## Wednesday, January 18, 2012

### Gluons , Just Because They're Awesome

From Wikipedia:

Gluons
(; from English glue) are elementary particles which act as the exchange particles (or gauge bosons) for the color force between quarks, analogous to the exchange of photons in the electromagnetic force between two charged particles.[6]
Since quarks make up the baryons, and the strong interaction takes place between baryons, one could say that the color force is the source of the strong interaction, or that the strong interaction is like a residual color force which extends beyond the baryons, for example when protons and neutrons are bound together in anucleus.[7]
In technical terms, they are vector gauge bosons that mediate strong interactions of quarks in quantum chromodynamics (QCD). Unlike the electrically neutral photonof quantum electrodynamics (QED), gluons themselves carry color charge and therefore participate in the strong interaction in addition to mediating it, making QCD significantly harder to analyze than QED.

## Properties

In Feynman diagrams, gluons are represented by spirals
The gluon is a vector boson; like the photon, it has a spin of 1 (see Ellis–Karliner angle). While massive spin-1 particles have three polarization states, massless gauge bosons like the gluon have only two polarization states because gauge invariance requires the polarization to be transverse. In quantum field theory, unbroken gauge invariance requires that gauge bosons have zero mass (experiment limits the gluon's mass to less than a few MeV/c2). The gluon has negative intrinsic parity.

## Numerology of gluons

Unlike the single photon of QED or the three W and Z bosons of the weak interaction, there are eight independent types of gluon in QCD.
This may be difficult to understand intuitively. Quarks carry three types of color charge; antiquarks carry three types of anticolor. Gluons may be thought of as carrying both color and anticolor, but to correctly understand how they are combined, it is necessary to consider the mathematics of color charge in more detail.

### Color charge and superposition

In quantum mechanics, the states of particles may be added according to the principle of superposition; that is, they may be in a "combined state" with a probability, if some particular quantity is measured, of giving several different outcomes. A relevant illustration in the case at hand would be a gluon with a color state described by:
$(r\bar{b}+b\bar{r})/\sqrt{2}$
This is read as "red–antiblue plus blue–antired". (The factor of the square root of two is required for normalization, a detail which is not crucial to understand in this discussion.) If one were somehow able to make a direct measurement of the color of a gluon in this state, there would be a 50% chance of it having red–antiblue color charge and a 50% chance of blue–antired color charge.

### Color singlet states

It is often said that the stable strongly interacting particles (Hadrons) observed in nature are "colorless", but more precisely they are in a "color singlet" state, which is mathematically analogous to a spin singlet state.[8] Such states allow interaction with other color singlets, but not with other color states; because long-range gluon interactions do not exist, this illustrates that gluons in the singlet state do not exist either.[9]
The color singlet state is:[10]
$(r\bar{r}+b\bar{b}+g\bar{g})/\sqrt{3}$
In words, if one could measure the color of the state, there would be equal probabilities of it being red-antired, blue-antiblue, or green-antigreen.

### Eight gluon colors

There are eight remaining independent color states, which correspond to the "eight types" or "eight colors" of gluons. Because states can be mixed together as discussed above, there are many ways of presenting these states, which are known as the "color octet". One commonly used list is:[10]
 $(r\bar{b}+b\bar{r})/\sqrt{2}$ $-i(r\bar{b}-b\bar{r})/\sqrt{2}$ $(r\bar{g}+g\bar{r})/\sqrt{2}$ $-i(r\bar{g}-g\bar{r})/\sqrt{2}$ $(b\bar{g}+g\bar{b})/\sqrt{2}$ $-i(b\bar{g}-g\bar{b})/\sqrt{2}$ $(r\bar{r}-b\bar{b})/\sqrt{2}$ $(r\bar{r}+b\bar{b}-2g\bar{g})/\sqrt{6}$
These are equivalent to the Gell-Mann matrices; the translation between the two is that red-antired is the upper-left matrix entry, red-antiblue is the left middle entry, blue-antigreen is the bottom middle entry, and so on. The critical feature of these particular eight states is that they are linearly independent, and also independent of the singlet state; there is no way to add any combination of states to produce any other. (It is also impossible to add them to make rr, gg, or bb[11] otherwise the forbidden singlet state could also be made.) There are many other possible choices, but all are mathematically equivalent, at least equally complex, and give the same physical results.

### Group theory details

Technically, QCD is a gauge theory with SU(3) gauge symmetry. Quarks are introduced as spinor fields in Nf flavors, each in the fundamental representation (triplet, denoted 3) of the color gauge group, SU(3). The gluons are vector fields in the adjoint representation (octets, denoted 8) of color SU(3). For a general gauge group, the number of force-carriers (like photons or gluons) is always equal to the dimension of the adjoint representation. For the simple case of SU(N), the dimension of this representation is N2 − 1.
In terms of group theory, the assertion that there are no color singlet gluons is simply the statement that quantum chromodynamics has an SU(3) rather than a U(3) symmetry. There is no known a priori reason for one group to be preferred over the other, but as discussed above, the experimental evidence supports SU(3).[12]

