# Weak interaction in a relativistic frame?

Particle is said to be right-handed (right-helicity) if the direction of particle's spin is in the same direction with it's motion and left-handed (left-helicity) if they are opposite. Picture below was taken from Wikipedia

In the relativistic frame of reference, right-handed down quarks and right-handed up quarks will be seen as left-handed down quarks and left-handed up quarks. Then, when there was no weak interaction in one frame, there will be weak interaction in another frame. This seems to me like a contradiction, or I'm missing something very fundamental. What is wrong with this gedankenexperiment?

This feels like a perfect storm of misconceptions, unleashed by unscrupulous popular science writing.

• Helicity is Lorentz-variant, so, as you envision, may be reversed by changing your frame. It is either positive or negative; never left-or right handed.

• Chirality is relativistically invariant, so a left-handed particle is left-handed in any frame, and respectively ditto for right handed ones.

• Helicity and chirality coincide for massless particles, whose sense of motion cannot be reversed by a Lorentz transformation. Hence the correlation your see in the picture: you may associate positive helicity massless particles with right-chirality, and negative-helicity massless particles with left-handed chirality.

• Strong interactions are chirality-blind (vector), and handle left-and right-chiral particles identically. So the left-chiral quarks may also interact weakly by the charged current, but the right-chiral ones cannot. No Lorentz transformation affects that.

• Both left- and right-handed quarks may interact through the weak neutral current, (10.2), (10.5a).

• Clear and detailed answer! So "no interaction" in the article for right-chiral quarks refers to that there's no interaction mediated by $W^{\pm}$ bosons yet they can still interact by $Z^{0}$? Feb 18, 2021 at 1:34
• Correct! that's right. Feb 18, 2021 at 3:07