Quarks

1
Quarks
Over the years inquiring minds have asked Can
we describe the known physics with just a few
building blocks ? Þ Historically the answer has
been yes. Elements of Mendeleevs Periodic Table
(chemistry) nucleus of atom made of protons,
neutrons proton and neutron really same
particle (different isotopic spin)
By 1950s there was evidence for many new
particles beyond g, e, p, n It was realized that
even these new particles fit certain
patterns pions p(140 MeV) p-(140
MeV) po(135 MeV) kaons k(496 MeV) k-(496
MeV) ko(498 MeV)
Some sort of pattern was emerging, but
........... lots of questions Þ If mass
difference between proton neutrons, pions, and
kaons is due to electromagnetism then how
come Mn gt Mp and Mko gt Mk but Mp gt Mpo
Lots of models concocted to try to explain why
these particles exist Þ Model of Fermi and Yang
(late 1940s-early 50s) pion is composed of
nucleons and anti-nucleons (used SU(2) symmetry)
note this model was proposed before discovery of
anti-proton !
With the discovery of new unstable particles (L,
k) a new quantum number was invented Þ
strangeness
2
Quarks
Gell-Mann, Nakano, Nishijima realized that
electric charge (Q) of all particles could be
related to isospin (3rd component), Baryon number
(B) and Strangeness (S) Q I3 (S B)/2 I3
Y/2 Coin the name hypercharge (Y) for (SB)
Interesting patterns started to emerge when I3
was plotted vs. Y
Particle Model of Sakata (mid 50s) used Q
I3 (S B)/2 assumed that all particles could
be made from a combination of p,n, L tried to
use SU(3) symmetry In this model
This model obeys Fermi statistics and explains
why Mn gt Mp and Mko gt Mk and Mp gt Mpo
Unfortunately, the model had major problems.
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Quarks
Problems with Sakatas Model Why should the p,
n, and L be the fundamental objects ? why not
pions and/or kaons This model did not have the
proper group structure for SU(3) What do we
mean by group structure ? SU(n) (nxn) Unitary
matrices (MTM1) with determinant 1
(Special) and nsimplest non-trivial matrix
representation
Example With 2 fundamental objects obeying SU(2)
(e.g. n and p) We can combine these objects
using 1 quantum number (e.g. isospin) Get 3
Isospin 1 states that are symmetric under
interchange of n and p
11gt 1/2 1/2gt 1/2 1/2gt 1-1gt 1/2 -1/2gt
1/2 -1/2gt 10gt 1/Ö2(1/2 1/2gt 1/2 -1/2gt
1/2 -1/2gt 1/2 1/2gt) Get 1 Isospin state that is
anti-symmetric under interchange of n and
p 00gt 1/Ö2(1/2 1/2gt 1/2 -1/2gt - 1/2
-1/2gt 1/2 1/2gt) In group theory we have 2
multiplets, a 3 and a 1 2 Ä 2 3 Å1 Back to
Sakata's model For SU(3) there are 2 quantum
numbers and the group structure is more
complicated 3 Ä 3 Ä 3 1 Å 8 Å 8 Å
10 Expect 4 multiplets (groups of similar
particles) with either 1, 8, or 10
members. Sakatas model said that the p, n, and L
were a multiplet which does not fit into the
above scheme of known particles! (e.g. could not
account for So, S)
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Early 1960s Quarks
Three Quarks for Muster Mark, J. Joyce,
Finnegans Wake Model was developed by
Gell-Mann, Zweig, Okubo, and Neeman
(Salam) Three fundamental building blocks 1960s
(p,n,l) Þ 1970s (u,d,s) mesons are bound states
of a of quark and anti-quark Can make up
"wavefunctions" by combing quarks
baryons are bound state of 3 quarks proton
(uud), neutron (udd), L (uds) anti-baryons
are bound states of 3 anti-quarks
These 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(SB) I3 Y/2 Group Structure is
SU(3) For every quark there is an
anti-quark quarks feel all interactions (have
mass, electric charge, etc)
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Early 1960s Quarks
The additive quark quantum numbers are given
below Quantum u d s c b t electric
charge 2/3 -1/3 -1/3 2/3 -1/3 2/3 I3 1/2 -1/2 0
0 0 0 Strangeness 0 0 -1 0 0 0 Charm 0 0 0 1 0 0
bottom 0 0 0 0 -1 0 top 0 0 0 0 0 1 Baryon
number 1/3 1/3 1/3 1/3 1/3 1/3 Lepton
number 0 0 0 0 0 0
Successes of 1960s Quark Model Classify all
known (in the early 1960s) particles in terms of
3 building blocks predict new particles (e.g.
