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After SBB you can distinguish between an up quark (generation I) and a charm quark (generation II) because of their mass. But here, we don't even have that difference. All quantum numbers are the same.

All quantum numbers are the same, but you can tell the difference between a u and a c, because you effectively already put it in by hand, with malice aforethought, for that very purpose! You have observed the low mass of the u, and the higher mass of the c, and you have, plausibly, but arbitrarily, really, decided to assign them to the I and II generations, respectively.

You structure the arbitrary Yukawa couplings, then, in $$ -Y^d_{ij}\bar Q^i H d_R^j -Y^u_{ij}\bar Q^i \tilde H u_R^j + \hbox{h.c.}, $$ such that, after SSB, suppressing the generation indices of the Yukawa matrices, the mass part of the above collapses to the celebrated mass terms $$ -{v\over \sqrt 2} ( \bar d _L Y_d d_R + \bar u _L Y_u u_R ) + \hbox{h.c.}, $$ dialed to yield (postdict) the observed answers, as follows.

The two matrices $Y_d$ and $Y_u$ matrices are biunitarily diagonalizable, as your text probably explains, $$ Y_d= U_d M_d K_d^\dagger, \qquad Y_u= U_u M_u K_u^\dagger, $$ so the smallest and middle eigenvalue of the diagonal $M_u$ are then proportional to the masses of the u and c, after you have absorbed their adjoints into the definitions of the quarks, thus defining the mass basis $$ d_R\to K_d d_R; \qquad u_R\to K_u u_R;\qquad d_L\to U_d u_L;\qquad u_L\to U_u u_L. $$

(You then construct the CKM matrix out of the Us and the Ks, but that outranges your question.)

• The takeaway is that the differentiation between the u and the c is already there from the very start, at the level of the Yukawa matrices Y, an input to be suitably (implicitly) fitted through post-SSB observation. Nobody has ever plausibly derived those from first principles (yet). But the Yukawa matrices' fitted eigenvalues are there before SSB.

After SBB you can distinguish between an up quark (generation I) and a charm quark (generation II) because of their mass. But here, we don't even have that difference. All quantum numbers are the same.

All quantum numbers are the same, but you can tell the difference between a u and a c, because you effectively already put it in by hand, with malice aforethought, for that very purpose! You have observed the low mass of the u, and the higher mass of the c, and you have, plausibly, but arbitrarily, really, decided to assign them to the I and II generations, respectively.

You structure the arbitrary Yukawa couplings, then, in $$ -Y^d_{ij}\bar Q^i H d_R^j -Y^u_{ij}\bar Q^i \tilde H u_R^j + \hbox{h.c.}, $$ such that, after SSB, suppressing the generation indices of the Yukawa matrices, the mass part of the above collapses to the celebrated mass terms $$ -{v\over \sqrt 2} ( \bar d _L Y_d d_R + \bar u _L Y_u u_R ) + \hbox{h.c.}, $$ dialed to yield (postdict) the observed answers, as follows.

The two matrices $Y_d$ and $Y_u$ matrices are biunitarily diagonalizable, as your text probably explains, $$ Y_d= U_d M_d K_d^\dagger, \qquad Y_u= U_u M_u K_u^\dagger, $$ so the smallest and middle eigenvalue of the diagonal $M_u$ are then proportional to the masses of the u and c, after you have absorbed their adjoints into the definitions of the quarks, thus defining the mass basis $$ d_R\to K_d d_R; \qquad u_R\to K_u u_R;\qquad d_L\to U_d u_L;\qquad u_L\to U_u u_L. $$

(You then construct the CKM matrix $U^\dagger_u U_d$, but that outranges your question.)

• The takeaway is that the differentiation between the u and the c is already there from the very start, at the level of the Yukawa matrices Y, an input to be suitably (implicitly) fitted through post-SSB observation. Nobody has ever plausibly derived those from first principles (yet). But the Yukawa matrices' fitted eigenvalues are there before SSB.

After SBB you can distinguish between an up quark (generation I) and a charm quark (generation II) because of their mass. But here, we don't even have that difference. All quantum numbers are the same.

All quantum numbers are the same, but you can tell the difference between a u and a c, because you effectively already put it in by hand, with malice aforethought, for that very purpose! You have observed the low mass of the u, and the higher mass of the c, and you have, plausibly, but arbitrarily, really, decided to assign them to the I and II generations, respectively.

You structure the arbitrary Yukawa couplings, then, in $$ -Y^d_{ij}\bar Q^i H d_R^j -Y^u_{ij}\bar Q^i \tilde H u_R^j + \hbox{h.c.}, $$ such that, after SSB, suppressing the generation indices of the Yukawa matrices, the mass part of the above collapses to the celebrated mass terms $$ -{v\over \sqrt 2} ( \bar d _L Y_d d_R + \bar u _L Y_u u_R ) + \hbox{h.c.}, $$ dialed to yield (postdict) the observed answers, as follows.

The two matrices $Y_d$ and $Y_u$ matrices are biunitarily diagonalizable, as your text probably explains, $$ Y_d= U_d M_d K_d^\dagger, \qquad Y_u= U_u M_u K_u^\dagger, $$ so the smallest and middle eigenvalue of the diagonal $M_u$ are then proportional to the masses of the u and c, after you have absorbed their adjoints into the definitions of the quarks, thus defining the mass basis $$ d_R\to K_d d_R; \qquad u_R\to K_u u_R;\qquad d_L\to U_d u_L;\qquad u_L\to U_u u_L. $$

(You then construct the CKM matrix out of the Us and the Ks, but that outranges your question.)

• The takeaway is that the differentiation between the u and the c is already there from the very start, at the level of the Yukawa matrices Y, an input to be suitably (implicitly) fitted through post-SSB observation. Nobody has ever plausibly derived those from first s principles (yet).

