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The Fundamental Forces 1. Costituents of Matter 2. Fundamental Forces 3. Particle Detectors (N. Neri) 4. Experimental highlights (N. Neri) 5. Symmetries and Conservation Laws 6. Relativistic Kinematics 7. The Static Quark Model 8. The Weak Interaction 9. Introduction to the Standard Model 10. CP Violation in the Standard Model (N. Neri) 1 The concept of Force In Classical Physics : In Quantum Physics : • Instantaneous action at a distance • Field (Faraday, Maxwell) • Exchange of Quanta k F 2 r Inverse square law 2 Classical and Quantum concepts of Force: an analogy Let us consider two particles at a separationdistance r . If a source particle emits a quantum that reaches the other particle, the change in momentum will be: And since: We have: c t r r . r p p c t r r p k F 2 t r A concept of force based on the exchage of a force carrier. In a naive representation: 3 Fundamental Forces of Nature Gravity Strong Nuclear Force Weak Nuclear Force Elettromagnetism Guideline: explain all fundamental phenomena (phenomena between particles) with these interactions 4 Electromagnetism Affects all particles with electric charge (Quarkl, Leptons, W) Responsible of the bound between charged particles, e.g. atomic stability Coupling constant: the electric charge Range of the force: infinite Classical theory: Maxwell Equations (1861) F J F F F 0 F: Electromagnetic Field Tensor J: 4-current 5 Quantum Electrodynamics (QED) is the quantum relativistic theory of electromagnetic interactions. Its story begins with the Dirac Equation (1928) and goes on to its formulation as a gauge field theory as well as the study of its renormalizability (Bethe, Feynman, Tomonaga, Schwinger, Dyson 1956). F. Dyson showed the equivalence between the method of Feynman diagrams and the operatorial method of Tomonaga and Schwinger, making commonplace the use of Feynman diagrams for the description of fundamental interactions. A Feynman Diagram is a pictorial representation of a fundamental physical process that corresponds in a rigorous way to a mathematical expression. The pictorial representation is – however – more intuitive. The basic structure of the electromagnetic interaction (CGS): e2 1 c 137 dyne cm cm erg cm Fine structure constant It determines the intensity of the coupling at vertices of electromagnetic Feynman diagrams e e 6 The Feynman Diagram and the (bosonic) Propagator: • Does not correspond to any physical process • If interpreted as a physical process, it would violate E-p conservation law • Two (or more) vertices diagrams have physical meaning time e e The concept of exchange of quanta (represented by the propagator) is the analog of the classical concept of a force field between two charges Initial state Final state Propagator Interaction range estimate by using the static Klein-Gordon equation: g er / R U (r ) 4 r m 2c 2 U (r ) U (r ) 0 2 2 Interaction strength (electric charge) g R mc Interaction range U(r) plays the role of scattering potential in configuration space. In the (Fourier transformed) momentum space…… 7 Momentum space u Scattering amplitude for a particle in a potential Let us imagine a particle interacts with a coupling with a potential U i qr g g f (q ) g 0 U (r ) e dV 2 0 2 q m Or, more precisely, including also energy : q2 E 2 q 2 Scattering amplitude for a particle in a (boson-mediated) potential Propagator Potential Particle g0 g er / R U (r ) 4 r g u f (q) 1 q2 Photon Propagator g g f (q) 2 0 2 q m g er / R U (r ) 4 r Momentum