Neither left nor right particles.

Question

Are there such particles? which are neither left nor right.

Perhaps a good candidate for dark matter. (I am partly joking partly serious).

Comments

As far as they are dark particles, nobody can tell whether they are left or right or anything in between.

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Assuming that by "left" and "right" you refer to chirality, how would one define the chirality of a scalar particle? Would the Higgs boson be neither "left" nor "right"?

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@Flamma as I said I was half joking half serious.

I don't know how to write this mathematically.

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Did you have Majorana particles in mind, or something else and more exotic?

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@Dilaton how can a particle be its own antiparticle?

I mean if a particle has a charge q then its anti-particle will have a negative charge -q.

Unless of course it doesn't have charge, but I once in Physicsforums been given an answer that there's a neutron and anti-neutron both having the same zero charge, how can this be true?

Really clueless here.

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@MathematicalPhysicist
Yes only neutral particles can be described as Majorana spinors.
The Majorana $4$-component description of a neutral fermion is mathematically equivalent to the description using one $2$-component Weyl spinor of definite chirality.
So I guess as for the neutron a distinguished anti-neutron can be observed, using the $2$- component Weyl spinor description both chirality states are needed, it can not be described as a Majorana particle, and its mass is a conventional dirac mass.