Up & Down Quark Mass or Charge Problem? [Archive]

GoldenBoar

Aug27-04, 09:17 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nHere are the masses and charges for quarks.\n\nUp quark (1-5) (2/3)\nDown quark (3-9) (-1/3)\nStrange quark (75-170) (-1/3)\nCharm quark (1,150-1,350) (2/3)\nBottom quark (4,000-4,400) (-1/3)\nTop quark (174,000) (2/3)\n\nAs you can see from this table, the quarks are arrayed in order from\nlight to heavy, starting with the up quark. You should notice an\nirregularity with the up and down quarks compared to the others.\n\nThe top quark has charge of 2/3 and can decay into a bottom quark with\na charge of -1/3.\nThe bottom quark can decay into a charm quark with a charge of 2/3.\nThe charm quark can decay into a strange quark with a charge of -1/3.\n\nAs you can see, a pattern is emerging (2/3, -1/3, 2/3, -1/3) which\nsuggests that the next quark will have a charge of 2/3. But the next\nquark is a down quark with a charge of -1/3.\n\nCould it be possible that either\nan up quark has a charge of -1/3 and a down quark has a charge of 2/3.\nor\nan up quark has a mass of 3-9 and a down quark has a mass of 1-5.\ntherefore restoring the pattern?\n\nHow is it that these properties were attributed to these quarks in the\nfirst place?\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Here are the masses and charges for quarks.

Up quark (1-5) (2/3)
Down quark (3-9) (-1/3)
Strange quark (75-170) (-1/3)
Charm quark (1,150-1,350) (2/3)
Bottom quark (4,000-4,400) (-1/3)
Top quark (174,000) (2/3)

As you can see from this table, the quarks are arrayed in order from
light to heavy, starting with the up quark. You should notice an
irregularity with the up and down quarks compared to the others.

The top quark has charge of 2/3 and can decay into a bottom quark with
a charge of -1/3.
The bottom quark can decay into a charm quark with a charge of 2/3.
The charm quark can decay into a strange quark with a charge of -1/3.

As you can see, a pattern is emerging (2/3, -1/3, 2/3, -1/3) which
suggests that the next quark will have a charge of 2/3. But the next
quark is a down quark with a charge of -1/3.

Could it be possible that either
an up quark has a charge of -1/3 and a down quark has a charge of 2/3.
or
an up quark has a mass of 3-9 and a down quark has a mass of 1-5.
therefore restoring the pattern?

How is it that these properties were attributed to these quarks in the
first place?