space Configuration space f (q) 1 g0 g 2 2 q m Propagator Couplings (the details) i qr g g f (q ) g 0 U (r ) e dV 2 0 2 q m q q in this section i qr f (q ) g 0 U (r )e dV g 0 U (r )eiqrcos r 2 d sin d 2 0 0 0 0 0 g 0 d d dr U (r )eiqrcos r 2 sin 2 g 0 drU (r ) r 2 d eiqrcos sin 1 1 iqr iqr 1 iqrcos iqrcos 0 d sin e iqr 0 d e iqr e e qr 2sin qr 4 g 0 sin qr 4 g 0 g r / R 4 g 0 dr U (r ) r 2 dr U ( r ) sin qr dr e r sin qr qr q 0 q 0 4 r 0 iqr iqr g0 g g0 g e e r / R ( iq1/ R ) r ( iq1/ R ) r dr e dr e e q 0 2i 2iq 0 g0 g e g 0 g (iq 1/ R)e e (iq 1/ R)e 2i q (iq 1/ R) (iq 1/ R) 0 2iq (iq 1/ R)(iq 1/ R) ( iq1/ R ) r ( iq1/ R ) r ( iq1/ R ) r ( iq1/ R ) r 0 9 g 0 g (iq 1/ R)e e (iq 1/ R)e f (q ) 2iq (i 2 q 2 1/ R 2 ) iqr r / R iqr r / R e g 0 g (iq 1/ R) (iq 1/ R) 1 0 2iq q2 2 R g 0 g 2iq g0 g 2 2 2 2 2iq q m q m R mc In the chosen system of units 10 Scattering amplitude and cross section u v Propagator Particle Particle g0 Let us imagine the interaction of two Dirac (charged) particles g u v f (q) A typical matrix element for this process will have the form : 1 q2 Photon Propagator M g0 g u ( p1' ) u( p1 ) D (k )u ( p2' ) u( p2 ) And the Cross Section will have the form : d M if dq 2 2 ( PS ) 2 u u g J 1 ( PS ) g v v 0 q2 J ' Dirac currents Phase Space Flux PS Dirac Spinors u, u , v, v 11 e e 1 2 q Scattering Rutherford The Feynman Diagrams Electrons in initial and final states time Intermediate virtual photon 2 e e e e e e 2 d 2 4 2 dq q q Rutherford Scattering Well defined initial and final states The simplest Feynman Diagram given the initial and final states («tree level»). The diagram contains two vertices where the coupling constants appear The diagram REPRESENTS the exchange of a virtual particle (the photon) between the charged particles that are the sources of the electromagnetic field 12 A taste of the S-Matrix expansion (and Feynman Diagrams) In a Theory of Interacting Quantum Fields L L0 LI 1 L0 N [ (i m) ( A ) ( A ) ] 2 LI N[ e A ] Normal Product Free Fermion field with mass m Free E.M. field The evolution of the system in the Interaction Picture is described by: Fermion current interacting with the electromagnetic field d i (t ) H I (t ) (t ) dt H I (t ) eiH0 (t t0 ) He iH0 (t t0 ) 13 () i In a Scattering Process : Non-interacting particles in the initial state () S () S i S i f The solution of the general problem i d (t ) H I (t ) (t ) dt () i Non-interacting particles in the final state t (t ) i (i ) dt1 H I (t1 ) (t1 ) 14 t (t ) i (i ) dt1 H I (t1 ) (t1 ) t Can be solved by iteration : 1 (t ) i (i ) dt1 H I (t1 ) i t t 2 (t ) i (i ) dt1 H I (t1 ) i (i ) dt 2 H I (t 2 ) 1 (t ) t i (i ) dt1 H I (t1 ) i (i ) 2 t1 t dt dt 1 2 H I (t 2 ) H I (t1 ) i Power series expansion (Dyson Expansion) of the Scattering Matrix (power series in the Interaction Hamiltonian. Or power series in the interaction coupling constant S n ( i ) dt1 n 0 t n1 t1 dt ..... dt 2 n H I (t1 ) H I (t 2 )......H I (t n ) 15 Feynman diagrams are a pictorial representation of this kind of perturbative series To every term of the series a diagram is associated following precise formal rules t S i (i ) dt1 H I (t1 ) i (i ) 2 To every term in the S expansion a diagram can be drawn, following precise formal rules (outside of the goal of this course) t1 t dt dt 1 2 H I (t 2 ) H I (t1 ) i + Fundamental (“tree level”) 2 First order in Perturbation Theory While Feynman diagrams are NOT a picture of the real physical process (just a representation of a mathematical expression) they can give a lot of grasp on the physics at work. After all, Quantum Mechanics is just a representation! 