# Elementary Particles Presented

1. Sep 19, 2004

### marlon

Hi everyone...

I have answered already a lot of questions here on the topic of the different elementary particles in the Standard Model. For this reason I will give the interested reader this site that describes this subject very clearly...

If you have more questions, please don't hesitate to post them here...

regards
marlon

2. Sep 25, 2004

### humanino

The Standard Model relies on several assumptions, among which the existence of a certain fields, whose quanta are point-like particles, divided first in two categories : matter and force particles.

Matter particles

Those fundamental particles are fermionic, which implies one can fill a box with them until none can be added (as long as the box is strong enough to resist electric repulsion for instance). Fermi-Dirac statistics is a deep phenomenon, linked to the intrinsic angular momentum called spin : fundamental fermions are spin $$1/2$$ (spinor) particles, and it implies that after a rotation of $$2\pi$$, their wavefunction changes sign !. This is not a real problem, since only the (hermitean) square of the wavefunction is observable, that is the probability density. Notice also that after $$4\pi$$ the double sign reverses cancel, and there are deep reasons why $$4\pi$$ rotations are always equivalent to no rotation. Let us first stare at a list of them :

First family
Second family
Third family
1. electron $$e^-$$​
muon $$\mu^-$$​
tau $$\tau^-$$​
2. electronic neutrino $$\nu_{e}$$​
muonic neutrino $$\nu_{\mu}$$ ​
tauonic neutrino $$\nu_{\tau}$$
3. up quark $$u$$​
charm quark $$c$$​
top quark $$t$$​
4. down quark $$d$$​
strange quark $$s$$​
bottom (beauty) quark $$b$$​

Botanistic classification : 1 and 2 are leptons, while 3 and 4 are hadrons. Leptons do not feel the strong force (on which more latter). Etymology : "hadron" comes from a greek word sounding like "hadros" and meaning "strong, robust, bulky, thick, or stout", and "lepton" from "leptos" : "fine, thin, slender, small". To this list you could add anti-particles, or consider they are ordinary particles travelling backwards in time. Anti-particles have opposite charges except mass and spin, are denoted by an upper bar on the particle symbol, and sometimes have a special name, such as the positron $$\bar{e}^+$$. Each of those might have a supersymetric bosonic partner (supersymetry relates bosons and fermions) but this is not part of the standard model. Although supersymetry has shown relevance in nuclei, it has not been observed for fundamental particles. Some basic facts :
1. Carry minus one unit of electrical charge : $$-e$$.
2. Zero electric charge, and at most a very small mass (zero in the standard model)
3. $$+2/3 e$$, and color charge (red, blue or green) which is "hidden" : free particles are "white", or more accurately "invariant under color rotations".
4. $$-2/3 e$$. Also colored. It is difficult to define mass for 3 and 4 guys because they are never free, especially difficult for the lightest, first family members.

The quarks are "contained in a white bag", either they pair in mesons (quark/antiquark bound state) or in baryons (three quarks bound states). Recent proposal of "pentaquarks" seem nowadays unlikely : only intermediate energy have published low statistics evidences, high energy experiments lead to negative results. Confirmation or rejection of this hypothesis will be available soon, when the analyzing process of data from dedicated experiments will be over.

