- Email: [email protected]
Mass spectrum of neutrinos and lepton flavor violation processes
Nuclear Physics B (Proc. Suppl.) 155 (2006) 351–352 www.elsevierphysics.com
Mass spectrum of neutrinos and lepton flavor violation processes ∗ Serguey Petcova Tetsuo Shindoua† Yasutaka Takanishib a
Scuola Internazionale Superiore di Studi Avanzati, I-34014 Trieste, Italy
b
The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, I-34100 Trieste, Italy
We investigate the lepton flavor violation decays in the minimal supersymmetric standard model with righthanded neutrinos. We consider cases with typical spectrum of light and heavy neutrinos and discuss the correlation among the several lepton flavor decays.
Large hadron collider (LHC) and international linear collider (ILC) are the most promising ways to approach the new physics beyond the standard model. LHC is planned to start in 2007 and it is expected to find some signals of new physics. If LHC/ILC find an evidence of the new physics, the flavor physics becomes much more important to explore the detail of the new physics. Supersymmetry (SUSY) is one of the most attractive candidates of the new physics. There are several motivations for introducing SUSY. (i) SUSY can be a solution of the gauge hierarchical problem. (ii) There is a candidate of the cold dark matter in the model. (iii) Well-defined light Higgs mass is predicted. (iv) gauge coupling unification is modified. In minimal supersymmetric standard model (MSSM), there are rich source of flavor violations and CP violations due to the existence of SUSY partner of the quarks and leptons. On the other hand, we have already known an evidence of new physics, which is the finite neutrino mass. From the recent neutrino oscillation experiments, the finite neutrino masses are established. Seesaw model is the most interesting mechanism which can explain the smallness of neutrino masses. MSSM and seesaw model meet on the lepton flavor violation[1]. In the SUSY seesaw models, the flavor mixing in slepton sector is induced by neutrino Yukawa couplings, even if there is no ∗ Presentation
given by T. Shindou
† [email protected]
0920-5632/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2006.02.098
mixing at the scale where the soft SUSY breaking terms are given, Then the lepton flavor violation processes are the very powerful tool to study both the SUSY sector and the neutrino sector. Introducing right handed neutrinos, the superpotential of lepton sector can be written as W =(YE )ij Eic Lj Hd + (YN )ij Nic Lj Hu 1 + (M )ij Nic Njc . 2
(1)
Hereafter, we take the base where the charged lepton mass matrix and the Majorana mass matrix of right handed neutrinos are diagonal. Integrating out the heavy right-handed neutrinos N c , we obtain 1 W =(YEi )Eic Li Hd + (κN )ij (Li Hu )(Lj Hu ), 2 (2)
κN = − YNT M −1 YN ,
(3)
where the dimension five operator in the above superpotential gives the neutrino mass matrix after the electroweak symmetry breaking. Then the neutrino Yukawa couplings can be written as[2,3] YN =
1 DN R Dν U † , 2 Hu
(4)
where DN and Dν are the mass eigenvalues matrix for right handed neutrinos and the standard model neutrinos, DN = diag(M1 , M2 .M3 ) and
352
S. Petcov et al. / Nuclear Physics B (Proc. Suppl.) 155 (2006) 351–352
Dν = diag(m1 , m2 , m3 ), U is the Pontecorvo– Maki–Nakagawa–Sakata matrix, and R is a complex orthogonal matrix as RT R = 1. It is known[3–5] that the complex phases in R significantly affects on the lepton flavor violation decays. Here we consider the inverted hierarchical light neutrinos. For inverted hierarchical neutrinos, we can use the approximation as Dν diag(m, m, 0). For heavy neutrinos, we consider three typical cases: (H) hierarchical case, DN ∼ diag(0, 0, M ), (IH) inverted hierarchical case, DN ∼ diag(M, M, 0), and (QD) quasi degenerate case, DN ∼ diag(M, M, M ). When the universal soft SUSY breaking terms at the scale MX > M , the branching ratios of lepton flavor violation decays, µ → eγ, τ → eγ, and τ → µγ can be estimated as B(li → lj γ)
α3 Hu 2 /Hd 2 G2F m8S
2 1 MX † 2 2 ij × 2 (3 + |A0 | )m0 (YN YN ) ln , 8π M (5) where m0 is universal soft scalar mass, A0 is a proportional constant of trilinear couplings, and mS denotes a typical SUSY mass scale. mS can be estimated as[6] m8S 0.5m20 m21/2 (m20 + 0.6m21/2 )2 .
