Particle Physics II CP violation (also known as Physics of Antimatter ) Lecture 1. N. Tuning. Niels Tuning (1)

 Bruno Rich
 8 months ago
 Views:
Transcription
1 Particle Physics II CP violation (also known as Physics of Antimatter ) Lecture 1 N. Tuning Niels Tuning (1)
2 Plan 1) Mon 2 Feb: Antimatter + SM 2) Wed 4 Feb: CKM matrix + Unitarity Triangle 3) Mon 9 Feb: Mixing + Master eqs. + B 0 J/ψK s 4) Wed 11 Feb: CP violation in B (s) decays (I) 5) Mon 16 Feb: CP violation in B (s) decays (II) 6) Wed 18 Feb: CP violation in K decays + Overview 7) Mon 23 Feb: Exam on part 1 (CP violation) Final Mark: if (mark > 5.5) mark = max(exam, 0.8*exam + 0.2*homework) else mark = exam In parallel: Lectures on Flavour Physics by prof.dr. R. Fleischer Tuesday + Thrusday Niels Tuning (2)
3 Plan 2 x 45 min 1) Keep track of room! 1) Monday + Wednesday: Start: 9:00 9:15 End: 11:00 Werkcollege: 11:00 ? Niels Tuning (3)
4
5 Grand picture. These lectures Main motivation Universe Niels Tuning (5)
6 Introduction: it s all about the charged current CP violation is about the weak interactions, In particular, the charged current interactions: The interesting stuff happens in the interaction with quarks Therefore, people also refer to this field as flavour physics Niels Tuning (6)
7 Motivation 1: Understanding the Standard Model CP violation is about the weak interactions, In particular, the charged current interactions: Quarks can only change flavour through charged current interactions Niels Tuning (7)
8 Introduction: it s all about the charged current CP violation is about the weak interactions, In particular, the charged current interactions: In 1 st hour: Pparity, Cparity, CPparity the neutrino shows that Pparity is maximally violated Niels Tuning (8)
9 Introduction: it s all about the charged current CP violation is about the weak interactions, In particular, the charged current interactions: b In 1 st hour: W  gv ub Pparity, Cparity, CPparity Symmetry related to particle antiparticle u b gv* ub W + u Niels Tuning (9)
10 Motivation 2: Understanding the universe It s about differences in matter and antimatter Why would they be different in the first place? We see they are different: our universe is matter dominated Equal amounts of matter & anti matter (?) Matter Dominates! Niels Tuning (10)
11 Where and how do we generate the Baryon asymmetry? No definitive answer to this question yet! In 1967 A. Sacharov formulated a set of general conditions that any such mechanism has to meet 1) You need a process that violates the baryon number B: (Baryon number of matter=1, of antimatter = 1) 2) Both C and CP symmetries should be violated 3) Conditions 1) and 2) should occur during a phase in which there is no thermal equilibrium In these lectures we will focus on 2): CP violation Apart from cosmological considerations, I will convince you that there are more interesting aspects in CP violation Niels Tuning (11)
12 Introduction: it s all about the charged current CP violation is about the weak interactions, In particular, the charged current interactions: Same initial and final state Look at interference between B 0 f CP and B 0 B 0 f CP Niels Tuning (12)
13 Motivation 3: Sensitive to find new physics CP violation is about the weak interactions, In particular, the charged current interactions: Box diagram: ΔB=2 Penguin diagram: ΔB=1 b s b s b s μ μ B s b s b g s x x s g b s b B s B 0 b d b g x s s μ K * μ B s s b g b x s μ μ Are heavy particles running around in loops? Niels Tuning (13)
14 Recap: CPviolation (or flavour physics) is about charged current interactions Interesting because: 1) Standard Model: in the heart of quark interactions 2) Cosmology: related to matter antimatter asymetry 3) Beyond Standard Model: measurements are sensitive to new particles Matter Dominates! b s s b Niels Tuning (14)
15 Grand picture. These lectures Main motivation Universe Niels Tuning (15)
16 Personal impression: People think it is a complicated part of the Standard Model (me too:). Why? 1) Nonintuitive concepts? Imaginary phase in transition amplitude, T ~ e iφ Different bases to express quark states, d =0.97 d s b Oscillations (mixing) of mesons: K 0 > K 0 > 2) Complicated calculations? 3) Many decay modes? Beetopaipaigamma B f A 2 f g+ t g t 2 g+ t g t B f Af g+ t g 2  t 2 g+ t g t + + PDG reports 347 decay modes of the B 0 meson: Γ 1 l + ν l anything ( ± 0.28 ) 10 2 Γ 347 ν ν γ < CL=90% And for one decay there are often more than one decay amplitudes Niels Tuning (16)
17 Antimatter Dirac (1928): Prediction Anderson (1932): Discovery Presentday experiments Niels Tuning (17)
18 Schrödinger Classic relation between E and p: Quantum mechanical substitution: (operator acting on wave function ψ) Schrodinger equation: Solution: (show it is a solution) Niels Tuning (18)
19 KleinGordon Relativistic relation between E and p: Quantum mechanical substitution: (operator acting on wave function ψ) KleinGordon equation: or : Solution: with eigenvalues: But! Negative energy solution? Niels Tuning (19)
20 Dirac Paul Dirac tried to find an equation that was relativistically correct, but linear in d/dt to avoid negative energies (and linear in d/dx (or ) for Lorentz covariance) He found an equation that turned out to describe spin1/2 particles and predicted the existence of antiparticles Niels Tuning (20)
21 Dirac How to find that relativistic, linear equation?? Write Hamiltonian in general form, but when squared, it must satisfy: Let s find α i and β! So, α i and β must satisfy: α 2 1 = α 2 2 = α 2 3 = β 2 α 1,α 2,α 3, β anticommute with each other (not a unique choice!) Niels Tuning (21)
22 Dirac What are α and β?? The lowest dimensional matrix that has the desired behaviour is 4x4!? Often used PauliDirac representation: with: So, α i and β must satisfy: α 1 2 = α 2 2 = α 3 2 = β 2 α 1,α 2,α 3, β anticommute with each other (not a unique choice!) Niels Tuning (22)
23 Dirac Usual substitution: Leads to: Multiply by β: (β 2 =1) Gives the famous Dirac equation: Niels Tuning (23)
24 Dirac The famous Dirac equation: R.I.P. : Niels Tuning (24)
25 Dirac The famous Dirac equation: Remember! μ : Lorentz index 4x4 γ matrix: Dirac index Less compact notation: Even less compact : What are the solutions for ψ?? Niels Tuning (25)
26 Dirac The famous Dirac equation: Solutions to the Dirac equation? Try plane wave: Linear set of eq: 2 coupled equations: If p=0: Niels Tuning (26)
27 Dirac The famous Dirac equation: Solutions to the Dirac equation? Try plane wave: 2 coupled equations: If p 0: Two solutions for E>0: (and two for E<0) with: Niels Tuning (27)
28 Dirac Tuning (28) The famous Dirac equation: Solutions to the Dirac equation? Try plane wave: 2 coupled equations: If p 0: Two solutions for E>0: (and two for E<0) + 0 / 0 1 (1) m E p u + m E p u / (2)
29 Dirac Niels Tuning (29) The famous Dirac equation: ψ is 4component spinor 4 solutions correspond to fermions and antifermions with spin+1/2 and 1/2 Two solutions for E>0: (and two for E<0) + 0 / 0 1 (1) m E p u + m E p u / (2)
30 Discovery of antimatter Lead plate positron Nobelprize 1936 Niels Tuning (30)
