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Tom Blake� ! Warwick Week 2018 An introduction to 3WCTMFlavour Physics @ ! Part 1 ! Tom Blake! ! Warwick Week 2018 1 An introduction to Flavour Physics • What’s covered in these lectures: 1. An introduction to flavour in the SM. ! ➡ A few concepts and a brief history of flavour physics. ! 2. CP violation (part 1) 3. CP violation (part 2). 4. Flavour changing neutral current processes. T. Blake 2 Questions for the LHC era? • What is the mechanism for EW symmetry breaking? ✓ We now know that this is the Higgs mechanism. • What “new physics” lies between the EW and Planck scale? x No idea! There is no evidence for new particles being directly produced at the TeV scale. • What is dark matter? x No idea! Dark matter could be heavy or it could be light. There is no evidence for large missing energy in BSM searches at CMS and ATLAS, which constrains EW scale dark matter, or in direct detection experiments. • Can we explain the matter antimatter asymmetry of the Universe? x No! The SM cannot explain the baryon asymmetry of the Universe. T. Blake 3 SM particle content { x3 colours T. Blake 4 Flavour in the SM • Particle physics can be described to excellent precision by a very simple theory: ! = (A , )+ (φ,A , ) LSM LGauge a i LHiggs a i with: ➡ Gauge terms that deals with the free fields and their interactions by the strong and electroweak interactions. ➡ Higgs terms that gives mass to the SM particles. T. Blake 5 Flavour in the SM • The Gauge part of the Lagrangian is experimentally very well verified, 1 = i ¯ ⇢⇢D F a F µ⌫,a . ! LGauge j j − 4g2 µ⌫ a a Xj, X • The fields are arranged a left-handed doublets and right-handed singlets = QL,uR,dR,LL,eR ! u ⌫ Q = L ,L = L ! L d L e ✓ L◆ ✓ L◆ • The Lagrangian is invariant under a specific set of symmetry groups: SU(3) SU(2) U(1) c ⇥ L ⇥ Y • There are three replicas of the basic fermion families, which without the Higgs would be identical (huge degeneracy). T. Blake 6 Flavour in the SM • The Higgs part of the Lagrangian, on the other hand, is much more ad-hoc. It is necessary to understand the data but is not stable with respect to quantum corrections (often referred to as the Hierarchy problem). It is also the origin of the flavour structure of the SM. ! ! • Masses of the fermions are generated by the Yukawa mechanism: Q¯i Y ijdj φ + ... d¯i M ijdj + ... L D R ! L D R Q¯i Y ijdj φ + ... u¯i M ijuj + ... L U R c ! L U R T. Blake 7 Flavour in the SM • Can pick a basis in which one of the Yukawa matrices is diagonal, e.g. yd 00 yu 00 ! mi Y = 0 y 0 ,Y = V † 0 y 0 ,y D 0 s 1 U 0 c 1 i ⇡ 174GeV ! 00yb 00yt @ A @ A ! • The matrix V is complex and unitary (V†V = 1). • To diagonalise both mass matrices it is necessary to rotate uL and dL separately. Consequently, V also appears in charged current interactions, J µ =¯u γµd u¯ V γµd W L L ! L L • V is known as the Cabibbo, Kobayashi, Maskawa matrix. T. Blake 8 Flavour in the SM mass eigenstates ≠ weak eigenstates! ! d, s, b ↔ d’, s’, b’ T. Blake 9 Free parameters of the SM • 3 gauge couplings • Higgs mass and vacuum expectation value Flavour parameters • 6 quark masses • 3 quark mixing angles and one complex phase (in V) • 3 charged lepton masses • 3 neutrino masses • 3 lepton mixing angles and (at least) one complex phase T. Blake 10 Why is flavour important? • Most of the free parameters of the SM are related to the flavour sector. ➡ Why are there as so many parameters and why do they have the values they do? • The flavour sector provides the only source of CP violation in the SM. • Flavour changing neutral current processes can probe mass scales well beyond those accessible at LHC. ➡ If there are new particles at the TeV-scale, why don’t they manifest themselves in FCNC processes (the so-called flavour problem)? T. Blake 11 Puzzles? • Why do we have a flavour structure with three generations? ➡ We know we need 3+ generations to get CP violation. Are there more generations to discover? • Why do the quarks have a flavour structure that exhibits both smallness and hierarchy? ➡ Why is the neutrino flavour sector so different (neither small nor hierarchical)? T. Blake 12 Flavour hierarchy? CKM matrix for quark sector PMNS matrix for neutrino sector T. Blake 13 Mass hierarchy? • 12 Large hierarchy in 10 scale between the 9 masses of the fermions. 10 mass [eV] 6 • Equivalent to having a 10 large hierarchy in the 3 10 Yukawa couplings. 