Chapter 2 Elementary particles
2.1 Classification of Particles 2.2 Leptons 2.3 Quarks 2.4 Hadrons 2.5 Interactive Exercise
2.3 Quarks
Elementary particles
Particle Physics
Quarks From Simplicity → Complexity → Simplicity Around 1930, life seemed pretty good for our understanding of “elementary (fundamental) particles”. There was protons, neutrons & electrons. Together, they made up atoms molecules → DNA → People ! AAHHHHH, nature is simple, elegant, aaahhhh…
Who ordered that” ?
But the discoveries of dozens of more particles in accelerator experiments lead many to question whether the proton and neutron were really “fundamental”. Is nature really this cruel ? I. I. Rabi’s famous quote when the muon was discovered. Needless to say, the “zoo of new particles” that were being discovered at accelerators appeared to reveal that nature was not simple, but complicated? Until…. Dayalbagh Educational Institute
4
Elementary particles
Particle Physics
Quarks ? First things things first: first: Where Where did did the the name name “quarks” “quarks” come come First from? from? Murray Gell-Mann had just been reading Finnegan's Wake by James Joyce which contains the phrase "three quarks for Muster Mark". He decided it would be funny to name his particles after this phrase. Murray Gell-Mann had a strange sense of humor! In In 1964, 1964, Murray Murray Gell-mann Gell-mann && George George Zweig Zweig (independently) (independently) came came up up with with the the idea idea that that one one could could account account for for the the entire entire “Zoo “Zoo of of Particles”, Particles”, if if there there existed existed objects objects called called quarks. quarks.
The The quarks quarks come come in in 33 types types (“flavors”): (“flavors”): up(u), up(u), down(d), down(d), and and strange(s) strange(s) and and they they are are fractionally fractionally charged charged with with respect respect to to the the electron’s electron’s charge charge Dayalbagh Educational Institute
5
Elementary particles
Particle Physics
George Zweig
Flavor
Q/e
u
+2/3
d
-1/3
s
-1/3 Murray Gell-Mann
How sure was Gell-Mann of quarks ? When the quark model was proposed, it was just considered to be a convenient description of all these particles.. A mathematical convenience to account for all these new particles… After all, fractionally charged particles… come on ! An excerpt from Gell-Mann’s 1964 paper: “A search for stable quarks of charge –1/3 or +2/3 and/or stable di-quarks of charge –2/3 or +1/3 or +4/3 at the highest energy accelerators would help to reassure us of the non-existence of real quarks”.
Dayalbagh Educational Institute
6
Elementary particles
Particle Physics
Scattering Experiments Rutherfored, deBroglie, and others taught us that we can learn about the structure of matter by colliding high energy particles into matter, and seeing what happens. Recall, Rutherford determined that the atom must contain a dense core of positive charge to account for the large angular deflections of incoming alpha particles. Also, as we discussed earlier, in order to probe matter of size, say A, the wavelength which you use to probe it must be at least this size, or smaller‌ YES, this works !
Fig: 1
NO, this doesn’t really work !
Fig: 2 Dayalbagh Educational Institute
7
Elementary particles
Particle Physics
Rutherford Example What was the “wavelength” of the alpha particles used in Rutherford’s scattering experiments on Gold foils ? Note -27 [kg], Note that: that: m maa== 6.7x10 6.7x10-27 [kg], vvaa== 1.6x10 1.6x1077 [m/s]) [m/s]) de de Broglie Broglie taught taught us us that that particles particles have have wave wave length length given given by: by: λλ == h/p h/p So, first get momentum: p = mv = (6.7x10-27 [kg])(1.6x107 [m/s]) = 1.0x10-19 [kg m/s]
λλ == h/p -34 // 1x10 -19 = -15 [m] h/p == 6.6x10 6.6x10-34 1x10-19 = 6.2x10 6.2x10-15 [m] Since the gold nucleus is about 10x10 -15 , this wavelength is small enough to “resolve” the fact that there is a nucleus there…
Probing Deeper Into Matter If we really want to understand if there is anything “inside” a proton or neutron (aka nucleon), we have to examine it with particles whose wavelengths are smaller than the size of a proton. Since λ = h/p, we must produce higher momentum particles. That is, the higher the momentum of the particle, the smaller it’s de Broglie wavelength can “see”, or “probe” smaller things Since the proton’s size is very small, about 1x10 -15 [m], We need very energetic beams of particles (high momentum) to probe it’s structure. Dayalbagh Educational Institute
8
Elementary particles
Particle Physics
By the 1960’s, physicists had learned how to produce high energy, well-focused, beams of particles, such as electrons or protons (particle accelerators !) This has been the driving force behind understanding “What is matter at its most fundamental level?”
