Introduction. Introduction to Elementary Particle Physics. Diego Bettoni Anno Accademico

Transcription

1 Introduction Introduction to Elementary Particle Physics Diego Bettoni Anno Accademico

2 Course Outline 1. Introduction.. Discreet symmetries: P, C, T. 3. Isosin, strangeness, G-arity. 4. Quark Model (Hadron structure I) 5. Electromagnetic interactions. 6. Weak interactions. 7. Strong interactions (Hadron structure II) htt://

3 Introduction Particle hysics is concerned with the study of the elementary constituents of matter and their interactions. An elementary article is a article with no internal structure. Elementary articles can be found in cosmic rays. They can be roduced in the laboratory in collisions between high-energy article beams, in accelerators. For this reason Particle Physics is also called High-Energy Physics.

4 Why High Energy? To robe the internal structure of a article we need high resolution. Assuming the robing beam itself consists of ointlike articles, the resolution is limited by the De Broglie wavelength of these articles. where is the momentum of the robing article and h is Planck s constant. In order to obtain high satial resolutions, and thus resolve smaller and smaller structures, it is necessary to use high-energy articles as robes. Furthermore many elementary articles have large masses and require corresondingly high-energies (mc ) for their creation and study. h

5 Units in High-Energy Physics quantity HEP unit value in SI units natural units = c =1 length 1 fm m 1 GeV -1 = fm time 1 s 1 s 1 GeV -1 = s energy 1 GeV = 10 9 ev J 1 GeV mass (E/c ) 1 GeV/c Kg 1 GeV momentum(e/c) 1 GeV/c Kg m s -1 1 GeV = h/ GeV s Js 1 c fm/s m/s 1 c GeV fm Jm 1 Fine structure constant = e /4 = 1/ Heaviside-Lorentz units 0 = 0 = = c = 1

6 More Units and Conversion Factors 1 Kg = GeV 1 m = GeV -1 1 s = GeV -1 1 barn = 10-8 m (cross section) 1 TeV = 10 3 GeV = 10 6 MeV = 10 9 KeV = 10 1 ev 1 fm = 5.07 GeV -1 1 fm = 10 mb = 10 4 b = 10 7 nb =10 10 b 1GeV - = mb

7 Particle Classification Fermions Letons (e, e,,,, ) Baryons (, n,...) Hadrons Bosons Mesons (, K,...) Gauge Bosons (, W, Z, g) Hadrons = articles with strong interaction

8 Bosons and Fermions Let us suose that we have tow identical articles, defined by the sets of observables 1 and. Let ( 1, ) be their wave function. 1 1 ), ( ), ( 1 1 ), ( ), ( ), ( i i i e e e ), ( ), ( 1 1

9 Identical Bosons (integral sin): ( 1, ) = +(, 1 ) symmetric wave function Identical Fermions (half-integral sin): ( 1, ) = -(, 1 ) antisymmetric wave function As a consequence of these rules we obtain Pauli s Exclusion Princile: Two or more identical fermions cannot exist in the same quantum state. If two identical articles are in the same quantum state, the wave function is necessarily symmetric, whereas for fermions it must be antisymmetric. On the other hand there are no restrictions on the number of bosons in the same quantum state.

10 All matter is comosed of fundamental sin ½ fermions (quarks and letons), whereas article interactions are mediated by bosons. Letons e -1 e 0 quarks u c t +/3 d s b -1/3 Gauge Bosons bosons interaction sin/arity(j P ) gluon, G strong 1 - hoton, electromagnetic 1 - W, Z 0 weak 1 -,1 + graviton, g gravitational +

11 Quarks u (u) and down (d) I = ½ m u m d 0.31 GeV/c strange (s) S=-1 m s 0.50 GeV/c charm (c) C= 1 m c 1.6 GeV/c bottom or beauty (b) B=-1 m b 4.6 GeV/c to [or truth] (t) T= 1 m t 180 GeV/c Hadrons Baryons q 1 q q 3 (uud), n(udd), (uds) Mesons q 1 q + (ud), K 0 (ds), J/ (cc)

12 Letons e m e = MeV/c e m e < 3 ev m = MeV/c m < 0.19 MeV m = 1777 MeV/c m < 18. MeV Neutrinos are left-handed (helicity H=-1) Antineutrinos are right-handed (helicity H=+1) Charged letons undergo weak and electromagnetic interaction. Neutrinos can only have weak interaction. Leton Numbers: e + e L L L e

13 The quantity Helicity H 1 is called helicity (or handedness). It measures the sign of the comonent of the sin of the article in the direction of motion. H = - 1 the article is left-handed (LH) H = +1 the article is right-handed (RH) Helicity is a well-defined, Lorentz-invariant quantity for a massless article. For interactions mediated by vector or axial vector bosons helicity is conserved in the relativistic limit. For this reason helicity is conserved in strong, electromagnetic and weak interactions, which are all mediated by vector of axial vector bosons.