After SBB you can distinguish between an up quark (generation I) and a charm quark (generation II) because of their mass. But here, we don't even have that difference. All quantum numbers are the same.

All quantum numbers are the same, but you can tell the difference between a u and a c, because you effectively already put it in by hand, with malice aforethought, for that very purpose! You have observed the low mass of the u, and the higher mass of the c, and you have, plausibly, but arbitrarily, really, decided to assign them to the I and II generations, respectively.

You structure the arbitrary Yukawa couplings, then, in $$ -Y^d_{ij}\bar Q^i H d_R^j -Y^u_{ij}\bar Q^i \tilde H u_R^j + \hbox{h.c.}, $$ such that, after SSB, suppressing the generation indices of the Yukawa matrices, the mass part of the above collapses to the celebrated mass terms $$ -{v\over \sqrt 2} ( \bar d _L Y_d d_R + \bar u _L Y_u u_R ) + \hbox{h.c.}, $$ dialed to yield (postdict) the observed answers, as follows.

The two matrices $Y_d$ and $Y_u$ matrices are biunitarily diagonalizable, as your text probably explains, $$ Y_d= U_d M_d K_d^\dagger, \qquad Y_u= U_u M_u K_u^\dagger, $$ so the smallest and middle eigenvalue of the diagonal $M_u$ are then proportional to the masses of the u and c, after you have absorbed their adjoints into the definitions of the quarks, thus defining the mass basis $$ d_R\to K_d d_R; \qquad u_R\to K_u u_R;\qquad d_L\to U_d u_L;\qquad u_L\to U_u u_L. $$

(You then construct the CKM matrix out of the Us and the Ks, but that outranges your question.)

• The takeaway is that the differentiation between the u and the c is already there from the very start, at the level of the Yukawa matrices Y, an input to be suitably (implicitly) fitted through post-SSB observation. Nobody has ever plausibly derived those from first principles (yet). But the Yukawa matrices' fitted eigenvalues are there before SSB.

After SBB you can distinguish between an up quark (generation I) and a charm quark (generation II) because of their mass. But here, we don't even have that difference. All quantum numbers are the same.

All quantum numbers are the same, but you can tell the difference between a u and a c, because you effectively already put it in by hand, with malice aforethought, for that very purpose! You have observed the low mass of the u, and the higher mass of the c, and you have, plausibly, but arbitrarily, really, decided to assign them to the I and II generations, respectively.

You structure the arbitrary Yukawa couplings, then, in $$ -Y^d_{ij}\bar Q^i H d_R^j -Y^u_{ij}\bar Q^i \tilde H u_R^j + \hbox{h.c.}, $$ such that, after SSB, suppressing the generation indices of the Yukawa matrices, the mass part of the above collapses to the celebrated mass terms $$ -{v\over \sqrt 2} ( \bar d _L Y_d d_R + \bar u _L Y_u u_R ) + \hbox{h.c.}, $$ dialed to yield (postdict) the observed answers, as follows.

The two matrices $Y_d$ and $Y_u$ matrices are biunitarily diagonalizable, as your text probably explains, $$ Y_d= U_d M_d K_d^\dagger, \qquad Y_u= U_u M_u K_u^\dagger, $$ so the smallest and middle eigenvalue of the diagonal $M_u$ are then proportional to the masses of the u and c, after you have absorbed their adjoints into the definitions of the quarks, thus defining the mass basis $$ d_R\to K_d d_R; \qquad u_R\to K_u u_R;\qquad d_L\to U_d u_L;\qquad u_L\to U_u u_L. $$

(You then construct the CKM matrix out of the Us and the Ks, but that outranges your question.)

• The takeaway is that the differentiation between the u and the c is already there from the very start, at the level of the Yukawa matrices Y, an input to be suitably (implicitly) fitted through observation. Nobody has ever plausibly derived those from first principles (yet).

After SBB you can distinguish between an up quark (generation I) and a charm quark (generation II) because of their mass. But here, we don't even have that difference. All quantum numbers are the same.

All quantum numbers are the same, but you can tell the difference between a u and a c, because you effectively already put it in by hand, with malice aforethought, for that very purpose! You have observed the low mass of the u, and the higher mass of the c, and you have, plausibly, but arbitrarily, really, decided to assign them to the I and II generations, respectively.

You structure the arbitrary Yukawa couplings, then, in $$ -Y^d_{ij}\bar Q^i H d_R^j -Y^u_{ij}\bar Q^i \tilde H u_R^j + \hbox{h.c.}, $$ such that, after SSB, suppressing the generation indices of the Yukawa matrices, the mass part of the above collapses to the celebrated mass terms $$ -{v\over \sqrt 2} ( \bar d _L Y_d d_R + \bar u _L Y_u u_R ) + \hbox{h.c.}, $$ dialed to yield (postdict) the observed answers, as follows.

The two matrices $Y_d$ and $Y_u$ matrices are biunitarily diagonalizable, as your text probably explains, $$ Y_d= U_d M_d K_d^\dagger, \qquad Y_u= U_u M_u K_u^\dagger, $$ so the smallest and middle eigenvalue of the diagonal $M_u$ are then proportional to the masses of the u and c, after you have absorbed their adjoints into the definitions of the quarks, thus defining the mass basis $$ d_R\to K_d d_R; \qquad u_R\to K_u u_R;\qquad d_L\to U_d u_L;\qquad u_L\to U_u u_L. $$

(You then construct the CKM matrix out of the Us and the Ks, but that outranges your question.)

• The takeaway is that the differentiation between the u and the c is already there from the very start, at the level of the Yukawa matrices Y, an input to be suitably (implicitly) fitted through post-SSB observation. Nobody has ever plausibly derived those from first s principles (yet).