Jamie Vicary

Aug28-04, 04:27 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>GoldenBoar wrote:\n> Here are the masses and charges for quarks.\n>\n> Up quark (1-5) (2/3)\n> Down quark (3-9) (-1/3)\n> Strange quark (75-170) (-1/3)\n> Charm quark (1,150-1,350) (2/3)\n> Bottom quark (4,000-4,400) (-1/3)\n> Top quark (174,000) (2/3)\n>\n> As you can see from this table, the quarks are arrayed in order from\n> light to heavy, starting with the up quark. You should notice an\n> irregularity with the up and down quarks compared to the others.\n>\n> The top quark has charge of 2/3 and can decay into a bottom quark with\n> a charge of -1/3.\n> The bottom quark can decay into a charm quark with a charge of 2/3.\n> The charm quark can decay into a strange quark with a charge of -1/3.\n>\n> As you can see, a pattern is emerging (2/3, -1/3, 2/3, -1/3) which\n> suggests that the next quark will have a charge of 2/3. But the next\n> quark is a down quark with a charge of -1/3.\n>\n> Could it be possible that either\n> an up quark has a charge of -1/3 and a down quark has a charge of 2/3.\n> or\n> an up quark has a mass of 3-9 and a down quark has a mass of 1-5.\n> therefore restoring the pattern?\n>\n> How is it that these properties were attributed to these quarks in the\n> first place?\n\nQuarks are buggers because they can\'t exist by themselves, only in\ntightly bound pairs. This means that the mass of the particles which\nquarks comprise -- called the hadrons -- is *less* than the mass of the\nisolated quarks. What does it mean to talk about an "isolated" quark?\nNot very much, as it is possible that an isolated quark can never occur\nin reality, even "in principle"; "isolated" here meaning that\nmeasurements can be made upon it to determine its mass, the outcome of\nwhich is only a function of the state of the quark under investigation.\nNobody even knows if quarks /have/ a "defined" mass, because nobody\nreally knows what mass is, however much they tell you that they do. This\nis really at the edge of science.\nAs to how we know "which is which" between the bottom and top quarks -\nwhich is really what you\'re asking - I\'m not so sure, given that the\ndifference between the possible masses of the up and down quarks is\nvastly less than the uncertainties in the masses of each of the heavier\nquarks. I suspect looking at pairs of mesons such as (up anti-strange)\nand (strange anti-down) would shed some light, as the strange mass\ncancels out in such comparisons. A bit of theoretical waffling could\ngive an argument as to what the coulomb repulsion in each of the two\nconfigurations is, and after cancelling that out, the only difference in\nthe meson masses would be the difference between the up and the down.\n\nRegards,\n\nJamie Vicary.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>GoldenBoar wrote:
> Here are the masses and charges for quarks.
>
> Up quark (1-5) (2/3)
> Down quark (3-9) (-1/3)
> Strange quark (75-170) (-1/3)
> Charm quark (1,150-1,350) (2/3)
> Bottom quark (4,000-4,400) (-1/3)
> Top quark (174,000) (2/3)
>
> As you can see from this table, the quarks are arrayed in order from
> light to heavy, starting with the up quark. You should notice an
> irregularity with the up and down quarks compared to the others.
>
> The top quark has charge of 2/3 and can decay into a bottom quark with
> a charge of -1/3.
> The bottom quark can decay into a charm quark with a charge of 2/3.
> The charm quark can decay into a strange quark with a charge of -1/3.
>
> As you can see, a pattern is emerging (2/3, -1/3, 2/3, -1/3) which
> suggests that the next quark will have a charge of 2/3. But the next
> quark is a down quark with a charge of -1/3.
>
> Could it be possible that either
> an up quark has a charge of -1/3 and a down quark has a charge of 2/3.
> or
> an up quark has a mass of 3-9 and a down quark has a mass of 1-5.
> therefore restoring the pattern?
>
> How is it that these properties were attributed to these quarks in the
> first place?

Quarks are buggers because they can't exist by themselves, only in
tightly bound pairs. This means that the mass of the particles which
quarks comprise -- called the hadrons -- is *less* than the mass of the
isolated quarks. What does it mean to talk about an "isolated" quark?
Not very much, as it is possible that an isolated quark can never occur
in reality, even "in principle"; "isolated" here meaning that
measurements can be made upon it to determine its mass, the outcome of
which is only a function of the state of the quark under investigation.
Nobody even knows if quarks /have/ a "defined" mass, because nobody
really knows what mass is, however much they tell you that they do. This
is really at the edge of science.
As to how we know "which is which" between the bottom and top quarks -
which is really what you're asking - I'm not so sure, given that the
difference between the possible masses of the up and down quarks is
vastly less than the uncertainties in the masses of each of the heavier
quarks. I suspect looking at pairs of mesons such as (up anti-strange)
and (strange anti-down) would shed some light, as the strange mass
cancels out in such comparisons. A bit of theoretical waffling could
give an argument as to what the coulomb repulsion in each of the two
configurations is, and after cancelling that out, the only difference in
the meson masses would be the difference between the up and the down.

Regards,

Jamie Vicary.

Matthew Nobes

Aug29-04, 12:55 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Sat, 28 Aug 2004, Jamie Vicary wrote:\n\n> Quarks are buggers because they can\'t exist by themselves, only in\n> tightly bound pairs. This means that the mass of the particles which\n> quarks comprise -- called the hadrons -- is *less* than the mass of the\n> isolated quarks. What does it mean to talk about an "isolated" quark?\n> Not very much, as it is possible that an isolated quark can never occur\n> in reality, even "in principle"; "isolated" here meaning that\n> measurements can be made upon it to determine its mass, the outcome of\n> which is only a function of the state of the quark under investigation.\n\nWell, that\'s correct at low energies/temperatures. However, in the very\nearly universe the temperature was high enough that quarks and gluons\nexisted in a deconfined "quark-gluon plasma" phase. The RHIC experiment\nat Brookhaven is probing this phase of matter.\n\nIn this phase quarks and gluons behave like weakly interacting\nfree particles. So it is possibly to talk about what happens to\na single quark.\n\n> Nobody even knows if quarks /have/ a "defined" mass, because nobody\n> really knows what mass is, however much they tell you that they do.\n\nMass is a parameter in a Lagrangian. It\'s hard to define a quark mass\nbecause you have to infer it from properties of Hadrons. But in principle\nit\'s no more difficult than infering the mass of an electron from the\nproperties of positronium.\n\n> This is really at the edge of science.\n> As to how we know "which is which" between the bottom and top quarks -\n> which is really what you\'re asking - I\'m not so sure, given that the\n> difference between the possible masses of the up and down quarks is\n> vastly less than the uncertainties in the masses of each of the heavier\n> quarks. I suspect looking at pairs of mesons such as (up anti-strange)\n> and (strange anti-down) would shed some light, as the strange mass\n> cancels out in such comparisons. A bit of theoretical waffling could\n> give an argument as to what the coulomb repulsion in each of the two\n> configurations is, and after cancelling that out, the only difference in\n> the meson masses would be the difference between the up and the down.\n\nThere are papers by Winberg from the 60s which address these questions.\nYou can use chiral perturbation theory to assign quarks to masses.\n\n--\nMatthew Nobes\nNewman Lab, Cornell Univesity, Ithaca, NY 14853\nhttp://www.lepp.cornell.edu/~nobes\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Sat, 28 Aug 2004, Jamie Vicary wrote:

