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CosPA 2015 and the Standard Model
W-Y. Pauchy Hwang
Y.T. Lee Outstanding-Scholar Chair Professor
Institute of Astrophysics
National Taiwan University
My first encounter with Inspire
I usually don’t play with the Web’s, feeling that it
wastes my time that way.
 Now I feel that it is occupying my time for
thinkings.


My advice to a young physics student would be:
Try to save time for thinkings; no alternative for
thinkings, otherwise, the other smart people
would think on your behalf.
My Search & Research with the
Standard Model
Our universe – 5% (visible) ordinary matter;

25% dark matter;

70% dark energy.

Since 2000 when I led the research
excellence project on Cosmology and Particle
Astrophysics (for a period of about 10 years).


To understand the dark matter part, it is the most
nontrivial. I think some generalized Standard
Model would do the job.
My early struggles with the
Standard Model

Why do we need Higgs mechanism in SU_L(2) x
U(1) electroweak theory but not in SU_c(3)
[QCD]?
 The toilets in a house – Glashow’s remark at
Indiana University (1982-1983?).
 A useless paper and rejected (Phys. Lett. B) by
H. Georgi:
W-Y. P. Hwang, Phys. Rev. D32, 824 (1985).

The idea of “colored Higgs mechanism”.
What is the final Standard
Model?

Why do we have three generations ? It cannot
be “final” without understanding it.

Neutrino oscillations – from one family into
another. “Not final” if without understanding it.

Very excited when I conceived (2008 summer
night, at U. Penn) why I can’t use the colored
Higgs mechanism as the family one.
I believe that the God wouldn’t create a
particle that is so boring in just knowing
only weak interactions.

Neutrinos now have tiny masses these days. So,
they, naturally, have 4-components in the Dirac
space. Note that in the (old) minimal Standard
Model their masses were suspected to vanish.

There is so much dark matter (25 % of the
Universe), compared to so little “visible” ordinary
matter (5 % of the Universe), the latter as
described by the minimal Standard Model.

My remark at 2012 CosPA Symposium.
As time goes by, the strange role of
neutrinos has become clearer and clearer.

Note that right-handed neutrinos never appear in
the construction of the Minimal Standard Model,
as though they are unwanted.

The mystery may lie with the neutrinos. There is
nothing called “neutrino flavor eigen-states”,
some ill-defined concept.
Eleven Science Questions for the New Century:
The First Four Questions
U.S. Science Academy Report, 4/17/2002

Q1: What is the dark matter?
Our Universe has 25% in Dark Matter while
only 5% in ordinary matter. It clusters.

Q2: What is the nature of the dark
energy?


Q3: How did the universe begin?
Q4: Did Einstein have the last word
on gravity?
In view of the minimal Standard Model, we could
write down two working “rules”:
similarity principle – our struggle of
eighty years to describe the point-like
Dirac particle such as the electron.
 The “minimum Higgs hypothesis” is the
other mysterious conjecture – after forty
years we finally get glimpse over the SM
Higgs particle, and nothing more.
 By “induction”, we may write down these
two working rules for the much “larger”
dark matter world.
 Dirac
At the beginning of 2010, I realized that we’d
better begin with the two working “rules”.
similarity principle – We put
(nu_{e,L}, e_L) as an SU_L(2) doublet; it
implies that two members would have the
same characteristics. Similarly for the
SU_f(3) triplet members, such as ((nu_tau,
tau)_L, (nu_mu, mu)_L, (nu_e, e)_L)
(column), as in Hwang/Yan.
 The “minimum Higgs hypothesis” – Why is
it so difficult in finding any of them?
 Dirac
Dirac may be the first “physicist” to formulate
some equation for “point-like” particles.

Dirac didn’t know that the electrons are point-like
particles, the size certainly less than 10**(-20)
cm in length, these days.

It turns out that, for over eighty years, we
recognize only a few point-like particles, those
building blocks of the Standard Model.

