Standard Model And High-Energy Lorentz Violation

1. Standard Model AndHigh-Energy Lorentz Violation DamianoAnselmi Cortona 27/05/2010

2. The papers about the Lorentz violating Standard Model are [1] D.A., Standard Model Without Elementary Scalars And High Energy Lorentz Violation, Eur. Phys. J. C 65 (2010) 523 and arXiv:0904.1849 [hep-ph] [2] D.A., Weighted power counting, neutrino masses and Lorentz violating extensions of the Standard Model, Phys. Rev. D 79 (2009) 025017 andarXiv:0808.3475 [hep-ph]

3. The papers about the Lorentz violating Standard Model are [1] D.A., Standard Model Without Elementary Scalars And High Energy Lorentz Violation, Eur. Phys. J. C 65 (2010) 523 and arXiv:0904.1849 [hep-ph] [2] D.A., Weighted power counting, neutrino masses and Lorentz violating extensions of the Standard Model, Phys. Rev. D 79 (2009) 025017 andarXiv:0808.3475 [hep-ph] Then QED: [3] D.A. and M. Taiuti, Renormalization of high-energy Lorentz violating QED,Phys. Rev. D 81 (2010) 085042arxiv:0912.0113 [hep-ph]

4. The papers about the Lorentz violating Standard Model are [1] D.A., Standard Model Without Elementary Scalars And High Energy Lorentz Violation, Eur. Phys. J. C 65 (2010) 523 and arXiv:0904.1849 [hep-ph] [2] D.A., Weightedpowercounting, neutrino masses and Lorentzviolatingextensionsof the Standard Model, Phys. Rev. D 79 (2009) 025017 andarXiv:0808.3475 [hep-ph] Then QED: [3] D.A. and M. Taiuti, Renormalization of high-energy Lorentz violating QED,Phys. Rev. D 81 (2010) 085042arxiv:0912.0113 [hep-ph] Four fermion models: [4] D.A. and E. Ciuffoli, Renormalization of high-energy Lorentz violating four fermion models, Phys. Rev. D 81, (2010) 085043 and arXiv:1002.2704 [hep-ph].  

5. The papers about the Lorentz violating Standard Model are [1] D.A., Standard Model Without Elementary Scalars And High Energy Lorentz Violation, Eur. Phys. J. C 65 (2010) 523 and arXiv:0904.1849 [hep-ph] [2] D.A., Weightedpowercounting, neutrino masses and Lorentzviolatingextensionsof the Standard Model, Phys. Rev. D 79 (2009) 025017 andarXiv:0808.3475 [hep-ph] Then QED: [3] D.A. and M. Taiuti, Renormalization of high-energy Lorentz violating QED,Phys. Rev. D 81 (2010) 085042arxiv:0912.0113 [hep-ph] Four fermion models: [4] D.A. and E. Ciuffoli, Renormalization of high-energy Lorentz violating four fermion models, Phys. Rev. D 81, (2010) 085043 and arXiv:1002.2704 [hep-ph].   and previous, more technical papers [5] D.A. and M. Halat, RenormalizationofLorentzviolatingtheories, Phys. Rev. D 76 (2007) 125011 andarxiv:0707.2480 [hep-th] [6] D.A., Weighted scale invariant quantum fieldtheories, JHEP 02 (2008) 05 and arxiv:0801.1216 [hep-th] [7] D.A., Weightedpowercounting and Lorentzviolatinggaugetheories. I: General properties, Ann. Phys. 324 (2009) 874and arXiv:0808.3470 [hep-th] [8] D.A., Weightedpowercounting and Lorentzviolatinggaugetheories. II: Classification, Ann. Phys. 324 (2009) 1058 and arXiv:0808.3474 [hep-th]

6. Outlook of the talk

7. Outlook of the talk If we assume that Lorentz symmetry is violated at high energies we can renormalize otherwise non-renormalizable interactions, such as two-scalar-two-fermion vertices and four-fermion vertices.

