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Beyond the Standard Model Special Topics in Particle Physics Beyond the Standard Model Jonghee Yoo Korea Advanced Institute of Science and Technology 2018 Fall Physics Course Lecture Series PH489 Note 04 PH489 Contact Professor Yoo, Jonghee E-mail: [email protected] - E-mail is the easiest way to reach me Classes: E11-208 (2:30PM - 4:00PM, Monday and Wednesday) Office hours: There will be no regular office hours Email me ([email protected]) to organize meeting time - Office#1: KAIST Main Campus, E6-2, room 2306 (2nd floor) - Office#2: KAIST Munji Campus, Creation Hall, room C307-A (3rd floor) Web-page: yoo.kaist.ac.kr/lectures/ - course materials, corrections, useful links etc. KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !2 PH489 Make up Classes? S M T W T F S ! 24 regular lecture opportunities 9 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 10 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 11 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 12 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !3 Standard Model of Particle Physics KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !4 Standard Model of Particle Physics Particle Physics What are the fundamental constituents of the Universe? How do they interact each other? Standard Model of Particle Physics Matter Particles: Fermions Leptons and quarks Force Carrier Particles: Bosons Electromagnetic force (photon) Strong force (gluons) Weak force (W/Z bosons) Introduction to the Standard Model can be found at: http://yoo.kaist.ac.kr/lectures/2018/1/files/YooKAISTPH450Lecture03.pdf KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !5 Standard Model of Particle Physics Matter Particles Leptons note: No right-handed neutrinos Quarks x 3 colors (r,g,b) KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !6 Gauge Principle The gauge principle is based on the fact that both classical physics and quantum theory involve quantities which, in principle, cannot be measured. ➔ It is possible to gauge a theory by a suitable choice of the non-measurable parameters in order to simplify the equation of motion. Maxwell Equations Coulomb Gauge: Lorentz Gauge: KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !7 Gauge Transformation Global gauge transformation: For example Dirac equation: ➔ Local gauge transformation: The requirement for invariance under a local transformation is much more stringent For example the Dirac equation is not invariant under the local transformation and requires modification of derivative ➔ covariant derivative For gauge transformation: µ iγ (@ ieA ie@ ⇠(x)) m 0(x)=0 { µ − µ − µ − } the Dirac equation retains its original form if the gauge field is transformed as: µ iγ (@ ieA0 (x)) m 0(x)=0 µ − µ − µ (iγ D0 m) 0(x)=0 µ − KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !8 Standard Model of Particle Physics Three gauge forces (based on local gauge invariance) Standard Model Yang-Mills Theory + Higgs Mechanism " 1 vector field (B) coupled to hypercharge g1 = e/cosθW " 3 vector fields (W) coupled to weak isocharge g2 = e/sinθW " 8 vector fields (G) coupled to color charge g3 = gs KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !9 Standard Model of Particle Physics Electro-Weak mixing Gauge fields mix and produce physical fields Photon-field Z-field Photon field coupled to electric charge Z-field coupled to weak charge KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !10 Standard Model of Particle Physics Higgs mechanism Higgs gives masses to W/Z, higgs, and fermions Higgs potential: Spontaneous Symmetry Breaking & Vacuum Expectation Value Mass of particles via Higgs mechanism W/Z and Higgs Fermions KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !11 Standard Model of Particle Physics Flavor mixings in Neutrino Mixing Quark Mixing KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !12 Standard Model of Particle Physics Free parameters in the Standard Model " Coupling constants: e, g, sinθW " Boson masses: mW, mZ, mH " Fermion masses: (m#e, m#µ, m#$, me, mµ, m$), (mu, md, ms,mc, mt, mb) " Quark mixing parameters UCKM : (%1,%2,%3,&CP)CKM " Neutrino mixing parameters UMNS: (%1,%2,%3,&CP)MNS More than 20 free parameters! Depends on who you are asking to the number of free parameters and representation of the parameters in SM may vary. For example Majorana phases, number of fermion generations are not included in the above number counting. The higgs mass can be expressed with free parameters of VEV (v) and ' etc. KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !13 Standard Model of Particle Physics Full Lagrangian: SU(3)C × SU(2)L × U(1) Standard Model is a beautiful theory based on a simple principle of local gauge invariance It describes almost all particle physics observations up to 100 GeV (down to length scale of 10-18m) It has been tested better than 0.1% of accuracy Discoveries and achievements - W/Z bosons! - top quark discovery ! - CP violation in B-meson system! - higgs discovery - …… KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !14 