1. Gauge Coupling Unification in Radiative Models Stella Riad, KTH Royal Institute of Technology Neutrinos from GUTs down to low energies, Munich, November 2015

2. Outline Motivation RG running in the SM Radiative neutrino mass models RG running in low-energy neutrino mass models (with C. Hagedorn, T. Ohlsson, M. Schmidt) Conclusions 2 Stella Riad, RG running in radiative models, MIAPP, 26/11-2015

3. Motivation 3 Stella Riad, RG running in radiative models, MIAPP, 26/11-2015 -Neutrinos have small, but non-zero masses -New mechanism needed -Discussed in EFT framework

4. Standard model problems 4 Stella Riad, RG running in radiative models, MIAPP, 26/11-2015 - Gauge coupling unification at high scale - Embed SM in larger gauge group (SU(5), SO(10),…)

5. Renormalization Group Running 5 Extra dimensions GUTs: -SU(5) -SO(10) Accelerators (LHC) Neutrino experiments String theory Loop quantum gravity ? Favorite model Low energy High energy Stella Riad, RG running in radiative models, MIAPP, 26/11-2015

6. SM running at two-loops The gauge coupling running at two-loop in general renormalizable theory with scalar, spin-1/2, and vector gauge bosons. Machacek, Vaughn, Nucl.Phys. B222 (1983) Depending only on particle content 6 Determined analytically or numerically Stella Riad, RG running in radiative models, MIAPP, 26/11-2015

7. PyR@TE “Python Renormalization group equations At Two-loop for Everyone”. Lyonnet, Schienbein, Staub, Wingerter, Comput.Phys.Commun. 185 (2014) Python code which calculates the RGEs for any non- supersymmetric model Specify gauge group, particle content and scalar couplings Output to LaTeX, Pickle and Mathematica Same function as in SARAH 7 Stella Riad, RG running in radiative models, MIAPP, 26/11-2015

8. 8 Neutrino mass models Seesaw Radiative models Stella Riad, RG running in radiative models, MIAPP, 26/11-2015 Zee model Zee-Babu model Chen, McDonald, Nasri 2014

9. Neutrino mass operators Neutrino masses generated by d>4 operators Weinberg operator, d=5: Majorana masses, 129 LNV operators, d=5,7,9,11. (Babu, Leung, 2001, de Gouvea, Jenkins, 2008) 9 Stella Riad, RG running in radiative models, MIAPP, 26/11-2015

10. Procedure: -Make choice of model, identify representations -Determine contribution from each representation analytically or using PyR@TE Running in radiative models 10 Idea: Study RG running in radiative neutrino mass models - SM gauge group + additional representation Stella Riad, RG running in radiative models, MIAPP, 26/11-2015 -Solve RGEs -Does it unify? If so, at a reasonable scale? (10^16) Model can be categorized: 1.Those unifying 2.Those which doesn’t unify but also doesn’t diverge 3.Those which fail miserably

11. Minimal d=7 models 11 Cai, Clarke, Schmidt, Volkas, 2015 15 models with d = 7 Additional requirements: SM gauge symmetry only, additional particles scalars, vectorlike fermions, or Majorana fermions One- or two-loop radiative models Stella Riad, RG running in radiative models, MIAPP, 26/11-2015 Weinberg-like

12. Minimal d=7 models 12

13. 13 Minimal d=7 models New particle masses 1 TeV Particle generations Possible to achieve GUT scale Symmetries to forbid certain diagrams Stella Riad, RG running in radiative models, MIAPP, 26/11-2015

14. Dark matter candidates 14 Minimal dark matter (Cirelli, Fornengo, Strumia, Nucl.Phys. B753, 2006) Color neutral. As is required for any dark matter candidate. DM are n-tuplets of SU(2) The hypercharge must be such that one component is electrically neutral. Lightest component stable and neutral Only renormalizable interactions are of gauge type Stella Riad, RG running in radiative models, MIAPP, 26/11-2015

15. 15 Adding dark matter Reasonable to add DM candidate Again low unification scale “Basic model” + DM Stella Riad, RG running in radiative models, MIAPP, 26/11-2015

16. Neutrino masses and dark matter 16 Stella Riad, RG running in radiative models, MIAPP, 26/11-2015 Restrepo, Zapata, Yaguna, 2013 At most 4 new particles 35 non-equivalent models Singlets, doublets, or triplets under SU(2) Color neutral

17. Neutrino masses and dark matter 17 9 models with unification Low unification scale Gauge coupling in same ball park Stella Riad, RG running in radiative models, MIAPP, 26/11-2015

18. Ignore the DM condition color all the particles Neutrino masses and DM: coloring the particles 18 Stella Riad, RG running in radiative models, MIAPP, 26/11-2015

19. 19 Model with octet Angel, Cai, Rodd, Schmidt, Volkas, JHEP 1310 (2013) d=9 operator Two leptoquarks and one Majorana fermion Stella Riad, RG running in radiative models, MIAPP, 26/11-2015

20. Scale of unification Low unification scale, GUT scale Push up scale with colored particles/SU(2) multiplets Unification? 20 Stella Riad, RG running in radiative models, MIAPP, 26/11-2015

21. One loop vs two-loop 21 Stella Riad, RG running in radiative models, MIAPP, 26/11-2015

22. Sources of uncertainty Mass of new particles  Depend on the loop order of the radiative model Threshold effects Loop order SM Yukawa couplings New Yukawa couplings 22 Stella Riad, RG running in radiative models, MIAPP, 26/11-2015 Running for new particle mass ranging from 100 GeV to 5 TeV

23. Conclusions SM RG running for the gauge couplings well known Connect low-energy neutrino mass models with high energy GUTs. Gauge unification can occur in some cases (though often low scale) 23 Stella Riad, RG running in radiative models, MIAPP, 26/11-2015

24. 24 THANK YOU! Stella Riad, RG running in radiative models, MIAPP, 26/11-2015

25. Grand Unified Theories 25

26. Neutrino masses and dark matter 26 Restrepo, Zapata, Yaguna, JHEP 1311 (2013) Both neutrino masses and dark matter Neutrino masses generated at one loop At most 4 new particles 35 non-equivalent models Singlets, doublets, or triplets under SU(2) Color neutral Stella Riad, RG running in radiative models, MIAPP, 26/11-2015

27. Mass of new particles Running for new particle mass ranging from 100 GeV to 5 TeV 27 Stella Riad, RG running in radiative models, MIAPP, 26/11-2015

28. RG running (and GUTs) can be discussed either in a top- down and bottom-up framework. Top-down: start from the unified theory and run down to effective theory. Predicts values at EW scale. Bottom-up: start from effective theory and run up. Renormalization Group Running 28 Stella Riad, RG running in radiative models, MIAPP, 26/11-2015