M. Zubkov ITEP Moscow 2011 A.I.Veselov, M.A.Zubkov, JHEP 0812:109,2008

1. M. Zubkov ITEP Moscow 2011 A.I.Veselov, M.A.Zubkov, JHEP 0812:109,2008 M.A.Zubkov, Phys.Lett.B684:141-146,2010 M.A.Zubkov, Phys.Rev.D82:093010,2010 M.I.Polikarpov, M.A.Zubkov, Phys.Lett.B700 (2011) pp. 336 M.A.Zubkov, arXiv1108.3300 Investigation of lattice Weinberg – Salam Model

2. Abstract 1. Continuum physics is approached in the vicinity of the phase transition between physical Higgs phase and unphysical symmetric phase of the lattice model. 2. In the vicinity of this phase transition nonperturbative phenomena may become important. In particular, Nambu monopoles dominate vacuum close to the transition point.

3. Fields • Lattice gauge fields (defined on links) • Fundamental Higgs field (defined on sites) Lattice action Higgs phase: Symmetric phase:

4. Phase transition at Physical phase Unphysical phase 4

5. Fluctuational region in Weinberg-Salam model Perturbation theory can be applied if 5

6. When lattice methods can be applied? 6

7. Phase transition at Physical phase Unphysical phase 7

8. Along the line of constant physics if we neglect gauge loop corrections to One loop weak coupling expansion: bare and are increased when the Ultraviolet cutoff is increased along the line of constant physics

9. 9

10. 10

11. Evaluation of lattice spacing Z – boson mass in lattice units: (the sum is over “space” coordinates of the Z boson field) are imaginary “time” coordinates 11

12. in lattice units Phase transition 12

13. Ultraviolet cutoff Condensation of Nambu monopoles Fluctuactional region Physical phase Unphysical phase

14. Higgs boson mass in lattice units 14

15. NAMBU MONOPOLES (unitary gauge) NAMBU MONOPOLE Standard Model NAMBU MONOPOLE Z string 15

16. Worldsheet of Z – string on the lattice NAMBU MONOPOLE WORLDLINE 16

17. Percolation Nambu monopole density Phase transition Monopole size Distance between monopoles 17

18. Percolation 18

19. Transition Nambu monopoles Nambu monopoles Line of constant renormalized fine structure constant 19 Ultraviolet cutoff

20. Phase transition at Physical phase Unphysical phase 20

21. Effective constraint potential 1. Ultraviolet potential 2. Infrared potential 21

22. 0-order approximation 1. Ultraviolet potential 2. Infrared potential 22

23. Minimum of the potential at

24. Condensate in GeV

25. Phase transition at Physical phase Unphysical phase 25

26. Realistic value of Weinberg angle The fine structure constant (Higgs phase) The fine structure constant (symmetric phase) The majority of the results were obtained on the lattices Some results were checked on the lattices 26

27. AHM estimate for the Wilson loop 27

28. Polyakov lines correlator Right – handed lepton Wilson loop the lattice Yukawa potential 28

29. 1 – loop (1 TeV) 29

30. Phase transition at Physical phase Unphysical phase 30

31. Conclusions • Nonperturbative effects may be relevant in Weinberg-Salam model at the TeV scale: • Nambu monopoles begin to dominate vacuum at the TeV scale; they are condensed for the cutoff above 1 TeV 2. Scalar field condensate can be defined in several ways. Its values differ from 273 GeV when the cutoff is around 1 TeV. 3. Running fine structure constant is close to its 1-loop estimate. 31