The (extended) Standard ModelThe (extended) Standard Model

W-Y. Pauchy HwangW-Y. Pauchy HwangY.T. Lee Outstanding-Scholar Chair ProfessorY.T. Lee Outstanding-Scholar Chair Professor

Institute of AstrophysicsInstitute of AstrophysicsNational Taiwan UniversityNational Taiwan University

My early struggles with the My early struggles with the Standard ModelStandard Model

Why do we need Higgs mechanism in SU_L(2) x Why do we need Higgs mechanism in SU_L(2) x U(1) electroweak theory but not in SU_c(3) U(1) electroweak theory but not in SU_c(3) [QCD]?[QCD]?

The toilets in a house – Glashow’s remark at The toilets in a house – Glashow’s remark at Indiana (early 1980). Indiana (early 1980).

A useless paper and rejected (Phys. Lett. B) by H. A useless paper and rejected (Phys. Lett. B) by H. Georgi:Georgi:W-Y. P. Hwang, Phys. Rev. D32, 824 (1985).W-Y. P. Hwang, Phys. Rev. D32, 824 (1985).

The idea of “colored Higgs mechanism”.The idea of “colored Higgs mechanism”.

What is the final Standard What is the final Standard Model? Model?

Why do we have three generations ? It cannot be Why do we have three generations ? It cannot be “final” without understanding it.“final” without understanding it.

Neutrino oscillations – from one family into Neutrino oscillations – from one family into another. “Not final” if without understanding it.another. “Not final” if without understanding it.

Very excited when I conceived (2008 summer Very excited when I conceived (2008 summer night, at U. Penn) why I can’t use the colored night, at U. Penn) why I can’t use the colored Higgs mechanism as the family one. Higgs mechanism as the family one.

I believe that the God wouldn’t create a I believe that the God wouldn’t create a particle that is so boring in just knowing particle that is so boring in just knowing

only weak interactions. only weak interactions.

Neutrinos now have tiny masses these days. So, Neutrinos now have tiny masses these days. So, they, naturally, have 4-components in the Dirac they, naturally, have 4-components in the Dirac space. Note that in the minimal Standard Model space. Note that in the minimal Standard Model their masses were suspected to vanish.their masses were suspected to vanish.

There is so much dark matter (25 % of the There is so much dark matter (25 % of the Universe), compared to so little “visible” ordinary Universe), compared to so little “visible” ordinary matter (5 % of the Universe), the latter as matter (5 % of the Universe), the latter as described by the minimum Standard Model. described by the minimum Standard Model. Why? Why?

As time goes by, the strange role of As time goes by, the strange role of neutrinos has become clearer and clearer. neutrinos has become clearer and clearer.

Note that right-handed neutrinos never appear in Note that right-handed neutrinos never appear in

the construction of the Minimal Standard Model, the construction of the Minimal Standard Model, as though they are unwanted. as though they are unwanted.

The mystery may lie with the neutrinos, which The mystery may lie with the neutrinos, which oscillate between different generations and play oscillate between different generations and play dual roles between the ordinary-matter world dual roles between the ordinary-matter world and the dark-matter world.and the dark-matter world.

Q1:Q1: What is the dark matter? What is the dark matter? Our Universe has 25% in Dark Matter whileOur Universe has 25% in Dark Matter while

only 5% in ordinary matter. The dark-matter particles also only 5% in ordinary matter. The dark-matter particles also tend to cluster – another obstacle to analyze the tend to cluster – another obstacle to analyze the problem.problem.

Q2:Q2: What is the nature of the dark What is the nature of the dark energy? energy? (The overwhelming 70% question, but (The overwhelming 70% question, but

maybe with uniformly “distributed”.) maybe with uniformly “distributed”.)

Q3:Q3: How did the universe begin? How did the universe begin? Q4:Q4: Did Einstein have the last word Did Einstein have the last word

on gravity? on gravity?

Eleven Science Questions for the New Century: Eleven Science Questions for the New Century: The First Four QuestionsThe First Four Questions

U.S. Science Academy Report, 4/17/2002U.S. Science Academy Report, 4/17/2002

Q1:Q1: What is the dark matter? What is the dark matter? Q2:Q2: What is the nature of the dark What is the nature of the dark

energy? energy?

