Quarks and Hadrons

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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

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

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

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

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

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 Quarks

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

3 / 43 Mustafa Amin1 & Mustafa Ashry1,2 Quarks and Hadrons Quarks and Hadrons Quarks

Quarks Interactions Quarks are elementary fermions that interact via strong, weak and electromagnetic 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. The W ± and Z bosons are the carriers of the weak force. Quarks interact via electromagnetic interactions, as they have electric charges. Photons is the carrier of the electromagnetic force.

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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) according to their mass diﬀerence minima [1].

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

6 / 43 Mustafa Amin1 & Mustafa Ashry1,2 Quarks and Hadrons Quarks and Hadrons General Properties of 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

7 / 43 Mustafa Amin1 & Mustafa Ashry1,2 Quarks and Hadrons Quarks and Hadrons General Properties of Hadrons

There are no isolated quarks. But more than two hundred of their bound 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 freedom that exists for quarks, but not for leptons, called colour. Quarks are triplets under the group of strong interactions and the color charge for each quark is red, green, or blue. For color conservation and being the electric charges of quark bound states are integers, there are only three types of quark bound states are allowed.

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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 three quarks (qqq). The antibaryons are the antiparticles of baryons and they are bound states of three antiquarks (¯qq¯q¯). The mesons have integer spin and are bound states of a quark and an antiquark (qq¯).

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Examples (Lightest Mesons): For q = u, d,q ¯ =u ¯, d¯, and the allowed 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 thatq ¯ is of anticolor charge opposite to the color charge of q. On the other hand, there is no a two-quark bound state of the form qq orq ¯q¯,(uu, ud, dd, u¯u¯, u¯d¯, d¯d¯) because, they would have neither a zero 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 states uu¯ and dd¯. Indeed, they form an isospin triplet.

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Examples (Lightest Baryons): The allowed three-quark bound states are qqq Q color spin/particle(mass) 1 3 ++ uuu +2 0 2 /? (why?!) or 2 /∆ 1 + 3 + uud, udu, duu +1 0 2 /p = N (938.27 MeV) or 2 /∆ 1 0 3 0 udd, dud, ddu 0 0 2 /n = N (939.66 MeV) or 2 ∆ 1 3 − ddd −1 0 2 /? (why?!) or 2 /∆ Here we assumed that all the three quarks have diﬀerent color charges. The meson state qq¯ is already colorless and of integer electric charge. Hence a state qqq¯ or qq¯q¯ would violate the color charge or the electric charge (indeed, both). The (lightest) spin-1/2 baryons are the proton p = uud, and the neutron n = udd. Indeed, they form an isospin doublet.

11 / 43 Mustafa Amin1 & Mustafa Ashry1,2 Quarks and Hadrons Quarks and Hadrons General Properties of 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 are grouped by Gell-Mann in the following meson octets and baryon octet and decouplet, respectively:

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

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We may also proceed considering a four-quark model in which q = u, d, s, b and ﬁnd all expected mesons and baryons. We may then proceed considering the quark model in which q = u, d, s, c, b and ﬁnd all expected mesons and baryons. The top quark doesn’t constitute baryons as it is very decaying.

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Quark Numbers: We deﬁne the following quark numbers strangeness S = −Ns = −[N(s) − N(¯s)] (1) charm C = Nc = N(c) − N(¯c) (2) bottom B˜ = −Nb = −[N(b) − N(b¯)] (3) top T = 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)

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Also we deﬁne the Baryon number, B, to be 1 B = [N(q) − N(¯q)]. (6) 3 The baryon number B = 1 for baryons, B = 1 for antibaryons and B = 0 for mesons. The baryon number can be given in terms of the quark numbers as 1 B = [N + N + N + N + N + N ] 3 u c t d s b 1 = [N + C + T + N − S − B˜] (7) 3 u d The electric charge Q in terms of the quark numbers is 2 1 Q = [N + N + N ] − [N + N + N ] 3 u c t 3 d s b 2 1 = [N + C + T ] − [N − S − B˜] (8) 3 u 3 d

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The quantum numbers (1)-(8) are called internal quantum numbers, because they are not associated with motion or the spatial properties of wave functions. In strong and electromagnetic interactions quarks and antiquarks are only created or destroyed in particle−antiparticle pairs. For example, the quark description of the strong interaction process

p + p → p + n + π+

(uud) + (uud) → (uud) + (uud) + γ∗/g ∗ → (uud) + (uud) + d + d¯ → (uud) + (udd) + (ud¯)

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

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The β-decay − n → p + e +ν ¯e whose the the quark interpretation is − (udd) → (uud) + e +ν ¯e

violate both the quark numbers Nu and Nd and hence can be interpreted only via the weak interaction as follows −∗ − (udd) → (uud) + W → (uud) + e +ν ¯e

