Dark Ma'er and Gauge Coupling Unifica6on in Non- SUSY SO() Grand Unified Models Natsumi Nagata Univ. of Minnesota/Kavli IPMU PANCK 2015 May 25-29, 2015 Ioannina, Greece Based on Y. Mambrini, N. Nagata, K. A. Olive, J. Quevillon, J. Zheng, Phys. Rev. D91, 0950 (2015) [arxiv:1502.06929].
Evidence for Dark Ma'er (DM) GalacUc scale Scale of galaxy clusters Cosmological scale D [µk 2 ] 6000 5000 4000 3000 2000 00 90 18 Angular scale 1 0.2 0.1 0.07 Begeman et. al. (1991) Clowe et. al. (2006) 0 2 50 500 00 1500 2000 2500 Multipole moment, Planck (2013)
Stability of DM DM parucle should be stable or have a lifeume longer than the age of the Universe. Example Discrete symmetry Z N R- parity in supersymmetric models KK- parity in the universal extra- dimensional models etc. Introducing a discrete symmetry by hand? Is there any mechanism for the symmetry?
Discrete symmetry as a remnant U(1) Suppose that there is a U(1) gauge symmetry: Field φ i φ H Charge Q i Q H Higgs field which breaks the extra U(1) symmetry Q H 0 (mod. N) Aeer the Higgs field φ H gefng a VEV, both the agrangian and the VEV are invariant under the following transformauons: There remains a Z N symmetry! U(1) φ H Z N T. W. B. Kibble, G. azarides and Q. Shafi (1982). M. Krauss and F. Wilczek (1989). E. Ibanez and G. G. Ross (1991) S. P. MarUn (1992)
SO() GUT SM gauge symmetries + an addiuonal U(1) Rank 5 SO() GUT H. Georgi (1975) H. Fritzsch and P. Minkowski (1975) In fact, non- SUSY SO() GUT is quite promising. SM fermions + right- handed neutrinos are embedded into 16. Gauge coupling unificauon is realized with an intermediate gauge symmetry. SO() G int G SM M GUT M int Small neutrino masses are explained by heavy right- handed neutrinos. M int M R M int
Discrete symmetry in SO() In non- SUSY SO() GUTs, the extra U(1) is broken at M int By appropriately choosing the intermediate Higgs field, we can obtain SO() G int G SM Z N Group analysis M. De MonUgny and M. Masip (1994) Higgs 126 672 Symmetry Z 2 Z 3 Equivalent to maser parity SO() contains U(1) B- If we focus on rather small representauons, Z 2 is the only possibility. SO() can explain the stability of DM! M. KadasUk, K. Kannike and M. Raidal (2009) M. Frigerio and T. Hambye (2009)
Our work Y. Mambrini, N. Nagata, K. A. Olive, J. Quevillon, J. Zheng, Phys. Rev. D91, 0950 (2015). We systemaucally examine DM in SO() GUT models. Construct SO() models which realize gauge coupling unificauon with an appropriate GUT scale. Two classes of DM candidates Non- equilibrium thermal DM (NETDM) WIMP DM Study the phenomenological consequences of our models DM relic abundance Proton decay lifeume Neutrino mass DM muluplet affects the gauge coupling running
Our work Y. Mambrini, N. Nagata, K. A. Olive, J. Quevillon, J. Zheng, Phys. Rev. D91, 0950 (2015). We systemaucally examine DM in SO() GUT models. Construct SO() models which realize gauge coupling unificauon with an appropriate GUT scale. Two classes of DM candidates Non- equilibrium thermal DM (NETDM) DM muluplet affects the gauge coupling running WIMP DM (in progress) Study the phenomenological consequences of our models DM relic abundance Proton decay lifeume Neutrino mass
Non- equilibrium thermal DM (NETDM) Y. Mambrini, K. A. Olive, J. Quevillon, B. Zaldivar (2013). SM singlet fermion DM Does not come into thermal equilibrium Non- thermally produced via heavy parucle exchange SM parucles DM Thermal bath Heavy parucles We can use intermediate- scale parucles as a mediator!
Setup SO() GUT- scale parucles M GUT M int G int Broken by 126 Right- handed neutrinos Intermediate parucles T R G SM Z 2 DM EW SM parucles Mass spectrum is obtained with fine- tuning. Just like doublet- triplet splifng
Models Model I Model II G int SU(4) C SU(2) SU(2) R SU(4) C SU(2) SU(2) R D R DM (1, 1, 3) D in 45 D (15, 1, 1) W in 45 W R 1 2 R 54 R R 2 (, 1, 3) C (1, 1, 3) R (, 1, 3) C (, 3, 1) C (15, 1, 1) R log (M int ) 8.08(1) 13.664(5) log (M GUT ) 15.645(7) 15.87(2) g GUT 0.53055(3) 0.5675(2) We have obtained two promising models! R DM : DM muluplet R 1 : GUT- scale Higgs R 2 : intermediate Higgs D : ee- right parity (, 1, 3) C 126 Other Higgs fields make only the DM field light. Y. Mambrini, N. Nagata, K. A. Olive, J. Quevillon, J. Zheng, Phys. Rev. D91, 0950 (2015).
