The Constituent Quark Models
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Transcript of The Constituent Quark Models
The Constituent Quark Models
Outline The Quark Model
Original Quark Model Additions to the Original Quark Model Color
Harmonic Potential Model
Isgur-Karl Model
M.I.T. Bag Model Assumptions Predictions
Constituent Quark Model(Non-relativistic)
Quasi–particles, have same quantum number like fundamental quarks of QCD: electric charge, baryon number, color, flavor and spin.
Bare quark dressed by clouds of quark-antiquark pairs and gluons. Mass is more than 300MeV, compared to bare quark about 10MeV. Allow treatment similar to nuclear shell model
Simpler: only three players ( for baryons ) while nuclei can have many nucleons.
Harder: more freedom, three colors, while nucleons are colorless three flavors, while nucleons only have neutrons and
protons.
Original Quark Model1964 The model was proposed independently by Gell-Mann and Zweig Three fundamental building blocks 1960’s (p,n,) 1970’s (u,d,s)
mesons are bound states of a of quark and anti-quark:Can make up "wave functions" by combining quarks:
+ = ud, - = du, o =12
(uu - d d), k+= ds, ko= ds
baryons are bound state of 3 quarks:proton = (uud), neutron = (udd), = (uds)
anti-baryons are bound states of 3 anti-quarks:
p u u d n u d d u d s
Λ= (uds))( ud
QuarksThese quark objects are:• point like• spin 1/2 fermions • parity = +1 (-1 for anti-quarks)• two quarks are in isospin doublet (u and d), s is an
iso-singlet (=0)• Obey Q = I3 +1/2(S+B) = I3 +Y/2• Group Structure is SU(3)• For every quark there is an anti-quark• The anti-quark has opposite charge, baryon number and strangeness• Quarks feel all interactions (have mass, electric charge, etc)
Early 1960’s QuarksSuccesses of 1960’s Quark Model: • Classify all known (in the early 1960’s) particles in terms of 3 building blocks• predict new particles (e.g. -)• explain why certain particles don’t exist (e.g. baryons with spin 1)• explain mass splitting between meson and baryons• explain/predict magnetic moments of mesons and baryons• explain/predict scattering cross sections (e.g. p/pp = 2/3)Failures of the 1960's model:• No evidence for free quarks (fixed up by QCD)• Pauli principle violated (++= (uuu) wave function is totally symmetric) (fixed up by color)• What holds quarks together in a proton ? (gluons! )• How many different types of quarks exist ? (6?)
Additions to the Original Quark Model – Charm Another quark was needed to account for
some discrepancies between predictions of the model and experimental results
Charm would be conserved in strong and electromagnetic interactions, but not in weak interactions
In 1974, a new meson, the J/Ψ was discovered that was shown to be a charm quark and charm antiquark pair
More Additions – Top and Bottom Discovery led to the need for a more elaborate
quark model This need led to the proposal of two new quarks
t – top (or truth) b – bottom (or beauty)
Added quantum numbers of topness and bottomness
Verification b quark was found in a meson in 1977 t quark was found in 1995 at Fermilab
Quantum Chromodynamics (QCD) QCD gave a new theory of how quarks interact with
each other by means of color charge The strong force between quarks is often called the
color force The strong force between quarks is carried by
gluons Gluons are massless particles There are 8 gluons, all with color charge
When a quark emits or absorbs a gluon, its color changes
Quantum Chromodynamics (QCD) Asymptotic freedom
Quarks move quasi-free inside the nucleon Perturbation theoretical tools can be applied in
this regime Quark confinement
No single free quark has been observed in experiments
Color force increases with increasing distance Chiral symmetry
Quark confinement Spatial confinement
Quarks cannot leave a certain region in space String confinement
The attractive( color singlet) quark-antiquark Color confinement
What Models do we have?