Remark 1:Remark 1: To To push our understandings of the Cosmos, I push our understandings of the Cosmos, I think that question No.1 is far more nontrivial think that question No.1 is far more nontrivial than question No.2.than question No.2.

Remark 2:Remark 2: We don’t even know the dark-matter world – We don’t even know the dark-matter world – what particles are they?what particles are they?

Cosmology: Eleven Science Questions for the New Cosmology: Eleven Science Questions for the New CenturyCentury

U.S. Academy Report, 4/17/2002U.S. Academy Report, 4/17/2002

Neutrinos do oscillate !! Neutrinos do oscillate !!

Neutrinos oscillate. Neutrinos oscillate.

nu_e <=> nu_mu; nu_mu <=> nu_tau; nu_tau nu_e <=> nu_mu; nu_mu <=> nu_tau; nu_tau <=> nu_e.<=> nu_e.

This is occurring at the level of point-like Dirac This is occurring at the level of point-like Dirac

particles. It differs from the K^0 - \bar K^0 system, particles. It differs from the K^0 - \bar K^0 system, a composite system. a composite system.

Note that neutrino oscillations “move around” Note that neutrino oscillations “move around” different generations, or, changing flavors. different generations, or, changing flavors.

In view of the minimal Standard Model, we could In view of the minimal Standard Model, we could write down two working “rules”:write down two working “rules”:

Dirac similarity principle – our struggle of eighty Dirac similarity principle – our struggle of eighty years to describe the point-like Dirac particle years to describe the point-like Dirac particle such as the electron.such as the electron.

The “minimum Higgs hypothesis” is the other The “minimum Higgs hypothesis” is the other mysterious conjecture – after forty years we mysterious conjecture – after forty years we finally get glimpse over the SM Higgs particle, finally get glimpse over the SM Higgs particle, and nothing more.and nothing more.

By “induction”, we may write down these two By “induction”, we may write down these two working rules for the much “larger” dark matter working rules for the much “larger” dark matter world.world.

Dirac may be the first “physicist” to formulate Dirac may be the first “physicist” to formulate

some equation for “point-like” particles. some equation for “point-like” particles. Dirac didn’t know that the electrons are point-like Dirac didn’t know that the electrons are point-like

particles, the size certainly less than 10**(-20) particles, the size certainly less than 10**(-20) cm in length, these days.cm in length, these days.

It turns out that, for over eighty years, we It turns out that, for over eighty years, we recognize only a few point-like particles, those recognize only a few point-like particles, those building blocks of the Standard Model. building blocks of the Standard Model.

These “point-like” Dirac particles are described These “point-like” Dirac particles are described by “quantized” Dirac fields.by “quantized” Dirac fields.

Finally some Higgs after searching for 40 yearsFinally some Higgs after searching for 40 years

Quantized Klein-Gordon (scalar) fields – in Quantized Klein-Gordon (scalar) fields – in fact, our first lesson for QFT. fact, our first lesson for QFT.

We use the scalar fields to “modulate” We use the scalar fields to “modulate” quite a number of things, SSB (the Higgs quite a number of things, SSB (the Higgs mechanisms), etc. But we still look for mechanisms), etc. But we still look for them, after 40 years.them, after 40 years.

Maybe we should work with “the minimum Maybe we should work with “the minimum Higgs hypothesis” or “conjecture”. Higgs hypothesis” or “conjecture”.

The point is: Without the two working rules, we The point is: Without the two working rules, we

have too many choices on the extended SM. have too many choices on the extended SM. Maybe our space-time only allows for Maybe our space-time only allows for

“point-like” Dirac particles, those can be “point-like” Dirac particles, those can be created and can communicate among created and can communicate among them. them.

Besides, we use the scalar fields to Besides, we use the scalar fields to “modulate” quite a number of things, SSB “modulate” quite a number of things, SSB (the Higgs mechanisms), etc. Their (the Higgs mechanisms), etc. Their existences appear to be “minimal”. existences appear to be “minimal”.