Gauge coupling unifica6on Model I Model II We use 2- loop RGEs. W/ DM W/O DM Y. Mambrini, N. Nagata, K. A. Olive, J. Quevillon, J. Zheng, Phys. Rev. D91, 0950 (2015).
Proton Decay W/ DM W/O DM Model I Model II M X : mass of GUT- scale gauge boson Future proton decay experiments can probe the models. Y. Mambrini, N. Nagata, K. A. Olive, J. Quevillon, J. Zheng, Phys. Rev. D91, 0950 (2015).
Neutrino mass Neutrino masses are given by the seesaw mechanism. P. Minkowski (1977), T. Yanagida (1979) M. Gell- Mann, P. Ramond, R. Slansky (1979) S.. Glashow (1980) R. N. Mohapatra and G. Senjanovic (1980) Model I Model II Model I is disfavored on the basis of small neutrino masses. Possible soluuon IntroducUon of (15, 2, 2) Higgs field to modify the neutrino Dirac mass. Scarcely affects the gauge coupling running
Non- equilibrium thermal DM (NETDM) SM#par'cles Model I DM h ψ 0 f ψ 0 φ +,W + R ψ + γ,z φ 0,WR 0, ψ + φ +,W + R h ψ 0 f ψ 0 Thermal#bath Heavy#par'cles Model II Boltzmann equauon h φ 0 ψ 0 h φ ψ 0 DM relic abundance is given as a funcuon of DM mass M DM and the reheaung temperature T RH.
DM relic abundance Model I Model II Model I predicts low reheaung temperature T RH in Model II is relauvely high challenging for baryogengesis Y. Mambrini, N. Nagata, K. A. Olive, J. Quevillon, J. Zheng, Phys. Rev. D91, 0950 (2015).
Conclusion We discuss SM singlet fermion DM candidates in SO(). Stability of DM is explained in terms of a remnant Z 2. Such DM parucles are produced via the exchange of intermediate parucles (NETDM scenario). We have found two promising models. Gauge coupling unificauon is achieved in the models. We computed reheaung temperature which realizes the correct DM density. Future proton decay experiments can probe the models.
Backup
Discrete symmetry in SO() Table 1: Irreducible representations containing µ N. Representation Highest weight Z 2 µ 0 45 (0 1 0 0 0) + 54 (2 0 0 0 0) + 2 (0 0 0 1 1) + µ 1 16 (0 0 0 0 1) 144 (1 0 0 1 0) µ 2 126 (0 0 0 0 2) + Generic expression for a weight that is singlet under G SM. µ N =( NN N 0 N) A VEV of μ N yields Z N symmetry
Candidates for intermediate gauge group Table 2: Candidates for the intermediate gauge group G int. G int R 1 SU(4) C SU(2) SU(2) R 2 SU(4) C SU(2) SU(2) R D 54 SU(4) C SU(2) U(1) R 45 SU(3) C SU(2) SU(2) R U(1) B 45 SU(3) C SU(2) SU(2) R U(1) B D 2 SU(3) C SU(2) U(1) R U(1) B 45, 2 SU(5) U(1) 45, 2 Flipped SU(5) U(1) 45, 2
Candidates for NETDM Table 3: Candidates for the NETDM. G int R DM SO() SU(4) C SU(2) SU(2) R (1, 1, 3) 45 (15, 1, 1) 45, 2 (, 1, 3) 126 (15, 1, 3) 2 SU(4) C SU(2) U(1) R (15, 1, 0) 45, 2 (, 1, 1) 126 SU(3) C SU(2) SU(2) R U(1) B (1, 1, 3, 0) 45, 2 (1, 1, 3, 2) 126 SU(3) C SU(2) U(1) R U(1) B (1, 1, 1, 2) 126 SU(5) U(1) (24, 0) 45, 54, 2 (1, ) 126 (75, 0) 2 Flipped SU(5) U(1) (24, 0) 45, 54, 2 (50, 2) 126 (75, 0) 2 SM fermion DM SM Higgs SM fermions: Z 2 - odd SM Higgs: Z 2 - even DM should be Z 2 - even