31 Why antimatter must exist! FeynmanStueckelberg interpretation One observer s electron is the other observer s positron Niels Tuning (31)
32 CPT theorem CPT transformation: C: interchange particles and antiparticles P: reverse spacecoordinates T: Reverse timecoordinate CPT transformation closely related to Lorentzboost CPT invariance implies Particles and antiparticles have same mass and lifetime Lorentz invariance Niels Tuning (32)
33 CPT is conserved, but does antimatter fall down? Niels Tuning (33)
34 Experiments Need to have neutral antimatter Otherwise electrostatic forces spoil the weak gravitational force Make antiprotons Accelerator Antiproton factory Decelerator Storage Produce antihydrogen for study Trap Observe (spectroscopy, ) Thanks to Rolf Landua (CERN) Niels Tuning (34)
35 Antiproton beam CERN (1980): SppS: led to discovery of W, Z Niels Tuning (35)
36 Antiproton production Acceleration effciency ~ 103 Production efficiency ~ 104 Collection efficiency ~ 102 Niels Tuning (36)
37 Antiproton storage AC: Accumulator (3.57 GeV) PS: Decelarator (0.6 GeV) LEAR: Low Energy Antiproton ring (1982) Niels Tuning (37)
38 Antihydrogen 1995: First 9 antihydrogen atoms made: 1997: Replace LEAR by AD (antiproton decelerator) Niels Tuning (38)
39 Antihydrogen: challenge Beam energy: ~ GeV Atomic energy scale: ~ ev Trap charged particles: Niels Tuning (39)
40 Antihydrogen production ATHENA and ATRAP experiments Niels Tuning (40)
41 Antihydrogen production ATRAP, ALPHA, ASACUSA, AEGIS experiments: Niels Tuning (41)
42 Antihydrogen production Niels Tuning (42)
43 Antihydrogen detection ATRAP, ATHENA: pioneering the trapping technique ALPHA: trapped antihydrogen for 16 minutes Niels Tuning (43)
44 Antihydrogen detection ASACUSA: 2011: trapped antiproton in He (replacing an electron), measuring mass to Jan 2014: The ASACUSA experiment at CERN has succeeded for the first time in producing a beam of antihydrogen atoms. In a paper published today in Nature Communications, the ASACUSA collaboration reports the unambiguous detection of 80 antihydrogen atoms 2.7 metres downstream of their production, where the perturbing influence of the magnetic fields used initially to produce the antiatoms is small. This result is a significant step towards precise hyperfine spectroscopy of antihydrogen atoms. Niels Tuning (44)
45 Antihydrogen detection AEgIS Does antihydrogen fall with the same acceleration as hydrogen? Niels Tuning (45)
46 C, P, T C, P, T transformation: C: interchange particles and antiparticles P: reverse spacecoordinates T: Reverse timecoordinate CPT we discussed briefly After the break we deal with P and CP violation! Niels Tuning (46)
47 Break Niels Tuning (47)
48 P and C violation What is the link between antimatter and discrete symmetries? C operator changes matter into antimatter 2 more discrete symmetries: P and T Niels Tuning (48)
49 Continuous vs discrete symmetries Space, time translation & orientation symmetries are all continuous symmetries Each symmetry operation associated with one ore more continuous parameter There are also discrete symmetries Charge sign flip (Q Q) : C parity Spatial sign flip ( x,y,z x,y,z) : P parity Time sign flip (t t) : T parity Are these discrete symmetries exact symmetries that are observed by all physics in nature? Key issue of this course Niels Tuning (49)
50 Three Discrete Symmetries Parity, P Parity reflects a system through the origin. Converts righthanded coordinate systems to lefthanded ones. Vectors change sign but axial vectors remain unchanged x x, p p, but L = x p L Charge Conjugation, C Charge conjugation turns a particle into its antiparticle e + e , K  K Time Reversal, T Changes, for example, the direction of motion of particles t t Niels Tuning (50)
51 Example: People believe in symmetry Instruction for Abel Tasman, explorer of Australia (1642): Since many rich mines and other treasures have been found in countries north of the equator between 15 o and 40 o latitude, there is no doubt that countries alike exist south of the equator. The provinces in Peru and Chili rich of gold and silver, all positioned south of the equator, are revealing proofs hereof. Niels Tuning (51)
52 Example: People believe in symmetry Award Ceremony Speech Nobel Prize (1957): it was assumed almost tacitly, that elementary particle reactions are symmetric with respect to right and left. In fact, most of us were inclined to regard the symmetry of elementary particles with respect to right and left as a necessary consequence of the general principle of rightleft symmetry of Nature. only Lee and Yang asked themselves what kind of experimental support there was for the assumption that all elementary particle processes are symmetric with respect to right and left. Niels Tuning (52)
53 A realistic experiment: the Wu experiment (1956) Observe radioactive decay of Cobalt60 nuclei The process involved: 60 27Co 60 28Ni + e  + n e 60 27Co is spin5 and 60 28Ni is spin4, both e and n e are spin½ If you start with fully polarized Co (S Z =5) the experiment is essentially the same (i.e. there is only one spin solution for the decay) 5,+5> 4,+4> + ½,+½> + ½,+½> S=1/2 S=4 S=1/2 Niels Tuning (53)
54 Intermezzo: Spin and Parity and Helicity We introduce a new quantity: Helicity = the projection of the spin on the direction of flight of a particle H S S p p H=+1 ( righthanded ) H=1 ( lefthanded ) Niels Tuning (54)
55 The Wu experiment 1956 Experimental challenge: how do you obtain a sample of Co(60) where the spins are aligned in one direction Wu s solution: adiabatic demagnetization of Co(60) in magnetic fields at very low temperatures (~1/100 K!). Extremely challenging in Niels Tuning (55)
56 The Wu experiment 1956 The surprising result: the counting rate is different Electrons are preferentially emitted in direction opposite of 60 Co spin! Careful analysis of results shows that experimental data is consistent with emission of lefthanded (H=1) electrons only at any angle!! Backward Counting rate w.r.t unpolarized rate 60 Co polarization decreases as function of time Forward Counting rate w.r.t unpolarized rate Niels Tuning (56)
57 The Wu experiment 1956 Physics conclusion: Angular distribution of electrons shows that only pairs of lefthanded electrons / righthanded antineutrinos are emitted regardless of the emission angle Since righthanded electrons are known to exist (for electrons H is not Lorentzinvariant anyway), this means no lefthanded antineutrinos are produced in weak decay Parity is violated in weak processes Not just a little bit but 100% How can you see that 60 Co violates parity symmetry? If there is parity symmetry there should exist no measurement that can distinguish our universe from a parityflipped universe, but we can! Niels Tuning (57)
58 So P is violated, what s next? Wu s experiment was shortly followed by another clever experiment by L. Lederman: Look at decay p + m + n m Pion has spin 0, m,n m both have spin ½ spin of decay products must be oppositely aligned Helicity of muon is same as that of neutrino. m + p + n m OK OK Nice feature: can also measure polarization of both neutrino (p + decay) and antineutrino (p  decay) Ledermans result: All neutrinos are lefthanded and all antineutrinos are righthanded Niels Tuning (58)
