Gauge invariant Barr-Zee type contributions to fermionic EDMs in the two-Higgs doublet models 北原鉄平 (Teppei Kitahara) University of Tokyo Collaborators : 阿部智広 (Tomohiro Abe) [KEK], 久野純治 (Junji Hisano) [Nagoya Univ.], 飛岡幸作 (Kohsaku Tobioka) [Kavli IPMU] Based on T. Abe, J. Hisano, T.K and K. Tobioka, JHEP 1401 (2014) 106, arXiv:1311.4704 BURI 2014 February 13, 2014, Toyama University BURI 2014 Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 2/21 BURI 2014 Basis of the Universe with ー ary Ideas 2014 Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 2/21 http://seriable.com/nbc-network/revolution-nbc-network/ Our Revolutionary Idea Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 3/21 Our Revolutionary Idea We derive improved Barr-Zee type contributions → first make BZ contributions gauge invariant + We become able to evaluate theoretical value of EDM more correctly conceptually and numerically Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 3 /21 Introduction Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 4/21 Electric Dipole Moment (EDM) What is EDM? L= eQ` ¯ a` ` 4m` µ⌫ `F Magnetic dipole moment term µ⌫ i ¯ d` ` 2 Electric dipole moment term EDM : d l Non-relativistic Hamiltonian H= ~ · ~sˆ µ` B Spin-Magnetic field int. C-even P-even T-even µ⌫ 5 `F µ⌫ ~ · ~sˆ d` E Spin-Electric field int. C-even P-odd T-odd ✔ Non-zero EDM violates T and CP symmetry Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 5/21 Electric Dipole Moment (EDM) Why does one focus on EDM? ✔ Observation of EDM implies NEW CP violation source New Physics!! SM EDM is too small to observe... Since our Universe experiences Baryogenesis, new CP violation source is needed in somewhere. ✔ Experiments of EDM are very precise. We can seek TeV scale physics indirectly. Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 6/21 The Model 2HDMs with softly-broken Z2 symmetry Z2 transformation Higgs potential ✔ CP violation phase relative phase of VEVS 2i 2 Im m3 5e Feb 13, 2014 BURI 2014 ✔redefine Higgs field ✔stationary condition Teppei KITAHARA -Univ. of Tokyo one CP violation physical phase 5e 2i 7 /21 The Model • The Yukawa interaction in this model is classified into the 4 types Z2 transformation Flipped type SM + extra Doublet SUSY type Lepton Specific One can avoid the dangerous FCNC problem Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 8 /21 EDM in 2HDM • In 2HDMs, leading EDM contributions come from not one-loop but two-loop diagrams [S. M. Barr and A. Zee, Phys. Rev. Lett. 65, 21(1990)] = H1 , H2 , H3 e e 1 m3e ⇠ ⇠ 10 2 4 (4⇡) v 36 [cm] ↵↵2 me ⇠ ⇠ 10 2 2 (4⇡) v = H1 , H2 , H3 e e Barr-Zee diagram Feb 13, 2014 BURI 2014 27 [e cm] Because electron Yukawa is too small, ↵↵2 Yukawa2 cf. SM (4 loop) Teppei KITAHARA -Univ. of Tokyo < 10 40 [e cm] 9 /21 Gauge invariance of Barr-Zee diagram • Actually, The Barr-Zee contribution to EDM is not gauge invariant [R. G. Leigh, S. Paban, R. M. Xu, Nucl. Phys. B 352, 45(1991)] = H1 , H2 , H3 e e Barr-Zee diagram Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 10 /21 Gauge invariance of Barr-Zee diagram • µ p 1 Mµ Actually, The Barr-Zee contribution to EDM is not gauge invariant 6= 0 µ p1 = H1 , H2 , H3 e [R. G. Leigh, S. Paban, R. M. Xu, Nucl. Phys. B 352, 45(1991)] The previous works did not care about the gauge invariance of BZ contributions e Barr-Zee diagram Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 10 /21 Gauge invariance of Barr-Zee diagram • µ p 1 Mµ Actually, The