Charge Symmetry Charge Symmetry Breaking/Isospin Breaking/Isospin NonconservationNonconservation

Willem T.H. van Oers

ECT June 13-17, 2005*

1)1) IntroductionIntroduction

2)2) Classification of N-N ForcesClassification of N-N Forces

3)3) Evidence for Class III InteractionsEvidence for Class III Interactions

4)4) Evidence for Class IV InteractionsEvidence for Class IV Interactions

5)5) Time Reversal InvarianceTime Reversal Invariance

6)6) Charge Symmetry Breaking and Charge Symmetry Breaking and HypernucleiHypernuclei

System

Isospin:

2

1,

2

13 II According to their

chargeCharge Independence:

0],[ IH or ppnpnn

Charge Symmetry:

,2Iics eP ,0],[ csPH ,pnnp ppnn

system, isospin conserved, no mixing of I=0,1 states np

N System

2

1,

2

3I

Charge Symmetry

np np pnnp 00

pn, :

NN

Hadron Multiplet Mass Splittings

At the quark level: M

0K

du || ; ud ||

Hadron Valence Quarks Mass(MeV)

(MeV)

sd 497.648(22)+3.972(27)

K0* )892(K

D0D0BB

np

00

)892(*K

0

su

sd

cd

su

cu

bdbu

duduud

ddsuds

dusuus

dssuss

493.677(16)

896.10(27)891.66(26)

1869.4(5)1864.6(5)

5279.4(0.5)5279.0(0.5)

939.56536(8)938.27203(8)

1197.449(30)1192.642(24)

1192.642(24)1189.37(7)

1321.31(13)1314.83(20)

+4.44(37)

+4.78(10)

-0.33(28)

+1.2933317(5)

+4.807(35)

+3.27(8)

+6.48(24)

Note Coulomb effects have the opposite sign; for the np system MeVM Coul

np 6.0

One concludes therefore

MeVmm ud 4

But then at the quark level in the scheme at the scale of 2 GeV

%30

ud

du

mm

mCSB !

45.1 um

84 dm

MeV

MeV

%1)(

tconstituenud

du

mm

mHowever

which is the scale of CSB in hadrons and nuclei

The electromagnetic interaction among the quarks also plays a role

du|| dduu|

2

1| 0

Coulomb repulsion Coulomb attraction)35(57018.139

m

mm 0

)6(9766.1340 m

] No contribution from dum !

du||

MS

The electromagnetic interaction among the quarks is of importance also for the mass splittings of

|

|and 0|

)5.0(8.775 m

)6.1(3.150

0| a

0| a

and

00| a

)2.1(7.9840

am

10050

dum Gives isospin mixing of the neutral mesons

)1,0()1,1( 00 )0,0()0,1( '0

dum Allows for G-parity violating decays 0

dum Also predicts

0)]()([

2

1)()(

xuxd

xuxd

np

np

! 0.05-0.10 ?

implications for the G0 experiment:

possible experiments:

Induced Drell-Yan processes at 30 GeV(FNAL, JPARC)

compare

{Xp Xn

i.e.i.e.

pdd nuu

or W production in np collider

i.e.

i.e.

Wdupn

v Wud

np

W Wp n

CLASSIFICATION OF N-N FORCES:

CLASS I: CHARGE INDEPENDENT FORCES

)2()1( ttbaVI npppnn

CLASS II: CHARGE SYMMETRIC BUT CHARGE DEPENDENT FORCES

)]2()1(3

1)2()1([ 33 ttttcVII

npppnn CLASS III: ISOSPIN CONSERVING BUT CHARGE

)]2()1([ 33 ttdVIII npppnn

-NO ISOSPIN MIXINGCLASS IV: ISOSPIN NON-CONSERVING, CHARGE ASYMMETRIC

333 )]2()1([)]2()1([ ttgtteVIV

0IVV FOR IDENTICAL PARTICLES(nn&pp)

