The Standard Model of particle physics The ultimate goal (for some at least...) A consistent view of the world AGE-OLD Questions What are the fundamental constituents which comprise the universe? How do they interact? What holds them together? Who will win the World Championship? AGE-OLD Questions What are the fundamental constituents which comprise the universe? How do they interact? What holds them together? Who will win the World Championship? AGE-OLD Questions What are the fundamental constituents which comprise the universe? How do they interact? What holds them together? Who will win the World Championship? AGE-OLD Questions What are the fundamental constituents which comprise the universe? How do they interact? What holds them together? Periodic Table circa 425 BC Earth Water Fire Air “The periodic table.” Sidney Harris Periodic Table circa 425 BC Earth Water Fire Air “The periodic table.” Sidney Harris Periodic Table circa 425 BC Earth Water Fire Air “The periodic table.” Sidney Harris Periodic Table circa 425 BC Earth Water Fire Air “The periodic table.” Sidney Harris Periodic Table circa 425 BC Earth Water Fire Air “The periodic table.” Compact Easy to remember Fits on a T-shirt Periodic Table circa 425 BC Earth Water Fire Air “The periodic table.” Compact Easy to remember Sidney Harris Fits on a T-shirt Periodic Table circa 425 BC Earth Water Fire Air “The periodic table.” Compact Easy to remember Sidney Harris Fits on a T-shirt Physics Beyond the Standard Model? The Higgs field? Unification Earth Plato: Since the four elements can Water transform into each other, it is reasonable to assume that Fire there is only one fundamental substance Air and the four elements are “The periodic table.” just different manifestations Compact of it! Easy to remember Fits on a T-shirt Periodic Table circa 1900 Dimitri Mendeleev (1834-1907) Periodic Table circa 1900 Dimitri Mendeleev (1834-1907) 66 elements! The Standard Model and Beyond PredictionsAtoms Event simulations Challenge The Standard Model: matter (1) ✦ At the atomic scale, matter is composed of atoms:! ! ✤ A core: the nucleus, made of! ★ Protons ( )! ★ Neutrons ( )! ! ✤ Peripheral electrons ( ) ✦ Naively, protons and neutrons are composed objects:! ! ✤ Proton: two up quarks and one down quark ✤ Neutron: one up quarks and two down quarks! ! ! ! ! ✦In reality, they are dynamical objects:! ! ✤ Made of many interacting quarks and gluons! (see later) CERN summer student program 2015 - MADGRAPH Guillaume Chalons & Benjamin Fuks - August 2015 - 3 The Standard Model and Beyond PredictionsAtoms Event simulations Challenge The Standard Model: matter (1) ✦ At the atomic scale, matter is composed of atoms:! ! ✤ A core: the nucleus, made of! ★ Protons ( )! ★ Neutrons ( )! ! ✤ Peripheral electrons ( ) ✦ Naively, protons and neutrons are composed objects:! ! ✤ Proton: two up quarks and one down quark ✤ Neutron: one up quarks and two down quarks! ! ! ! ! ✦In reality, they are dynamical objects:! ! ✤ Made of many interacting quarks and gluons! (see later) CERN summer student program 2015 - MADGRAPH Guillaume Chalons & Benjamin Fuks - August 2015 - 3 The Standard Model and ElementaryBeyond PredictionsMatter Constituents Event simulations