Why is the nucleon axial charge a charge?
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Lets take a look at the definition of the nucleon axial charge gA" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">gAgA
⟨p|Aμa|p⟩=gAu¯(p)γμγ5τau(p)" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">⟨p|Aaμ|p⟩=gAu¯(p)γμγ5τau(p)⟨p|Aμa|p⟩=gAu¯(p)γμγ5τau(p) with the QCD axial current Aμa=ψ¯γμγ5τaψ" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">Aaμ=ψ¯γμγ5τaψAμa=ψ¯γμγ5τaψ.
Synonymous to "nucleon axial charge" the term "(isovector) axial coupling constant" is used.
What is the motivation to call the object in front of the Dirac spinors a "charge"? Does this have to do with Noether's theorem which states that to each continuous symmetry there's a conserved current with an associated conserved charge? If so, what is the conserved symmetry in the case of the baryon axial charge in general, or the nucleon axial charge in particular?
Second part of the question: Is there a Feynman diagram vertex corresponding to the above matrix element ⟨p|Aμa|p⟩" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">⟨p|Aaμ|p⟩⟨p|Aμa|p⟩? Let me elaborate: The matrix element ⟨π|q¯γμq|π⟩" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">⟨π|q¯γμq|π⟩⟨π|q¯γμq|π⟩ is the vector current between two pions and describes the coupling of a photon to a pion and can be drawn as three-particle interaction, namely an incoming pion, a photon and an outgoing pion.
⟨p|Aμa|p⟩=gAu¯(p)γμγ5τau(p)" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">⟨p|Aaμ|p⟩=gAu¯(p)γμγ5τau(p)⟨p|Aμa|p⟩=gAu¯(p)γμγ5τau(p) with the QCD axial current Aμa=ψ¯γμγ5τaψ" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">Aaμ=ψ¯γμγ5τaψAμa=ψ¯γμγ5τaψ.
Synonymous to "nucleon axial charge" the term "(isovector) axial coupling constant" is used.
What is the motivation to call the object in front of the Dirac spinors a "charge"? Does this have to do with Noether's theorem which states that to each continuous symmetry there's a conserved current with an associated conserved charge? If so, what is the conserved symmetry in the case of the baryon axial charge in general, or the nucleon axial charge in particular?
Second part of the question: Is there a Feynman diagram vertex corresponding to the above matrix element ⟨p|Aμa|p⟩" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">⟨p|Aaμ|p⟩⟨p|Aμa|p⟩? Let me elaborate: The matrix element ⟨π|q¯γμq|π⟩" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">⟨π|q¯γμq|π⟩⟨π|q¯γμq|π⟩ is the vector current between two pions and describes the coupling of a photon to a pion and can be drawn as three-particle interaction, namely an incoming pion, a photon and an outgoing pion.
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