Introduction to Charge Symmetry Breaking

• Introduction

• What do we know?

• Remarks on computing cross sections for 0 production

G. A. Miller, UW

Charge Symmetry: QCD if md=mu, L invariant under u$ d

Isospin invariance [H,Ti]=0, charge independence, CS does NOT imply CI

Example- CS holds, charge dependent strong force

• m(+)>m(0) , electromagnetic

• causes charge dependence of 1S0 scattering lengths

• no isospin mixing

Example:CIB is not CSB

• CI ! (pd! 3He0)/(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

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>0.8 +1.3 MeV

Miller,Nefkens, Slaus 1990

• 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

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)

Importance of md-mu

• >0, influences extraction of sin2W

from neutrino-nucleus scattering

• ¼ 0, to extract strangeness form factors of nucleon from parity violating

electron scattering

Outline of remainder

comments on

pn! d0

dd!4He0

Old stuff- NN scattering, nuclear binding energy differences

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

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 P0 TRIUMF, IUCF expts

md-mu

CLASS III:Miller, Nefkens, Slaus 1990

meson exchange vs EFT?

Search for class IV forces

A -see next slide

Where is EFT?

ant

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

Summary of NN CSB

meson exchange

Where is EFT?

old strong

int. calc.

np! d0

Theory Requirements

• reproduce angular distribution of strong cross section, magnitude

• use csb mechanisms consistent with NN csb, cib and N csb, cib,

Gardestig talk

Gardestig, Nogga, Fonseca, van Kolck, Horowitz, Hanhart , Niskanen

plane wave, simple wave function, = 23 pb

14pb

Bacher

Initial state interactions

Initial state OPEP, +

HUGE, need to cancel

Nogga, Fonseca

plane wave, Gaussian w.f. photon in NNLO, LO not included

23 pb vs 14 pb

et al

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

3P0

Theory requirements: dd!4He0

• start with good strong, csb

np! d0

• good wave functions, initial state interactions-strong and electromagnetic

• great starts have been made

• 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

Suggested plans: dd!4He0

Much to do, let’s do as much as

possible here