Spin-half fermions with mass dimension one: theory, phenomenology, and dark matter

Abstract

Abstract:We provide the first details on the unexpected theoretical discovery of a spinone-half matter field with mass dimension one. It is based upon a complete set of dualhelicity eigenspinors of the charge conjugation operator. Due to its unusual properties with respect to charge conjugation and parity, it belongs to a non-standard Wigner class. Consequently, the theory exhibits non-locality with (CP T ) 2 = −I. We briefly discuss its relevance to the cosmological 'horizon problem'. Because the introduced fermionic field is endowed with mass dimension one, it can carry a quartic self-interaction. Its dominant interaction with known forms of matter is via Higgs, and with gravity. This aspect leads us to contemplate the new fermion as a prime dark matter candidate. Taking this suggestion seriously we study a supernova-like explosion of a galactic-mass dark matter cloud to set limits on the mass of the new particle and present a calculation on relic abundance to constrain the relevant cross-section. The analysis favours light mass (roughly 20 MeV) and relevant cross-section of about 2 pb. Similarities and differences with the WIMP and mirror matter proposals for dark matter are enumerated. In a critique of the theory we bare a hint on non-commutative aspects of spacetime, and energy-momentum space.Keywords: dark matter, quantum field theory on curved space.To celebrate the birthday of my wife Dr I S Ahluwalia-Khalilova and in memory of my father Shri B S Ahluwalia (1933-1977

From Dirac spinor fields to eigenspinoren des ladungskonjugationsoperators

“…Recall that if the quantities P = + J + ␥ 0123 and Q = S + K␥ 0123 are defined, 20,21 in type-͑1͒ DSF we have P =−͑ + ␥ 0123 ͒ −1 KQ and also =−i͑ + ␥ 0123 ͒ −1 . In type-͑2͒ DSF, P is a multiple of 1 / 2 ͑ + J͒ and looks like a proper energy projection operator, commuting with the spin projector operator given by 1 2 ͑1−i␥ 0123 K / ͒. Also, P = ␥ 0123 KQ / .…”

“…It is well known that spinor fields have three different, although equivalent, definitions: the operatorial, the classical, and the algebraic one. 47 In particular, the operatorial definition allows us to factor-up to signthe DSF as = ͑ + ␥ 0123 ͒ −1/2 R, where R spin 1,3 e . Denoting K k = ␥ k ˜, where ˜d enotes the reversion of , the set ͕J , K 1 , K 2 , K 3 ͖ is an orthogonal basis of R 1,3 .…”

“…The plus sign stands for self-conjugate spinors, S ͑p͒, while the minus yields anti-self-conjugate spinors, A ͑p͒. Explicitly, the complete form of ELKO spinor fields can be found by solving the equation of helicity ͑ · p ͒ ± = ± ± in the rest frame and subsequently make a boost, to recover the result for any p. 1 Here p ª p / ʈpʈ. The four spinor fields are given as follows:…”

“…Any invertible map that takes Dirac particles and leads to ELKO is also capable to make mass dimension transmutations, since DSFs present mass dimension 3 / 2, instead of mass dimension 1 associated with ELKO. The main physical motivation of this paper is to provide the initial prerequisites to construct a natural extension of the standard model ͑SM͒ in order to incorporate ELKO, and consequently a possible description of dark matter 1,2,6 in this context.…”

“…Also, the Lounesto classification of spinor fields is presented together with the definition of ELKO spinor fields, 1 showing that ELKO is indeed a flagpole spinor field with opposite ͑dual͒ helicities. 1,2,22 In Sec. IV the mapping from Dirac spinor fields to ELKO is widely investigated in detail.…”