From Luigi DiLella, Summer Student Program 2005. 2.

Particle Physics Study

2009/07/27Grass

From Luigi DiLella, Summer Student Program 2005

2

Outline

Before We Move to Particle PhysicsNeutrinosFundamental InteractionParticle Interactions and Conservation LawsQuarksElastic Scattering and Inelastic Scattering“Dynamic” Evidence for Quarks

Elementary Particles

3

Before We Move to Particle Physics

Thomson’s atomic modelRutherford’s scattering experimentsE = h ν; λ=h /pPauli’s exclusion principle

Richard Feynman: Whatever is not expressly forbidden is

mandatory.

4

Neutrinosn -> p + e- -Expect well defined energy

b- decay: n p + e- + nb+ decay: p n + e+ + n (e.g., 14O8 14N7 + e+ + n)

No electric chargeSpin ½No mass A very small mass

Steve Dye, HPU 520 January 2005

Neutrino Detection

http://www.ps.uci.edu/physics/reinesphotos.html

http://www-sk.icrr.u-tokyo.ac.jp/doc/sk/photo/normal.html

http://www-personal.umich.edu/~jcv/IMBdiverbig.jpg

Prediction of Fermi’s theory: n + p e+ + n

6

Fundamental InteractionInteractio

nStrong Electromagnet

ic Weak Gravitation

Mediators Gluons Photons W and Z bosons

gravitons

Relative Strength

1038 1036 1025 1

Range (m) 10-15 ∞ 10-18 ∞

7

Strong Interaction

It holds quarks and gluons together to form protons, neutrons and other particles.It is also the force that binds protons and neutrons together. In this context it is called the nuclear force (or residual strong force), and it is the residue strong interaction between the quarks that make up the protons and neutrons.

It acts directly only upon elementary quark and gluon particles.The strong force acting between quarks, unlike other forces, does not diminish in strength with increasing distance, after a limit (about the size of a hadron) has been reached. It remains at a strength of about 100 000 newtons, no matter how far away from each other the particles are, after this limiting distance has been reached.

gluon

8

Weak interactionIt is the only force affecting neutrinos.It is the only interaction capable of changing flavor.

It is the only interaction which violates parity symmetry P (because it almost exclusively acts on left-handed particles). It is also the only one which violates CP (CP Symmetry).It is mediated by massive gauge bosons. This unusual feature is explained in the Standard Model by the Higgs mechanism.

Particle Interactions and Conservation Laws

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Conservation of Baryon Number

Conservation of Lepton Number

Conservation of Strangeness

0 0 1 1 1 pnp

B

1- 1 1 1 1 1 pnp

BppnNo ! O.K.

10 0 pn

ele

1- 10 0 pn

e

e

le No ! O.K.

S = +1: K+, K° ; S = –1: L, S±, S° ; S = –2 : X°, X– ; S = 0 : all other particles(and opposite strangeness –S for the corresponding antiparticles)

1 - 1 0 0 S 0

Kp

1 - 0 0 0 S 0

pNo ! O.K.

0 0 1 e

l

No !

1 0 1 0 0 1 0 1

e

e

e

ll

O.K.

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Quarks

Quark Symbol

Spin

Charge

BaryonNumber S C B T Mass*

Up U 1/2 +2/3 1/3 0 0 0 0 360 MeV

Down D 1/2 -1/3 1/3 0 0 0 0 360 MeV

Charm C 1/2 +2/3 1/3 0 +1 0 0 1500 MeV

Strange S 1/2 -1/3 1/3 -1 0 0 0 540 MeV

Top T 1/2 +2/3 1/3 0 0 0 +1 174 GeV

Bottom B 1/2 -1/3 1/3 0 0 -1 0 5 GeV

Ex: uud -> p ;Q=1, spin=1/2, Baryon Number=1udd -> n ;Q=0,spin=1/2, Baryon Number=1

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Elastic Scattering

Inelastic Scattering

In this process, the kinetic energy of the incident particles is conserved, only their direction of propagation is modified.

Conservation of Kinetic energy :

Conservation of momentum :

In this process, the kinetic energy of an incident particle is not conserved.

