The Static Quark Model The Piedra del Sol, an aztec monolith, located a the Museo Nacional de Antropologia of Mexico City, is also called «TheTenochtitlan Stone". It has a circular shape with 3.6 m diameter and a weight of 25 tons. It was discovered in 1790 below the south side of the Main Square of Mexico City (the "Zocalo"). The Piedra del Sol has a strongly symbolic meaning, centered around the Sun figure, center of the Stone and of the Universe, Mediator between Mankind and the Heavens. 1 1. Costituents of Matter 2. Fundamental Forces 3. Particle Detectors 4. Symmetries and Conservation Laws 5. Relativistic Kinematics 6. The Static Quark Model 7. The Weak Interaction 8. Introduction to the Standard Model 9. CP Violation in the Standard Model (N. Neri)
Transcript
The Static Quark Model
The Piedra del Sol, an aztec monolith, located a the Museo Nacional de Antropologia of Mexico City, is also called «TheTenochtitlan Stone". It has a circular shape with 3.6 m diameter and a weight of 25 tons. It was discovered in 1790 below the south side of the Main Square of Mexico City (the "Zocalo").
The Piedra del Sol has a strongly symbolic meaning, centered around the Sun figure, center of the Stone and of the Universe, Mediator between Mankind and the Heavens.
1
1. Costituents of Matter2. Fundamental Forces3. Particle Detectors 4. Symmetries and Conservation Laws5. Relativistic Kinematics6. The Static Quark Model7. The Weak Interaction8. Introduction to the Standard Model9. CP Violation in the Standard Model (N. Neri)
Starting point: the discovery of many particles, both baryons and mesons.Regularities are interpreted in terms of combination of Quarks.
The Quark hypotesis was put forward in 1964 by Gell-Mann and Zweig
From the dynamic viewpoint:
- Parton Model - Deep Inelastic Scattering test
--> Partons = Quarks
Classification based on regularities and an underlying (approximate) SU(3) symmetry
2
Flavor
B J I I3 S Q
u 1/3
½ 1/2 +1/2
0 2/3
d 1/3
½ ½ -1/2 0 -1/3
s 1/3
1/2 0 0 -1 -1/3
Three quarks are used to classify all hadrons
3
The Elementary Particles Zoo
The rate of discovery of new particles increased dramatically after 1945
The proliferation concerned the strongly interacting particles (hadrons).
4
Evidence of internal structure also from the magnetic moment of particles
There is plenty of evidence for hadrons that are not fundamental
5
General idea of an underlying symmetry. Subdivide strongly interacting particles (Hadrons) in Mesons (quark-antiquark
states) and Baryons (3-quarks combinations). States are grouped in isotopic spin multiples. Different multiplets have different strangeness. Isotopic spin multiples contain states that are equivalent with respect to the
Strong Interaction. Inside an isospin multiplet, different I(3) values correspond to different states
(rotational symmetry in Isospin space). Degeneracy in a multiplet is removed by the Electromagnetic Interaction.
Proposal by Gell-Mann and Ne’emann (1961) SU(3) as the symmetry group
SU(3) flavor : three light quarks to explain all the observed hadronic states
Mesons: 1 quark and 1 antiquarkBaryons: 3 quarks
(The «Eightfold Way»)
How to classify strongly interacting particles ?
The Baryon Decuplet
The ten lowest lying baryon states having JP = 3/2+
6
3I
S0
1
2
3
2/31 2/1 2/1 2/31
dddddu duu
uuu
dds uusdus
dss uss
sss
4-plet of Isospin
3-plet of Isospin S = -1
Doublet of Isospin S = -2
Singlet of Isospin S = -3
7
3I
S0
1
2
3
2/31 2/1 2/1 2/31
0
* *0*
* 0*
I = 3/2
I = 1
I = 1/2
I = 0
The mass difference between I-spin multiplet members are of the order of a few MeV this is typical of electromagnetic mass differences.
)1232(
)1384(
)1533(
)1672(
152 MeV
149 MeV
139 MeV
An additional s quark typically entails an increase of mass of about 145 MeV
8
Can we conclude about the mass difference between an s and an u,d ?
MeVsm
MeVdm
MeVum
150)(
5)(
3)(
MeVdmumumuudM p 938)()()()(
Reasonable values for the naked quark masses
For a proton :
MeV10
MeVdmsmumusdM 1116)()()()( For a Lambda:
Assuming p
MeVumsm 178)9381116()()(
9
0KKpK
0
0
p
This Quark Model allowed to predict the existence of the Ω baryon, whose discovery took place in 1964
Strangeness changes (from a multiplet to another multiplet) take place by means of the Weak Interaction
s
s
s
10
100
10
1063.2)(
109.2)(
1082.0)(
Production and decay of the Ω particle
A cascade of weak decays
10
Baryon decuplet states are spin 3/2 Baryons of lowest mass, with no orbital angular momentum. Their spins are parallel, adding up to 3/2.
