HL-2 May 2006Kernfysica: quarks, nucleonen en kernen1 Outline lecture (HL-2) Quarkonium Charmonium spectrum quark-antiquark potential chromomagnetic interaction

HL-2 May 2006 Kernfysica: quarks, nucleonen en kernen 1

Outline lecture (HL-2)Quarkonium

•Charmonium spectrum•quark-antiquark potential•chromomagnetic interaction•strong / em. decay widths

Mesons in the quark model•multiplets•meson masses•neutral Kaon decay•CP violation

Literature: PR 13-14; BJ 10.3,10.5,10.7


Intermediate hadron state(decaying into leptons, hadrons)interpreted as bound state (JP=1-)

hadron resonances J/ production

4/)12(

)(22

2

msJ

s

c fif

scfm 203 10/103

qq

eeee

hadronsee

ee

J/ resonance: e== 4.8 keV, h = 59 keV (lepton universality) = 69 keV

e

h+ -

e- e+

cc bound states : transitions between excited states


Crystal Ball (structure like Plastic Ball, now at KVI)

hollow sphere from ca. 900 NaI crystals around interaction point


charmonium decay spectrum

Level scheme remindsof positronium statesn 2S+1 Lj

states characterized by parity P = (-1)L+1

charge conjugation parity C = (-1)L+S

strong electric dipole L=1, S=0transitions


charmonium level scheme

narrow states below threshold:hindered by energy limit and suppressed (“OZI rule”)

DD

only JPC = 1–

directly accessible in e+ e- production

C states reached bymagnetic dipoleL=0, S=1 spin-flip transitions (weaker than electric transitions)

D mesons:)();();( 0 dcDucDdcD


low-energy hadron resonances+ -

e- e+

uu

u

dd

u

0

K- K +

e- e+

ss

s

uu

s

0

K0

e- e+

ss

ss

0

dd 0K

=150 MeV

=4.4 MeV, why not 3 decay? (18%)

suppressed by OZI rule(Okubo, Zweig, Iizuka)

requires 3g coupling, amplitude 3

S 2.0)(,5.0)( / JSS mm

stronger suppression for J/


quark-antiquark potential

level sequence reminds of positronium system:Coulomb-like potential (g exchange force, short range

color charge 4/3 )with linear confinement (asymptotic freedom)

)5.1(2.0

/1

)(

34

),(

2 GeVcm

fmGeVk

rkr

cmmrV

cS

Sqq

hints for ln(r) dependencefrom bottonium levels


realistic qq potential from Lattice QCDsolving Schrödinger equation with

QCD Lagrangian on a discrete space-time lattice

r0=0.5 fm

hybrid potential fromglue excitations:

gcc states predicted

ground statepotential

cc

discovery possible atfuture GSI accelerator


Hot News!


access to charmonium states in annihilationpp

many unknown statesand transitions

hyperfine S-state splitting 120 MeV


chromomagnetic interactionstrong (hyperfine) splitting of S states, like in positronium:zero-range spin-spin interaction,point interaction of magnetic moments of e+ e-

i

ii m

e 2

rmmc

eeVee

ss 213

32

)(

modified for color-magnetic qq force: (eff. interaction, constituent mass)

1for 1

0for 3 with

32

34

)(3

S

Sr

mmcqqV qq

qq

qqSss

color-magnetic energy splitting

MeVrmmc

qqEqq

Sss 120

98

4)(3


charmonium and bottonium levels

smaller hyperfine splitting in system due to larger b-quark massbb


bottonium level scheme

flavour independent qq potential,surprising: very similarmass difference of loweststates:

(9460) = resonance “upsilon” =53 keV

bb

: m(2S-1S) = 563 MeV

: m(2S-1S) = 589 MeV

sensitive to long-range partof qq potential r, ln(r)

2

2.,

2

n 2E :levels Coulomb

n

cm redqS

similar level structure (mc 1.3 GeV, mb 4.3 GeV) :


quarkonium em / strong decay width

positronium decay width: rcm

Se

32

2

01 4)21(

)1(43)21( .3

2

24

01

radq

q rcm

zS

qq 2 decay width:

(including higher order radiative corrections rad. )

qq 2g decay width: )1(432

)21( .3

2

2

01

radq

S rcm

gS

ratio of decay widths:

-0.5

106)1(9

8

)21(

)21( 4exp2

2

01

01

eriment

SgS

S

17.0)(

20.0)(2

2

cm

cm

bbS

ccS

consistent with S from level spectrum

cc


Outline lecture (HL-2)Quarkonium

•Charmonium spectrum•quark-antiquark potential•chromomagnetic interaction•strong / em. decay widths

Mesons in the quark model•multiplets•masses•neutral Kaon decay•CP violation


mesons in the quark model

ss

and

u

d

d

u

axisaboutrotationisospinC

CCiCRG

GG

C

qq

parityG

2 and

01

10

|)1(| :parity-

for seigenvalue good no :parity-

triplet- - ofproduct 33

22

00

0

conjugate triplet

I- I+

in isospin (I3) and hypercharge (Y)

similar light quark masses: treated on same footing:

Y=B+S


products of SU(3) representations

Y=B+S

I3

add conjugate representation to each point of fundamental triplet

1/3

1

1/2

su

ds us

sd

ud

s

meson nonet 1833

reduced tosinglet {1} and octet {8} states

|)|2|(|6

10,0|8

|)|(|2

10,1|8

||1,1|8

)||(|3

10,0|1

0

ssdduu

dduu

du

ssdduu ´


meson multiplets (lowest L=0 states)

su sd

ds us

pseudoscalar (JP = 0- ) octet + singlet vector (JP = 1- ) octet + singlet


mixing of multiplet states

SU(3) symmetry broken by s-quark mass larger than u, d massmixing of I=0 multiplet states of same JP

physical states

8

1

8

1

cossin

sincos

from experimental meson masses:for pseudoscalar (0-), vector (1-) and tensor (2+) mesonsideal mixing (35o) octet state pure explanation of branching fractions:

32,40,11 TVP

ss

0%89

%83

KK


color-magnetic energy splitting

1for 1

0for 3 with

3

2

3

4)(

3

J

Jr

mmcqqV qq

qq

qq

Sss

J = 1

mass gap 600 MeV/c2

J = 0

remember: charmonium S-state splitting 120 MeV


meson massescalculated from constituent quark masses and color-magnetic mass splitting: ´JJqqqq

MmmM

2

2,

/483

/310

cMeVm

cMeVm

s

du

free parameters:constituent q masses:


decay channels of lightest mesons

strong decay I-spin forbidden

strong decay

strong decay notpossible for lightest meson

mixing


CP eigenstates

Parity violating decay fast slow (phase-space restricted)

3 and 20 K

320

2

02

0232

222

22

)1()1()1(

)1()1()1(

11

111

1111

C

CPCPCPCP

CCP ll

0000 )1( and )1( KKKK CPCP

construct CP eigenstates (physical states) as linear combination of S-eigenstates

0

2000

2

01

0001

)1(2

1

)1(2

1

KKKK

KKKK

CPCP

CPCP

S- but not CP eigenstates


K0 mixing and regeneration

450 GeV p0 50% LK 0 100% LK

0 .reg

)1()1(

)()1(10

10

fnKpSK

ffYMNSKf

f

0%50 SK

00LS KK

)1(

2

1

)1(2

1

8

11

10500002

10900001

CPKKKK

CPKKKK

sL

sS

02

0100. 222

1K

ffK

ffKfKfreg

! violation i.e. )103( 3 CPBR


Summary lecture (HL-2)Quarkonium•Charmonium spectrum (partly explored)

quark-antiquark potential (Coulomb like)•level splitting: chromomagnetic interaction

long range part (asymptotic freedom)•strong / em. decay widths

coupling strength

Mesons in the quark model•multiplets•masses broken SU(3) symmetry: mixing•neutral Kaon decay: CP eigenstates•CP violation


Addition:Baryons in the quark model

•production•multiplets•masses

Literature: PR 15; BJ 9, 10.4 -10.6


pion nucleonscattering

Isospin coupling,invariant mass (4-mom. sum)and phase-shift analysisyield energy (mass), I, L, J

resonance assignment:L2I,2J (mass)and width (lifetime)

(1232) P33

(1950)

N(1680)

N(1520)


phase-shift analysisquantum scattering in 3 dimensions (halfplane =0)

ikzin e

)( fr

eikr

scatt

0)(cot

2/

2/11

2

1)(

)()(cos)12(1

)(

)2/(

.

2

0

.

.

lreson

resonl

EEl

reson

EEill

lll

E

iEEie

iET

ETPlk

f


phase-shift analysis (2)

0

2

1( ) (2 1) (cos ) ( )

( )

l ll

f l P T Ek

df

d

will contain interferences of partial waves l particular angular distributions

total cross section:

0

2

20

1( ) (2 1) (cos ) ( )

(2 1) 2 ( )

l ll

ll

f l P T Ek

dd l iT E

d k



22

0

1

4(2 1)sin

l

elastic ll

lk

elastic scattering:

max. cross section for:resonance condition!

/ 2l

1 1

( ) sin2 cot ( )

l l l li i i il l

l

T E e e e ei E i

at resonance energy E = ER: / 2l ( )l RT E i purely imaginary!!



2

0 cot ( ) 0 cot ( ) :

2

2cot ( )

1 1 / 2( ) 1

2 / 2

R

R

Rl

l R R l E E

R

l E E

E Eil l

R

dE E E E

dE

E E

dE

dE

T E ei i E E i

expand partial wave amplitude Tl around resonance energy:


2

2

2

22 2

42 1

4 / 42 1

/ 4

lelastic R l R

R

E E l T E Ek

lk E E


generalization:

1 21 2

2 1( )

2 1 2 1

Jg J for J s s

s s

��

Breit-Wigner resonance (non-relativistic):

( )( ) 22 2

( )/ 4

elastic in elasticlin elastic R

R

E E g Jk E E


quark-flow diagrams

quark composition in intermediate (10-23 s) state


baryon multiplets

colorspinflavorspace

total

A

color-neutrallowest energy (L=0)qqq states requiresymmetric spinflavor

small (.1%) e.m. splittingof Isospin multiplets;strong SU(3) breaking


baryon mass spectrum

- mass splitting80 MeV/c2

due tospin-spin interaction

I()=0=I(s)=I(ud)(ud) antisymmetric(ud) antisymmetric spin(ud)=0spin()=spin(s)=1/2

uds

usd


Summary addition:Baryons in the quark model•multiplets and SU(3) breaking•masses: spin-spin interaction

Documents

HL-2 May 2006Kernfysica: quarks, nucleonen en kernen1 Outline lecture (HL-2) Quarkonium Charmonium spectrum quark-antiquark potential chromomagnetic interaction