> Quarks are buggers because they can't exist by themselves, only in
> tightly bound pairs. This means that the mass of the particles which
> quarks comprise -- called the hadrons -- is *less* than the mass of the
> isolated quarks. What does it mean to talk about an "isolated" quark?
> Not very much, as it is possible that an isolated quark can never occur
> in reality, even "in principle"; "isolated" here meaning that
> measurements can be made upon it to determine its mass, the outcome of
> which is only a function of the state of the quark under investigation.

Well, that's correct at low energies/temperatures. However, in the very
early universe the temperature was high enough that quarks and gluons
existed in a deconfined "quark-gluon plasma" phase. The RHIC experiment
at Brookhaven is probing this phase of matter.

In this phase quarks and gluons behave like weakly interacting
free particles. So it is possibly to talk about what happens to
a single quark.

> Nobody even knows if quarks /have/ a "defined" mass, because nobody
> really knows what mass is, however much they tell you that they do.

Mass is a parameter in a Lagrangian. It's hard to define a quark mass
because you have to infer it from properties of Hadrons. But in principle
it's no more difficult than infering the mass of an electron from the
properties of positronium.

> This is really at the edge of science.
> As to how we know "which is which" between the bottom and top quarks -
> which is really what you're asking - I'm not so sure, given that the
> difference between the possible masses of the up and down quarks is
> vastly less than the uncertainties in the masses of each of the heavier
> quarks. I suspect looking at pairs of mesons such as (up anti-strange)
> and (strange anti-down) would shed some light, as the strange mass
> cancels out in such comparisons. A bit of theoretical waffling could
> give an argument as to what the coulomb repulsion in each of the two
> configurations is, and after cancelling that out, the only difference in
> the meson masses would be the difference between the up and the down.

There are papers by Winberg from the 60s which address these questions.
You can use chiral perturbation theory to assign quarks to masses.

--
Matthew Nobes
Newman Lab, Cornell Univesity, Ithaca, NY 14853
http://www.lepp.cornell.edu/~nobes

Arnold Neumaier

Aug30-04, 03:57 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\nMatthew Nobes wrote:\n> On Sat, 28 Aug 2004, Jamie Vicary wrote:\n>\n>>Nobody even knows if quarks /have/ a "defined" mass, because nobody\n>>really knows what mass is, however much they tell you that they do.\n>\n> Mass is a parameter in a Lagrangian.\n\nNo. The parameters in the Lagrangian all diverge under renormalization.\nThe mass is described by a pole in the Green\'s function,\nor in terms of decay constants of correlations (in lattice gauge theory).\nIn nonrelativistic quark models, however, the (effective) mass is a\nparameter in an effective Hamiltonian.\n\nhttp://pdg.lbl.gov/2004/reviews/contents_sports.html#partpropetc\ncontains online documents by the particle data group, among others one\non \'Quark Masses\'. This is the yearly updated official consensus of\nthe physics community.\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Matthew Nobes wrote:
> On Sat, 28 Aug 2004, Jamie Vicary wrote:
>
>>Nobody even knows if quarks /have/ a "defined" mass, because nobody
>>really knows what mass is, however much they tell you that they do.
>
> Mass is a parameter in a Lagrangian.