Force particles

There are 12 bosonic fundamental particles with spin 1 (vector) in the standard model, plus one additional not yet confirmed and spin zero (scalar) particle. They are beautifully unified by a so-called gauge model, formulated entirely in terms of symmetries. One would contemplate a $$U(1)\otimes SU(2)\otimes SU(3)$$ gauge group. Let us emphasized here that gauge symmetry is not a real symmetry, but rather a very elegant mean to deal with constrained systems
• The photon is the quantum of light, it is usually denoted $$\gamma$$ and carries the electromagnetic interaction. It is massless, and this fact is related to the $$U(1)$$ Quantum ElectroDynamic (QED) part of the standard gauge group which is not broken. Broken symmetries occur when the laws have a certain symmetry, but the ground state (vacuum) does not. So all the tower of states constructed form the vacuum do not exhibit this symmetry.
• The 3 massive vector bosons $$W^+$$, $$W^-$$ and $$Z^0$$ are responsible for the weak interaction. This is for instance what causes $$\beta$$ decay of the proton into a neutron, at the quark level : $$d\rightarrow u + e^- + \bar{\nu}_e$$. There are also so-called "neutral currents" with the $$Z^0$$ able to go from one family to another. The gauge part is $$SU(2)$$, but this symmetry is spontaneously broken, giving mass to the vector bosons by the so-called Higgs mechanism. The weak interaction is very peculiar, in that is does not respect some basic symmetries of Nature the other interactions seem to : especially $$P$$ symmetry, the parity which consists in "taking the mirror image", is maximally broken : the $$\nu$$ (if massless) is always left handed, while the $$\bar{\nu}$$ (if massless) is always right handed. So physicists first hoped $$CP$$ would not be broken, with addition of the exchange particle-antiparticle exchange $$C$$. It appears not to be the case, but then it is only slightly broken, such as in the decay modes of the some mesons. Today, we strongly believe that by adding time reversal, the all-important $$CPT$$ symmetry is the fundamental for the theory. The spin-statistics theorem relies on this symmetry.
• The 8 massless gluons, with gauge group the color $$SU(3)$$. Gluons are also peculiar in that themselves carry color charge : a red gluon turn blue by emitting a red/antiblue gluon absorbed by a blue quark turning red for instance. This fact makes gluons interact with each other. There are three gluons and four gluons vertices in the standard model. The non-linearity makes the equation hopelessly unsolvable until now. Also, this is likely the cause of confinement, the property that color is always hidden in color-invariant bound states. Another striking feature is asymptotic freedom, the fact that at very low distances, or alternatively at high energy, quarks look like free particles.

The Glashow-Weinberg-Salam model has already unified the first two in the so-called electroweak unification $$U(1)\otimes SU(2)=U(2)$$. This leads us to the Higgs mechanism : for each broken symmetry, a massless Goldstone boson appears. The Higgs mechanism permits this degree of freedom to be "eaten" by the massless gauge boson thus acquiring mass. We can even refine the model to make all fundamental particles massless acquiring mass by interaction with the Higgs scalar boson. This particle should soon be discovered at the LHC facility (Geneva)

A good source of general information is wikipedia

Another specifically on physics, somewhat at lower level but good illustrations is hyperphysics

The the particle adventure is the source of the link provided by Marlon, and this link leads to the gateway to it, a very friendly introduction.

The CERN is the main European research center.

Of course, the Particle Data Group has a reference site with all particles informations, and more, quite up-to-date and reliable,
The less technical particle adventure is also from the PDG.

etymology

3. Sep 25, 2004

### humanino

Beyond the standard model :
There are many extensions to the standard model. Grand unification to include Quantum ChromoDynamics (QCD) and the Electroweak theory in a single $$SU(5)$$ theory implies for instance proton decay, which has not been observed, and should anyway occur at very large time scales. Other schemes exist, such as $$SO(10)$$ for instance. Those elegant theories cry for experimental evidences.

Also, anybody noticed that the historically first discovered interaction has not been mentioned yet : Gravity ! The graviton is supposed to be a massless spin-2 boson, an assumption from which Einstein's equation can be recovered. Yet it is difficult to identify the physical field of the graviton. It is usually defined as the departure of the metric from the flat Minkiwski one, but for two reasons this seems a priori wrong : this does not obviously look like a background independent formulation, whereas General Relativity is. Besides, fermions require the introduction of a "square-root" of the metric field, so this is more likely a candidate for the graviton. It is especially difficult to make sens of gravity in a quantum field theory, because it is notoriously non-renormalizable. Renormalization is a technical well-defined procedure to remove infinites in the theory, which appear form contributions where the validity of the model cannot be proven at least yet. The gravitation coupling constant having mass dimension $$-2$$, and one can easily see that an expansion in the coupling constant will not converge. So new physics must appear, in other terms Einstein beautiful geometrical formulation of gravity might only be a low-energy approximation to a deeper interaction.

4. Sep 25, 2004

### Orion1

Unity Unification...

If I understand the course of the Standard Model based upon the above information, the next expected unification is:
$$U(2)\otimes SU(3)=U(3) \; \; 10^{14} GeV$$

Resulting in the Electrostrong unification and the production of a Goldstone boson called a X-boson.

The next expected unification is:
$$U(3)\otimes SU(1)=U(4) \; \; 10^{19} GeV$$

Resulting in the Electrostrong Gravitation unification and the production of a Goldstone boson called a g-boson?.