Conservation of momentum

Ex: Compton Scattering, Deep Inelastic Scattering.

22112211 '' vmvmvmvm

222

211

222

211 '

2

1'

2

1

2

1

2

1vmvmvmvm

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Deep Inelastic ScatteringIf we can use electrons to "see" protons inside the nucleus, can we also use them to see inside protons?The direct evidence for the existence of quarks inside the proton is provided by deep inelastic scattering. The idea is to accelerate electrons to very high energies, then allow them to interact with a stationary proton, and investigate what happens.  But why is this called deep inelastic scattering? At high energies, the wavelengths associated with the electrons are much smaller than the size of a proton.  Hence the electrons can probe distances that are small compared with the proton - that is, DEEP within the proton.   However, the high energies tend to disrupt the proton, so that it produces several new particles (hadrons).  This means the scattering is INELASTIC because the target has been changed in the process.Deep inelastic scattering may be viewed in two ways: as inelastic scattering off a proton because it has constituents inside, or as elastic scattering from one of the constituents inside (ignoring the whole proton and other constituents). We are able to say that the constituents appear to be point-like and so can be considered to be fundamental particles.  

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“Dynamic” Evidence for QuarksElectron – proton scattering using a 20 GeV electron beam from theStanford two – mile Linear Accelerator (1968 – 69).

The modern version of Rutherford’s original experiment:resolving power wavelength associated with 20 GeV electron 10-15 cm

Three magnetic spectrometers to detect the scattered electron: 20 GeV spectrometer (to study elastic scattering e– + p e– + p) 8 GeV spectrometer (to study inelastic scattering e– + p e– + hadrons) 1.6 GeV spectrometer (to study extremely inelastic collisions)

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Electron – proton scatteringElectron elastic scattering from a point-like charge |e| at high energies:differential cross-section in the collision centre-of-mass (Mott’s formula)

ME

c

d

d

)2/(sin

)2/(cos

8

)(4

2

2

22 137

12

c

e

Scattering from an extended charge distribution: multiply sM by a “form factor”:

MFd

d

)Q( 2

|Q| = ħ / D : mass of the exchanged virtual photon D: linear size of target region contributing to scattering Increasing |Q| decreasing target electric charge

|Q2| (GeV2)

F(|Q2|)

F (|Q2| ) = 1 for a point-like particle the proton is not a point-like particle

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Inelastic electron – proton collisions

F(|Q2|)

|Q2| (GeV2)

incident electron ( Ee , p )

scattered electron ( Ee’ , p’ )

incident proton ( Ep , – p )

g q

Hadrons(mesons, baryons)

2

22

2 cpEWi

ii

i

Total hadronic energy :

For deeply inelastic collisions,the cross-section depends only weaklyon |Q2| , suggesting a collisionwith a POINT-LIKE object

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Interpretation of deep inelastic e - p collisionsDeep inelastic electron – proton collisions are elastic collisions with point-like,electrically charged, spin ½ constituents of the proton carrying a fraction x of theincident proton momentumEach constituent type is described by its electric charge ei (units of | e |)

and by its x distribution (dNi /dx) (“structure function”)If these constituents are the u and d quarks, then deep inelastic e – p collisionsprovide information on a particular combination of structure functions:

dx

dNe

dx

dNe

dx

dN dd

uu

22

pe

Comparison with nm – p and nm – p deep inelastic collisions at high energies

under the assumption that these collisions are also elastic scatterings on quarks nm + p m– + hadrons : nm + d m– + u (depends on dNd / dx )

nm + p m+ + hadrons : nm + u m+ + d (depends on dNu / dx )

(Neutrino interactions do not depend on electric charge)

All experimental results on deep inelastic e – p , nm – p, nm –

pcollisions are consistent with eu

2 = 4 / 9 and ed2 = 1 / 9

the proton constituents are the quarks

17

Physics with e+e– CollidersTwo beams circulating in opposite directions in the same magnetic ringand colliding head-on

e+ e–

E , p E , – p

A two-step process: e+ + e– virtual photon f + f f : any electrically charged elementary spin ½ particle ( m , quark)

