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Quarks and their bound states are the only particles which interact strongly

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(1)Quarks.

(2) Quarks • Quarks are s = ½ fermions, subject to all kind of interactions. • They have fractional electric charges • Quarks and their bound states are the only particles which interact strongly ⎛ u ⎞ ⎛ c ⎞ ⎛ t ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ • Like leptons, quarks occur in 3 generations: ⎝ d ⎠ ⎝ s ⎠ ⎝ b ⎠ • Corresponding antiquarks are:. ⎛ d ⎞ ⎛ s ⎞ ⎛ b ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ u ⎠ ⎝ c ⎠ ⎝ t ⎠.

(3) Brief history of hadron discoveries • First known hadrons were proton and neutron • The lightest are pions π. There are charged pions π+, π-, with mass of 0.140 GeV/c2, and neutral ones π0, with mass of 0.135 GeV/c2 • Pions and nucleons are the lightest particles containing u- and d-quarks: were discovered in 1947 in cosmic rays, using photoemulsion to detect particles → p+n+π+ • Some reactions induced by cosmic rays:. p+ p. → p+ p+π0 → p+ p+π+ +π+. • Same reactions can be reproduced in accelerators, with higher rates (but cosmics may provide higher energies).

(4) The Neutral Pion.

(5) The Neutral Pion.

(6) The Neutral Pion. m (π 0 ) = 135.0 MeV / c 2. π 0 → γ γ , γ e+e−. Decay mode Electromagnetic. BR =98.8%. BR =1.2%. τ = 0.84 ×10 −16 s. Decay lifetime. Experimental evidence. Cosmic ray studies of «star-like» events in high resolution nuclear emulsions (1950, Carlson, Hooper, King). High energy experiments at the Berkeley +Cyclotron. e. e−. γ. p. e+ “Primary” vertex. γ. e−. The detachment from the “primary vertex” of the interaction is caused by the neutral pion lifetime.

(7) Charged pions decay mainly to the muon-neutrino pair (BR ~99.99%) having lifetimes of 2.6x10-8 s. In quark terms:. (ud ) → µ + +ν µ Neutral pions decay mostly by the electro- magnetic interaction, having shorter lifetime of 0.8x10-16 s. π 0 →γ +γ At the beginning discovered pions were believed to be responsible for the nuclear forces However, at ranges comparable with the size of nucleons this description fails..

(8) Particles with Strangeness Presence of unknown particles in experiments with cloud chambers or emulsions on atmospheric balloons (1947, Rochester and Butler). They turned out to be secondary particles with a characteristic “V” shape decay. π p → ΛK → p π π π −. −. +. −. These particles were produced in pairs and characterised by: • Strong Interaction production (cross section) • Weak Interaction decays (lifetimes). π. π. Interazione forte. p. •. Interazione debole. σ ≈ mb τ ≈ 10 −10 s. π π. p 8.

(9) Particles with Strangeness π–p→ΛK˚ a ≈ 1 GeV/c nella camera a bolle a H2 liquido da 180 cm di Alvarez. Metà anni ‘50. Solution given by Gell-Mann (1953-56) and independently by Nisishima (1955): a new quantum number, additive, the strangeness S S of the “old” particles = 0 S of strange mesons = +1 And of their anti-particles = –1 S of hyperons = – 1 And of anti-hyperons = +1. Strong interactions save S π − p → K 0 Λ 0 permesso π − p → K 0n. vietato. π − p → K − Σ + vietato nn → ΛΛ vietato. Weak interactions violate S. Λ → pπ − permesso Σ − → nπ − permesso Σ 0 → Λγ permesso.

(10) Strange particles: kaon discovery.

(11) Particles with Strangeness s a new quark (different from u,d) ! Λ → p π − , nπ 0. (τ = 2.6 ×10 −10 s). BR = 64.1%. BR = 35.7%. m (Λ) = 1115.6 MeV / c 2. Λ = (u , d , s ). K s0 → π +π − , π 0π 0 (τ = 0.895 ×10 −10 s ). BR = 69.2%. BR = 30.7%. m (π − ) = 139.6 MeV / c 2 m (π 0 ) = 135.0 MeV / c 2 m( K ) ≅ 495 MeV / c 2. The long lifetime was explained by the disappearance of a «strange» quark. K particles (Kaons), similar to Pions but with the s Quark.

