Can someone explain to me further on QCD

[Agave tequilana]

Since I am a beginner in particle physics I was wondering if anyone could explain to me the concepts of Quantum Chromo Dynamics rather than saying it is the study of the colour force.

1. What are the concepts of QCD?
2. If QCD has more to it than colour, what are the other concepts?
3. Can you further explain the quark colours

 

[Orodruin]

Since I am a beginner in particle physics I was wondering if anyone could explain to me the concepts of Quantum Chromo Dynamics rather than saying it is the study of the colour force.

Since you are a beginner, it would be very difficult to explain the actual concepts behind QCD at a level which is understandable in any other way than what you will find in your general popular science. Instead of electric charge, you have colour charge, each quark can be in one of three states which we call (by convention, it has nothing to do with actual colours) red, green, and blue - or, since it is quantum mechanics, a linear combination of those. The force carriers of QCD are the gluons which have one colour and one anti-colour and come in eight varieties (consider the combinations red-antired, red-antigreen, etc - that makes nine and one disappears because it is not allowed by the theory).

Unlike photons, which are the carriers of electromagnetic interactions, gluons are charged under the interaction they couple to and therefore interact with themselves. This leads to quark confinement, which is essentially that quarks can only come together in colourless combinations.

1. What are the concepts of QCD?
2. If QCD has more to it than colour, what are the other concepts?
3. Can you further explain the quark colours

To really explain the answers to those questions, you would essentially have to take 4-5 years of university studies in physics specialising in theoretical particle physics.

 

[Agave tequilana]

Thank you for the information. I guess I will have to wait until I get to university that explains to know the rest.

 

[nikkkom]

In cases like this, these days a good starting point would be Wikipedia. It's usually reasonably correct, reasonably simple, and extremely easy to access.

 

[Agave tequilana]

Thank you for the advice I will check it out now.

 

[Agave tequilana]

Based on Wikipedia, there are 2 properties of QCD known as Confinement which means that the gluons do not lose influence on each other through distance and Asymptotic which means during high energy reactions, the quark and gluon weakly interact causing a quark-gluon plasm.

 

[ChrisVer]

Confinement means that the quarks cannot be arbitrarily separated from each other (they are confined within the hadrons).. if you'd try to separate them, you'd get enough energy (due to the strong interactions/ gluon field energy) to create a pair of quark-antiquark (thus you'd end up again with 2 hadrons)...

 

[Agave tequilana]

Oh. Thank you for the explanation.

 

[ohwilleke]

One of the better introductions of QCD for a layman who wants more than the barest bones introduction to it would be the last chapter of the book (adapted from lectures given in New Zealand) by Richard Feynman called "QED" which explains QCD by analogy to QED (both of which are part of the Standard Model). A few key concepts:

1. Each quark has a "color charge" which is just an arbitrary label unrelated to color in real life that can take one of three values (conventionally red, blue and green) in quarks, and one of three values (conventionally, anti-red, anti-blue and anti-green) in antiquarks. Net color charge is a perfectly conserved quantity in the Standard Model, just as electrical charge is. Any time a new blue color charge quark is created, for example, a new anti-blue color charge quark is created at the same time. The charged leptons (electron, muon, tau), the neutrinos, the photon, the W bosons, and the Z bosons have no color charge and do not participate in QCD interactions.

2. There are six quark flavors (u, d, s, c, b and t in order of mass) plus anti-quarks for each quark flavor. Five of the six quark flavors form hadrons (generally speaking two quark mesons and three quark baryons), while top quarks decay so rapidly via the weak force (99.9%+ of the time into b quarks) that they don't have time to form hadrons. U stands for up, d stands for down, s stands for charm, b stands for bottom or archaically beauty (or colloquially "jerk" which rhymes with ditch), and t stands for top. Up and down quarks are in the first generation of fermions along with electrons and electron-neutrinos. Charm and strange quarks are in the second generation of fermions along with muons and muon-neutrinos. Top and bottom quarks are in the third generation of fermions along with tau leptons and tau-neutrinos. W boson emission can change the flavor of a quark according to the square of the CKM matrix entry probabilities. Quarks u, c and t have electric charge +1/3, while quarks d, s and b have electric charge -2/3, and W boson flavor changing interactions always shift quarks from the u/c/t column (up type quarks) to the d/s/b column (down type quarks) or visa versa. There is no meaningful explanation in the Standard Model for why the masses of the quarks and the elements of the CKM matrix have the values that they do, nor is there an explanation for the strength of the strong force coupling constant.

