New Physics for Muon g-2 anomaly Kazuhiro Tobe (Nagoya University - PowerPoint PPT Presentation

New Physics for Muon g-2 anomaly Kazuhiro Tobe (Nagoya University and KMI) References M.M. Nojiri, M. Takeuchi, and KT ★JHEP 1505 (2015) 028 [arXiv:1507.05028] and arXiv:1511.08880 (to be published in PRD), Y. Omura, E. Senaha, KT, 素粒子物理学の進展 2016 @ 基研 Sep. 5‒9 ★ PRD86, 095025 (2012) [arXiv: 1207.1313], S. Kanemitsu and KT ★ JHEP 1403, 105 (2014) [arXiv:1311.0870], K. Harigaya, T. Igari, ★ arXiv:1607.04447, KT

Introduction The standard model has been very successful Discovery of SM Higgs (-like) particle and no discovery of other new particles

But, we believe that there is more fundamental theory of elementary particles! Where is it?

“Naturalness” has been a strong driving force to think of new physics beyond the SM. SUSY, extra-dimension, little Higgs, etc But, there are no indication of such new physics at the LHC, so far. Maybe, it is good time to consider new physics differently

e.g. Kobayashi-Maskawa Motivated from the observation of CP violation in Kaon system Three generations in the standard model Good experimental data lead us to the right answer! Learn from the history……… Bottom-Up approach

2018?: COMET/Mu2E ( conversion ) start 2018?: SuperKEKB starts Many (big) experiments are coming soon! We expect lots of interesting data. and more … 2017-2019?: New muon g-2 exps. start 2015: LHC restarted again at √ s = 13 TeV e µ − e

But, even now, I think we have lots of observable [3.7σ in ] PRL111(2013)191801 早川さん、横崎さん、… 村山さん、大道さん、藤間さん、山本さん、山中さん、… 龍田さん、清水さん、… PRL113, 151601 (2014) interesting data 山本さん、… moment (muon g-2) [3-4σ] • non-zero, but tiny neutrino masses • dark matter and dark energy in our universe • baryon asymmetry in our universe • anomaly of muon anomalous magnetic B → K ∗ µ + µ − • LHCb anomaly in angular P 0 5 R K • LHCb anomaly in [2.6σ] R K ≡ B ( B + → K + µ + µ � ) B ( B + → K + e + e � ) = 0 . 745 +0 . 090 � 0 . 074 (stat) ± 0 . 036 (syst) .

北原さん、山本さん、… • Deviations in 早坂さん、… Belle: arXiv: 1607.07923, 1608.06391 CMS and LHCb: Nature 522, 68 (2015) [2.2σ] [3.9σ] LHCb: arXiv: 1506.08614 BaBar: PRL 109, 101802(2012), Belle: PRD 92.072014, • Deviations ? in CMS: arXiv: 1502.07400 h → τ µ • CMS anomaly of [2.4σ] V ub V cb • , problem (inclusive vs. exclusive) • ε’ problem R ( D ( ∗ ) ) = BR( ¯ ν ) / BR( ¯ B → D ( ∗ ) τ ¯ B → D ( ∗ ) l ¯ ν ) s → µ + µ − ) SM = 0 . 76 +0 . 20 BR( B 0 s → µ + µ − ) / BR( B 0 − 0 . 18 [1.2σ] BR( B 0 → µ + µ − ) / BR( B 0 → µ + µ − ) SM = 3 . 7 +1 . 6 − 1 . 4

LHC run2 ATLAS: ATLAS-CONF-2015-081 CMS: CMS-PAS-EXO-15-004 陣内さん We have many interesting data! • Diphoton excess at 750 GeV ?? • several 2-3σ excesses talked by 江成さん、斎藤さん、

muon g-2 anomaly may be interesting because ……

muon g-2 magnetic moment 早川さん (including the quantum corrections) It can be a good test of the standard model (muon g-2) anomalous magnetic moment • by radiative corrections • at tree level (Dirac fermion) g-factor 三部さん ⇣ e ⌘ µ · ~ ~ H = − ~ B, ~ µ = S g 2 m g = 2 g 6 = 2 a µ = g − 2 γ 2

15.4 (0.1): Higgs mass fixed (Grendiger et al ’13) Status of muon g-2 .895 (0.008): 5-loop calculation (Aoyama et al ’12) − QED contribution 11 658 471.808 (0.015) Kinoshita & Nio, Aoyama et al EW contribution 15.4 (0.2) Czarnecki et al Hadronic contributions LO hadronic 694.9 (4.3) HLMNT11 NLO hadronic − 9.8 (0.1) HLMNT11 light-by-light 10.5 (2.6) Prades, de Rafael & Vainshtein Theory TOTAL 11 659 182.8 (4.9) Experiment 11 659 208.9 (6.3) world avg Exp − Theory 26.1 (8.0) 3.3 σ discrepancy (in units of 10 − 10 . Numbers taken from HLMNT11, arXiv:1105.3149) n.b.: hadronic contributions: . . LO NLO l-by-l γ had. µ µ µ had. had. . . D. Nomura (YITP) Indirect searches for new physics Nov. 28, 2013 61 / 86

is comparable to the electroweak contribution If this anomaly is due to new physics, ..... The size of anomaly we expect new particles with EW scale mass strong constraints from EW precision data good target at near future experiments We may be able to discover the new physics before new experiment or/and new (improved) calculation for muon g-2. So, we should study it NOW! δ a µ = (26 . 1 ± 8 . 0) × 10 − 10 a EW = (15 . 4 ± 0 . 1) × 10 − 10 µ

model muon g-2 SUSY ○ Little Higgs × Extra dimension x ．．．．． Not many (interesting) models can explain it. complementary to known (interesting) models What kind of new physics ? 横崎さん

What is an important point to explain the muon g-2 anomaly while avoiding the experimental constraints? Not many (interesting) models can explain it.