(12) Particle Classification e ,e −. +. µ−, µ+. Λ = (u , d , s ). γ. p = (u , u , d ) n = (u, d , d ). Photon. Proton-like particles (baryons). Leptons (heavier copies of the electron). π + = (u, d ) , π − = (d , u ) Mesons π0 ,K. The neutrino, postulated to explain beta decay and observed in inverse beta decay, is always associated to a charged lepton.. ν The hadrons, particles made up of quarks and obeying mainly to strong nuclear interaction 12.

(13) Strange mesons K mesons are the only strange mesons which decay weakly, the others decay strongly in very short time. Q. S. m(MeV). τ(ns) Decadimenti comuni. K+ (us). +1. +1. 494. 12. µ+νµ, π+ π+ π–, π+ π0. K0(ds). 0. +1. (498). n.a.. n.a.. K–(db). –1. –1. 494. 12. µ-νµ, π+ π– π–, π–π0. K0 (us). 0. –1. (498). n.a.. n.a. K˚ and K˚ are electrically neutral, but different since they have opposite strangeness..

(14) The strange Hyperons The lightest ones are: Q. S. m(MeV). τ(ps). dec. princ.. 0. –1. 1116. 263. pπ–/nπ˚. Q. S. m(MeV). τ(ps). dec. princ. Σ+(uus). +1. –1. 1189. 80. pπ0/nπ+. Σ0(uds). 0. –1. 1193. 7.4 ×10–8. Λ γ. Σ–(dds). –1. –1. 1197. 148. nπ–. Q. S. m(MeV). τ(ps). dec. princ.. Ξ0(uss). 0. –2. 1315. 290. Λ π0. Ξ–(dss). –1. –2. 1321. 164. Λ π–. Λ (uds). Masses increase with the increase of the s-quark number Σ– is not the antiparticle of Σ+ No strange hyperon, except Σ0 can decay without changing its strangeness, then through weak interaction.

(15) More strange particles: S=2.

(16)

(17) Heavy quarks: the Charm 1974: the October revolution. J/ψ discovery in 2 experiments. 1) Brookhaven experiment: 28 GeV protons on a fixed target. p + Be → J /ψ + X e+e−. 2) SLAC experiment: electron-positron collider. e + e − → J /ψ. e + e − , µ + µ − , adroni. Invariant mass distribution for the final states. (. ). m 2 e+ e− = 2me2 + 2E1E2 + 2 p1 p2 cos (θ1 + θ 2 ).

(18) The charm quark.

(19) J/Ψ.

(20) Width dominated by experimental resolution Real width from knowledge of cross section and BRs. Width Γ= 0.093 MeV. Lifetime 10-20 s 20.

(21) A problem with the J/ψ: Usually the hadron resonances have large widths since they decay via strong interactions and have a very short lifetime. 10. − 22. / 10. − 23.  s =τ ≅ Γ. ⇒ Γ =10 − 200 MeV. Γ( J /ψ ) = 93 keV. As comparison:. Γ( ρ ) =150 MeV. Γ(ω ) = 8.5 MeV. Γ(φ ) = 4.3 MeV. How can a resonance have a width100/1000 times smaller thn usual but still being a strong interacting particle? To answer to this question we have to know other particles containing the c-quark. 21.

(22) Studying better the production region of a J/Ψ , one could notice also states of the J/ψ type much larger, over a certain threshold.. 22.

(23) J/ψ contains a new quark, the charm.. J /ψ = c c , m = 3097, τ =10 −20 s J /ψ = c c. C = 0 Hidden charm. Particles with “visible” charm were discovered at SLAC in the following years. D + = c d , m = 1870, τ =10 −12 s. D− = cd. D 0 = c u , m =1865, τ = 4 ×10 −13 s. D 0 = cu c. One would expect than that the J/ψ decays as: But this is not possible, since:. c. u. u. c. c. m( J /ψ ) = 3097 < 2m( D) = 3730 MeV. J / ψ → DD impossibile. 23.

(24) For all the J/ψ states such that:. 3 gluons exchange. m < 2 m( D ) Suppressed by Zweig rule. For all the J/ψ states such that:. M > 2m( D). Excited states have high enough mass to decay in charmed mesons.

(25) Other Ψ tests. ψ '→ψ +π+ +π−. ψ → e+ + e−.

