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Allowed through an s-channel W boson. The initial up quark and down antiquark annihilate into a virtual $W^{+}$, which produces the final charm quark and strange antiquark. The two weak charged current vertices contain the nonzero CKM matrix elements $V_{ud}$ and $V_{cs}$, with complex conjugations determined by fermion-flow conventions.

The left panel shows the unique physical-particle tree-level Feynman diagram. A neutral exchanged gauge boson cannot connect these charged annihilation currents, and flavour-diagonal neutral vertices cannot turn an up quark into a charm quark. There is no additional elementary charged scalar in the minimal Standard Model.

Let ${\theta }^{\star }$ be the angle from the incoming up quark, along the proton direction, to the outgoing charged antilepton in the W boson rest frame. The initial and final spin projections in ii are $-1$ and $+1$. The Wigner small-d matrix therefore givesAfter squaring and normalizing over $c=\cos {\theta }^{\star }$, the charged-lepton angular distribution isIts integral is one since ${\int }_{-1}^1(1-c{)}^{2}dc=8/3$. The charged antilepton is preferentially emitted toward the antiproton. Measuring the angle from the incoming down antiquark instead replaces $c$ by $-c$ and produces $(1+c{)}^2$; the axis convention is part of the answer. Per unit solid angle the normalized density is $3(1-\cos {\theta }^{\star }{)}^2/(16\pi )$.

Neglect the participating quark and lepton masses, so that the weak charged current selects a left-helicity $u$ and a right-helicity $\bar{d}$. Choose $+z$ along the proton beam in the partonic centre-of-momentum frame. Then the up quark moves along $+z$ with spin projection $-1/2$, while the down antiquark moves along $-z$ with helicity $+1/2$ and also has spin projection $-1/2$ along $+z$. ThusThe collinear two-body initial state has no orbital projection about its collision axis. In this approximation the produced W boson therefore has the indicated transverse polarization; its longitudinal spin state is absent. The unpolarized hadron beams contain other constituent spin states, but these do not participate in this massless charged-current subprocess.

In the final state the Positron has helicity $+1/2$ and the electron neutrino has helicity $-1/2$. Along the outgoing charged-lepton direction their combined angular-momentum projection is $+1$, because the oppositely moving neutrino has spin projection $+1/2$ on that axis. Finite masses, noncollinear production and sea contributions modify the ideal configuration.

A leading valence-level process is $u\bar{d}\to W^{+}\to e^{+}{\nu }_e$, with the up quark supplied by the proton and the down antiquark by the antiproton. The same Feynman diagram works with $e^{+}{\nu }_e$ replaced by ${\mu }^{+}{\nu }_{\mu }$. Both vertices are weak charged current vertices; the production scattering amplitude contains the CKM matrix element $V_{ud}$ or its conjugate according to the chosen fermion-flow convention. The intermediate W boson is produced near its mass shell.