Magnetic moment (g 2) µ and beyond the Standard Model physics

Magnetic moment (g 2) µ and beyond the Standard Model physics TU Dresden Lepton Moments Symposium, Cape Cod, July 2014

Discrepancy SM prediction too low by (28.7±8.0) 10 10 Note: discrepancy twice as large as a SM,weak µ ( ) but we expect: aµ NP aµ SM,weak MW 2 M NP couplings

Outline 1 Impact on New Physics in general Complementary Model dependent 2 Dark photon 3 SUSY Can explain the deviation tension with LHC data? details, new results Complementarity

Why is a µ special? µ R µ L CP- and Flavour-conserving, chirality-flipping, loop-induced b sγ compare: EDMs, B τν µ eγ EWPO

Why is a µ special? µ R µ L CP- and Flavour-conserving, chirality-flipping, loop-induced b sγ compare: EDMs, B τν µ eγ EWPO Note relation to m µ µ R µ L

Very different contributions to a µ generally: C = δm ( µ(n.p.) mµ ) 2, δa µ (N.P.) = O(C) m µ M classify new physics: C very model-dependent Very useful constraints on new physics

Very different contributions to a µ generally: C = δm ( µ(n.p.) mµ ) 2, δa µ (N.P.) = O(C) m µ M classify new physics: C very model-dependent Very useful constraints on new physics O(1) supersymmetry (tan β), unparticles [Cheung, Keung, Yuan 07] O( α 4π...) extra dim. (ADD/RS) (n c)... [Davioudasl, Hewett, Rizzo 00] [Graesser, 00][Park et al 01][Kim et al 01] O( α 4π ) Z, W, UED, Littlest Higgs (LHT)... generic analysis talk S. Westhoff

Very different contributions to a µ generally: C = δm ( µ(n.p.) mµ ) 2, δa µ (N.P.) = O(C) m µ M classify new physics: C very model-dependent Very useful constraints on new physics O(1) radiative muon mass generation... [Czarnecki,Marciano 01] [Crivellin, Girrbach, Nierste 11][Dobrescu, Fox 10] supersymmetry (tan β), unparticles [Cheung, Keung, Yuan 07] O( α 4π...) extra dim. (ADD/RS) (n c)... [Davioudasl, Hewett, Rizzo 00] [Graesser, 00][Park et al 01][Kim et al 01] O( α 4π ) Z, W, UED, Littlest Higgs (LHT)... generic analysis talk S. Westhoff

Very different contributions to a µ generally: C = δm ( µ(n.p.) mµ ) 2, δa µ (N.P.) = O(C) m µ M classify new physics: C very model-dependent Very useful constraints on new physics O(1) radiative muon mass generation... [Czarnecki,Marciano 01] [Crivellin, Girrbach, Nierste 11][Dobrescu, Fox 10] supersymmetry (tan β), unparticles [Cheung, Keung, Yuan 07] O( α 4π...) extra dim. (ADD/RS) (n c)... [Davioudasl, Hewett, Rizzo 00] [Graesser, 00][Park et al 01][Kim et al 01] O( α 4π ) Z, W, UED, Littlest Higgs (LHT)... generic analysis talk S. Westhoff α 4π dark photon...

Complementarity Checking models with large a µ contributions electroweak scale models generic collider signals [Freitas,Lykken,Westhoff 14] SUSY specific LHC signals depending on scenario [Endo,Hamaguchi,Iwamoto,Yoshinaga 13] correlation to µ eγ,... dark photons low-energy signals Different types of new physics lead to very different δa µ (N.P.) very useful, complementary constraints on N.P. 28.7 10 10 only possible if M NP < 2TeV (for C 1)

Outline 1 Impact on New Physics in general Complementary Model dependent 2 Dark photon 3 SUSY Can explain the deviation tension with LHC data? details, new results Complementarity

What if the LHC does not find new physics? Dark sector still possible and appealing: L =... ǫ 2 Fµν d F µν A µ diag. L int =...(A µ +ǫa µ )Jµ e.m. Aµ d two parameters: coupling ǫ, mass m A is generic if there is new U(1) gauge boson (GUT, strings,...) window to possibly many new, SM-neutral particles Motivation: dark matter, (g 2) µ (assume specific coupling/mass range)

Dark photon and a µ A µ R µ L = ǫ 2 α ( ) 4π F mµ m A explain a µ without messing up a e : M A 1MeV 3 10 κ 2 4 10 Excluded by electron g-2 vs α Excluded by muon g-2 5 10 muon g-2 <2σ 6 10 [Pospelov 08] 10 MeV 100 MeV 500 MeV m V [Snowmass rept. 13] constrained by (g 2) e, Υ,K,φ,π meson decays,...