I Challenge The Standard Model: matter (2) ✦ Elementary matter constituents! ! ! ! ! ✤ Up quarks! ! ! ✤ Down quarks! } ! Protons and neutrons Nucleus ! ! ! Atoms ✤ Electrons } The neutrino ✦ Neutrons can be converted to protons: the beta decay Sidney Harris CERN summer student program 2015 - MADGRAPH Guillaume Chalons & Benjamin Fuks - August 2015 - 4 The Standard Model and ElementaryBeyond PredictionsMatter Constituents Event simulations II Challenge The Standard Model: matter (3) ✦ Elementary matter constituents: we have three families ✤ Three up-type quarks! ★ Up ( u )! ★ Charm ( c )! ★ To p ( t )! ✤ Three down-type quarks! ★ Down ( d )! ★ Strange ( s )! ★ Bottom ( b )! ✤ Three neutrinos! ★ Electron ( ⌫ e )! ★ Muon ( ⌫ µ )! ★ Tau ( ⌫ ⌧ )! ✤ There charged leptons! ★ Electron ( e )! ★ Muon ( µ )! ★ Tau ( ⌧ ) The only differences are the masses! All other properties are identical CERN summer student program 2015 - MADGRAPH Guillaume Chalons & Benjamin Fuks - August 2015 - 5 The Standard Model and BeyondFour fundamental Predictions Interactions Event simulations Challenge The Standard Model: interactions !✦ Electromagnetism! ✤ Interactions between charged particles (quarks, charged leptons)! ✤ Mediated by massless photons γ !✦ Weak interactions! ✤ Interactions between all matter fields! ✤ Mediated by massive weak W-bosons and Z-bosons !✦ Strong interactions! ✤ Interactions between colored particles (quarks)! ✤ Mediated by massless gluons g ✤ Responsible for binding protons and neutrons within the nucleus !✦ Gravity! ✤ Not included in the Standard Model CERN summer student program 2015 - MADGRAPH Guillaume Chalons & Benjamin Fuks - August 2015 - 6 The Standard Model and Beyond The Predictions Higgs boson Event simulations Challenge The last pieces: the Higgs boson ✦ The masses of the particles! ✤ Elegant mechanism to introduce them ! ✤ Price to pay: a new particle, the so-called Higgs boson! CERN summer student program 2015 - MADGRAPH Guillaume Chalons & Benjamin Fuks - August 2015 - 7 The Standard Model and Beyond The Predictions Higgs boson Event simulations Challenge The last pieces: the Higgs boson ✦ The masses of the particles! ✤ Elegant mechanism to introduce them ! ✤ Price to pay: a new particle, the so-called Higgs boson! discovered in 2012 CERN summer student program 2015 - MADGRAPH Guillaume Chalons & Benjamin Fuks - August 2015 - 7 The Standard Model and Beyond Predictions Event simulations Challenge ThePeriodic Standard Table Model: circa 2017the full AD picture ✦ All the particles have been observed:! ✤ The last one: the Higgs (2012)! ✤ The next-to-last one: the top quark (1995) ✦ Tested over 30 orders of magnitude:! ✤ from 10-18 eV (photon mass limit)! ✤ to 10+13 eV (LHC energy) Compact Easy to remember Fits on a T-shirt The Standard Model (SM) for the strong, weak, and electromagnetic interactions CERN summer student program 2015 - MADGRAPH Guillaume Chalons & Benjamin Fuks - August 2015 - 8 The Standard Model of particle physics (2nd round) The Standard Model • ... provides currently our best understanding of the world • ... is a beautiful theory, based on a few principles • ... has really weird input parameters • ... is an extremly successful theory • There are