OutlineOutline Language: (Renormalizable) Quantum Language: (Renormalizable) Quantum

Fields. (a much powerful than you thought)Fields. (a much powerful than you thought) No. 1 Question: What is the Dark Matter?No. 1 Question: What is the Dark Matter? Dirac Similarity Principle Dirac Similarity Principle ““Minimum Higgs Hypothesis” Minimum Higgs Hypothesis”

My struggles with the Standard Model.My struggles with the Standard Model.

ConclusionConclusion

The Language: The Axiom BoxThe Language: The Axiom Box

Classical Mechanical Systems Classical Fields

Quantum Mechanical Systems

Quantum Fields

dc

dc

d → c: discreteness to continuum

Dirac CP: Dirac Correspondence Principle

Dirac CP Dirac CP

Fields as the generalized coordinates (quantum mechanics of Fields as the generalized coordinates (quantum mechanics of the continuum = quantum fields):the continuum = quantum fields):

Classical Mechanical System:Classical Mechanical System:“For a given system, we can find a function (lagrangian) of “For a given system, we can find a function (lagrangian) of the coordinates and velocities such that the integral (action) the coordinates and velocities such that the integral (action) between two instants is an extremum for the real motion.” between two instants is an extremum for the real motion.”

Quantum Mechanical System:Quantum Mechanical System: “ “For the coordinates we can find the conjugate momenta For the coordinates we can find the conjugate momenta

such that the basic (elementary) commutation relations such that the basic (elementary) commutation relations hold.” – Now, they are operators.hold.” – Now, they are operators.

Classical Field:Classical Field:“For a given system, we can find a function (lagrangian) of “For a given system, we can find a function (lagrangian) of the coordinates and velocities such that the integral (action) the coordinates and velocities such that the integral (action) between two instants is an extremum for the real motion.” – between two instants is an extremum for the real motion.” – except that quantities take continuum meaning. except that quantities take continuum meaning.

Quantum Field (= Quantum Mechanics for the Continuum):Quantum Field (= Quantum Mechanics for the Continuum): “ “For the coordinates we can find the conjugate momenta For the coordinates we can find the conjugate momenta

such that the basic (elementary) commutation relations such that the basic (elementary) commutation relations hold.” – except that quantities take continuum meaning and hold.” – except that quantities take continuum meaning and we also generalize the notion to include fermions (I.e. anti-we also generalize the notion to include fermions (I.e. anti-commutation relations).commutation relations).

Remarks on the above axioms for QFT:Remarks on the above axioms for QFT: (1) no second quantization(1) no second quantization (2) no infinite electron sea(2) no infinite electron sea

This is so far a consistent language This is so far a consistent language framework. Complete ? Too early to tell.framework. Complete ? Too early to tell.

Now, “What is the dark matter?” Could we Now, “What is the dark matter?” Could we describe it or them? If yes, what would be describe it or them? If yes, what would be the language? The first guess would be to the language? The first guess would be to use the language which we set up for the use the language which we set up for the Standard Model – a gauge theory Standard Model – a gauge theory with/without Higgs Mechanism. If not, what with/without Higgs Mechanism. If not, what else? else?

In what follows, we try to sell the SU_c(3) In what follows, we try to sell the SU_c(3) x SU(2) x U(1) x SU_f(3) Standard Model x SU(2) x U(1) x SU_f(3) Standard Model via a renormalizable way.via a renormalizable way.

My Struggles with the Standard My Struggles with the Standard Model: Part No.1 Model: Part No.1

How to add a Z’ but with a minimum number of How to add a Z’ but with a minimum number of Higgs fields?Higgs fields?W-Y. P. Hwang, Phys. Rev. D36, 261 (1987).W-Y. P. Hwang, Phys. Rev. D36, 261 (1987).

When we go beyond the Standard Model, the When we go beyond the Standard Model, the Higgs sector depends on the sector of gauge Higgs sector depends on the sector of gauge bosons – extra Z, then extra Higgs. bosons – extra Z, then extra Higgs.

Thus, ….Thus, ….

Neutrinos have tiny masses. => another Z’. Neutrinos have tiny masses. => another Z’. It may sound strange, but it requires another It may sound strange, but it requires another

Higgs.Higgs. How to add a Z’ but with a minimum number of How to add a Z’ but with a minimum number of

Higgs fields?Higgs fields?W-Y. P. Hwang, Phys. Rev. D36, 261 (1987).W-Y. P. Hwang, Phys. Rev. D36, 261 (1987).