Barr-Zee contribution to EDM is not gauge invariant 6= 0 µ p1 = H1 , H2 , H3 e [R. G. Leigh, S. Paban, R. M. Xu, Nucl. Phys. B 352, 45(1991)] The previous works did not care about the gauge invariance of BZ contributions e Barr-Zee diagram Feb 13, 2014 BURI 2014 We improved BZ contribution to be gauge invariant one Teppei KITAHARA -Univ. of Tokyo 10 /21 [John M. Cornwall, Phys. Rev. D26, 6(1982)] Pinch Technique • Pinch technique is general method which can decompose gauge fixing parameter ξ independent subamplitudes T1 (t, ⇠) = Tˆ1 (t) f (t, ⇠) T2 (t, mi , ⇠) = Tˆ2 (t, mi ) + f (t, ⇠) h(t, mi , ⇠) T3 (t, s, mi , ⇠) = Tˆ3 (t, s, mi ) + h(t, mi , ⇠) • Diagrammatic representation T2 (t, mi , ⇠) Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 11 /21 [John M. Cornwall, Phys. Rev. D26, 6(1982)] Pinch Technique • Pinch technique is general method which can decompose gauge fixing parameter ξ independent subamplitudes T1 (t, ⇠) = Tˆ1 (t) f (t, ⇠) T2 (t, mi , ⇠) = Tˆ2 (t, mi ) + f (t, ⇠) h(t, mi , ⇠) T3 (t, s, mi , ⇠) = Tˆ3 (t, s, mi ) + h(t, mi , ⇠) • Diagrammatic representation T2 (t, mi , ⇠) Feb 13, 2014 BURI 2014 pinch! Teppei KITAHARA -Univ. of Tokyo 11 /21 [John M. Cornwall, Phys. Rev. D26, 6(1982)] Pinch Technique • Pinch technique is general method which can decompose gauge fixing parameter ξ independent subamplitudes T1 (t, ⇠) = Tˆ1 (t) f (t, ⇠) T2 (t, mi , ⇠) = Tˆ2 (t, mi ) + f (t, ⇠) h(t, mi , ⇠) T3 (t, s, mi , ⇠) = Tˆ3 (t, s, mi ) + h(t, mi , ⇠) • Diagrammatic representation T2 (t, mi , ⇠) Feb 13, 2014 BURI 2014 f (t, ⇠) pinch! Teppei KITAHARA -Univ. of Tokyo 11 /21 [John M. Cornwall, Phys. Rev. D26, 6(1982)] p Pinch Technique k q ! Pinch : k+p gauge 3 point vertex or gauge propagator k+q p-q gauge-fermion-fermion vertex kµ µ = (6 k+ 6 p Feb 13, 2014 BURI 2014 m) (6 p m) Teppei KITAHARA -Univ. of Tokyo 12 /21 [John M. Cornwall, Phys. Rev. D26, 6(1982)] p Pinch Technique k q ! Pinch : k+p gauge 3 point vertex or gauge propagator p-q k+q gauge-fermion-fermion vertex kµ µ = (6 k+ 6 p m) (6 p ✓ ◆ 1 i =i 6 k+ 6 p m Feb 13, 2014 BURI 2014 m) Equation of mortion (6 p m) Teppei KITAHARA -Univ. of Tokyo u ¯6p=u ¯m second term cancel out 12 /21 [John M. Cornwall, Phys. Rev. D26, 6(1982)] p Pinch Technique k q ! Pinch : k+p gauge 3 point vertex or gauge propagator p-q k+q gauge-fermion-fermion vertex kµ pinch! µ = (6 k+ 6 p m) (6 p ✓ ◆ 1 i =i 6 k+ 6 p m m) Equation of mortion (6 p m) u ¯6p=u ¯m second term cancel out First term pinch fermion propagator Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 12 /21 Pinch Technique pinch! ! Pinch : ! In order to obtain gauge invariant BZ type contribution, we should sum these diagrams + Pinch Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 13 /21 All charged particle run O(100) two-loop diagrams! • calculate all gauge invariant Barr-Zee contributions • check the gauge invariance analytically • get analytical formula of improved BZ contributions Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 14 /21 Results of electron EDM @YbF molecule @ThO molecule current bound Recently ACME Collaboration got new upper bound by ThO molecule! [ACME Collaboration, Science 17 Vol.343 no.6168 (2014)] Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 15 /21 Parameter as a benchmark tan 1 = 3 = O(10), = 4 2 = 5 sin 2 = 0.5, = 0.25 tan v2 = v1 ✔ Vacuum stability is safe ✔ EW precisions are safe @ M > 200GeV ✔ Lightest neutral scalar mass ⇠ 126GeV ✔ not unnatural parameter region Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 16 /21 Gauge-inv. Barr-Zee vs. Ordinary Barr-Zee We found that the difference between gauge-invariant and ordinary (= not gauge invariant) Barr-Zee contribution to electron EDM is about 5 - 8 % Di↵erence between de (gauge-inv. BZ) and de (ordinary BZ) tanβ = 10 Type II [T.Abe, J.Hisano, T.K, K.Tobioka, (2013)] Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 17 /21 Gauge-inv. Barr-Zee vs. Ordinary Barr-Zee Weisfound that difference between gauge-invariant andof This not so bigthe improvement from the numerical point ordinary (= notwe gauge invariant) contribution to view. However, would like to Barr-Zee emphasize that our result EDM invariant, is about 5 - which 8 % must be satisfied is electron now gauge Di↵erence between de (gauge-inv. BZ) and de (ordinary BZ) when we discuss observables. tanβ = 10 Type II [T.Abe, J.Hisano, T.K, K.Tobioka, (2013)] Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 17 /21 Electron EDM ● Contour Plot of eEDM [e・cm] Current exp. bound (90% CL) Heavy Higgs mass ThO Future Prospects Fr YbF, WN [T.Abe, J.Hisano, T.K, K.Tobioka, (2013)] Electron EDM ● eEDM vs Heavy Higgs scale [T.Abe, J.Hisano, T.K, K.Tobioka, (2013)] tanβ = 10 Current exp. bound (90% CL) tanβ = 10 Exclude ThO Future Prospects Fr Future Prospects YbF, WN Heavy Higgs mass ● Type X Type II, Type Y Feb 13, 2014 BURI 2014 Heavy Higgs mass Type I Teppei KITAHARA -Univ. of Tokyo 19 /21 Electron EDM ● eEDM vs Heavy Higgs scale [T.Abe, J.Hisano, T.K, K.Tobioka, (2013)] tanβ = 10 Current exp. bound (90% CL) tanβ = 10 Exclude ThO Future Prospects Fr Future Prospects YbF, WN Heavy Higgs mass 2 TeV ● Type X Type II, Type Y Feb 13, 2014 BURI 2014 Heavy Higgs mass 20 TeV Type I Teppei KITAHARA -Univ. of Tokyo 19 /21 Summary • New 2HDMs with Z2 symmetry have one new phase, and are constrained by the electron/neutron EDM 10 An analytical formulae of full gauge-inv. Barr Zee contribution is first derived by Using Pinch Technique D @%D • 8 6 4 2 tanβ = 10 0 200 + New • 600 800 MH + @GeVD 1000 Type II In Type II, X, Y 2HDMs, the future expeRIments of electron/neutron EDM are expected to reach O(10) TeV new Heavy scalars Feb 13, 2014 BURI 2014 400 Type II Teppei KITAHARA -Univ. of Tokyo tanβ = 10 20 TeV 20 /21 Discussions • EDM vs Electroweak Baryogenesis at the same parameter region [G. C. Dorsch, S. J. Huber and J. M. No, JHEP 1310, 029 (2013)] EWBG prefers low tanβ region Is there a tension between EWBG and EDM? Teppei Kitahara arXiv:1311.4704 Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 21 /21 Backup Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo /21 neutron EDM • The neutron EDM is obtained by QCD sum rule as follows assume PQ mechanism dn = 0.79dd C 0.20du + e(0.59dC + 0.30d d u) (QCD sum rules) [J. Hisano, J. Y. Lee, N. Nagata, Phys. Rev. D85, 114044(2012)] current bound @Ultra cold neutron Future prospects can improve to 2 orders of magnitude Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 35 /21 Neutron EDM ● Contour Plot of nEDM [e・cm] Current exp. bound (90% CL) Future Prospects Parameter Two Heavy Higgs Mass MH+ Lightest Higgs Mass 126 GeV 5 sin 2 = 0.5 [T.Abe, J.Hisano, T.K, K.Tobioka, (2013)] Parameter Neutron EDM 5 sin 2 = 0.5 Two Heavy Higgs Mass MH+ Lightest Higgs Mass = 126 GeV ● nEDM vs Heavy Higgs scale Current exp. bound (90% CL) Exclude Future Prospects tanβ = 10 [T.Abe, J.Hisano, T.K, K.Tobioka, (2013)] ● In Type I and Type X, neutron EDM is too small ● Type