several reasons to look for theories beyond the SM • We will now discuss some of these aspects to set the stage The beautiful SM The Beautiful SM • QFT = QM + SR • Matter content: 3 generations of • Quarks (u,d),(s,c),(b,t) • Leptons (e,νe),(μ,νμ),(τ,ντ) • local gauge symmetry SU(3)c × SU(2)L × U(1)Y + - • 8 gluons, W , W , Z, Photon • Renormalizability • Electroweak symmetry breaking (EWSB) • Higgs boson 2 The Standard Model 2 The Standard Model 2.1 One-page Summary of the World 22.1Gauge2 The One-page The group Standard Standard Summary Model of Model the World SU(3) SU(2) U(1) Gauge group c ⇥ L ⇥ Y 2.1 One-page Summary of the World 2.1ParticleSU(3) One-page contentc SU(2)L SummaryU(1)Y of the World One page⇥ summary⇥ of the world Gauge group Particle content Gauge groupSU(3) SU(2) MatterU(1) Higgs Gauge c ⇥ L ⇥ Y + Gauge group SU(3)uc SU(2)L U(1)Y ⌫ h Particle contentL⇥ Matter⇥ L Higgs Gauge Q = 0 1 (3, 2) 1/3 L = 0 1 (1, 2)-1 H = 0 1 (1, 2)1 B (1, 1)0 0 u dL ⌫ eL h+ h Particle contentBL C Matter LB C HiggsB C Gauge Particle Q = 0 1 (3, 2) 1/3 L = 0 1 (1, 2)-1 H = 0 1 (1, 2)1 A (1, 1)0 @c A @c A 0 @ A duLR u (3, 1)-4/3 e⌫LeR (1, 1) 2 h+ h W (1, 3)0 content B CL B LC B C Q@= 0A 1 (3, 2) 1/3 L =@0 A1 (1, 2)-1 H = 0 @1 A(1, 2)1 B (1, 1)0 c c Matter c c 0 Higgs Gauge uR dR dL (3, 1(3)-4, 1/3) 2/3 eR eL⌫R (1, 1)(12, 1) 0 h W (1G, 3)0 (8, 1)0 B C B C B C @ A @ A @ A + c uuLc (3, 1) ecc ⌫L (1, 1) h W (1, 3) dR R (3, 1) 2/-43/3 ⌫RR (1, 1)2 0 G 0(8, 1)0 Q = 0 1 (3, 2) 1/3 L = 0 1 (1, 2)-1 H = 0 1 (1, 2)1 A (1, 1)0 Lagrangiandc (Lorentz(3, 1) + gauge⌫c + renormalizable)(1, 1) 0 G (8, 1) dLR 2/3 R eL 0 h 0 LagrangianB1 (LorentzC↵ ↵µ⌫ + gauge + renormalizable)B C µ 2 B λC 2 = @c GAµ⌫G +...QkDQ/ k+@...c (DAµH)†(D H) µ H†@H A(H†H) +...Yk`QkH(uR)` L Lagrangianu−R4 (Lorentz(3, 1) +-4/ gauge3 + renormalizable)eR (1, 1) 2 − −4! W (1, 3)0 1 ↵ ↵µ⌫ µ 2 λ 2 Lagrangian = G G +...Q DQ/ +...(D H)†(D H) µ H†H (H†H) +...Y Q H(u ) µ1⌫ k k µ λ k` k R ` (Lorentz + gauge + L −4 c ↵ ↵µ⌫ / c µ −2 −4! 2 Spontaneous=dR Gµ⌫G symmetry(3+,...1)Q2/k3DQ breakingk+...(⌫DRµH)†(D (H1), 1µ) H0 †H (H†H) +...Yk`QkH(uR)`G (8, 1)0 renormalizable) L −4 − −4! Spontaneous symmetry breaking0 SpontaneousH H symmetry+ 1 breaking 0 p2 v Lagrangian• ! (Lorentz1 0 + gauge + renormalizable) H H0 + 1 ✓0 ◆ H H0 p+2 • 1•! ! p2v v λ SSB SU(2)↵ L↵µ⌫ U(1)✓ ✓◆Y◆ U(1)Q µ 2 2 = • Gµ⌫G ⇥+...Qk!DQ/ k+...(DµH)†(D H) µ H†H (H†H) +...Yk`QkH(uR)` L −SU(2)4 SU(2)L LU(1)U(1)Y Y U(1)U(1)QQ − −4! • • ⇥3 ⇥ !0! 1 2 + B,W γ,Z and Wµ ,Wµ W ,W− • B,W3 3 !γ,Z0 0 and W11,W22 W!++,W SpontaneousA, W symmetryγ,Z and breakingWµµ,Wµµ W ,W−− • •Fermions! ! acquire mass through! Yukawa couplings to Higgs Fermions• Fermions acquire acquire mass mass through through Yukawa couplings couplings to to Higgs Higgs • 1 0 • H H0 + • ! p2 v ✓ ◆ SU(2) U(1) U(1) • L ⇥ Y ! Q 3 0 1 2 + A, W γ,Z and W ,W 3 W ,W− • ! µ µ ! 3 3 Fermions acquire mass through Yukawa couplings to Higgs • 3 The Higgs mechanism • The Higgs potential: V =μ2 ϕ†ϕ + λ (ϕ†ϕ)2 • Vacuum = Ground state = Minimum of V: 2 • If μ >0 (massive particle): ϕmin = 0 (no symmetry breaking) 2 2 1/2 • If μ <0: ϕmin = ±v = ±(-μ /λ) These two minima in one dimension correspond to a continuum of minimum values in SU(2).