By the 1950s, when Yang–Mills theory, also known as non-abelian gauge
theory, was discovered, it was already known that Quantum Electrodynamics (QED) gives an extremely accurate account of electromagnetic fields and forces. So it was natural to inquire whether non-abelian gauge theory described other forces in nature, notably the weak force and the strong or nuclear force. The massless nature of classical Yang–Mills waves was a
serious obstacle to applying Yang–Mills theory to the other forces, for the weak and nuclear forces are short range and many of the particles are massive. Hence these phenomena did not appear to be associated with long-range fields describing massless particles. In the 1960s and 1970s, physicists overcame these obstacles to the physical interpretation of non-abelian gauge theory. In the case of the weak force, this was accomplished by the Glashow–Salam– Weinberg electroweak theory. By elaborating the theory with an additional “Higgs field,” one avoided the massless nature of classical Yang–Mills waves. The solution to the problem of massless Yang–Mills fields for the strong interactions has a completely different nature. That
solution did not come from adding fields to Yang–Mills theory, but by discovering a remarkable property of the quantum Yang–Mills theory itself, called “asymptotic freedom”.Asymptotic freedom, together with other experimental and theoretical discoveries made in the 1960s and 1970s involving the symmetries and high-energy behaviour of the strong
interactions, made it possible to describe the nuclear force by a non-abelian gauge theory in which the gauge group is G = SU(3). The non-abelian gauge theory of the strong force is called Quantum Chromodynamics (QCD). But classical non-abelian gauge theory is very different from the observed world of strong interactions; for QCD to describe the strong force successfully, it must have at the quantum level the mass-gap and related color confinement
properties. Both experiment—since QCD has numerous successes in confrontation with experiment—and computer simulations carried out since the late 1970s, have given strong encouragement that QCD does have the properties of mass-gap and color confinement cited above. But they are not fully understood theoretically. In the attached link, http://dx.doi.org/10.13140/RG.2.1.1637.3205 the theoretical understanding of mass-gap and related color confinement property have been provided during mathematical calculation of the gluon emission cross section for QCD process by taking over the corresponding results from closely related aforesaid QED process under the assumption that color interactions in perturbative sector are “a copy of electromagnetic interactions.
As such, the direct mathematical calculation for QCD process has been
avoided because the presence of point-like Dirac particles inside hadrons through Bjorken scaling and the carriage of a substantial portion of proton’s momentum by neutral partons, as revealed by the ‘asymptotic freedom’ based analysis of the data on deep inelastic scattering of leptons by nucleons, do not constitute direct evidence that the aforesaid Dirac particles and neutral partons can be identified with quarks and gluons respectively for making QCD the correct physical theory.
dx.doi.org/10.13140/RG.2.1.1637.3205
No-the mass gap and color confinement of Yang-Mills theories are quantum effects, that are sensitive to much more than, just, tree level effects. They are found in lattice simulations, that, indeed, probe non-perturbative properties of the theory-the only reason that the lattice calculations don't provide a mathematical proof is that it's not possible to prove, in a mathematically rigorous way, how the lattice results converge to results in the scaling limit.
In the attached link (http://dx.doi.org/10.13140/RG.2.1.1637.3205), the pedestrian tree level calculation result (i.e., Equation 11.41) of the gluon emission cross section in 3-jet event is in-fact probability distribution of the emitted gluon in space at the time of its emission in 3-jet event. In order to have direct experimental evidence for vector gluon case, a ‘wave nature’ analysis of about 1.3 x 100000 hadronic events obtained with OPAL detector at LEP during 1990 data taking run, collected around the pole Z0 is presented in ref. [4] of aforesaid attached link.