(6)
with the gaugino mass at MX , m1/2 . Then the lepton flavor violation decays li → lj γ is very sensitive to (YN† YN )ij . In Fig. 1, the correlation between µ → eγ and τ → µγ is shown for |Ue3 | = 0. One can find that every spectrum type of heavy neutrinos has typical pattern. Then it may be possible to distinguish the spectrum of heavy neutrinos. As for the correlation between τ → eγ and µ → eγ, the relation B(τ → eγ) 0.18B(µ → eγ) is found for every type of heavy neutrino spectrum in |Ue3 | = 0.0 case. We have analyzed the lepton flavor violation processes in the case of inverted hierarchical light neutrinos case and pointed out the possibility to distinguish the heavy neutrino spectrum by the correlation between τ → µγ and µ → eγ.
Figure 1. The correlation between B(µ → eγ) and B(τ → µγ). For SUSY parameters, we set tan β = 10, m0 = 100GeV, m1/2 = 250GeV, and A0 = −100GeV. In addition, M is assumed to be 2 × 1012 GeV.
If SUSY at a few TeV scale is realized in nature, LHC or ILC is likely to provide some evidence of SUSY. Then the role which flavor physics plays becomes more and more important. At present, the experiments of lepton flavor violation processes give one of the strongest constraints on the parameter space of SUSY. That is to say, the lepton flavor violation will be the most powerful tool to explore the SUSY flavor structure in future. REFERENCES 1. F. Borzumati and A. Masiero, Phys. Rev. Lett. 57, 961 (1986); J. Hisano et al., Phys. Lett. B 357, 579 (1995); J. Hisano, et al. Phys. Rev. D 53, 2442 (1996). 2. J. A. Casas and A. Ibarra, Nucl. Phys. B 618, 171 (2001); 3. S. Pascoli, S. T. Petcov and C. E. Yaguna, Phys. Lett. B 564, 241 (2003). 4. S. Kanemura et al., Phys. Rev. D 72, 055012 (2005). 5. S. T. Petcov, T. Shindou and Y. Takanishi, arXiv:hep-ph/0508243. 6. S. T. Petcov et al., Nucl. Phys. B 676, 453 (2004).
Mass spectrum of neutrinos and lepton flavor violation processes ∗ Serguey Petcova Tetsuo Shindoua† Yasutaka Takanishib a
Scuola Internazionale Superiore di Studi Avanzati, I-34014 Trieste, Italy
b
The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, I-34100 Trieste, Italy
We investigate the lepton flavor violation decays in the minimal supersymmetric standard model with righthanded neutrinos. We consider cases with typical spectrum of light and heavy neutrinos and discuss the correlation among the several lepton flavor decays.
Large hadron collider (LHC) and international linear collider (ILC) are the most promising ways to approach the new physics beyond the standard model. LHC is planned to start in 2007 and it is expected to find some signals of new physics. If LHC/ILC find an evidence of the new physics, the flavor physics becomes much more important to explore the detail of the new physics. Supersymmetry (SUSY) is one of the most attractive candidates of the new physics. There are several motivations for introducing SUSY. (i) SUSY can be a solution of the gauge hierarchical problem. (ii) There is a candidate of the cold dark matter in the model. (iii) Well-defined light Higgs mass is predicted. (iv) gauge coupling unification is modified. In minimal supersymmetric standard model (MSSM), there are rich source of flavor violations and CP violations due to the existence of SUSY partner of the quarks and leptons. On the other hand, we have already known an evidence of new physics, which is the finite neutrino mass. From the recent neutrino oscillation experiments, the finite neutrino masses are established. Seesaw model is the most interesting mechanism which can explain the smallness of neutrino masses. MSSM and seesaw model meet on the lepton flavor violation[1]. In the SUSY seesaw models, the flavor mixing in slepton sector is induced by neutrino Yukawa couplings, even if there is no ∗ Presentation
given by T. Shindou
† [email protected]
0920-5632/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2006.02.098
