Quarks and Hadrons - CERN

Transcript of Quarks and Hadrons - CERN

Quarks and Hadrons

Mustafa Amin1 & Mustafa Ashry1,2

1Center for Fundamental Physics (CFP) at Zewail City of Science and Technology.

2Department of Mathematics, Faculty of Science, Cairo University.

Mini-school on ”experimental tools in particle physics”at

CFP at Zewail City of Science and Technology

Friday - 2015, March, 27

Mustafa Amin1 & Mustafa Ashry1,2 Quarks and Hadrons

Quarks and Hadrons

Outline

1 Quarks

2 General Properties of Hadrons

3 Pions and Nucleons

4 Short-Lived Hadrons

5 Allowed Quantum Numbers and Exotics

6 Questions, References & Thanks

2 / 43 Mustafa Amin1 & Mustafa Ashry1,2 Quarks and Hadrons

Quarks and Hadrons

Outline

1 Quarks

Quarks and Hadrons

Outline

1 Quarks

Quarks and Hadrons

Outline

1 Quarks

Quarks and Hadrons

Outline

1 Quarks

Quarks and Hadrons

Outline

1 Quarks

Quarks and Hadrons

Quarks

Outline

1 Quarks

Quarks and Hadrons

Quarks

Quarks Interactions

Quarks are elementary fermions that interact via strong, weak andelectromagnetic interactions.Quarks interact via strong interactions, as they have color charges.Gluons (eight) are the carriers of the strong force.Quarks interact via weak interactions, as they have weak isospin. TheW± and Z bosons are the carriers of the weak force.Quarks interact via electromagnetic interactions, as they have electriccharges. Photons is the carrier of the electromagnetic force.

Quarks and Hadrons

Quarks

Quarks Interactions

Quarks and Hadrons

Quarks

Quarks Interactions

Quarks and Hadrons

Quarks

Quarks Interactions

Quarks and Hadrons

Quarks

There are six flavors of quarks. They are up (u), down (d), charm(c), strange (s), top (t) and bottom (b) quarks, and their antiquarks.

Quarks are grouped in three generations (isospin doublets) accordingto their mass difference minima [1].

Quarks and Hadrons

Quarks

There are six flavors of quarks. They are up (u), down (d), charm(c), strange (s), top (t) and bottom (b) quarks, and their antiquarks.

Quarks are grouped in three generations (isospin doublets) accordingto their mass difference minima [1].

Quarks and Hadrons

Quarks

There is no convincing evidence for the existence of isolated freequarks, or any other fractionally charged particles, despite greatefforts to find them [1].

Quarks and Hadrons

General Properties of Hadrons

Outline

1 Quarks

Quarks and Hadrons

There are no isolated quarks. But more than two hundred of theirbound states have been discovered.

All these bound states are of integer electric charges.

The reason for this is closely associated with a new degree of freedomthat exists for quarks, but not for leptons, called colour.

Quarks are triplets under the group of strong interactions and thecolor charge for each quark is red, green, or blue.

For color conservation and being the electric charges of quark boundstates are integers, there are only three types of quark bound statesare allowed.

Quarks and Hadrons

The bound states of quarks are called Hadrons. They are the baryons,the antibaryons and the mesons.The baryons have half-integer spin and are bound states of threequarks (qqq).The antibaryons are the antiparticles of baryons and they are boundstates of three antiquarks (qqq).The mesons have integer spin and are bound states of a quark and anantiquark (qq).

Quarks and Hadrons

Examples (Lightest Mesons): For q = u, d , q = u, d , and theallowed two-quark bound states are

qq Q color spin/particle (mass)

uu, dd 0 0 0/π0 (134.9 MeV) or 1/ρ0 (775.49 MeV)ud +1 0 0/π+ (139.5 MeV) or 1/ρ+ (775.4 MeV)du −1 0 0/π− (139.5 MeV) or 1/ρ− (775.4 MeV)

Here we assumed that q is of anticolor charge opposite to the colorcharge of q.On the other hand, there is no a two-quark bound state of the formqq or qq, (uu, ud , dd , uu, ud , d d) because, they would have neither azero color charge nor an integer electric charge.It is worth mentioning that the (lightest) spin-0 mesons π+ = ud ,π− = du and the meson π0 is a combination of the two bound statesuu and dd . Indeed, they form an isospin triplet.

Quarks and Hadrons

Examples (Lightest Baryons): The allowed three-quark boundstates are

qqq Q color spin/particle(mass)

uuu +2 0 12/? (why?!) or 3

2/∆++

uud , udu, duu +1 0 12/p = N+ (938.27 MeV) or 3

2/∆+

udd , dud , ddu 0 0 12/n = N0 (939.66 MeV) or 3

2∆0

ddd −1 0 12/? (why?!) or 3

2/∆−

Here we assumed that all the three quarks have different colorcharges.The meson state qq is already colorless and of integer electric charge.Hence a state qqq or qqq would violate the color charge or theelectric charge (indeed, both).The (lightest) spin-1/2 baryons are the proton p = uud , and theneutron n = udd . Indeed, they form an isospin doublet.