3. Color charge is mediated via particles with zero rest mass, and zero electric or weak force charge called gluons. Typically one thinks of a gluon as having a color and an anti-color, but this isn't strictly correct, because there are actually only eight and not nine possible combinations of gluons, something that flows from the math of the SU(3) group in abstract algebra that describes QCD interactions. But, in infrared settings, gluons dynamically acquire mass or at least a property that behaves like mass, in the hundreds of MeVs or so when the Dyson–Schwinger equations are used to approximate their behavior in QCD. Each color charge has the same magnitude (with gluons having pairs of color charges in magnitude).

4. The force that binds quarks to each other via gluons is called the strong force, which is a bit confusing because sometimes people call the force that binds protons and neutrons in an atomic nucleus which occurs mostly via mesons called pions exchanged between protons and neutrons as a residual component to the strong force that binds quarks together the strong force or the strong nuclear force or the nuclear binding force.

5. Due to the strong force, quarks are confined, which is to say that they are always observed in nature in mesons that are net color neutral because they have a quark with a given color and an anti-quark of the anti-color of the same type, or a baryon with a red, blue and green quark in it, or with an anti-red, anti-blue and anti-green quark in it. Confinement has the notable side effect that all composite objects made of quarks have integer electric charge (examine the possibilities to see why this is so as an exercise). Top quarks are the one exception to confinement which is useful in determining the properties of the bare quarks.

6. Like QED, QCD calculations involve considering every possible path from the point of origin to the end point to be calculated and its probability (which the equations of QCD calculate) and adding up all of those probabilities some of which interfere with each other. This equation called the gluon propagator is superficially similar in form to the analogous formula for photons and electron motion, but has complicating terms due to flavors and colors. One of the main generalizations of this equation was developed by http://www.kyodonews.net/news/2015/07/17/24888 who also co-invented the notion of the Goldstone boson and the concept of color charge. Since quarks have color charge, unlike photons which lack electric charge, they interact with each other as well as with quarks, which is one of the things that makes the math of QCD much, much harder than the math of QED (i.e. quantum mechanical electromagnetism). The multiple flavors, self-interaction of gluons, and greatly increased number of paths involving "virtual particles" that are absent in both the original and end state of a path, greatly complicate the calculations. Paths that involve intermediate virtual particles that would seemingly be matter-energy conservation barred are probability suppressed but not forbidden. In general, an exact QCD calculation is "non-renormalizable" making the math tricks used for QED and the weak force unavailable and forcing us to use numerical approximations instead.

7. QCD interactions do not violate CP symmetry, unlike weak force interactions, in the Standard Model, even though there is an obvious way to do so. The fact that they don't is called the "strong CP problem."

8. The strong force is strongest at a distance on the order of the size of an atom, gets weaker with distance and at higher energies, and gets weaker at shorter distances and lower energies. The weakness of the strong force at distances within hadrons is called "asymptotic freedom". The low energy behavior of the strong force equation has not been rigorously proven mathematically and solving this equation rigorously is the subject of one of the Millenium problems in mathematics. http://dispatchesfromturtleisland.blogspot.com/2011/11/millenium-problem-in-yang-mills-theory.html

9. The strong force is not a 1/r^2 force. It behaves more like a rubber band around the quarks bound in a hadron, not impacting quarks within its boundary in asymptotic freedom, while holding especially tight to quarks pulled away from its bounds and forming "flux tubes" that are long and narrow force fields when one quark is pulled far from the other quarks in its hadron. Within a baryon like a proton, the mass due to gluon fields is heavily concentrated in a sphere in the middle one-third of the total composite object's spherical volume. The QCD Lagrangian that is a key part of the Standard Model is a specific subtype of more general Yang-Mills equations. The complete Standard Model Lagrangian (including but not limited to QCD) is not nearly as compact as the equations of GR or classical gravity or classical electromagnetism. It just barely fits on a t-shirt with smallish print and takes about 36 lines of print, without any definitions of the symbols used, stylistic conventions chosen, or listing of any physical constants, and much of it is relevant to QCD, although some of which is relevant only to the electromagnetic or weak forces.