“Like the case of a double-slit diffraction experiment with so weak a light beam that only one photon at a time is in the apparatus and reaches the screen – the observer (or more likely his instrument) would find a series of apparently random flashes which points to particle nature of light and the observer keeps track of the flashes for long enough though, he will find the characteristic diffraction pattern, the aforesaid ‘wave-nature’ analysis of about 1.3 x 100000 hadronic events (particle phenomenon) is exactly the same.” However, the detection of gluon jet at a particular Ellis – Karliner angle in any one of the aforesaid 1.3 x 100000 hadronic events is a particle phenomenon just like ‘apparently random flashes’ in aforesaid double-slit diffraction experiment. This particle phenomenon i.e., the detection of gluon jet obviously happens when the emitted gluon loses its kinetic energy due to soft radiation with passage of time and becomes massive in IR limit. In the attached link, it is shown that the emitted gluon at finite energy becomes a spatial coordinate singularity at first Gribov horizon and as such, exhibits mass-gap i.e., gluon propagator has no spectrum beyond first Gribov horizon.
In view of the above, the answer ‘No’ to the asked question is not justified.
Gluons don't become massive in the infrared limit-that statement is incorrect. Nor is the statement about the gluon jet losing kinetic energy correct, either. The references to the two slit experiment aren't relevant. It's useful to consult textbooks or lectures on the subject, that's now background knowledge, e.g.
http://hedberg.web.cern.ch/hedberg/lectures/ch7_lec1.pdf
The statement ``the emitted gluon at finite energy becomes a spatial coordinate singularity'' is meaningless and the statement that the gluon propagator doesn't have a spectrum beyond the first Gribov horizon is meaningless, also. What the Gribov ambiguity means is, simply, that it's not possible to fix the gauge uniquely, one must use coordinate patches in field space. Cf. http://projecteuclid.org/euclid.cmp/1103904019
However, when performing a tree-level computation one isn't sensitive to the Gribov ambiguity, since one is working in the coordinate patch about the identity in field space, anyway.
Finally, the quoted text doesn't have anything to do with any comparison between a tree-level calculation and a higher loop calculation, so is completely irrelevant to the issue. It certainly doesn't produce either a mass gap or an example of color confinement. Cf. http://arxiv.org/abs/1008.1936 for how gluon jets are studied.
It is true that the emitted Gluon in 3-jet event does not become massive in Infrared limit, rather it becomes massive somewhere in deep infrared region. But I have never stated in my earlier answer that the gluon jet loses kinetic energy. This is misrepresentation of facts. What I have stated is that “the emitted gluon loses its kinetic energy due to soft radiation with passage of time”. This is very much true because gluon soft radiation, that produces additional particles moving in the same direction, without deflecting the overall flow, is responsible for production of gluon jet in 3-jet event. Therefore, the reference of double slit experiment is very much relevant.
At the time of emission, the momentum operator of the emitted gluon in 3-jet event has got two parts, viz. transverse part and longitudinal part. The transverse part is canonically conjugate to the transverse gluon field in standard Coulomb gauge, whereas the longitudinal part [see Equation (1) in the attached link (http://dx.doi.org/10.13140/RG.2.1.1637.3205)] is obtained by resolving Gauss law in standard Coulomb gauge. The pedestrian tree level calculation result (i.e., Equation 11.41 of the aforesaid attached link) of the gluon emission cross section in 3-jet event pertains to the first loop interaction (between transverse part and the emitting quark) which is familiar; the gluon can fluctuate into a virtual quark-antiquark pair, just as a photon can fluctuate into virtual electron-positron pair. This first loop interaction is nothing but quark-gluon vertex in 3-jet event. The longitudinal part has no role to play in this quark-gluon vertex. However, the longitudinal part starts building up with the passage of time as the emitted gluon loses energy via soft radiation to produce gluon jet. The longitudinal part is in-fact called the instantaneous Coulomb field (of the gluon) with which longitudinal gluons are associated. Such longitudinal gluons are never produced as real physical states because the introduction of ‘ghost’ particles in QCD cancels the unphysical polarisation of these longitudinal gluons. But these ‘ghost’ particles can contribute to the higher loops without leading to the production of physical particles.