Consider 2+2 Higgs Scenario. The second, and Consider 2+2 Higgs Scenario. The second, and “remote”, Higgs doublet could give tiny neutrinos “remote”, Higgs doublet could give tiny neutrinos masses naturally. masses naturally.

““The Minimum Higgs Hypothesis”The Minimum Higgs Hypothesis”

No.1. On the coupling strengths.No.1. On the coupling strengths.

lambda’ ~ lambda x (vev / vev’)**2lambda’ ~ lambda x (vev / vev’)**2 My conjecture for the couplings to remote Higgs My conjecture for the couplings to remote Higgs

No. 2. On the choice of Higgs multipletsNo. 2. On the choice of Higgs multiplets

There is no redundant Higgs multiplet..There is no redundant Higgs multiplet..

It is a useful “empirical” rule.It is a useful “empirical” rule.

Another ThoughtAnother Thought SU_c(3) × SU_L(2) ×SU_R(2) x U(1) : The SU_c(3) × SU_L(2) ×SU_R(2) x U(1) : The

missing right-handed sector !!missing right-handed sector !! R.N. Mohapatra and J.C. Pati, Phys. Rev. D11, R.N. Mohapatra and J.C. Pati, Phys. Rev. D11,

2558 (1975).2558 (1975). Here we also have an extra Z’ but with another Here we also have an extra Z’ but with another

right-handed doublet almost eaten up via SSB. right-handed doublet almost eaten up via SSB.

Mohapatra, Pati, and Salam in fact have many Mohapatra, Pati, and Salam in fact have many models (by choice of Higgs multiplets) but the models (by choice of Higgs multiplets) but the “minimum Higgs hypothesis” selects the unique “minimum Higgs hypothesis” selects the unique one – unfortunately, it may violate the criterion of one – unfortunately, it may violate the criterion of choosing “the basic units”.choosing “the basic units”.

The thought of Dec 2012The thought of Dec 2012

Why the weak interactions break the left-Why the weak interactions break the left-right symmetry is one of the deepest right symmetry is one of the deepest questions.questions.

Reason: When we write the Dirac theory in Reason: When we write the Dirac theory in terms of the left-right basic units, each unit terms of the left-right basic units, each unit appears once and only once – to ensure appears once and only once – to ensure that there is one kinetic-energy term.that there is one kinetic-energy term.

W-Y. Pauchy Hwang and Tung-Mow Yan, W-Y. Pauchy Hwang and Tung-Mow Yan, arXiv:1212.4944 [hep-ph] 20 Dec 2012.arXiv:1212.4944 [hep-ph] 20 Dec 2012.

My Struggles with the Standard My Struggles with the Standard Model: Part No. 2 Model: Part No. 2

Why should we have the standard case, i.e., Why should we have the standard case, i.e., Higgs in the electroweak sector but not in the Higgs in the electroweak sector but not in the strong QCD case.strong QCD case.W-Y. P. Hwang, Phys. Rev. D32, 824 (1985).W-Y. P. Hwang, Phys. Rev. D32, 824 (1985).

The idea of “colored Higgs mechanism”.The idea of “colored Higgs mechanism”.

Higgs mechanism in QCD?Higgs mechanism in QCD?

Almost thirty years ago I was curious by the absence of Almost thirty years ago I was curious by the absence of the Higgs mechanism in the strong interactions but not in the Higgs mechanism in the strong interactions but not in the weak interaction sector – a question still remains the weak interaction sector – a question still remains unanswered till today. A renormalizable gauge theory unanswered till today. A renormalizable gauge theory that does not have to be massless is already reputed by that does not have to be massless is already reputed by ‘t Hooft and others, for the standard model. Maybe our ‘t Hooft and others, for the standard model. Maybe our question should be whether the electromagnetism would question should be whether the electromagnetism would be massless.be massless.

It is a deep question – how to write down a It is a deep question – how to write down a renormalizable theory. Remember that, during old days, renormalizable theory. Remember that, during old days, a massive gauge theory is used to be believed as a a massive gauge theory is used to be believed as a nonrenormalizable theory.nonrenormalizable theory.