These are states with a wave function which is parallel with respect to space (l=0), spin (parallel). Flavor can be symmetrized to account for particle indistinguishability (e.g. in case of uud):
dududdddu 3
1
But, since they are fermions, every ψ must be antisymmetric
Quark Spin and Color
For instance in the case: uuu
bgrrbggrb uuuuuuuuu 3A new quantum number (the color) is necessary:
11
More evidence for color:
• The Pi-zero decay rate
• The value of the cross section
0
)(/)( eehadronsee
iic QN
ee
hadronseeR 2
)(
)(
In the Pi-zero decay rate, color alters the axial quark current
Let us now introduce the ratio R, by considering decays into hadrons or leptons starting from an e+e- initial state
e
e
q
q
Behaviour of R as a function of the energy available in the center of mass :Sensitivity to the total number of colorsSensitivity to the new kinematically possible quark production (c and b)
12
The ratio displays resonances due to Vector Meson production (and the Z)
C threshold
B threshold
Z peak
13
R value is sensitive to the number of quark states active at that energy
Crossing the Charm Quark production threshold
14
Crossing the Beauty Quark production threshold
The Baryon Octet
15
3I
S
0
1
2
11 2/12/1
udd uud
uds
dds uus
dss uss
Isospin doublet S=0
Isospin tripletS = -1
Isospin singlet S = -1
Isospin doublet S = -2
The lowest lying eight baryonic states with JP = 1/2+
16
3I
S
0
1
2
11 2/12/1
)6.939(n )3.938(p
)1192(0
)1197( )1189(
)1321( )1315(0
I = 1/2 )939(N
I = 1
I = 0
)1193()1116(
)1116(
I = 1/2 )1318(
177 MeV
202 MeV
The actual particles:
Neutron Proton
17
Mesons: general ideas
Baryons are formed by 3 quarks and do have anti-multiplets (antibaryons)
Mesons: a multiplet already contains quarks and antiquarks
Predictions of the Quark Model on the cross sections
Under the assumption that one can incoherently sum the amplitudes of the scattering on constituent quarks
Nucleon: made of three quarks
Meson: composed by quark and antiquark
So, the model predicts :3
2
)(
)(
NN
N
mbpp 24)()( mbnppp 38)()(
And experiments say, at an energy of 60 GeV for the incoming beam :
Hyperfine Interaction and masses
28
Mass differences in the Static Quark Model are due to:
• Differences between bare masses of constituent quarks costituenti (an s substituting an u or a d)
• Changes in the color binding energy
• Hyperfine color interaction between quarks (e.g. decuplet-octet difference for baryons)
• Hyperfine electromagnetic interaction between quarks
Hyperfine interaction in the case of two fermions (electromagnetic) :
i jjir
ii
ii m
e 2
3ji
ji
rE
29
22
)0(3
2e
mm
eeE ji
ji
ji
This interaction is of the order of MeV ( it cannot explain the baryon octet-decuplet difference, for instance).
However, the hyperfine color splitting is instead :
jiji
s
mmqqE 2
)0(9
8)( ji
ji
s
mmqqE 2
)0(9
4)(
The interaction depends on the spin state and it is different between the octet and the decuplet. In the case of two quarks:
)1()1()1(24 jjiijiji ssssSSss
03
11
Sse
Sseji ssS
2221
22121
22
21
221 242 ssSssssssSssS
30
)1(3)1(24 ssSSss jiji
2/13
2/33
Sse
Sse
Different sign for octet and decuplet
For instance in the case N (spin ½) and ∆ (spin 3/2):
MeVm
KK
mK
mEE N 3006
33222
9
)0(4
2 sK
)(293 observedMeVmm N
In the case of baryons, three quarks :
Octet-decuplet mass difference in Baryons can be explained at the few % level by the hyperfine color splitting !
31
Using these factors, also vector-pseudoscalar (spin1-spin 0) mass differences can be estimated reasonably well.
These effects are generally a factor of two more important for mesons.
Experimentally :
MeVm 776)( MeVm 140)( 636 MeV
In the case of mesons the correction is more important because :
•In the hyperfine color splitting formula, a quark-antiquark term is bigger than a quark-quark term :
•The factor is typically bigger for mesons (radius of ~0.6 fm) than for baryons (radius of ~0.8 fm)
jiji
s
mmqqE 2
)0(9
8)( ji
ji
s
mmqqE 2
)0(9
4)(
30
2/1)0( R
More on masses
32
The mass of a hadron is composed by:
• Color binding energy (Strong Interaction) Of the order of a GeV in the case of Baryons
• Mass of its constituents (the bare quark mass) Introducing differences of order 150 MeV
• Strong Interaction hyperfine term (How are the spins oriented? Baryons: Decuplet.vs.Octet. Mesons: Vector.vs.Pseudoscalar ) Difference of order 300 MeV for Baryons and 500 MeV for Mesons
• Electromagnetic correction inside the same multiplet
Physical origin and typical values ?