No. The parameters in the Lagrangian all diverge under renormalization.
The mass is described by a pole in the Green's function,
or in terms of decay constants of correlations (in lattice gauge theory).
In nonrelativistic quark models, however, the (effective) mass is a
parameter in an effective Hamiltonian.

http://pdg.lbl.gov/2004/reviews/contents_sports.html#partpropetc
contains online documents by the particle data group, among others one
on 'Quark Masses'. This is the yearly updated official consensus of
the physics community.

Arnold Neumaier

Matthew Nobes

Aug30-04, 07:54 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nOn 30 Aug 2004, Arnold Neumaier wrote:\n\n> Matthew Nobes wrote:\n> > On Sat, 28 Aug 2004, Jamie Vicary wrote:\n> >\n> >>Nobody even knows if quarks /have/ a "defined" mass, because nobody\n> >>really knows what mass is, however much they tell you that they do.\n> >\n> > Mass is a parameter in a Lagrangian.\n>\n> No. The parameters in the Lagrangian all diverge under renormalization.\n\nWell, if we want to be picky, you can set up the Lagrangian in terms\nof the renormalized mass (which is finite), and a counterterm.\n\n> The mass is described by a pole in the Green\'s function,\n\nThat\'s only one definition of the quark mass. Since a free quark cannot\nbe isolated, the pole in the quark propagator does not have a direct\nrelationship to a hadron mass.\n\n> or in terms of decay constants of correlations (in lattice gauge theory).\n\nThose masses are typically bound state masses.\n\n> In nonrelativistic quark models, however, the (effective) mass is a\n> parameter in an effective Hamiltonian.\n\nUsually this is choosen to be the pole mass in matching calculations.\n\n> http://pdg.lbl.gov/2004/reviews/contents_sports.html#partpropetc\n> contains online documents by the particle data group, among others one\n> on \'Quark Masses\'. This is the yearly updated official consensus of\n> the physics community.\n\nThat\'s a usful read, since it makes it clear how hard it is to define\nan unambigous quark mass.\n\nMatt\n\n--\nMatthew Nobes\nNewman Lab, Cornell Univesity, Ithaca, NY 14853\nhttp://www.lepp.cornell.edu/~nobes\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On 30 Aug 2004, Arnold Neumaier wrote:

> Matthew Nobes wrote:
> > On Sat, 28 Aug 2004, Jamie Vicary wrote:
> >
> >>Nobody even knows if quarks /have/ a "defined" mass, because nobody
> >>really knows what mass is, however much they tell you that they do.
> >
> > Mass is a parameter in a Lagrangian.
>
> No. The parameters in the Lagrangian all diverge under renormalization.

Well, if we want to be picky, you can set up the Lagrangian in terms
of the renormalized mass (which is finite), and a counterterm.

> The mass is described by a pole in the Green's function,

That's only one definition of the quark mass. Since a free quark cannot
be isolated, the pole in the quark propagator does not have a direct
relationship to a hadron mass.

> or in terms of decay constants of correlations (in lattice gauge theory).

Those masses are typically bound state masses.

> In nonrelativistic quark models, however, the (effective) mass is a
> parameter in an effective Hamiltonian.

Usually this is choosen to be the pole mass in matching calculations.

> http://pdg.lbl.gov/2004/reviews/contents_sports.html#partpropetc
> contains online documents by the particle data group, among others one
> on 'Quark Masses'. This is the yearly updated official consensus of
> the physics community.

That's a usful read, since it makes it clear how hard it is to define
an unambigous quark mass.

Matt

--
Matthew Nobes
Newman Lab, Cornell Univesity, Ithaca, NY 14853
http://www.lepp.cornell.edu/~nobes

