Mass dimension one fermions

In theoretical physics and cosmology the mass dimension one fermions of spin one half are a dark matter candidate. These fermions are fundamentally different from the hitherto known matter particles, like electrons or neutrinos. Despite being endowed with spin one half they are not described by the celebrated Dirac formalism but, instead, by a spinorial Klein-Gordon formalism.

In 2004 Dharam Vir Ahluwalia (IIT Guwahati) in collaboration with Daniel Grumiller presented an unexpected theoretical discovery of spin one-half fermions with mass dimension one.[1][2] In the decade that followed a significant number of groups explored intriguing mathematical and physical properties of the new construct while Ahluwalia and his students developed the formalism further.[3][4][5][6][7][8][9][10][11][12][13][14][15][16]

However, the formalism suffered from two troubling features, that of non-locality and a subtle violation of Lorentz symmetry. The origin of both of these issues has now been traced to a hidden freedom in the definition of duals of spinors and the associated field adjoints.[17] As a result there now exists an entirely new quantum theory of spin one-half fermions that is free from all the mentioned issues. The interactions of the new fermions are restricted to dimension-four quartic self interaction, and also to a dimension-four coupling with the Higgs. A generalised Yukawa coupling of the new fermions with neutrinos provides an hitherto unsuspected source of lepton-number violation. The new fermions thus present a first-principle dark matter partner to Dirac fermions of the standard model with contrasting mass dimensions — that of three halves for the latter versus one of the former without mutating the statistics from fermionic to bosonic.

Mass dimension one fermionic field of spin one half uses ELKO as its expansion coefficients. ELKO is an acronym of the original German term "Eigenspinoren des Ladungskonjugationsoperators", designating spinors that are eigenspinors of the charge conjugation operator.

Since the new fermions have a mass dimensionality mismatch with standard model matter fields they were suggested as a dark matter candidate. As a result of their scalar-like mass dimension they differ significantly from the mass dimension 3/2 Dirac fermions.[18]

Mass dimension one fermions have unexpected implications for cosmology by providing first principle dark matter and dark energy fields. Immediately after the publication of the Ahluwalia-Grumiller papers in 2005, Christian Boehmer pioneered application of Elko to cosmology and argued that Elko "are not only prime dark matter candidates but also prime candidates for inflation."[19] Einstein–Cartan–Elko system was first introduced in cosmology by Boehmer.[20] Saulo Pereira and colleagues have shown that Elko can also induce a time varying cosmological constant.[21] Abhishek Basak and colleagues have argued that the fast-roll inflation attractor point is unique for Elko and it is independent of the form of the potential.[22][23][24] Roldao da Rocha has argued that Elko can also be used as a tool for probing exotic topological features of spacetime.[25] Elko localization on the branes has been investigated in,[26][27] and.[28] The following references serve as a guide to the lively activity on Elko, and mass dimension one fermions:[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]

Earlier history of Elko is summarized in references:[47][48][49][50] and [51].

How Weinberg no go theorem is evaded is explained by Ahluwalia in 2017.[52] Also in 2017[53], it was shown that mass-dimension-one fermions, even in the absence of a cosmological constant, can induce a 'cosmological constant' term by quantum effects. These effects, leading to the non-vanishing Λ could be responsible for the inflationary phase at early universe stages. Furthermore, for the late time evolution, corresponding to a model with a time varying cosmological term, such quantum effects are in agreement with a previous recent work.[54]

Detailed discussion of the subject can be found in.[55]