No. 3: I started thinking that my No. 3: I started thinking that my miserable life has some meaning. miserable life has some meaning.

In 2008 (four years after I was struck by cerebral In 2008 (four years after I was struck by cerebral haemorrhage), I went to U. Penn (my Alma haemorrhage), I went to U. Penn (my Alma Mater) to attend Lepton-Photon Conference. I Mater) to attend Lepton-Photon Conference. I woke up one night to ask why the idea of woke up one night to ask why the idea of colored Higgs mechanism be “copied” as the colored Higgs mechanism be “copied” as the family SU(3) gauge theory.family SU(3) gauge theory.

That sets off a series of talks and papers – That sets off a series of talks and papers – maybe nobody appreciate the idea.maybe nobody appreciate the idea.

My Struggles with the Standard My Struggles with the Standard Model: Part No. 3 Model: Part No. 3

W-Y. Pauchy Hwang, Nucl. Phys. A844, 40c W-Y. Pauchy Hwang, Nucl. Phys. A844, 40c (2012); W-Y. Pauchy Hwang, International J. (2012); W-Y. Pauchy Hwang, International J. Mod. Phys. A24, 3366 (2009); W-Y. Pauchy Mod. Phys. A24, 3366 (2009); W-Y. Pauchy Hwang, Intern. J. Mod. Phys. Conf. Series 1, 5 Hwang, Intern. J. Mod. Phys. Conf. Series 1, 5 (2011); W-Y. Pauchy Hwang, AIP 978-0-7354-(2011); W-Y. Pauchy Hwang, AIP 978-0-7354-0687-2/09, pp. 25-30 (2009).0687-2/09, pp. 25-30 (2009).

In SU(3), an octet of gauge bosons plus a In SU(3), an octet of gauge bosons plus a pair of complex scalar triplets turns out to pair of complex scalar triplets turns out to be the simplest choice as long as all be the simplest choice as long as all gauge bosons become massive while the gauge bosons become massive while the remaining Higgs are also massive.remaining Higgs are also massive.

The standard model is the gauge theory The standard model is the gauge theory based on the group SU_c(3) × SU(2) × based on the group SU_c(3) × SU(2) × U(1). Now the simple extension is that U(1). Now the simple extension is that based on SU_c(3) × SU(2) × U(1) based on SU_c(3) × SU(2) × U(1) multiplied another independent SU_f(3).multiplied another independent SU_f(3).

That is, the eight gauge bosons all become That is, the eight gauge bosons all become massive. On the other hand, by choosingmassive. On the other hand, by choosing

we find that the remaining four (Higgs) particles we find that the remaining four (Higgs) particles are massive (with \mu^2 < 0, we have v^2 = are massive (with \mu^2 < 0, we have v^2 = －－ \\mu^2 / \lambda > 0).mu^2 / \lambda > 0).

Because the neutrino-neutrino-Z vertex is now in Because the neutrino-neutrino-Z vertex is now in our theory augmented by the neutrino-our theory augmented by the neutrino-neutrino-“dark boson” vertices;neutrino-“dark boson” vertices; these dark species should be very massive. these dark species should be very massive.

2† †

2 2† † † †

2

2 , (8)4

V

In the SU_f(3) model, the couplings to ordinary In the SU_f(3) model, the couplings to ordinary matter is only through the neutrinos. This would matter is only through the neutrinos. This would make some loop diagrams, involving neutrinos make some loop diagrams, involving neutrinos and familons, very interesting and, albeit likely to and familons, very interesting and, albeit likely to be small, should eventually be investigated[6]. be small, should eventually be investigated[6]. For example, in the elastic quark (or charged For example, in the elastic quark (or charged lepton) - neutrino scattering, the loop corrections lepton) - neutrino scattering, the loop corrections would involve the Z^0 and in addition the familon would involve the Z^0 and in addition the familon loops and if the masses of the familons were loops and if the masses of the familons were less than that of Z^0 then the loop corrections less than that of Z^0 then the loop corrections due to familons would be too big. Thus, we may due to familons would be too big. Thus, we may assume that the familon masses would be much assume that the familon masses would be much greater than the Z^0 mass, say a few TeV.≧greater than the Z^0 mass, say a few TeV.≧