-AFFECTS NP SYSTEM ONLY

)1,2()2,1( IVIV VV

ASYMMETRIC AND CHARGE DEPENDENT FORCES

AND CHARGE-DEPENDENT FORCES

The Two-nucleon system and Isospin

1 0 -1T

1

0

pp

np

nn

np

3T

space spin

isospin

np

T=1

np

T=0

S

A

S

A

A

S

S

A

S

S

A

AClass IV charge-asymmetric, charge dependent interactions:1) Affect np system only2) Cause isospin mixing3) Or cause spin triplet-singlet transitions

Evidence for Class III Interactions

1) Low energy nucleon-nucleon scattering observables

2) Okamoto-Nolen-Schiffer effect:

Binding energy differences of mirror nuclei

Low Energy Nucleon-Nucleon Scattering Observables

nn nn np pp pp

)( fma

)( fmr

)32(45.18

)11(80.2 )11(75.2 )5(75.2 )14(794.2

)3(8.18 )9(748.23 )26(8063.7 )4(3.17

)4(85.2

n-p Elastic Scattering

Basic Principle of the CSB Experiments:

CS Operation

Rotation

nA pA

p ppn n n

pn AAA

,0 ACS CSBA 0

)( pnpn PPAPA

zxA

xyz

xzA

xz

y)()()( zxxz AAC

Mechanisms of charge symmetry breaking in n-p elastic scattering

Charge asymmetric, charge dependent interaction, antisymmetric under the exchange of nucleons i and j in isospin space, class IV interaction of Henley and Miller

fk

ik

fk

ik

)1

(1

)]2()1()][2()1([44 332

2

rdr

d

rL

M

KeV n

)770(0 1,1 JT

)782(0 1,0 JT

0 0

emH

)(11

)]2()1()][2()1([||

44 3322

0

2rmrmemn ee

rdr

d

rL

mm

H

M

KggV

)

1(

1)]2(*)1([)]2(*)1([

24 32

2rme

rdr

d

rL

M

gV

)()]2()1()][2()1([ 33' rLVIV

Neutron-proton magnetic interaction 00 mixing

Angular distribution

)(A similar to

)(A MeVTn 300

)()]2(*)1()][2(*)1(['' rLVIV

Neutron-proton mass difference a and exchang

e State dependent phase J)1( so

'i s have different signs

according J values

affecting

Iqbal & Niskanen’s Prediction at 350 MeV

by comparing the experimental results for A With theoretical

predictions ,one can establish an upper limit on a P-even/T-oddinteraction[M.Simonius,Phys.Rev.Lett.78,4161(1997)]

this translates into a P-even/T-odd N coupling constant

in terms of the strong N coupling constant3107.6|| g [95% C.L.]

Note that the upper limit on the neutron edm gives

|/|1053.0|| .3 measDDH ffg

but ?15|/| . measDDH ff

So comparable results!

2 new possibilities1 measure A in pnpn at 320 MeV with improved

precision.2 measure the attenuation of polarized proton through an aligned deuterium target

2/

)Im()Re(

0

**

hcfb

AA ooonoono

AAAAA pnooonoono

A (TRI violation) [410)4.78.1(

410)106( 410)238(

183 MeV347 MeV477 MeV

2/

)Im()(

0

*

hc

TRIVA

Take c from SAID FA95 solution::8.72,347 0 cmMeV

110314.0)Re( c110369.0)Im( c

677.10

fmfm

srmb /183 MeV347 MeV477 MeV

410)8320( g410)3722(

410)7727( or 0067.0|| g (95% C.L.)neutron electric dipole moment gives an indirect limit of 310g(dependent on '

f !)

|/|1053.0|| 3 ffg DDH

Considerably lower than the limits inferred from direct tests of TRI

Binding Energies(MeV), Mirror Hypernuclei

H4

Li8

Li9

Be10

B12

He4

Be8

B9

B10

C12

04.004.2

03.080.6

15.053.8

22.011.9

06.037.11

03.039.2 05.084.6

15.088.7

12.089.8

19.076.10

If isospin is an exact symmetry and therefore also no N

CSB, then the B of mirror hypernuclei should be identical.

Differences could be due to:- Coulomb effects + other electromagnetic effects- nuclear CSB

N- CSB