range: Δσ(s) =ɛσ(s) (s) [ s0 δ/2, s 0 + δ/2] 21

22 Shifts of a μ HLO and had (5) (M Z ) If this shift (s) in is adjusted to bridge the g-2 discrepancy, the value of (5) had (M Z ) increases by: Δb( s 0 +δ/2 s0 δ/2 s 0,δ)=Δa g(t2 ) σ(t 2 ) tdt μ s 0 +δ/2 s0 δ/2 f(t2 ) σ(t 2 ) tdt Adding this shift to (5) had (M Z ) = (22) [HMNT07], with a μ = 302(88) x [HMNT07], we obtain: Δσ(s) =ɛσ(s 0 ) Δσ(s) =ɛ δ(s s 0 ) 22

23 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, (5) had (M Z ) and 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 and we get = (25) GeV [LEP+Tevatron] = (16) [LEP+SLC] had (5) (M Z ) = (22) [HMNT 07] M top = (1.2) GeV [CDF-D0, Aug 08] s (M Z ) = (2) [PDG 08] M H = GeV & M H < 145 GeV 95%CL The value of had (5) (M Z ) is a key input of these EW fits 23

24 The muon g-2: connection with the SM Higgs mass How much does the M H upper bound change when we shift (s) by (s) [and thus had (5) (M Z ) by b] to accommodate a μ? 24

25 The muon g-2: connection with the SM Higgs mass (2) The LEP direct-search lower bound is M H LB = GeV (95%CL). The hypothetical shifts = (s) that bridge the muon g-2 discrepancy conflict with the LEP lower limit when s 0 > ~1.2GeV (for bin widths up to several hundreds of MeV). While using tau data in the calculation of a μ HLO almost solves the muon g-2 discrepancy, it increases the value of had (5) (M Z ), leading to M H < 133 GeV (95%CL), in near conflict with M H LB. Recent claim: e + e - & tau data consistent below ~1 GeV (after isospin viol. effects & vector meson mixings). We could thus assume that a μ is fixed by hypothetical errors above ~1GeV (where disagreement persists). If so, M H UB falls below M H LB!! Scenarios where a μ is accommodated without affecting M H UB are possible, but considerably more unlikely. 25

26 How realistic are these shifts (s)? How realistic are these shifts (s) when compared with the quoted exp. uncertainties? Study the ratio = (s)/ (s): 26

27 How realistic are these shifts (s)? (2) The minimum is ~ +4%. It occurs if is multiplied by (1+ ) in the whole integration region (!), leading to M H UB ~ 70 GeV (!!) As the quoted exp. uncertainty of (s) below 1 GeV is ~ a few per cent (or less), the possibility to explain the muon g-2 with these shifts (s) appears to be unlikely. If, however, we allow variations of (s) up to ~6% (7%), M H UB is reduced to less than ~130 GeV (131 GeV). E.g., the ~6% shift in the interval [0.6, 1.2] GeV, required to fix a μ, lowers M H UB to 126GeV. Tension with the M H > 120GeV vacuum stability bound. Reminder: the above M H upper bounds, like the LEP-EWWG ones, depend on the value of sin 2 θ lept eff. They also depend on M t & its unc. M t. We prepared simple formulae to translate easily M H upper bounds discussed above into new values corresponding to M t & M t inputs different from those employed here. 27

Conclusions g: Beautiful examples of interplay between theory and experiment: g e probed at <ppt and extraordinary test of QED s validity; g μ probed at <ppb test of the full SM and great opportunity

28 Conclusions g: Beautiful examples of interplay between theory and experiment: g e probed at <ppt and extraordinary test of QED s validity; g μ probed at <ppb test of the full SM and great opportunity to unveil (or just constrain) New Physics effects! The discrepancy a μ is more than 3 if e + e - data are used. With tau data, the deviation is only ~ 1. BaBar 2? If confirmed, e + e - data in turmoil! QED & EW solid and ready for exp Finale. LBL?? a μ can be due to New Physics, or to problems in a μ SM (or a μ EXP ). Can it be due to hypothetical mistakes in the hadronic (s)? An increase (s) could bridge a μ, leading however to a decrease on the EW upper bound on the SM Higgs mass M H... By means of a detailed analysis we conclude that solving a μ via an increase of (s) is unlikely in view of current exp. error estimates. However, if this turns out to be the solution, then the M H upper bound drops to about 130 GeV which, in conjunction with the LEP 114 GeV direct lower limit, leaves a rather narrow window for M H. 28

29 The End 29

30 ALEPH, CLEO & BELLE vs BaBar M. Davier, Tau08, Novosibirsk, September

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