Reference:
http://hyperphysics.phy-astr.gsu.edu/hbase/forces/unify.html
http://hyperphysics.phy-astr.gsu.edu/hbase/forces/unigrav.html#c1
http://en.wikipedia.org/wiki/SU(3)XSU(2)XU(1)

Last edited: Sep 25, 2004
5. Sep 25, 2004

### meteor

There are various extensions of the Standard model including supersymmetric particles: The MSSM, and its constrained version, the constrained minimal supersymmetric Standard model (cMSSM ) ,(there are indeed various differents cMSSM: mSUGRA, the GMSB model, SGUT,...). Which of these theories offers better perspectives, which is more appreciated by the physics community?

Last edited: Sep 25, 2004
6. Sep 26, 2004

### Orion1

Gutted GUT's...

Reference:
http://en.wikipedia.org/wiki/Grand_unified_theory
http://en.wikipedia.org/wiki/Magnetic_monopoles
http://en.wikipedia.org/wiki/Cosmic_strings
http://en.wikipedia.org/wiki/Monopole_problem

7. Sep 26, 2004

### zefram_c

Slight inaccuracy?

I enjoyed reading this thread - it is a very good introduction to the SM for the uninitiated. However, I think there's a slight technical inaccuracy here:
This is not *entirely* correct. When the SU(2) group alone is gauged, the result is three vector bosons. However, they are not the W and Z. Two of them are indeed the mediators of charged currents (the W+ and W-). However, the third boson is not the Z - it is usually denoted the W0 in texts. The coupling of this W0 to fermions doesn't match the experimentally observed weak neutral currents.

Enter the remaining group, U(1)Y. This group is also part of the electroweak interaction, and comes with its own neutral boson, usually denoted B. The B is also non-physical. What happens in symmetry breaking is that the B and the W0 mix and produce two orthogonal states: the photon and the Z. The latter also acquires mass, while the former does not, by the choice of the vacuum expectation value of the Higgs. The Z is the physical mediator of weak neutral currents, and the photon mediates the (seemingly unrelated) EM interaction. Being a mixture of the two gauge fields is what gives the Z the correct couplings to the fermions.

The point of all this is that the SU(2) gauge group alone is insufficient to account for the weak interactions (charged and neutral currents), even after symmetry breaking. This was actually going to be part of a quiz I was planning to post

Last edited: Sep 27, 2004
8. Sep 27, 2004

### meteor

This is a god summary of GUT. Some of these GUT (all?) propose the existence of particles not appearing in the SM. For example, the technicolor model proposes tthe existence of the coloron. Flipped SU(5) proposes the existence of the crypton

In what year appeared E6 GUT?

9. Sep 27, 2004

### humanino

The original, I cannot provide access but reference : Gursey F, Ramond P, Sikivie P. "A Universal Gauge Theory Model Based on $$E_6$$", Phys. Lett. B60:177,1976.

A nice introduction to begin with :
"The quest for unification" by Witten

A recent paper by N. Maekawa (University of Kyoto) with 30 references, and phenomenology :
E6 Unification, large neutrino mixings, and SUSY flavor problem

Plus three papers by Gregory W. Anderson, Tomas Blazek :

$$E_6$$ unification model building III. Clebsch-Gordan coefficients in $$E_6$$ tensor products of the 27 with higher dimensional representations here

$$E_6$$ unification model building II : Clebsch-Gordan coefficients of $$78\otimes78$$ here

$$E_6$$ unification model building I: Clebsch-Gordan coefficients of $$27\otimes \ol{27}$$ here

Last edited: Sep 27, 2004
10. Sep 30, 2004

### humanino

The non-discovery of the Higgs boson is anticipated for a while. Theoreticians lacking data cannot bet on only one possibility. Anyway, we do not know yet, and I like "minimal hypothesis" models. So here is a recent paper about electroweak theory :
Massive Gauge Bosons in Yang-Mills Theory without Higgs Mechanism
whose title speaks by itslef.
It is short, and gives a brief introduction to playing with the standard notations. Ghosts are discussed, renormalization is very likely, yet parity violation as well as down quark mixing are not included, at least at this step.

