1. Introduction to Charge Symmetry Breaking
G. A. Miller, UW
Introduction
What do we know?
Remarks on computing cross sections for 0 production

2. Charge Symmetry: QCD if md=mu, L invariant under u$ d
Isospin invariance [H,Ti]=0, charge independence, CS does NOT imply CI

3. Example- CS holds, charge dependent strong force
m(+)>m(0) , electromagnetic
causes charge dependence of 1S0 scattering lengths
no isospin mixing

4. Example:CIB is not CSB CI ! (pd! 3He0)/(pd ! 3H+)=1/2
NOT related by CS
Isospin CG gives 1/2
deviation caused by isospin mixing
near  threshold- strong  N! N contributes, not ! mixing

5. Example –proton, neutron
proton (u,u,d) neutron (d,d,u)
mp=938.3, mn=939.6 MeV
If mp=mn, CS, mp<mn, CSB
CS pretty good, CSB accounts for mn>mp
(mp-mn)Coul¼ 0.8 MeV>0
md-mu> MeV

6. Miller,Nefkens, Slaus 1990

7. All CSB arises from md>mu & electromagnetic effects–
Miller, Nefkens, Slaus, 1990
All CIB (that is not CSB) is dominated by fundamental electromagnetism (?)
CSB studies quark effects in hadronic and nuclear physics

8. Importance of md-mu >0, p, H stable, heavy nuclei exist
too large, mn >mp + Binding energy, bound n’s decay, no heavy nuclei
too large, Delta world: m(++)<mp,
<0 p decays, H not stable
Existence of neutrons close enough to proton mass to be stable in nuclei a requirement for life to exist, Agrawal et al(98)

9. Importance of md-mu >0, influences extraction of sin2W
from neutrino-nucleus scattering
¼ 0, to extract strangeness form factors of nucleon from parity violating
electron scattering

10. Outline of remainder
Old stuff- NN scattering, nuclear binding energy differences
comments on
pn! d0
dd!4He0

11. NN force classification-Henley Miller 1977
Coulomb: VC(1,2)=(e2/4r12)[1+(3(1)+3(2))+3(1)3(2)]
I: ISOSCALAR : a +b 1¢2
II: maintain CS, violate CI, charge dep.
3(1)3(2) = 1(pp,nn) or -1 (pn)
III: break CS AND CI: (3(1)+3(2))
IV: mixes isospin

12. VIV»(3(1)-3(2)) (3(1)-3(2)) |T=0,Tz=0i=2|T=1,Tz=0i isospin mixing
VIV=e(3(1)-3(2))((1)-(2))¢L
+f((1)£(2))3 ((1)£(2))¢ L
magnetic force between p and n is Class IV, current of moving proton int’s with n mag moment
spin flip 3P0!1 P TRIUMF, IUCF expts

14. CLASS III:
Miller, Nefkens, Slaus 1990
meson exchange vs EFT?
md-mu

15. Search for class IV forces
 A -see next slide

16. ant
Where is EFT?

17. A=3 binding energy difference
B(3He)-B(3H)=764 keV
Electromagnetic effects-model independent, Friar trick use measure form factors EM= 693 § 20 keV, missing 70
verified in three body calcs
Coon-Barrett - mixing NN, good a, get 80§ 10 keV
Machleidt- Muther TPEP-CSB, good a get 80 keV
good a get 80 keV

19. Summary of NN CSB
meson exchange
Where is EFT?

22. old strong int. calc.

23. np! d0 Theory Requirements
reproduce angular distribution of strong cross section, magnitude
use csb mechanisms consistent with NN csb, cib and  N csb, cib,
Gardestig talk

24. plane wave, simple wave function,  = 23 pb
Bacher
14pb
Gardestig, Nogga, Fonseca, van Kolck, Horowitz, Hanhart , Niskanen
plane wave, simple wave function,  = 23 pb

25. Initial state interactions
Initial state OPEP, +
HUGE, need to cancel
Nogga, Fonseca

26. et al
plane wave, Gaussian w.f. photon in NNLO, LO not included 23 pb vs 14 pb

27. Initial state LO dipole  exchange
d*(T=1,L=1,S=1), d*d OAM=0,  emission makes dd component of He, estimate using Gaussian wf

28. Theory requirements: dd!4He0
start with good strong, csb
np! d0
good wave functions, initial state interactions-strong and electromagnetic
great starts have been made

29. Suggested plans: dd!4He0
Stage I: Publish existing calculations, Nogga, Fonseca, Gardestig talks, HUGE 
LO photon exchange absent now,
no need to reproduce data
present results in terms of input parameters, do exercises w. params
Stage II: include LO photon exchange, Fonseca

30. Much to do, let’s do as much as possible here