16 Perturbation Theory: a few more ideas The occurrence probability of : ee ee It can by calculated by summing up the amplitudes due to various diagrams: P (e e e e ) 2 = + Fundamental (“tree level”) + 2 + …… + 2 2 First order in Perturbation Theory Higher-order terms in the expansion, which are negligible if the coupling constant is small. Which is the case of QED. The graphs have constituent lines (electrons) exchanging force carriers ( photons). 17 Lowest order of other electromagnetic processes : e Z e Z Z Bremsstrahlung 2 3 Z2 Z Z e e Z Z 2 3 Z 2 Pair Production Z 18 d M if 2 dq Cross Section : R NT 2 ( PS ) 2 1 ( PS ) u u e 2 ev v q 1029 cm2 105 barn (typical cross section of electromagnetic processes) Reaction rate Lifetimes: Total amplitude h Number of targets Incident flux t h Branching ratio of different final states 1 2 ..... n ( B1 B2 .... Bn ) Partial amplitudes to different final states B1 B2 .... Bn 1 Decay processes are represented by the same kind of diagrams that are used to describe scattering processes. The lifetime has a similar dependence on the coupling constants Electromagnetic processes: 1018 s 1 2 19 Gravity Concerns all forms of energy of the Universe (mass included) Responsible of bounds between macroscopic bodies 2 4 G Classical field theory (Newton, 1687) for the masses Gravitational potential Mass density “Geometrized” spacetime field theory (Einstein, 1915) General Relativity The Principle of Equivalence between inertial mass (inertia to a force) and gravitational mass (gravitational charge) made it possible to consider gravity as a property of the spacetime background Einstein Tensor Cosmological Costant G g 8 G T 4 c 1 0 0 0 1 0 g ( x) 0 0 1 0 0 0 0 0 0 1 Far away from sources of mass/energy (in a flat spacetime) Energy-Momentum Tensor Metric Tensor G G ( g ) 20 Gravity and Electromagnetism at the particle scale (the two classical theories) Gmm ee ?? 2 2 r r e2 (4.8 10 10 ) 2 dyne cm cm 1 c 1.054 10 27 3 1010 erg s cm 137 s G 6.674 10 11 2.12 1015 G c 2 kg Same dependence on distance Fine structure constant m m 6.67 1011 c 11 N m 2 6.674 10 kg 1.05 1034 s kg 2 1.05 1034 kg 2 3 108 Gravity constant (written in a way to show h and c Now let us compare: Need to choose charges and masses. For the case of two protons 2.12 1015 m m 2.12 1015 c ?? 2 c mm ?? kg 2 kg 2 r2 r 2.12 1015 (1.67 1027kg) 2 ?? 2 kg 1 5.9 10 39 137 ….gravity weaker by many orders of magnitude 21 Gravity is normally negligible at the atomic and subatomic level. But not at the Planck Mass: 2.12 1015 2 M P ?? 2 kg M P 1019 GeV / c 2 1019 1.78 1027 kg 1.78 108 kg 2.12 1015 (1.78 108 kg) 2 2 kg The Planck Mass can be defined as the mass that an elementary particle should have so that its gravitational interactions would be similar in strength to that of other interactions (electromagnetic,strong). Currently we have no valid quantum theory of gravity. If however such a theory exists, perhaps it could have a structure similar to QED: Electromagnetism e Photon Spin1 e Gravity R Charge e2 (4.8 10 10 ) 2 dyne cm cm 1 c 1.054 10 27 3 1010 erg s cm 137 s Electromagnetism M G M G Graviton Spin 2 R Energy Two adimensional constants (at the mass and charge of the proton) GM 2 2.12 1015 M 2 (kg 2 ) c 1039 2 c kg c Gravity 22 The Planck scale The Schwarzschild Radius : the radius of a sphere such that, if all the mass of an object is compressed within that sphere, the escape speed from the surface of the sphere would