More on bounds on dark photons beam dump: dark bremsstrahlung (works for specific coupling range) electron fixed target (APEX,A1) Babar, KLOE, WASA: meson decays often assumed: A e + e dominant if not: K πa, A invisible and e + e γ+invisible lead to bounds [Davoudiasl,Lee,Marciano 14][Izaguirre et al 13] generalization: also mass mixing dark Z with more general couplings, also strongly constrained

Outline 1 Impact on New Physics in general Complementary Model dependent 2 Dark photon 3 SUSY Can explain the deviation tension with LHC data? details, new results Complementarity

SUSY and the MSSM ( 100GeV aµ SUSY 12 10 10 tanβ sign(µ) M SUSY SUSY could be the origin of the observed (28±8) 10 10 deviation! ) 2

SUSY and the MSSM ( 100GeV aµ SUSY 12 10 10 tanβ sign(µ) M SUSY SUSY could be the origin of the observed (28±8) 10 10 deviation! But has the LHC ruled out SUSY? ) 2

SUSY and the MSSM ( 100GeV aµ SUSY 12 10 10 tanβ sign(µ) M SUSY SUSY could be the origin of the observed (28±8) 10 10 deviation! But has the LHC ruled out SUSY? No! ) 2

SUSY and the MSSM ( 100GeV aµ SUSY 12 10 10 tanβ sign(µ) M SUSY SUSY could be the origin of the observed (28±8) 10 10 deviation! But has the LHC ruled out SUSY? No! Motivation: natural Higgs and EWSB, dark matter, GUT ) 2 free parameters: p masses and mixings, µ and tan β

LHC-data! The tension is increasing... LHC: a µ m q, g > 1TeV m µ,χ < 700GeV m h = 126 GeV m t > 1TeV finetuning m t,µ small

LHC-data! The tension is increasing... LHC: a µ m q, g > 1TeV m µ,χ < 700GeV m h = 126 GeV m t > 1TeV finetuning m t,µ small Distinguish SUSY from concrete models/scenarios Constrained MSSM links m q m µ m h cannot explain a µ Tension motivates non-traditional models: [Endo, Hamaguchi, Ibe, Yanagida, D.P. Roy, et al] sleptons squarks [1303.4256,1210.3122] 2nd gen 3rd gen [1303.6995] new extra matter or U(1) (e.g. M 2 µ) [1108.3071,1112.6412]

It is worthwhile to look at the details

g 2 in the MSSM: chirality flips, λ µ, and H u tanβ = Hu H d, µ = H u H d transition H + d H + u W + W + some terms λ µ H u µ = m µ tanβ µ a SUSY µ tanβsign(µ) µ R ν µ µ L m 2 µ M 2 SUSY potential enhancement tanβ = 1...50 (and sign(µ))

Physics of subleading contributions (examples) H + u W+ 1-loop bino B B 1-loop µ R H u B H + d W + H d B µ R ν µl µ L standard W H µ L µ L µ L µ R µ R µ for µ B µ L µ R µ L µ R µ R B H µ R other sign! [Fargnoli,Gnendiger,Passehr,DS,Stöckinger-Kim 13] note: at least 3 light (<TeV) masses

Physics of subleading contributions (examples) H + u W+ 1-loop bino B B 1-loop µ R H u B H + d W + H d B µ R ν µl µ L standard W H µ L µ L µ L µ R µ R µ for µ B µ L µ R µ L µ R µ R B H µ R other sign! small/large µ [Fargnoli,Gnendiger,Passehr,DS,Stöckinger-Kim 13] small/large M µl

Complementarity to LHC: a µ central for BSM analyses 60 50 SPS4 DS12 aμ SUSY 10 10 40 30 20 10 0 10 SPS1b SPS1a SPS3 SPS2 SPS7 SPS6 SPS8 SPS5 SPS9 E1 E4 NS1 DS7 DS8 DS9 20 30 DS3 DS1 40 50 60 SPS benchmark points [v.weitershausen,schäfer, Stöckinger-Kim,DS 10] DS6 LHC Inverse Problem (300fb 1 ) can t be distinguished at LHC [Sfitter: Adam, Kneur, Lafaye, Plehn, Rauch, Zerwas 10] a µ sharply distinguishes BSM models here SUSY helps measure parameters [Hertzog, Miller, de Rafael, Roberts, DS 07] [Miller, de Rafael, Roberts, DS 12]

