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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 m d =m u , L invariant under u $ d. Isospin invariance [H,T i ]=0, charge independence, CS does NOT imply CI. - PowerPoint PPT Presentation
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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