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Why is the approximate $U$\rm U(2)\times U(2)$ global symmetry of QCD that has a special importance?

I was looking at Peskin and Schroeder (Section 19.3, page $667-668$). They talk about $U(2)\times U(2)$$\rm U(2)\times U(2)$ symmetry for the QCD Lagrangian in the limit of massless $u$ and $d$ quarks. However, this must be an approximate symmetry because $u$ and $d$ are not actually massless. If this is so, why does it not talk about $U(3)\times U(3)$$\rm U(3)\times U(3)$ symmetry including $s$ quark as well? Or even better, why not talk about $U(6)\times U(6)$$\rm U(6)\times U(6)$ symmetry involving all six flavours of quarks? What is so special about $U(2)\times U(2)$$\rm U(2)\times U(2)$ which too is approximate?

Why is the approximate $U(2)\times U(2)$ global symmetry of QCD that has a special importance?

I was looking at Peskin and Schroeder (Section 19.3, page $667-668$). They talk about $U(2)\times U(2)$ symmetry for the QCD Lagrangian in the limit of massless $u$ and $d$ quarks. However, this must be an approximate symmetry because $u$ and $d$ are not actually massless. If this is so, why does it not talk about $U(3)\times U(3)$ symmetry including $s$ quark as well? Or even better, why not talk about $U(6)\times U(6)$ symmetry involving all six flavours of quarks? What is so special about $U(2)\times U(2)$ which too is approximate?

Why is the approximate $\rm U(2)\times U(2)$ global symmetry of QCD that has a special importance?

I was looking at Peskin and Schroeder (Section 19.3, page $667-668$). They talk about $\rm U(2)\times U(2)$ symmetry for the QCD Lagrangian in the limit of massless $u$ and $d$ quarks. However, this must be an approximate symmetry because $u$ and $d$ are not actually massless. If this is so, why does it not talk about $\rm U(3)\times U(3)$ symmetry including $s$ quark as well? Or even better, why not talk about $\rm U(6)\times U(6)$ symmetry involving all six flavours of quarks? What is so special about $\rm U(2)\times U(2)$ which too is approximate?

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SRS
SRS
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  • 106
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I was looking at Peskin and Schroeder (Section 19.3, page $667-668$). They talk about $U(2)\times U(2)$ symmetry for the QCD Lagrangian in the limit of massless $u$ and $d$ quarks. However, this must be an approximate symmetry because $u$ and $d$ are nornot actually massless. If this is so, why does it not talk about $U(3)\times U(3)$ symmetry including $s$ quark as well? Or even better, why not talk about $U(6)\times U(6)$ symmetry involving all six flavours of quarks? What is so special about $U(2)\times U(2)$ which too is approximate?

I was looking at Peskin and Schroeder. They talk about $U(2)\times U(2)$ symmetry for the QCD Lagrangian in the limit of massless $u$ and $d$ quarks. However, this must be an approximate symmetry because $u$ and $d$ are nor actually massless. If this is so, why does it not talk about $U(3)\times U(3)$ symmetry including $s$ quark as well? Or even better, why not talk about $U(6)\times U(6)$ symmetry involving all six flavours of quarks? What is so special about $U(2)\times U(2)$ which too is approximate?

I was looking at Peskin and Schroeder (Section 19.3, page $667-668$). They talk about $U(2)\times U(2)$ symmetry for the QCD Lagrangian in the limit of massless $u$ and $d$ quarks. However, this must be an approximate symmetry because $u$ and $d$ are not actually massless. If this is so, why does it not talk about $U(3)\times U(3)$ symmetry including $s$ quark as well? Or even better, why not talk about $U(6)\times U(6)$ symmetry involving all six flavours of quarks? What is so special about $U(2)\times U(2)$ which too is approximate?

Source Link
SRS
SRS
  • 27.2k
  • 12
  • 106
  • 341

Why is the approximate $U(2)\times U(2)$ global symmetry of QCD that has a special importance?

I was looking at Peskin and Schroeder. They talk about $U(2)\times U(2)$ symmetry for the QCD Lagrangian in the limit of massless $u$ and $d$ quarks. However, this must be an approximate symmetry because $u$ and $d$ are nor actually massless. If this is so, why does it not talk about $U(3)\times U(3)$ symmetry including $s$ quark as well? Or even better, why not talk about $U(6)\times U(6)$ symmetry involving all six flavours of quarks? What is so special about $U(2)\times U(2)$ which too is approximate?