10. It is not possible to do the math analytically and exactly to apply the equations of QCD to real circumstances of any complexity. Perturbative QCD is used to approximate its high energy (aka ultraviolet) behavior. Perturbative QCD calculations are usually carried out to NLO (next to leading order), or NNLO (next to next to leading order) in a balance of computational difficulty and precision. The LO (or leading order) calculation is sometimes called the "tree-level" calculation. Some key assumptions used in perturbative QCD are the parton distribution functions (PDFs) of composite particles the interaction with each other that describes the probability that an interaction will involve a particle in a "sea" of virtual particles in addition to the simplified dominant components of, for example, a proton or neutron, during an interaction (in practice these are determined by fitting large data tables to a formula with a number of degrees of freedom using experimental data), and the "factorization theorem" which in a nutshell allows certain calculations which are not really independent to be calculated as if they were in high energy situations. One important first order modification of the rules of perturbative QCD is the OZI rule https://en.wikipedia.org/wiki/OZI_rule which suppresses in probability the likelihood of certain kinds of QCD probabilities in certain kinds of Feynman diagrams relative to the naive perturbative QCD expectation for rather difficult to explain reasons (in particular, "We know that quarkonium states are usually suppressed in hardonic decays, something which can also be stated in the form that "diagrams that destroy the initial quark and antiquark are strongly suppressed with respect to those that do not."). A discrete approximation called lattice QCD that breaks up space to discrete units is used to approximate its low energy (infrared) behavior. Another key tool used to make QCD predictions is called the "QCD Sum Rules" that provide boundaries on what other means of approximation can produce as answers. So is the Coleman-Glashow relation which shows that certain sums of hadron masses must equal certain other sums of hadron masses due to symmetry considerations.

11. It is possible to do perturbative QCD and lattice QCD calculations using an arbitrary number of quark flavors, and to do them in a hypothetical simplified world where up and down quarks have the same mass. For example, many calculations are done using 2+1 quark flavors (i.e. degenerate mass up and down quarks plus a strange quark). Often electromagnetic forces are ignored in these calculations since electromagnetism is so weak relative to the strong force in these interactions. It also isn't usual, for example, to do the math with 20, 15 and 10 quarks and then use those data points to extrapolate down to the physical number of quark flavors that are relevant. Often this is done with one or more arbitrary mass scales (e.g. a 500 MeV and 250 MeV pion rather than a physical 140 MeV pions) and extrapolated to a physical scale. All of these things are done to simplify the calculations which are harder to do with the true physical number of flavors and physical pion mass, in part, because you can run up against singularities (and for other reasons). It isn't uncommon to use an unphysical number of dimensions of space-time and extrapolate as well. The physical values do matter, however. For example, neutrons are stable in a hypothetical QCD with a significantly higher than physical pion mass, but are not stable in real life.

12. One way to make QCD calculations is to have computer programs with the relevant probabilities of different possible QCD events put in and then using a random number generator to simulate the event over and over since managing so many random variables analytically is harder. Very large number of events are run and the resulting number of outcomes is used to predict the true likelihood of something happening and its variance. This is called a Monte Carlo method. A faster variant of Monte Carlo models uses a statistical sampling of random calculations rather than all of them to make a prediction. See http://dispatchesfromturtleisland.blogspot.com/2012/03/qcd-with-monte-carlo-methods.html

13. The accuracy of the QCD calculation of the proton mass from first principles is about 1% due to limitations in the accuracy of the constants such as the strong coupling constant (a dimensionless constant of the Standard Model whose world average mean value is about 0.1185 and is known to about 0.5% accuracy), the quark masses (the lighter ones are known to more absolute precision but the heavier ones are known to more percentage precision), and the inaccuracies due to ignored terms in the calculation (i.e. calculating only to NLO or NNLO rather than with more terms in an infinite series approximation of the right answer). High energy events and empirical data on high energy events can be used to make more accurate calculations, but since the strong force coupling constant runs with energy scale and that is often hard to determine in events involving "jets" uncertainty in jet energy often creates lots of systemic error in these calculations. It is not uncommon for theoretical predictions made using different numerical approximation methods to be inconsistent with each other, and sometimes with the experimental data as well, and frustratingly there is no one numerical approximation approach that is consistently superior to the others in all contexts. Different methods have different domains of applicability and it isn't always possible to accurately guess in advance which will be more accurate. Nonetheless, almost everyone blames this lack of agreement on flaws in the approximation methods and not on the correctness of the true equations of QCD themselves, because it is very hard to devise an alternative that is consistent, well motivated and reasonably accurate over such a broad range of phenomena and usually some approximation is reasonably close, and the flaws of the numerical approximations are often well known and sufficient in magnitude to explain the issues.

