Status and Prospects of New Physics Models in light of Muon g-2

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1 Status and Prospects of New Physics Models in light of Muon g-2 Motoi Endo (Tokyo) Winter School,

2 Standard Model ~126GeV

3 Hints of New Physics Proof Questions: Hint Signal Energy Scale neutrino oscillation RH neutrino [early universe] inflation very high baryogenesis models dark matter thermal history dark energy 10-3 ev GUT GeV(?) [fine-tuning problems] strong CP problem What is new physics? hierarchy problem what kinds of features, in which scale,... experimental anomalies PQ (> 10 9 GeV) TeV TeV In particular, cosmology is (e.g. there dark rad., anything cosmic ray) in TeV scale?

4 Hints of New Physics Proof Hint Signal neutrino oscillation [early universe] inflation baryogenesis dark matter dark energy GUT [fine-tuning problems] strong CP problem hierarchy problem experimental anomalies cosmology (e.g. dark rad., cosmic ray) Energy Scale RH neutrino very high models thermal history 10-3 ev GeV(?) PQ (> 10 9 GeV) TeV TeV

5 Anomalies from Experiments mode significance muon anomalous magnetic moment (muon g-2) >3σ Br(B D*τν)/Br(B D*lν) [cf. 2σ for Br(B Dτν)] 2.8σ inclusive and exclusive sin(2φ1) and Br(B τν) >2σ ICHEP2012 Direct CP violation of B K + π - and B + K + π 0 [5σ from 0] inclusive and exclusive determinations of Vub 2-3σ Direct CP violation of D K + K - and D π + π - [4σ from 0] like-sign dimuon charge asymmetry [D0] 3.9σ tight bound on Bs top forward-backward asymmetry [CDF, D0] >3σ electroweak precision [bottom FB asymmetry, NuTeV, SLD] >2σ proton charge radius >5σ neutrino anomalies [LSND, MiniBooNe, reactor, Gallium] >2σ Br(W τν)/br(w lν) [LEP] 2.8σ

6 Anomalies from Experiments mode significance muon anomalous magnetic moment (muon g-2) >3σ Br(B D*τν)/Br(B D*lν) [cf. 2σ for Br(B Dτν)] 2.8σ inclusive and exclusive sin(2φ1) and Br(B τν) >2σ ICHEP2012 Direct CP violation of B K + π - and B + K + π 0 [5σ from 0] New Physics implied in TeV scale inclusive and exclusive determinations of Vub 2-3σ It is crucial to understand Direct CP violation of D K + K - and D π + π - [4σ from 0] like-sign dimuon charge asymmetry [D0] 3.9σ tight bound on Bs Standard Model and Experiment top forward-backward asymmetry [CDF, D0] >3σ electroweak precision [bottom FB asymmetry, NuTeV, SLD] >2σ proton charge radius >5σ neutrino anomalies [LSND, MiniBooNe, reactor, Gallium] >2σ Br(W τν)/br(w lν) [LEP] 2.8σ

7 Anomalies from Experiments mode significance muon anomalous magnetic moment (muon g-2) >3σ Br(B D*τν)/Br(B D*lν) [cf. 2σ for Br(B Dτν)] 2.8σ inclusive and exclusive sin(2φ1) and Br(B τν) >2σ ICHEP2012 Direct CP violation of B K + π - and B + K + π 0 [5σ from 0] Today, we focus on muon g-2. inclusive and exclusive determinations of Vub 2-3σ Status and future prospect of new Direct CP violation of D K + K - and D π + π - [4σ from 0] like-sign dimuon charge asymmetry [D0] 3.9σ tight bound on Bs physics model will be explored. top forward-backward asymmetry [CDF, D0] >3σ electroweak precision [bottom FB asymmetry, NuTeV, SLD] >2σ proton charge radius >5σ neutrino anomalies [LSND, MiniBooNe, reactor, Gallium] >2σ Br(W τν)/br(w lν) [LEP] 2.8σ

8 Contents Introduction Current status of muon g-2-3-4σ deviation between SM and experimental result Status of New Physics Models Heavy photon model SUSY model - general MSSM - SUSY model Summary