59 Charge conjugation symmetry Introducing Csymmetry The C(harge) conjugation is the operation which exchanges particles and antiparticles (not just electric charge) It is a discrete symmetry, just like P, i.e. C 2 = 1 m + p + n m (LH) OK C m  p  n m (LH) OK C symmetry is broken by the weak interaction, just like P Niels Tuning (59)
60 The Weak force and C,P parity violation What about C+P CP symmetry? CP symmetry is parity conjugation (x,y,z x,y,z) followed by charge conjugation (X X) n m Intrinsic spin m + m  p + P C p  p + CP appears to be preserved in weak interaction! m + CP n m n m Niels Tuning (60)
61 What do we know now? C.S. Wu discovered from 60 Co decays that the weak interaction is 100% asymmetric in Pconjugation We can distinguish our universe from a parity flipped universe by examining 60 Co decays L. Lederman et al. discovered from π + decays that the weak interaction is 100% asymmetric in Cconjugation as well, but that CPsymmetry appears to be preserved First important ingredient towards understanding matter/antimatter asymmetry of the universe: weak force violates matter/antimatter(=c) symmetry! C violation is a required ingredient, but not enough as we will learn later Niels Tuning (61)
62 Conserved properties associated with C and P C and P are still good symmetries in any reaction not involving the weak interaction Can associate a conserved value with them (Noether Theorem) Each hadron has a conserved P and C quantum number What are the values of the quantum numbers Evaluate the eigenvalue of the P and C operators on each hadron P y> = p y> What values of C and P are possible for hadrons? Symmetry operation squared gives unity so eigenvalue squared must be 1 Possible C and P values are +1 and 1. Meaning of P quantum number If P=1 then P y> = +1 y> (wave function symmetric in space) if P=1 then P y> = 1 y> (wave function antisymmetric in space) Niels Tuning (62)
63 Figuring out P eigenvalues for hadrons QFT rules for particle vs. antiparticles Parity of particle and antiparticle must be opposite for fermions (spinn+1/2) Parity of bosons (spin N) is same for particle and antiparticle Definition of convention (i.e. arbitrary choice in def. of q vs q) Quarks have positive parity Antiquarks have negative parity e  has positive parity as well. (Can define other way around: Notation different, physics same) Parity is a multiplicative quantum number for composites For composite AB the parity is P(A)*P(B), Thus: Baryons have P=1*1*1=1, antibaryons have P=1*1*1=1 (Anti)mesons have P=1*1 = 1 Excited states (with orbital angular momentum) Get an extra factor (1) l where l is the orbital L quantum number Note that parity formalism is parallel to total angular momentum J=L+S formalism, it has an intrinsic component and an orbital component NB: Photon is spin1 particle has intrinsic P of 1 Niels Tuning (63)
64 Parity eigenvalues for selected hadrons The p + meson Quark and antiquark composite: intrinsic P = (1)*(1) = 1 Orbital ground state no extra term P(p + )=1 The neutron Three quark composite: intrinsic P = (1)*(1)*(1) = 1 Orbital ground state no extra term P(n) = +1 Meaning: P p + > = 1 p + > Experimental proof: J.Steinberger (1954) πd nn n are fermions, so (nn) antisymmetric S d =1, S π =0 L nn =1 1) final state:p nn> = (1) L nn> = 1 nn> 2) init state: P d> = P pn> = (+1) 2 pn> = +1 d> To conserve parity: P π> = 1 π> The K 1 (1270) Quark antiquark composite: intrinsic P = (1)*(1) = 1 Orbital excitation with L=1 extra term (1) 1 P(K 1 ) = +1 Niels Tuning (64)
65 Figuring out C eigenvalues for hadrons Only particles that are their own antiparticles are C eigenstates because C x> x> = c x> E.g. p 0,h,h,r 0,f,w,y and photon C eigenvalues of quarkantiquark pairs is determined by L and S angular momenta: C = (1) L+S Rule applies to all above mesons C eigenvalue of photon is 1 Since photon is carrier of EM force, which obviously changes sign under C conjugation Example of C conservation: Process p 0 g g C=+1(p 0 has spin 0) (1)*(1) Process p 0 g g g does not occur (and would violate C conservation) Experimental proof of Cinvariance: BR(π 0 γγγ)< Niels Tuning (65)
66 This was an introduction to P and C Let s change gear Niels Tuning (66)
67 CP violation in the SM Lagrangian Focus on charged current interaction (W ± ): let s trace it u L I d L I g W +m Niels Tuning (67)
68 The Standard Model Lagrangian L L + L + L SM Kinetic Higgs Yukawa L Kinetic : Introduce the massless fermion fields Require local gauge invariance gives rise to existence of gauge bosons L Higgs : Introduce Higgs potential with <f> 0 Spontaneous symmetry breaking G SU(3) SU(2) U(1) SU(3) U(1) SM C L Y C Q The W +, W ,Z 0 bosons acquire a mass L Yukawa : Ad hoc interactions between Higgs field & fermions Niels Tuning (68)
69 Fields: Notation Fermions: 1 g5 1+ g5 y L y ; y R y 2 2 Y = Q  T 3 with y = Q L, u R, d R, L L, l R, n R Quarks: Under SU2: Left handed doublets Right hander singlets Leptons: u d I I I n I (3,2,1 6) (3,2,1 6) Li I u Ri (3,1,2 3) d I Ri (3,1, 1 3) l (1,2, 1 2) (1,2, 1 2) Li I l (1,1, 1) Ri I Q Li Lefthanded Interaction rep. SU(3) C SU(2) Hypercharge Y L generation index I n Ri (3,2,1 6) I L Li (1,2, 1 2) (=avg el.charge in multiplet) Scalar field: f (1, 2,1 2) + 0 Note: Interaction representation: standard model interaction is independent of generation number Niels Tuning (69)
70 Fields: Notation Q Y = Q T TY 3 Explicitly: The left handed quark doublet : Q I Li I I I I I I I I I ur, ug, u b cr, cg, c b tr, tg, t b (3,2,1 6),, I I I I I I I I I dr, dg, d b sr, sg, s b br, bg, b b L L L T T ( Y 16) Similarly for the quark singlets: u I Ri I I I I I I I I I ur ur ur c R r cr cr t R r tr tr R Y 23 I I I I I I I I I dr dr r sr sr r br br r Y 13 (3,1, 2 3),,,,,,,, I d (3,1, 1 3),, d,,, s,,, b Ri R R R The left handed leptons: L I I I n n 3 12 I e m n T + Li (1,2, 1 2),, Y  I I I e m T312 L L L 12 And similarly the (charged) singlets: l I (1,1, 1) e I, m I, I Y 1 Ri R R R Niels Tuning (70)
71 LSM L Kinetic + L Higgs + LYukawa :The Kinetic Part L Kinetic : Fermions + gauge bosons + interactions Procedure: Introduce the Fermion fields and demand that the theory is local gauge invariant under SU(3) C xsu(2) L xu(1) Y transformations. m Start with the Dirac Lagrangian: L iy ( g ) y m m m m m m D + ig G L + igw T + igb Y Replace: s a a b b m Fields: G m a : 8 gluons W m b : weak bosons: W 1, W 2, W 3 B m : hypercharge boson Generators: L a : GellMann matrices: ½ a (3x3) SU(3) C T b : Pauli Matrices: ½ b (2x2) SU(2) L Y : Hypercharge: U(1) Y For the remainder we only consider Electroweak: SU(2) L x U(1) Y Niels Tuning (71)