11. Sep 30, 2004

### humanino

A very nice introduction to the standard electroweak model :
introduction
to balance with the previous paper

12. Oct 1, 2004

### marlon

when studying electrowrak interactions the first question should be : why using this famous V - A current ??? What is it and what does it do...
Some nice anwers are provided on this site, just look at the "sessions" on the bottom of the page. They may be introductory but this is the main intention of this thread...you will acquire a nice perspective on these subjects...

http://www.shef.ac.uk/physics/teaching/phy604/electroweak.html

enjoy

regards
marlon

13. Oct 1, 2004

### marlon

This is a nice site on quarkconfinement...very interesting...i did my master-thesis on this subject. "One of the biggest problems in contemporary theoretical physics : why are quarks confined ???"

In this paper magnetical monopoles are used...very spectacular :tongue2:

http://arxiv.org/PS_cache/hep-ph/pdf/0310/0310102.pdf
regards
marlon

ps : it may take a while before the pdf-file is loaded so be patient...you will be extensively rewarded...

14. Oct 4, 2004

### humanino

Grand Unification and Physics Beyond the Standard Model
Ernest Ma (UC Riverside)
12 pages, no figure, talk at V-SILAFAE, Lima, Peru (July 2004)

Very short paper, good for introduction to the beginner.

15. Oct 12, 2004

### Haelfix

If you like minimality, you probably should go with non SUSY SO(10). Its also amongst the few GUTs with some amount of experimental evidence (neutrino mixing). There are of course a number of inequivalent ways of breaking the group.

Normally we live in the 16 of SO(10), and like to break it down to SU(5), which we understand a little better. However, you can also break it via the Salam left-right model (SU(4)*Su(2)*SU(2))

However it has a few problems (all GUTS have problems), namely the Higgs sector involves some nasty fine tuning. So then people sometimes boost the representation up to some big number (127 or something like that, I forget), and you end up with some sort of Higgs SeeSaw mechanism.

The only GUT that is ruled out atm, is non SUSY SU(5), b/c of proton decay bounds.

16. Dec 6, 2004

### marlon

This is for all you out there, who are wondering about gluons and pions...

The strong force holds baryons and mesons together and is mediated through gluon-exchange between the constituent quarks. I have studied models (dual abelian Higgs-model) where the distance between such quarks (in a baryon or meson) is estimated to be less then 0.7fm when we assume that the three quarks of the baryon are placed on the corners of a triangle. In this case the whole system is to be looked at as one three-body-problem. Bigger inter-quark-distances will give rise to a Y-shaped structure.

The atomic nucleus is bound together by the residual strong force and is mediated by the lightest mesons called the pions. Now, when two baryons (like a proton and a neutron) come close enough to each other, the valence quarks of the first baryon will interact with the valence quarks of the second baryon. What happens is this : two valence quarks from the two different baryons will feel a linear potential between them. When they are pulled apart, the potential rises which leads to an unstable connection between the two quarks. This leads to the fact that the connection is broken apart and the available energy is used to form a quark-anti-quark pair which is the pion. Energy is converted into matter via E =mc² and when enough energy is available this created pair can exists for quite a while because of Heisenberg uncertainty. All these things are described by QFT, which needs to be seen as the unification of special relativity and QM because of the previous two reasons (E=mc² and Heisenberg uncertainty from QM). At distances of about 1fm, the quark pair creation speed is maximal, yielding a maximal interaction between baryons of the atomic nucleus.

It needs to be said that these are result that are predicted by the denoted model above and other models will give you other numbers, although they are in the same range. If you wish i can give you a link to the model i mentioned as some sort of reference, but you are gonna have to know your QFT thoroughly because it is heavy material.

The main difference between gluons and pions is the fact that gluons are elementary in nature, pions are not. Basically this means that gluons arise because of the local colour symmetry of QCD, which provides a fundamental
description of this field theory. The quark-colours can be used to write down this entire theory at it's most fundamental level.

Also notice the fact that pions are the lightest meson. Thus they are constituted out of TWO quarks. The reason for this is that one quark would require an quasi "infinite" amount of energy to exist as a single identity. Reason ? : well, asymptotic freedom. The strong force coupling constant (which expresses the strength of this interaction) becomes smaller when energy rises. Basically this means that high-energy-quarks (for example quarks with high kinetic energy in accelerators) will be less tightly bound to each other because of this principle. Clearly, at the vaccuum-state, energy is low and quarks will therefore never arise as single identities. This property is called the quark-confinement and this years Nobel prize for physics is awarded to the "discoverers" of this principle (ie asymptotic freedom).

regards
marlon

17. Dec 6, 2004

### marlon

Hello everyone,...