Neutrino oscillations: How does a “point-like”
Dirac particle change itself into the other “pointlike” Dirac particle? We miss an “interaction”.
The point is: Without the two working rules, we
have too many choices on the extended SM.
 Maybe
our space-time only allows for
“point-like” Dirac particles, those can be
created and can communicate among
them.
 Besides, we use the complex scalar fields
to “modulate” quite a number of things,
SSB (the Higgs mechanisms), etc. Their
existences appear to be “minimal”.
 Starting at 2010 – two working rules.
 Now,
“What is the dark matter?” Could we
describe it or them? If yes, what would be
the language? The first guess would be to
use the language which we set up for the
Standard Model – a gauge theory
with/without Higgs Mechanism. If not, what
else?
 In what follows, we wish to present that, in
the 4-dimensional Minkowski space-time
with the SU_c(3) x SU(2) x U(1) x SU_f(3)
gauge-group structure built-in from the
outset, there is the Standard Model, with
(123) the quark world and with another
(123) the lepton world.
My Struggles with the Standard
Model: Part No.1

How to add a Z’ but with a minimum number of
Higgs fields?
W-Y. P. Hwang, Phys. Rev. D36, 261 (1987).

When we go beyond the Standard Model, the
Higgs sector depends on the sector of gauge
bosons – extra Z, then extra Higgs.
My Struggles with the Standard
Model: Part No. 2

Why should we have the standard case, i.e.,
Higgs in the electroweak sector but not in the
strong QCD case.
W-Y. P. Hwang, Phys. Rev. D32, 824 (1985).

The idea of “colored Higgs mechanism”.
No. 3: I started thinking that my
miserable life has some meaning.

In 2008 (four years after I was struck by cerebral
haemorrhage), I went to U. Penn (my Alma
Mater) to attend some high energy Conference. I
woke up one night to ask why the idea of colored
Higgs mechanism be “copied” as the family
SU(3) gauge theory.

That sets off a series of talks and papers –
maybe nobody appreciate the idea.
My Struggles with the Standard
Model: Part No. 3

W-Y. Pauchy Hwang, Nucl. Phys. A844, 40c
(2012); W-Y. Pauchy Hwang, International J.
Mod. Phys. A24, 3366 (2009); W-Y. Pauchy
Hwang, Intern. J. Mod. Phys. Conf. Series 1, 5
(2011); W-Y. Pauchy Hwang, AIP 978-0-73540687-2/09, pp. 25-30 (2009).

In fact, the evolution of the idea culminates in rewriting of the Standard Model.
My Struggles with the Standard
Model: Part No. 4

Last June (2012) I went to Groningen to attend
SSP2012 and suddenly realized the role of
neutrino oscillations in all these.
W-Y. Pauchy Hwang, arXiv:1207.6837v1 [hepph] 30 Jul 2012;
 W-Y. Pauchy Hwang, arXiv:1207.6443v1 [hepph] 27 Jul 2012;
 W-Y. Pauchy Hwang, arXiv:1209.5488v1 [hepph] 25 Sep 2012.

So, let’s come back to neutrino oscillations:

The origin of neutrino masses comes from the coupling
between the neutrino triplet and the family Higgs triplets:

i
2
L (3,2)  R (3,1)   (3,2)  h.c.
resulting a mass matrix which is off diagonal (but is perfectly
acceptable). Note that the imaginary is needed to make it
hermitian.

This turns out to be that it is not a standard matrix operation,
but a unique SU(3) operation – the unique singlet out of three
given triplets. And from left- and right-handed as usual.

From, e.g., Hwang/Yan, The Universe, 1-1, 5 (2013).
My Struggles with the Standard
Model: Part No. 5

Nevertheless, we ventured to put the three
generation of leptons together, as the triplets
under SU_f(3).

W-Y. Pauchy Hwang and Tung-Mow Yan,
arXiv:1212.4944 [hep-ph] 20 December 2012;
The Universe, 1-1, 5 (2013).
My Struggles with the Standard
Model: Part No. 6
Finally, I worked on the “combined” Higgs
mechanisms – using the scalar/Higgs fields
Phi(3,2), Phi(3,1), and the standard Phi(1,2) –
from the renormalizability.
 Everything still quite complicated !!


W-Y. Pauchy Hwang, arXiv:1304.4705v1 [hepph] 17 April 2013.
I realized that what “the Origin
of Mass” is !! No. 7 & more !!