In the literature, it was first announced in Regensburg at the Lattice 2007 Conference (arXiv:0710.0412) that gluon propagator never goes to zero with momenta but rather reaches a plateau with a finite value at zero momenta. This went called the decoupling solution in literature. Similarly, the ghost propagator is seen to behave as that of a free particle. The ghost field just decouples from the gauge field and becomes free in the deep infrared. Other groups at the same conference confirmed similar results (arXiv:0710.1968 and arXiv:0710.1424). In the present context, the meaning of the two statements that ``the emitted gluon at finite energy becomes a spatial coordinate singularity'' and that “the gluon propagator doesn't have a spectrum beyond the first Gribov horizon” becomes clear in the light of the aforesaid statement “gluon propagator never goes to zero with momenta but rather reaches a plateau with a finite value at zero momenta”. Also, the stated fact in the attached link, that related color confinement also takes place at first Gribov Horizon, becomes clear in the light of the aforesaid statement that “the ghost propagator is seen to behave as that of a free particle. The ghost field just decouples from the gauge field and becomes free in the deep infrared”.
The concept of Gribov ambiguity becomes redundant one with the restriction of the gauge field to the first Gribov region (or more specifically to Fundamental Modular Region (FMR) that shares some common boundary with first Gribov region to allow for the possibility that the emitted gluon at finite energy becomes a spatial coordinate singularity at first Gribov Horizon). It is true that while performing a tree level computation (i.e., the derivation of Equation 11.41 in the attached link), one is in perturbative region that is contained around origin well inside the first Gribov region (or FMR).
Lastly, in case of gluon emission in 3-jet event, the tree level computation (i.e., the derivation of Equation 11.41 in the attached link) and higher order loop calculations involving ghost particles at first Gribov horizon are performed over distinct time slices that are separated from each other by finite time interval. This time separation is exactly like the time interval involved between passing of single photon at a time through double slit and its arrival at screen – observer (or more likely his instrument) as random flashes. The former case, that involves tree level computation (i.e., the derivation of Equation 11.41 in the attached link) is exactly like the passing of a single photon at a time through double slit and the latter case that involves higher order loop calculations pertaining to the analysis of about 1.3 x 100000 hadronic events obtained with OPAL detector at LEP during 1990 data taking run, collected around the pole Z0 as presented in ref. [4] of aforesaid attached link, is exactly like the observer keeping track of the random flashes produced by a series of photons with a single photon passing at a time through double slit. Thus, there is clear cut analogy between quoted text of my earlier answer and comparison between a tree level calculation and higher loop calculation and so, the quoted text is completely relevant to the issue and certainly produces an example of both mass-gap and related color confinement.
In view of the above, the answer ‘No’ to the asked question is not justified.
No, you need one-loop field theory. For a 'simple' explanation without detailed calculation, see `Introduction to the Weak and Hypoweak Interactions,'' {\it
Adv.\ Nucl.\ Phys.} {\bf 18}, 315-444 (1987); pp.379-381
My humble submission is that at the time of gluon emission in 3-jet event, the emitting quark – gluon coupling involves fluctuation of the emitted transverse gluon (read ‘transverse amplitude’) into virtual quark-antiquark pair – one loop for each quark flavour. This is nothing but one loop field theory. With passage of time, the emitted gluon loses its momentum or energy due gluon soft radiation. In other words, there is a gradual build-up of longitudinal gluons with the emitted gluon at its centre. This gradual build-up of longitudinal gluons is the effective gluon color charge that is measured by an experimentalist. These longitudinal gluons are never produced as physical states since the ‘ghost’ particles are introduced for the cancellation of unphysical polarisation of these longitudinal gluons. As such, the aforesaid ghost particles contribute to the higher order loops without leading to the production of physical particles. At some sufficiently low level say ‘X’ of emitted gluon momentum or energy, the effective gluon color charge, measured by an experimentalist, becomes very large and one introduces anomalous mass scale at ‘X’ for the emitted gluon. The value of ‘X’ is not predicted by theory; it is a free parameter to be determined from experiment. In this regard, my paper in the attached link (http://dx.doi.org/10.13140/RG.2.1.1637.3205) theoretically identifies the value of ‘X’ with the gluon energy at first Gribov Horizon where the emitted gluon at finite energy becomes a spatial coordinate singularity.
In view of the above, the answer ‘NO’ to the question is not justified
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Particle Physics
- Elementary Particle Physics