72 LSM L Kinetic + L Higgs + LYukawa : The Kinetic Part L kinetic m m : iy ( g ) y iy ( D g ) y m with y Q, u, d, L, l m I I I I I Li Ri Ri Li Ri For example, the term with Q Li I becomes: L m ( Q ) iq g D Q I I I kinetic Li Li m Li I m i m i m i m iq g m ( + gsg + gw + gb ) Q I Li a a b b Li Writing out only the weak part for the quarks: 0 I 2 Weak I I m i m m m u i Lkinetic( u, d) L iu, d g L m + g W1 1 + W2 2 + W3 3 2 d L 3 I m I I m I g I m I g I m I iulg m ul + idlg m dl  ulg mw  dl  dlg mw + ul u L I i d L I g W +m L=J m W m W + = (1/ 2) (W 1 + i W 2 ) W  = (1/ 2) (W 1 i W 2 ) Niels Tuning (72)
73 L L + L + L SM Kinetic Higgs Yukawa L 1 Dmf D f  V V m f f + f f 2 : The Higgs Potential 2 m 2 Higgs Higgs Higgs Symmetry 2 m 0: 0 V(f) f Broken Symmetry 2 m 0: 0 v 2 Vf f 2 v m ~ 246 GeV Spontaneous Symmetry Breaking: The Higgs field adopts a nonzero vacuum expectation value Procedure: e + imf f e + imf And rewrite the Lagrangian (tedious): (The other 3 Higgs fields are eaten by the W, Z bosons) Substitute: 0 e v+ H 2 1. G : SU. (3) SU(2) U(1) SU(3) U(1) 2. The W +,W ,Z 0 bosons acquire mass 3. The Higgs boson H appears SM C L Y C EM 0 Niels Tuning (73)
74 LSM LKinetic + LHiggs + LYukawa : The Yukawa Part Since we have a Higgs field we can (should?) add (adhoc) interactions between f and the fermions in a gauge invariant way. The result is: doublets singlet Li.. L + Yukawa Yij y f y Rj hc I I I ~ I I I Q f d.. Li Rj ij Q f u L j L f lrj h c Y + Y + Y i + d u l ij i Rj Li i, j : indices for the 3 generations! 0 1 f 0 * * With: f i 2 f f f  (The CP conjugate of f To be manifestly invariant under SU(2) ) Y, Y, Y d u l ij ij ij are arbitrary complex matrices which operate in family space (3x3) Flavour physics! Niels Tuning (74)
75 LSM LKinetic + LHiggs + LYukawa : The Yukawa Part Writing the first term explicitly: + d I I Yij ( ul, dl) i d 0 I Rj d I I d I I d I I Y11 ul, dl Y 0 12 ul, dl Y 0 13 ul, dl 0 I d R d I I d I I d I I I Y21 cl, sl Y 0 22 cl, sl Y 0 13 cl, sl 0 sr I br d I I d I I d I I Y31 tl, bl Y 0 32 tl, bl Y 0 33 tl, b L 0 Niels Tuning (75)
76 LSM LKinetic + LHiggs + LYukawa : The Yukawa Part There are 3 Yukawa matrices (in the case of massless neutrino s): Y, Y, Y d u l ij ij ij Each matrix is 3x3 complex: 27 real parameters 27 imaginary parameters ( phases ) many of the parameters are equivalent, since the physics described by one set of couplings is the same as another It can be shown (see ref. [Nir]) that the independent parameters are: 12 real parameters 1 imaginary phase This single phase is the source of all CP violation in the Standard Model Revisit later Niels Tuning (76)
77 L Yukawa S.S.B L Mass : The Fermion Masses Start with the Yukawa Lagrangian + d I I I u l LYuk Yij ( ul, dl ) i d Rj + Yij + ij 0... : v+ H S S B e 2 After which the following mass term emerges: L  L d M d + u M u I l I + l M l + h.. c Y I d I I u I Yuk Mass Li ij Rj Li ij Rj Li ij Rj with M v Y, M v Y, M v Y d d u u l l ij ij ij ij ij ij L Mass is CP violating in a similar way as L Yuk Niels Tuning (77)
78 L Yukawa S.S.B L Mass : The Fermion Masses Writing in an explicit form: I I I d u e I I I I I I I I I I I I d, s, b d s u, c, t u M M c e, m, M l  L m h. c. Mass + + L L L + I I I b t V M V M f f f f L R diagonal R The matrices M can always be diagonalised by unitary matrices V L f and V R f Then the real fermion mass eigenstates are given by: d I d V L VR d d d d I Li ij Lj Ri ij Rj u I u V L VR u u u u I Li ij Lj Ri ij Rj l I l V i V l l l l I Li L ij Lj R R ij Rj d I L, u I L, l I L are the weak interaction eigenstates d L, u L, l L are the mass eigenstates ( physical particles ) R f,, VL V L M V R R such that: d d s b V s b I I I f f f f I R L I Niels Tuning (78) I R
79 L Yukawa S.S.B L Mass : The Fermion Masses In terms of the mass eigenstates: md d mu u LMass d, s, b ms s u, c, t m c L + t L c L m b b m R t me e + e, m, mm m h. c. L + m m uu + m cc + m tt Mass u c t + m dd + m ss + m bb d s b + m ee + m mm + m e m In flavour space one can choose: Weak basis: The gauge currents are diagonal in flavour space, but the flavour mass matrices are nondiagonal Mass basis: The fermion masses are diagonal, but some gauge currents (charged weak interactions) are not diagonal in flavour space In the weak basis: L Yukawa = CP violating In the mass basis: L Yukawa L Mass = CP conserving R R What happened to the charged current interactions (in L Kinetic )? Niels Tuning (79)
80 LW L CKM : The Charged Current The charged current interaction for quarks in the interaction basis is: L The charged current interaction for quarks in the mass basis is: L L W W W g 2 g 2 g 2 u V Li I Li g u m d L L Li The unitary matrix: V u d CKM VL VL d u c t V L CKM s b,, V d W is the Cabibbo Kobayashi Maskawa mixing matrix: n l Lepton sector: similarly VMNS VL VL u g m d I Li L W + m With: However, for massless neutrino s: V n L = arbitrary. Choose it such that V MNS = 1 There is no mixing in the lepton sector g m + m W + m V CKM V CKM 1 Niels Tuning (80)
81 L Charged Currents g I m I g I m I m m u g W d + d g W u J W + JCC W CC Li m Li Li m Li CC m m L The charged current term reads: g 1g 1g g 1g 1g u W d + d W u g m  5 g m + * 5 uig WmVij 1 g d j + d jg WmVi j 1 g ui m  m + i g mvij j j g mvji i Under the CP operator this gives: CP g m + 5 g m i * 5 d g WmVij 1 g u + u g WmVij 1 g d 2 2 CC j i i j A comparison shows that CP is conserved only if V ij = V ij * (Together with (x,t) > (x,t)) In general the charged current term is CP violating Niels Tuning (81)
82 The Standard Model Lagrangian (recap) LSM L Kinetic + L Higgs + LYukawa L Kinetic : Introduce the massless fermion fields Require local gauge invariance gives rise to existence of gauge bosons CP Conserving L Higgs : Introduce Higgs potential with <f> 0 Spontaneous symmetry breaking CP Conserving G SU(3) SU(2) U(1) SU(3) U(1) SM C L Y C Q The W +, W ,Z 0 bosons acquire a mass L Yukawa : Ad hoc interactions between Higgs field & fermions CP violating with a single phase L Yukawa L mass : fermion weak eigenstates:  mass matrix is (3x3) nondiagonal fermion mass eigenstates:  mass matrix is (3x3) diagonal CPviolating CPconserving! L Kinetic in mass eigenstates: CKM matrix CP violating with a single phase Niels Tuning (82)
83 LSM LKinetic + LHiggs + LYukawa Recap + d I I I LYuk Yi j ( ul, dl ) i d... 0 Rj + L g I m  I g I m + I u g Wmd + dlig WmuL i Kinetic Li Li Diagonalize Yukawa matrix Y ij Mass terms Quarks rotate Off diagonal terms in charged current couplings I d d I s VCKM s I b b md d mu u LMass d, s, b ms s u, c, t mc c... L + L + m b b m t t L g m  5 g m + * 5 u g WmVij 1 g d + d g WmVi 1  g u CKM i j j j i R L L + L + L SM CKM Higgs Mass R Niels Tuning (83)
84 Ok. We ve got the CKM matrix, now what? It s unitary probabilities add up to 1 : d =0.97 d s b ( =1) How many free parameters? How many real/complex? How do we normally visualize these parameters? Niels Tuning (84)
85 Personal impression: People think it is a complicated part of the Standard Model (me too:). Why? 1) Nonintuitive concepts? Imaginary phase in transition amplitude, T ~ e iφ Different bases to express quark states, d =0.97 d s b Oscillations (mixing) of mesons: K 0 > K 0 > 2) Complicated calculations? 3) Many decay modes? Beetopaipaigamma B f A 2 f g+ t g t 2 g+ t g t B f Af g+ t g 2  t 2 g+ t g t + + PDG reports 347 decay modes of the B 0 meson: Γ 1 l + ν l anything ( ± 0.28 ) 10 2 Γ 347 ν ν γ < CL=90% And for one decay there are often more than one decay amplitudes Niels Tuning (85)