33
So, electromagnetic mass differences are small.They are originated by two effects :
1. Coulomb Energy due to differenc charges of the quarks. Estimate of what happens when you have a different charge over a Fermi :
MeVfm
fmMeV
R
c
c
e
R
eE 4.1
1
197
137
1
0
2
0
2
2. Electromagnetic hyperfine energy:
MeVR
e
Rmc
e
mm
eeE ji
ji
ji 4.11
)0(3
2
0
2
30
22
For instance in the case of the Baryon Octet:
MeVmm pn 3.1 MeVmm 1.8 MeVmm 5.60
34
Beyond the Octet Way. The fourth Quark.Electroweak Interactions and the GIM Mechanism.
In 1970 Glashow, Iliopolous and Maiani (GIM) predicted the existence of a fourth quark: Charm. The prediction was based on the absence of strangeness-changing neutral currents.
The 3 quarks Neutral Current has the form :
CCCCCC
CC
CCwk sdsduudduu
d
udu
d
uduJ sincossincos,, 3
0
CCC sdd sincos
CCCCCC ssdssddduu 22 sincossinsincoscos
And the third quark enters in the (Cabibbo-rotated) combination
Here’s a puzzle !
35
CCC
CCCC
CCCC
CC
Cwk
ssccs
cscssds
sddduus
csc
d
uduJ
............,sincossin
sincoscos,,
2
233
0
And taking into account Cabibbo-angle mixing matrix style with just 2 flavors
s
d
s
d
CC
CC
C
C
cossin
sincos
ccssdduussdssd
dddssdccssdduu
sdsdccssds
sddduus
csc
d
uduJ
CCCCC
CCCCCCC
CCCCCCC
CCCC
CC
Cwk
2
222
2
233
0
cossincoscossin
sinsincossincossincos
cossincossinsincossin
sincoscos,,
The introduction of the fourth quark removes the term driving strangeness-changing Neutral Currents (This is the GIM Mechanism)
Heavy Quarks: Charm
36
1974: the «november revolution». The discovery of the J/ψ particle by two experiments:
/Jee
XJBep /
Brookhaven experiment: 28 GeV protons hitting a fixed target
ee
SLAC experiment: electron-positron collisions
hadronsee ,,
Final State Invariant Mass Distribution
37
The observed width was dominated by the experimental resolution
Intrinsic width obtained from the knowledge of the cross section and the branching ratio
Resonance width: Γ= 0.093 MeV
Lifetime of 10-20 s
38
Final states: e+e- hadrons, e+e- e+e-, e+e μ+μ-
39
The J/ψ as an experimental «problem»:
Hadronic resonances are normally WIDE since they decay by Strong Interaction and have very short lifetimes:
MeVs 2001010/10 2322
keVJ 93)/(
As a comparison :
MeVMeVMeV 3.4)(5.8)(150)(
How can a resonance be 100/1000 times smaller than usual and still be a strongly interacting particle ?
To answer this question, we should first know something about other particles containing the charm quark.
40
The J/Psi production energy range actually turns out to be rich in several other structures
41
smccJ 2010,3097,/
eimpossibilDDJ /
c
c
c
c
u
u
And now, a J/ψ decay like :
The J/ψ contains a new quark, charm.
0/ CccJ Hidden charm
Particles with «open» charm (C not zero) were discovered at SLAC in the following years :
ucDsmucD
dcDsmdcD
0130
12
104,1865,
10,1870,
Cannot take place because:
MeVDmJm 3730)(23097)/(
42
u
c
c
dddd
Zweig suppression
)(2 Dmm
For J/ψ-like states such that :
For J/ψ-like states such that:
)(2 DmM
c
c
c
c
u
u
3-gluons decay
43
The J/ψ as quarkonium : a non relativistic state with a potential of the form
krr
rV ss
3
4)(
Quarkonium
Systems made by heavy quark-antiquark pairs have masses much higher than the Strong Interaction scale parameter (Λ ≈ 200 MeV).One can use the nonrelativistic Schoedinger Equation to study bound states :
)()()()2/(2
2
rErrVmQ
...)(
9
32
3
4)(
221 r
m
ss
rkrrV
Q
SS
44
S
Onia systems !
45
Charmonium system studies
Study of the transitions between charmonium states require the ability to detect gammas (example: the Crystal Ball detector at Stanford).
