0:17

We've seen several times that the strong interactions have special properties.

Â Quarks behave as almost as free particles at short distances inside the hadrons.

Â Nonetheless, free quarks have never been observed outside hadrons.

Â This indicates that the strong force confines them within bound states and

Â does not allow to separate them to large distances.

Â In this fourth video weâ€™ll qualitatively discuss

Â these seemingly incompatible properties.

Â After following this video, you will know the main properties of strong

Â interactions, including its different vertices in Feynman diagrams,

Â color charge, gluons and their role in binding quarks together, and

Â 1:21

We also saw the immediate consequence to triple the cross section for

Â e+ e- annihilation into hadrons in video 4.5.

Â Color is the quark property responsible for their strong interaction.

Â The formal theory of this interaction is quantum chromodynamics, also called QCD.

Â 1:44

Color can take three different values, red, blue, and green for quarks.

Â We indicate it by a lower index when appropriate.

Â A quark can carry only one non zero color, antiquarks carry one anti-color.

Â The interaction between quarks proceeds through the exchange of color.

Â The intermediate vector bosons transmitting the strong force are the eight gluons, g.

Â They carry a color and an anti-color, and therefore are not color neutral.

Â This is in contrast to the photon which couples to the electromagnetic charge but

Â does not carry one itself.

Â 2:26

For strong interaction, there are eight gluons in total.

Â With three colors and

Â three anti-colors one would expect a total of nine combinations.

Â One of them, the fully symmetric combination, that is

Â red-antired plus green-antigreen plus blue-antiblue,

Â has no net color, it does not participate in strong interaction and

Â so cannot be produced.

Â The remaining eight gluons are vector bosons,

Â they are electromagnetically neutral and have zero mass.

Â 3:01

The basic vertex of the strong quark interactions changes

Â the color of the quark.

Â The coupling constant g appearing in the vertex

Â enters into the cross section through its square.

Â Alpha strong is equal to g^2/(4Ï€),

Â in analogy to the electromagnetic fine structure constant alpha.

Â The interaction has the same strength for the three colors or

Â any of their superpositions.

Â So there is invariance under an overall rotation in color space.

Â According to Noether's theorem, this requires a conservation law for colors.

Â The vertex conserves color.

Â The corresponding amplitude is also independent of the flavors of

Â quarks and their electromagnetic charge, which are both ignored and

Â conserved by strong interactions.

Â If gluons carry themselves color,

Â they should be able to interact among themselves.

Â Because they carry even color and anti color, there are two additional vertices.

Â The color indices indicated here are only examples.

Â The three-gluonvertex is proportional to g and

Â has the same strength as the quark-gluon vertex.

Â We must, in each calculation, consider the fact that there are many more different

Â colors for gluons than for quarks.

Â The vertex with four gluons on the contrary is proportional to g^2

Â and thus disfavored with respect to the other two.

Â 5:06

has discovered pentaquark states consisting of five quarks.

Â However it's still unclear whether these are bound

Â baryon-meson states as shown in the picture on the left or

Â genuine compact multi-quark states as sketched on the right.

Â LHCb has also confirmed the existence of a tetra-quark state

Â first observed by the BELLE collaboration in Japan.

Â Again, the same reservations apply.

Â It could still be a meson-meson bound state,

Â rather than a compact four-quark state.

Â Mesons contain a superposition of quark-antiquark pais with

Â all colors in equal proportions.

Â A snapshot is shown here for the interior of a positive pion.

Â Gluons are constantly exchanged between quarks to maintain binding,

Â changing the color of quarks, as in this sketch,

Â while keeping the overall hadron white.

Â The same mechanism works inside baryons.

Â Between hadrons, for example in a nucleus, objects of neutral color

Â are exchanged to create binding, except at very short distances.

Â It follows that an ab initio description of the nuclear force stays very difficult,

Â although we dispose of a well-established quantum theory for

Â interaction between quarks and gluons, namely QCD.

Â At short distances, comparable to the hadron size,

Â the exchange of gluons produces a potential between quark and antiquark

Â which is similar to the one established by photons in a positronium bound state.

Â This potential varies with distance as 1/r like the Coulomb potential.

Â At large distances, there is a different behavior,

Â the potential becomes larger with distance.

