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Properties of Quarks Isospin Many Groupings of Particles of Similar Mass and Properties Fitted in to Common Patterns

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Properties of Quarks Isospin Many Groupings of Particles of Similar Mass and Properties Fitted in to Common Patterns Properties of Quarks Isospin Many groupings of particles of similar mass and properties fitted in to common patterns. So far, we have discussed three families of leptons but isotopic spin or principally concentrated on one doublet of quarks , the One way to characterise these is using isospin , I. u and d. This quantity has nothing to do with the real spin of the particle, but obeys the same addition laws as the We will now introduce other types of quarks, along quantum mechanical rules for adding angular with the new quantum numbers which characterise momentum or spin. them. When the orientation of an isospin vector is considered, it is in some hypothetical space, not in terms of the x, y and z axes of normal co-ordinates. 1 2 Nucleons (p, n) , pi mesons ( π+, π0, π–) and the baryons known as ∆ (∆++ , ∆+, ∆0, ∆–) are three examples of groups of similar mass particles differing in charge by one unit. The rule for electric charge can then be written, The charge Q in each case can be considered as due to =( 1 + ) Q e2 B I 3 the orientation of an “isospin vector” in some where B is the baryon number which is 1 for nucleons hypothetical space, such that Q depends on the third and the ∆ and 0 for mesons such as the π. component I3. Thus the nucleons belong to an isospin doublet ≡ = 1 1 =1 − 1 In terms of quarks, the u and d form an isospin doublet, pI , I 3 2 , 2 n2 , 2 u= 1 , 1 =1 − 1 Similarly the pions form an isospin triplet , 2 2 d2 , 2 + 0 − 1 π = 1,1 π = 1, 0 π =1, − 1 (both with B = /3). 3 The ∆ forms a quadruplet with I = /2. 4 6 Strangeness 1 Three quarks with I = /2 can combine to form It was observed that some unstable particles produced in 1 3 Itot = /2 or /2. strong interactions had a long lifetime. This unusual stability for strongly interacting particles led to the term of strangeness . I = 1/ gives the nucleons while I = 3/ forms the ∆. tot 2 tot 2 Such particles are always produced in pairs (associated production), and the quantum number of strangeness , S, was introduced, which is conserved in strong In strong interactions, the total isospin vector (as well as interactions. Thus in the interaction π– p → Λ0 K0, the Λ is assigned I3) is conserved. S = –1 and the K S = +1. The strange particles can only decay by the weak This is not true in electromagnetic or weak interactions. interaction, which does not conserve strangeness (as we 7 will discuss later). 8 (Table) Hadrons, quarks and quantum numbers: The formula for electric charge must now be modified to read the story so far =( ++1 1) =( + 1 ) QeI32 B 2 S eI 3 2 Y where Y = B + S is known as the hypercharge . ° Groups of particles with similar properties are characterised by same quantum numbers, (This formula is known as the Gell-Mann Nishijima e.g. isospin I and strangeness S relation.) ° Electric charge determined by 3 rd component of isospin, I3 Families of particles with similar properties (e.g. same ° Up and down quark form isospin doublet, I = ½ spin and parity) can be plotted in terms of Y versus I3, and form regular geometrical figures (see plots). =( + 1 ) Q eI3 2 Y where Y = B + S is known as the hypercharge . 9 10 Y = S Y = S + + K 0 (ds ) +1 K (us ) K*0 +1 K* − η + − φ + π (du ) π (ud ) ρ ω ρ 0 0 –1 − 1 π 1 +1 I 3 –1 − 1 ρ 1 +1 I 3 2 2 2 2 − ( ) 0 *− *0 K su –1 K (sd ) K –1 K The lowest-lying pseudoscalar-meson states The vector-meson nonet ( JP = 1 –). (JP = 0 –), with quark assignments indicated. 12 13 Y Y − ∆0 ∆+ ++ p N( 939 ) ∆ ∆ n +1 I = 3 (1232) 2 +1 Σ− Σ0 Σ+ = I 1 I 3 (1384) –1 − 1 1 +1 Σ− Σ0 Σ+ Σ (1193 ) 2 2 I 3 –1 − 1 Λ 1 +1 Λ (1116 ) 2 2 = 1 Ξ− Ξ0 I 2 –1 (1533) Ξ− Ξ0 –1 Ξ (1318 ) − –2 (1672) I = 0 Ω P + The baryon octet of spin-parity ( J ) ½ P 3 + The baryon decuplet of spin-parity ( J ) /2 14 15 (with masses in MeV/ c2). (with masses in MeV/ c2). Quark Quantum Numbers In terms of quarks we can introduce a new flavour of quark, the strange quark s . Flavour charge/ e BII3 S ... This has charge –1/ and baryon number 1/ (like a 3 3 d –1/ 1/ 1/ –1/ 0 d quark) but I = 0 and S = –1. 