8. Outlook of the talk If we assume that Lorentz symmetry is violated at high energies we can renormalize otherwise non-renormalizable interactions, such as two-scalar-two-fermion vertices and four-fermion vertices. It is possible to give Majorana masses to left-handed neutrinos without adding extra fields. Indeed, the interaction is renormalizable as a fundamental vertex. A match with the expected Majorana masses gives a scale of Lorentz violation (with preserved CPT symmetry) of about 10^14 GeV.

9. Outlook of the talk • If we assume that Lorentz symmetry is violated at high energies we can renormalize otherwise non-renormalizable interactions, such as two-scalar-two-fermion vertices and four-fermion vertices. • It is possible to give Majorana masses to left-handed neutrinos without adding extra fields. • Indeed, the interaction is renormalizable as a fundamental vertex. A match with the • expected Majorana masses gives a scale of Lorentz violation (with preserved CPT symmetry) of about 10^14 GeV. • It is possible to explain proton decay. • Lorentz violating quantum field theory in flat space is perfectly consistent. All basic properties, such as causality, unitarity, stability, the Kallen-Lehman representation, etc., as well as renormalizability, locality and polynomiality, therefore predictivity, can be proved without assuming Lorentz symmetry.

10. Outlook of the talk • If we assume that Lorentz symmetry is violated at high energies we can renormalize otherwise non-renormalizable interactions, such as two-scalar-two-fermion vertices and four-fermion vertices. • It is possible to give Majorana masses to left-handed neutrinos without adding extra fields. • Indeed, the interaction is renormalizable as a fundamental vertex. A match with the • expected Majorana masses gives a scale of Lorentz violation (with preserved CPT symmetry) of about 10^14 GeV. • It is possible to explain proton decay. • Lorentz violating quantum field theory in flat space is perfectly consistent. All basic properties, such as causality, unitarity, stability, the Kallen-Lehman representation, etc., as well as renormalizability, locality and polynomiality, therefore predictivity, can be proved without assuming Lorentz symmetry. • There exists a Lorentz violating Standard Model extension with these features. The inclusion of four-fermion vertices allows us to give masses to fermions and gauge-bosons by means of a Nambu-Jona-Lasinio mechanism, even if scalars, such as the Higgs field, are absent at the elementary level. Higgs composite fields arise as low-energy effects. The scalarless model is quite simple and predictive.

11. Several new phenomena appear when Lorentz symmetry is violated, such as Cherenkov radiation in vacuum, pair production from a single photon, and so on [Coleman-Glashow]. Such processes allow us to make comparisons with experimental tests and put bounds on the Lorentz violation.

12. Several new phenomena appear when Lorentz symmetry is violated, such as Cherenkov radiation in vacuum, pair production from a single photon, and so on [Coleman-Glashow]. Such processes allow us to make comparisons with experimental tests and put bounds on the Lorentz violation. The predictions of my models can be used to make comparisons with presently known experimental data and astrophysical observations, or propose new experiments and observations, to test the models, search for signals of the symmetry violation or extend the present bounds on the validity of the symmetry.

13. Several new phenomena appear when Lorentz symmetry is violated, such as Cherenkov radiation in vacuum, pair production from a single photon, and so on [Coleman-Glashow]. Such processes allow us to make comparisons with experimental tests and put bounds on the Lorentz violation. The predictions of my models can be used to make comparisons with presently known experimental data and astrophysical observations, or propose new experiments and observations, to test the models, search for signals of the symmetry violation or extend the present bounds on the validity of the symmetry. We may assume that there exists an energy range that is well described by a Lorentz violating, but CPT invariant quantum field theory.