86
Parity violation. no lefthanded ν$ are produced
Parity violation Wu experiment: b decay of polarized nuclei of Cobalt: Co (spin 5) decays to Ni (spin 4), electron and antineutrino (spin ½) Parity changes the helicity (H). Ø Pconservation assumes a
More informationLecture III: Higgs Mechanism
ecture III: Higgs Mechanism Spontaneous Symmetry Breaking The Higgs Mechanism Mass Generation for eptons Quark Masses & Mixing III.1 Symmetry Breaking One example is the infinite ferromagnet the nearest
More informationOutline. Charged Leptonic Weak Interaction. Charged Weak Interactions of Quarks. Neutral Weak Interaction. Electroweak Unification
Weak Interactions Outline Charged Leptonic Weak Interaction Decay of the Muon Decay of the Neutron Decay of the Pion Charged Weak Interactions of Quarks CabibboGIM Mechanism CabibboKobayashiMaskawa
More informationThe Higgs Boson and Electroweak Symmetry Breaking
The Higgs Boson and Electroweak Symmetry Breaking 1. Minimal Standard Model M. E. Peskin Chiemsee School September 2014 The Higgs boson has an odd position in the Standard Model of particle physics. On
More informationFlavour physics Lecture 1
Flavour physics Lecture 1 Jim Libby (IITM) XI th SERC school on EHEP NISER Bhubaneswar November 2017 Lecture 1 1 Outline What is flavour physics? Some theory and history CKM matrix Lecture 1 2 What is
More informationParticle Physics. Michaelmas Term 2011 Prof. Mark Thomson. Handout 2 : The Dirac Equation. NonRelativistic QM (Revision)
Particle Physics Michaelmas Term 2011 Prof. Mark Thomson + e  e +  + e  e +  + e  e +  + e  e +  Handout 2 : The Dirac Equation Prof. M.A. Thomson Michaelmas 2011 45 NonRelativistic QM (Revision)
More informationParticle Physics. Dr Victoria Martin, Spring Semester 2012 Lecture 1: The Mysteries of Particle Physics, or Why should I take this course?
Particle Physics Dr Victoria Martin, Spring Semester 2012 Lecture 1: The Mysteries of Particle Physics, or Why should I take this course? Contents: Review of the Standard Model! What we know! What we don
More informationNeutrino Masses & Flavor Mixing 邢志忠. Zhizhong Xing. (IHEP, Winter School 2010, Styria, Austria. Lecture B
Neutrino Masses & Flavor Mixing Zhizhong Xing 邢志忠 (IHEP, Beijing) @Schladming Winter School 2010, Styria, Austria Lecture B Lepton Flavors & Nobel Prize 2 1975 1936 = 1936 1897 = 39 Positron: Predicted
More information2.4 Parity transformation
2.4 Parity transformation An extremely simple group is one that has only two elements: {e, P }. Obviously, P 1 = P, so P 2 = e, with e represented by the unit n n matrix in an n dimensional representation.
More informationWeak interactions and vector bosons
Weak interactions and vector bosons What do we know now about weak interactions? Theory of weak interactions Fermi's theory of weak interactions VA theory Current  current theory, current algebra W and
More informationOUTLINE. CHARGED LEPTONIC WEAK INTERACTION  Decay of the Muon  Decay of the Neutron  Decay of the Pion
Weak Interactions OUTLINE CHARGED LEPTONIC WEAK INTERACTION  Decay of the Muon  Decay of the Neutron  Decay of the Pion CHARGED WEAK INTERACTIONS OF QUARKS  CabibboGIM Mechanism  CabibboKobayashiMaskawa
More informationWeak interactions, parity, helicity
Lecture 10 Weak interactions, parity, helicity SS2011: Introduction to Nuclear and Particle Physics, Part 2 2 1 Weak decay of particles The weak interaction is also responsible for the β + decay of atomic
More informationSM predicts massless neutrinos
MASSIVE NEUTRINOS SM predicts massless neutrinos What is the motivation for considering neutrino masses? Is the question of the existence of neutrino masses an isolated one, or is connected to other outstanding
More informationCKM Matrix and CP Violation in Standard Model
CKM Matrix and CP Violation in Standard Model CP&Viola,on&in&Standard&Model&& Lecture&15& Shahram&Rahatlou& Fisica&delle&Par,celle&Elementari,&Anno&Accademico&2014815& http://www.roma1.infn.it/people/rahatlou/particelle/
More informationQuantum Field Theory. and the Standard Model. !H Cambridge UNIVERSITY PRESS MATTHEW D. SCHWARTZ. Harvard University
Quantum Field Theory and the Standard Model MATTHEW D. Harvard University SCHWARTZ!H Cambridge UNIVERSITY PRESS t Contents v Preface page xv Part I Field theory 1 1 Microscopic theory of radiation 3 1.1
More informationAdding families: GIM mechanism and CKM matrix
Particules Élémentaires, Gravitation et Cosmologie Année 200708 08 Le Modèle Standard et ses extensions Cours VII: 29 février f 2008 Adding families: GIM mechanism and CKM matrix 29 fevrier 2008 G. Veneziano,
More informationLecture 01. Introduction to Elementary Particle Physics
Introduction to Elementary Particle Physics Particle Astrophysics Particle physics Fundamental constituents of nature Most basic building blocks Describe all particles and interactions Shortest length
More informationLecture 3: Quarks and Symmetry in Quarks
Lecture 3: Quarks and Symmetry in Quarks Quarks Cross Section, Fermions & Bosons, Wave Eqs. Symmetry: Rotation, Isospin (I), Parity (P), Charge Conjugate (C), SU(3), Gauge symmetry Conservation Laws: http://faculty.physics.tamu.edu/kamon/teaching/phys627/
More informationElectroweak interactions of quarks. Benoit Clément, Université Joseph Fourier/LPSC Grenoble
Electroweak interactions of quarks Benoit Clément, Université Joseph Fourier/LPSC Grenoble HASCO School, Göttingen, July 1527 2012 1 PART 1 : Hadron decay, history of flavour mixing PART 2 : Oscillations
More informationSymmetry Groups conservation law quantum numbers Gauge symmetries local bosons mediate the interaction Group Abelian Product of Groups simple
Symmetry Groups Symmetry plays an essential role in particle theory. If a theory is invariant under transformations by a symmetry group one obtains a conservation law and quantum numbers. For example,
More informationThe God particle at last? Science Week, Nov 15 th, 2012
The God particle at last? Science Week, Nov 15 th, 2012 Cormac O Raifeartaigh Waterford Institute of Technology CERN July 4 th 2012 (ATLAS and CMS ) A new particle of mass 125 GeV Why is the Higgs particle
More informationKern und Teilchenphysik I Lecture 13:Quarks and QCD
Kern und Teilchenphysik I Lecture 13:Quarks and QCD (adapted from the Handout of Prof. Mark Thomson) Prof. Nico Serra Dr. Patrick Owen, Dr. Silva Coutinho http://www.physik.uzh.ch/de/lehre/phy211/hs2016.html
More informationIoP Masterclass FLAVOUR PHYSICS. Tim Gershon, University of Warwick April 20 th 2007
IoP Masterclass FLAVOUR PHYSICS Tim Gershon, University of Warwick April 20 th 2007 The Standard Model Tim Gershon, IoP Masterclass, April 20 th 2007 2 Some Questions What is antimatter? Why are there
More informationThe Hunt for the Higgs (and other interesting stuff at the Tevatron) Robert Roser Fermi National Accelerator Laboratory
