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Standard Model Upgrading & Enhancement

Standard Model Upgrading & Enhancement - Physics Forum

Standard Model Upgrading & Enhancement - Physics Forum. Discuss and ask physics questions, kinematics and other physics problems.


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  #1  
Old 11-09-2003, 12:08 AM
cinquirer
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Default Standard Model Upgrading & Enhancement



In the Scientific American June 2003 article "Dawn of Physics Beyond
the Standard Model". It stated

"Other reasons for extending the Standard Model arise from phenomena
it cannot explain or cannot even accommodate:

1. All our theories today seem to imply that the universe should
contain a tremendous concentration of energy, even in the emptiest
regions of space. The gravitational effects of this so-called vacuum
energy would have either quickly curled up the universe long ago or
expanded it to much greater size. The Standard Model cannot help us
understand this puzzle, called the cosmological constant problem.

2. The expansion of the universe was long believed to be slowing down
because of the mutual gravitational attraction of all the matter in
the universe. We now know that the expansion is accelerating and that
whatever causes the acceleration (dubbed "dark energy") cannot be
Standard Model physics.

3. There is very good evidence that in the first fraction of a second
of the big bang the universe went through a stage of extremely rapid
expansion called inflation. The fields responsible for inflation
cannot be Standard Model ones.

4. If the universe began in the big bang as a huge burst of energy, it
should have evolved into equal parts matter and antimatter (CP
symmetry). But instead the stars and nebulae are made of protons,
neutrons and electrons and not their an. tiparticles (their antimatter
equivalents). This matter asymmetry cannot be explained by the
Standard Model.

5. About a quarter of the universe is invisible cold dark matter that
cannot be particles of the Standard Model.

6. In the Standard Model, interactions with the Higgs field (which is
associated with the Higgs boson) cause particles to have mass. The
Standard Model cannot explain the very special forms that the Higgs
interactions must take.

7. Quantum corrections apparently make the calculated Higgs boson mass
huge, which in turn would make all particle masses huge. That result
cannot be avoided in the Standard Model and thus causes a serious
conceptual problem.

8. The Standard Model cannot include gravity, because it does not have
the same structure as the other three forces.

9. The values of the masses of the quarks and leptons (such as the
electron and neutrinos) cannot be explained by the Standard Model.

10. The Standard Model has three "generations" of particles. The
everyday world is made up entirely of first-generation particles, and
that generation appears to form a consistent theory on its own. The
Standard Model describes all three generations, but it cannot explain
why more than one exists."

(The author continues

"In expressing these mysteries, when I say the Standard Model cannot
explain a given phenomenon, I do not mean that the theory has not yet
explained it but might do so one day. The Standard Model is a highly
constrained theory, and it cannot ever explain the phenomena listed
above. Possible explanations do exist. One reason the supersymmetric
extension (see description below - Cinquirer) is attractive to many
physicists is that it can address all but the second and the last
three of these mysteries. String theory (in which particles are
represented by tiny, one-dimensional entities instead of point
objects) addresses the last three [see "The Theory Formerly Known as
Strings," by Michael J. Duff; SCIENTIFIC AMERICAN, February 1998. The
phenomena that the Standard Model cannot explain are clues to how it
will be extended.

It is not surprising that there are questions that the Standard Model
cannot answer - every successful theory in science has increased the
number of answered questions but has left some unanswered. And even
though improved understanding has led to new questions that could not
be formulated earlier, the number of unanswered fundamental questions
has continued to decrease.

Some of these 10 mysteries demonstrate another reason why particle
physics today is entering a new era. It has become clear that many of
the deepest problems in cosmology have their solutions in particle
physics, so the fields have merged into "particle cosmology." Only
from cosmological studies could we learn that the universe is matter
(and not antimatter) or that the universe is about a quarter cold dark
matter. Any theoretical understanding of these phenomena must explain
how they arise as part of the e volution of the universe after the big
bang. But cosmology alone cannot tell us what particles make up cold
dark matter, or how the matter asymmetry is actually generated, or how
inflation originates. Understanding of the largest and the smallest
phenomena must come together."

(Below described the Minimal Supersymmetric Standard Model that can
supersede the Standard Model. If you have any better model to offer,
or know the answers to any of the above 10 top mysteries. Pls. share
your thoughts - Cinquirer)

"THE MOST WIDELY FAVORED THEORY to supersede the Standard Model is the
Minimal Supersymmetric Standard Model. In this model, every known
particle species has a superpartner particle that is related to it by
supersymmetry. Particles come in two broad classes: bosons (such as
the force particles), which can gather en masse in a single state, and
fermions (such as quarks and leptons), which avoid having identical
states. The superpartner of a fermion is always a boson and vice
versa.

Indirect evidence for supersymmetry comes from the extrapolation of
interactions to high energies, In the Standard Model, the three forces
become similar but not equal in strength (top). The existence of
superpartners changes the extrapolation so that the forces all
coincide at one energy (bottom) - a clue that they become unified if
supersymmetry is true."
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  #2  
Old 11-10-2003, 03:09 AM
Mark
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Default Striking Regularities In The Standard Model

[Only registered users see links. ] (cinquirer) writes:

Actually, no, the first generation is not self-contained. The
charge eigenstates of the weak force are mixtures across the generations
of the mass eigenstates, and vice versa. So, the origin of the
generational structure is directly linked to whatever is behind the
origin of mass.

