The MSSM confronts the precision electroweak data and muon g 2 (KEK, JSPS Research Fellow) I. Overview/Introduction II. Muon g 2 vs MSSM III. EW data vs MSSM IV. Summary Based on K. Hagiwara, A.D. Martin, DN and T. Teubner (HMNT), Phys. Lett. B557 (3) 69; Phys. Rev. D69 (4) 093003; Phys. Lett. B649 (7) 173. and G.-C. Cho, K. Hagiwara, Yu Matsumoto and DN, work in progress.
Overview Motivation for new physics at TeV scale Hierarchy Problem in the Standard Model t W H.. Radiative corrections to m 2 H diverges as Λ2. Physical Higgs mass m 2 weak. (Fine-tuning necessary if Λ m weak ) In SUSY Standard Models this is automatically solved since (softly broken) SUSY ensures the cancellation of the quad. divergences. For example,. λ t λ t. λ 2
Overview Motivation for MSSM Running Gauge Couplings SM case MSSM case Amaldi-de Boer-Fürstenau 91 Gauge coupling unification still remains a strong motivation for the MSSM.
Overview Searches for MSSM Until the LHC starts operation, we have to rely on indirect searches for new particles/interactions. Representative ones include: Muon g 2: Powerful probe for New Physics at TeV scale. 3.4σ deviation between exp. and theory (SM) reported = Signal of new physics? Electroweak (EW) precision data: Useful probe for New Physics ( S, T, U parameters ) Recently final LEP data appeared (hep-ex/0509008) A natural question everyone thinks of: Suppose that the MSSM is responsible for the muon g 2 anomaly. Where is the SUSY parameter region favored by the final LEP EW data? Important question to study BEFORE the LHC
Muon g 2
Muon g 2 Introduction Lepton magnetic moment µ: µ = g e 2m s, ( s = 1 2 σ (spin), g = 2 + 2F 2(0)) where u(p + q)γ µ u(p) = u(p + q) ( ) γ µ F 1 (q 2 ) + iσµν q ν 2m F 2(q 2 ) u(p) Anomalous magnetic moment: a (g 2)/2 (= F 2 (0)) Historically, g = 2 (tree level, Dirac) a = α/(2π) (1-loop QED, Schwinger) Today, still important, since... One of the most precisely measured quantities a exp µ = 11 659 208.0(6.3) 10 10 [0.5ppm] Extremely useful in probing/constraining physics beyond the SM
Recent News Concerning Muon g 2 EXP TH Feb 01 new exp. result (BNL) 2.6 σ Nov 01 The famous l-by-l sign error found 2.6 σ 1.6 σ (Knecht & Nyffeler) Dec 01 new e + e π + π data (CMD-2) July 02 new exp. result (BNL) 1.6 σ 2.6 σ Aug 02 new eval. of the LO had. contribution 2.6 σ 3.0 σ (DEHZ, e + e ) using the new CMD-2 data 3.3 σ (HMNT, e + e ) (DEHZ, HMNT, Jegerlehner) (0.9 σ) (DEHZ, τ) Aug 03 error found in the CMD-2 data 3.3 σ 2.4 σ analysis Dec 03 new eval. of the l-by-l contribution 2.4 σ 2.0 σ (Melnikov & Vainshtein) Jan 04 new exp result (BNL) 2.0 σ 2.9 σ Feb 04 improved QED calculation 2.9 σ 2.7 σ (Kinoshita & Nio) July 04 new F π data from KLOE June 05 new e + e π + π data from SND May 06 error found in the SND analysis Oct 06 new e + e π + π data from CMD-2 Nov 06 updated analysis of the LO had contrib. 3.4 σ (HMNT)
Standard Model Prediction for Muon g 2 QED contribution 11 658 471.809 (0.016) 10 10 Kinoshita & Nio EW contrib. 15.4 (0.2) 10 10 Czarnecki et al Hadronic contrib. LO hadronic 689.4 (4.5) 10 10 HMNT NLO hadronic 9.8 (0.1) 10 10 HMNT light-by-light 13.6 (2.5) 10 10 Melnikov & Vainshtein Theory TOTAL 11 659 180.4 (5.1) 10 10 Experiment 11 659 208.0 (6.3) 10 10 world avg. (6) δa µ a exp µ asm µ = (27.6 ± 8.1) 10 10 : 3.4σ discrepancy n.b.: hadronic contributions:.. LO µ had. NLO µ had... γ l-by-l µ had.
ICRR Theory Meeting, Dec. 11, 7 SUSY Contribution to Muon g 2 IF the 3.4σ deviation is due to SUSY,... Numerically, Dominant SUSY contributions: which is, very roughly, given by a SUSY µ =(sgnµ) 13 10 10 ( ) 2 100GeV tan β m In order for this to be 19.5 a SUSY µ 10 10 35.7 (1-σ range), a SUSY µ = (sgn µ) α(m Z) m 2 µ 8π sin 2 tan β, θ W m 2 where m is the SUSY scale. (Many people have published papers more or less related to this.) m = 190 580 GeV for tan β = 10 50. (Very rough estimate!)
SUSY Contribution to Muon g 2 (II) Favored parameter region in the M 2 -mẽ plane (a) tanβ=10, µ=396 GeV, A µ =0 (b) tanβ=50, µ=396 GeV, A µ =0 1000 3000 mẽ 900 800 700 tan β = 10 case mẽ 2500 0 tan β = 50 case m~ E (GeV) 600 500 m~ E (GeV) 1500 400 1000 300 500 100 100 300 400 500 600 700 800 M 2 (GeV) 400 600 800 1000 1 1400 1600 1800 M 2 (GeV) M 2 (GeV) M 2 (GeV) Favored slepton mass: < 300 GeV for tan β = 10, and < 900 GeV for tan β = 50 (1-σ range. Rough estimate!)