The Crystal Ball was then used at DESY for b-physics
46
Charm Particles
ucDsmucD
dcDsmdcD
0130
12
104,1865,
10,1870,
Lightest charmed
mesons
Main decay modes: c s type, by means of Weak Interactions. For instance:
%14,%6, 000 BRKDBRKD
Mesons with charm and strangeness:
)1,1(,)1,1(,105,1969, 13 SCscDSCsmscD Ss
Typical decay, with cs: %5, BRKKDs
Charmed Baryons: ducsmcud cc 13102,2285,
Typical decay, with cs: %5, BRKpc
47
Charm Physics: as an example, a classification of non-strange charmed baryons !
The ordinary spin-3/2 baryon decuplet is just the first floor
The ordinary spin-1/2 baryon octed is just the first floor
Different amount of charm are possible (3,2,1,0) and Weak Interactions makes it possible to change the Charm quantum number.
Antibaryons with anticharm are of course there!
48
Heavy Quark Physics : welcome to the complexity !
• Lifetimes of the order of 10-13 s (Weak Decays)• Many possible decay modes (each with a low branching ratio)• Complex Topology of the event• Not trivial to reconstruct
)(ccdcc
Tracks in detectors downstream
Tracks in detectors downstream
First hints of a third family: the beauty quark
49
Charm introduces an additional (flavor) degree of freedom in the particle classification scheme
Third family
s
d
s
d
CC
CC
C
C
cossin
sincos
Before charm, just two families were known. It was also known that they entered in Weak Interaction through a rotation (Cabibbo angle) :
Actually, the mixing involves all flavors (CKM Matrix, introduced in 1973)
Charm was predicted in 1970.
Charm was discovered in 1974-1977.
The Beauty quark was discovered in 1977, at about the same time as the Tau lepton.
50
The discovery of beauty (Lederman et al. experiment ,1977). Study of two-muon final states in high-energy (400 GeV) proton collisions on a fixed target. The usual tool: invariant mass distribution.
The state discovered was:
keVmbb 54,9460,
In analogy with what happened for the J/ψ case
These particles are made of a new quark, still heavier than charm: Beauty. Similar to charm, there are particles with hidden and open beauty.
51
1,1,105.1,5366,
1,105.1,5279,
1,106.1,5279,
120
0120
12
SBsmbsB
bdBBsmbdB
buBBsmbuB
S
The Upsilon landscape
States hadronically decaying in 3 gluons
Y(4s), the first state having sufficient mass to decay to B-antiB
BBS )4(
Y has hidden beauty. The lightest particles with open beauty are:
The lightest beauty baryon : smbudb120 104.1,5620,
52
Beauty particles decays : dominance of (Weak Interaction driven) bc.Charmed particles in the final state.
WcbInvariant mass reconstruction of beauty particle states :
DB0 *0 DB
ss DB0
cb0
53
Heavy Quark Physics : welcome to beauty complexity
Beauty states : welcome to some more spectroscopy. For example, in the case of the B+
Beauty states : noticeable improvements in the experimental resolution (CDF is a hadron collider!)
The search is on for radially excited states (one unit of angular momentum between the quark and the antiquark)
55
More experimental complexity : A primary vertex PV. This is where the first subnuclear interaction took place
A B particle flies and then decays generating a secondary vertex SV
The Charm particle flies and then decays generating a tertiary vertex TV
56
Quark Top: the discovery
The sixth quark, called Top, was discovered in 1994 at Fermilab. The first evidence was obtained by the CDF and D0 experiments in proton/antiproton collisions at 1.8 TeV center of mass energy. The Top mass is 174 GeV !
Get familiar with Feynman diagrams at very high energy:
57
The CDF detector at Fermilab
900 GeV Proton 900 GeV Antiproton
The complexity of a top event
58
Events are characterized by several jets :
and by the reconstruction of invariant masses that are partial :
Phenomenological features of Top events :
59
The Top quark : some distinctive features
The top quark mass (176 GeV) makes it different from lighter quarks.
Since its main decay mode proceeds through Weak Interaction :
One would have beauty particles in the final state
Wbt
Can we then observe toponium, or top mesons/baryons ? NO This is because the hadronization time :
scfmcRt 2410/1/ Can be thought of as the time necessary for a gluon to cross a hadron
But the weak decay rate of the Top quark is proportional to (a power of) its mass, so that :
s251 105
Top quark decays before forming any hadron !
60
Breaking News : the discovery of a particle that is neither a quark triplet, nor a quark-antiquark pair. Mamma mia!
The form of the color force potential and the symmetry group allows for more complex combinations of quarks.They have been searched for during several decades. Many candidates (tetraquarks, pentaquarks) were found.
Recently, the first solid evidence was found (2014) at LHCb of a pentaquark state, called Z(4430) . This state behaves as a «good» strong resonance.
