In the following subsections, we employ the obtained results in the previous section to determine the mass spectra of scalar, vector, pseudoscalar, and pseudovector of B, [B.sub.s], D, and [D.sub.s] mesons in the N-dimensional space in comparison with the experimental data (PDG 2016) [95] and with other recent studies.
In Table 5, we observe that all the values of pseudovector mesons are close to the experimental results except the value of B meson which is in good agreement with the experimental value.
The unit
pseudovector [??] points along local average uniaxial LC orientational ordering, exhibiting head-to-tail symmetry (i.e., states [+ or -][??] are physically equivalent).
For any two vectors [??] = ([x.sub.1], [x.sub.2], [x.sub.3]) and [??] = ([y.sub.1], [y.sub.2], [y.sub.3]) in the space [R.sup.3.sub.1], the
pseudovector product of [??] and [??] is defined by
For any [??] = ([x.sub.1], [x.sub.2], [x.sub.3]) and [??] = ([y.sub.1], [y.sub.2], [y.sub.3]) in the space [R.sup.3.sub.1], the
pseudovector product of [??] and [??] is defined by
* [F.sub.i][[OMEGA]*i] = 0, so the acting gravitational inertial force [F.sub.i] is orthogonal to the space rotation
pseudovector [[OMEGA]*.sup.i];
where besides the vector components [p.sup.[mu]] we have the scalar component [mu], the 2-vector components [S.sup.[mu]v], that are connected to the spin as shown by [14]; the
pseudovector components [[pi].sup.[mu]] and the pseudoscalar component m.
If we relate a
pseudovectors [t.sub.i] to these rototranslations, in analogy with the two-dimensional planar lattice we can define reciprocal
pseudovectors [t.sup.*.sub.i] such that