Catalina Update Fail Purgeable Storage
OK, I suspect I understand your puzzlement...You are simply faked out by the inappropriate sloppy language "right handed helicity". There is no such thing.
For simplicity, take the spin up to be in the z direction, and the momentum in the z direction, $p^\mu= (\sqrt{m^2+p^2},0,0,p)$, and inspect your spinor in the Weyl (chiral) basis, $\psi_L=\frac12(1-\gamma^5)\psi=\begin{pmatrix} I_2 & 0 \\0 & 0 \end{pmatrix}\psi,\quad \psi_R=\frac12(1+\gamma^5)\psi=\begin{pmatrix} 0 & 0 \\0 & I_2 \end{pmatrix}\psi$, $$ u(p)= \left(\begin{array}{c} \sqrt{p ·\sigma}\xi_{\uparrow} \\ \sqrt{p ·\bar\sigma}\xi_{\uparrow} \end{array}\right) = \left(\begin{array}{c} \psi_L \\ \psi_R \end{array}\right).$$
Now $ \sqrt{p ·\sigma}\xi_{\uparrow}= \sqrt{E-p} ~\xi_{\uparrow}$, and $ \sqrt{p ·\bar\sigma}\xi_{\uparrow}= \sqrt{E+p}~\xi_{\uparrow}$, so that $$ u(p)= \left(\begin{array}{c} \sqrt{E-p} ~\xi_{\uparrow} \\ \sqrt{E+p}~\xi_{\uparrow}\end{array}\right), $$ of course both left- and right-chiral. The upper component does not vanish, in general, for positive helicity.
Inspect 3 limits. For p=0, E=m and $$ u(0)= \sqrt{m} \left(\begin{array}{c} \xi_{\uparrow} \\ \xi_{\uparrow}\end{array}\right), $$ completely even-handed--helicity is undefined.
For m=0, the upper two components are projected out, and only the lower two (actually only the third) survive(s), $$ u(p)= \sqrt{2p} \left(\begin{array}{c} 0 \\ \xi_{\uparrow}\end{array}\right), $$ so truly right-handed: the origin of sloppily referring to positive helicity as "R", as helicity and chirality are identical.
For $p\gg m$, $$ u(p)\longrightarrow \sqrt{2p} \left(\begin{array}{c}m/2p ~ \xi_{\uparrow} \\ \xi_{\uparrow}\end{array}\right), $$ so there is a left-chiral piece, as well, but wildly subdominant to the right-chiral piece. Again, this is a positive helicity spinor not divorced from its left chiral piece.
The obverse statement is provided in Wikipedia: For massive particles, distinct chirality states (e.g., as occur in the weak interaction charges) have both positive and negative helicity components, in ratios proportional to the mass of the particle.
The textbook of Itzykson & Zuber, 2-2-1, provides a serviceable definition of the helicity operator; in our case, $$ \hat{h}= \tfrac{1}{2} \begin{pmatrix} \sigma^3 & 0 \\0 & \sigma^3 \end{pmatrix}, $$ comporting with the above: it reads off an eigenvalue of +1/2 for both the upper, $\psi_L$, and the lower, $\psi_R$, component, as it should.
Unless one were safely clear of the language pitfall to avoid, or one were a sucker for paradoxical statements to keep the audience on edge, it is an untoward idea to be tossing around chirality terms to quantify helicity...
- PS. A more apposite title would have been "Helicity with indefinite chirality"!
Change permissions on the file first:
sudo chmod u+w /etc/nsswitch.conf
That will give write permission to the owner (should be root). Then try editing it as you tried before:
sudo vi /etc/nsswitch.conf