Are protons/neutrons fundamental? In 1969, a Stanford-MIT Collaboration was performing scattering experiments
e- + p
e- + X
(X = anything)
Fig: 3
What they found was remarkable; the results were as surprising as what Rutherford had found more than a halfcentury earlier! The The number number of of high high angle angle scatters scatters was was far far in in excess excess of of what what one one would would expect expect based based on on assuming assuming aa uniformly uniformly distributed distributed charge charge distribution distribution inside inside the the proton. proton. It’s as if the proton itself contained smaller constituents
Dayalbagh Educational Institute
9
Elementary particles
Particle Physics
Quarks Since 1969, many other experiments have been conducted to determine the underlying structure of protons/neutrons. All the experiments come to the same conclusion. Protons and neutrons are composed of smaller constituents. These quarks are the same ones predicted by Gell-Mann & Zweig in 1964. 1x 10-18 m (at most)
(1.6 x 10-15 m)
Protons 2 “up” quarks 1 “down” quark
Fig: 4
Neutrons 1 “up” quark 2 “down” quarks
Are Arethere thereany anyother otherquarks quarksother otherthan thanUP UPand andDOWN DOWN??
Dayalbagh Educational Institute
10
Elementary particles
Particle Physics
Three Families of Quarks Generations
Woohhh, fractionally charged particles?
Increasing mass
Charge = -1/3
Table 1
Charge = +2/3
I
II
III
d
s
b
(down)
(strange)
(bottom)
u
c
t
(up)
(charm)
(top)
Also, Also, each each quark quark has has aa corresponding corresponding antiquark. antiquark. The The antiquarks antiquarks have have opposite opposite charge charge to to the the quarks. quarks.
The 6 Quarks, when & where‌ Quark
Date
Where
Mass [GeV/c2]
Comment Constituents of hadrons, most prominently, proton and neutrons.
up, down
-
-
~0.005, ~0.010
strange
1947
-
~0.2
discovered in cosmic rays
charm
1974
~1.5
Discovered simultaneously in both pp and e+e- collisions.
bottom
1977
~4.5
Discovered in collisions of protons on nuclei
top
1995
~175
Discovered in pp collisions
Notice the units of mass !!!
SLAC/ BNL Fermilab Fermilab Table 2
Dayalbagh Educational Institute
SLAC = Stanford Linear Accelerator BNL = Brookhaven National Lab 11
Elementary particles
Particle Physics
Major High Energy Physics Labs Fermilab Fermilab
DESY DESY
SLAC SLAC KEK KEK
CERN CERN
CESR CESR BNL BNL Fig: 5
How do we know any of this? Recall that high energy particles provide a way to probe, or “see� matter at the very smallest sizes. (Recall Electron microscope example). Today, high energy accelerators produce energetic beams which allow us to probe matter at its most fundamental level. As we go to higher energy particle collisions: 1) Wavelength probe is smaller
see finer detail
2) Can produce more massive objects, via E = mc2
Dayalbagh Educational Institute
12
Elementary particles
Particle Physics
Back to matter & quarks…
Fig: 6
Fundamental particles We consider quarks to be fundamental, because so far we have been unable to “break them apart”. As we increase the momentum of particles in our accelerators, we are able to resolve, or see, deeper into matter. We are currently able to accelerate particles to energies of ~1 [TeV] = 1x1012 [eV]. To what wavelength does this correspond? First convert [eV] to [J] !!!!