Y Type II Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 37 /21 Parameter Neutron EDM 5 sin 2 = 0.5 Two Heavy Higgs Mass MH+ Lightest Higgs Mass = 126 GeV ● nEDM vs Heavy Higgs scale Current exp. bound (90% CL) Exclude Future Prospects tanβ = 10 5 TeV [T.Abe, J.Hisano, T.K, K.Tobioka, (2013)] ● In Type I and Type X, neutron EDM is too small ● Type Y Type II Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 37 /21 Barr-Zee diagram • In Barr-Zee diagrams calculation, we separated them into HVV effective couplings part and other part Generalize At first, we consider HVV effective couplings Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 13 /21 Tensor structure of effective coupling on-shell photon off-shell vector general tensor structure µ p1 µ⌫ Feb 13, 2014 BURI 2014 gauge symmetry =0 (Ward-Takahashi identity) Teppei KITAHARA -Univ. of Tokyo 14 /21 Tensor structure of effective coupling on-shell photon off-shell vector If HVV effective vertex is gauge invariant µ p1 µ⌫ Barr-Zee diagram is gauge invariant µ p 1 Mµ =0 Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo =0 15 /21 Effective coupling -W loop- • We explicitly calculate W loop contribution, and result is as follows on-shell photon All set of W loop off-shell vector Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 16 /21 Effective coupling -W loop- • We explicitly calculate W loop contribution, and result is as follows on-shell photon All set of W loop off-shell vector gauge invariant term gauge non-invariant term Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo /21 Effective coupling -W loop- • We explicitly calculate W loop contribution, and result is as follows on-shell photon All set of W loop off-shell vector gauge non-invariant term These terms drop when all external lines are on-shell. However, in this situation (external lines are off-shell), these term do not drop. Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo /21 Effective coupling -W loopWe can transform pinch term into effective coupling form on-shell photon off-shell vector Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 22 /21 Effective coupling -W loopWe can transform pinch term into effective coupling form on-shell photon off-shell vector Feb 13, 2014 BURI 2014 second term cancel out Teppei KITAHARA -Univ. of Tokyo 22 /21 Effective coupling -W loopWe can transform pinch term into effective coupling form on-shell photon off-shell vector Feb 13, 2014 BURI 2014 last two terms does not contribute to dipole operator Teppei KITAHARA -Univ. of Tokyo 22 /21 Effective coupling -W loopWe can transform pinch term into effective coupling form on-shell photon off-shell vector last two terms does not contribute to dipole operator We checked analytically and found that these sum become gauge invariant Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 22 /21 Some demands to parameter region • Before we calculate EDMs, we should consider the following some demands to parameter region demands to parameter region • • • Vacuum Stability of Higgs potential Electroweak Precessions Higgs mass = 126 GeV Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 26 /21 Vacuum stability • The stability condition of the Higgs potential at treelevel (one demand that EW vacuum becomes global minimum) Tree-level stability condition [N. G. Deshpande and E. Ma, Phys. Rev. D 18 (1978) 2574] [A. W. El Kaffas, W. Khater, O. M. Ogreid and P. Osland, Nucl. Phys. B 775, 45 (2007)] Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 27 /21 Electroweak precision / ρ (T) parameter • ⇢⌘ The custodial SU(2) symmetry is broken in the CP violation 2HDM at the tree level, and ρ(T) parameter might deviate from 1 at one-loop level m2W m2Z cos2 ✓w WW ↵EM T = ⇧ [A. Pomarol and R. Vega, Nucl. Phys. B 413, 3 (1994)] =1+ (0) m2W ⇢ ' 1 + ↵EM T 2 2 m m ⇧ (0) H H± / m2Z m2W ZZ @BSM effect @ not mH >> VEVs experimental bound Texp. = 0.05 ± 0.12 (1 Theρ(T) parameter depends on the quadratic mass splitting among particles in the same isospin multiplet. If mass splitting is small, or heavy Higgs mass scale is large, theρ(T) parameter is small. Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 28 /21 ) Higgs mass = 126 GeV • 2HDM with CP violation have physical scalar bosons as 3 neutral Higgs and 1 charged Higgs 1 neutral Higgs is light 3 neutral Higgs mh1 ' v sin 2 p 2 2 neutral Higgs and 1 charged Higgs are 1 charged Higgs same mass scale M where Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 29 /21 Higgs mass = 126 GeV We require the mass of lightest neutral scalar to be 126 GeV, then parameter λ2 is uniquely determined 0.270 λ2 Plot 0.265 demand h1 = 126.0 GeV mh1 ' v sin l2 0.260 2 p 2 0.255 0.250 0.245 200 Feb 13, 2014 BURI 2014 400 600 M @GeVD Teppei KITAHARA -Univ. of Tokyo 800 1000 30 /21 QCD correction from Four Fermi Operator [J. Hisano, K. Tsumura, M. J. S. Yang, Phys. Lett. B713, 473(2012)] Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo /21 gg -> bb H/A, H/A -> tautau search Type II [CMS PAS HIG 12 050] Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo /21 Flavor constraint Type I Type II Type Y Type X [F. Mahmoudi and O. Stal, Phys.Rev. D81 (2010) 035016] Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo /21 electron EDM tanB = 3 Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo /21 electron EDM tanB = 50 Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo /21 2. ¥ 10-27 1. ¥ 10-27 dêe @cmD 2. ¥ 10-27 dêe @cmD 4. ¥ 10-27 0 -27 -2. ¥ 10 -4. ¥ 10-27 - p2 0 -1. ¥ 10-27 -2. ¥ 10-27 - p4 0 f p 4 M_H+ = 150 GeV Feb 13, 2014 BURI 2014 p 2 - p2 - p4 0 f p 4 p 2 M_H+ = 380 GeV Teppei KITAHARA -Univ. of Tokyo /21 Higgs mass Neutral Higgs Mass 1000 mh @GeVD 800 600 400 h3 h1 200 0 0 Feb 13, 2014 BURI 2014 h2 200 400 600 MH+ @GeVD Teppei KITAHARA -Univ. of Tokyo 800 1000 /21 Top couplings Axial coupling Vector coupling 1.0 h1 0.6 0.4 h2 h3 0.2 0 200 400 600 MH+ @GeVD 800 h2 0.06 »gtthA »êSM »gtthV »êSM 0.8 0.0 0.07 0.05 0.04 0.03 0.02 h1 0.01 1000 0.00 0 200 絶対値 Feb 13, 2014 BURI 2014 h3 Teppei KITAHARA -Univ. of Tokyo 400 600 MH+ @GeVD 800 1000 絶対値 /21 Bottom couplings Axial coupling Vector coupling 7 h2 5 h3 »gbbhA »êSM »gbbhV »êSM 6 4 3 2 0 0 200 400 600 MH+ @GeVD Feb 13, 2014 BURI 2014 h2 6 5 3 h1 1 800 1000 h3 4 2 h1 1 7 0 0 200 Teppei KITAHARA -Univ. of Tokyo 400 600 MH+ @GeVD 800 1000 /21 WWh couplings 1.0 h1 »gWWh»êSM 0.8 0.6 0.4 0.2 h3 0.0 0 Feb 13, 2014 BURI 2014 200 400 600 MH+ @GeVD Teppei KITAHARA -Univ. of Tokyo h2 800 1000 /21 geehA êSM * gtthV êSM 1.0 h2 0.5 0.0 -0.5 h1 -1.0 h3 -1.5 0 200 400 600 MH+ @GeVD Feb 13, 2014 BURI 2014 800 geehV êSM * gtthA êSM Some couplings 1000 h3 0.4 0.2 h1 0.0 -0.2 h2 -0.4 0 200 Teppei KITAHARA -Univ. of Tokyo 400 600 MH+ @GeVD 800 1000 /21 Electroweak precision / ρ (T) parameter -0.02 -0.04 -0.04 experimental bound Texp. = 0.05 ± 0.12 (1 ) Feb 13, 2014 BURI 2014 Teppei KITAHARA -Univ. of Tokyo 11 /21
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