Â We already saw a potential that fits the description of the spectra of J/Psi and

Â Upsilon states in video 5.3.

Â 7:37

The second term is created by the interaction between gluons.

Â In terms of a chromostatic language,

Â the additional force between gluons concentrates the color field

Â along a corridor that connects the two color charges.

Â Because of the particular shape of the field,

Â one also call this a string that connects the colors.

Â The potential proportional to

Â k times r does not allow color and anti-color to be separated,

Â but confines them to distances of the order of 1 fm.

Â 8:15

The potential inside hadrons ought to be generated dynamically

Â by the interaction between the quarks and gluons.

Â Obtaining results is complicated by difficulties which are both conceptual and

Â technical.

Â Both the confinement of color at large distance and

Â the relativistic and quasi-free movement of quarks must be incorporated.

Â One must treat states with multiple quarks and gluons.

Â The evolution of the strong coupling

Â 8:55

Calculation techniques are considerably simplified if one replaces

Â the space-time continuum by a mesh of equidistant discrete points,

Â similar to a crystal lattice with sides a.

Â One defines the quark fields on the sites of the lattice,

Â and gluon fields on the links.

Â The continuum of space-time is recovered in the limit of an infinitely large lattice

Â with a -> 0.

Â This discretization introduces a lower limit on momentum-transfer

Â of the order of 1/a,

Â and thus regularizes the divergences inherent to pertulative QCD.

Â Numerical calculations of this kind require tremendous computing resources.

Â They are performed on the most powerful supercomputers.

Â With this non-perturbative method, one arrives, fo

Â example, at results for the spectrum of light hadrons.

Â The calculated masses are the average for the different particle types.

Â For instance, the mass of nucleon is the average of the mass of the proton and

Â the neutron.

Â Parameters of the calculation are the strong coupling constant, alpha_strong,

Â and the masses of light quarks up and down, and the quark strange.

Â They are fixed using the measured mass of pions, kaons and

Â Xi as reference.

Â This results in a pretty impressive understanding of

Â the hadron spectrum, suggesting that QCD is indeed a correct theory for

Â strong interaction also at larger distances.

Â Distance laws for electromagnetic and

Â strong interaction are fundamentally different.

Â The electromagnetic potential decreases as 1/r as a function of distance.

Â The strong potential increases at long distances proportional to r.

Â To understand this difference,

Â we must consider quantum correction to the photon and to the gluon propagators.

Â A significant correction to the photon propagator

Â is the one which introduces an electron-positron loop.

Â This loop creates additional electric charges between the projectile and target.

Â We call this phenomenon vacuum polarization.

Â In electrostatic language we can say that these additional

Â charges screen the target charge.

Â Therefore the effective charge decreases with distance.

Â 11:37

That is, it increases with growing momentum transfer q^2.

Â This is, indeed, what we find experimentally.

Â For electrodynamics, this is a small effect.

Â To see a change of alpha of a few percent, we have to compare momentum

Â transfer at almost zero that is at very large distances,

Â where alpha is measured to be about 1/137

Â â€“ see the example of the Penning trap in video 4.3 â€“

Â to the energy of the Large Electron Positron collider at CERN,

Â where the momentum transfer q^2 is around 10^4 GeV^2.

Â That is at very short distances.

Â 12:24

For strong interactions, the effect of vacuum polarisation is much more

Â pronounced. Because of the size of the strong coupling, the vacuum polarization

Â and the change in the net charge with distance are more important.

Â In addition, the sign of the effect is reversed.

Â The strong force becomes stronger with distance.

Â This is because there are two types of vacuum polarization graphs for gluons.

Â The analogue of electromagnetic polarization introduces quark-antiquark

Â loops in the gluon propagator which shield the colors charge.

Â But in addition, the coupling of gluons between them

Â introduces gluon loops which have the opposite sign.

Â And in the chromostatic language, we can say that the gluon loops

Â introduce additional color-anticolor charges which are attractive.

Â 13:35

Consequently, the color charge of the target increases with

Â distance proportional to the inverse of the momentum transfer.

Â Indeed one experimentally finds that this effect is

Â more significant than its electromagnetic counterpart.

Â In the next video we will see how these properties of strong

Â interaction keep us from seeing free quarks.

Â [MUSIC]

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