λ =hc/E = (6.6x10-34)(3x108) / 1.6x10-7 = 1.2x10-18[m] Dayalbagh Educational Institute
13
Elementary particles
Particle Physics
So, if quarks were bigger than this, we would be able to discern their substructure. So far, they look to be smaller than this ! That is they are at least 1000 times smaller than the proton ! Same is true for electron considered “fundamental�
quarks (and electrons) are
Anti-particles too ! We also know that every particle has a corresponding antiparticle! That is, there are also 6 anti-quarks, they have opposite charge to the quarks. So, the full slate of quarks are: Particle
Anti-Particle
Q= +2/3 Q= -1/3
u , c , t d , s ,b
Q= -2/3 Q= +1/3
u , c , t d , s ,b
Quarks Anti-Quarks
Quark masses 6 different kinds of quarks. Matter is composed mainly of up quarks and down quarks bound in the nuclei of atoms. The masses vary dramatically (from ~0.005 to 175 [GeV/c2]) The heavier quarks are not stable, and decay to lighter quarks quite rapidly Dayalbagh Educational Institute
14
Elementary particles
Particle Physics
Example: Example: -23 tt→ (~10 →bb (~10-23[s]) [s]) -12 bb→ (~10 →cc (~10-12[s]) [s]) -12 -12 cc→ (~10 →ss (~10 [s]) [s]) -7-10 ss→ →uu (~10 (~10-7-10 10-10[s]) [s]) 1000
Gold atom top
100
Silver atom
Mass [GeV/c2]
10
bottom
Proton
charm
1
strange
0.1
down
0.01
up
Table 3 0.001
0
Quark Confinement
2
4
6
8
Hadron Jail
q Fig 7
Proton
Quarks are “confined” inside objects known as “hadrons”. We’ll learn more about hadrons in a bit… This is a result of the “strong force” which we will discuss later… Dayalbagh Educational Institute
15
Elementary particles
Particle Physics
Protons & Neutrons To make a proton: We bind 2 up quarks of Q = +2/3 and 1 down quark of Q = -1/3. The total charge is 2/3 + 2/3 + (-1/3) = +1 !
To make a neutron: We bind 2 down quarks of Q = -1/3 with 1 up quark of Q = +2/3 to get: (-1/3) + (-1/3) + (2/3) = 0 !
Fig: 8
So, it all works out ! But, yes, we have FRACTIONALLY CHARGED PARTICLES!
Why does the nucleus stay together ? So far, the only “fundamental� forces we know about are: (a) Gravity (b) EM force (Electricity + Magnetism) Which one of these is responsible for binding protons to protons and protons to neutrons ???
Fig: 9 Dayalbagh Educational Institute
16
Elementary particles
Particle Physics
Since like sign charges repel, it can’t be EM force? Gravity is way, way, way too weak… Then what is it??? Strong Strong Force Force This is the third fundamental force in nature and is by far the strongest of the four forces. More on forces later…
Dayalbagh Educational Institute
17
Elementary particles
Particle Physics
Hadrons / Baryons The forces which hold the protons and neutrons together in the nucleus are VERY strong. They interact via the STRONG FORCE. Protons and neutrons are among a class of particles called “hadrons” (Greek for strong). Hadrons interact very strongly with other hadrons! Baryons are hadrons which contain 3quarks (no antiquarks). Anti-baryons are hadrons which contain 3 anti-quarks (no quarks). Wow, I’m somebody… I’m a Baryon!
Me too, me too…
Are there baryons other than protons and neutrons? Good question, my dear Watson… The answer is a resounding YES ! Other quarks can combine to form other baryons. For example:
u s
d
This combination is called a Lambda baryon, or Λ0 for short What is the charge of this object?)
