Structure of Hadrons quarks

1. Structure of Hadrons quarks Hadrons baryons mesons fermions made up of three quarks must have half-integer spins bosons made up of quark-antiquarks* must have integer spins estimates based on properties of hadrons! • the least massive are u- and d-quarks (hence the lightest baryons and mesons must be made exclusively of these two quarks) • strange quark carries a quantum number called strangeness S. Strange particles (such as kaons) carry this quark • there are also six antiquarks • they are fermions; they carry half-integer spins * Bosons can be annihilated; strong interactions conserve the # of quarks

2. Structure of Hadrons antiparticles particle-antiparticle annihilation • particle and antiparticle have opposite charges, baryon numbers, etc. • they must have opposite intrinsic parities • they must have opposite isospins baryon number charge number third component of isospin Charge conjugation transforms particles into antiparticles particles antiparticles Particles into antiparticles are not independent of each other; they transform into each other through charge conjugation! the same relation holds for quarks

3. Structure of Hadrons isospin of quarks d- and u-quarks form an isospin doublet quark wave functions of pions Consider p- (t=1 and t0=1). The only possible combination is In general, it is possible to find several linearly independent components corresponding to the same t and t0. The appropriate combination is given by isospin coupling rules. Furthermore, the wave function must be antisymmetric among the quarks T=1 triplet What about the symmetric combination? T=0 singlet To produce heavier mesons we have to introduce excitations in the quark-antiquark system or invoke s- and other more massive quarks

4. Structure of Hadrons strange mesons The lightest strange mesons are kaons or K-mesons. They come in two doublets with t=1/2: This means that s-quark has zero isospin (no strange mesons with t=3/2 have been seen), generalization strangeness is conserved! 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!).

5. Structure of Hadrons color Consider a D-particle. It has isospin 3/2 with four different charge states: Since it is nonstrange baryon, is has to be made of u- and d-quarks. D++ has Q=2 and the only possiblity is a (uuu) combination. The intrinsic parity of D++ is known to be positive, its intrinsic spin is 3/2, and isospin is also 3/2. How to get the wave function that is untisymmetric with respect to a permutation of any two of the three quarks? Is Pauli wrong? Color saves the day. It is a property of quarks. There are three colors: R (red), G (green) and B (blue). The wave function has to be antisymmetric in the color degree of freedom: the net color in hadron must vanish! Since color is an unobserved property, all hadrons must be colorless oblects!

6. Structure of Hadrons static quark model of hadrons pseudoscalar mesons S can be either 0 or 1. The mesons with the relative zero orbital angular momentum are lower in energy. For the pion, S=0, hence J=0. Consequently, pions are “scalar” particles. But what about their parity? The parity of the pion is a product of intrinsic parities of the quark (+1), antiquark (-1) and the parity of the spatial wave function (-1)l=+1. Hance the pion has negative parity. It is a pseudoscalar meson. With (u,d,s) quarks, one can construct 9 pseudoscalar mesons: 9=8 (octet)+1 (singlet) Members of the octet transform into each other under rotations in flavor space (SU3 group!). The remaining meson, h0, forms a 1-dim irrep. 497.67 493.67 134.98 547.45 139.57 957.77 I3 =I0=-T0 High-energy physics nuclear physics masses are given in MeV/c2

7. Structure of Hadrons static quark model of hadrons In reality, since the SU3 (flavor) symmetry is not exact one, the observed mesons are: J Cabibbo angle, ~10o for pseudoscalar mesons vector mesons Here S=1, hence J=1. This implies negative parity. The vector mesons are more massive than their pseudoscalar counterparts, reflecting the differences in the interaction between a quark and an antiquark in the S=0 and S=1 states. 891.6 1019.4 768.5 781.9 masses are given in MeV/c2

8. Structure of Hadrons static quark model of hadrons baryons With three flavors, one can construct a total of 3x3x3=27 baryons for a given set of (l,S)-values. 27=10+8+8+1 baryon singlet Completely asymmetric under a transformation in flavor baryon decuplet Completely symmetric under a transformation in flavor

9. Structure of Hadrons static quark model of hadrons baryon octet The remaining 16 members of the 27 possible baryons constructed from u-, s-, and d-quarks have mixed symmetry in flavor. The lower energy octet contains protons and neutrons as its members. The wave functions for each member in the group is symmetric under the combined exchange of flavor and intrinsic spin (the quarks are antisymmetric in color!) 939.6 938.3 1115.7 1197.4 1192.5 1189.4 masses are given in MeV/c2 1321.3 1314.9 example: proton wave function In order to get the neutron wave function, one has to substitute all the u-quarks by d-quarks and vice versa.

