all fundamental with no underlying structure

P461 - particles I 1

• all fundamental with no underlying structure• Leptons+quarks spin ½ while photon, W, Z, gluons

spin 1• No QM theory for gravity• Higher generations have larger mass


When/where discovered

Mostly Europe 1895-1920 Roentgen (sort of)1901

W/Z CERN 1983 Rubbia/vanderMeer1984gluon DESY 1979 NOelectron Europe 1895-1905 Thomson 1906muon Harvard 1937 Notau SLAC 1975 Perl 1995

e US 1953 Reines/Cowan 1995

BNL 1962 Schwartz/Lederman/Steinberger 1988

FNAL 2000 NOu,d SLAC 1960s Friedman/Kendall/Taylor 1990s mostly US 1950s NOc SLAC/BNL 1974 Richter/Ting 1976b FNAL 1978 NO (Lederman)t FNAL 1995 NO

muon – Street+Stevenson had “evidence” but Piccione often gets credit in the 1940s as measured lifetime

Nobel Prize?


Couplings and Charges• All charged particles interact electromagnetically

• All particles except gamma and gluon interact

weakly (have nonzero “weak” charge) (partially semantics on photon as mixing defined in this way) A WWZ vertex exists

• Only quarks and gluons interact strongly; have non-zero “strong” charge (called color). This has been tested by:

magnetic moment electron and muon H energy levels (Lamb shift) “muonic” atoms. Substitute muon for electron pi-mu atoms• EM charge just electric charge q• Weak charge – “weak” isospin in i=1/2 doublets

used for charged (W) and have I3-Aq for neutral current (Z)

• Strong charge – color charge triplet “red” “green” “blue”


Pi-mu coupling

)(

)(

anomaliesno

K atomL


Strong Force and Hadrons• p + p -> p + N* • N* are excited states of proton or neutron (all of

which are baryons)• P = uud n = udd (bound by gluons) where

u = up quark (charge 2/3) and d = down quark (charge -1/3)

• About 20 N states spin ½ mass 938 – 2700 MeV• About 20 states spin 3/2• Charges = uuu(2) uud(1) udd(0) ddd(-1)• N, decay by strong interaction N p/n + with

lifetimes of 10-23 sec (pion is quark-antiquark meson). Identify by looking at the invariant mass and other kinematic distributions

ud

dduu

du

)(2

10


ISOSPIN

• Assume the strong force is ~identical between baryons (p,n,N*) and between three pions

• Introduce concept of Isospin with (p,n) forming an isopsin doublet I=1/2 and pions in an isopsin triplet I=1, and quarks (u,d) in a I=1/2 doublet

• Isospin isn’t spin but has the same group algebra SU(2) as spin and so same quantum numbers and addition rules

p

ndoub let

and and

I I I I

pp

pn np pn np

nn

Z z

1 2

1 2

2 2 3 1 1 0

1 0

1

0 0

1

12

12

12

12

/

/

( ) ( )


Baryons and Mesons

• 3 quark combinations (like uud) are called baryons. Historically first understood for u,d,s quarks

• “plotted” in isospin vs strangeness. Have a group of 8 for spin ½ (octet) and 10 (decuplet) for spin 3/2. Fermions and so need antisymmetric wavefunction (and have some duplication of quark flavor like p = uud)

• Gell-Mann tried to explain using SU(3) but badly broken (seen in different masses) but did point out underlying quarks

• Mesons are quark-antiquark combinations and so spin 0 or 1. Bosons and need symmetric wavefunction (“simpler” as not duplicating quark flavor)

• Spin 0 (or spin 1) come in a group of 8 (octet) and a group of 1 (singlet). Again SU(3) sort of explains if there are 3 quarks but badly broken as seen in both the mass variations and the mixing between the singlet and octet


Baryons and Mesons

• Use group theory to understand: -what states are allowed - “mixing” (how decay) - state changes (step-up/down) - magnetic moments of

• as masses are so different this only partially works – broken

• SU(2) Isospin –very good (u/d quark same mass) SU(3) for s-quark – good with caveats SU(4) with c-quark – not so good


Baryons


Baryon Wave Functions• Totally Antisymmetric as 3 s=1/2 quarks -

Fermions• S=3/2. spin part must be symmetric (all

“aligned”). There are some states which are quark symmetric (uuu,ddd,sss). As all members of the same multiplet have the same symmetries quark and spin are both symmetric

• to be antisymmetric, obey Pauli exclusion, need a new quantum number “color” which comes in 3 (at least) indices. Color wavefunctions:

r g b

r g b

r g b

rgb gbr brg rbg grb bgr


Baryon Wave Functions• S=1/2. color part is like S=3/2. So spin*quark

flavor = symmetric. Adding 3 spin = ½ to give S=1/2 produces “mixed” spin symmetry.