9 Magnetic Moment of Muon g-factor: interaction of spin-magnetic field B - tree level (Dirac equation): g = 2 - radiative correction: aμ = (g-2)/2 Experiment: Brookhaven E821 spin Larmor Precession Calorimeter Number of events at calorimeter electron/positron emitted towards μ spin direction

10 Standard Model Prediction Exp (E821) (63) [10-11 ] QED (α 5, Rb) (0.080) EW (W/Z/HSM, NLO) (1.0) Hadronic [HLMNT] (43)* (leading) [DHMZ] (42) had Hadronic (α higher) (0.7) Hadronic (LbL) [RdRV] 105 (26)* [NJN] 116 (39) had > 3σ deviation

11 Hadronic Vacuum Polarization experimental data with dispersion relation and optical theorem [Hagiwara,Liao,Martin,Nomura,Teubner ;Davier,Hoecker,Malaescu,Zhang] K(s)/s is larger in lower energy hadron

12 Hadronic Vacuum Polarization experimental data with dispersion relation and optical theorem K(s)/s is larger in lower energy [Hagiwara,Liao,Martin,Nomura,Teubner ;Davier,Hoecker,Malaescu,Zhang] Contribution This work 2m π 0.32 GeV (ChPT, 2π) 2.36 ± m π 0.66 GeV (ChPT, 3π) 0.01 ± 0.00 m π 0.60 GeV (ChPT, π 0 γ) 0.13 ± 0.01 m η 0.69 GeV (ChPT, ηγ) 0.00 ± 0.00 φ unaccounted modes 0.04 ± GeV ± GeV (excl. only) ± GeV (incl. only) ± GeV (incl.-excl. avg.) ± GeV ± 0.82 J/ψ + ψ 7.80 ± 0.16 Υ(1S 6S) 0.10 ± (pqcd) 2.11 ± 0.00 Sum (excl. excl. incl.) ± 3.64 Sum (excl. incl. incl.) ± 4.23 Sum (excl. avg. incl.) ± 3.60 [Hagiwara,Liao,Martin,Nomura,Teubner]

13 Hadronic Vacuum Polarization experimental data with dispersion relation and optical theorem [Hagiwara,Liao,Martin,Nomura,Teubner ;Davier,Hoecker,Malaescu,Zhang] BaBar (09) New Fit KLOE (10) KLOE (08) K(s)/s is larger in lower energy 1.4 had,lo VP a µ 0.9 value (error) 2 m π 2 rad m π σ 0 (e + e - π + π - ) [nb] s [GeV] [Hagiwara,Liao,Martin,Nomura,Teubner]

14 Hadronic Vacuum Polarization small tension between BaBar and KLOE σ 0 (e + e - π + π - ) [nb] BaBar (09) New Fit KLOE (10) KLOE (08) CMD-2 (07) SND (06) CMD-2 (04) F π 2 KLOE10 KLOE KLOE10 KLOE s [GeV] require new experiments e.g.,vepp-2m, SuperKEKB Fig. 8. (M 0 ππ) 2 [GeV 2 ] Left: the pion form factor obtained in from the measurement with the photon at large c.f. inconsistency with τ decay data may be solved by ρ-γ mixing [Jegerlehner,Szafron] fractional difference between the two F 2 mea

15 Standard Model Prediction Exp (E821) (63) [10-11 ] QED (α 5, Rb) (0.080) EW (W/Z/HSM, NLO) (1.0) Hadronic [HLMNT] (43)* (leading) [DHMZ] (42) had Hadronic (α higher) (0.7) Hadronic (LbL) [RdRV] 105 (26)* [NJN] 116 (39) had > 3σ deviation

16 Hadronic Light-by-Light require hadronic models or lattice model: common features - dominant: pseudo-scalar meson exchange had [π 0 : largest contribution] - small: axial vector, scalar, π ± /K ± loop - small: quark loop (not small in DS approach) (a) [L.D.]. (b) [L.D.]. (c) [S.D.]. : p > Λ~1-2GeV