My Struggles with the Standard My Struggles with the Standard Model: Part No. 4 Model: Part No. 4

Last June (2012) I went to Groningen to attend Last June (2012) I went to Groningen to attend SSP2012 and suddenly realized the role of SSP2012 and suddenly realized the role of neutrino oscillations in all these.neutrino oscillations in all these.W-Y. Pauchy Hwang, arXiv:1207.6837v1 [hep-W-Y. Pauchy Hwang, arXiv:1207.6837v1 [hep-ph] 30 Jul 2012; ph] 30 Jul 2012;

W-Y. Pauchy Hwang, arXiv:1207.6443v1 [hep-W-Y. Pauchy Hwang, arXiv:1207.6443v1 [hep-ph] 27 Jul 2012;ph] 27 Jul 2012;

W-Y. Pauchy Hwang, arXiv:1209.5488v1 [hep-W-Y. Pauchy Hwang, arXiv:1209.5488v1 [hep-ph] 25 Sep 2012.ph] 25 Sep 2012.

So, let’s come back to neutrino oscillations: So, let’s come back to neutrino oscillations:

The origin of neutrino masses comes from the coupling The origin of neutrino masses comes from the coupling between the neutrino triplet and the family Higgs triplets:between the neutrino triplet and the family Higgs triplets:

resulting a mass matrix which is off diagonal (but is perfectly resulting a mass matrix which is off diagonal (but is perfectly acceptable). Note that alpha = i eta, which is needed to make it acceptable). Note that alpha = i eta, which is needed to make it hermitian.hermitian.

This turns out to be that it is not a standard matrix operation, 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 but a unique SU(3) operation – the unique singlet out of three given triplets. And from left- and right-handed as usual.given triplets. And from left- and right-handed as usual.

This is the new way to add a renormalizable term, a curl-dot This is the new way to add a renormalizable term, a curl-dot term.term.

, (9)

So, in the SU(3) family gauge theory, we write So, in the SU(3) family gauge theory, we write down the renormalizable term by using a curl-dot down the renormalizable term by using a curl-dot product, a new term indeed.product, a new term indeed.

The masses of the neutrino triplet come from the The masses of the neutrino triplet come from the coupling to some Higgs field - a pair of complex coupling to some Higgs field - a pair of complex scalar triplets, as worked out in the previous scalar triplets, as worked out in the previous publication[1]. publication[1].

The neutrino masses do not come from the The neutrino masses do not come from the minimal Standard Model, but mainly from the minimal Standard Model, but mainly from the Higgs in the dark sector.Higgs in the dark sector.

At this point, we had to ask two difficult At this point, we had to ask two difficult questions:questions:

Why do we need to make the SU(3) family Why do we need to make the SU(3) family gauge theory massive?gauge theory massive?

Whether is (nu_tau, nu_mu, nu_e) the only Whether is (nu_tau, nu_mu, nu_e) the only triplet from the ordinary-matter world (as triplet from the ordinary-matter world (as described by the minimal Standard described by the minimal Standard Model)?Model)?

In the construction of the minimal Standard In the construction of the minimal Standard Model, the right-handed neutrinos do not Model, the right-handed neutrinos do not appear. So, we could construct an appear. So, we could construct an independent SU_f(3) gauge theory with the independent SU_f(3) gauge theory with the neutrinos as a triplet, to the least.neutrinos as a triplet, to the least.

We should write the extended SU_c(3) x We should write the extended SU_c(3) x SU_L(2) x U(1) x SU_f(3) theory altogether SU_L(2) x U(1) x SU_f(3) theory altogether – each of the basic units has one kinetic-– each of the basic units has one kinetic-energy term and only one. W-Y. Pauchy energy term and only one. W-Y. Pauchy Hwang and Tung-Mow Yan, Hwang and Tung-Mow Yan, arXiv:1212.4944 [hep-ph] 20 Dec 2012.arXiv:1212.4944 [hep-ph] 20 Dec 2012.

