Physics of flavour PPSS 2019 Olga Werbycka 1 18/07/2019 Institute of Nuclear Physics PAS Outline ★ Symmetry ★ Flavor ★ Standard Model ★ Weak interaction ★ FCNC ★ B-physics ★ Belle/Belle II experiments 2 Symmetry 3 Symmetries in Physics ★ A symmetry of a system is a property or feature of the system that remains the same under a transformation (or change). ★ For us the most important aspect of symmetry is the invariance of Physical Laws under an arbitrary differentiable transformation ★ Noether’s Theorem (1918) - symmetry properties of a physical system are closely related to Conservation Laws for the system Noether E (1918). “Invariante Variationsprobleme” Nachr. D. Kónig. Gesellsch. D. Wiss. Zu Gottingen, Math-Phys. Klasse 1918: 235-257. http://arxiv.org/abs/physics/0503066v1. 4 Continuous Symmetries and Conservation Laws Standard Model is written as symmetry group U(1) x SU(2) x SU(3) The simplest internal symmetry group is U(1). SU(2) is the rotatio- Similarly, SU(3) Geometrically, it is the nal symmetry of a rotational symmetry of a sphere - a set of 2 x is for strong circle - Circle rotated 2 matrices with unit nuclear forces - by an angle in 3D space. determinant. They between 8 bosons So, SU(1) is set of 1 x model the weak nuclear 1 matrices - a symmetry (gluons) and a group for electromagne- interactions - between tic interactions pair of fermions set of three (fermions acting as (e.g. electron and fermions (e.g. singles). For instance, neutrino) and a set red, green and interaction of photons of three bosons: Z (a massless gauge boson) and W (+,-) blue quarks). and electron. 5 CP symmetry ★ CP symmetry is the combined operation of C and P ★ C (Charge Conjugation): Charge Conjugation changes a particle to its antiparticle. In particular, it reverses the sign of the electric charge and magnetic moment of the particle. ○ Strong and e/m interactions are found to be invariant under the C operation ○ BUT in Weak interaction C invariance is broken ★ P (Parity): Parity operation reverses the direction of any spatial vector (Mirror reflection). ○ Under parity a left-handed particle transforms to a left-handed. ○ Parity is conserved in strong and e/m interactions ○ But not in weak 6 Symmetry Summary: Transformation Symmetry Type Conserved Quantity translation global, continuous linear momentum rotation global, continuous angular momentum time global, continuous energy additive rotation in global, continuous isospin “isospin-space” (“internal”) electromagnetic local, continuous, gauge charge scalar/vector potential --- global, continuous, gauge barion number --- global, continuous, gauge lepton number 7 Symmetry Summary (2): Transformation Symmetry Type Conserved Quantity multiplicative parity global, discreet “P-value” charge conjugation global, discreet “C-value” time reversal global, discreet none! In addition: Local, Lorentz-Invariant, Quantum Field Theories ⇒ CPT 8 What is flavour? Flavour refers to the species of an elementary particle. The Standard Model counts 6 flavours of quarks and 6 flavours of leptons. They are conventionally parameterized with flavour quantum numbers that are assigned to all subatomic particles. Within the Standard Model (SM), flavour physics refers to the weak and Yukawa interactions. 9 What is flavour? Flavour refers to the species of an elementary particle. The Standard Model counts 6 flavours of quarks and 6 flavours of leptons. They are conventionally parameterized with flavour quantum numbers that are assigned to all subatomic particles. Bottomness Isospin Strangeness Charm Topness 10 Isospin (original motivation) Isospin was introduced as a concept in 1932, well before the 1960s development of the quark model by Werner Heisenberg in order to explain symmetries of the neutron: ➔ The mass of the neutron and the proton (symbol p) are almost identical: they are nearly degenerate, and both are thus often called nucleons. Although the proton has a positive electric charge, and the neutron is neutral ➔ The strength of the strong interaction between any pair of nucleons is the same, independent of whether they are interacting as protons or as neutrons. The neutron and the proton are assigned to the doublet (the spin -½ ,2) of SU(2). The pions are assigned to the triplet (the spin-1, 3) of SU(2). Though there is a difference from the theory of spin: the group action does not preserve flavor. Similar to a spin ½ particle, which has two states, protons and neutrons were said to be of isospin ½. The proton and neutron were then associated with different isospin projections I3 = ½ and -½ respectively. 