mixing at the scale where the soft SUSY breaking terms are given, Then the lepton flavor violation processes are the very powerful tool to study both the SUSY sector and the neutrino sector. Introducing right handed neutrinos, the superpotential of lepton sector can be written as W =(YE )ij Eic Lj Hd + (YN )ij Nic Lj Hu 1 + (M )ij Nic Njc . 2
(1)
Hereafter, we take the base where the charged lepton mass matrix and the Majorana mass matrix of right handed neutrinos are diagonal. Integrating out the heavy right-handed neutrinos N c , we obtain 1 W =(YEi )Eic Li Hd + (κN )ij (Li Hu )(Lj Hu ), 2 (2)
κN = − YNT M −1 YN ,
(3)
where the dimension five operator in the above superpotential gives the neutrino mass matrix after the electroweak symmetry breaking. Then the neutrino Yukawa couplings can be written as[2,3] YN =
1 DN R Dν U † , 2 Hu
(4)
where DN and Dν are the mass eigenvalues matrix for right handed neutrinos and the standard model neutrinos, DN = diag(M1 , M2 .M3 ) and
352
S. Petcov et al. / Nuclear Physics B (Proc. Suppl.) 155 (2006) 351–352
Dν = diag(m1 , m2 , m3 ), U is the Pontecorvo– Maki–Nakagawa–Sakata matrix, and R is a complex orthogonal matrix as RT R = 1. It is known[3–5] that the complex phases in R significantly affects on the lepton flavor violation decays. Here we consider the inverted hierarchical light neutrinos. For inverted hierarchical neutrinos, we can use the approximation as Dν diag(m, m, 0). For heavy neutrinos, we consider three typical cases: (H) hierarchical case, DN ∼ diag(0, 0, M ), (IH) inverted hierarchical case, DN ∼ diag(M, M, 0), and (QD) quasi degenerate case, DN ∼ diag(M, M, M ). When the universal soft SUSY breaking terms at the scale MX > M , the branching ratios of lepton flavor violation decays, µ → eγ, τ → eγ, and τ → µγ can be estimated as B(li → lj γ)
α3 Hu 2 /Hd 2 G2F m8S
2 1 MX † 2 2 ij × 2 (3 + |A0 | )m0 (YN YN ) ln , 8π M (5) where m0 is universal soft scalar mass, A0 is a proportional constant of trilinear couplings, and mS denotes a typical SUSY mass scale. mS can be estimated as[6] m8S 0.5m20 m21/2 (m20 + 0.6m21/2 )2 .
(6)
with the gaugino mass at MX , m1/2 . Then the lepton flavor violation decays li → lj γ is very sensitive to (YN† YN )ij . In Fig. 1, the correlation between µ → eγ and τ → µγ is shown for |Ue3 | = 0. One can find that every spectrum type of heavy neutrinos has typical pattern. Then it may be possible to distinguish the spectrum of heavy neutrinos. As for the correlation between τ → eγ and µ → eγ, the relation B(τ → eγ) 0.18B(µ → eγ) is found for every type of heavy neutrino spectrum in |Ue3 | = 0.0 case. We have analyzed the lepton flavor violation processes in the case of inverted hierarchical light neutrinos case and pointed out the possibility to distinguish the heavy neutrino spectrum by the correlation between τ → µγ and µ → eγ.
Figure 1. The correlation between B(µ → eγ) and B(τ → µγ). For SUSY parameters, we set tan β = 10, m0 = 100GeV, m1/2 = 250GeV, and A0 = −100GeV. In addition, M is assumed to be 2 × 1012 GeV.
If SUSY at a few TeV scale is realized in nature, LHC or ILC is likely to provide some evidence of SUSY. Then the role which flavor physics plays becomes more and more important. At present, the experiments of lepton flavor violation processes give one of the strongest constraints on the parameter space of SUSY. That is to say, the lepton flavor violation will be the most powerful tool to explore the SUSY flavor structure in future. REFERENCES 1. F. Borzumati and A. Masiero, Phys. Rev. Lett. 57, 961 (1986); J. Hisano et al., Phys. Lett. B 357, 579 (1995); J. Hisano, et al. Phys. Rev. D 53, 2442 (1996). 2. J. A. Casas and A. Ibarra, Nucl. Phys. B 618, 171 (2001); 3. S. Pascoli, S. T. Petcov and C. E. Yaguna, Phys. Lett. B 564, 241 (2003). 4. S. Kanemura et al., Phys. Rev. D 72, 055012 (2005). 5. S. T. Petcov, T. Shindou and Y. Takanishi, arXiv:hep-ph/0508243. 6. S. T. Petcov et al., Nucl. Phys. B 676, 453 (2004).