• First combine two quarks giving symmetric 1<->2

• Add on third quark to get first term

• Cycle 1 2 3 1 8 more terms. And then multiply by 6 color terms from S=3/2 page (4*9*6=216 terms)

• Why no charge 2 or charge -1particles like the proton or neutron exist the need for an antisymmetric wavefunction makes the proton the lightest baryon (which is a good thing for us)

12

12

1

21

2

( )

( )

asym

u d ud du asym

( )u d d u u d d u u1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 3 3


Meson Wave Functions• quark antiquark combinations. Governed by

SU(2) (spin) and strangenessSU(3) (SU(4)) for c-quark). But broken symmetries

• pions have no s quarks. The ’s (or the mix to find real particles break SU(3)

meson mass Decay 135,140 no s

little s

’ 958 mostly s 770 no s 782 little s 1019 85% KK, 15%

)(3

1

)2(6

1

)(2

1

0

8

0

ssdduu

ssdduu

ud

dduu

du

conventiondCduCu

asC

000

sincos'

cossin

08

08


Hadron + Quark masses• Mass of hadron = mass of constituent quarks

plus binding energy. As gluons have F=kx, increase in energy with separationpositive “binding” energy

• Bare quark masses: u = 1-5 MeV d = 3-9 MeV s = 75-170 MeV c = 1.15 – 1.35 GeV b = 4.0–4.4 GeV t = 169-179 GeV

• Top quark decay so quickly it never binds into a hadron. No binding energy correction and so best determined mass value (though < 300 t quark decays observed)

• Other quark masses determined from measured hadron masses and binding energy model pion = “2 u/d quarks” = 135 Mev proton = “3 u/d quarks” = 940 MeV kaon = “1 s and 1 u/d” = 500 MeV Omega = “3 s quarks” = 1672 MeV

• High energy p-p interactions really q-q (or quark-gluon or gluon-gluon). “partons” emerge but then hadronize. Called “jets” whose energy and momentum are mostly original quark or gluon


Hadrons, Partons and Jets• The quarks and gluons which make up a hadron

are called partons (Feynman, Field, Bjorken)• Proton consists of: -3

valence quarks (about 40% of momentum) -gluons (about 50% opf the momentum) -“sea” quark-antiquark pairs

• The sea quarks are constantly being made/annihilated from gluons and can include heavier quarks (s,c,b) with probability mass-dependent

• X = p/p(total) is the momentum fraction and each type of particle has a probability to have a given X (parton distribution function or pdf)

• PDFs mostly measured in experiments using nu,e,mu,p etc. Some theoretical modeling

• Even at highest energy collisions, quarks still pointlike particles (no structure) as distances of 0.002 F (G. Blazey et al)

• single quark produces other gluons and quarks jet. Have similar fragmentation function


Fragmentation functions

p

u,d,s

c

bfraction of energy which quark (or gluon) has for

either particle or jet


Lepton and Baryon Conservation

• Strong and EM conserve particle type. Weak can change but always leptonlepton or quarkquark

• So number of quarks (#quarks-#antiquarks) conserved. Sometimes called baryon conservation B.