11 Why do we care about flavour? Flavour physics can predict new physics (NP) before it’s directly observed. Some examples are: ★ + − + + The smallness of Γ(KL → μ μ )/Γ(K → μ ν) allowed for the prediction of the charm quark ★ The size of ΔmK allowed for the charm mass prediction ★ The measurement of K allowed for the prediction of the third generation ★ ∼ The size of ΔmB allowed for a quite accurate top mass prediction ( 150 GeV) ★ The measurement of neutrino flavour transitions led to the discovery of neutrino masses 12 13 Weak interaction Properties: ★ It is the only interaction capable of changing the flavor of quarks (i.e., of changing one type of quark into another) ★ It is the only interaction that violates P symmetry. It is also the only one that violates charge-parity (CP) symmetry. ★ It is propagated by intermediate bosons that have significant masses, an unusual feature which is explained in the Standard Model by the Higgs mechanism. Weak isospin is a quantum number relating to the weak interaction (an equivalent of the isospin for strong interactions). The weak isospin conservation law relates the conservation of I3 ; all weak interactions must preserve I3. It is also conserved by the electromagnetic and strong interactions. Weak charge: vector coupling of nucleons to the Z boson, namely 2I3 - 4Qsin2ΘW, where Θ is the weak mixing angle. 14 Universality of weak interactions? ➔ Do all leptons and quarks carry the same unit of weak charge? ◆ “YES” for leptons ◆ “NO” for quarks ➔ for quarks, the couplings for the weak gauge bosons depend on the quark flavors, due to “quark mixing” -> CKM mechanism 15 Weak decays of quarks ➔ Consider the (semileptonic) weak decay Assuming universality of weak decays of quarks we expect both decays would happen with similar rate, but…. 16 Weak decays of quarks (2) It was also noticed that the value of Fermi constant GF deduced from nuclear β-decay was slightly less than that obtained from muon decay So what are we going to do? Discard the universality of weak interaction? 17 Cabibbo theory ➔ Try to keep the universality, but modify the quark doublet structure… ➔ Assume that the charged current (W±) couples the “rotated” quark states ➔ Where d’, s’ (weak interaction eigenstates) are linear combinations of mass eigenstates d, s. Θc: the quark mixing angle “Cabibbo” angle 18 Cabibbo theory (2) ➔ What we have done is to change our mind about the charged current: “Cabibbo-favoured” vs. “Cabibbo-suppressed” ➔ → effective weak coupling for ΔS = 0 (d uW) is cosΘc ➔ → effective weak coupling for ΔS = 1 (s uW) is sinΘc ⇒ Θc ≈ 12º 19 Suppression of flavor changing neutral currents ➔ A very stringent suppression of flavor-changing neutral current reactions 20 Flavor-changing neutral currents (FCNC) Neutral current reactions for (u, d’) quarks In this picture, is FCNC perfectly allowed by theory??? 21 GIM mechanism for FCNC suppression ➔ In 1970, Glashow, Iliopoulos and Maiani (GIM) proposed the introduction of a new quark Q = ⅔ , with label c for ‘charm’. ➔ With this new quark a second doublet is also introduced ➔ Then we have additional terms for the neutral current reactions 22 GIM mechanism (2) FCNC has disappeared!!! 23 GIM mechanism (3) ➔ At the price of new quark ‘charm’ and another quark doublet, the (experimentally) unwanted FCNC has been removed! ➔ Later, in 1974, the bound state of charm-- anti-charm was discovered: J/ψ ➔ Indeed, just before this discovery, it had been possible to estimate the mass of the new quark! ← by considering K0K0 -bar mixing 24 Extension of Cabibbo theory to 3 quark generations ➔ Leptons are not involved in the strong interactions ➔ Quarks & Leptons do not change its flavor when interacting with neutral gauge bosons ◆ quarks do not change flavor under strong interaction ◆ leptons & quarks do not change flavor when interacting with γ or Z0 ◆ leptons & quarks only change flavor when interacting with W±, and only within its family ± ↕ W 25 The strengths of the weak interactions between the six quarks. 26 CKM matrix Cabibbo–Kobayashi–Maskawa matrix is a unitary matrix which contains information on the strength of the flavour-changing weak interaction. ➔ CKM is 3 × 3 and unitary ◆ only 3 generations in Standard Model ➔ CKM is almost 1, but not exactly 27 CKM matrix in the Wolfenstein parametrization ★ In 1983, it was realized that the bottom quark decays predominantly to the charm quark: ★ Wolfenstein then noticed that and introduced an approximate parametrization of the CKM matrix |λ| ≈ O(0.1) 3 real parameters (λ, A, ρ) and 1 phase (η) 28 Types of CP Violation ❖ Direct CPV ❖ Indirect CPV ❖ CP interference between mixing and decay 29 Direct CP Violation ★ CP violation arises from the difference between the magnitudes of a decay amplitude and its CP conjugate amplitude. ★ The measurement is to compare the decay rate of B meson and its CP conjugate. ★ Only possible source of CP asymmetry in charged meson decays 30 Beauty of the b meson ➔ The beauty of B meson lies