(26) Charmed mesons The Mark I detector started the search of the charmed pseudoscalar mesons at √s=4.02 GeV in 1976 (having improved its K to π discrimination ability) in:. e+ + e – → D 0 + D 0 + X. e+ + e – → D + + D _ + X. Mesons appear as resonances in the final state. Neutral D were observed decaying in the final states D 0 → K + π − D 0 → K − π + Charged D-mesons observed in: D + → K – π +π + D − → K +π −π −. No resonance in: D + → K +π +π − D − → K −π +π − Mass =1869 MeV. 26.

(27) Charmed mesons D + = c d , m = 1870, τ =10 −12 s. D− = cd. D 0 = c u , m =1865, τ = 4 ×10 −13 s. D 0 = cu. Lightest mesons with charm. Main decay modes: type c à s, via weak interactions. For example:. D + → K +π 0π +π + , BR = 6%. D0 → K −π +π 0 , BR = 14%. Mesons with charm and strange quarks: Ds+ = c s , m = 1969, τ = 5 ×10 −13 s , (C = +1, S = +1). Typical decay, with c à s: Barions with charm:. DS− = c s, (C = −1, S = −1). Ds+ → K + K −π + , BR = 5%. Λ+c = cud , m = 2285, τ = 2 ×10 −13 s. Typical decay, with c à s:. Λ+c → p K − π + , BR = 5%. Λ−c = c u d.

(28) Even heavier charmed mesons were found which contained strange quark as well:. Ds+ (1969) = cs , D (1969) = sc − s. Lifetimes of the lightest charmed particles are of ~10-13 s, well in the expected range of weak decays • Discovery of “charmed” particles was a triumph for electroweak theory, which demanded number of quarks and leptons to be equal.

(29) First sign of the 3rd family: the beauty quark Two families were known in 1977. In the weak interactions, the two families appear rotated (Cabibbo angle). ⎛ dC ⎞ ⎡ cosθ C ⎜⎜ ⎟⎟ = ⎢ ⎝ sC ⎠ ⎣− sin θ C. sin θ C ⎤ ⎛ d ⎞ ⎜⎜ ⎟⎟ ⎥ cosθ C ⎦ ⎝ s ⎠. Third family. The mixing in fact, involves all three families (CKM matrix).

(30) b-quark discovery Lederman et al. Experiment at Fermilab in 1977. Final state with two muons in proton (400 GeV) collision on a fixed target. The particle discovered was. Υ = bb , m = 9460, Γ = 54 keV In complete analogy with the J/ψ case. These particles are composed by an even heavier quark: the b-quark..

(31) The two arms muon spectrometer Fermilab 1977. 31.

(32) Again, in analogy with the J/ψ Y(4s) state, the first one which has enough mass to decay in a B and anti-B. Υ (4S ) → B B. States which decays hadronically in 3 gluons. Y has a hidden beauty, while mesons with “visibile” beauty are:. B + = u b , m = 5279, τ =1.6 ×10 −12 s, B = +1. B− = ub. B 0 = d b , m = 5279, τ =1.5 ×10 −12 s, B = +1. B 0 = db. BS0 = sb , m = 5366, τ =1.5 ×10 −12 s, B = +1, S = −1 The lightest barion with beauty is:. Λ0b = bud , m = 5620, τ =1.4 ×10 −12 s.

(33) Onia systems J/ψ as quarkonium: nonrelativistic combination determined by a basic Coulomb potential Vs (r) = −. αS. 4 αs + kr 3 r. α. 33.

(34) Decays of particles with beauty, with prevalence of b à c The decays happen in particles with charm. b → cW − Examples of invariant mass reconstruction of particles with beauty.

(35) Top quark discovery. Quark annihilation. The sixth quark was found in 1994 at Fermilab. The first evidence came from the CDF experiment in proton/antiproton collisions at the energy of 1.8 TeV. Gluon-gluon fusion. Typical Feynman diagrams for production. Topology of a top event.

(36) Top quark discovery • Searched at hadrons colliders for more than a decennium (difficult due to its very large mass mt=173 GeV). Need CoM energy > 400 GeV • In a pp collision at √s = 2 TeV a ttbar pair is produced every 1010 collisions.. p + p → t + t + X;. t → W + + b; t → W − + b. • Look in the “clean” channels W → eν e o → µν µ • W decays most often in quark antiquark, but background is huge due to strong interactions • Good tag: detect a b in the hadronic jet t → W + + b → W + + jet(b); t → W − + b → W − + jet(b ) W → eν e o → µν µ e W → qq ' → jet + jet.