Arnold Neumaier

Aug30-04, 09:59 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\nMatthew Nobes wrote:\n> On 30 Aug 2004, Arnold Neumaier wrote:\n>\n>\n>>Matthew Nobes wrote:\n>>\n>>>Mass is a parameter in a Lagrangian.\n>>\n>>No. The parameters in the Lagrangian all diverge under renormalization.\n>\n>\n> Well, if we want to be picky, you can set up the Lagrangian in terms\n> of the renormalized mass (which is finite), and a counterterm.\n\nBut this does not _define_ the renormalized mass, since any value can be\nmatched by a corresponding counterterm. One needs a pole condition to\nfix (and hence define) the renormalized mass.\n\n\n>>The mass is described by a pole in the Green\'s function,\n>\n> That\'s only one definition of the quark mass. Since a free quark cannot\n> be isolated, the pole in the quark propagator does not have a direct\n> relationship to a hadron mass.\n\nOf course, hadron masses have no direct relationship to quark masses,\nsince hadrons are bound states of several quarks. But there is no other\nway to define masses for relativistic _quarks_.\n\n\n>>or in terms of decay constants of correlations (in lattice gauge theory).\n>\n> Those masses are typically bound state masses.\n\nTrue, but in a deconfined quark phase, they define quark masses.\nIn the confined phase, poles in the renormalization schemes are the\nonly way to identify quark masses.\n\n\n>>In nonrelativistic quark models, however, the (effective) mass is a\n>>parameter in an effective Hamiltonian.\n>\n> Usually this is choosen to be the pole mass in matching calculations.\n\nYes if one derives the model from basic principles. For pure\nphenomenology, one simply treats it as a parameter in a fit to the data.\n\n\n>>http://pdg.lbl.gov/2004/reviews/contents_sports.html#partpropetc\n>>contains online documents by the particle data group, among others one\n>>on \'Quark Masses\'. This is the yearly updated official consensus of\n>>the physics community.\n\nActually, my memory was poor: it is biannually updated. See\nhttp://www.slac.stanford.edu/library/pdg/particles.html\n\n\n> That\'s a useful read, since it makes it clear how hard it is to define\n> an unambigous quark mass.\n\nOf course. As any physical concept, quark masses depends on the scheme\nused for defining them. p.11:\n\'\'When using the data listings, it is important to remember\nthat the numerical value for a quark mass is meaningless without\nspecifying the particular scheme in which it was obtained.\'\'\nGiven a definite scheme, they are well-defined\nin the low energy limit. (At high energies, they are \'running\' and depend\nalso on the energy scale used for modeling. Similarly, in lattice\ncalculations, they depend on the lattice spacing used.)\n\nThe proper scheme should be nonperturbative QCD. But since we know so\nlittle about how to exploit QCD at low energies, this is not the\nscheme used. This explains the ambiguity.\n\n\nArnold Neumaier\n\n\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Matthew Nobes wrote:
> On 30 Aug 2004, Arnold Neumaier wrote:
>
>
>>Matthew Nobes wrote:
>>
>>>Mass is a parameter in a Lagrangian.
>>
>>No. The parameters in the Lagrangian all diverge under renormalization.
>
>
> Well, if we want to be picky, you can set up the Lagrangian in terms
> of the renormalized mass (which is finite), and a counterterm.

But this does not _define_ the renormalized mass, since any value can be
matched by a corresponding counterterm. One needs a pole condition to
fix (and hence define) the renormalized mass.

>>The mass is described by a pole in the Green's function,
>
> That's only one definition of the quark mass. Since a free quark cannot
> be isolated, the pole in the quark propagator does not have a direct
> relationship to a hadron mass.

Of course, hadron masses have no direct relationship to quark masses,
since hadrons are bound states of several quarks. But there is no other
way to define masses for relativistic _quarks_.

>>or in terms of decay constants of correlations (in lattice gauge theory).
>
> Those masses are typically bound state masses.

True, but in a deconfined quark phase, they define quark masses.
In the confined phase, poles in the renormalization schemes are the
only way to identify quark masses.

>>In nonrelativistic quark models, however, the (effective) mass is a
>>parameter in an effective Hamiltonian.
>
> Usually this is choosen to be the pole mass in matching calculations.

Yes if one derives the model from basic principles. For pure
phenomenology, one simply treats it as a parameter in a fit to the data.

>>http://pdg.lbl.gov/2004/reviews/contents_sports.html#partpropetc
>>contains online documents by the particle data group, among others one
>>on 'Quark Masses'. This is the yearly updated official consensus of
>>the physics community.

Actually, my memory was poor: it is biannually updated. See
http://www.slac.stanford.edu/library/pdg/particles.html

> That's a useful read, since it makes it clear how hard it is to define
> an unambigous quark mass.

Of course. As any physical concept, quark masses depends on the scheme
used for defining them. p.11:
''When using the data listings, it is important to remember
that the numerical value for a quark mass is meaningless without
specifying the particular scheme in which it was obtained.''
Given a definite scheme, they are well-defined
in the low energy limit. (At high energies, they are 'running' and depend
also on the energy scale used for modeling. Similarly, in lattice
calculations, they depend on the lattice spacing used.)

The proper scheme should be nonperturbative QCD. But since we know so
little about how to exploit QCD at low energies, this is not the
scheme used. This explains the ambiguity.

Arnold Neumaier