## References

1. ↑ Ahluwalia-Khalilova, D. V.; Grumiller, D. (2005). "Spin-half fermions with mass dimension one: Theory, phenomenology, and dark matter". Journal of Cosmology and Astroparticle Physics 2005 (7): 012. doi:10.1088/1475-7516/2005/07/012. Bibcode: 2005JCAP...07..012A.
2. ↑ Ahluwalia-Khalilova, D. V.; Grumiller, D. (2005). "Dark matter: A spin one-half fermion field with mass dimension one?". Physical Review D 72 (6): 067701. doi:10.1103/PhysRevD.72.067701. Bibcode: 2005PhRvD..72f7701A.
3. ↑ Ahluwalia, Dharam Vir; Nayak, Alekha Chandra (2014). "Elko and mass dimension one field of spin one-half: Causality and Fermi statistics". International Journal of Modern Physics D 23 (14). doi:10.1142/S0218271814300262. Bibcode: 2014IJMPD..2330026A.
4. ↑ Ahluwalia, D.V.; Horvath, S.P. (2010). "Very special relativity as relativity of dark matter: The Elko connection". Journal of High Energy Physics 2010 (11): 78. doi:10.1007/JHEP11(2010)078. Bibcode: 2010JHEP...11..078A.
5. ↑ Ahluwalia, D. V.; Lee, Cheng-Yang; Schritt, D. (2011). "Self-interacting Elko dark matter with an axis of locality". Physical Review D 83 (6): 065017. doi:10.1103/PhysRevD.83.065017. Bibcode: 2011PhRvD..83f5017A.
6. ↑ Ahluwalia, D.V.; Lee, Cheng-Yang; Schritt, D. (2010). "Elko as self-interacting fermionic dark matter with axis of locality". Physics Letters B 687 (2–3): 248–252. doi:10.1016/j.physletb.2010.03.010. Bibcode: 2010PhLB..687..248A.
7. ↑ Bernardini, A.E.; Da Rocha, Roldão (2012). "Dynamical dispersion relation for ELKO dark spinor fields". Physics Letters B 717 (1–3): 238–241. doi:10.1016/j.physletb.2012.09.004. Bibcode: 2012PhLB..717..238B.
8. ↑ Da Rocha, R.; Rodrigues, W. A. (2006). "Where Are Elko Spinor Fields in Lounesto Spinor Field Classification?". Modern Physics Letters A 21 (1): 65–74. doi:10.1142/S0217732306018482. Bibcode: 2006MPLA...21...65D.
9. ↑ Da Rocha, R.; Hoff Da Silva, J. M. (2007). "From Dirac spinor fields to eigenspinoren des ladungskonjugationsoperators". Journal of Mathematical Physics 48 (12): 123517. doi:10.1063/1.2825840. Bibcode: 2007JMP....48l3517D.
10. ↑ Fabbri, Luca (2012). "Conformal gravity with the most general ELKO matter". Physical Review D 85 (4): 047502. doi:10.1103/PhysRevD.85.047502. Bibcode: 2012PhRvD..85d7502F.
11. ↑ Fabbri, L.; Vignolo, S. (2012). "The most general ELKO matter in torsional f(R)-theories". Annalen der Physik 524 (2): 77–84. doi:10.1002/andp.201100006. Bibcode: 2012AnP...524...77F.
12. ↑ Fabbri, Luca (2011). "The most general cosmological dynamics for ELKO matter fields". Physics Letters B 704 (4): 255–259. doi:10.1016/j.physletb.2011.09.024. Bibcode: 2011PhLB..704..255F.
13. ↑ Wunderle, K.E.; Dick, R. (2012). "A supersymmetric Lagrangian for fermionic fields with mass dimension one". Canadian Journal of Physics 90 (12): 1185–1199. doi:10.1139/p2012-075. Bibcode: 2012CaJPh..90.1185W.
14. ↑ Fabbri, Luca (2011). "Zero energy of plane-waves for ELKOs". General Relativity and Gravitation 43 (6): 1607–1613. doi:10.1007/s10714-011-1143-4. Bibcode: 2011GReGr..43.1607F.
