8 - 11 October 2018, CINVESTAV, Mexico SYMMETRIES AND THEIR BREAKING IN THE FUNDAMENTAL LAWS OF PHYSICS José Bernabéu IFIC - Valencia SYMMETRY OF OBJECTS Characteristic feature of geometric forms, of material objects, Symmetry Group of sphere ATLAS experiment of LHC of biological bodies, related to their invariance under definite transformations. Vitrubio, Leonardo da Vinci (1487) One object is symmetric if, after a transformation is applied, the result remains the same: it remains “invariant”. SYMMETRY BREAKING This three-span arch, painted bright blue and orange, appears perfectly symmetric when viewed directly from below, but has a carefully calculated asymmetry from its other views. The former Fermilab Director R.R. Wilson freely adopted the style of the sculptor A.Calder for giving an example of Symmetry and Symmetry Breaking, which are so important in the field of elementary particle physics. SYMMETRIES IN THE LAWS OF PHYSICS WORDING FLAVOUR FAMILIES COLOUR CHARGES, CONFINEMENT PARTONS, JETS, HADRONISATION ASYMPTOTIC FREEDOM QUANTUM ANOMALIES CHIRALITY SYMMETRY VIOLATION OSCILLATIONS SPONTANEOUS BREAKING I.- STRONG INTERACTION Symmetries as Guiding Principle of Particles and Interactions Flavour SU(3): Are Quarks real? Flavour and Colour of Quarks QCD: From Scale Invariance to Dimensional Transmutation SYMMETRY AS GUIDING PRINCIPLE FOR PARTICLES AND INTERACTIONS -Symmetry implemented by Unitary Transformation of states and observables Invariant Dynamics under the transformation - Under infinitesimal transformation with Ĝ the Generator Ĝ is Hermitian, it corresponds to an Observable Symmetry conservation law For LOCAL Gauge Symmetries, Ĝ is a "charge" and the requirement of Invariance leads to a Covariant Derivative with a Mediator Field responsible of Interactions. Yang-Mills Theory -> SYMMETRY DICTATES INTERACTION Proliferation of Hadrons -> FLAVOUR SU(3) - The fundamental representations 3, 3 are the elementary building blocks for arbitrary higher-dimensional representations. - Baryons Combination of three u, d, s states in Strangeness, Charge and Isospin axes Ω- - Gell Mann-Nishijima Charge Q = I3+Y/2 , Hypercharge Y=B+S ARE QUARKS REAL? Mesons 3 x ퟑ = 1 + 8, Baryons 3 x 3 x 3 = 1 + 8s + 8a + 10 Deep Inelastic Scattering "Jet" of hadrons: probing the insides of hadrons narrow cone of hadrons produced by the hadronization of a quark Leptons (electrons, muons, neutrinos) find PARTONS in the proton Quarks exist!, but they cannot propagate asymptotically with high momentum transfer events Quarks are CONFINED Quark EXCHANGE SYMMETRY: COLOUR ++ ↑ ↑ ↑ 3 3 The Δ puzzle: u u u ; S = 2 , + 2 Symmetric under exchange of space (L=0), spin (↑) and flavour (u) !? A new degree of freedom is necessary for Quarks, its "colour“ (r, g, b), with ANTISYMMETRY for its exchange in Baryons. The singlet colour wave function is antisymmetric i.e., qqq bound states exist, but hadrons are colourless! Colour is confined Experimental evidence that Nc = 3 comes from 휎 푒+푒−→퐻푎푑푟표푛 2 = 푁퐶표푙표푢푟 푞 + − + − 푓 + − 휎 푒 푒 →휇 휇 푖푛 푒 푒 → 푓푓 reactions 푓 QUANTUM CHROMODYNAMICS (QCD) Colour Charge as generator of SU(3) Local Gauge Symmetry Colour Interaction of