My Struggles with the Standard My Struggles with the Standard Model: Part No. 5Model: Part No. 5

I invited Tung-Mow Yan to lecture on the I invited Tung-Mow Yan to lecture on the Standard Model last Fall. On one day, it was Standard Model last Fall. On one day, it was clear to us that we could put the three lepton clear to us that we could put the three lepton doublets, six of them altogether, as an SU_f(3) doublets, six of them altogether, as an SU_f(3) triplet.triplet.

W-Y. Pauchy Hwang and Tung-Mow Yan, W-Y. Pauchy Hwang and Tung-Mow Yan, arXiv:1212.4944v1 [hep-ph] 20 Dec 2012.arXiv:1212.4944v1 [hep-ph] 20 Dec 2012.

My Struggles with the Standard My Struggles with the Standard Model: Part No. 6Model: Part No. 6

Finally, I worked out the “combined” Higgs Finally, I worked out the “combined” Higgs mechanisms – using the scalar/Higgs fields mechanisms – using the scalar/Higgs fields Phi(3,2), Phi(3,1), and the standard Phi(1,2); it is Phi(3,2), Phi(3,1), and the standard Phi(1,2); it is like a magic.like a magic.

W-Y. Pauchy Hwang, arXiv:1304.4705v1 [hep-W-Y. Pauchy Hwang, arXiv:1304.4705v1 [hep-ph] 17 April 2013.ph] 17 April 2013.

After Thoughts After Thoughts

I think that the SU_f(3), a GeV or sub-Fermi I think that the SU_f(3), a GeV or sub-Fermi family gauge theory, is meant to protect the family gauge theory, is meant to protect the lepton world from the QED Landau ghost and it lepton world from the QED Landau ghost and it is asymptotically free.is asymptotically free.

So, this Standard Model has SU(3) everywhere. So, this Standard Model has SU(3) everywhere. Indeed, it looks like a magic.Indeed, it looks like a magic.

W-Y. Pauchy Hwang, arXiv:1301.6464v5 [hep-W-Y. Pauchy Hwang, arXiv:1301.6464v5 [hep-ph] 29 April 2014.ph] 29 April 2014.

Ultraviolet divergencesUltraviolet divergences

Fig. 1: The cancelations for all quadratic and logarithmic divergences.

Fig. 2

Fig. 3

Fig. 4: Cancelations of divergences essential to make a theory a true theory.

What is the “complete” theory? What is the “complete” theory?

I believe that ultraviolet divergences could I believe that ultraviolet divergences could be there for some diagrams, owing to be there for some diagrams, owing to uncountable infinite DOF’s but altogether uncountable infinite DOF’s but altogether they should be canceled out.they should be canceled out.

We should work on the SU_c(3) x SU_L(2) We should work on the SU_c(3) x SU_L(2) x U(1) x SU_f(3) Standard Model, as a x U(1) x SU_f(3) Standard Model, as a complete theory.complete theory.

ConclusionConclusion

II finally arrived at the Standard Model that finally arrived at the Standard Model that have SU_f(3) to protect the lepton world have SU_f(3) to protect the lepton world and have neutrino oscillations in a natural and have neutrino oscillations in a natural way.way.

This is the SU_c(3) x SU_L(2) x U(1) x This is the SU_c(3) x SU_L(2) x U(1) x SU_f(3) extended Standard Model. It is SU_f(3) extended Standard Model. It is renormalizable. renormalizable.

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mechanism”.mechanism”.2.2. Particle Data Group, “Review of Particle Physics”, J. Phys. G: Nucl. Part. Particle Data Group, “Review of Particle Physics”, J. Phys. G: Nucl. Part.

Phys. 33 (2006) 1; on neutrino mass and mixing, see pp. 156 - 164.Phys. 33 (2006) 1; on neutrino mass and mixing, see pp. 156 - 164.3.3. For example, see Stuart Raby and Richard Slansky, Los Alamos Science, For example, see Stuart Raby and Richard Slansky, Los Alamos Science,

No. 25 (1997) 64.No. 25 (1997) 64.4.4. For notations, see T-Y. Wu and W-Y. Pauchy Hwang, Relativistic Quantum For notations, see T-Y. Wu and W-Y. Pauchy Hwang, Relativistic Quantum

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