15. ↑ Fabbri, Luca (2010). "CAUSALITY FOR ELKOs". Modern Physics Letters A 25 (29): 2483–2488. doi:10.1142/S0217732310033712. Bibcode: 2010MPLA...25.2483F.
16. ↑ Da Rocha, R.; Da Silva, J. M. Hoff (2010). "ELKO, Flagpole and Flag-Dipole Spinor Fields, and the Instanton Hopf Fibration". Advances in Applied Clifford Algebras 20 (3–4): 847–870. doi:10.1007/s00006-010-0225-9.
17. ↑ Ahluwalia, Dharam Vir (2017). "The Theory of Local Mass Dimension One Fermions of Spin One Half". Advances in Applied Clifford Algebras 27 (3): 2247–2285. doi:10.1007/s00006-017-0775-1.
18. ↑ Dias, M.; De Campos, F.; Hoff Da Silva, J.M. (2012). "Exploring Elko typical signature". Physics Letters B 706 (4–5): 352–359. doi:10.1016/j.physletb.2011.11.030. Bibcode: 2012PhLB..706..352D.
19. ↑ Boehmer, C.G. (2007). "The Einstein-Elko system – Can dark matter drive inflation?". Annalen der Physik 16 (5–6): 325–341. doi:10.1002/andp.200610237. Bibcode: 2007AnP...519..325B.
20. ↑ Boehmer, C.G. (2007). "The Einstein–Cartan–Elko system". Annalen der Physik 16 (1): 38–44. doi:10.1002/andp.200610216. Bibcode: 2007AnP...519...38B.
21. ↑ Pereira, S.H.; s.s, A. Pinho; Silva, J.M. Hoff da; Jesus, J.F. (2017). "Λ(t) cosmology induced by a slowly varying Elko field". Journal of Cosmology and Astroparticle Physics 2017 (1): 055. doi:10.1088/1475-7516/2017/01/055. Bibcode: 2017JCAP...01..055P.
22. ↑ Basak, Abhishek; Bhatt, Jitesh R.; Shankaranarayanan, S.; Varma, K.V. Prasantha (2013). "Attractor behaviour in ELKO cosmology". Journal of Cosmology and Astroparticle Physics 2013 (4): 025. doi:10.1088/1475-7516/2013/04/025. Bibcode: 2013JCAP...04..025B.
23. ↑ Mohseni Sadjadi, H. Mohseni (2012). "On coincidence problem in ELKO dark energy model". General Relativity and Gravitation 44 (9): 2329–2336. doi:10.1007/s10714-012-1392-x. Bibcode: 2012GReGr..44.2329S.
24. ↑ Pereira, S.H.; s.s, A. Pinho; Silva, J.M. Hoff da (2014). "Some remarks on the attractor behaviour in ELKO cosmology". Journal of Cosmology and Astroparticle Physics 2014 (8): 020. doi:10.1088/1475-7516/2014/08/020. Bibcode: 2014JCAP...08..020P.
25. ↑ Da Rocha, Roldão; Hoff Da Silva, J. M.; Bernardini, Alex E. (2011). "Elko Spinor Fields as a Tool for Probing Exotic Topological Spacetime Features". International Journal of Modern Physics: Conference Series 03: 133–142. doi:10.1142/S201019451100122X. Bibcode: 2011IJMPS...3..133D.
26. ↑ Jardim, I. C.; Alencar, G.; Landim, R. R.; Costa Filho, R. N. (2015). "Solutions to the problem of Elko spinor localization in brane models". Physical Review D 91 (8): 085008. doi:10.1103/PhysRevD.91.085008. Bibcode: 2015PhRvD..91h5008J.
27. ↑ Liu, Yu-Xiao; Zhou, Xiang-Nan; Yang, Ke; Chen, Feng-Wei (2012). "Localization of 5D Elko spinors on Minkowski branes". Physical Review D 86 (6): 064012. doi:10.1103/PhysRevD.86.064012. Bibcode: 2012PhRvD..86f4012L.
28. ↑ Li, Yan-Yan; Zhang, Yu-Peng; Guo, Wen-Di; Liu, Yu-Xiao (2017). "Fermion localization mechanism with derivative geometrical coupling on branes". Physical Review D 95 (11): 115003. doi:10.1103/PhysRevD.95.115003. Bibcode: 2017PhRvD..95k5003L.
