Elementary Particles

~ Harris Chapter 11; plus some.

~ ER Chapter 18; yea, right.

Rohlf: “Modern Physics from to Zo”

www.pdg.lbl.gov

Particle Adventure at http://pdg.lbl.gov/2005/html/outreach.html

OUTLINE

• The Basics: Harris 11.4, 11.3• Cross section calculation techniques: Harris 11.5• Early proofs of quarks & gluons• QED (quantum electro dynamics)• QCD (quantum color dynamics)• QFD (quantum flavor dynamics)• Buzz Words & Unanswered Questions: Harris 11.6, 11.7

– CKM Matrix / Neutrino Oscillations– Unification– Parity & Time-Reversal Violation– the Higgs / where does mass come from?

The basics

• Equipment

• Fundamental Objects

• Fundamental Interactions

Equipment

• Electron Collider– DESY– Stanford

• Proton Collider– FermiLab– CERN

• Electron fixed target– Bates– CEBAF / JLab

e+e

p+ p

e

e

Fundamental Objects

e

e

d

u

s

c

b

t

leptons

quarks

3 generations3 families6 flavors

3 generations3 families6 flavors

0.511 MeV~0 eV

105 MeV< 0.37 MeV

1784 MeV< 35 MeV

~350 MeV~700 MeV

1500 MeV~500 MeV

174000 MeV4700 MeV

all spin ½ objects

Fundamental Objects

e

e

d

u

s

c

b

t

leptons

quarks

3 generations3 families6 flavors

3 generations3 families6 flavors

Binding energy is a major effect

proton = uud = 350 + 350 + 700 = 1400 >> true mass 938 MeV

Fundamental Objects

e

e

d

u

s

c

b

t

leptons

quarks

3 generations3 families6 flavors

3 generations3 families6 flavors

all spin ½ objects

Electric charge of leptons

0

1

Electric charge of quarks

313

2

Fundamental Objects

Field particles or

gauge bosons

other required objects

oZW , 8 gluons (graviton)

< 6E17 eV 80, 91 GeV --- ---

Higgs bosons

LR bosons

> 114 GeV > 715 GeV

Fundamental Interactions

“Charge”

Gauge

boson

“strength”

Coupling

constant

Vertex

function

Range

of

influence

QCD

color

RGB

8 gluons

g s ~ 1 G < 1 fm

QED

electric charge

e

Photon

EM ~ 1/137 Ze ∞

QFD

flavor

I.V.B.

W± Zo WI ~ 10 gw ~ 10 fm

(gravity) mass

(graviton)

grav ~ 10 -- ∞

= (vertex fn)2

Comments on Fundamental Interactions

• Range •

– photons are ‘stable’ E = 0 ct = ∞– IVB are ‘unstable’ E ~ 2 GeV ct ~ 0.1 cm– gluons – no info

• Electric Charge– all quarks and e and W± can participate in QED– since has no charge, cannot interact with ‘s.

• Color– only quarks & gluons have color participate in QCD– Since g has color, g can interact with g‘s “glueballs”

• Flavor– all quarks and leptons have “flavor”, therefore can participate in QFD

tEE

ctc

Composite Objects

• Hadrons– mesons – qq

– baryons – qqq

– quaterions – not observed

– pentaquarks – i.d.i.

• .

suKdududduu 0

ddunuudp

Cross Section Techniques

Feymann diagrams

How to calculate cross sections

W

vel

Vol

speedincidentVolnorm

ratetransition

fluxincident

ratecountd

.1

ffif iVfMW 22 22

dI

Io

dxd

dnIdI o

simplified* Feymann rules• Each vertex gives

– QED: Ze

– QCD: G

– QFD: g

• Each propagator gives– massless:

– massive:

2

1

q

resEE 1

momentumtransfer

energyof the

compound state

* dropping various constants, spin-info, ... other details

Eres = Eo + i /2

pi incident particle p f sc

attered particle q m

omentum

transfer

pi = pf + q

before after

Eres = Eo + i /2 tE

total decay widthlifetime

/)2/(/, tiEitiE ores erertr

/*/** ,,Pr tt errerrtrtrob

SP

333

or T

ime-

Dep

Per

turb

Th

Exa

mpl

e

Nuc

lear

Phy

sics

Exa

mpl

e2nd

ord

er p

ertu

rb th

eory

What makes us thinkquarks and gluons

exist?