14. Most of the mass in light hadrons (.e.g. protons and neutrons) comes from the QCD binding energy, and not from the quarks themselves. As a first order of approximation, a hadron's mass is equal to the sum of the quark mass and the binding energy inferred that way from other hadrons with the same spin and parity. There is also a phenomenological relationship between the binding energy of a hadron and a binding energy of the same hadron except with higher spin. The pion is the lightest hadron (ca. 140 MeV). The proton is the lightest baryon (ca. 940 MeV) and the only stable hadron (neutrons are stable bound in nuclei and have a mean lifetime of about 15 minutes outside a nucleus). The heaviest theoretically possible hadron has a mass on the order of 15 GeV (an excited baryon with three bottom quarks and spin-3/2+), although the observed heaviest hadron is under 10 GeV in mass. There are a couple hundred possible ground state hadrons, and a theoretically infinite number of heavier excited states of hadrons.

15. Composite objects made of two quarks called mesons, even though they are made up of spin-1/2 quarks, behave as bosons (like photons, gluons, W bosons and Z bosons), rather than like fermions (like quarks, charged leptons, neutrinos, protons and neutrons). Mesons come in categories based upon their spin and parity, the most common being pseudo-scalar mesons (spin-0, negative parity), vector mesons (spin-1 negative parity), scalar mesons (spin-0 positive parity), and axial vector mesons (spin-1 positive parity). We understand psuedo-scalar and vector mesons much better than we do scalar and axial vector mesons whose composition is widely debated. An excited state spin-2 meson is called a "tensor meson". All other things being equal, higher spin mesons are heavier than lower spin mesons. Baryons usually come in spin-1/2 and spin-3/2 versions depending on the alignment of the spins. All other things being equal, higher spin baryons are heavier than lower spin baryons. There is a set of rules that explain how to assign names to hadrons which are more complicated than they should be because the earlier hadrons were given names before physicists understood the general rules and those archaic names are still in used as exceptions to the general naming rules. The rules are explained here: http://dispatchesfromturtleisland.blogspot.com/2014/02/hadron-nomenclature.html Knowing the naming rules demystifies a lot of QCD papers in print.

16. In principle, QCD can have particles made of four or five or more quarks in a bound state (tetraquarks, pentaquarks) or zero quarks (glueballs). But, no observation of these composite states has been made definitively. Some states have been shown to be "meson molecules" where two mesons are bound much as protons and neutrons in a nucleus are bound to each other yet separate, or meson-hadron molecules, or bi-baryon molecules. Some of the lighter mesons (such as pions which are made up some combination of up and down quarks) and certain kaons (which also have a strange quark component as well as up and down quarks) are mixes of pure u-u* and d-d* mesons (with the star to indicate antiparticles due to my inability to format that correctly). Glueballs are also expected to be mixed with other particles with similar quantum properties which helps explain why they have not been observed. We don't fully understand the rules that govern mixing of hadron types.

17. Gluons can break up to product quark-antiquark pairs, and can be formed from the fusion of quark-antiquark pairs.

18. With the exception of top quarks, the strong force usually hadronizes quarks more quickly than the weak force acts.

19. The decay time of a particle (other than protons, which are stable) can be calculated from first principles based upon all decays that are possible from a composite particle in light of conserved quantities in the Standard Model (e.g. baryon number, lepton number, color charge, electric charge, total angular momentum aka spin). Particles that can only decay via the weak force bosons take longer to decay than those that can decay via strong force interactions with gluons. Confusingly, while a hadron's spin can be calculated trivially from the spin of its component quarks, the mechanism by which this happens is not trivial and indeed is quite mysterious with lots of spin not carried in the partons you would expect them to be carried in when you poke and prod a hadron.

20. Defining quark masses other than the top quark mass is tricky because they always appear in hadrons and can't be directly measured separately. There is more than one way of doing so and one has to carefully convert between methods to get consistent data.

Caveat: These are generalizations from a forest level view to give you the basic gist of what QCD is about and is not intended to substitute for rigorous textbook based understanding to the theory at a mathematical level.