The Hunt for the Higgs (and other interesting stuff at the Tevatron) Robert Roser Fermi National Accelerator Laboratory The Past Century ~90 years ago ~60 years ago ~40 years ago Present atom electron
More informationThe God particle at last? Astronomy Ireland, Oct 8 th, 2012
The God particle at last? Astronomy Ireland, Oct 8 th, 2012 Cormac O Raifeartaigh Waterford Institute of Technology CERN July 4 th 2012 (ATLAS and CMS ) A new particle of mass 125 GeV I The Higgs boson
More informationIsospin. K.K. Gan L5: Isospin and Parity 1
Isospin Isospin is a continuous symmetry invented by Heisenberg: Explain the observation that the strong interaction does not distinguish between neutron and proton. Example: the mass difference between
More informationQED and the Standard Model Autumn 2014
QED and the Standard Model Autumn 2014 Joel Goldstein University of Bristol Joel.Goldstein@bristol.ac.uk These lectures are designed to give an introduction to the gauge theories of the standard model
More informationThe Standard Model of Particle Physics  I
The Standard Model of Particle Physics  I Lecture 3 Quantum Numbers and Spin Symmetries and Conservation Principles Weak Interactions Accelerators and Facilities Eram Rizvi Royal Institution  London
More informationModern physics 1 Chapter 13
Modern physics 1 Chapter 13 13. Particle physics Particle studied within the ATLASproject CERN In the beginning of 1930, it seemed that all the physics fundaments was placed within the new areas of elementary
More informationS 3 Symmetry as the Origin of CKM Matrix
S 3 Symmetry as the Origin of CKM Matrix Ujjal Kumar Dey Physical Research Laboratory October 25, 2015 Based on: PRD 89, 095025 and arxiv:1507.06509 Collaborators: D. Das and P. B. Pal 1 / 25 Outline 1
More information12.2 Problem Set 2 Solutions
78 CHAPTER. PROBLEM SET SOLUTIONS. Problem Set Solutions. I will use a basis m, which ψ C = iγ ψ = Cγ ψ (.47) We can define left (light) handed Majorana fields as, so that ω = ψ L + (ψ L ) C (.48) χ =
More informationTHE STANDARD MODEL AND THE GENERALIZED COVARIANT DERIVATIVE
THE STANDAD MODEL AND THE GENEALIZED COVAIANT DEIVATIVE arxiv:hepph/9907480v Jul 999 M. Chaves and H. Morales Escuela de Física, Universidad de Costa ica San José, Costa ica Emails: mchaves@cariari.ucr.ac.cr,
More informationOption 212: UNIT 2 Elementary Particles
Department of Physics and Astronomy Option 212: UNIT 2 Elementary Particles SCHEDULE 26Jan15 13.00pm LRB Intro lecture 28Jan15 12.00pm LRB Problem solving (2Feb15 10.00am E Problem Workshop) 4Feb15
More informationAn Introduction to Particle Physics
An Introduction to Particle Physics The Universe started with a Big Bang The Universe started with a Big Bang What is our Universe made of? Particle physics aims to understand Elementary (fundamental)
More information129 Lecture Notes Relativistic Quantum Mechanics
19 Lecture Notes Relativistic Quantum Mechanics 1 Need for Relativistic Quantum Mechanics The interaction of matter and radiation field based on the Hamitonian H = p e c A m Ze r + d x 1 8π E + B. 1 Coulomb
More informationPhysics 129, Fall 2010; Prof. D. Budker
Physics 129, Fall 2010; Prof. D. Budker Some introductory thoughts Reductionists science Identical particles are truly so (bosons, fermions) We will be using (relativistic) QM where initial conditions
More informationBack to Gauge Symmetry. The Standard Model of Par0cle Physics
Back to Gauge Symmetry The Standard Model of Par0cle Physics Laws of physics are phase invariant. Probability: P = ψ ( r,t) 2 = ψ * ( r,t)ψ ( r,t) Unitary scalar transformation: U( r,t) = e iaf ( r,t)
More informationThe Why, What, and How? of the Higgs Boson
Modern Physics The Why, What, and How? of the Higgs Boson Sean Yeager University of Portland 10 April 2015 Outline Review of the Standard Model Review of Symmetries Symmetries in the Standard Model The
More informationCurrent knowledge tells us that matter is made of fundamental particle called fermions,
Chapter 1 Particle Physics 1.1 Fundamental Particles Current knowledge tells us that matter is made of fundamental particle called fermions, which are spin 1 particles. Our world is composed of two kinds
More informationParticle Physics. Lecture 11: Mesons and Baryons
Particle Physics Lecture 11: Mesons and Baryons Measuring Jets Fragmentation Mesons and Baryons Isospin and hypercharge SU(3) flavour symmetry Heavy Quark states 1 From Tuesday: Summary In QCD, the coupling
More informationParticle Physics (concise summary) QuarkNet summer workshop June 2428, 2013
Particle Physics (concise summary) QuarkNet summer workshop June 2428, 2013 1 Matter Particles Quarks: Leptons: Antimatter Particles Antiquarks: Antileptons: Hadrons Stable bound states of quarks Baryons:
More informationReview Chap. 18: Particle Physics
Final Exam: Sat. Dec. 18, 2:454:45 pm, 1300 Sterling Exam is cumulative, covering all material Review Chap. 18: Particle Physics Particles and fields: a new picture Quarks and leptons: the particle zoo
More informationPhoton Coupling with Matter, u R
1 / 16 Photon Coupling with Matter, u R Consider the up quark. We know that the u R has electric charge 2 3 e (where e is the proton charge), and that the photon A is a linear combination of the B and
More informationNovember 24, Scalar Dark Matter from Grand Unified Theories. T. Daniel Brennan. Standard Model. Dark Matter. GUTs. Babu Mohapatra Model
Scalar from November 24, 2014 1 2 3 4 5 What is the? Gauge theory that explains strong weak, and electromagnetic forces SU(3) C SU(2) W U(1) Y Each generation (3) has 2 quark flavors (each comes in one
More informationElectroweak physics and the LHC an introduction to the Standard Model
Electroweak physics and the LHC an introduction to the Standard Model Paolo Gambino INFN Torino LHC School Martignano 1218 June 2006 Outline Prologue on weak interactions Express review of gauge theories
More informationLecture 6:Feynman diagrams and QED
Lecture 6:Feynman diagrams and QED 0 Introduction to current particle physics 1 The Yukawa potential and transition amplitudes 2 Scattering processes and phase space 3 Feynman diagrams and QED 4 The weak
More informationIX. Electroweak unification
IX. Electroweak unification The problem of divergence A theory of weak interactions only by means of W ± bosons leads to infinities e + e  γ W  W + e + W + ν e ν µ e  W  µ + µ Divergent integrals Figure
More informationSymmetries, Groups, and Conservation Laws
Chapter Symmetries, Groups, and Conservation Laws The dynamical properties and interactions of a system of particles and fields are derived from the principle of least action, where the action is a 4dimensional
More informationElectroweak Symmetry Breaking and the Higgs Mechanism
Electroweak Symmetry Breaking and the Higgs Mechanism Roger Wolf 06. Mai 2014 INSTITUTE OF EXPERIMENTAL PARTICLE PHYSICS (IEKP) PHYSICS FACULTY KIT University of the State of BadenWuerttemberg and National
More informationThe ATLAS Experiment and the CERN Large Hadron Collider
The ATLAS Experiment and the CERN Large Hadron Collider HEP1012 April 5, 2010 A. T. Goshaw Duke University 1 HEP 101 Plan March 29: Introduction and basic HEP terminology March 30: Special LHC event:
More informationOddelek za fiziko. Top quark physics. Seminar. Author: Tina Šfiligoj. Mentor: prof. dr. Svjetlana Fajfer. Ljubljana, february 2012
Oddelek za fiziko Top quark physics Seminar Author: Tina Šfiligoj Mentor: prof. dr. Svjetlana Fajfer Ljubljana, february 2012 Abstract Top quark physics is a very active area in particle physics as it
More informationCP VIOLATION. Thomas Mannel. Theoretical Physics I, Siegen University. Les nabis School 2011
CP VIOLATION Thomas Mannel Theoretical Physics I, Siegen University Les nabis School 2011 Outline of the course Lecture 1: Basics of CP and the Standard Model Lecture 2: CP Violation in the Standard Model
More informationNeutrino Physics. KamBiu Luk. Tsinghua University and University of California, Berkeley and Lawrence Berkeley National Laboratory
Neutrino Physics KamBiu Luk Tsinghua University and University of California, Berkeley and Lawrence Berkeley National Laboratory 415 June, 2007 Outline Brief overview of particle physics Properties of
More informationDeep Inelastic Scattering in LeptonHadron Collisions Probing the Parton Structure of the Nucleon with Leptons Basic Formalism (indep.
Deep Inelastic Scattering in LeptonHadron Collisions Probing the Parton Structure of the Nucleon with Leptons Basic Formalism (indep. of strong dynamics and parton picture) Experimental Development Fixed
More informationThe Strong Interaction
The Strong Interaction What is the quantum of the strong interaction? The range is finite, ~ 1 fm. Therefore, it must be a massive boson. Yukawa theory of the strong interaction Relativistic equation for
More informationElectroweak Theory: 3
Electroweak Theory: 3 Introduction QED The Fermi theory The standard model Precision tests CP violation; K and B systems Higgs physics Prospectus STIAS January, 2011 Paul Langacker IAS 55 References Slides
More informationElectroweak Theory: 2
Electroweak Theory: 2 Introduction QED The Fermi theory The standard model Precision tests CP violation; K and B systems Higgs physics Prospectus STIAS (January, 2011) Paul Langacker (IAS) 31 References
More informationGauge Theory of ElectroWeak Interactions. Following slides based among others on
Gauge Theory of ElectroWeak Interactions Read Appendix D of Book Gauge Theories Following slides based among others on The ideas of particle physics: an introduction to scientists, by Coughlan, Dodd,
More informationEnergy Level Energy Level Diagrams for Diagrams for Simple Hydrogen Model
Quantum Mechanics and Atomic Physics Lecture 20: Real Hydrogen Atom /Identical particles http://www.physics.rutgers.edu/ugrad/361 physics edu/ugrad/361 Prof. Sean Oh Last time Hydrogen atom: electron in
More informationDirac Equation. Chapter 1
Chapter Dirac Equation This course will be devoted principally to an exposition of the dynamics of Abelian and nonabelian gauge theories. These form the basis of the Standard Model, that is, the theory
More informationA talk for string theorists.
WTF is a B physics? A talk for string theorists. Flip Tanedo Durham University IPPP and Cornell University 5th Annual Part III Return Conference Cambridge CMS, 1618 April 2008 Flip Tanedo, Durham University
More information. Thus his equation would have to be of the form. 2 t. but must also satisfy the relativistic energymomentum relation. H 2 φ = ( p 2 + m 2 )φ (3)
1 Antiparticles The KleinGordon equation 2 φ t 2 + 2 φ = m 2 φ 1 that we derived in the previous lecture is not satisfactory for dealing with massive particles that have spin. Such an equation must take
More informationLecture notes for FYS610 Many particle Quantum Mechanics
UNIVERSITETET I STAVANGER Institutt for matematikk og naturvitenskap Lecture notes for FYS610 Many particle Quantum Mechanics Note 20, 19.4 2017 Additions and comments to Quantum Field Theory and the Standard
More informationT 1! p k. = T r! k., s k. ', x' ] = i!, s y. ', s y
Time Reversal r k ' = r k = T r k T 1 p k ' = p k, s k ' = s k T cannot be represented by an unitary operator. Unitary opera$ons preserve algebraic rela$ons between operators, while T changes the sign
More informationSECTION A: NUCLEAR AND PARTICLE PHENOMENOLOGY
SECTION A: NUCLEAR AND PARTICLE PHENOMENOLOGY This introductory section covers some standard notation and definitions, and includes a brief survey of nuclear and particle properties along with the major
More informationThe Uncertainty Principle and the Quarks
The Uncertainty Principle and the Quarks Andrei Gritsan Johns Hopkins University August, 2007 JHU Quarknet Meeting Outline The Uncertainty Principle quantum mechanics with elementary particles The Quarks
More informationXIII Probing the weak interaction
XIII Probing the weak interaction 1) Phenomenology of weak decays 2) Parity violation and neutrino helicity (Wu experiment and Goldhaber experiment) 3) V A theory 4) Structure of neutral currents Parity
More informationThe Quark Parton Model
The Quark Parton Model Quark Model Pseudoscalar J P = 0 Mesons Vector J P = 1 Mesons Meson Masses J P = 3 /2 + Baryons J P = ½ + Baryons Resonances Resonance Detection Discovery of the ω meson Dalitz Plots
More information3 Quantization of the Dirac equation
3 Quantization of the Dirac equation 3.1 Identical particles As is well known, quantum mechanics implies that no measurement can be performed to distinguish particles in the same quantum state. Elementary
More informationFunctional determinants
Functional determinants based on S53 We are going to discuss situations where a functional determinant depends on some other field and so it cannot be absorbed into the overall normalization of the path
More informationTriplet Higgs Scenarios
Triplet Higgs Scenarios Jack Gunion U.C. Davis Grenoble Higgs Workshop, March 2, 203 Higgslike LHC Signal Fits with MVA CMS suggest we are heading towards the SM, but it could simply be a decoupling limit
More informationClebschGordan Coefficients
Phy489 Lecture 7 ClebschGordan Coefficients 2 j j j2 m m m 2 j= j j2 j + j j m > j m > = C jm > m = m + m 2 2 2 Two systems with spin j and j 2 and z components m and m 2 can combine to give a system
More informationAnything but... Leptogenesis. Sacha Davidson IPN de Lyon/CNRS, France
Anything but... Leptogenesis Sacha Davidson IPN de Lyon/CNRS, France CP Violation in µ e Conversion Sacha Davidson IPN de Lyon/CNRS, France 1. Why is CP in muon physics interesting? in general leptogenesis
More information1. Introduction. Particle and Nuclear Physics. Dr. Tina Potter. Dr. Tina Potter 1. Introduction 1
1. Introduction Particle and Nuclear Physics Dr. Tina Potter Dr. Tina Potter 1. Introduction 1 In this section... Course content Practical information Matter Forces Dr. Tina Potter 1. Introduction 2 Course
More informationElementary particles, forces and Feynman diagrams
Elementary particles, forces and Feynman diagrams Particles & Forces quarks Charged leptons (e,µ,τ) Neutral leptons (ν) Strong Y N N Electro Magnetic Y Y N Weak Y Y Y Quarks carry strong, weak & EM charge!!!!!