Quarks and Hadrons

Considering a quark model in which q = u, d , s, the spin-0 mesons,spin-1 mesons, the spin-1/2 baryons, and the spin-3/2 baryons aregrouped by Gell-Mann in the following meson octets and baryon octetand decouplet, respectively:

Quarks and Hadrons

We may proceed considering a four-quark model in whichq = u, d , s, c and find all expected mesons and baryons.

Quarks and Hadrons

We may also proceed considering a four-quark model in whichq = u, d , s, b and find all expected mesons and baryons. We may thenproceed considering the quark model in which q = u, d , s, c , b andfind all expected mesons and baryons. The top quark doesn’tconstitute baryons as it is very decaying.

Quarks and Hadrons

Quark Numbers: We define the following quark numbers

strangenessS = −Ns = −[N(s)− N(s)] (1)

charmC = Nc = N(c)− N(c) (2)

bottomB = −Nb = −[N(b)− N(b)] (3)

topT = Nt = N(t)− N(t) (4)

The top quantum number T = 0 for all known hadrons.The remaining quark numbers are given by

Nu = N(u)− N(u) , Nd = N(d)− N(d) (5)

Quarks and Hadrons

Also we define the Baryon number, B, to be

B =1

3[N(q)− N(q)]. (6)

The baryon number B = 1 for baryons, B = 1 for antibaryons andB = 0 for mesons.

The baryon number can be given in terms of the quark numbers as

B =1

3[Nu + Nc + Nt + Nd + Ns + Nb]

=1

3[Nu + C + T + Nd − S − B] (7)

The electric charge Q in terms of the quark numbers is

Q =2

3[Nu + Nc + Nt ]−

1

3[Nd + Ns + Nb]

=2

3[Nu + C + T ]− 1

3[Nd − S − B] (8)

Quarks and Hadrons

The quantum numbers (1)-(8) are called internal quantum numbers,because they are not associated with motion or the spatial propertiesof wave functions.

In strong and electromagnetic interactions quarks and antiquarks areonly created or destroyed in particle−antiparticle pairs. For example,the quark description of the strong interaction process

p + p → p + n + π+

is

(uud) + (uud) → (uud) + (uud) + γ∗/g∗

→ (uud) + (uud) + d + d

→ (uud) + (udd) + (ud)

The separate conservation of each quark number of (1)-(8) is acharacteristic of the strong and the electromagnetic processes.

Quarks and Hadrons

The β-decayn→ p + e− + νe

whose the the quark interpretation is

(udd)→ (uud) + e− + νe

violate both the quark numbers Nu and Nd and hence can beinterpreted only via the weak interaction as follows

(udd)→ (uud) + W−∗ → (uud) + e− + νe

Quarks and Hadrons

The quantum numbers (1)-(8) play an important role inunderstanding the long lifetimes of some hadrons.

The vast majority of hadrons are highly unstable and decay to lighterhadrons by the strong interaction with lifetimes of this order 10−23 s.However, each hadron is characterized by a set of values forB,Q,S ,C , B and T , and in some cases there are no lighter hadronstates with the same values of these quantum numbers to which theycan decay (e.g., proton!!!). These hadrons, which cannot decay bystrong interactions, are long-lived on a timescale of order 10−23 s andare often called stable particles. Here we shall call them long-livedparticles, because except for the proton they are not absolutely stable,but decay by either the electromagnetic or weak interaction.

Electromagnetic decay rates are suppressed by powers of the finestructure constant α leading to observed lifetimes in the range1016 − 1021 s. Weak decays give longer lifetimes that dependsensitively on the characteristic energy of the decay.

Quarks and Hadrons

Electromagnetic decay rates are suppressed by powers of the finestructure constant α leading to observed lifetimes in the range1016 − 1021 s. Weak decays give longer lifetimes that dependsensitively on the characteristic energy of the decay. Because of this,observed lifetimes for some weak hadron decays lie in the range1071013 s. Thus hadron lifetimes span some 27 orders of magnitude,from about 1024 s to about 103 s.Here are the typical lifetimes of hadrons decaying by the threeinteractions (the neutron lifetime is an exception).

Interaction Lifetime (s)

Strong 10−22 − 10−24

Electromagnetic 10−16 − 10−21

Weak 10−7 − 10−13

Quarks and Hadrons

Pions and Nucleons

Outline

1 Quarks

Quarks and Hadrons

Pions and Nucleons

The lightest known spin-0 mesons are the pions or pi-mesons

π+ = ud , π0 = uu, dd , π− = du

with masses

mπ± = 140 MeV , mπ0 = 135 MeV.