• 2 jet events

• 3 jet events

• R-ratio

• Zo width

CDF detector @ FermiLabhttp://www-cdf.fnal.gov/cdfphotos

2 Jet events

TASSO / PETRA / DESY

3 Jet events

R-ratio

ee

hadronseeR

quarksallowedall

quarkquarksallowedall

quark

Z

eq

e

eZq

e

R2

2

2

2

2

1

1

e

e

q

q

e

e

R =

32

9

6

3

1

3

1

3

2222

R

If NRG available in reaction ~ 1000 MeV, then uds

If NRG available in reaction ~ 3000 MeV, then udsc

If NRG available in reaction ~ 10,000 MeV, then udscb

If NRG available in reaction ~ 180,000 MeV, then udscbt

11.19

10

3

2

3

1

3

1

3

22222

R

22.19

11

3

1

3

2

3

1

3

1

3

222222

R

66.19

15

3

2

3

1

3

2

3

1

3

1

3

2222222

R

RWB

RYB

RGB

3·R

3 generations -- the Zo width

22 2/

ZEE

stuff

= e + ve

+ + v

+ + v

total decay width

22 2/

ZEE

stuff

e

e

at available NRG = 90 GeV

QED

• Stationary States

• Reactions

QED - Stationary States

Some kind of experiment

to excite the systemp

e

r

QqkrV )(

Note: even though we have quessed a good potential function, we realize that we will have to include s-o, rel KE, Darwin, Lamb shift, ... -- and the perturbations could have been big.

QED - Reactions

137

122

zZc

zZe

c

rdrdV

EM

r

ZezerV )(

zefunctionvertex EM

11 c

related to 2 vertices

e

e

e

e

e

ee

e

arrows are added to help identify particles versus antiparticles

ee

e

e

In a real experiment:

e

e

e

e

e

e

EM

(EM)2

EM ~ 1/137

+

+ ...

+

+ +

+QED is renormalizable , higher order diagrams can be accounted for by choosing an effective value for ‘e’

QED cross sections are ‘easy’ to calculate.

QCD

• Stationary States

• Reactions

QCD - Stationary States

cc

K1 ~ 50 MeVfm K2 ~ 1000 MeV/fm

rKr

KrV 2

1)(

-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

0 0.5 1 1.5 2

r (fm)

V

(M

eV)

?

?

confinement term

‘Coulomb’ term

As a matter of fact, must have V 0 by about 1 fm.

stretch

stretch

& break the color field

RUBBER BANDS

U = ½ k (x)22 ends 4 ends

q q q qq q q q

stretch

stretch

& break

rKr

KrV 2

1)(

QUARK PAIRS

-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

0 0.5 1 1.5 2

r (fm)

V

(M

eV)

QCD - Reactions

c

rKK

c

rdrdV

QCD

221

2

rKr

KrV 2

1)(

fmratfunctionvertex QCD 5.0~2.1~

11 c

K1 ~ 50 MeVfm K2 ~ 1000 MeV/fm

At r ~ 0.5 fm, QCD ~ 1.5

How-To: quark-quark reactions

p

p meson ?

meson ?

spectator quarks Which pairs of quarks interacted?

uR

uG

GR

uR uG

dG

dR

GR

uR uG

dG

dR

GR

Rq

Gq

q = uds...

GR

Because QCD > 1, higher order diagrams more important, can’t use perturbation theory.

“QCD is non-renormalizable.” (in this form)

must use anothertechnique to do calcs

“string theory”

The black box:

q

q

QCD

(QCD)2

QCD ~ 1.2

+

+ ...

+

+ +

+QCD is not-renormalizable , the power series expansion cannot be made to converge.

QCD cross sections are ‘impossible’ to calculate with perturbation theory. stringtheories

Hadronization

p

p meson ?

meson ?

Free quarks not observed

Hadronization

p

p meson ?

meson ?

q

q

The q’s can have more complicated pairings than indicated

meson ?

meson ?