17 Hadronic light-by-light scattering in the muon g 2: Summary Some results for the various contributions to a LbyL;had µ : Contribution BPP HKS, HK KN MV BP, MdRR PdRV N, JN FGW π 0, η, η 85± ±6.4 83±12 114±10 114±13 99 ± 16 84±13 axial vectors 2.5± ±1.7 22±5 15±10 22±5 scalars 6.8±2.0 3σ! 7±7 7±2 π, Kloops 19±13 4.5±8.1 19±19 19±13 π,k loops 0±10 +subl. N C other 0±20 quark loops 21±3 9.7± ±3 107±48 Total 83± ± ±40 136±25 110± ± ± ±81 BPP = Bijnens, Pallante, Prades 95, 96, 02; HKS = Hayakawa, Kinoshita, Sanda 95, 96; HK = Hayakawa, Kinoshita 98, 02; KN = Knecht, Nyffeler 02; MV = Melnikov, Vainshtein 04; BP = Bijnens, Prades 07; MdRR = Miller, de Rafael, Roberts 07; PdRV = Prades, de Rafael, Vainshtein 09; N = Nyffeler 09, JN = Jegerlehner, Nyffeler 09; FGW = Fischer, Goecke, Williams 10, 11 (used values from arxiv: v2 [hep-ph], 4 Feb 2011) Pseudoscalar-exchange contribution dominates numerically (except in FGW). But other contributions are not negligible. Note cancellation between π,k-loops and quark loops! PdRV: Do not consider dressed light quark loops as separate contribution! Assume it is already taken into account by using short-distance constraint of MV 04 on pseudoscalar-pole contribution. Added all errors in quadrature! Like HK(S). Too optimistic? N, JN: New evaluation of pseudoscalars. Took over most values from BPP, except axial vectors from MV. Added all errors linearly. LikeBPP,MV,BP,MdRR.Toopessimistic? FGW: new approach with Dyson-Schwinger equations. Is there some double-counting? Between their dressed quark loop (largely enhanced!) and the pseudoscalarexchanges. Nyffeler, INT workshop on The Hadronic LbL Contribution to the Muon Anomaly -p.32

18 Standard Model Prediction Exp (E821) (63) [10-11 ] QED (α 5, Rb) (0.080) EW (W/Z/HSM, NLO) (1.0) Hadronic [HLMNT] (43)* (leading) [DHMZ] (42) had Hadronic (α higher) (0.7) Hadronic (LbL) [RdRV] 105 (26)* [NJN] 116 (39) had > 3σ deviation

19 New Physics Contribution Δaμ gnew 2 (muon mass ~106MeV) 2 16π 2 (new particle mass) 2 In order to explain the discrepancy new gnew W boson coupling mnew W boson mass μ gnew particle gnew μ No such particles have been discovered γ

20 New Physics Contribution Δaμ gnew 2 (muon mass ~106MeV) 2 16π 2 (new particle mass) 2 weak interaction, small mass heavy photon model (~10-100MeV) strong interaction, large mass supersymmetry (~100GeV) Question: Are they still viable?

21 Contents Introduction Current status of muon g-2-3-4σ deviation between SM and experimental result Status of New Physics Models Heavy photon model SUSY model - general MSSM - SUSY model Summary

22 Heavy Photon extra U(1) symmetry - couple to SM only via kinetic mixing with U(1)Y - broken, e.g., by (hidden) Higgs mechanism g-2 = + SM New

23 Muon g-2 excluded (muon g-2 > 5σ) Muon g-2 anomaly can be explained by heavy photon exchange [original by Pospelov]

24 Three Types of Constraints electron g-2 KLOE BaBar MESA Dark/Light E774 HPS HPS test APEX test MAMI MAMI test APEX VEPP3 HPS E141 HPS test E137 [Endo,Hamaguchi,Mishima]

25 1. Beam Dump Experiments e - beam dump experiments: E774, E141,... beam detector target/shield A decays in shield production rate too low