Standard Model of Particle Physics Features of the Standard Model " No transitions between leptons and quarks the lepton number L and baryon number B are separately conserved " The charge of the proton is exactly the same as that of the positron " Neutrinos are massless " A family contains only the left-handed neutrino and the associated right-handed anti-neutrino " The weak interaction has a pure V-A structure (maximal parity violation) Predictions of the Standard Model " The proton is stable " The neutrinoless double beta decay is forbidden KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !15 Standard Model of Particle Physics Unanswered questions in Standard Model - gravity? - why 3 generations? - why 3 forces?! - neutrino masses?! - hierarchy problem?! - dark matter and dark energy? - ad hoc higgs mechanism (µ2 <0)? - too many (>20) free parameters? ➔ There must be physics beyond the Standard Model KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !16 Hierarchy Problem in Standard Model Contribution of fermion loops to Higgs mass is quadratically divergent … ( : cut-off parameter on the magnitude of the 4-momentum in the loop " If there is no new physics at higher energy scale, ! the ( is the Planck mass scale (MP = 1019 GeV). ! " The mass of higgs is measured to be MH = 120 GeV ➔ a fine-tuning over the level of 10-17 (=102GeV/1019GeV) is required!! This unnatural cut-off is called “hierarchy problem” Renormalization is the procedure of eliminating divergences in calculations of higher order corrections KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !17 Supersymmetry " Supersymmetric GUT model was introduced by Akulov and Volkov (1972) and Wess and Zumino (1974) — renomalizable theory ! " Supersymmetry introduce a symmetry between fermions and bosons; ➔ fermions and bosons are combined into supermultiplets KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !18 Supersymmetry " The symmetry between fermions and bosons is such that every fermion has a bosonic partner in the same multiplet, and vice versa. " In case of an unbroken symmetry the two partners have the same mass. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !19 Supersymmetry " In Supersymmetry this is essentially the s-top (squark) loop cancelling the effect of the top quark loop " If every fermion is accompanied by two scalars with couplings λs=λf2 the quadratic divergences cancel! " Impose a symmetry between fermions and bosons ➔ Supersymmetry " The correction reduces to logarithmic: KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !20 Supersymmetry Supersymmetric Operator ➔ transforms fermion to boson and vice versa SUSY operator Q: remove boson and put fermion: Qˆ = a†c + c†a a†c + c†a b = f a†c + c†a f = b | i | i | i | i annihilation operator of boson creation operator Qˆ 0 =0 of fermion | i * We will skip SUSY algebra which is quite complicated to introduce in PH489 class. However, advanced students are encouraged to refer supersymmetry text books. KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !21 Supersymmetry " Particle spin changes under the supersymmetric transformations: Q " Supersymmetry introduces a new quantum number: R-parity: ! Rp = (-1)3(B-L)+2S ! Rp = 1 (Standard Model particles) Rp = -1 (Supersymmetry particles) ! ! " Rp is conserved ➔ SUSY particles can only be produced in pairs of a SUSY particle and its antiparticle ● SUSY particles cannot decay directly to SM particles so the lightest SUSY particle has nothing to decay to. for example: stable, weakly interacting Dark Matter candidate lightest neutralino, sneutrino, Gravitino.... KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !22 Minimal Supersymmetric Standard Model (MSSM) MSSM Lagrangian Chiral superfields Superpotential Vector superfields Soft SUSY breaking term ➔ 124 free parameters in this minimal SUSY (MSSM) model! KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !23 MSSM ● The least number of particles added to the Standard Model to make a viable SUSY model (N=1 supersymmetry) ● Assume R-Parity is conserved (stable proton) ● Each SM particle has a SUSY partner ➔ Supersymmetry requires two Higgs doublets to cancel gauge anomalies and provide mass to both up and down-type particles SUSY is a broken symmetry Many different theories for SUSY breaking Generally spontaneous symmetry breaking in a hidden sector is communicated to the visible sector through corrections to the masses Constrained MSSM (CMSSM sometimes called mSUGRA) Impose GUT scale (Mpl) relations on the MSSM Set all scalar masses to one value m0 ! Set all gaugino masses to one value m1/2 Set trilinear couplings to one value A0! Set ratio of Higgs doublet VeVs to tan) Total 5 free parameters (including sign of the higgsino mass term µ) KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !24 MSSM Particles Neutralinos and charginos are often denoted as: X0, X± KAIST-PH489-Yoo-2018-Note04: Beyond the Standard Model !25 GUT: Running Coupling Constants At low energies where we are living in the GUT symmetry is broken.
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