Indirect Handle on the Down-Quark Yukawa Coupling

To measure the Yukawa couplings of the up and down quarks, $Y_{u,d}$, seems to be far beyond the capabilities of current and (near) future experiments in particle physics. By performing a general analysis of the potential misalignment between quark masses and Yukawa couplings, we derive predictions for the magnitude of induced flavor-changing neutral currents (FCNCs), depending on the shift in the physical Yukawa coupling of first-generation quarks. We find that a change of more than 50% in $Y_d$ would generically result in $ds$ transitions in conflict with kaon physics. This could already be seen as evidence for a nonvanishing direct coupling of the down quark to the newly discovered Higgs boson. The nonobservation of certain—already well-constrained—processes is thus turned into a powerful indirect measure of otherwise basically unaccessible physical parameters of the effective standard model. Similarly, improvements in limits on FCNCs in the up-type quark sector can lead to valuable information on $Y_u$.

Figure 1

Predictions for the correlation between the off-diagonal transition $|({\mathit{Y}}^d{)}_{13}({\mathit{Y}}^d{)}_{31}|$ and $|Y_d/Y_d^{\mathrm{SM}}|$. The current experimental constraint from $B_d^0$ oscillations is given as an orange dashed line, while a potential experimental improvement by around an order of magnitude is depicted as a green dot-dashed line. See text for details.

Figure 2

Predictions for the correlation between $|\mathrm{Re}[({\mathit{Y}}^{d*}{)}_{12}({\mathit{Y}}^d{)}_{21}]|$, $|\mathrm{Im}[({\mathit{Y}}^{d*}{)}_{12}({\mathit{Y}}^d{)}_{21}]|$, and $|Y_d/Y_d^{\mathrm{SM}}|$. The current experimental constraints from $K^0$ oscillations are given as orange dashed lines. See text for details.

Figure 3

Predictions for the correlation between the off-diagonal transition $|({\mathit{Y}}^u{)}_{12}({\mathit{Y}}^u{)}_{21}|$ and $|Y_u/Y_u^{\mathrm{SM}}|$. The current experimental constraint from $D_d^0$ oscillations is given as an orange dashed line, while a potential improvement by 2 to 3 orders of magnitude is depicted as a green dot-dashed line. See text for details.

Figure 4

Same plots as before, now with $v/\sqrt{2}|({\mathit{C}}_{u,d}{)}_{ij}|=[0,0.1]\mathrm{GeV}$. See text for details.

Figure 5

Same plots as before, now with $v/\sqrt{2}|({\mathit{C}}_{u,d}{)}_{1,1}|=[0,5]\mathrm{MeV}$. See text for details.