Structure of Hadrons. gluons. gluons

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Cameron Beasley
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1 gluons Gluons are the exchange particles which couple to the color charge. They carry simultaneously color and anticolor. What is the total number of gluons? According to SU 3, 3x3 color combinations 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 anticolors is a matter of convention. 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-definition of the color names (rotation in color space). Therefore, it has no effect in color space and cannot be exchanged between color charges. emission of a gluon by a uark Æ + g splitting of a gluon into a uarkantiuark pair g Æ + self-coupling of gluons g Æ g + g g + g Æ g + g

2 Hadrons as color neutral objects red antigreen antiblue blue green antired meson baryon p + = Ï Ô Ì Ô Ó u R d R u B d B u G d G Meson can exist in three different color combinations. The actual pion is a mixture of these color states. By exchange of gluons, the color combination continuously changes. g b g r bg g b r g g b g r

3 First, QED Lagrangian QCD Lagrangian L QED = F F mn mn -y e g m [ m + iea m ]y e - m e y e y e F mn = m A n - n A m A m g m y e EM field tensor four potential of the photon field Dirac 4x4 matrices Dirac four-spinor of the electron field e = 4pa, 1/a ª137, h = c =1 Now, QCD Lagrangian L QCD = G a mng mn a - n f Ây n g m [ m - igg a m t a ]y n -Âm n y n y n n=1 G a mn = m G a n - n G a m - gf abg G b m G g n G a m t a f abg y n g = 4pa s (h = c =1) n f n=1 color fields tensor four potential of the gluon fields (a=1,..8) 3x3 matrices; generators of the SU 3 color group structure constants of the SU 3 color group Dirac four-spinor of the uark field (n=1,..6) color charge

4 strong coupling constant In uantum field theory, the coupling constant is an effective constant, which depends on four-momentum Q 2 transferred. For strong interactions, the Q 2 dependence is very strong (gluons - as the field uanta - carry color and they can couple to other gluons). A first-order perturbative QCD calculation (valid at very large Q 2 ) gives ( ) = a s Q 2 running coupling constant! 12p ( 22-2n f ) ln Q 2 2 / L QCD number of uark flavors ~3-6 ( ) free parameter in QCD ( GeV) The spatial separation between uarks goes as D = h Q 2 Therefore, for very small distances and high values of Q 2, the interuark coupling decreases, vanishing asymptotically. In the limit of very large Q 2, uarks can be considered to be free (asymptotic freedom). On the other hand, at large distances, the interuark coupling increases so it is impossible to detach individual uarks from hadrons (confinement).

5 strong coupling constant (cont.) Michael Schmelling, hep-ex/ (theoretical prediction)

QCD vacuum http://www.physics.adelaide.edu.au/theory/staff/leinweber/visualqcd/qcdvacuum/ The uantum fluctuations of the QCD vacuum.

6 QCD vacuum The uantum fluctuations of the QCD vacuum. The images have been created via supercomputer simulations of QCD on a 24 3 x 36 space-time lattice using a 128-node Thinking Machines CM5 (D.B. Leinweber, Adelaide) According to the Standard Model, all space is filled with the QCD condensate. The interaction of particles with this background condensate gives rise to most of the mass that makes up ordinary hadronic matter. The computer simulation shown here is a snapshot of the gluon field that binds uarks together to make up particles such as protons and neutrons. The red color indicates areas of intense action in the gluon field, associated with winding of the field lines. The green and blue colors correspond to weaker gluon field strengths.

7 ñ0.5 Structure of Hadrons Fields of Color linear region V = kr (k =16 T) Lattice measurement of the uenched static potential Bali et al r (fm) mesons flux tubes/strings energy: Regge trajectories (suggested by Nambu 1970)

Structure of Hadrons Structure of the proton http://www.physics.adelaide.edu.

8 Structure of Hadrons Structure of the proton Three uarks indicated by red, green and blue spheres (lower left) are localized by the gluon field. A uark-antiuark pair created from the gluon field is illustrated by the green-antigreen (magenta) uark pair on the right. These uark pairs give rise to a meson cloud around the proton. The masses of the uarks illustrated in this diagram account for only 3% of the proton mass. The gluon field is responsible for the remaining 97% of the proton's mass and is the origin of mass in most everything around us. Experimentalists probe the structure of the proton by scattering electrons (white line) off uarks which interact by exchanging a photon (wavy line).

9 THE NUCLEON cm Inside the nucleon. Within the theory of QCD, the nucleon has a complex internal structure, consisting of three valence uarks (large dots), which are continually interacting by the exchange of gluons (depicted as springs in this schematic picture). In contrast to the photons that are exchanged between electric charges, gluons interact not only with the valence uarks, but also with each other, creating and destroying gluons and uark-antiuark pairs (small dots).

QCD Lagrangian. ψ qi. δ ij. ψ i L QCD. m q. = ψ qi. G α µν = µ G α ν ν G α µ gf αβγ G β µ G γ. G α t α f αβγ. g = 4πα s. (!

QCD Lagrangian. ψ qi. δ ij. ψ i L QCD. m q. = ψ qi. G α µν = µ G α ν ν G α µ gf αβγ G β µ G γ. G α t α f αβγ. g = 4πα s. (! QCD Lagrangian L QCD = ψ qi iγ µ! δ ij µ + ig G α µ t $ "# α %& ψ qj m q ψ qi ψ qi 1 4 G µν q ( ( ) ) ij L QED = ψ e iγ µ!" µ + iea µ # $ ψ e m e ψ e ψ e 1 4 F F µν µν α G α µν G α µν = µ G α ν ν G α µ