Quarks mediated by Gluons "q" are quark flavours, "a" is q-colour index and C runs from 1 to 8 Only mq break flavour independence, external to QCD! Quarks are in the fundamental, Gluons in the Adjoint Representation - The field tensor is covariant (A=1, ...,8) leading to gluon self-interaction - Gluon Jet Discovery Gluon self-interaction e+e− → qqg: 1979 at PETRA (DESY) experiments FROM SCALE INVARIANCE TO DIMENSIONAL TRANSMUTATION 2 푔푆 훼푆 = 4휋 dimensionless classical QCD field theory in the chiral limit is SCALE INVARIANT Conformal Symmetry In the perturbative quantum QCD, predictions for observables in terms of the renormalised 2 coupling 훼푆 휇푅 , function of the renormalisation scale. Taking it close to the momentum 2 2 transfer Q , 훼푆 푄 indicates the effective strength of the interaction. RUNNING COUPLING The coupling satisfies the RGE with the 1 loop beta-function coefficient b0 = (33-2nf)/(12 π) ASYMPTOTIC FREDOM ↔ The minus sign in the running. Approximate analytic solution, distinct to QED with Λ a constant of integration the non-perturbative scale of QCD Λ~250 MeV ↔ Conformal Anomaly, ORIGIN OF NUCLEON MASS and MASS OF UNIVERSE II.- ELECTROWEAK INTERACTION AND DISCRETE SYMMETRIES Chiral Gauge ElectroWeak Theory Flavour Physics Discrete Symmetries: CP, T, CPT Gauge Anomalies: Quark-Lepton Symmetry PARITY VIOLATION CHIRAL GAUGE ELECTROWEAK THEORY P, C, T are DISCRETE SYMMETRIES: -Parity rPr -Charge Conjugation qCq -Time Reversal t T t , Motion Reversal CHIRALITY A chiral phenomenon is not identical to its mirror image. The spin of a particle may be used to define a handedness, or helicity, which, in the case of a massless particle, is the same as chirality. Invariance under parity by a Dirac fermion ψ is called chiral symmetry 1 1 Using Projectors, 1 − 훾 휓 → 1 + 훾 휓 2 5 2 5 The UNIFIED ELECTROWEAK THEORY SU(2)L x U(1)Y distinguishes L- and R-projections L transform as Doublets under 푆푈(2)퐿 R transform as Singlets under 푆푈(2)퐿 CHIRAL GAUGE THEORY WEAK NEUTRAL CURRENTS SU(2)L× U(1)Y gauge group. gGauge bosons are: - The three W bosons of weak isospin from SU(2)L (W1, W2, and W3) - The B boson of weak hypercharge Y from U(1)Y Gauge symmetry is BROKEN by Mass Physical Fields with definite mass: W±, γ, Z 훾 푐표푠휃푤 푠푖푛푤 퐵 푀푊 0 = , 푀푧 = 푍 −푠푖푛휃푤푐표푠푤 푊3 푐표푠휃푤 with θW the weak mixing angle DISCOVERIES: Neutral Current Interaction 휈휇 푒 ⟶ 휈휇 푒 Massive W, Z Bosons + + 휈휇 휌 ⟶ 휈휇 푋 푢 푑 ⟶ 푊 ⟶ 푙 휈푙 + − 푢 푢 , 푑푑 ⟶ 푍 ⟶ 푙 푙 S푝 푝푆 푈퐴1, 푈퐴2 퐶퐸푅푁 1983 Gargamelle Bubble Chamber CERN 1973 Triumph of STANDARD MODEL GIM Mechanism -> Need of CHARM With u, d, s quarks ONLY Cabibbo d-s Mixing in Charged Weak Current leads by + - SU(2)L to Strangeness-Changing-Neutral Currents KL μ μ AGAINST experiment. 푢 푐 GIM 1970 With an additional fourth quark flavour , 푑 푠 cos 휃 −sin 휃 Cabibbo Mixing reinterpreted, with the two doublets, 푈 = sin 휃 cos 휃 as a Unitary Matrix for Charged Currents between Flavour and Mass eigenstates Neutral Currents U+ U = 1 are Diagonal and Universal Flavour-Conserving-Neutral-Current At higher orders, F-Changing-N-C can be induced, BUT highly suppressed by GIM ퟐ ퟐ 풎풄 −풎풖 with an additional factor ퟐ 푴푾 - Discovery of 푐 푐 J/ψ meson in 1974 at SLAC and BNL The "November Revolution" Charmed c푑 , 푐푠 , 푐푢푑... Hadrons discovered later CP VIOLATION -> MATTER-ANTIMATTER ASYMMETRY CP-symmetry Laws of Physics should be the same if a particle is interchanged with its antiparticle (C symmetry) while its spatial coordinates are inverted ("mirror" or P symmetry). 