Gauge coupling unifica6on without DM Table 4: log (M int ), log (M GUT ), and g GUT. For each G int, the upper shaded (lower) row shows the 2-loop (1-loop) result. M int and M GUT are given in GeV. The blank entries indicate that gauge coupling unification is not achieved. G int log (M int ) log (M GUT ) g GUT SU(4) C SU(2) SU(2) R 11.17(1) 15.929(4) 0.52738(4) 11.740(8) 16.07(2) 0.5241(1) SU(4) C SU(2) SU(2) R D 13.664(3) 14.95(1) 0.5559(1) 13.708(7) 15.23(3) 0.5520(1) SU(4) C SU(2) U(1) R 11.35(2) 14.42(1) 0.5359(1) 11.23(1) 14.638(8) 0.53227(7) SU(3) C SU(2) SU(2) R U(1) B 9.46(2) 16.20(2) 0.52612(8) 8.993(3) 16.68(4) 0.52124(3) SU(3) C SU(2) SU(2) R U(1) B D.51(1) 15.38(2) 0.53880(3).090(9) 15.77(1) 0.53478(6) SU(3) C SU(2) U(1) R U(1) B
Gauge coupling unifica6on without DM 16 14 12 SU(4) SU(2) SU(2) C R 1 loop 2 loops 16 14 12 11.22 11.2 SU(4) SU(2) SU(2) C R 13.68 13.675 SU(4) SU(2) SU(2) D C R 2 χ 8 2 χ 8 M int 11.18 M int 13.67 13.665 6 6 log 11.16 log 13.66 4 2 0 11.2 11.4 11.6 11.8 M int log 4 2 0 13.66 13.68 13.7 13.72 M int log 1 loop 2 loops SU(4) SU(2) SU(2) D C R 11.14 11.12 Best fit point 68% C 95% C 99% C 0.527 0.5272 0.5274 0.5276 0.5278 g GUT 13.655 13.65 13.645 Best fit point 68% C 95% C 99% C 0.5558 0.556 0.5562 g GUT 2 χ 16 14 12 8 6 4 2 log 1 loop 2 loops SU(4) SU(2) SU(2) C R 0 15.9 15.95 16 16.05 16.1 M GUT 2 χ 16 14 12 8 6 4 2 0 SU(4) SU(2) SU(2) D C R 15 15.1 15.2 M GUT log 1 loop 2 loops M GUT log 16 15.98 15.96 15.94 15.92 15.9 15.88 15.86 Best fit point 68% C 95% C 99% C SU(4) SU(2) SU(2) C R 0.527 0.5272 0.5274 0.5276 0.5278 g GUT M GUT log 15 14.98 14.96 14.94 14.92 14.9 SU(4) SU(2) SU(2) D C R Best fit point 68% C 95% C 99% C 0.5558 0.556 0.5562 g GUT 2 χ 16 14 12 8 SU(4) SU(2) SU(2) C R 1 loop 2 loops 2 χ 16 14 12 8 SU(4) SU(2) SU(2) D C R 1 loop 2 loops M int log 11.22 11.2 11.18 11.16 SU(4) SU(2) SU(2) C R M int log 13.68 13.675 13.67 13.665 13.66 SU(4) SU(2) SU(2) D C R 6 4 2 0 0.524 0.525 0.526 0.527 g GUT 6 4 2 0 0.552 0.553 0.554 0.555 0.556 g GUT 11.14 11.12 Best fit point 68% C 95% C 99% C 15.85 15.9 15.95 16 M GUT log 13.655 13.65 13.645 14.9 14.95 15 M GUT log Best fit point 68% C 95% C 99% C Figure 3: Contour plots for the allowed region in the g GUT -log (M int ), g GUT -log (M GUT ), and log (M GUT )-log (M int ) parameter planes in the top, middle, and bottom panels, respectively. eft panels are for G int = SU(4) C SU(2) SU(2) R, while right ones are for G int = SU(4) C SU(2) SU(2) R D. Stars represent the best-fit point. The colored regions correspond to 68, 95, and 99 % C.. limits determined from 2 ' 2.30, 5.99, 9.21.
Gauge coupling unifica6on with DM Table 5: Models that realize the gauge coupling unification. M int and M GUT are given in GeV. All of the values listed here are evaluated at one-loop level. SU(4) C SU(2) SU(2) R R DM R 2 log (M int ) log (M GUT ) g GUT (1, 1, 3) W (, 1, 3) C (1, 1, 3) R.8 15.9 0.53 (1, 1, 3) D (, 1, 3) C (1, 1, 3) R 9.8 15.7 0.53 SU(4) C SU(2) SU(2) R D R DM R 2 log (M int ) log (M GUT ) g GUT (15, 1, 1) W (, 3, 1) C (15, 1, 1) R 13.7 16.2 0.56 (, 1, 3) C (, 1, 3) C (, 3, 1) C (15, 1, 1) W (15, 1, 3) R (15, 3, 1) R 14.2 15.5 0.56 (, 1, 3) C (, 3, 1) C (15, 1, 1) D (15, 1, 3) R (15, 3, 1) R 14.4 16.3 0.58 SU(3) C SU(2) SU(2) R U(1) B R DM R 2 log (M int ) log (M GUT ) g GUT (1, 1, 3, 0) W (1, 1, 3, 2) C (1, 1, 3, 0) R 6.1 16.6 0.52