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Strong Interactions, Lattice and HQET

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Strong Interactions, Lattice and HQET Strong interactions, Lattice and HQET Vicent Gimenez´ Gomez´ Introduction Strong interactions, Lattice and HQET Historical background Quark model Vicent Gimenez´ Gomez´ Color The parton Departament de F´ısica Teorica-IFIC` model Universitat de Valencia-CSIC` QCD Lagrangian Feynman rules May 3, 2013 Elementary Calculations + e e− annihilation into hadrons 1 / 153 Renormalization Contents Strong interactions, Lattice and 1 Introduction HQET Vicent 2 Historical background Gimenez´ Gomez´ 3 Quark model Introduction 4 Color Historical background 5 The parton model Quark model Color 6 QCD Lagrangian The parton model 7 Feynman rules QCD Lagrangian 8 Elementary Calculations Feynman rules + Elementary 9 e e− annihilation into hadrons Calculations + e e− 10 Renormalization annihilation into hadrons 2 / 153 Renormalization Introduction Strong interactions, Lattice and HQET Quantum Chromodynamics (QCD), first introduced by Gell-Mann and Vicent Frizsch in 1972, is the theory of strong interactions. It is a renormaliz- Gimenez´ able nonabelian gauge theory based on the color SU(3) group which Gomez´ elementary fields are quarks and gluons. Introduction Why is QCD important for Particle Physics? Historical background Electroweak processes of hadrons necessarily involve strong • Quark model interactions. Color A quantitative understanding of the QCD background in • The parton searches for new physics at present and future accelerators is model crucial. QCD Lagrangian In this lectures we give an introduction to the foundation of perturba- Feynman rules tive and nonperturbative QCD and some important physical applications: Elementary Deep Inelastic Scattering (DIS) and e+ e annihilation into hadrons. Calculations − + e e− annihilation into hadrons 3 / 153 Renormalization History Strong interactions, The history that led to the discovery of QCD is fascinating. We briefly Lattice and comment on some turning points. HQET Vicent Neutron discovery Gimenez´ ´ Gomez Since the discovery of the neutron (Chadwick 1932), the strong interac- Introduction tions have been reconigned as a separate force of nature. It is attractive Historical at intermediate distances and so strong that it overcomes the electric re- background pulsion of the protons in atomic nuclei (typical electromagnetic distance: Quark model 10 electrons in an atom, 10− m to be compared with a typical strong- Color 15 interaction distance: protons in a nucleus, 10− m). The parton model Yukawa model QCD Lagrangian Yukawa in 1934 proposed that the exchange of pions is the source of Feynman rules the forces between protons and neutrons g mπ r Elementary U(r) = e− Calculations ± r + e e− annihilation The mass of the pion is just the inverse of the range of the force. into hadrons 4 / 153 Renormalization History (II) Strong interactions, Lattice and HQET Isospin formalism Vicent Gimenez´ Gomez´ Between 1935 and 1938, the charge invariance of strong interactions was experimentally established. Cassen and Condon invented the for- Introduction malism incorporating this proptery: isospin symmetry. The theory was Historical completed by Kemmer in 1938 by the introduction of a neutral pion background φ3 with the same mass of the charged pions φ . The Hamiltonian of the Quark model 1,2 strong interactions incorporating the isospin symmetry reads Color The parton ψ model H = gψ¯~τψ~φ ψ p QCD ≡ ψn Lagrangian Feynman rules On the experimental side, the π± were discovered by Powell in 1947 and 0 Elementary the π at Brookhaven in 1950. Calculations + e e− annihilation into hadrons 5 / 153 Renormalization History (III) Strong interactions, Lattice and The discovery of strangeness HQET Vicent The particles discovered in 1947 by Butler and Rochester were almost Gimenez´ 0 + Gomez´ certaintly the decays of K and K to two pions. Soon after this, it was + discovered the decay of K to three pions and a Ξ− to π−p. In 1955 Introduction Gell-Mann gave them the name of strange particles because behaved Historical background strangely. In fact, they were produced in collisions on cosmic rays with Quark model rates comparable to those of pions, but decayed many orders of magni- Color tud slower than as expected for a decay mediated by strong interactions. The parton Gell-Mann in 1953 solved the puzzle of new particle decays by making model clever isospin assignements to these particles. Then, isospin conserva- QCD Lagrangian tion prevented them from decaying into the observed decay modes via Feynman rules strong interactions, but allowed them to proceed via weak interactions, Elementary which explained their long lifetimes. Isospin assignements worked but Calculations + there was still the question: is there any deeper reason for it? e e− annihilation into hadrons 6 / 153 Renormalization History (IV) Strong Strangeness quantum number interactions, Lattice and HQET In 1954, Nishijima observed that the peculiar isospin assignement of Vicent Gell-Mann can be reformulated in terms of a new quantum number Gimenez´ Gomez´ called ”strangeness” which is conserved in strong interactions but vio- lated by weak forces. He wrote, Introduction Historical B + S background Q = I + hypercharge Y B + S 3 2 Quark model ≡ Color In Gell-Mann’s model, each particle is labelled by three quantum num- The parton bers I, I3 and Y or Q. model The introduction of strangeness was crucial because it opened the way QCD Lagrangian to unitary symmetry and and the consequent development of the quark Feynman rules model by Gell-Mann (Nobel prize in Physics in 1969 from the Eight- Elementary fold Way). The peculiar isospin assignments of Gell-Mann, Nakano and Calculations + Nishijima are, within the quark model, simply a consequence of the fact e e− annihilation into hadrons that the strange quark is an isospin singlet. 