• Number of each type (e,mu,tau) conserved L conservation

• Can always create particle-antiparticle pair• But universe breaks B,L conservation as there is

more matter than antimatter• At small time after big bang #baryons =

#antibaryons = #leptons = #antileptons (modulo spin/color/etc) = ~#photons (as can convert to particle-antiparticle pairs)

• Now baryon/photon ratio 10-10


Hadron production + Decay• Allowed production channels are simply quark

counting • Can make/destroy quark-antiquark pairs with the

total “flavor” (upness = #up-#antiup, downness, etc) staying the same

• All decays allowed by mass conservation occur quickly (<10-21 sec) with a few decaying by EM with lifetimes of ~10-16 sec) Those forbidden are long-lived and decay weakly and do not conserve flavor.

p K NO

du uud uus u s

p K YES

du uud uds s d

p K YES

du uud uds s u u d

0


Hadrons and QCD

• Hadrons are made from quarks bound together by gluons

• EM force QuantumElectroDynamics QED strong is QuantumChromoDynamics QCD

• Strong force “color” is equivalent to electric charge except three different (identical) charges red-green-blue. Each type of quark has electric charge (2/3 up -1/3 down, etc) and either r g b (or antired, antiblue, antigreen) color charge

• Unlike charge=0 photon, gluons can have color charge. 8 such charges (like blue-antigreen) combos, 2 are colorless. Gluon exchange usually color exchange. Can have gluon-gluon interaction


quark-gluon coupling

• why q-qbar and qqq combinations are stable

• 8 gluons each with color and anticolor. All “orthogonal”. 2 are colorless gluons

• coupling gluon-quark = +coupling gluon-antiquark = -

)(2

1

)2(6

1

ggrrbgrggr

bbggrrgbrbbr

r

r

b

b

br

rb

vertex 1 +

vertex 2 +

vertex 2 -

2

2


Group Theory• W/Z bosons and gluons carry weak charge and

color charge (respectively)Bosons couple to Bosons

• SU(2) and SU(3) which have 3 and 8 “base” vectors can be used to represent weak and strong forces. The base vectors are the W+,W-,Z and the 8 gluons. Exact (non-broken) symmetry

• The group algebra tells us about boson interaction. So for W/Z use

• SU(2) used for 3D rotations angular momentum (orbital and spin) isospin (hadrons – broken) weak interactions weak “isospin”

ZLWLiLLL

LiLLLLLL

zyx

zyxxyyx

,


Group Theory – SU(3)• 3x3 unitary matrices with det=1. 2n2-n2-1=8

parameters. Have group algebra

• and representation of generators

• and 3 color states

)(0)(02, kjifsameanyfif ijkijkijkji

010

100

000

000

010

001

200

010

001

3

1

00

000

00

000

00

00

00

00

000

001

000

100

000

001

010

63

852

741

i

i

i

i

i

i

)(2

1

)2(6

1

ggrrbgrggr

bbggrrgbrbbr

001

1

0

0

0

1

0

0

0

1

r

gbr 0

1

0

0

0

0

1

0

1

0

11


Pions• Use as strong interaction example• Produce in strong interactions

• Measure pion spin. Mirror reactions have same matrix element but different phase space/kinematics term. “easy” part of phase space is just the 2s+1 spin degeneracy term

• Find S=0 for pions

p p p p

p p p n

p n p p

0

A p p d

B d p p

function m m ms s

sA

Bp d

d

p

:

:

( , , )( )( )

( )

2 1 2 1

2 1 2


More Pions• Useful to think of pions as I=1 isospin triplet and

p,n is I=1/2 doublet (from quark plots)

• Look at reactions:

• p p -> d pi+ Total

I ½ ½ 0 1 1

Iz ½ ½ 0 1 1

p n -> d pi0 Total

I ½ ½ 0 1 0 or 1

Iz ½ - ½ 0 0 0

• in the past we combined 2 spin ½ states to form S=0 or 1

A p n d

B p p d

:

:

0

I Iz

I Iz

1 01

21 2 1 2 1 2 1 2

0 01

21 2 1 2 1 2 1 2

, ( / , / / , / )

, ( / , / / , / )


More Pions• Reverse this and say eigentstate |p,n> is

combination of I=1 and I=0

• reactions:

•

• then take the “dot product” between |p,n> and |d,pi0> brings in a 1/sqrt(2) (the Clebsch-Gordon coefficient)

• Square to get A/B cross section ratio of 1/2

A p n d

B p p d

:

:

0

p n I Iz I Iz

p p

, ( , , )

| , | ,

1

21 0 0 0

1 1

0)()( 0 ZZ IdI

all fundamental with no underlying structure

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