1 • Why is this hierarchy so -3 large? Why is yt ~ 1? 10 - - - ν ν ν e µ τ u d s c b t e µ τ T. Blake 14 Symmetries and flavour *KUVQTKECNRGTURGEVKXGQPHNCXQWTKPVJG5/ 15 Isospin • Proton and neutron have: ➡ Different charges but almost identical masses. ➡ An identical coupling to the strong force. • In 1932 Heisenberg proposed that they are both part of the an Isospin doublet and can be treated as the same particle with different isospin projections. p(I, IZ) = (½,½), n(I,IZ) = (½,-½) • Pions can be arranged as an Isospin triplet, π+(I, IZ) = (1,+1), π0(I, IZ) = (1, 0) , π-(I, IZ) = (1,-1) T. Blake 16 Isospin • Heisenberg proposed that strong interactions are invariant under rotations in Isospin space (an SU(2) invariance). ➡ Isospin was conserved in strong interactions. ➡ Isospin is violated in weak interactions. ! σ(p + p d + ⇡+):σ(p + n d + ⇡0)=2:1 ! ! ! • We now know that this is not the correct model but it is still a very useful concept. • It works because mu ~ md < ΛQCD and can be used to predict interaction rates. T. Blake 17 Clebsch-Gordon coefficients T. Blake 18 Kaon observation • In 1947, Rochester and Butler observed two new particles with masses around 500 MeV and relatively long lifetimes. 0 + + + K ⇡ ⇡− K µ ⌫µ S ! ! T. Blake 19 Quark model Iz • Concept of quarks introduced by Gell- Mann, Nishijima and Ne’eman to explain the “zoo” of particles. • Now understood to be real “fundamental” particles. • Strangeness conserved by the strong interaction but violated in weak decays. • Organised by Y = B + SQ= e(Iz + Y/2) baryon strangeness Isospin number T. Blake 20 Quark model meson } • Can only make colour neutral objects: q q¯ ➡ Quark anti-quark or three quark combinations (mesons and baryons). q q q } baryon T. Blake 21 SU(2) flavour mixing • Four possible combinations from u and d quarks ! uu, dd, ud, du • Under SU(2) symmetry, ➡ π0 is a member of an isospin triplet, � is a isosinglet 1 1 ⇡0 = (uu dd), ⌘ = (uu + dd) p2 − p2 T. Blake 22 SU(3) flavour mixing • Introducing the strange quark, under SU(3) symmetry we now have an octuplet and a singlet. ! 0 1 1 1 ⇡ = (uu dd), ⌘1 = (uu + dd + ss), ⌘8 = (uu + dd 2ss) ! p2 − p3 p6 − • Physical states involve a further mixing ⌘ = ⌘ cos ✓ + ⌘ sin ✓⌘0 = ⌘ sin ✓ + ⌘ cos ✓ 1 8 − 1 8 T. Blake 23 Quark model • Can only make colour neutral objects: q q¯ ➡ quark anti-quark or three quark combinations (mesons and baryons). Nearly all known q q q particles fall into one of these two categories. ➡ Can also build colour neutral states containing more quarks (e.g. 4 or 5 quark states). pentaquark hybrid tetraquark q q q q q¯ + … q¯ q q q q¯ q¯ q q q¯ q¯ weakly bound molecule glueball T. Blake 24 Exotic charmonium states • Several exotic states have recently been discovered: ➡ X(3872) by CDF, Z(4430)+ and Y(4140) by Belle etc • These states decay to charmonia and have masses below the b- quark mass. ➡ Z(4430)+ is charged, therefore has minimal quark content ccud • States could be weakly bound molecular D D states or genuine four quark states or an admixture of the two. T. Blake 25 Dalitz plot formalism • Often analyse three body decays in terms off the Dalitz plot formalism. • n-body decay rate: (2⇡)4 ! dΓ = 2dφ(p ...p ) 2M |M| 1 n ! • For a 3-body decay: ! 1 1 2 2 2 A,B parallel B dΓ = 3 3 dm12dm23 (2⇡) 32M |M| A at rest ! C C ie 3-body phasespace is flat in the Dalitz plot. T. Blake 26 Dalitz plot formalism • Often analyse three body decays in terms off the Dalitz plot formalism. spin-1 • Resonances appear as bands resonance in the Dalitz plot. ➡ Number of lobes is related to spin of the resonance. T. Blake 27 Pentaquark discovery ] 2 • In ⇤ J/ pK − decays, the 26 b ! LHCb LHCb experiment sees a [GeV p 24 ψ resonant contribution to the 2 J/ J/ p mass. m 22 J/ѱ p resonance? 20 • This contribution would have minimal quark content ccuud¯ 18 16 • To understand what the 2 3 4 5 6 2 2 contribution is, need to mKp [GeV ] perform an amplitude [LHCb, Phys. Rev. Lett. 115 (2015) 072001] analysis of the J/ pK− system. T. Blake 28 2200 data ] total fit 2000 (a) LHCb background Pentaquark P (4450) 1800 c Pc(4380) 1600 Λ(1405) Λ(1520) 1400 (1600) Events/(15 MeV) Λ 1200 Λ(1670) Λ(1690) 1000 Λ(1800) Λ(1810) • Perform an amplitude analysis of the 800 Λ(1820) 600 Λ(1830) Λ(1890) J/ pK − system allowing for 400 Λ(2100) Λ(2110) contributions from all known Λ 200 0 1.4 1.6 1.8 2 2.2 2.4 2.6 resonances.
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