equal the speed of light (wikipedia). Every massive object has a Schwarzschild radius : Escape velocity : This neutron star is about to become a black hole 2Gm c r Speed of light 2Gm rs 2 c Schwarzschild radius An object whose radius is smaller than the Schwarzschild radius is called a Black Hole Some notewhorty Schwarzschild radii : 2Gm 2.95 km c2 2Gm rs 2 8.87 mm c Sun: rs Earth: 23 The Compton Wavelength : instrinsic quantal space scale associated to a particle C mc The concept of a Planck scale: 1. Schwarzschild Radius = Compton Wavelength 2Gm rs 2 C c mc mP EP m P c 2 c 2G c 5 31019 GeV 2G The concept of a Planck scale: 2. Gravity on particles = Electromagnetism on particles (as shown before) 24 The three fundamental constants of the Universe G 6.7 10 11 m 3 kg 1 s 2 c 3.0 108 m s 1 1.110 34 Js G 35 1 . 6 10 m 3 c What is the (only) way to form a length with these constants ? lP What is the (only) way to form a mass with these constants ? MP c 2.2 108 kg G tP G 44 5 . 4 10 s 5 c What is the (only) way to form a time with these constants ? One then has a Planck energy ..and a Planck temperature EP M P c 2 2.0 109 J 1.2 1019 GeV TP EP / k 1.4 1032 K 25 In General Relativity : actually: Energy (not just matter) A notewhorty application of General Relativity (with some assumptions regarding the matter distribution of the Universe) Cosmology The weak equivalence principle, also known as the universality of free fall or the Galilean equivalence principle can be stated in many ways. The strong EP includes (astronomic) bodies with gravitational binding energy (e.g., 1.74 solar-mass pulsar PSR J1903+0327, 15.3% of whose separated mass is absent as gravitational binding energy). The weak EP assumes falling bodies are bound by non-gravitational forces only. Either way, The trajectory of a point mass in a gravitational field depends only on its initial position and velocity, and is independent of its composition and structure. 26 Electromagnetic radiator 2 t2 A 0 • Two polarization states 4-vector • Photon: spin 1 Graravitational radiator Flat spacetime g h curvature In the linearized (weak field) theory, far away from the source (and in the De Donder gauge): 2 t2 h 0 • Four polarization states • Graviton: spin 2 Trace reverse h (tensor-like) • Electromagnetic waves discovered in 1886 (Hertz). • Gravity waves not yet detected. 27 Gravity wave source candidates : • Systems whose mass distribution that changes rapidly in time. • High masses, small times. Black-holes, Neutron Stars merging. Supernovae. • Mass variation not having a spherical symmetry 1993 Hulse & Taylor measured the orbital decrease rate (7 mm/day) of the binary pulsar PSR B1913+16. This energy loss is in agreement with the prediction of General Relativity indirect evidence for the emission of Gravity Waves. Siccome esiste un segno solo della massa (diversamente dalle cariche!), il momento piu’ basso e’ il 4-polo Effect of a gravity wave: a space deformation with two polarization states : http://demonstrations.wolfram.com/GravitationalWavePolarizationAndTestParticles/ 28 The VIRGO Interferometer (Cascina, Pisa) for the detection of gravitational waves 29 Weak Nuclear Force Affects Quarks and Leptons (carriers of a “weak charge”) Generally, the Weak Nuclear process is dwarfed by Electromagnetic or Strong Nuclear processes. Weak Nuclear processes are commonplace whenever: • Conservation laws are violated (conserved in Strong or EM interactions) • Neutral particles and/or particles with no Strong Nuclear interaction intervene