## Confinement

Since gluons themselves carry color charge, they participate in strong interactions. These gluon-gluon interactions constrain color fields to string-like objects called "flux tubes", which exert constant force when stretched. Due to this force, quarks are confined within composite particles called hadrons. This effectively limits the range of the strong interaction to 10−15 meters, roughly the size of an atomic nucleus. Beyond a certain distance, the energy of the flux tube binding two quarks increases linearly. At a large enough distance, it becomes energetically more favorable to pull a quark-antiquark pair out of the vacuum rather than increase the length of the flux tube.
Gluons also share this property of being confined within hadrons. One consequence is that gluons are not directly involved in the nuclear forces between hadrons. The force mediators for these are other hadrons called mesons.
Although in the normal phase of QCD single gluons may not travel freely, it is predicted that there exist hadrons which are formed entirely of gluons — called glueballs. There are also conjectures about otherexotic hadrons in which real gluons (as opposed to virtual ones found in ordinary hadrons) would be primary constituents. Beyond the normal phase of QCD (at extreme temperatures and pressures), quark gluon plasma forms. In such a plasma there are no hadrons; quarks and gluons become free particles.

## Experimental observations

The first direct experimental evidence of gluons was found in 1979 when three-jet events were observed at the electron-positron collider PETRA. However, just before PETRA appeared on the scene, the PLUTO experiment at DORIS showed Y(9.46) decay event topologies very suggestive of a three-gluon decay. [3] [13]
By measuring the distribution of the Ellis–Karliner angle at the PETRA electron–positron storage ring at DESY, physicists determined that the gluon has spin one rather than spin zero or spin two.[14][15]Subsequent experiments[16] at the LEP storage ring at CERN confirmed this result.
Experimentally, confinement is verified by the failure of free quark searches. Free gluons have never been observed; however at Fermilab single production of top quarks has been statistically shown.[17] Although there have been hints of exotic hadrons, no glueball has been observed either. Quark-gluon plasma has been found recently at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL). [18]

## References

1. ^ M. Gell-Mann (1962). "Symmetries of Baryons and Mesons". Physical Review 125 (3): 1067–1084. Bibcode 1962PhRv..125.1067Gdoi:10.1103/PhysRev.125.1067.
2. ^ R. Brandelik et al. (TASSO collaboration) (1979). "Evidence for Planar Events in e+e Annihilation at High Energies". Physics Letters B 86 (2): 243–249. Bibcode 1979PhLB...86..243Bdoi:10.1016/0370-2693(79)90830-X.
3. a b I. Flegel, P. Söding (2004). "Twenty-Five Years of Gluons"Cern Courrier. Retrieved 2009-09-13.
4. a b W.-M. Yao et al. (2006). "Review of Particle Physics"Journal of Physics G 33: 1. arXiv:astro-ph/0601168Bibcode 2006JPhG...33....1Ydoi:10.1088/0954-3899/33/1/001.
5. ^ F. Yndurain (1995). "Limits on the mass of the gluon". Physics Letters B 345 (4): 524. Bibcode 1995PhLB..345..524Ydoi:10.1016/0370-2693(94)01677-5.
6. ^ http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
7. ^ http://hyperphysics.phy-astr.gsu.edu/hbase/forces/color.html
8. ^ D.J. Griffiths (1987), pp. 280–281
9. ^ D.J. Griffiths (1987), p. 281
10. a b D.J. Griffiths (1987), p. 280
11. ^ J. Baez. Why are there eight gluons and not nine?. Retrieved 2009-09-13.
12. ^ D.J. Griffiths (1980). "Particles & Fields". Scientific American. p. 281.
13. ^ B.R. Stella, H.-J. Meyer (2011). "Y(9.46 GeV) and the gluon discovery(a critical recollection of PLUTO results)"European Physical Journal H 36: 203-243. arXiv:1008.1869doi:10.1140/epjh/e2011-10029-3. Retrieved 2011-11-26.
14. ^ R. Brandelik et al. (TASSO Collaboration) (1980). "Evidence for a spin-1 gluon in three-jet events". Physics Letters B 97 (3–4): 453. Bibcode 1980PhLB...97..453Bdoi:10.1016/0370-2693(80)90639-5.
15. ^ C. Berger et al. (PLUTO Collaboration) (1980). "A study of multi-jet events in e+e annihilation". Physics Letters B 97 (3–4): 459. Bibcode 1980PhLB...97..459Bdoi:10.1016/0370-2693(80)90640-1.
16. ^ G. Alexander et al. (OPAL Collaboration) (1991). "Measurement of Three-Jet Distributions Sensitive to the Gluon Spin in e+e Annihilations at √s = 91 GeV". Zeitschrift für Physik C 52 (4): 543. Bibcode1991ZPhyC..52..543Adoi:10.1007/BF01562326.
17. ^ M. Chalmers (6 March 2009). "Top result for Tevatron"Physics World. Retrieved 2009-09-13.
18. ^ D. Overbye (15 February 2010). "In Brookhaven Collider, Scientists Briefly Break a Law of Nature". New York Times. Retrieved 19 February 2010.