퐾0 퐾 0 Mixing (ΔS=2) by weak interactions Physical KL, KS should be CP eigenstates KL π π should be FORBIDDEN, but OBSERVED! Can CPV be inserted in the SM? K-M 1973 discovered this possibility by particle content Enlarging to 3 Families, at lest, of Fermions U(CKM) has a physical relative phase such that for antifermions U*(CKM) NEED OF 3 FAMILES ACTIVE! α - b푏 Υ meson discovered in 1977 at Fermilab - CPV by U(CKM) in agreement with 푢 푐 푡 γ β experiments in K, B and D physics!!! 푑 푠 푏 Unitarity triangle Not enough to explain MATTER-ANTIMATTER ASYMMETRY IN THE UNIVERSE TOP QUARK Top Quark The most massive of all observed elementary particles. 2 Mass of 172.44 GeV/c , like an atom of tungsten! "Weak" Decay t b W, with lifetime 5×10−25 s., which is 1/20 of the timescale for Hadronisation "bare" quark studies! First "seen" in indirect non-decoupling virtual quantum effects 푩ퟎ 푩ퟎ Mixing Z boson self energy 풁 풃 풃 vertex UA1 & ARGUS 1987 Veltman LEP 1990's J.B.,Pich,Santamaria Direct detection 푝푝 TeVatron 1995 - A collision event involving top quarks - Top Quark Factory at LHC p p Collider Strong g g 푡푡 + Weak u 푑 t 푏 WHAT IS “TIME REVERSAL”? A symmetry transformation, T, that changes one physical system into another with an inverted sense of time evolution is called Time Reversal. The operator UT must be ANTI-UNITARY: Antilinear + Unitary ANTIUNITARITY introduces many intriguing subtleties: S T S i f UT f UT i T - Violation means Asymmetry under in out sates vi 0 - vi 0 v T - v v f - v f WHAT IS T-TRANSFORMATION EXPERIMENTALLY ? The problem is in the preparation and filtering of the appropriate initial and final meson states for a T-test: ENTANGLEMEND & DECAY Entangled state Entangled state projects projects B0 B Υ(4S) Υ(4S) t1 t1 J/ψ l T KL t1 t1 J/ψ 0 t2 t2 l B Tagging B Tagging It is NOT Ks the exchange t t projects 1 2 projects 0 0 B 0 B B B B B BABAR observes (PRL 2012) 14σ Genuine True TRV effect using this concept MESON TRANSITION PROBABILITY DOUBLE DECAY RATE INTENSITY In a B factory operating at the Υ(4S) peak, our initial two-meson state is Einstein- Podolsky-Rosen entangled, which maintains its antisymmetric entangled character in the H eigenstate basis. This implies the antisymmetric character of the two meson state at all times and ퟎ ퟎ for any two independent linear combinations of Entangled 푩풅 풂풏풅 푩풅. The corresponding evolution before the first decay is therefore trivial for perfect Entanglement. Given a decay "f", the Partner Meson is tagged by and the "filtered state" is its orthogonal The FILTERING IDENTITY establishes the connection between the Meson Transition Probability and the experimental "reduced" Intensity 2 푔 푇 퐵 푡 2 ↛푓 ⊥ 퐼 푓, 푔; 푡 = 2 2 = 퐵↛푔 퐵↛푓 푡 퐴푔 + 퐴푔 There are NO FAKE TERMS for a proof of Symmetry Breaking if the ratio of decay amplitudes 퐴/퐴 is a pure phase: 퐵− ↔ 퐽/ψ KS , 퐵+ ↔ 퐽/ψ KL .