Also, there is a little-known regularity that happens to arise in
the Standard Model, even though it's neither explicitly stipulated
nor a consequence of the Higgs mechanism. The mass matrix for the
boson fields are proportional to the squares of the (left - right)
action of the fields on the fermions.

So, whatever is behind the origin of masses in the bosons is directly
linked to the left-right assymmetry of the forces precisely in the very
places to the very extent the assymmetry arises.

There are other little-known regularities that also just arise in the
Standard Model, even though they are not explicitly incorporated that
way. The most notable is that the (3-fold degenerate) set of 32 fermion
states are precisely all those formed as +1/2 and -1/2 multiples of the
following set of quantum numbers:

a = (Baryon - Lepton)/2 + Hypercharge - Isospin
b = (Baryon - Lepton)/2 + Hypercharge + Isospin
c = (Lepton - Baryon)/2 + (L3 + L8/sqrt(3))
d = (Lepton - Baryon)/2 - 2 L8/sqrt(3)
e = (Lepton - Baryon)/2 + (-L3 + L8/sqrt(3))

(L3, L8 the SU(3) casimir charges)

and inverse relations:

Hypercharge = (a+b)/2 + (c+d+e)/3
Isospin = (b-a)/2
Electric Charge = Hypercharge + Isospin = b + (c+d+e)/3
Baryon-Lepton = -(c+d+e)/3
L3 = (c-e)/2
L8 = (c-2d+e)/sqrt(12)

and that the spectrum of charged bosons are the +1/-1 combinations
of pairs of these numbers:
W+: b = 1, a = -1
W-: a = 1, b = -1
color-exchange Gluons (there are no official names for the gluons,
the terms are mine):
R: d = 1, c = -1
O: e = 1, c = -1
Y: e = 1, d = -1
G: c = 1, d = -1
B: c = 1, e = -1
P: d = 1, e = -1;
the 4 hypothetical Higgs modes would be those with the
charges
phi_0: a = +1
anti phi_0: a = -1
phi+: b = +1
phi-: b = -1.
The a number is only one linked to left-right assymmetry (a becomes -a under
left-right reversal; b,c,d,e stay the same). So, whatever veracity the
Higgs mechanism has, it is directly linked to left-right assymmetry of the
forces.

Last, but not least, is the clincher. The charge equivalents of the 5
quantum numbers are:
a: Y = g'/2, I3 = -g/2, L3 = L8 = (B-L)/2 = 0
b: Y = g'/2, I3 = g/2, L3 = L8 = (B-L)/2 = 0
c: Y = g'/3, I3 = 0, L3 = gs/2, L8 = gs/sqrt(12), (B-L)/2 = -1
d: Y = g'/3, I3 = 0, L3 = 0, L8 = -gs/sqrt(3), (B-L)/2 = -1
e: Y = g'/3, I3 = 0, L3 = -gs/2, L8 = gs/sqrt(12), (B-L)/2 = -1
Y = Hypercharge, I3 = Isospin, g',g,gs the coupling constants for U(1),
SU(2) and SU(3), B-L = Baryon-Lepton.

When coupling constants are rescaled to units g' = 6, g = gs = sqrt(12),
(B-L)/2 scaled to 2, the result is:

a: (Y,I3,L3,L8,(B-L)/2) = (3, -sqrt(3), 0, 0, 0)
b: (Y,I3,L3,L8,(B-L)/2) = (3, sqrt(3), 0, 0, 0)
c: (Y,I3,L3,L8,(B-L)/2) = (2, 0, sqrt(3), 1, -2)
d: (Y,I3,L3,L8,(B-L)/2) = (2, 0, 0, -2, -2)
e: (Y,I3,L3,L8,(B-L)/2) = (2, 0, -sqrt(3), 1, -2)

-- 6 vectors of length 12 at 60 degrees each from one another: i.e.,
the edges of a 5-simplex.

Calling the vectors <a>,<b>,<c>,<d>,<e> respectively, they can be
embedded in a 6-D cartesian grid by adding an extra quantum number (N),
by:
X = ( 2, 0, 0, 0, -1, 1) = (Y,I3,L3,L8,(B-L)/2,N)
A = (-1, sqrt(3), 0, 0, -1, 1) = (Y,I3,L3,L8,(B-L)/2,N)
B = (-1, -sqrt(3), 0, 0, -1, 1) = (Y,I3,L3,L8,(B-L)/2,N)
C = ( 0, 0, -sqrt(3), -1, 1, 1) = (Y,I3,L3,L8,(B-L)/2,N)
D = ( 0, 0, 0, 2, 1, 1) = (Y,I3,L3,L8,(B-L)/2,N)
E = ( 0, 0, sqrt(3), -1, 1, 1) = (Y,I3,L3,L8,(B-L)/2,N)

with <a>=X-A,<b>=X-B,<c>=X-C,<d>=X-D,<e>=X-E.

The matrix U that rotates from the unit vectors <Y>,<I3>,<L3>,<L8>
<(B-L)/2>,<N> to the basis X,A,B,C,D,E has its transpose as its
own inverse:
U^{-1} = U^T = U^+,
i.e., U is unitary.
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