29. ↑ Pereira, S.H.; s.s, A. Pinho; Silva, J.M. Hoff da; Jesus, J.F. (2017). "Λ(t) cosmology induced by a slowly varying Elko field". Journal of Cosmology and Astroparticle Physics 2017 (1): 055. doi:10.1088/1475-7516/2017/01/055. Bibcode: 2017JCAP...01..055P.
30. ↑ Basak, Abhishek; Shankaranarayanan, S. (2015). "Super-inflation and generation of first order vector perturbations in ELKO". Journal of Cosmology and Astroparticle Physics 2015 (5): 034. doi:10.1088/1475-7516/2015/05/034. Bibcode: 2015JCAP...05..034B.
31. ↑ Lee, Joohan; Lee, Tae Hoon; Oh, Phillial (2014). "Inflation driven by dark spinor and Higgs fields". International Journal of Modern Physics D 23 (14). doi:10.1142/S0218271814440064. Bibcode: 2014IJMPD..2344006L.
32. ↑ Dos Santos Souza, A. P.; Pereira, S. H.; Jesus, J. F. (2015). "A new approach on the stability analysis in ELKO cosmology". The European Physical Journal C 75: 36. doi:10.1140/epjc/s10052-015-3260-9. Bibcode: 2015EPJC...75...36D.
33. ↑ Agarwal, Bakul; Jain, Pankaj; Mitra, Subhadip; Nayak, Alekha C.; Verma, Ravindra K. (2015). "ELKO fermions as dark matter candidates". Physical Review D 92 (7): 075027. doi:10.1103/PhysRevD.92.075027. Bibcode: 2015PhRvD..92g5027A.
34. ↑ Hoff da Silva, J.M. Hoff da; Pereira, S.H. (2014). "Exact solutions to Elko spinors in spatially flat Friedmann-Robertson-Walker spacetimes". Journal of Cosmology and Astroparticle Physics 2014 (3): 009. doi:10.1088/1475-7516/2014/03/009. Bibcode: 2014JCAP...03..009H.
35. ↑ Kouwn, Seyen; Lee, Joohan; Lee, TAE Hoon; Oh, Phillial (2013). "Elko Spinor Model with Torsion and Cosmology". Modern Physics Letters A 28 (29). doi:10.1142/S0217732313501216. Bibcode: 2013MPLA...2850121K.
36. ↑ Lee, Joohan; Lee, Tae Hoon; Oh, Phillial (2012). "Conformally coupled dark spinor and FRW universe". Physical Review D 86 (10): 107301. doi:10.1103/PhysRevD.86.107301. Bibcode: 2012PhRvD..86j7301L.
37. ↑ Boehmer, Christian G.; Burnett, James; Mota, David F.; Shaw, Douglas J. (2010). "Dark spinor models in gravitation and cosmology". Journal of High Energy Physics 2010 (7): 53. doi:10.1007/JHEP07(2010)053. Bibcode: 2010JHEP...07..053B.
38. ↑ Wei, Hao (2011). "Spinor dark energy and cosmological coincidence problem". Physics Letters B 695 (1–4): 307–311. doi:10.1016/j.physletb.2010.10.053. Bibcode: 2011PhLB..695..307W.
39. ↑ Boehmer, Christian G.; Burnett, James (2008). "Dark spinors with torsion in cosmology". Physical Review D 78 (10): 104001. doi:10.1103/PhysRevD.78.104001. Bibcode: 2008PhRvD..78j4001B.
40. ↑ Gredat, Damien; Shankaranarayanan, S. (2010). "Modified scalar and tensor spectra in spinor driven inflation". Journal of Cosmology and Astroparticle Physics 2010 (1): 008. doi:10.1088/1475-7516/2010/01/008. Bibcode: 2010JCAP...01..008G.
41. ↑ Pereira, S.H.; Guimarães, T.M. (2017). "From inflation to recent cosmic acceleration: The fermionic Elko field driving the evolution of the universe". Journal of Cosmology and Astroparticle Physics 2017 (9): 038. doi:10.1088/1475-7516/2017/09/038. Bibcode: 2017JCAP...09..038P.
