Skip to main content
SpringerLink
Log in

An Alternative Approach Concerning Elko Spinors and the Hidden Unitarity

  • Published:
Advances in Applied Clifford Algebras Aims and scope Submit manuscript

Abstract

In this theoretical communication we look towards understand the underlying phenomenology concerning the Elko spinors within VSR theory. The program to be accomplished here start when we define the eigenspinors of the charge conjugation operator as eigenstates of the helicity operator in the Cartesian coordinates system. This prescription is very useful in the sense of phenomenological point of view, so, we propose a set of Elko spinors ready to be computationally implemented. Regardless of, in order to show the application of given approach we impose to these spinors to be restrict to an axis, coincidentally the axis of locality (Ahluwalia-Khalilova and Grumiller in JCAP, 07:12 2005; Ahluwalia-Khalilova and Cheng-Yang Lee in Phys Rev D 83:065017, 2011) , and then, using the proposed prescription, we search for physical amounts and physical processes by analysing the Yukawa and the self-interaction in such framework.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Notes

  1. It is important to note the conceptual difference between Elko spinors (VSR invariant) and the new local fields (Lorentz invariant). Henceforth, we will make use of the correct nomenclature to distinguish them. For a better understanding, authors recommend Ref. [3].

  2. Where we have defined the boost factors as \(\mathcal {B}_{\pm } = \sqrt{\frac{E + m}{2m}}\left( 1 \pm \frac{|\varvec{p}|}{E+m}\right) \).

  3. Where we have defined the boost factors along the z-axis as \(\mathcal {B}^{z}_{\pm } = \sqrt{\frac{E + m}{2m}}\left( 1 \pm \frac{|\varvec{p_z}|}{E+m}\right) \).

  4. Regarding the physical observables (bilinear forms) given in [36], the authors in [27] classify Elko sinors as type-5. However the Elko norm (40), are defined taking into account the Elko dual structure, so, all the physical amounts should carry the same dual structure rather than the Dirac one. In this vein, in [28] authors perform a very same procedure to define the bilinear amounts as developed in [36].

References

  1. Ahluwalia, D.V.: Dark matter and its darkness. Int. J. Mod. Phys. D 15, 2267 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  2. Ahluwalia, D.V.: Evading Weinberg’s no-go theorem to construct mass dimension one fermions: constructing darkness. Europhys. Lett. 118, 60001 (2017)

    Article  Google Scholar 

  3. Ahluwalia, D.V.: The theory of local mass dimension one fermions of spin one half. In: Adv. in Appl. Clifford Algebras (2017) (to be published)

  4. Ahluwalia, D.V., Johnson, E.T. Goldman, M.B.: Majorana-like representation spaces: construction and physical interpretation. Mod. Phys. Lett. A 9, 439 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  5. Ahluwalia, D.V., Horvath, S.P.: Very special relativity as relativity of dark matter: the Elko connection. JHEP 11, 78 (2010)

    Article  ADS  Google Scholar 

  6. Ahluwalia-Khalilova, D.V., Grumiller, D.: Spin-half fermions with mass dimension one: theory, phenomenology, and dark matter. JCAP 07, 12 (2005)

    Article  ADS  Google Scholar 

  7. Ahluwalia-Khalilova, D.V., Cheng-Yang Lee, E.D.: Schritt, self-interacting Elko dark matter with an axis of locality, Phys. Rev. D 83, 065017 (2011)

  8. Alfaro, J.: A Sim(2) invariant dimensional regularization. Phys. Lett. B 772, 100 (2017)

    Article  ADS  Google Scholar 

  9. Alfaro, J.: Feynman Rules. Ward Identities and Loop Corrections in Very Special Relativity Standard Model Universe vol. 5, pp. 16 (2019)

  10. Alfaro, J., Gonzalez, P., Avila, R.: Electroweak standard model with very special relativity. Phys. Rev. D 91, 105007 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  11. Alfaro, J., Rivelles, V.O.: Non Abelian fields in very special relativity. Phys. Rev. D 88, 085023 (2013)

    Article  ADS  Google Scholar 

  12. Alfaro, J., Soto, A.: On the photon mass in very special relativity. arXiv:1901.08011 [hep-th] (2019)

  13. Alves, A., de Campos, F., Dias, M., Hoff da Silva, J.M.: Int. J. Mod. Phys. A 30(01), 1550006 (2015)

    Article  ADS  Google Scholar 

  14. Alves, A., Dias, M., de Campos, F., Duarte, L., da Silva, J .M.Hoff: Constraining Elko dark matter at the LHC with monophoton events. EPL 121(3), 31001 (2018)

    Article  ADS  Google Scholar 

  15. Barlette, V.E., Leite, M.M., Adhikari, S.K.: Am. J. Phys. 69, 1010 (2001)

    Article  ADS  Google Scholar 

  16. Bassalo, J.M.F.: Eletrodinâmica Quântica. Editorial Livraria da Física, São Paulo (2006)

    Google Scholar 

  17. Berestetskii, V.B., Lifshitz, E.M., Pitaevskii, L.P.: Quantum Eletrodynamics, 2nd edn. Pergamon Press, Oxford (1982)

    Google Scholar 

  18. Boya, L.J., Murray, R.: Phys. Rev. A 50, 4397 (1994)

    Article  ADS  Google Scholar 

  19. Bueno Rogerio, R.J., da Silva, J.M.Hoff: The local vicinity of spin sums for certain mass-dimension-one spinors. Europhys. Lett. 118, 10003 (2017)