I have posted this somewhere else a few days ago, but i think it is a good idea to put this text on "mass in QFT" in our joint encyclopedia...

Dynamical mass-generation refers to the vaccuum condensates in field theory...It can be shown that the perturbative vaccuum is unstable and the vaccuum energy can be lowered when certain condensates (the vaccuum condensates) are created. These condensates do not exist (i mean, the expectation value of them is zero) when they are calculated with perturbation theory. They reason for this is that symmetry of the physical models at hand do not allow a non-zero expectation value. In a non-perturbative field theory (like low energy-QCD) these condensates DO occur and as a consequence of this some symmetries of the models are broken. When symmetry is broken, mass is generated through the Higgs-mechanism. These condensates are thus responsible for giving massless-elementary particles some dynamically generated mass. For example the QCD Lagrangian contains massless quarks and exhibits as a consequence of this chiral symmetry. When vaccuumcondensates are allowed (low-energies or non-perturbative QCD) these quark-antiquarkpairs will break this chiral symmetry and will give the quark mass.

Effective mass is a concept that QFT took over from solid state physics. As an example : consider many electrons that interact with each other. This is one many-particle system with many coupled differential equations. We cannot solve this so what's the way out? Well take one electron and put all the "interactions" it makes with the surrounding electrons into the mass of the electron. What we get is the equation of motion (with adapted mass = effective mass)of an electron that moves around in the vaccuum, because all the interactions with neighbors are put into the effective mass. basically what you have done here is convert one many-body problem into many one body problems that we CAN solve...

Keep in mind that this is a simplified picture but it gives you an image...An effective field theory is a field theory of which the degrees of freedom are not elementary. For example , the degrees of freedom of QCD are quarks, which are elementary particles. In QHD, the degrees if freedom are hadrons (particles that consist out of quarks and feel the strong force), but they are not elementary since they are built out of quarks...

Particles are elementary when they can be used as a FUNDAMENTAL representation of the symmetry-group of the Lagrangian of the field theory...Like quarks with three colours form the fundamental representation of SU(3), the local colour symmetry of QCD which generates 8 gauge bosons (you know, the gluons...)

regards
marlon

Last edited: Dec 6, 2004
18. Dec 6, 2004

### humanino

ok with me
but Marlon started this

and I would like to add something to your last post Marlon. I already wanted to to add it in the other thread : there are other possibilities to generate mass dynamically, among which one I want to mention because of its role in QCD : instantons are also able to break chiral symmetry and give non-vanishing value to the quark condensate. In fact, instanton-based calculations are much in agreement with actual value of the quark condensate (this quark condensate is the order parameter in the phase transition where the breaking of chiral symmetry occurs). Unfortunately, I do not have much time right now to write an account on this.

Also in your post, should not QHC be replaced with QHD (quantum hadro-dynamics) ?

19. Dec 6, 2004

### marlon

Indeed this is very correct... I am planning to write down a text on instantons. Basically they are the QFT-variant of what we call tunneling in QM. The QM-tunneling lowers the vaccuum-energy-value and in QFT it is the instantons that are able to tunnel from one vacuum-gauge-configuration to another...

See this nice link for an indept explanation by Gerardus t'Hooft :
http://xxx.lanl.gov/abs/hep-th/0010225

Indeed, thanks for the correction...

regards
marlon

Last edited: Dec 7, 2004
20. Dec 7, 2004

### marlon

Magnetic monopoles are looked at as being point particles in QFT. Like i stated before, for example in the dual abelian Higgsmodell, they are used in order to describe the dual analogon of the Meissner-effect that pushes the magnetic field lines out of a superconductive specimen...The actual charge of such a monopole is determined in those points of the space-time where the gauge of the field theory is undetermined. This means, where this gauge becomes singular...

I attached a zip-document in which quantization of magnetic charge is explained. The reason for this phenomenon is the Dirac-quantization which makes sure that the Dirac string is not noticable when you pass through a surface that is subtended by a deformed world-line

regards
marlon

Last edited: Aug 6, 2006