14 Relativistic Kinematics The relativistic relation between the total energy E, the vector 3- momentum and the rest mass m for a free article is: or, in natural units: The comonents of the 3-momentum and the energy can be written as comonents of an energy-momentum 4-vector P : P 0 = E P 1 = x P = y P 3 = z whose square modulus equals the squared rest mass: in units = c = 1. 4 c m c E m E m E P P P P P

15 The square of a 4-vector is a relativistic invariant, i.e. it has the same value in all inertial reference frames. If E, are measured in a given reference frame, then in another frame moving along the x axis with velocity c we have: where These are the so-called Lorentz transformations. ) ( ) ( x z z y y x x E E E 1 / 1

16 The square of a 4-vector is an examle of a Lorentz scalar, i.e. the invariant scalar roduct of two 4-vectors. A 4-vector q can be either sace-like or time-like: sace-like if q < 0 time-like if q > 0 In the collision between a article with energy E A and momentum A and another one with energy E B and momentum B, the total 4-momentum squared is: B A B A B A B A B A E E m m P E E P ) ( ) (

17 The center-of-mass system (cms) is defined as the reference frame in which the total 3-momentum is zero. If the total energy in the cms is denoted s we also have P = s. If in the collision between two articles one is at rest in the lab frame (E B =m B ) (fixed target) we have: s P m m m E m In the case of two articles travelling in oosite directions (colliding beams): s P ( EAEB AB) ma mb s 4E (m A,m B << E A,E B ). A E A B B B A B E A In a collider the total cms energy increases linearly with the beam energy, whereas in fixed targed it increases as the square root of the beam energy.

18 Interactions Classically interaction at a distance is described in terms of a otential or a field. In quantum theory it is viewed in terms of exchange of quanta. Quanta are bosons associated with the articular tye of interaction. Examle: electrostatic interaction bewteen oint charges. Classica Quantistica Q 1 Q Q 1 Q F = Q E 1 γ we must have E t

19 In nature there are four tyes of interaction. The strong interaction binds quarks in hadrons and rotons and neutrons in nuclei. It is mediated by gluons. The electromagnetic interaction binds electrons and nuclei in atoms, and it is also resonsible for the intermolecular forces in liquids and solids. It is mediated by the hoton. The weak interaction is tyified by radioactive decays, for examle the slow decay. The quanta of the weak field are the W ± and Z 0 bosons. The gravitational interaction acts between all tyes of massive articles. It is by far the weakest of all the fundamental interactions.

20 To indicate the relative magnitudes of the four tyes of interaction, the comarative strenghts of the force between two rotons when just in contact are very roughly: strong electromagnetic weak gravity Ever since Einstein, hysicists have seculated that the 4 interactions might be different manifestations of a unified force. U to now only electromagnetic and weak forces have been unified: these would have the same strength at very high energies, whereas at lower energies this symmetry is broken and the two forces have the same strength. All four interactions lay a fundamental role in our universe.

21 Electromagnetic Interactions The couling constant of the electromagnetic interaction is the fine structure constant. 1 e 4 ( / mc) mc e 4c electrostatic energy of two e at a distance (ħ/mc) rest mass of the electron 0 = ( ) s The quantum of the electromagnetic interaction is the hoton. The field theory of the electromagnetic interaction is Quantum ElectroDynamics (QED). =

22 Weak Interactions n + e - + e e + n + e + decay absortion - n + - (dds) (ddu) 0 + (e.m. viola isosin) s s W The quanta of the weak interaction are the W and Z 0 bosons. M W = ( ) GeV/c M Z = ( ) GeV/c

23 Strong Interactions 0 (1385) + 0 =36 MeV 10-3 s 0 (119) s 19 S 10 e 1 g s The quanta of the strong interactions are the gluons. The strong charge is called color and it can assume 6 values R, G, B, R, G, B. Color symmetry is an exact symmetry, i.e. the force between quarks is color-indeendent. The field theory of strong interactions is Quantum Chromodynamics (QCD). Asymtotic freedom V s s /r q Confinement V s kr q 0 [r ]

24 Feynman Diagrams Feynman diagrams are a grahical way of reresenting the interaction between articles and fields. Solid straight lines reresent fermions. Wavy, curly or broken lines reresent bosons. Arrows along the lines indicate the time sense, with time increasing from left to right. Fermion and boson lines meet at vertices where charge, energy and momentum are conserved. The strength of the interaction is reresented by a couling constant associated to each vertex. Oen lines (i.e. entering or leaving the boundaries of a diagram) reresent real articles, closed lines and those joining vertices reresent virtual articles.

25 Feynman Diagrams e α e α basic electron-hoton vertex γ e + α e + γ + e - e - α e α ee scattering via exchange e + e + α α γ e - e - γ e + e - scattering via hoton exchange with two diagrams contributing in first order

26 Cross Section Let us consider the two-body rocess: a b c d i f where: n a = number of incident articles er unit volume. n b = number of target articles er unit surface. v i = relative velocity of a with resect to b. The number of interactions er unit surface and unit time is given by: d N dadt is the cross section for the rocess a+b c+d n b n a v i