3 3 2 2 u +2/ 1/ 1/ +1/ 0 It is also somewhat heavier than the u and d quarks. 3 3 2 2 s –1/ 1/ 0 0 –1 Since baryons consist of qqq , it is clear why no positive 3 3 baryons exist with | S| > 1, while negative baryons are . found with S = –2 or –3. Note that the type of quark is known as its flavour . Quarks. carry flavour and colour , and each flavour of quark exists in three colours. 16 18 The Standard Model of Particle Physics Further Quarks Fermions Bosons Other, still heavier quarks also exist. 2 The charm quark , c, has a charge of /3, like the u, and Leptons Quarks can be considered as a partner to the s. ν γ e e d u ± 0 µ νµ s c W , Z In 3 dimensions (see figure) particles containing τ ντ b t g c quarks can be plotted, and again show regular patterns. H0 19 22 Disputed claim 2002 Discovered 2017! Quark Quantum Numbers Not yet! Flavour charge/ e BII3 S c 1 1 1 1 d – /3 /3 /2 – /2 0 0 2 1 1 1 u + /3 /3 /2 + /2 0 0 1 1 s – /3 /3 0 0 –1 0 2 1 c + /3 /3 0 0 0 +1 Multiplets of hadrons containing up, down, strange and charm quarks. The slices through these figures where Charm = 0 correspond to the plane figures already shown in the previous diagrams, though containing new particles in 21 the case of the mesons, composed of cc . 23 Not yet! We thus have 2 doublets or generations of quarks – (d, u) and (s, c). Since there are 3 doublets of leptons, there are theoretical reasons for expecting a third doublet of quarks too. Particles containing b quarks (bottom or beauty ) were discovered in 1977. The b is an even heavier version of the d. Multiplets of hadrons containing up, down, strange and charm quarks. Example decays 24 25 Quark Quantum Numbers We thus have 2 doublets or generations of quarks – (d, u) and (s, c). Flavour charge/ e BII S c b 3 Since there are 3 doublets of leptons, there are 1 1 1 1 theoretical reasons for expecting a third doublet of d – /3 /3 /2 – /2 0 0 0 quarks too. u +2/ 1/ 1/ +1/ 0 0 0 3 3 2 2 Particles containing b quarks (bottom or beauty ) were 1 1 discovered in 1977. The b is an even heavier version s – /3 /3 0 0 –1 0 0 of the d. 2 1 c + /3 /3 0 0 0 +1 0 Its partner, the t (top or truth ) was first seen in 1994, 2 1 1 and its mass has now been measured at 174 GeV/c . b – /3 /3 0 0 0 0 –1 26 27 Quark Quantum Numbers The Standard Model of Particle Physics Flavour charge/ e BII S c b t 3 Fermions Bosons 1 1 1 1 d – /3 /3 /2 – /2 0 0 0 0 Leptons Quarks u +2/ 1/ 1/ +1/ 0 0 0 0 ν γ 3 3 2 2 e e d u s –1/ 1/ 0 0 –1 0 0 0 ± 0 3 3 µ νµ s c W , Z c +2/ 1/ 0 0 0 +1 0 0 3 3 τ ντ b t g 1 1 b – /3 /3 0 0 0 0 –1 0 t +2/ 1/ 0 0 0 0 0 +1 0 3 3 H 28 29 What you should have learned Quark Flavour and the Weak Interaction As we have already seen, the strong and electromagnetic • Isospin, multiplets and charge interactions conserve quark flavour , whereas the weak • Isospin and symmetry interaction may change it . • Strangeness and the strange quark In many weak decays, the changes are within a generation, • Hypercharge e.g. in beta decay the W couples a u to a d quark; +→0 π + • Multiplets in 2D ( Y versus I3) in the decay D K it couples a c to an s. • Charm – multiplets in 3D However, this is not always the case, e.g. in the decay −→ π0 − ν K e e the W couples an s to a u quark, • b and t quarks and it was seen that such strangeness-changing decays were slightly weaker than strangeness-conserving weak decays. 30 31 Reaction Coupling Constant Cabibbo explained this by proposing that the eigenstates of the weak interaction are different from those of the strong interaction. µ→ν+ + ν µ e e G The strong interaction eigenstates are the u, d, s, c, b →+ ν and t quarks, with well-defined isospin, strangeness etc. p n e e 0.97 G The eigenstates of the weak interaction, which does not π→π−0 − ν e e 0.97 G conserve I, S etc, are said to be those of “weak isospin” T.
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