<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\nbaez@math-cl-n03.math.ucr.edu (John Baez) wrote\n\n> alistair <alistair@goforit64.fsnet.co.uk> wrote:\n>\n> >What does CPT theorem have to say about the excess of\n> >matter over antimatter in the universe?\n>\n\n> Baryogenesis is the process whereby baryons (e.g. protons and neutrons)\n> were formed in the early universe, and one big thing any theory of\n> baryogenesis must explain is how more baryons were formed than antibaryons.\n>\n(...)\n>\n> In 1967 Sakharov enumerated 3 necessary conditions for baryogenesis:\n>\n> 1. Baryon number violation. If baryon number (B) is conserved in all\n> reactions, then the present baryon asymmetry can only reflect asymmetric\n> initial conditions [...]\n>\n> 2. C and CP violation. Even in the presence of B-violating reactions,\n> without a preference for matter over antimatter the B-violation will take\n> place at the same rate in both directions, leaving only a very tiny\n> statistical excess, perhaps only enough matter to make one star in the\n> observable universe.\n>\n> 3. Thermodynamic Nonequilibrium. Because CPT guarantees equal masses for\n> baryons and antibaryons, chemical equilibrium would drive the necessary\n> reactions to correct for any developing asymmetry.\n>\n> It turns out the Standard Model satisfies all 3 conditions:\n\nN.B. - the conditions are necessary but not sufficient!\n\n> 1. Though the Standard Model conserves B classically (no terms in the\n> Lagrangian violate B), quantum effects allow the universe to tunnel between\n> vacua with different values of B. (...)\n>\n> 2. C-violation is commonplace. CP-violation (that\'s "charge conjugation"\n> and "parity") has been experimentally observed in kaon decays, though strictly\n> speaking the Standard Model probably has insufficient CP-violation to give the\n> observed baryon asymmetry.\n\nNot "probably", definitely. There are papers from a decade ago showing\nthat the CKM matrix gives a CP asymmetry some orders of magnitude too\nsmall even with the most optimistic assumptions. See\nhttp://arxiv.org/abs/hep-ph/9407403 .\nBaryogenesis requires a new source of CP violation.\n\n> 3. Thermal nonequilibrium is achieved during first-order phase transitions\n> in the cooling early universe, such as the electroweak phase transition\n> (at T = 100 GeV or so). As bubbles of the "true vacuum" (with a nonzero\n> Higgs vev) percolate and grow, baryogenesis can occur at or near the bubble\n> walls.\n\nDepending on the Higgs mass, the phase transition may or may not be\nfirst order, and may be "weakly first order" meaning that the\nsphalerons are still active in the true vacuum and thus wipe out any\nasymmetry. With the current limits on the Higgs mass the strongly\nfirst order transition looks unlikely.\n\nBaryogenesis *undoubtedly* needs beyond the SM physics, and a *new*\nsource of CP violation which likely is not directly related to the CKM\nphase.\n\nNow, if you have some CPT violation (which is however severely\nconstrained by experimental data) then you don\'t necessarily need an\nout-of-equilibrium condition, since particle and antiparticle masses\nmay be different. See http://arxiv.org/abs/hep-ph/0108199 . Note that\nit is very difficult to make such a model theoretically consistent and\nfit with current data.\n\nThomas\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>baez@math-cl-n03.math.ucr.edu (John Baez) wrote
> alistair <alistair@goforit64.fsnet.co.uk> wrote:
>
> >What does CPT theorem have to say about the excess of
> >matter over antimatter in the universe?
>
> Baryogenesis is the process whereby baryons (e.g. protons and neutrons)
> were formed in the early universe, and one big thing any theory of
> baryogenesis must explain is how more baryons were formed than antibaryons.
>
(...)
>
> In 1967 Sakharov enumerated 3 necessary conditions for baryogenesis:
>
> 1. Baryon number violation. If baryon number (B) is conserved in all
> reactions, then the present baryon asymmetry can only reflect asymmetric
> initial conditions [...]
>
> 2. C and CP violation. Even in the presence of B-violating reactions,
> without a preference for matter over antimatter the B-violation will take
> place at the same rate in both directions, leaving only a very tiny
> statistical excess, perhaps only enough matter to make one star in the
> observable universe.
>
> 3. Thermodynamic Nonequilibrium. Because CPT guarantees equal masses for
> baryons and antibaryons, chemical equilibrium would drive the necessary
> reactions to correct for any developing asymmetry.
>
> It turns out the Standard Model satisfies all 3 conditions:
N.B. - the conditions are necessary but not sufficient!
> 1. Though the Standard Model conserves B classically (no terms in the
> Lagrangian violate B), quantum effects allow the universe to tunnel between
> vacua with different values of B. (...)
>
> 2. C-violation is commonplace. CP-violation (that's "charge conjugation"
> and "parity") has been experimentally observed in kaon decays, though strictly
> speaking the Standard Model probably has insufficient CP-violation to give the
> observed baryon asymmetry.
Not "probably", definitely. There are papers from a decade ago showing
that the CKM matrix gives a CP asymmetry some orders of magnitude too
small even with the most optimistic assumptions. See
http://arxiv.org/abs/http://www.arxiv.org/abs/hep-ph/9407403 .
Baryogenesis requires a new source of CP violation.
> 3. Thermal nonequilibrium is achieved during first-order phase transitions
> in the cooling early universe, such as the electroweak phase transition
> (at T = 100 GeV or so). As bubbles of the "true vacuum" (with a nonzero
> Higgs vev) percolate and grow, baryogenesis can occur at or near the bubble
> walls.
Depending on the Higgs mass, the phase transition may or may not be
first order, and may be "weakly first order" meaning that the
sphalerons are still active in the true vacuum and thus wipe out any
asymmetry. With the current limits on the Higgs mass the strongly
first order transition looks unlikely.
Baryogenesis *undoubtedly* needs beyond the SM physics, and a *new*
source of CP violation which likely is not directly related to the CKM
phase.
Now, if you have some CPT violation (which is however severely
constrained by experimental data) then you don't necessarily need an
out-of-equilibrium condition, since particle and antiparticle masses
may be different. See http://arxiv.org/abs/http://www.arxiv.org/abs/hep-ph/0108199 . Note that
it is very difficult to make such a model theoretically consistent and
fit with current data.
Thomas