The mass ranges for the dark antibaryon ψ_DS are determined by deriving the B_d → Λ ψ_DS branching fraction via light-cone QCD sum rules and comparing it to BaBar and Belle experimental bounds.
Generalized Fierz identities
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abstract
Low energy weak interactions calculations with fermions frequently involve a superposition of quartic products of Dirac spinors, in which the order of the spinors is not the same in all the contributing terms. A common trick that is used to bring them to a uniform ordering is the Fierz transformation. We show that the standard Fierz rearrangement formula quoted in textbooks is one element of a class of transformations of a quartic product amplitude, under which the spinors are rearranged with different orderings and, in the general case, some or all of the spinors are transformed to their Lorentz-invariant complex conjugate form. We give a pedagogical derivation of the explicit forms of all such transformation matrices. In addition to the usual Lorentz scalar quartic products, we consider pseudoscalar ones as well. Such manipulations and formulas are useful, in particular, when some of the fermions involved are Majorana particles.
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Mass of the dark antibaryon using $B_d\rightarrow \Lambda \psi_{DS}$ channel in light cone QCD
The mass ranges for the dark antibaryon ψ_DS are determined by deriving the B_d → Λ ψ_DS branching fraction via light-cone QCD sum rules and comparing it to BaBar and Belle experimental bounds.