Hadronization

p + o + Ko

ER Fig 18-9a

p + + K+

QFD

• Stationary States

• Reactions

QFD – Stationary States

• bound system of neutrinos– not experimentally feasible

• excited states of leptons– e* not observed below 90 GeV (1990)

– would imply lepton compositeness

must learn about QFD from reactions

need neutral & colorless system

e

e

QFD - Reactions

22~~ QFDifM

wZ

wif gEE

gM1

~

2wQFD g

Experimentally; gw = 1.7 !!!

QFD is considered “weak” only because Zo, W± are massive !

e

e

e

e

e

ee

e

arrows are added to help identify particles versus antiparticles

ee

e

e

W

u

d

(2/3)

(1/3)

QFD – charged current

W

u

d

(2/3)

(1/3)

W

v

e

(0)

(1)

W

e

Z

u

u

(2/3)

(/3)

QFD – neutral current

e

e

e

Z

Z

Z

e+

u

u

Z

s

d

(1/3)

(-1/3)

QFD – “flavor changing neutral

currents”

Z

e

Z

c

u

(2/3)

(2/3)

NOT OBSERVED – or at least very rare

neutrino experiments

d u(-1/3) (2/3)

? ?

W

neutrino experiments

d u(-1/3) (2/3)

v e

W

u d(-1/3)(2/3)

e+

W

v only interact with neg quarks

…converse…

Discovery of the Top Quark

Discovery of t quark

tb

(-1/3)

(2/3)

e+

W

Signature: high nrg e+

accompanied by b-hadrons

Eo + i /2

Eo = 174,000 MeV

= 1560 MeV

t ~ 4.2 * 10 sec

t never has a chance to form a long-lived composite with another quark; no R-ratio rise will be observed

Other Curious Mini-topics and Buzz Words

• CPT– Parity Violation– Regeneration of the kaons– Time Reversal Violation

• CKM & MNS Matrix– Quark mixing– Neutrino Mass-Mixing, a.k.a Neutrino Oscillations

• Unification• Electroweak Interaction • Where’s the Higgs?• Why are there only LH neutrinos?

CPT

• Parity– P:r = -r

– P:p = -p

– P:L = P:(r x p) = L

– P:S = S

– P:Ylm = (-)l Ylm

• Charge Conjug– C:e = e+ =

– C:p =

– C:v =

– C:S = S– C:I = I

• Time Reversal– T:r = r

– T:p = -p

– T:L = - L

– T:S = - S

epv

In classical physics, processes are invariant under operations of C, P, and T separately.

Lorentz Transformations (SpRel) require processes invariant under CPT combined.

handwaving proof: http://en.wikipedia.org/wiki/CPT_symmetry

Parity Violation

Helicity – relative orientation of p & S

p

S

Bizarre fact:only LH neutrinos existonly RH antineutrinos exist

-- an artifact of how the WI works (WR)

RH

pS

v LH Parity is maximally violated in the WI because the WI involves neutrinos.

CS Wu (1957) Demonstration ofC and P violation

but with combined CP conserved

CS Wu (1957) Demonstration ofC and P violation

but with combined CP conserved

CS Wu (1957) Demonstration ofC and P violation

but with combined CP conserved

CS Wu (1957) Demonstration ofC and P violation

but with combined CP conserved

CPT theorem implies if (CP) OK, then T must be OK too.

Neutral Kaon System

In our quark model (a.k.a. QCD eigenstates)

sdK o sdK o

mc2 = 498 MeV mc2 = 498 MeV

mc2 = 4 * 1012 MeV

Neutral Kaon System

oK

oK can change into by the 2nd order reactionoK

Time scale ~109 sec

Neutral Kaon System

oKoK

Produced in collisions

(QCD/SI)

oK

oooS KKK

2

1 oooL KKK

2

1

Weak / QFD Eigenstates

mc2 = 498 MeV mc2 = 498 MeV

mc2 = 4 * 106 MeV

= 0.89 * 1010 sec = 5 * 108 sec

in-flight only affected by WI / QFD

Neutral Kaon System: Regeneration

Collision regions(QCD)

QCDeigenstates

QCDeigenstates

WIeigenstates

Time Reversal Violation(CP Violation)

C

P

What does CP do to the kaons?

left

right

oKKCP 0:

oKKCP 0:

CP: KoS = + Ko

S

CP: KoL = Ko

L

Time Reversal Violation(CP Violation)

Time Reversal Violation(CP Violation)

KoS Ko

L

Decays are consistent with CP good

However ~ 0.2% of KoL decays have

CP violated on a small scale

T violated on a small scale

Is this a problem with “standard model”, new “force”, new …. ?