42. ↑ Boehmer, Christian G.; Mota, David F. (2008). "CMB anisotropies and inflation from non-standard spinors". Physics Letters B 663 (3): 168–171. doi:10.1016/j.physletb.2008.04.008. Bibcode: 2008PhLB..663..168B.
43. ↑ Chaves, Max; Singleton, Douglas (2008). "A Unified Model of Phantom Energy and Dark Matter". Symmetry, Integrability and Geometry: Methods and Applications 4: 009. doi:10.3842/SIGMA.2008.009. Bibcode: 2008SIGMA...4..009C.
44. ↑ Boehmer, Christian G. (2008). "Dark spinor inflation: Theory primer and dynamics". Physical Review D 77 (12): 123535. doi:10.1103/PhysRevD.77.123535. Bibcode: 2008PhRvD..77l3535B.
45. ↑ Gredat, Damien; Shankaranarayanan, S. (2010). "Modified scalar and tensor spectra in spinor driven inflation". Journal of Cosmology and Astroparticle Physics 2010 (1): 008. doi:10.1088/1475-7516/2010/01/008. Bibcode: 2010JCAP...01..008G.
46. ↑ Boehmer, Christian G.; Burnett, James (2008). "Dark spinors with torsion in cosmology". Physical Review D 78 (10): 104001. doi:10.1103/PhysRevD.78.104001. Bibcode: 2008PhRvD..78j4001B.
47. ↑ Ahluwalia, D.V. (1996). "Theory of Neutral Particles: Mclennan-Case Construct for Neutrino, ITS Generalization, and a New Wave Equation". International Journal of Modern Physics A 11 (10): 1855–1874. doi:10.1142/S0217751X96000973. Bibcode: 1996IJMPA..11.1855A.
48. ↑ Ahluwalia, D. V. (2002). Evidence for Majorana Neutrinos: Dawn of a new era in spacetime structure. Bibcode: 2002hep.ph...12222A.
49. ↑ Ahluwalia-Khalilova, D. V. (2003). Extended set of Majorana spinors, a new dispersion relation, and a preferred frame. Bibcode: 2003hep.ph....5336A.
50. ↑ Dvoeglazov, Valeri V. (1995). "Neutral particles in light of the Majorana-Ahluwalia ideas". International Journal of Theoretical Physics 34 (12): 2467–2490. doi:10.1007/BF00670779. Bibcode: 1995IJTP...34.2467D.
51. ↑ Dvoeglazov, Valeri V. (1995). "Neutral particles in light of the Majorana-Ahluwalia ideas". International Journal of Theoretical Physics 34 (12): 2467–2490. doi:10.1007/BF00670779. Bibcode: 1995IJTP...34.2467D.
52. ↑ Vir Ahluwalia, Dharam (2017). "Evading Weinberg's no-go theorem to construct mass dimension one fermions: Constructing darkness". Epl (Europhysics Letters) 118 (6): 60001. doi:10.1209/0295-5075/118/60001. Bibcode: 2017EL....11860001V.
53. ↑ Bueno Rogerio, R.J.; Hoff Da Silva, J.M.; Dias, M.; Pereira, S.H. (2018). "Effective lagrangian for a mass dimension one fermionic field in curved spacetime". Journal of High Energy Physics 2018 (2): 145. doi:10.1007/JHEP02(2018)145. Bibcode: 2018JHEP...02..145B.
54. ↑ Pereira, S.H.; s.s, A. Pinho; Silva, J.M. Hoff da; Jesus, J.F. (2017). "Λ(t) cosmology induced by a slowly varying Elko field". Journal of Cosmology and Astroparticle Physics 2017 (1): 055. doi:10.1088/1475-7516/2017/01/055. Bibcode: 2017JCAP...01..055P.
55. ↑ Ahluwalia, Dharam (2019). Mass Dimension One Fermions. doi:10.1017/9781316145593. ISBN 9781316145593.

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