n p e e Neutron Beta Decay 900 s Let us get familiar with why some process just cannot take place n p NO Violates E conservation n e NO Violates conservation of baryon and lepton numbers n p NO Violates electric charge conservation The number of Baryons and Leptrons cannot change arbitrarily: Proton stability 30 “Specific” particles: • The Photon. Its presence is indicative of the Electromagnetic Interaction. • The Neutrino. This particle interacts only weakly. • W,Z. Appear only in Weak Interactions. e p n e Antineutrino absorption Are there Weak Interactions without neutrinos? Yes! p It takes place through the Weak Interaction because it violates the Strangeness quantum number 10 2.6 10 (d , u ) The decay diagram W (u, u, d ) (u , d , s ) s d u s u d u d u p 31 The importance of Weak Interactions: the pp cycle in the Sun : 99,77% p + p d+ e+ + e 84,7% 0,23% p + e - + p d + e ~210-5 % d + p 3He + 13,8% 13,78% 7Be 3He + 4He 7Be + + e- 7Li + e 3He+3He+2p 7Li + p ->+ 7Be 8B 0,02% + p 8B + 8Be*+ e+ +e 3 ++ He+p+e e 2 The pp cycle is responsible for ~98% of the energy generation in the Sun 32 An estimate of the Weak Coupling Constant n (Weak) 1 0 1010 s 2 weak e c weak 10 4 10 10 10 weak 1 (Electromagnetic) 2 18 1019 s g2 c 2 Weak charge Weak Interaction Carriers and Propagator W± 80.4 GeV/c2 Spin 1 Z0 91.2 GeV/c2 Spin 1 u u g g W d e d g e e e e p n e g W Z0 g e e g e e 33 The Range of the Weak Nuclear Interaction: 10-18 m Compton Wavelength argument : Weak Interactions Propagator : R c 197 MeV fm 3 2 10 fm 2 mc mc 90 GeV g2 f (q) 2 q M W2 Z Low energies q2 << M2WZ g2 f (q) GF 2 MWZ u d g 1 M W2 Z e g The Fermi constant of the low energy Weak Interaction. An effective interaction of the form: J weak GF e ' J weak 2 g LFermi GF J J ' 2 J J ' MW Z 34 The Fermi Weak Coupling Constant GF 1.2 10 It is often quoted as: What is actually meant is: Using the usual expression: One finds: 5 GeV 2 GF 2 g2 (c) 3 8M W2 GF 5 2 1.2 10 GeV ( c )3 c 197 MeV fm GF 8.9 105 MeV fm3 As an example, the cross section for the process e e e e 2 GF2 me2 46 2 e 88 10 cm 4 35 Two fundamental types of Weak processes: • Charged Weak Currents: W exchange (a charged carrier W+ and W-) • Weak Neutral Currents: Z exchange (a neutral carrier, Z0) e q e q Photon-mediated e q e q Z-mediated e u e d W-mediated e e Z-mediated 36 Charged Currents Weak Interactions: Nuclear Beta Decay A(Z , N ) A(Z 1, N 1) e e n p e e d u e e (at the nuclear level) (at the free neutron level) (at the fundamental constituents level) Charged Currents Weak Interactions: Antineutrino Scattering e p e n (at the free proton level) e u e d (at the fundamental constituents level) At the fundamental level, weak processes involve Quarks and Leptons (as well as weak carriers) : 37 Neutrino classification. The Lepton families. While it is easy to distinguish between an electron and a positron (because of the opposite electric charge), this is not so trivial for neutrinos. One possibility is the dinamical distinction based on the lepton (electron) that is produced together with the (anti)neutrino. Definition of the ELECTRON NEUTRINO: this is the neutrino being emitted together with the positron in the process: A( Z , N ) A( Z 1, N 1) e e While the ELETRON ANTINEUTRINO is the one being emitted in the process: A(Z , N ) A(Z 1, N 1) e e ELECTRON NEUTRINO and ELECTRON ANTINEUTRINO NEUTRINO are associated to ELECTRON and ANTIELECTRON 38 Muons and Muon Neutrinos These neutrinos are different from the ones emitted in beta decays. In turn, they are a Neutrino