18 / 43 Mustafa Amin1 & Mustafa Ashry1,2 Quarks and Hadrons Quarks and Hadrons General Properties of Hadrons

The quantum numbers (1)-(8) play an important role in understanding the long lifetimes of some hadrons. The vast majority of hadrons are highly unstable and decay to lighter hadrons by the strong interaction with lifetimes of this order 10−23 s. However, each hadron is characterized by a set of values for B, Q, S, C, B˜ and T , and in some cases there are no lighter hadron states with the same values of these quantum numbers to which they can decay (e.g., proton!!!). These hadrons, which cannot decay by strong interactions, are long-lived on a timescale of order 10−23 s and are often called stable particles. Here we shall call them long-lived particles, 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 ﬁne structure constant α leading to observed lifetimes in the range 1016 − 1021 s. Weak decays give longer lifetimes that depend sensitively on the characteristic energy of the decay.

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Electromagnetic decay rates are suppressed by powers of the ﬁne structure constant α leading to observed lifetimes in the range 1016 − 1021 s. Weak decays give longer lifetimes that depend sensitively on the characteristic energy of the decay. Because of this, observed lifetimes for some weak hadron decays lie in the range 1071013 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 three interactions (the neutron lifetime is an exception). Interaction Lifetime (s) Strong 10−22 − 10−24 Electromagnetic 10−16 − 10−21 Weak 10−7 − 10−13

20 / 43 Mustafa Amin1 & Mustafa Ashry1,2 Quarks and Hadrons Quarks and Hadrons Pions and Nucleons

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

21 / 43 Mustafa Amin1 & Mustafa Ashry1,2 Quarks and Hadrons 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 reactions that conserve both charge and baryon number, e.g. in protonproton collisions

p + p → p + n + π+ p + p → p + p + π+ + π− p + p → p + p + π0

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The charged pions decay predominantly by the reactions

+ + π → µ + νµ − − π → µ +ν ¯µ

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

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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 proton and the neutron p = uud , n = udd

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Yukawa Theory

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

25 / 43 Mustafa Amin1 & Mustafa Ashry1,2 Quarks and Hadrons Quarks and Hadrons Short-Lived 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

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Short-lived Hadrons

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

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An Example of Resonances

K − + p → X − + p → K¯ 0 + π− + p

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Still With The Example

The distance between the points where the resonance is produced and decays 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 the K¯ 0π− pair is given by

2 2 2 2 2 2 W ≡ (EK + Eπ) − (pK + pπ) = E − p = M

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The Peak

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

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

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The Decay Width of the Resonance

This resonance particle we call K ∗− and it sits on a background arising from uncorrelated pairs produced by some other, non-resonant, mechanism. For a particle at rest, W = E and the energy-time uncertainty principle 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 then the corresponding decay width would be order 100 MeV, which is similar to the width of the resonance peak shown.

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The Breit-Wigner Formula

The shape of an isolated peak is conveniently approximated by the Breit-Wigner formula K N(W ) = 2 2 (W − Wr ) + Γ /4 where K is a constant that depends on the total number of decays observed and Wr is the position of the maximum. This formula is closely analogous to that used to describe the natural line width of an excited state of an atom, which is an unstable particle made of a nucleus and electrons, rather than quarks and antiquarks.

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The Breit-Wigner Formula

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Calculating Internal Quantum Numbers

Obtaining the internal quantum numbers of the K ∗− particle is straightforward using the known values of the other particles involved in 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¯

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Excited States

Do the same excercise for the resonance particle K¯ ∗0 involved in the interaction 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 numbers corresponding 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

− − − − 0 K → µ +ν ¯µ , K → π + π

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

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Excited States

This picture is not restricted to strange mesons, but applies qualitatively to all quark systems, ud¯, uud, uds, etc. Each system has a ground state, which is usually a long-lived particle decaying by weak or electromagnetic interactions, and a number of excited (resonance) states. The resulting spectra are qualitatively similar to that of K mesons and the analogy with energy-level diagrams of other composit systems, like atoms and nuclei, is obvious.

36 / 43 Mustafa Amin1 & Mustafa Ashry1,2 Quarks and Hadrons Quarks and Hadrons Allowed Quantum Numbers and Exotics

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

37 / 43 Mustafa Amin1 & Mustafa Ashry1,2 Quarks and Hadrons Quarks and Hadrons Allowed Quantum Numbers and Exotics

Exotic Hadrons

38 / 43 Mustafa Amin1 & Mustafa Ashry1,2 Quarks and Hadrons Quarks and Hadrons Allowed Quantum Numbers and Exotics

Exotic Hadrons

39 / 43 Mustafa Amin1 & Mustafa Ashry1,2 Quarks and Hadrons Quarks and Hadrons Questions, References & Thanks

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

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Qustions

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References

B. Martin and G. Shaw, Particle physics. John Wiley & Sons, 2013.

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Thanks

Thank you

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