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

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! 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

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 sin2W from neutrino-nucleus scattering ¼ 0, to extract strangeness form factors of nucleon from parity violating electron scattering

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

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

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

Search for class IV forces  A -see next slide

ant Where is EFT?

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! 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

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

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

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

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

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

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

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