Dayalbagh Educational Institute
18
Elementary particles
Particle Physics
This combination is called a Delta baryon, or Δ++ for short What’s this one’s charge? Flavor
Q/e
u
+2/3
d s
-1/3 -1/3
u u
u
Let’s make baryons! Quark
up
Charge Q Mass
down
+2/3 ~5 [MeV/c2] u
u
u
strange
-1/3 ~10 [MeV/c2] d
d
d
-1/3 ~200 [MeV/c2] s
s
u u d
u d d
Proton
Neutron
Q = +1 M=938 MeV/c2
Q= 0 M=940 MeV/c2
Fig: 10
s
Fig: 11
Note: The neutron differs from a proton only by “d”←→“u” quark replacement! Dayalbagh Educational Institute
19
Elementary particles
Particle Physics
Let’s make some more baryons ! Quark Charge, Q Mass
up +2/3
down -1/3
strange -1/3
~5 [MeV/c2]
~10 [MeV/c2]
~200 [MeV/c2]
u
u
u
d
u s
d
d
s
s
s
d
Lambda (Λ )
Fig: 12
Q= 0 M=1116 MeV/c2 Lifetime~2.6x10-10[s]
u s
d
u
s
d
Sigma (Σ + )
Sigma (Σ − )
Q = +1 M=1189 MeV/c2
Q = -1 M=1197 MeV/c2
Lifetime~0.8x10-10[s]
Lifetime~1.5x10-10[s] Fig: 13
These particles have been observed, they really exist, but decay fairly rapidly. -
+
Is Σ the antiparticle of Σ ??
Dayalbagh Educational Institute
20
Elementary particles
Particle Physics
Mesons Mesons are also in the hadron family. They are formed when a quark and an anti-quark “bind” together. (We’ll talk more later about what we mean by “bind”).
u
d
d
s
What’s the charge of this particle?
What’s the charge of this particle?
Q= 0, this strange meson is called a K0
Q=+1, and it’s called a π +
M~500 [MeV/c2 ] Lifetime~0.8x10 -10 [s]
M~140 [MeV/c2 ] Lifetime~2.6x10 -8 [s]
Fig: 15
Fig: 14
c
d
What’s the charge of this particle? Q= -1, and this charm meson is called a DM~1870 [MeV/c2 ] Lifetime~1x10-12 [s]
Dayalbagh Educational Institute
Fig: 16
21
Elementary particles
Particle Physics
Gell-Mann and Zweig proposals hadrons to be composite objects of bound state of spin ½ fermions called quarks, with three flavours: ‘up’, ‘down’ and ‘strange’. Flavour
I
I3
S
B
Q
u
½
½
0
⅓
+⅔
d
½
-½
0
⅓
-⅓
s
0
0
-1
⅓
-⅓
Table 4: Properties of Quarks proposed by Gell-Mann and Zweig.
Flavour
I
I3
S
B
Q
u
½
-½
0
-⅓
-⅔
d
½
+½
0
-⅓
+⅓
s
0
0
+1
-⅓
+⅓
Table 5: Properties of Anti quarks
Each quark has a corresponding antiquark for which the conserved quantities: charge, B, I3, S, have opposite sign. A quark- antiquark bound state produces B = 0, mesons, and baryons are bound states of three quarks, with B = ⅓ each. Quark model reproduces the properties of hadrons for octet of Jp = 0- mesons and octet of Jp = ½+ baryons. Plots of hypercharge vrs I3 for these mesons, baryons are shown with quark flavour content of the particles also.
Dayalbagh Educational Institute
22
Elementary particles
Particle Physics
Fig 17 The basic quark and antiquark triplet
Fig 18 (a) The octet of 0- mesons; (b) quark flavour assignments for the 0- mesons.
Dayalbagh Educational Institute
23
Elementary particles
Particle Physics
(c) the octet of ½+ baryons; d) quark flavour assignments for the ½ + baryons.
In mesons, the quark- antiquark pairs are bound with zero relative orbital angular momentum and spins anti parallel to give total spin J = 0. The parity is negative due to opposite intrinsic parity of fermions and antifermion. In baryon, ½+ are lowest lying baryons, the lightest also and assume that the relative orbital angular momenta ℓ and ℓ' are both equal to zero.
Fig 19: Orbital angular momentum in a three quark system. l is the relative orbital angular momentum between two of the quarks and l' that between the di-quark system and the remaining quark.
Dayalbagh Educational Institute
24
Elementary particles
Particle Physics
Two quark spin can couple to give a resultant zero, so net spin parity three-quark system is ½ +. Hence by introducing orbital angular momentum into the quark system, we find hadrons with different Jp values. An important case arises in baryon spectrum with ℓ = ℓ'=0, S = 3/2 gives Jp = 3/2+, shown below:
Fig 20 (a) The 3/2+ baryon decuplet ad (b) its quark flavour content.