Contents 1. Introduction 2. Enhancement of chirality flipping in muon g-2 4. Summary 3. General Two Higgs doublet model

Enhancement of chirality flipping in muon g-2

Note: Muon chirality has to be flipped. If there is some mechanism to enhance the chirality flipping, the new contribution to muon g-2 can be large. Effective operator for muon g-2 L = y v µ R σ µ ν µ L F µ ν + h . c . M 2 ¯

Toy models Kanemitsu and KT, PRD86, 095025 (2012) [arXiv: 1207.1313]

New Physics contributions to muon g-2 Model where has new Yukawa interaction with SU(2) singlet scalar ( ) and Dirac fermion ( ) x Note: The muon chirality is flipped in external fermion line ✴ φ φ † φ + · · · . χ R χ L + h . c . − m 2 L = − y N ¯ µ R χ L φ − m χ ¯ γ γ µ R µ L χ µ µ R χ L χ µ µ µ x µ L χ L µ R µ R φ φ γ φ φ ( b ) ( a )

特徴づけられる electroweak observables parameters φ , χ vertex corrections Z, γ oblique corrections → S,T パラメーターで

Constraints from EW observables muon g-2 total • Light new particles are favored. • The vertex corrections worsen the fit. 500  500 400 400  300 300  200 200  100 100  100 200 300 400 500 100 200 300 400 500      χ 2 / ( d.o.f ) = 34 . 8 / (22) for SM

enhancement of chirality flipping!! scalar mixing :SU(2) doublet :SU(2) singlet chirality flip The chirality is flipped in the internal fermion line x ✴ Model where and have new Yukawa interactions − y L ¯ = L 2 Φ χ R − y R ¯ µ R φχ L − m χ ¯ χ L χ R + h . c ., L L = y v µ R σ µ ν µ L F µ ν + h . c . M 2 ¯ Φ χ R χ L

Because of the enhancement, even small total muon g-2 Constraints from EW observables Yukawa couplings can induce large muon g-2 500 500 400 400 300 300 200 200 100 100 100 200 300 400 500 100 200 300 400 500 χ 2 / ( d.o.f ) = 34 . 8 / (22) for SM

enhancement Fayet PRD75(2007), Pospelov PRD80 (2009),... Davoudiasl, Lee, Marciano 横崎さん Abe, Sato, Yagyu JHEP 1507, 064 (2015), … •Lepton-specific two Higgs doublet model Some examples T. Moroi PRD53 (1996), ............. PRD86 (2012), Endo, Hamaguchi, Mishima PRD86 (2012), ....... • hidden (dark) photon ~very weak int. no enhancement (Z” model) Harigaya, Igari, Nojiri, Takeuchi, Tobe JHEP 1403, 105 (2014)… Villadoro, Zwirner JHEP (2010), Heeck, Rodejohann PRD84 (2011), PRD64 (2001), Ma, Roy, Roy PLB525 (2002),Salvioni, Strumia, He, Joshi, Lew, Volkas PRD43, 22 (1991), Baek, Deshpande, He, Ko, • model •SUSY U (1) L µ − L τ

SUSY (well-known example) x ~ chirality is flipped in the internal line tan β ˜ ˜ µ L µ R ˜ ˜ χ R χ L tan β enhancement

Endo, Hamaguchi, Kitahara, Yoshinaga, 1309.3065 Figure 3: The SUSY contributions to the muon g − 2 as a function of the lightest smuon mass, m ˜ µ 1 , and the lightest neutralino mass, m ˜ 1 . In the orange (yellow) χ 0 regions, the muon g − 2 discrepancy (1) is explained at the 1 σ (2 σ ) level. The left- right mixing is maximized under the vacuum stability condition. The parameters are ℓ L = m ˜ ℓ R , tan β = 40 and M soft = 10 TeV. The stau soft masses are equal to those m ˜ of the selectrons and smuons. The region below the green line is excluded by LHC.

enhancement no enhancement Omura, Senaha, Tobe 1507.05028, 1511.08880 Abe, Sato, Yagyu JHEP 1507, 064 (2015), … •Lepton-specific two Higgs doublet model Some examples T. Moroi PRD53 (1996), ............. PRD86 (2012), Endo, Hamaguchi, Mishima PRD86 (2012), ....... Fayet PRD75(2007), Pospelov PRD80 (2009),... Davoudiasl, Lee, Marciano • hidden (dark) photon ~very weak int. (Z” model) Harigaya, Igari, Nojiri, Takeuchi, Tobe JHEP 1403, 105 (2014)… Villadoro, Zwirner JHEP (2010), Heeck, Rodejohann PRD84 (2011), PRD64 (2001), Ma, Roy, Roy PLB525 (2002),Salvioni, Strumia, He, Joshi, Lew, Volkas PRD43, 22 (1991), Baek, Deshpande, He, Ko, • model •SUSY 横崎さん U (1) L µ − L τ • General Two Higgs doublet model

Contents 1. Introduction 2. Enhancement of chirality flipping in muon g-2 4. Summary 3. General Two Higgs doublet model