Electroweak Precision Study
Introduction to EW Precision Study LEP-I experiments ( 89-95): e + e annihilation experiments on the Z pole. The properties of Z bosons were studied in detail (mass, full/partial decay width, angular distributions of the decay products,...) using 17 millions of Z boson decays collected there. (Final report appeared recently : hep-ex/0509008) To confront the EW precision data with theory, the S, T, U parameters gives a useful framework (Peskin & Takeuchi). (One of) their main observations: In many cases, the most important radiative corrections to the EW observables appear in the gauge boson propagators.
1. Calculate Oi th ( S, T,...), where O i are EW precision observables (Γ Z, σh 0, A f,...). S-T Plane Analysis 0.2 0.15 SM 90% 39% 2. Construct the χ 2 function as χ 2 = i,j ( O th i ( S, T,...) O exp ) i ( V 1) ij ( O th j ( S, T,...) O exp ) j, where V is the covariance matrix (which can be constructed from the correlation matrix and the error, given by the LEP EW Working Group), V ij = (δo exp i )(δo exp j )ρ ij. 3. Find the minimum of χ 2 with respect to S, T etc. Draw the contours χ 2 χ 2 min = const if necessary. b T Z 46.1 g L + 9.2 b gr 0.1 0.05 0-0.05 100 176 m H m t -0.1 172-1σ +1σ (5) α had =0.02768 (22) 300 168-0.15-0.1-0.05 0 0.05 0.1 b b S Z 24.2 g L + 7.8 gr
b T Z 46.1 g L + 9.2 b gr 0.2 0.15 0.1 MSSM Electroweak Precision Data vs MSSM squarks m Q =300 A eff =0 300 90% 0.05 sleptons SPS4 500 SPS7 m SPS1a L =100 MAM1 GM1 0 MAM2 inos 1 140 10-0.05 120 176 m χ + =110 1 m M 2 /µ= 0.1 m t H 172-0.1-1σ +1σ 168 (5) 300 α had =0.02768 (22) -0.15-0.1-0.05 0 0.05 0.1 b b S Z 24.2 g L + 7.8 gr 39% Using the final LEP EW precision data, we can give a constraint on MSSM contributions to S and T. Our Results: The SM with m H 100 GeV gives a good description. In the MSSM, light sfermions tend to be disfavored. The MSSM sample points studied here, SPS1a, SPS4, SPS7,... are within the favored region. Cho-Hagiwara-Matsumoto-DN, in preparation
Electroweak Precision Data vs MSSM (II), M W 300 m H 120 168 172 m 176 t +1σ 1σ (5) α had =0.02768 (22) 1-σ allowed range MSSM m Q 500 300 A eff =0 squarks 300 m L sleptons 100 M 2 /µ=0.1 m χ + 140 110 1 inos 1 10 SPS1a SPS4 SPS7 GM1 MAM1 MAM2 Our Results: The MSSM with O(100) GeV SUSY masses gives a good description. Cho-Hagiwara-Matsumoto-DN, in preparation But this is not the full story... 80.28 80.32 80.36 80.40 80.44 m W (GeV)
Problem in Jet Asymmetry Data? leptonic asym data 0,l A FB A τ (P τ ) 0 A LR 0,b A FB jet asym data 0,c A FB lept sin 2 θ eff A b (0.018 ± 0.031) avg over lept asym avg over jet asym A c ( 0.0006 ± 0.0078) from lept. asym. data only (χ 2 min /dof=1.65/(3-1)) from jet asym. data only (χ 2 min /dof=0.39/(5-1)) average over the 8 observables (χ 2 min /dof=11.9/(8-1)) -0.0025-0.002-0.0015-0.001-0.0005 0 0.0005 0.001 0.0015 0.002 s 2 s 2 The value of the effective mixing angle s 2 determined only from leptonic asymmetry data and that determined only from jet asym. data do not agree very well = problem in jet asym. data (or in the analysis of them)?
Electroweak Precision Data w/o Jet Asym. Data vs MSSM b T Z 46.4 g L + 8.1 b gr 0.2 0.15 0.1 MSSM 90% 39% squarks m Q =300 A eff =0 300 0.05 sleptons SPS4 500 m L =100 SPS1a SPS7 MAM1 GM1 0 MAM2 inos 1 140 10-0.05 120 176 m χ + =110 1 m M 2 /µ= 0.1 m t H 172-0.1-1σ +1σ 168 (5) 300 α had =0.02768 (22) -0.15-0.1-0.05 0 0.05 0.1 b b S Z 25.2 g L + 4.4 gr If we do not use the jet asym. data, light sleptons tend to be favored. Cho-Hagiwara-Matsumoto-DN, in preparation
Summary Until the LHC starts operation, we have to rely on indirect searches, such as muon g 2 and the EW precision study, to probe new physics. From the EW precision fit in the MSSM using the LEP final EW precision data, we have concluded the following. If all the data are used, the SM with a light Higgs gives a good description. Light sfermions tend to be disfavored. However, there is a slight discrepancy ( 3σ) between the leptonic asymmetry data and the jet asymmetry data. If we neglect the jet asymmetry data, light sleptons are favored, which can explain the muon g 2 anomaly more easily.