These particles are produced copiously in many hadronic reactionsthat conserve both charge and baryon number, e.g. in protonprotoncollisions

p + p → p + n + π+

p + p → p + p + π+ + π−

p + p → p + p + π0

Quarks and Hadrons

Pions and Nucleons

The charged pions decay predominantly by the reactions

π+ → µ+ + νµ

π− → µ− + νµ

with lifetime 2.6× 10−8 s, typical of weak interactions.

Quarks and Hadrons

Pions and Nucleons

The neutral pion decay by the electromagnetic interaction

π0 → γ + γ

with a lifetime 0.8× 10−16 s, typical of weak interactions.

The lightest known spin-1/2 baryons are the nucleons, i.e., the protonand the neutron

p = uud , n = udd

Quarks and Hadrons

Pions and Nucleons

Yukawa Theory

In 1935 Yukawa proposed that nuclear forces were due to theexchange of spin-0 mesons, and from the range of the forces (whichwas not precisely known at that time) predicted that these mesonsshould have a mass of approximately 200 MeV. The discovery ofpions was a great triumph for the Yukawa theory.

Quarks and Hadrons

Short-Lived Hadrons

Outline

1 Quarks

Quarks and Hadrons

Short-Lived Hadrons

Short-lived Hadrons

Resonances

Resonances are hadrons that decay by strong interactions.They are far short-lived to be observed directly, and their existencemust be inferred from observations on the more stable hadrons towhich they decay.

Quarks and Hadrons

Short-Lived Hadrons

An Example of Resonances

K− + p → X− + p → K 0 + π− + p

Quarks and Hadrons

Short-Lived Hadrons

Still With The Example

The distance between the points where the resonance is produced anddecays is too small to be measured.

The observed reaction is therefore

K− + p → K 0 + π− + p

If the decaying particle has mass M, energy E and momentum p,then by energy-momentum conservation the invariant mass W of theK 0π− pair is given by

W 2 ≡ (EK + Eπ)2 − (pK + pπ)2 = E 2 − p2 = M2

Quarks and Hadrons

Short-Lived Hadrons

The Peak

If we plot the event distribution against the invariant mass W of theoutputs K 0π− it will show a sharp peak at the resonance mass M.

If uncorrelated K 0 and π− particles were produced by some othermechanism, a smooth destribution would be expected.

Quarks and Hadrons

Short-Lived Hadrons

The Decay Width of the Resonance

This resonance particle we call K ∗− and it sits on a backgroundarising from uncorrelated pairs produced by some other, non-resonant,mechanism.

For a particle at rest, W = E and the energy-time uncertaintyprinciple leads to

∆W = ∆E ≈ Γ ≡ 1/τ

and Γ is called the decay width of the state.

The characteristic life-time of a strong decay is of order 10−23 s thenthe corresponding decay width would be order 100 MeV, which issimilar to the width of the resonance peak shown.

Quarks and Hadrons

Short-Lived Hadrons

The Breit-Wigner Formula

The shape of an isolated peak is conveniently approximated by theBreit-Wigner formula

N(W ) =K

(W −Wr )2 + Γ2/4

where K is a constant that depends on the total number of decaysobserved and Wr is the position of the maximum.

This formula is closely analogous to that used to describe the naturalline width of an excited state of an atom, which is an unstable particlemade of a nucleus and electrons, rather than quarks and antiquarks.

Quarks and Hadrons

Short-Lived Hadrons

The Breit-Wigner Formula

Quarks and Hadrons

Short-Lived Hadrons

Calculating Internal Quantum Numbers

Obtaining the internal quantum numbers of the K ∗− particle isstraightforward using the known values of the other particles involvedin the interaction.

Q = −1,B = 0, S = −1,C = B = T = 0

We thus arrive at a unique quark assignment for the K ∗− which is su

Quarks and Hadrons

Short-Lived Hadrons

Excited States

Do the same excercise for the resonance particle K ∗0 involved in theinteraction

K− + p → K ∗0 + n→ K− + π+

Notice that K ∗− have the same quark structure as K−, but is heavier.

A spectrum of states (particles) with these quantum numberscorresponding to su have been discovered.

The lightest of these states (the ground state) is the long-lived K−meson which decays by the weak interaction processes

K− → µ− + νµ , K− → π− + π0

The heavier states (excited states) are resonances that decay by thestrong interaction with widths typically of the order 50-250 MeV.

Quarks and Hadrons

Short-Lived Hadrons

Excited States

This picture is not restricted to strange mesons, but appliesqualitatively to all quark systems, ud , uud , uds, etc.

Each system has a ground state, which is usually a long-lived particledecaying by weak or electromagnetic interactions, and a number ofexcited (resonance) states.

The resulting spectra are qualitatively similar to that of K mesonsand the analogy with energy-level diagrams of other compositsystems, like atoms and nuclei, is obvious.