14. Several new phenomena appear when Lorentz symmetry is violated, such as Cherenkov radiation in vacuum, pair production from a single photon, and so on [Coleman-Glashow]. Such processes allow us to make comparisons with experimental tests and put bounds on the Lorentz violation. The predictions of my models can be used to make comparisons with presently known experimental data and astrophysical observations, or propose new experiments and observations, to test the models, search for signals of the symmetry violation or extend the present bounds on the validity of the symmetry. We may assume that there exists an energy range that is well described by a Lorentz violating, but CPT invariant quantum field theory. Glast:

15. High-energy Lorentz violating QED

16. High-energy Lorentz violating QED Gauge symmetry is unmodified

17. High-energy Lorentz violating QED Gauge symmetry is unmodified A convenient gauge-fixing lagrangian is

18. Integrating the auxiliary field B away we find

19. Integrating the auxiliary field B away we find Propagators

20. Integrating the auxiliary field B away we find Propagators This gauge exhibits the renormalizability of the theory, but not its unitarity

21. Coulomb gauge

22. Coulomb gauge

23. Coulomb gauge Two degrees of freedom with dispersion relation

24. Coulomb gauge Two degrees of freedom with dispersion relation The Coulomb gauge exhibits the unitarity of the theory, but not its renormalizability

25. Coulomb gauge Two degrees of freedom with dispersion relation The Coulomb gauge exhibits the unitarity of the theory, but not its renormalizability Correlation functions of gauge invariant objects are both unitary and renormalizable

26. Weighted power counting

27. Weighted power counting The theory is super-renormalizable Counterterms are just one- and two-loops

28. Weighted power counting The theory is super-renormalizable Counterterms are just one- and two-loops

29. High-energy one-loop renormalization

30. High-energy one-loop renormalization

31. High-energy one-loop renormalization

32. Low-energy renormalization

33. Low-energy renormalization

34. Low-energy renormalization Two cut-offs, with the identification

35. Low-energy renormalization Two cut-offs, with the identification Logarithmic divergences give

36. More generally, the theory can have 2n spatial derivatives, at most, which can improve the UV behavior even more.

37. More generally, the theory can have 2n spatial derivatives, at most, which can improve the UV behavior even more. The number n is crucial for the weighted power counting, together with the weighted dimension

38. More generally, the theory can have 2n spatial derivatives, at most, which can improve the UV behavior even more. The number n is crucial for the weighted power counting, together with the weighted dimension Our previous case had n=3 n=odd is necessary to describe chiral fermions

39. More generally, the theory can have 2n spatial derivatives, at most, which can improve the UV behavior even more. The number n is crucial for the weighted power counting, together with the weighted dimension Our previous case had n=3 n=odd is necessary to describe chiral fermions A general property of gauge theories is that in four dimensions gauge interactions are always super-renormalizable from the weighted power-counting viewpoint

40. More generally, the theory can have 2n spatial derivatives, at most, which can improve the UV behavior even more. The number n is crucial for the weighted power counting, together with the weighted dimension Our previous case had n=3 n=odd is necessary to describe chiral fermions A general property of gauge theories is that in four dimensions gauge interactions are always super-renormalizable from the weighted power-counting viewpoint Indeed, the weight of the gauge coupling is

41. The case allows us to formulate a consistent Lorentz violating extended Standard Model that contains both the dimension-5 vertex that gives Majorana masses to left-handed neutrinos after symmetry breaking,

42. The case allows us to formulate a consistent Lorentz violating extended Standard Model that contains both the dimension-5 vertex that gives Majorana masses to left-handed neutrinos after symmetry breaking, and the four fermion interactions that can describe proton decay. Such vertices are renormalizable by weighted power counting

43. The case allows us to formulate a consistent Lorentz violating extended Standard Model that contains both the dimension-5 vertex that gives Majorana masses to left-handed neutrinos after symmetry breaking, and the four fermion interactions that can describe proton decay. Such vertices are renormalizable by weighted power counting Matching the vertex with estimates of the electron neutrino Majorana mass the scale of Lorentz violation has roughly the value

44. The (simplified) model reads

45. The (simplified) model reads

46. The (simplified) model reads where

47. The (simplified) model reads where

48. The (simplified) model reads where

49. The (simplified) model reads where

50. The (simplified) model reads where At low energies we have the Colladay-Kostelecky Standard-Model Extension