(excluding e+e– elastic scattering)Virtual photon energy – momentum : Eg = 2E , pg = 0 Q2 = Eg2 – pg

2c 2 = 4E 2

Cross - section for e+e– f f : )3(3

2 22

222

feQ

ca = e2/(ħc) 1/137ef : electric charge of particle f (units |e

|)b = v/c of outgoing particle f

(formula precisely verified for e+e– m+m– )

Assumption: e+e– quark ( q ) + antiquark ( q ) hadrons

at energies E >> mqc2 (for q = u , d , s) b 1:

3

2

9

1

9

1

9

4

)ee(

hadrons)e(e 222

sdu-eeeR

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Experimental results from the Stanford e+e– collider SPEAR (1974 –75):

R

Q = 2E (GeV) For Q < 3. 6 GeV R 2. If each quark exists in three different states, R 2 is consistent with 3 x ( 2 / 3). This would solve the W– problem.

Between 3 and 4.5 GeV, the peaks and structures are due to the production of quark-antiquark bound states and resonances of a fourth quark (“charm”, c) of electric charge +2/3

Above 4.6 GeV R 4.3. Expect R 2 (from u, d, s) + 3 x (4 / 9) = 3.3 from the addition of the c quark alone. So the data suggest pair production of an additional elementary spin ½ particle with electric charge = 1 (later identified as the t – lepton (no strong interaction) with mass 1777 MeV/c2 ).

The Modern Theory of Strong Interactions

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the interactions between quarks based on “Colour Symmetry”Quantum ChromoDynamics (QCD) formulated in the early 1970’s Each quark exists in three states of a new quantum number named “colour”

Particles with colour interact strongly through the exchange of spin 1 particles named “gluons”, in analogy with electrically charged particles interacting electromagnetically through the exchange of spin 1 photons

A MAJOR DIFFERENCE WITH THE ELECTROMAGNETIC INTERACTIONElectric charge: positive or negativePhotons have no electric charge and there is no direct photon-photon interactionColour: three varietiesMathematical consequence of colour symmetry: the existence of eight gluons witheight variety of colours, with direct gluon – gluon interaction

The observed hadrons (baryons, mesons ) are colourless combinations of coloured quarks and gluons

The strong interactions between baryons, mesons is an “apparent” interaction between colourless objects, in analogy with the apparent electromagnetic interaction between electrically neutral atoms

20

Free quarks, gluons have never been observed experimentally;only indirect evidence from the study of hadrons – WHY?

CONFINEMENT: coloured particles are confined withincolourless hadrons because of the behaviour of the colour forcesat large distancesThe attractive force between coloured particles increases withdistance increase of potential energy production of quark – antiquark pairs which neutralize colour formationof colourless hadrons (hadronization)

CONFINEMENT, HADRONIZATION: properties deducedfrom observation. So far, the properties of colour forces atlarge distance have no precise mathematical formulation in QCD.

At high energies (e.g., in e+e– q + q ) expect the hadrons tobe produced along the initial direction of the q – q pair production of hadronic “jets”

21

Elementary Particles

http://en.wikipedia.org/wiki/File:Elementary_particle_interactions.svghttp://www-visualmedia.fnal.gov/VMS_Site/gallery/stillphotos/2005/0400/05-0440-01D.hr.jpg

The Higgs spin 0 particle (NOT YET DISCOVERED) responsible for generating the masses of all particles

The End

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24

Neutrino detection

Target:surface S, thickness dxcontaining n protons cm–3

Incident n:Flux F [ n cm–2 s–1 ](uniform over surface S)

dx

Prediction of Fermi’s theory: n + p e+ + n

n – p interaction probability in thickness dx of hydrogen-rich material (e.g., H2O)

n p interaction rate = F S n s dx interactions per second

s : n – proton cross-section (effective proton area, as seen by the incident n )

n p interaction probability = n s dx = dx / l

Interaction mean free path: l = 1 / n sInteraction probability for finite target thickness T = 1 – exp(–T / l)

s( n p) 10–4 3 cm2 for 3 MeV n l 150 light-years of water !

Interaction probability T / l very small (~10–18 per metre H2O) need very intense sources for antineutrino detection