The masses as the result of the family SSB, but
not neccessary of EW SSB.

W-Y. Pauchy Hwang, The Universe, 2-2, 47
(2014).

Maybe this brings “Universe” to the attention of
Inspire (inspirehep.net).
Theta_P = Pauchy’s angle.
Important rationale:
We are dealing with three Scalar fields – Phi(1,2) (SM Higgs),
Phi(3,2) (mixed family Higgs), and Phi(3,1) (purely family Higgs).
Phi(3,2) – required when family combined with EW (Hwang/Yan);
Phi(3,1) – all family gauge bosons are massive.
These are fields of “energy” – so, it must be bounded from below.
The so-called “positive definiteness”.
Lambda (phi* phi)^2 in the 4-dimensional Minkowski space-time =>
lambda is a pure number !! Where the magic comes from !!
Many interesting stories
followed, afterward:

I started to think what the SU_f(3) really is, a
ten’s GeV or sub-sub-Fermi family gauge theory!!
In our case, SU_f(3) is meant to protect the
lepton world from the QED Landau ghost and it
is asymptotically free. g-2 would be a testing
ground.
 So, this Standard Model has SU(3) everywhere.
Indeed, it works like a magic.

W-Y. Pauchy Hwang, arXiv:1301.6464v5 [hepph] 29 April 2014.
The Origin of Mass
We may turn off all the “mass” terms (such as
high enough temperature) except the family SSB
driving term – keeping all interaction terms
among the various Higgs. The masses arise
naturally out of family SSB – a big surprise!!
Remember that all fermion masses, including
neutrino oscillations, also come out in one way
or the other.
 So, this Standard Model is everybody’s Standard
Model.


W-Y. Pauchy Hwang, The Universe, 2-2, 47
(2014).
The origin of fields (point-like
particles)

The complex scalar field phi(x):

m^2 phi* phi + lambda (phi*phi)^2

m^2 =0 if T from above; lambda is
dimensionless, we find lambda=1/8 as
determined by the 4-dimensional Minkowski
space-time (not by the field itself).

4-dimension means so many things, even the
origin of our world.

W-Y. Pauchy Hwang, The Universe, 3-1, 3
(2015).
The origin of fields

We live in the (quantum) 4-dimensional
Minkowski space-time with the force-fields
gauge group SU_c(3) x SU_L(2) x U(1) x SU_f(3)
built-in from the outset. That sets the
“background”.
 The quark world is accepted because of the
(123) symmetry while the lepton world is also
accepted for another (123) symmetry.

W-Y. Pauchy Hwang, The Universe, 3-1, 3
(2015).
This is supposed be a “complete”
theory!!

All those divergences would canceled out by our
belief (or, by my conjecture). The system of all
point-like Dirac particles appears to be such
remarkable physical system in Nature.
 At first, dimensional regularization and the
adoption of U-gauge seems to work. But it is
incorrect in view of the lack of the causality
requirement.
 I started with the wave-function renormalization.

W-Y. Pauchy Hwang, arXiv:1301.6464v5 [hepph] 29 April 2014.
Lambda=1/8 and non-renormalization
 We
note that the lambda value is
determined by the 4-dimension Minkowski
space-time – so the non-renormalization
theorem should apply in some way.
 We
have to admit that, even if QFT
appears to be the right language, the
details are quite complicated to be worked
out.
A precise definition of the
Standard Model
 Maybe
it should be like this:
 We live in the 4-dimensional Minkowski
space-time with the force-fields gauge
group SU_c(3) x SU_L(2) x U(1) x SU_f(3)
built-in from the outset. It supports the
lepton world and it also supports the quark
world.
 It is a force-field, or a gauge-field,
Minkowski space-time.
Conclusion
 These
stories sort of tell you that the
physics all comes from the Standard
Model (of particle physics). And the
Standard model is extremely simple.
 We live in the (quantum) 4-dimensional
Minkowski space-time with the group
SU_c(3) x SU_L(2) x U(1) x SU_f(3),
force-fields gauge-group structure built-in
from the outset. This is the “background”
of everything. So, the dark matter !!