and an Antineutrino. Lederman, Schwartz, Steinberger Experiment (1962) Use of a muon antineutrinos beam from kaon decays in flight (at Brookhaven): Muon Neutrino Muon Electron (muon) neutrinos produce electrons (muons) when brought to interact with matter. p n YES p e n NO Lepton masses are well known. Neutrino masses are a non-trivial subject (Neutrino Oscillations) but in general they are not zero. 39 How to build a Neutrino Beam ? Schematics of an example: the CERN (to Gran Sasso) beam : • Production of particles • Selection of particles (energy, type) • Kaon and pions decay to muons • Muon decays p+C (interactions) , K (decay in flight) 40 The third Lepton: the Tau. Its mass is 1.78 GeV. Its associate neutrino is the Neutrino τ. Discovered in 1977 at SLAC (Stanford, California). Detection reaction (in e+e- collisions) e e e X X: undetected particles (neutrinos!). This reaction featured a threshold at 3.56 GeV. With hindsight, this is twice the tau lepton mass ! Further analysis revealed that the reactions actually taking place where of the type: e e e e Tau neutrino interactions where subsequently discovered in 2002 (DoNUT experiment) three fundamental leptons and neutrinos 41 Donut experiment in a nutshell: discovery of the tau neutrino ! While the electron is stable, muon and tau neutrinos decay (weakly) : e e (Lifetime 2x10-6 sec) 17.4% BR e e 17.8% BR 9.3% BR (Lifetime 5x10-13 sec) 42 Lepton Numbers: Ne N (e ) N (e ) N ( e ) N ( e ) Electron Lepton Number N N ( ) N ( ) N ( ) N ( ) Muon Lepton Number N N ( ) N ( ) N ( ) N ( ) Tau Lepton Number To the best of our knowledge, these three numbersa are conserved in all interactions (with the exception of NEUTRINO OSCILLATIONS). As a consequence, the decay : e is not seen to take place. The TOTAL LEPTON NUMBER (the sum of all three numbers) is conserved in all known interactions N l N e N N A fundamental property of Weak Interactions: all leptons and associated neutrinos behave exactly in the same way, when mass differences are taken into account. «Weak Interactions Universality» 43 Strong Nuclear Force Affects the Quarks constituting the hadrons Responsible of hadron stability (baryons, mesons) Quarks have a strong charge (color) Mediated by GLUONS Force strength ? Strong decay Electromagnetic decay K p 0 (1385) 0 1023 s 0 (1192) 1019 s strong 10 18 2 10 10 23 A «strong» s g 1 coupling constant ! 2 s 44 The gluon m0 However, the gluon has a very short range Confinement: range limitated to 10-15 m R mc s 1 Two independent polarizazion states The six color charges (sources of the strong nuclear field): Color neutrality: colorless states (color singlet states): 1 ( r r bb g g ) 3 Antiquarks carry anticolor Quarks carry color 1 ( grb gbr bgr rgb rbg brg ) 6 45 A few color singlets: The pion: 3 ur d r ub d b u g d g The proton: 3 p ub ur d g u g ub d r ur u g d b udu s duu s The strong force is mediated by 8 gluons rg rb r gb gr br 1 rr gg 2 bg gs 1 rr gg 2bb 6 b gs gs s rb b gs Gluons are colored ! r Gluons, being colored, carry the strong charge themselves. 