More informationCoupling of Angular Momenta Isospin NucleonNucleon Interaction
Lecture 5 Coupling of Angular Momenta Isospin NucleonNucleon Interaction WS0/3: Introduction to Nuclear and Particle Physics,, Part I I. Angular Momentum Operator Rotation R(θ): in polar coordinates the
More informationMaxwell s equations. based on S54. electric field charge density. current density
Maxwell s equations based on S54 Our next task is to find a quantum field theory description of spin1 particles, e.g. photons. Classical electrodynamics is governed by Maxwell s equations: electric field
More informationParticle physics: what is the world made of?
Particle physics: what is the world made of? From our experience from chemistry has told us about: Name Mass (kg) Mass (atomic mass units) Decreasing mass Neutron Proton Electron Previous lecture on stellar
More informationIntroduction. Read: Ch 1 of M&S
Introduction What questions does this field address? Want to know the basic law of nature. Can we unify all the forces with one equation or one theory? Read: Ch 1 of M&S K.K. Gan L1: Introduction 1 Particle
More informationQFT. Unit 1: Relativistic Quantum Mechanics
QFT Unit 1: Relativistic Quantum Mechanics What s QFT? Relativity deals with things that are fast Quantum mechanics deals with things that are small QFT deals with things that are both small and fast What
More informationElectroweak Theory: The Experimental Evidence and Precision Tests PPPII Lecture 8 (FS 2012)
1 Electroweak Theory: The Experimental Evidence and Precision Tests PPPII Lecture 8 (FS 2012) Michael Dittmar (ETHZürich/CMS) 17.4.2012 1950ies From the messy world of hadrons to weak decays and neutrinos.
More informationThe KleinGordon equation
Lecture 8 The KleinGordon equation WS2010/11: Introduction to Nuclear and Particle Physics The bosons in field theory Bosons with spin 0 scalar (or pseudoscalar) meson fields canonical field quantization
More informationHigh Energy Physics. Lecture 9. Deep Inelastic Scattering Scaling Violation. HEP Lecture 9 1
High Energy Physics Lecture 9 Deep Inelastic Scattering Scaling Violation HEP Lecture 9 1 Deep Inelastic Scattering: The reaction equation of DIS is written e+ p e+ X where X is a system of outgoing hadrons
More informationNicholas I Chott PHYS 730 Fall 2011
Nicholas I Chott PHYS 730 Fall 2011 The Standard Model What is BetaDecay? Beta decay leads to ν discovery Early History of the Double Beta Decay Why is 0νββ Important? ββdecay 2νββ vs. 0νββ Conclusion
More informationExperimental Tests of the Standard Model. Precision Tests of the Standard Model
Experimental Tests of the Standard Model Precision Tests of the Standard Model  History of EW theory  Discovery of the Z and W Boson by the UA1/UA2 experiments (1983)  Precision tests of the Z sector
More informationHidden twohiggs doublet model
Hidden twohiggs doublet model C, Uppsala and Lund University SUSY10, Bonn, 20100826 1 Two Higgs doublet models () 2 3 4 Phenomenological consequences 5 Two Higgs doublet models () Work together with
More informationLecture 39, 40 Supplement: Particle physics in the LHC era
Lecture 39, 40 Supplement: Particle physics in the LHC era The Matter Particles (Fermions) plus their antiparticles... What is measured? quarks confined into hadrons A zoo of strongly interacting particles...
More informationThe mass of the Higgs boson
The mass of the Higgs boson LHC : Higgs particle observation CMS 2011/12 ATLAS 2011/12 a prediction Higgs boson found standard model Higgs boson T.Plehn, M.Rauch Spontaneous symmetry breaking confirmed
More informationwave functions PhD seminar FZ Juelich, Feb 2013
SU(3) symmetry and Baryon wave functions Sedigheh Jowzaee PhD seminar FZ Juelich, Feb 2013 Introduction Fundamental symmetries of our universe Symmetry to the quark model: Hadron wave functions q q Existence
More informationThe Standard Model. Zack Sullivan
The Standard Model Zack Sullivan Illinois Institute of Technology CTEQ Collaboration July 11, 2011 Zack Sullivan ( IIT) The Standard Model CTEQ Summer School 2011 1 / 24 What is the Standard Model? Definition
More informationMasses and the Higgs Mechanism
Chapter 8 Masses and the Higgs Mechanism The Z, like the W ± must be very heavy. This much can be inferred immediately because a massless Z boson would give rise to a peculiar parityviolating longrange
More informationLecture 9. Isospin The quark model
Lecture 9 Isospin The quark model There is one more symmetry that applies to strong interactions. isospin or isotopic spin It was useful in formulation of the quark picture of known particles. We can consider
More informationString Theory in the LHC Era
String Theory in the LHC Era J Marsano (marsano@uchicago.edu) 1 String Theory in the LHC Era 1. Electromagnetism and Special Relativity 2. The Quantum World 3. Why do we need the Higgs? 4. The Standard
More informationPhysics Highlights from 12 Years at LEP
Physics Highlights from 12 Years at LEP Colloquium Frascati,, 8.2.2001 Dieter Schlatter CERN / Geneva 1 Standard Model In 1989 ingredients of Standard Model were known: Matter particles: u,d,s,c,b,t quarks
More informationElectroweak Theory: 5
Electroweak Theory: 5 Introduction QED The Fermi theory The standard model Precision tests CP violation; K and B systems Higgs physics Prospectus STIAS (January, 2011) Paul Langacker (IAS) 162 References
More informationIntroduction to particle physics Lecture 4
Introduction to particle physics Lecture 4 Frank Krauss IPPP Durham U Durham, Epiphany term 2009 Outline 1 Mesons and Isospin 2 Strange particles 3 Resonances 4 The quark model Nuclei, nucleons, and mesons
More informationAn Introduction to. Michael E. Peskin. Stanford Linear Accelerator Center. Daniel V. Schroeder. Weber State University. Advanced Book Program
An Introduction to Quantum Field Theory Michael E. Peskin Stanford Linear Accelerator Center Daniel V. Schroeder Weber State University 4B Advanced Book Program TT AddisonWesley Publishing Company Reading,
More informationThe Discovery of the Higgs Boson: one step closer to understanding the beginning of the Universe
The Discovery of the Higgs Boson: one step closer to understanding the beginning of the Universe Anna Goussiou Department of Physics, UW & ATLAS Collaboration, CERN Kane Hall, University of Washington
More informationLecture 5 The Renormalization Group
Lecture 5 The Renormalization Group Outline The canonical theory: SUSY QCD. Assignment of Rsymmetry charges. Group theory factors: bird track diagrams. Review: the renormalization group. Explicit Feynman
More informationA Two Higgs Doublet Model for the Top Quark
UR 1446 November 1995 A Two Higgs Doublet Model for the Top Quark Ashok Das and Chung Kao 1 Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA Abstract A two Higgs doublet
More information