7 / 153 Renormalization History (V) Strong In the annual conference on high energy physics in Pisa in 1955, the interactions, Lattice and properties of the observed strange particles were stablished. Gell-Mann HQET predicted the existence of Σ0 (found in 1956), Ξ0 (found in 1959) and, Vicent Gimenez´ most remarkably, of Ω− (discovered in 1964), assigned to an isosinglet. Gomez´ Non abelian gauge theories Introduction Historical In 1954, Yang and Mills created nonabelian gauge theories. QCD,as we background will see, is a non abelian gauge theory based on color SU(3). Quark model Sakata model Color The parton The Sakata model (1959) postulated that the hadrons could be consid- model ered to be composite states of p, n and Λ particles. Ikeda, Ohnuki and QCD Lagrangian Ogawa in 1959 suggested that the triplet of particles transformed in the fundamental representation 3 of . They correctly said that the Feynman rules SU(3) mesons could be build out bound states of 3 and 3: Elementary Calculations 3 3 = 8 1 + e e− ⊗ ⊕ annihilation but several of their assigments were incorrect. into hadrons 8 / 153 Renormalization History (VI) Strong interactions, The Eightfold Way and quark model Lattice and HQET In 1961, Gell-Mann and Ne’eman, made the correct SU(3) assignments: Vicent Gimenez´ baryons and mesons were arranged in what they called the Eightfold Gomez´ Way. Introduction The Gell-Mann and Zweig proposed that these SU(3) assignments could Historical be generated if one postulated the existence of new constituents, called background ”quarks”, which transformed as a triplet 3. All other higher representa- Quark model tions could be generated beginning by quarks by taking multiple products Color of the fundamental representation. In the fundamental representation of The parton model SU(3), the quarks were called up, u, down, d, and strange, s. QCD The u and d quarks formed an SU(2) isodoublet. The strange quarks Lagrangian was introduced because in the 1950s, as we said before, it was observed Feynman rules that strangeness, a new quantun number in addition to isospin, was con- Elementary Calculations served by hadronic processes. The SU(3) paradigm explains the new + e e− quantum number because it is a rank two Lie group. annihilation into hadrons 9 / 153 Renormalization History (VII) Strong interactions, Quark model Lattice and HQET SU(3) representations are labeled by two numbers: third component of Vicent Gimenez´ isospin I3 and hypercharge Y = B + S, where B is the baryon number Gomez´ and S the strangeness. But these quantum numbers are not indepen- Introduction dent. Nishijima and Gell-Mann proposed the relation Historical background Y Q = I3 + Quark model 2 Color where Q is the electric charge. To fit the known spectrum, mesons were The parton postulated to be composite states of a quark and an antiquarrk, and model baryons are composite of three quarks, QCD Lagrangian 3 3 = 8 1 3 3 3 = 10 8 8 1 Feynman rules ⊗ ⊕ ⊗ ⊗ ⊕ ⊕ ⊕ Elementary Calculations The theory predicted that the mesons should be arranged in terms of + e e− octets and singlets, whyle baryons should be in octets and decuplets. annihilation into hadrons 10 / 153 Renormalization History (VIII) Strong In order to reproduce the known charges of mesons and baryons, the interactions, Lattice and quarks are postulated to have fractional charges HQET Vicent 2 1 1 Gimenez´ Qu = Qd = Qs = Gomez´ 3 −3 −3 Introduction Since three quarks make up a baryon, quarks have baryon number 1/3. Historical More in the next section. background Quark model Turning points to be disccussed in the lectures Color The parton The observation of scaling in deep-inelastic scattering (DIS). model • QCD The proposal of color a symmetry of the strong interactions. Lagrangian • Asymptotic Freedom Feynman rules • Elementary Calculations DIS made Quantum Chromodynamics (QCD), a quantum theory of fields + with color as a local symmetry, the unique explanation of the strong in- e e− annihilation teractions, through its property of asymptotic freedom. into hadrons 11 / 153 Renormalization State of particle physics in the early sixties Strong interactions, In the early sixties of the last century, QED had been formulated as a Lattice and HQET Quantum Field Theory (QFT) to describe electromagnetic interactions. Vicent Many precise QED predictions were confirmed experimentally.
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