46 Quark – Gluon Interactions Interaction between Quarks is mediated by Gluons S Gluons carry the Quarks color (by contrast: the photon DOES NOT carry the electron charge) Color charge is conserved in Strong Interactions Gluon propagator Color lines are continuous 47 Asymptotic Freedom and Confinement s low q 2 1 The two Strong Interaction regimes Running coupling constant ln (q / ) 2 2 270 MeV high q 2 The coupling constant is small (adimensional: <<1) The perturbative expansions converges rapidly The coupling constant is big The perturbative expansion has problems High distances and confinement regimes Vs (r ) 4 s kr 3 r Phenomenological potential Confinement part “Coulombian” part, one gluon-exchange Two Quarks Q Q Moving apart Q Q The energy stored increases up to the creation of a Quark-Antiquark pair Q Q Q Q Q Q 48 A few aspects of the Strong Force (QCD, Quantum Chromodynamics) 3-gluon vertex (typical of non abelian gauge theories) Color lines representation antib b g anti g The inside of a hadron Strong flux tube Gluon force lines Compare with electric dipole: 49 The Fragmentation (Hadronization) Process First step: a fundamental process described by a Feynman diagram (however, the quarks live inside a proton) Second step: hadronization. The final state gets enriched by many particles (pions…) extracted from vacuum as the quarks get farther apart Two hadrons collide Partons in hadrons collide as described by Structure Functions (we assume, perturbatively). Scattered parton emits a shower of quarks and gluons Hadronization Partons pick up color matching partner from sea of virtual quarks and gluons We can then observe these hadrons or their decays p T 300 MeV 50 Cross Sections R NT h Lifetimes 1026 cm2 102 barn 10 13 cm 23 t 10 s 10 3 10 cm / s Hadron crossing time ≈100 MeV 10-23 s Hadron lifetime measurements: • Invariant mass reconstruction • Intrinsic width is determined • Use of the Uncertainty Principle Invariant Mass: relativistic invariant which is equal to the total mass in the center-of-mass system 2 2 M 2 Ei Pi i i 51 Unification of Forces Unification of Forces: a constant concept in the development of Physics The Coupling Constants are not really constant GUT hypotesis: the unification of all forces at high energies The exact value of the grand unification energy (if grand unification is indeed realized in nature) depends on the precise physics present at shorter distance scales not yet explored by experiments. If one assumes supersymmetry, it is at around 1016 GeV. 52 Interactions unified at high energies. Interactions are different at lower energies because of symmetry breaking If true, all of this has taken place during the history of the Universe Careful: this is a theoretical (fascinating) hypotesis 53 g2 f (q) 2 q M W2 Z The most recent case: Electroweak Unification Guideline: Electromagnetic and Weak Forces as manifestations of a unique Force at q2>104 GeV2, with only one coupling constant e. At low energies, the symmetry is broken. The presence of Weak Neutral Currents was required based on the rinomalizability of the theory. So, the diagrams of the interactions look like: e g W e e e e e W W e W W e g2 e2 GF 2 2 MWZ MWZ W Z0 Weak Neutral Currents allow the renormalization process, provided there is the right connection between the coupling constants g e g e W Z0 g g e g W g e 54 The Fundamental Interactions Gravity Elettro magnetism Weak Nuclear Strong Nuclear Graviton Photon W,Z 8 Gluons Spin 2 1 1 1 Mass 0 0 82,91 GeV 0 Range ∞ ∞ 10-18 m 10-15 m Source Mass Electric charge Weak charge Color Coupling Constant (proton) 10-39 1/137 10-5 1 1 GeV Cross Section 10-29 cm2 10-42 cm2 10-27 cm2 Lifetime for decay 10-19 s 10-8 s 10-23 s 55 The Coupling Costants Gravity (proton mass) GM 2 2.12 1015 M 2 (kg 2 ) 39 c 10 c kg 2 c E.M. (proton charge) e2 (4.8 1010 ) 2 dyne cm cm 1 c 1.054 1027 3 1010 erg s cm 137 s Weak (proton mass) GF 2 5 2 2 5 m c 1 . 2 10 GeV m c 10 p c 3 p Strong (proton mass) s 1 (high q 2 ) s 1 (low q 2 ) 56