The W and Z particles are a little more different. The W+- particles only interact with L-hilarity particles. The Z particle "prefers" the L particles, but also interacts with the R particles.
It's more complicated. There is a W^0 particle that is the neutral equivalent of the W^+ and W^- particles, all of them have the same mass. There is another particle called A, that is like a photon with mass (but it "sees" the hypercharge of the particles, not the charge)
Combining the W^0 and A particles, it's possible to get two new particles the Z^0 and the photon. In this combination the Z^0 has all the mass and the photon has no mass. It's more easy to understand some experiments using the Z^0 and the photon, so to make some explanations more clear it's better to use them instead of the W^0 and the A.
IIRC, for low energy experiments it'd better to use Z^0 and photons, and for high energy experiments it's better to use W^0 and A.
You are mixing conjectures from string theory and other theories with known physics.
I can found no info on the W^0 or the A, R and L are a type of conjectured parity, not actual particles, and hypercharge is an obsolete concept.
You should be more careful about where you learn physics, and very very careful to distinguish known physics, or theories with evidence from conjectures and ideas. Both are necessary - but don't mix them up.
What?! I'm taking only about particle physic (I don't know almost anything about string theory).
The W^+,W^0 and W^- are a weak-isospin triplet of bosons that are the carriers of the "real" weak force, assuming that the SU(2)_L symmetry holds for the weak-isospin doublets (electron_L-neutrilo_L), ...,(up_quark_L, down'_quark_L),...
(Sometimes the weak-isospin triplet is written as W_0,W_1 and W_2, using another base.)
I rememberd incorrectly the name of of the particles "A". Sorry. The correct name is B^0. This is the of the field associated to the weak hypercharge with the U(1) symmetry. I know hat the old hypercharge is not more a very useful concept, but I was trying to simplify a little the notation and I dropped the weak part.
In this theory each fermions can be classified as L or R chirality (it's a "property" of the particles, not an independent thing) (the mass of the particles makes this a little more complicated). The "real" weak" force only interacts with the L version of the particles.
This has many experimental results, for example the ratio between the mass of the Z^0 and the W^+- particle is indirectly related to the ratio between the coupling of the Z^0 and the L and R electrons.
All of this id proved beyond doubt, but it assumes that the particles doesn't have mass. They have an apparent mass created by the Higgs mechanisms (or something equivalent), so there must be Higgs bosons out there. So the only missing part is to prove the existence of the Higgs bosons, and it's almost done (5-sigmas next year?).
It's more complicated. There is a W^0 particle that is the neutral equivalent of the W^+ and W^- particles, all of them have the same mass. There is another particle called A, that is like a photon with mass (but it "sees" the hypercharge of the particles, not the charge)
Combining the W^0 and A particles, it's possible to get two new particles the Z^0 and the photon. In this combination the Z^0 has all the mass and the photon has no mass. It's more easy to understand some experiments using the Z^0 and the photon, so to make some explanations more clear it's better to use them instead of the W^0 and the A.
IIRC, for low energy experiments it'd better to use Z^0 and photons, and for high energy experiments it's better to use W^0 and A.