26 2. Rare Decay KLOE: [ ] form factor depends on model: uncertainty bound on A production rate Note: large background for small M A (=U) (or Mee) Data K S K L + ωπ 0 φ ηe + e - φ ηγ Events upper limit of A events at 90% π + π - π 0 π 0 π 0 π M ee (MeV) cosψ * BR(φ ηu ηe + e - ) M U (MeV) π + π - π 0 π 0 π 0 π 0 Combined M U (MeV)

27 Three Types of Constraints electron g-2 KLOE BaBar MESA Dark/Light E774 HPS HPS test APEX test MAMI MAMI test APEX VEPP3 E141 HPS electron g-2 region is most difficult to search HPS test E137 [Endo,Hamaguchi,Mishima]

28 3. Contribution to lepton g-2 muon additive to SM, favored to solve anomaly electron additive to SM, must be suppressed

29 Electron g-2 Exp (Harvard) (0.28) [10-12 ] QED (α 5 ) (0.77) EW (W/Z/HSM, NLO) (0.0005) Hadronic vac. pol. [Nomura, Teubner] leading (0.011) higher (0.0014) had Hadronic (LbL) (0.010) had Note:

30 Status previous result exclude Recently, electron g-2 constraint was updated by factor ~10 [Endo,Hamaguchi,Mishima]

31 Prospects electron g-2 KLOE BaBar MESA Dark/Light E774 HPS HPS test APEX test MAMI MAMI test APEX VEPP3 HPS E141 HPS test E137 [Endo,Hamaguchi,Mishima]

32 Prospects e - fixed target experiments: HPS, APEX, DarkLight,... - beam is not shielded - background suppressed by kinematics: energy, angle - After update of electron g-2 constraint, muon g-2 region can be tested in near future (HPS test planned in 2014) signal background

33 Contents Introduction Current status of muon g-2-3-4σ deviation between SM and experimental result Status of New Physics Models Heavy photon model SUSY model - general MSSM - SUSY model Summary

34 New Physics Contribution Δaμ gnew 2 (muon mass ~106MeV) 2 16π 2 (new particle mass) 2 weak interaction, small mass heavy photon model (~10-100MeV) strong interaction, large mass supersymmetry (~100GeV) c.f. current discrepancy is as large as EW contribution

35 SUSY chargino neutralino SUSY contrib. enhanced by tanβ: for

36 SUSY chargino neutralino diagram mass coupling condition usually dominant mass ~ 100GeV tanβ ~ 10 enhanced by μ mass ~ 100GeV tanβ ~ 10

37 LHC Search Two scenarios are searched for at LHC chargino dominance: ( decoupled) neutralino dominance: (large ) Other soft parameters favored to be large: - Higgs boson mass (~126GeV), FCNCs of K, D, B less constrained: - GUT mass relation: - decouple:

38 LHC Search GUT mass relation: light gluino mass - dominant channel: - signal: multi-jets + large MET ATLAS (8TeV, 5.8fb -1 ) [ATLAS-CONF ] Note: non-colored particle production - dominant channel: - signal: three-leptons + MET ATALS (8TeV, 13fb -1 ) [ATLAS-CONF ]

39 Cut: multi-jets + MET Channel [ATLAS-CONF ] Requirement A B C D E 2-jets 3-jets 4-jets 5-jets 6-jets E miss T [GeV] > 160 p T ( j 1 ) [GeV] > 130 p T ( j 2 ) [GeV] > 60 p T ( j 3 ) [GeV] > p T ( j 4 ) [GeV] > p T ( j 5 ) [GeV] > p T ( j 6 ) [GeV] > 60 (jet, E miss T ) min [rad] > 0.4 (i = {1, 2, (3)}) 0.4 (i = {1, 2, 3}), 0.2 (p T > 40 GeV jets) ET miss /m e (Nj) > 0.3/0.4/0.4 (2j) 0.25/0.3/ (3j) 0.25/0.3/0.3 (4j) 0.15 (5j) 0.15/0.25/0.3 (6j) m e (incl.) [GeV] > 1900/1300/ /1300/ 1900/1300/ / / 1400/1300/1000 meff = scalar sum of jet pt and ETmiss: choose heavy particle prod.