Harmonic Potential Model (for N and N* states, mu=md=m)
2( )2ij ijKV r r
1 2 3
1 2
1 2 3
1 ( )31 ( )2
1 ( 2 )6
R r r r
r r
r r r
R
λ
ρ
3
21
23
01
1 1( ) ( ) ( )2 2 2
ii ij ss ij
i ij iji
pH m V r V r
m
Solution of Harmonic Potential Model
2 2int 2 20
3 32 2 2 2p pK KHm m
0 0NE E N 03Km
N N N L l l ( 1)l lP
1 2 2 2
1 2 2 2
3 4 (3 ) ( ) 200 2
(3 ) ( ) 211 3 2
3( )
3 ( )
Km
Kmx y
Km e
Km i e
Spin-Spin Contact Interaction34( ) ( )
9i i
ss i j si j
V q q xc m m
3
, 1
3 for S=1/23 for S=3/2i i
i ji j
The three parametersms,d , αs|ψ(0)|2, ω0
are obtained by fitting to experimental data
32
3 2,
32
3 2,
43 (0) for N9
43 (0) for 9
s
u dss
s
u d
c mM
c m
Spectrum of low lying N and N* states
ms,d = 360MeV , ω0 =500MeV
Non-relativistic quark model with the salt of QCD
eg. Isgur-Karl Model
Start with a non-relativistic quark model with SU(3)xSU(2) spin-flavor symmetry.
SU(3) flavor breaking via quark mass difference.
(mu,d is not equal to ms).
Long range confining force independent of flavor and spin. Only one gluon exchange accounts for short range spin and flavor
dependent interaction.
(similar to electrodynamics of two slow moving fermions)
Isgur-Karl Model
No spin-orbit interaction, comparing to shell model Spin-spin contact interaction acts when L is zero Tensor interaction acts when L is Nonzero
232
01
33
( ) ( )2 2 4
3( )( )2 8 ( )3 3
i j hypi si ij ij
i i j i ji ij
i ij j ij i jhyp sij ij i j
i j ij
p KH m r Vm r
s r s r s sV r s s
m m r
Nstar Spectrum
M.I.T. Bag Model Developed in 1974 at
Massachusetts Institute of Technology
It models spatial confinement only
• Quarks are forced by a fixed external pressure to move only inside a given spatial region
• Quarks occupy single particle orbitals
• The shape of the bag is spherical, if all the quarks are in ground state
M.I.T Bag Model Inside the bag, quarks are allowed to move
quasi-free. An appropriate boundary condition at the bag
surface guarantees that no quark can leave the bag
This implies that there are no quarks outside the bag
M.I.T. Bag Model The boundary condition generates discrete
energy eigenvalues.
Rxn
n R - radius of the Bag
x1=2.04
BRRE
RxNRE
pot
nqkin
3
34)(
)(
Nq = # of quarks inside the bag
B – bag constant that reflects the bag pressure
M.I.T. Bag Model Minimizing E(R), one gets the equilibrium radius of
the system
4133
41
434
4
nqn
nqn
xBNE
BxN
R
Fixing the only parameter of the model B, by fitting the mass of the nucleon to 938MeV we have first order predictions
One gluon exchange Model so far excluded all interactions between the
quarks There should be some effective interaction that is
not contained in B( how do we know that?)
RM
E qsX
αs – the strong coupling constant
Mq depends on the quantum no. of the coupled quarks
Predictions
The masses of N, Δ, Ω, ω were used to fit the parameters.
Conclusions
The quark model classifies all known particles in terms of 6 building blocks Explains mass splitting between meson and baryons Explain/predict magnetic moments of mesons and baryons Explain/predict scattering cross sections
The MIT Bag Model predicts fairly accurate masses of the particles Explains color confinement Helps predict heavy quark spectrum
Simple models can give us a very good picture!
Bibliography Y. IWAMURA and Y. NOGAMI, IL NUOVO CIMENTO VOL. 89 A, N.
3(1985) Peter HASENFRATZ and Julius KUTI, PHYSICS REPORTS (Section C
of Physics Letters) 40, No. 2 (1978) 75-179. T. Barnes, arXiv:hep-ph/0406327v1 Carleton E. DeTar, John 12. Donoghue, Ann. Rev. Nucl. Part. Sci.
(1983) E. Eichten et al. , Phys. Rev. D, 203 (1980) E. Eichten et al. , Phys. Rev. Lett, 369 (1975) Stephan Hartmann, Models and Stories in Hadron Physics Theoretical papers
N. Isgur and G. Karl, Phys. Rev. D 18, 4187 (1978); 20, 1191 (1979). L. G. Landsberg, Phys. At. Nucl. 59, 2080 (1996). J.W. Darewych, M. Horbatsch, and R. Koniuk, Phys. Rev. D 28,1125 (1983). E. Kaxiras, E. J. Moniz, and M. Soyeur, Phys. Rev. D 32, 695 (1985).