On studying Δ++ (1232) state with quark content uuu, have three identical spin ½ quarks with same spatial positions and occupying same spin state. To solve this, quarks have internal degree of freedom ‘colour’; similar to charge. We have three types of ‘strong charge’ or colours: red, green and blue, with each quark having equal probability in any of these states. Rule1: every hadron is a colour singlet i.e. ‘white’, hence Δ++ (1232) has μR μG μB. Dayalbagh Educational Institute
25
Elementary particles
Particle Physics
Rule2: Similar to both signs of electric charge exist so there are complementary colours: cyan, magenta and yellow or 'anti-red' – R ‘anti green’ G and ‘anti blue’ B. Rule3: The antiquarks are assigned anti colours, colour singlet can be formed from equal mixtures of three colour states or equal mixtures anti colours (R G B) or equal mixtures colour- anticolour RR, GG, BB. Thus these constructions produce baryons, antibaryons, meson respectively.
Dayalbagh Educational Institute
26
Elementary particles
Particle Physics
Problem 1 What values of electric charges are possible for, a) Baryon
b) Meson in the quark model?
Solution 1 In the quark model a baryon is a combination of three quark charges +2/3 or -1/3. All possible combinations lead to charges ++, +, 0 and Mesons are qq combination with charges +2/3, -1/3 and -2/3, 1/3. The possible charges are +, 0 and -.
Problem 2 The
is an isosinglet baryon with strangeness S=-1.
What is its quark content?
Solution 2 The
has S = -1 and therefore must contain an S
quark (Q= -1/3) the other quarks necessary to give a neutral baryon are u (Q=2/3) and d (Q= -1/3). Hence
Ξ
uds
Note: In Quark wavefunction as opposed to the quark content, the u and d quarks must be in an I=0 combination
Dayalbagh Educational Institute
27
Elementary particles
Particle Physics
Problem 3 The
Ξ
baryons form an isospin doublet with S=-2. What
charge states are possible?
Solution 3 The Ξ baryons have S=-2 and therefore must contain two s quarks. The third quark is either a u quark corresponding to the Ξ0 (Q=0, I3=1/2) or a d quark corresponding to the Ξ- (Q=-1, I3= -1/2)
Problem 4 Determine the quark content of the K +, K0 (S=+1) and K-, K0 (S=-1) mesons.
Solution 4 Mesons are qq combinations. The K+ and K0 with S=+1 must contain an s quark with Q=1/3. Hence K+ ≡ su and K0
≡
sd.
Similarly K0 ≡ su and K0 ≡ sd
Problem 5 How many different meson combinations can we make with 1,2,3,4,5 or 6 different quark flavors? What is the general formula for n flavors? Dayalbagh Educational Institute
28
Elementary particles
Particle Physics
Solution 5
With 1 quark (u) : one meson (uu) With 2 quarks (u,d) : four meson ( uu , ud , du , dd ) With 3 quarks (u,d,s) : nine mesons With 4 quarks (u,d,s,c) : sixteen mesons With 5 quarks (u,d,s,c,b) : twenty five mesons With 6 quarks (u,d,s,c,b,t) : thirty six mesons Hence general formula for n flavors is n2
Problem 6 How many different baryon combinations can you make with 1,2,3,4,5 or 6 different quark flavors? What is the general formula for n flavors?
Solution 6
For 1 quark (u), we have 1 baryon (u,u,u); For 2 quarks (u,d), we have 4 baryons (uuu, uud, udd, ddd). For 3 quarks (u,d,s), we get 10 baryons (baryon decaplet) For n quarks we shall have, all three quarks the same : n ways two quarks same, one different : n(n-1) ways All three quarks different :
ways
Comment : In last case, we divide by 6 to cover the equivalent permutations:(uds=usd=dus=dsu=sud=sdu) Dayalbagh Educational Institute
29
Elementary particles
Particle Physics
Hence the total is = = So for 4 quarks we have
=20 baryon types
for 5 quarks we get
=35 baryons
for 6 quarks we get
= 56 baryons
Dayalbagh Educational Institute
30