40 Cut: three-leptons + MET select events with three hard leptons suppress leptons from WZ background - cuts on msfos, mt, ETmiss b-veto constrain leptons from heavy flavor decay the Z mass. Selection SR1a SR1b SR2 Targeted χ 0 2 decay l ( ) or Z on-shell Z m SFOS m Z > 10 GeV < 10 GeV Number of b-jets 0 any ET miss > 75 GeV > 120 GeV m T any > 110 GeV > 110 GeV p T of leptons > 10 GeV > 30 GeV > 10 GeV [ATLAS-CONF ]

41 SUSY chargino neutralino diagram mass coupling condition usually dominant mass ~ 100GeV tanβ ~ 10 enhanced by μ mass ~ 100GeV tanβ ~ 10

42 Chargino: GUT mass relation small Wino mass region is excluded by gluino production GUT mass relation funnel region is due to multilepton channel smaller μ allows larger M2 lower lepton branching ratio for higgsino decay gluino production events will increase significantly g-2 1σ 2σ c.f. sneutrino LSP disfavored as DM [Endo,Hamaguchi,Iwamoto,Yoshinaga, in preparation]

43 Chargino: GUT mass relation small Wino mass region is excluded by gluino production funnel region is due to multilepton slepton off-shell channel smaller μ allows larger M2 lower lepton branching ratio slepton on-shell for higgsino decay gluino production events will increase significantly c.f. sneutrino LSP disfavored as DM GUT mass relation g-2 1σ sneutrino LSP [Endo,Hamaguchi,Iwamoto,Yoshinaga, in preparation] 2σ

44 Chargino: gluino decoupling small Wino mass region is due to off-shell slepton exchange c.f. on-shell for funnel region chargino production events will increase significantly gluino decouple g-2 1σ 2σ need sensitivity study smaller μ allows larger M2 - W, Z channels suffer from large background - possibly by Higgs channel [Endo,Hamaguchi,Iwamoto,Yoshinaga, in preparation]

45 SUSY chargino neutralino diagram mass coupling condition usually dominant mass ~ 100GeV tanβ ~ 10 enhanced by μ mass ~ 100GeV tanβ ~ 10

46 Neutralino: GUT mass relation LHC exclusion is similar to chargino case large M2 is allowed by g-2, as long as smuons are light very challenging to search for large M 2 region at LHC slepton direct production: GUT mass relation 2σ 1σ - small cross section - large background for dilepton [Endo,Hamaguchi,Iwamoto,Yoshinaga, in preparation]

47 Neutralino: GUT mass relation LHC exclusion is similar to chargino case large M2 is allowed by g-2, slepton off-shell as long as smuons are light very challenging to search for large M 2 region at LHC slepton direct production: - small cross section - large background for dilepton slepton on-shell GUT mass relation sneutrino LSP [Endo,Hamaguchi,Iwamoto,Yoshinaga, in preparation] 2σ 1σ

48 Neutralino: gluino decoupling LHC exclusion is similar to chargino case gluino decouple large M2 is allowed by g-2, as long as smuons are light very challenging to search for large M 2 region at LHC slepton direct production: 2σ 1σ - small cross section - large background for dilepton [Endo,Hamaguchi,Iwamoto,Yoshinaga, in preparation]

49 Status & Prospects [Status] LHC search for gluino and gaugino productions SUSY searches start to constrain muon g-2 region [Prospect] In future, gluino and gaugino events increase Challenging at LHC chargino: light higgsino region (large M2) neutralino: heavy higgsino region (large M2) search for direct slepton productions may be used

50 Contents Introduction Current status of muon g-2-3-4σ deviation between SM and experimental result Status of New Physics Models Heavy photon model SUSY model - general MSSM - SUSY model (motivated by phenomenology) Summary

51 Why is MSSM unnatural? too large flavor/cp violations - scalar fermion mass, scalar trilinear coupling, μ - constraints: K, B, D, μlfv, τlfv, EDM s,... cosmological gravitino problems - gravitino production depends on TR and Einf - constraints: BBN, DM abundance SUSY breaking/mediation mechanism colored and non-colored soft masses are correlated to each other