W-) explain why certain particles dont exist
(e.g. baryons with S 1) explain mass
splitting between meson and baryons explain/predi
ct magnetic moments of mesons and
baryons explain/predict scattering cross
sections (e.g. spp/spp 2/3) Failures of the
1960's model No evidence for free quarks (fixed
up by QCD) Pauli principle violated (D uuu
wavefunction is totally symmetric) (fixed up by
color) What holds quarks together in a
proton ? (gluons!) How many different
types of quarks exist ? (6?)
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Dynamic Quarks
Dynamic Quark Model (mid 70s to now!) Theory of
quark-quark interaction Þ QCD includes
gluons Successes of Quark Model (QCD) Real
Field Theory i.e. Gluons instead of
photons Color instead of electric
charge explains why no free quarks Þ confinement
of quarks calculate lifetimes of baryons,
mesons Failures/problems of the model Hard to
do calculations in QCD (non-perturbative)
Polarization of hadrons (e.g. Ls) in high
energy collisions How many quarks are there ?
Historical note Original quark model assumed
approximate SU(3) for the quarks. Once charm
quark was discovered SU(4) was considered.
But SU(4) is a badly broken symmetry. Standard
Model puts quarks in SU(2) doublet, COLOR
exact SU(3) symmetry.
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From Quarks to Particles
How do we "construct" baryons and mesons from
quarks ? Use SU(3) as the group (1960s
model) This group has 8 generators (n2-1,
n3) Each generator is a 3x3 linearly independent
traceless hermitian matrices Only 2 of the
generators are diagonal Þ 2 quantum
numbers Hypercharge Strangeness Baryon
number Y Isospin (I3) In this model (1960s)
there are 3 quarks, which are the eigenvectors (3
row column vector) of the two diagonal
generators (Y and I3) Baryons are made up of a
bound state of 3 quarks Mesons are a
quark-antiquark bound state The quarks are added
together to form mesons and baryons using the
rules of SU(3).
MS P133-140
It is interesting to plot Y vs. I3 for quarks and
anti-quarks
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Making Mesons with Quarks
Making mesons with (orbital angular momentum
L0) The properties of SU(3) tell us how many
mesons to expect
Thus we expect an octet with 8 particles and a
singlet with 1 particle.
If SU(3) were a perfect symmetry then all
particles in a multiplet would have the same
mass.
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Baryon Octet
Making Baryons (orbital angular momentum
L0). Now must combine 3 quarks together
Expect a singlet, 2 octets, and a decuplet (10
particles) Þ 27 objects total. Octet with J1/2
10
Baryon Decuplet
Baryon Decuplet (J3/2) Expect 10
states. Prediction of the W- (mass 1672 MeV/c2,
S-3) Use bubble chamber to find the event. 1969
Nobel Prize to Gell-Mann!
Observation of a hyperon with strangeness minus
3 PRL V12, 1964.
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Quarks and Vector Mesons
Leptonic Decays of Vector Mesons What is the
experimental evidence that quarks have
non-integer charge ? Þ Both the mass splitting of
baryons and mesons and baryon magnetic moments
depend on (e/m) not e.   Some quark models with
integer charge quarks (e.g. Han-Nambu) were also
successful in explaining mass patterns of mesons
and baryons. Need a quantity that can be measured
that depends only on electric charge !   Consider
the vector mesons (Vr, w, f, y, U)
quark-antiquark bound states with mass ¹
0 electric charge 0 orbital angular
momentum (L) 0 spin 1 charge parity (C)
-1 parity -1 strangeness charm
bottomtop 0 These particles have the same
quantum numbers as the photon.
The vector mesons can be produced by its
coupling to a photon ee- g V e.g. ee-
g Y(1S) or y The vector mesons can decay by
its coupling to a photon V g ee- e.g. r
g ee- (BR6x10-5) or yg ee- (BR6.3x10-2)
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Quarks and Vector Mesons
The decay rate (or partial width) for a vector
meson to decay to leptons is
The Van Royen- Weisskopf Formula
In the above MV is the mass of the vector meson,
the sum is over the amplitudes that make up the
meson, Q is the charge of the quarks and y(0) is
the wavefunction for the two quarks to overlap
each other.
SaiQi2
GL(exp) SaiQi-2
meson
quarks
GL(exp)
If we assume that y(o)2/M2 is the same for r,
w, f, (good assumption since masses are 770 MeV,
780 MeV, and 1020 MeV respectively)
then expect GL(r) GL(w) GL(f) 9 1
2 measure (8.8 2.6) 1 (1.7
0.4) Good agreement!