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Color, Gluons Gluons Are the Exchange ParCles Which Couple to the Color Charge

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Color, Gluons Gluons Are the Exchange Par�Cles Which Couple to the Color Charge Color, Gluons Gluons are the exchange par1cles which couple to the color charge . They carry simultaneously color and an1color. red antigreen antiblue blue green antired What is the total number of gluons? according to SU3, 3x3 color combinaons form a singlet and an octet. The octet states form a basis from which all other color states can be constructed. The way in which these eight states are constructed from colors and an1colors is a maer of conven1on. One possible choice is: RG , RB , GB , GR , BR , BG , 1/ 2 ( RR − GG ), 1/ 6 ( RR + GG − 2 BB ) The color singlet: 1/ 3( RR + GG + BB ) is invariant with respect of a re-defini1on of the color names (rotaon in color space). Therefore, it has no effect in color space and cannot be exchanged between color charges. emission of a gluon splitting of a gluon self-coupling of gluons by a quark into a quark-antiquark pair q → q + g g → q + q g → g + g g + g → g + g hEp://www.par1clezoo.net/shop.html hp://commons.wikimedia.org/wiki/File:Neutron_QCD_Animaon.gif meson baryon _ _ ! g g u d b g # R R + # _ π = " uBdB # b _ b # u d g b $ G G _ g Meson can exist in three different color g combinaons. The actual pion is a mixture of _ _ these color states. By exchange of gluons, the r g r color combinaon con1nuously changes. r QCD vacuum In QED vacuum polarizaon effects are extremely weak, because the electron has a small charge and a non-zero rest mass. On the other hand, the QCD gluons are massless, and their strong interac1on is not damped by a small parameter. as a result, the QCD vacuum polarizaon effect is extremely strong, and the empty space is not empty at all - it must contain a soup of spontaneously appearing, interac1ng, and disappearing gluons. Moreover, in the soup there also must be pairs of virtual quark-an1quark pairs that are also color-charged, and emit and absorb more virtual gluons. It turns out that the QCD ground state of an “empty” space is extremely complicated. at present, we do not have any glimpse of a possibility to find the vacuum wave func1on analy1cally. Some ideas of what happens are provided by the QCD lace calculaons, in which the gluon and quark fields are discre1zed on a four-dimensional lace of space-1me points, and the differen1al field equaons are transformed into finite-difference equaons solvable on a computer. hEp://www.physics.adelaide.edu.au/theory/staff/leinweber/VisualQCD/Nobel/index.html The typical four-dimensional structure of gluon-field configuraons averaged over in describing the vacuum proper1es of QCD. The volume of the box is 2.4 by 2.4 by 3.6 fm, big enough to hold a couple of protons. • Three quarks indicated by red, green and blue spheres (lower leb) are localized by the gluon field. • a quark-an1quark pair created from the gluon field is illustrated by the green-an1green (magenta) quark pair on the right. These quark pairs give rise to a meson cloud around the proton. hEp://www.physics.adelaide.edu.au/theory/staff/leinweber/VisualQCD/Nobel/index.html The posi1ons of the three quarks composing the proton are illustrated by the colored spheres. The surface plot illustrates the reduc1on of the vacuum ac1on density in a plane passing through the centers of the quarks. The vector field illustrates the gradient of this reduc1on. The posi1ons in space where the vacuum ac1on is maximally expelled from the interior of the proton are also illustrated by the tube-like structures, exposing the presence of flux tubes. a key point of interest is the distance at which the flux-tube formaon occurs. The animaon indicates that the transi1on to flux-tube formaon occurs when the distance of the quarks from the center of the triangle is greater than 0.5 fm. again, the diameter of the flux tubes remains approximately constant as the quarks move to large separaons. Quarks In 1968, deep inelasc scaering experiments at the Stanford Linear accelerator Center showed that the proton contained much smaller, point-like objects and was therefore not an elementary par1cle 2 Flavor A t tz S C B T Q(e) Mc (GeV) u (up) 1 1 1 0 0 0 0 2 0.002 0.003 3 2 − 2 + 3 − d (down) 1 1 1 0 0 0 0 1 0.004 0.006 3 2 + 2 − 3 − s (strange) 1 0 0 1 0 0 0 1 0.08 0.13 3 − − 3 − c (charm) 1 0 0 0 1 0 0 2 1.2 1.3 3 + 3 − b (bottom) 1 0 0 0 0 1 0 1 4.1 4.3 3 − − 3 − t (top) 1 0 0 0 0 0 1 2 173 1 3 + 3 ± • The least massive are u- and d-quarks (hence the