Correlation with µ eγ [talks by Gouvea, Lim] same structure additional mixing δ LL = m 2 L / m 2 L11 m 2 L22 12 H u W H d W µ R ν µ ν e e L study correlation for fixed δ LL aµ measured upper bound BR(µ eγ) < 5.7 10 13 (MEG) e.g. can predict possible range of δll given aµ SUSY [Chacko,Kribs 01;Isidori,Mescia,Paradisi,Temes 07]

Correlation with µ eγ study correlation for fixed δ LL = 2 10 5 However: strong correlation of individual diagrams does not imply strong correlation of the sum! Strong correlations for strong parameter constraints or domination of certain diagrams [Kersten,Park,DS,Velasco-Sevilla 14] black: from [Isidori et al]; other regions have looser constraints parameter regions where single diagrams dominate

Alternative: radiative muon mass in SUSY m tree µ = λ µ v d 1 λ µ = 0 generate m µ via A µ µ L µ R H u [Borzumati et al 99][Crivellin et al 11] 2 v d 0, tanβ generate m µ via coupling to v u [Dobrescu, Fox 10][Altmannshofer, Straub 10]

Radiative muon mass: MSSM for tanβ [Bach,Park,DS,Stöckinger-Kim, soon] standard case (equal masses, 1-loop) ( 100GeV aµ SUSY 12 10 10 tanβ sign(µ) M SUSY ) 2

Radiative muon mass: MSSM for tanβ [Bach,Park,DS,Stöckinger-Kim, soon] H + u W+ actually, including higher order effects [Marchetti,Mertens,Nierste,DS 08] λ µ H + d W + µ R ν µ µ L m µ v d +v u(1-loop) = λ tree µ (1+ µtanβ) a SUSY µ 12 10 10 tanβ sign(µ) 1 0.0018 tanβ sign(µ) ( 100GeV M SUSY ) 2

Radiative muon mass: MSSM for tanβ [Bach,Park,DS,Stöckinger-Kim, soon] limit tanβ ( ) 1000GeV 2 aµ SUSY 70 10 10 M SUSY tanβ and sign(µ) drop out, large contributions for M SUSY TeV!

Radiative muon mass: MSSM for tanβ [Bach,Park,DS,Stöckinger-Kim, soon] limit tanβ standard case: sign wrong! ( ) 1000GeV 2 aµ SUSY 70 10 10 M SUSY

Radiative muon mass: MSSM for tanβ [Bach,Park,DS,Stöckinger-Kim, soon] limit tanβ ( ) 1000GeV 2 aµ SUSY +37 10 10 M SUSY sign positive e.g. if µ M SUSY (then B µ L µ R dominates)

What is it good for? Big questions EWSB, Higgs, mass generation? hierarchy M Pl /M W? Naturalness? Unification of the Coupling Constants in the SM and the minimal MSSM 1/α i 60 50 1/α i 60 50 1/α 1 MSSM 40 40 1/α 2 30 30 20 20 dark matter? 10 10 1/α 3 0 0 5 10 15 10 log Q Grand Unification? 0 0 5 10 15 10 log Q...point to the TeV scale...and to new physics

Why new physics? Big questions also motivate new physics at other scales Unification of the Coupling Constants in the SM and the minimal MSSM 1/α i 60 50 1/α i 60 50 1/α 1 MSSM 40 40 1/α 2 30 30 20 20 dark matter? 10 10 1/α 3 0 0 5 10 15 10 log Q Grand Unification? 0 0 5 10 15 10 log Q Why three generations? Origin of flavor? m ν? Baryon asymmetry of the universe? Strong CP problem? dark forces, new CP/flavor violation, seesaw mechanism, axions,...

7. 10 9 6. 10 9 5. 10 9 4. 10 9 3. 10 9 2. 10 9 1. 10 9 500 1000 1500 2000 Conclusions Many appealing BSM scenarios a BSM µ model-dependent, typically O(±1...50) 10 10 complementary models with large aµ BSM for M BSM < 1 GeV (dark photon) 100 GeV [talk Westhoff] 500 GeV (SUSY) > 1 TeV (rad. m µ ) already constrained by data details important New experiments very promising!!