52 Tension in Models enhancement of muon g-2 small soft mass (~100 GeV) large tanβ (~10) enhancement of Higgs mass large soft mass (~ TeV) appropriate trilinear coupling

53 Tension in Models enhancement of muon g-2 small soft mass (~100 GeV) large tanβ (~10) 1 loop level [Draper,Meade,Reece,Shih] enhancement of Higgs mass large soft mass (~ TeV) appropriate trilinear coupling

54 msugra mh~125gev is too large for muon g-2 in msugra excluded Higgs>124GeV large scalar mass small scalar muon g-2 1σ 2σ mass [mh maximized by At, Br(b

55 Why is MSSM unnatural? too large flavor/cp violations - scalar fermion mass, scalar trilinear coupling, μ - constraints: K, B, D, μlfv, τlfv, EDM s,... cosmological gravitino problems - gravitino production depends on TR and Einf - constraints: BBN, DM abundance SUSY breaking/mediation model - tension between muon g-2 and Higgs mass

56 Simple Approaches Model Flavor/CP gravitino problems Higgs mass muon g-2 dark matter cmssm fine-tuning severe limit tension neutralino large soft masses suppressed OK OK hopeless neutralino GMSB suppressed OK too small OK gravitino

57 Simple Approaches Model Flavor/CP gravitino problems Higgs mass muon g-2 dark matter cmssm fine-tuning severe limit tension neutralino large soft masses suppressed OK OK hopeless neutralino GMSB suppressed OK too small OK gravitino extended GMSB OK OK

58 Extended GMSB Idea: enhance Higgs mass by extra effects large At term - messenger-top coupling extra vector-like matter - t coupling with Higgs extra gauge symmetry - Z and a charge for Higgs - singlet Higgs: Higgs mass enhanced when tanβ is small - triplet Higgs: may spoil perturbative GUT -...

59 Extra Vector-like Matter [Moroi,Okada] introduce [10:(Q,U,E )] MSSM extra top couples to Higgs Hu Hu T,QT Yt Higgs mass raised by U, Q loop Hu Hu vector ms(f): vector scalar(fermion) mass Hu U,Q Hu cf. A suppressed by RG running and irrelevant for Higgs mass. mh-max scenario is not realized Hu Y Hu

60 Muon g-2 and Higgs mass muon g-2 and Higgs mass can be explained simultaneously upper bound on soft mass by muon g vacuum instability stau NLSP neutralino upper bound on extra matter (t ) mass by Higgs mass - vector mass < (1-2) TeV - need higher order calculation 20 g-2 1σ 2σ Higgs [Endo,Hamaguchi,Ishikawa,Iwamoto,Yokozaki]

61 LHC Constraints LSP: gravitino, stable NLSP: long-lived neutralino NLSP - multi-jets + MET [ATLAS-CONF ] - Monte Carlo simulation stau NSLP - heavy charged track [CMS: ] Excluded stau NLSP neutralino [Endo,Hamaguchi,Ishikawa,Iwamoto,Yokozaki]

62 Maximally allowed Mass 1800 neutralino NLSP 300 stau NLSP muon g-2, 2σ muon g-2, 2σ σ excluded by LHC σ muon g-2 1σ region has been excluded by LHC all regions are expected to be covered by 13-14TeV LHC [c.f. Baer,Barger,Lessa,Tata]

63 Extra Top (t ) Searches stable extra matters spoil cosmology ( matter parity can be assigned) weak mixing with SM matters - extra matter searches current bounds [LHC,TVT] LHC, Tevatron - Flavor and CP violations similar to 4th generations interesting to see EDM, B decays,... * no (detailed) studies on future sensitivity

64 Summary Muon g-2 is a hint of physics beyond SM New physics models are classified into two categories - small mass with small coupling: heavy photon - large mass with large coupling: SUSY Current status and future prospects were discussed - HPS exp. (2014-) will check heavy photon model - Wide region will be tested by LHC for MSSM - Extra vector-like matter model - 1σ region of g-2 is excluded by LHC - 2σ region will be checked in future