lightest baryons and mesons are made exclusively of these two quarks) • Each quark has baryon number A=1/3. • Strange quark carries a quantum number called strangeness S. Strange particles (such as kaons) carry this quark • Six antiquarks complement the list • Quarks are all fermions; they carry half-integer spins • d- and u-quarks form an isospin doublet τ + u = d τ − d = u • Strong interactions conserve the total number of each type of quarks. However, quarks can be transformed from one flavor to another through weak interactions (CKM matrix!). Nucl. Phys. A750, 84 (2005) 1000000 QCD mass 100000 Higgs mass 10000 1000 100 Mass (MeV) 10 1 u d s c b t GeV HOW does the rest of the proton mass arise? HOW does the rest of the proton spin (magnetic moment,…), arise? Mass from nothing Dyson-Schwinger and Lattice QCD It is known that the dynamical chiral symmetry breaking; namely, the generation of mass from nothing, does take place in QCD. It arises primarily because a dense cloud of gluons comes to clothe a low- momentum quark. The vast bulk of the constituent-mass of a light quark is contained in a cloud of gluons, which are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies acquires a large constituent mass at low energies. Chiral symmetry For massless quarks, QCD Lagrangian preserves helicity. Indeed, since a massless quark travels at the speed of light, the handedness or chirality of the quark is independent of any Lorentz frame from which the observaon is made. L = L (ψ )+L (ψ ) the QCD interaction does not couple the QCD QCD L QCD R left and right-handed quarks The mass term explicitly breaks the chiral symmetry as: mqψqψq = mqψqLψqR + mqψqRψqL The main origin of the chiral symmetry breaking, however, may be described in terms of the fermion condensate (vacuum condensate of bilinear expressions involving the quarks in the QCD vacuum) formed through nonperturbative action of QCD gluons. Spontaneous symmetry breaking due to the strong low-energy QCD dynamics, which rearranges the QCD vacuum: 3 ψqLψqR ∝ ΛQCD ≠ 0 Spontaneous Symmetry Breaking (SSB) I SSB is associated with the observance of massless excitaons called Goldstone bosons. (In prac8ce, they may be merely unusually light rather than massless if there is also explicit symmetry breaking; this is the case for pions.) The case of the ferromagnet with spins is easiest to visualize. Imagine a lace of spins at high temperatures, which fluctuate in direc8on such that the net magne8zaon is always zero. The Hamiltonian for this system respects rotaonal symmetry: there is no preferred direc8on. However, the lowest energy configuraon would In this case, there is s8ll rotaonal symmetry have all spins pointed in the same direc8on. But about the axis of the direc8on picked out. what direc8on? All possible choices are degenerate Now think of the lowest energy excitaons. in energy. If we cool the system from a high If we imagine a long wavelength quan8zed temperature, below a cri8cal temperature, one spin wave, in which the direc8on of the spin direc8on will be picked out. This is spontaneous changes very slowly, then within the symmetry breaking: the vacuum (ground state) of wavelength, the energy of the excitaon is the system breaks the symmetry of the Hamiltonian, near zero, because they are simply spins at least in part. poin8ng in another direc8on. Spontaneous Symmetry Breaking (SSB) II The more formal way to think of this is in terms of an effec8ve poten8al, e.g., for a scalar field, which tells us about possible ground states for a field theory. The Mexican hat poten8al shown above manifests SSB. All choices in the boPom of the valley have the same energy. But one is picked out in the vacuum --- this is spontaneously symmetry breaking. But then low-lying excitaons in the original symmetry direc8on cost very liPle. Therefore SSB leads to massless Goldstone bosons. Light pions are the Goldstone bosons of chiral symmetry breaking in QCD. Low-lying Hadron Spectrum Dürr, Fodor, Lippert et al., BMW Collaboration Science 322, 1224 (2008) More than 99% of the mass of the visible universe is made up of protons and neutrons. Both particles are much heavier than their quark and gluon constituents, and the Standard Model of particle physics should explain this difference. We present a full ab initio calculation of the masses of protons, neutrons, and other light hadrons, using lattice quantum chromodynamics. Pion masses down to 190 mega–electron volts are used to extrapolate to the physical point, with lattice sizes of approximately four times the inverse pion mass.
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