(37) Top quark discovery Important detector elements • Si microstrip high spatial resolution vertex detector • Tracking detectors • Hermetic calorimetry (in the transversal plane) ⇒ missing momenum, neutrinos.

(38) Top at LHC. R. CHIERICI. 30. Events / ( 10 GeV/c2 ). !(tt) (pb). CMS, 3.54 fb-1 at CMS di-leptons (L=2.3/fb) ATLAS di-leptons (L=0.7/fb) CDF D0. 102. R. CHIERICI. s = 7 TeV CMS data: 3136 events. 350. tt component. 300. multijet QCD background. 250. combined tt and QCD. f sig = 0.351 ± 0.025. 200 NLO QCD (pp) Approx. NNLO QCD (pp) Scale uncertainty Scale " PDF uncertainty Approx. NNLO QCD (pp) Scale uncertainty Scale " PDF uncertainty. 10. 150 100 50. Langenfeld, Moch, Uwer, Phys. Rev. D80 (2009) 054009 MSTW 2008 (N)NLO PDF, 90% C.L. uncertainty. 1. 2. 3. 4. 5. 6. 7. 8. s (TeV). 0 100. 150. 200. 250. 300. 350. 400. 450. 500. 550. mtop (GeV/c2). Fig. 9. – Left: three-jets invariant masspair in candidate +jets events in to CMS. Right: result of e most precise ATLAS and CMS top quark cross sections are compared the section fit on data of top pair signal and QCD multi-jet cross evolution withquark the centre-of-mass energy. Lower energybackground results from to the reconstructed Invariant mass of the jets top quark in CMS; cross the uncertainty also shown. Topmass production section in the signal fraction, indicated in the figure, is just statistical.. copared to QCD calculations. selected as compatible with all hadronic decay of top. 38. tion (CMS thisYukawa last example, consistency easure directly[193]). the top In quark couplingthe at the tree level. of the signal region with top quark pair production can be tested by cutting on the MVA discriminant and looking,.

(39) Top quark properities The top quark mass, of about 175 GeV, makes it different from the b- and c-quark. Almost always it decays in :. t → bW + Can we observe a toponium state, as mesons and barions composed by a quark top? NO. The hadronization time is of order:. t ≅ R / c =1 fm / c ≅10 −24 s We can think it as the time a gluon needs to cross a nucleon. The decay rate of a quark top is proportional to its mass and we have:. τ ≈ Γ −1 ≅5×10−25 s The top quark decay in a b-quark before hadronizing..

(40) The quark model: Baryons and antibaryons are bound states of 3 quarks Mesons are bound states of a quark and an anti-quark Barions and Mesons are: Hadrons.

(41) Hadrons.

(42) Quantum Numbers and flavours.

(43) • Strange, charmed, bottom and top quarks each have an additional quantum number: strageness S, charm C, beauty B and truth T respectively. • In strong interactions the flavour quantum number is conserved • Quarks can change flavours in weak interactions (DS =±1, DC =±1). Theory postulated in 1964 (Gell-Mann). e. e’ p. In the 70’s, deep inelastic scattering of electrons on p and bound n show evidence for the quark model.

(44) Particles and Interactions Quarks. Strong. EM. Weak. Charged leptons. Neutrini.

(45) Hadrons and lifetime.

(46) • Majority of hadrons are unstable and tend to decay by the strong interaction to the state with the lowest possible mass (t ~ 10-23 s) • Hadrons with the lowest possible mass for each quark number (S, C, etc.) may live much more before decaying weekly (t ~ 10-7- 10-13 s) or electromagnetically (mesons, t~10-16- 10-21 s) Such hadrons are called stable particles.

(47) Strangeness is such that S=-1 for s-quark and S =1 for the anti s-quark. Further, C=1 for c-quark, B=-1 for b-quark and T=1 for t-quark Since t-quark is a very short living one, there are no hadrons containg top, i,e, T=0 for all Quark numbers for up and down quarks have no name, but just like any other flavour, they are conserved in strong and em interactions Baryons are assigned own quantum number B: B=1 for baryons, B=-1 for antibaryons, B=0 for mesons.

(48)

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