10. Structure of Hadrons magnetic dipole moments of the baryon octet The magnetic dipole moment of a baryon comes from two sources: the intrinsic dipole moment of the constituent quarks and the orbital motion of the quarks. For the baryon octet, l=0. For Dirac particles (I.e., particles devoid of internal structure), g=2 for s=1/2. Unfortunately, we do not know quark masses. Assuming that the masses of u- and d-quarks are equal, one obtains: Consider the proton wave function written in terms of u- and d-quarks. The net contribution from u-quarks is 4/3 and that from d-quarks is -1/3. Hence By the same token This gives (=-0.685 experimentally) quark magnetic moments

11. Structure of Hadrons 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 SU3, 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: The color singlet: 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 quark splitting of a gluon into a quark-antiquark pair self-coupling of gluons

12. Structure of Hadrons Hadrons as color neutral objects _ _ b b _ g g b _ g r _ _ _ r g g red antigreen antiblue blue green antired baryon meson g b 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. r

13. Structure of Hadrons QCD Lagrangian First, QED Lagrangian… EM field tensor four potential of the photon field Dirac 4x4 matrices Dirac four-spinor of the electron field Now, QCD Lagrangian… color fields tensor four potential of the gluon fields (a=1,..8) 3x3 matrices; generators of the SU3 color group structure constants of the SU3 color group Dirac four-spinor of the quark field (n=1,..6) color charge

14. Structure of Hadrons strong coupling constant In quantum field theory, the coupling constant is an effective constant, which depends on four-momentum Q2 transferred. For strong interactions, the Q2 dependenceis very strong (gluons - as the field quanta - carry color and they can couple to other gluons). A first-order perturbative QCD calculation (valid at very large Q2) gives running coupling constant! free parameter in QCD (0.1-0.5 GeV) number of quark flavors ~3-6 The spatial separation between quarks goes as Therefore, for very small distances and high values of Q2, the interquark coupling decreases, vanishing asymptotically. In the limit of very large Q2, quarks can be considered to be “free” (asymptotic freedom). On the other hand, at large distances, the interquark coupling increases so it is impossible to detach individual quarks from hadrons (confinement).

15. Structure of Hadrons strong coupling constant (cont.) Michael Schmelling, hep-ex/9701002 (theoretical prediction)

16. Structure of Hadrons QCD vacuum http://www.physics.adelaide.edu.au/theory/staff/leinweber/VisualQCD/QCDvacuum/ The quantum fluctuations of the QCD vacuum. The images have been created via supercomputer simulations of QCD on a 243 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 quarks 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.

17. Structure of Hadrons Fields of Color linear region Lattice “measurement” of the quenched static potential Bali et al. Regge trajectories (suggested by Nambu 1970) flux tubes/strings

18. Structure of Hadrons Structure of the proton http://www.physics.adelaide.edu.au/theory/staff/leinweber/VisualQCD/QCDvacuum/ • Three quarks indicated by red, green and blue spheres (lower left) are localized by the gluon field. • A quark-antiquark pair created from the gluon field is illustrated by the green-antigreen (magenta) quark pair on the right. These quark pairs give rise to a meson cloud around the proton. • The masses of the quarks 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 quarks which interact by exchanging a photon (wavy line).

19. Structure of Hadrons Probing proton’s spin How do the proton’s various constituents contribute to its overall spin? As illustrated by the diagram, the quarks, antiquarks, and gluons are all believed to have their own intrinsic spins, and these must contribute. But so also must the relative orbital motions of the quarks and gluons inside the proton. The first measurements of the proton’s spin substructure have been made recently, employing the technique of deep inelastic scattering with spin-polarized beams bombarding spin-polarized targets. By combining these measurements with constraints from other data, one can infer the fraction of the proton’s spin carried by the intrinsic spin of quarks (and antiquarks) of different flavors. The results of experiments performed at CERN, SLAC, and DESY, summarized in the graph, point to an unexpected outcome: all the quarks and antiquarks together account for no more than one-third of the total spin. More direct probes of the spin alignment of different flavors of quarks, separation of the contributions from quarks and antiquarks, and extraction of information on the gluon spin contributions are goals of ongoing and planned second-generation experiments.

20. Structure of Hadrons Probing charge form-factors Although the neutron and proton are equally important in building nuclei, the quality of experimental information available about their internal structure has been vastly different, because one cannot make a target of free neutrons. For example, the graphs here compare what we know from electron-scattering experiments about the amount of electric charge per unit radial distance from the center of a neutron (on the left) versus a proton. The width of the blue band for the neutron and of the curve for the proton indicate the approximate level of uncertainty in the currently available experimental information. The crude data for the neutron suggest that smaller charged particles do indeed reside inside, with positive charges preponderant near the center and negative charges near the periphery, but provide little additional constraint on nucleon structure calculations. Our knowledge of the neutron will be brought closer to a par with the proton (as suggested by the yellow band on the left) by a new series of experiments, made possible by the advent of continuous-beam electron accelerators and by advances in the technology for measurements of spin polarization.

21. Structure of Hadrons Origin of the nucleon-nucleon force The simplest contributions to the force between nucleons, as viewed from (a) QCD and (b) conventional nuclear theory. In (a), the exchange of two colored gluons causes two quarks in each nucleon to change their colors (blue changes to green and vice versa in the case illustrated). This process produces a force without violating the overall color neutrality of the nucleons. The strength of the force depends on the separation of the different quark colors within each nucleon. On the other hand, low-energy nuclear physics measurements show clearly that the longest-range part of the force arises from the exchange of a single pi meson between two nucleons, as in (b). In this low-energy view, the internal structure of each nucleon is generally attributed to three pseudo-quarks, which somehow combine the properties of the valence quarks, sea quarks, and gluons predicted by QCD.