Time Reversal Violation(CP Violation)

• bottom system

• npol Apol scattering

• neutron electric dipole moment

• Cs electric dipole moment

Is this a problem with “standard model”, new “force”, new …. ?

CP violation has now been observed in the D ( ), B ( ), and Bs ( ) systems. bsbduc

The balance of decay rates, oscillations, lifetime splitting determines how bizaare the system behaves in the lab.

CKM matrixCabibbo-Kobayashi-Maskawa matrix

bsd

tcu

cc sdd sincos 22.0sin c

are QCD or ‘mass’ eigenstates

W W W

u edve

v

W

us

cc sds cossin

CKM matrix

bsd

tcu

999.0039.0009.0

040.0975.0221.0

003.0221.0975.0

are QCD or ‘mass’ eigenstates

In the presence of the weak interaction the states are perturbed

bsd

tcu

weak eigenstates

CKM matrix – alternate form

1=12o 2= 3= =

With approx values:

Written in terms of angles mixing each pair of quarks (Euler angles)

If quark mixing, why not…?

e

e

d

u

s

c

b

t

MNS matrixMaki-Nakagawa-Sakata matrix

12 ~ 34o 13 < 13o 23 ~ 45o = ?

Neutrino Oscillations

• Solar Neutrino Expts– Homestake Mine, SD (Ray Davis)– Explanation w/i previously existing physics with proper calculation

(MSW effect)– MSW effect: ve propagate through dense electrons in Sun

• Atmospheric (vacuum oscill)– Super Kamiokande– Improper ratio of v to ve events.

• Reactor Based (vacuum oscill)– KamLAND, 53 reactors, anti-ve from fission product decay .– Event rate and energy spectrum– Energy spectrum inconsistent with ‘no oscillation’

• Accelerator Based (vacuum oscill)– FermiLab vs Los Alamos

Vacuum Neutrino Oscillation

)0()( )(i

xptEii vetv ii

http://en.wikipedia.org/wiki/MNS_matrix

E

mE

p

mpmpE ipcE

i

iiiii 22

2~

222

)0()()2(

2

i

xptEmtEi

i vetvi

)0()0()( 22.

22

i

LE

miLct

i

tE

mifactphasecommondrop

i vevetvii

approx difference btw wavefunctions

Vacuum Neutrino Oscillation

For just the ve and v, relax notation 12 ~ 34o

Electron neutrino oscillations, long range. Here and in the following diagrams black means electron neutrino, blue means muon neutrino and red means tau neutrino.

http://en.wikipedia.org/wiki/Image:Electron_neutrino_oscillation_long.png

Electron neutrino oscillations, short range

http://en.wikipedia.org/wiki/Image:Electron_neutrino_oscillation_short.png

Unification-- trying to express all forces as aspects of one

• Motivations– Theory…gauge/phase…transformation…blah, blah, blah…

– The Zo and are interchangable in all diagrams• And no flavor-changing neutral currents

– Relative strengths seem to converge

Electroweak InteractionER pg 702-b

EW Interaction

QED QFD

4-component field: ( B, W1, W2, W3 )

( or, W+, W, Zo )

= cos w B + sin w W3

= sin w B + cos w W3

W± = W1 ± i W2

sin w = 0.23

-- one Hamiltonian works for both forces

Q: Why are IVB so heavy? ww

ee

sin

Electroweak Interaction

• Successful Predictions / Treatments– Zo and interference at e+e > 15 GeV, ~10%

– Parity violating effects in atomic transitions• Optical rotation of light for forbidden transitions & high Z

– Polarization effects in scattering of polarized electrons off nuclei

– .

– .

– .

Is gravity a force?Or

Quantum Gravity?There are a number of proposed quantum gravity theories:String theory/superstring theory/M-theory Supergravity AdS/CFT correspondence Wheeler-deWitt equation Loop quantum gravity Euclidean quantum gravity Causal Sets Twistor theory Sakharov induced gravity Regge calculus Acoustic metric and other analog models of gravity Process physics Causal Dynamical Triangulation An Exceptionally Simple Theory of Everything

Where’s the Higgs?What’s the Higgs?