Status of SUSY prediction 1-Loop 2-Loop (SUSY 1L) 2-Loop (SM 1L) tanβ e.g. log M SUSY m µ e.g. tanβµm t χ 0,± f t χ 0,± f H γ µ µ µ, ν [Fayet 80],... [Kosower et al 83],[Yuan et al 84],... [Lopez et al 94],[Moroi 96] µ µ µ, ν [Degrassi,Giudice 98] [Marchetti, Mertens, Nierste, DS 08] [Schäfer, Stöckinger-Kim, v. Weitershausen, DS 10] µ µ,ν µ µ [Chen,Geng 01][Arhib,Baek 02] [Heinemeyer,DS,Weiglein 03] [Heinemeyer,DS,Weiglein 04] complete photonic complete (tanβ) 2 aim: full calculation (65000 diagrams)

The new contributions with f f loops γ f,f f χ 0, j χ 0, i µ µ µ, ν µ Motivation: Split spectra remaining class with dependence on squarks maximum complexity: 5 heavy + 2 light scales

Result contains large logs, ρ χ i µ m, ν µ 1 µ µ a 1L µ ρ γ f,f 2 f χ 0, j χ 0, i µ µ, νµ µ a 1L µ log(m f )

Result contains large logs, ρ χ i µ m, ν µ 1 µ µ a 1L µ ρ γ f,f 2 f χ 0, j χ 0, i µ µ, νµ µ a 1L µ log(m f ) Old γ t 3 H t µ µ µ Z a 1L µ 1 m 2 f

Results for f f-loops: Large contributions from heavy squarks [Fargnoli, Gnendiger, Passehr, DS, Stöckinger-Kim 13] 0.15 BM4 r 0.10 0.05 0.00 non-decoupling can be largest 2L contribution O(10%...30%) 0.05 0.10 10 3 10 4 10 5 10 6 M GeV M U3, D3, Q3, E3, L3 M U, D, Q M Q3 ; M U3 1 TeV tan Β 2 photonic 2 L a µ = 160, M 1 = 140, m µr = 200, M 2 = m µl = 2000 GeV, tanβ = 50

Results for f f-loops: Large contributions from heavy squarks [Fargnoli, Gnendiger, Passehr, DS, Stöckinger-Kim 13] r 0.10 0.05 0.00 0.05 BM1 0.10 10 3 10 4 10 5 10 6 M GeV non-decoupling can be largest 2L contribution O(10%...30%) M U3, D3, Q3, E3, L3 M U, D, Q M Q3 ; M U3 1 TeV tan Β 2 photonic 2 L a µ = 350, M 2 = 2M 1 = 300, m µr,l = 400 GeV, tanβ = 40

EWSB Models Large a µ possible? Randall Sundrum Littlest Higgs + T-Parity ( Bosonic SUSY ) 2-Higgs doublet model + 4th generation

EWSB Models Large a µ possible? Randall Sundrum Littlest Higgs + T-Parity ( Bosonic SUSY ) 2-Higgs doublet model + 4th generation Randall Sundrum KK-gravitons large [Kim, Kim, Song 01] However, challenged by electroweak precision data [Hewett et al 00] and γγ γγ unitarity [Kim,Kim,Song 01] non-graviton contributions small [Beneke, Dey, Rohrwild 12]

EWSB Models Large a µ possible? Randall Sundrum Littlest Higgs + T-Parity ( Bosonic SUSY ) 2-Higgs doublet model + 4th generation Littlest Higgs + T-Parity [Cheng, Low 03] [Hubisz, Meade, Noble, Perelstein 06] Tiny a µ from Z H, W H contributions [Blanke et al 07]

EWSB Models 5e-09 4e-09 Large a µ possible? Randall Sundrum a µ 3e-09 2e-09 M H + = 500 GeV m ν =100 GeV (black) 1e-09 =200 GeV (red) =400 GeV (blue) 0 0 0.008 0.016 0.024 0.032 0.04 δ Σ2.δ U2 Littlest Higgs + T-Parity ( Bosonic SUSY ) 2-Higgs doublet model + 4th generation 2-Higgs doublet model + 4th generation [Bar-Shalom, Nandi, Soni 11] Large contributions from ν H ± possible in agreement with LFV, FCNC constraints

Other types of new physics What if the LHC does not find new physics? Hide new particles at colliders large a µ possible Dark force? [Pospelov, Ritz...] very light, weakly interacting C 10 8, M < 1GeV 3 10 κ 2 4 10 Excluded by electron g-2 vs α Excluded by muon g-2 Light Z from gauged L µ L τ [Ma, Roy, Roy 02][Heeck, Rodejohann 11] flavour-dependent couplings, hidden at LEP C C SM,weak, M Z M Z 5 10 6 10 [Pospelov 08] muon g-2 <2σ 10 MeV 100 MeV 500 MeV m V