SUSY N=1 masless supermultiplet

[Jesus]

In the massless case of N=1 simple supersimetry, the states are labeled by the helicity λ and the four-momentum.
In this case we have two states in the supermultiplet plus CPT conjugates: |p^μ, ± λ> and |p^μ, ± (λ-½)>

Then there is a λ= {0, ½} supermultiplet (where for example a quark with λ=½ has a partner squark of λ=0)
and a λ= {1, ½} supermultiplet (where for example a gluon with λ=1 has a partner gluino of λ=½)

My question is why do we put the matter fields in the λ= {0, ½} supermultiplet? I mean why the squark can not have λ=1 for example?.

 

[samalkhaiat]

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My question is why do we put the matter fields in the λ= {0, ½} supermultiplet? I mean why the squark can not have λ=1 for example?.

This is still an open possibility, at least in extended supersymmetry. However, relating matter fields(quarks and leptons) with spin-1 superpartners would require a very large gauge group and, therefore, a large number of new gauge fields (bosons), as well as many additional spin-0 bosons, associated with the spontaneous breakdown of this large gauge symmetry. So, relating all fermions (quarks and leptons) with spin-0 superfermions (squarks and sleptons) represents the simplest and most economic possibility, i.e. it does not require a very large gauge group.
Okay, here are two questions for you to think about: 1) Why did supersymmetry fail to relate the spin-1 photon with a massless spin-1/2 neutrino; and, at the same time, their charged electroweak partners, the spin-1 $W^{ \pm }$ with the spin-1/2 $e^{ \pm }$, which is possible in principle? 2) What goes wrong when we relate the left-handed fermionic doublet $( \ (\nu)_{ L } \ , \ (\ell^{-})_{ L } )^{ t }$ with the spin-0 doublet $( \ \varphi^{ 0 } \ , \ \varphi^{ - } )^{ t }$?