    Article  ADS  Google Scholar 

  20. Bufalo, R., Upadhyay, S.: Axion mass bound in very special relativity. Phys. Lett. B 772, 420–425 (2017)

    Article  ADS  Google Scholar 

  21. Böhmer, C.G., Corpe, L.: Helicity—from Clifford to graphene. J. Phys. A 45, 205206 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  22. Cavalcanti, R.T., Hoff da Silva, J.M., da Rocha, R.: VSR symmetries in the DKP algebra: the interplay between Dirac and Elko spinor fields. Eur. Phys. J. Plus 129, 246 (2014)

  23. Cheon, S., Lee, C., Lee, S.J.: SIM(2)-invariant modifications of electrodynamic theory. Phys. Lett. B 679, 73 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  24. Cohen, A.G., Glashow, S.L.: Very special relativity. Phys. Rev. Lett. 97, 021601 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  25. CoronadoVillalobos, C.H., Rogerio, R.J.B., Sabbas, E.F.T.S.: Type-4 spinors: transmuting from Elko to single-helicity spinors. Eur. Phys. J. C 79, 308 (2019)

    Article  ADS  Google Scholar 

  26. da Rocha, R., Hoff da Silva, J.M.: From Dirac spinor fields to ELKO. J. Math. Phys. 48, 123517 (2007)

  27. da Rocha, R., Rodrigues Jr., W.A.: Mod. Phys. Lett. A 21, 65 (2006)

    Article  ADS  Google Scholar 

  28. da Silva, J.M.Hoff, Villalobos, C.H.Coronado, Rogerio, R.J.Bueno, Scatena, E.: On the bilinear covariants associated to mass dimension one spinors. Eur. Phys. J. C 76, 563 (2016)

    Article  ADS  Google Scholar 

  29. Dias, M., de Campos, F., da Silva, J.M.Hoff: Exploring Elko typical signature. Phys. Let. B 706, 352 (2012)

    Article  ADS  Google Scholar 

  30. Hoff da Silva, J.M., da Rocha, R.: From dirac action to ELKO action. Int. J. Mod. Phys. A 24, 3227–3242 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  31. Horejsi, J.: Introduction to electroweak unification: standard model from tree unitarity. PRA-HEP-93-8

  32. Horvath, S.P.: On the Relativity of Elko dark matter, Master’s Thesis. University of Canterbury, New Zealand (2011)

  33. Hovakimian, L.B.: Optical theorem in N dimensions. Phys. Rev. A 72, 064701 (2005)

    Article  ADS  Google Scholar 

  34. Lee, C.Y.: Elko in 1+1 dimensions. arXiv:1011.5519 [hep-th] (2015)

  35. Lee, C.Y.: Symmetries and unitary interactions of mass dimension one fermionic dark matter. Int. J. Mod. Phys. A 31, 1650187 (2016)

    Article  ADS  Google Scholar 

  36. Lounesto, P.: Clifford Algebras and Spinors, 2nd edn. Editorial Cambridge University Press, Cambridge (2002)

    MATH  Google Scholar 

  37. Marinov, M.S.: Construction of invariant amplitudes for interactions of particles with any spin. Ann. Phys. 49, 357 (1968)

    Article  ADS  Google Scholar 

  38. Nayak, A.C., Jain, P.: Phenomenological implications of very special relativity. Phys. Rev. D 96, 075020 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  39. Nayak, A.C.: Very special relativity induced phase in neutrino oscillation. arXiv:1901.07835 [hep-ph] (2019)

  40. Sperança, L.D.: An identification of the Dirac operator with the parity operator. Int. J. Mod. Phys. D 2, 1444003 (2014)

    Article  MathSciNet  Google Scholar 

  41. Selvaganapathy , J., Konar, P., Das, P. Kumar: Inferring the covariant \(\Theta \)-exact noncommutative coupling in the top quark pair production at linear colliders. arXiv:1903.03478 (2019)

  42. Peskin, M.E., Schroder, D.: An Introduction to Quantum Field Therory, 1st edn. Editorial Addison-Wesley Publishing Company, New York (1995)

    Google Scholar 

Download references

Acknowledgements

LCD, RdCL, RJBR and CHCV are grateful to Professor José Abdalla Helayël-Neto for the appreciation, helpful discussions and suggestions on the original manuscript during its writing stage, authors also thanks to Eslley Scatena for the privilege of his revision, comments and appreciation of this work and thanks to Dino Beghetto for discussions and advices on this essay. Authors also thanks the Referees, their questions helped to substantially improve the manuscript. LCD and RdCL thank to CAPES, RJBR thanks to CNPq (Grant number 155675/2018-4) and CHCV thanks CNPq (Grant number 300236/2019-0) for the financial support.

Author information

Authors and Affiliations

  1. Faculdade de Engenharia, Guaratinguetá, Departamento de Física e Química, Universidade Estadual Paulista (Unesp), Guaratinguetá, SP, 12516-410, Brazil

    L. C. Duarte & R. de C. Lima

  2. Instituto de Física e Química, Universidade Federal de Itajubá-IFQ (UNIFEI), Av. BPS 1303, Itajubá, MG, CEP 37500-903, Brazil

    R. J. Bueno Rogerio

  3. Instituto Nacional de Pesquisas Espaciais (INPE), São José dos Campos, SP, 12227-010, Brazil

    C. H. Coronado Villalobos

Authors
  1. L. C. Duarte
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. de C. Lima
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. J. Bueno Rogerio
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. C. H. Coronado Villalobos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. de C. Lima.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Duarte, L.C., Lima, R.d.C., Rogerio, R.J.B. et al. An Alternative Approach Concerning Elko Spinors and the Hidden Unitarity. Adv. Appl. Clifford Algebras 29, 66 (2019). https://doi.org/10.1007/s00006-019-0988-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00006-019-0988-6

Keywords

Search

Navigation