Weak Interactions in the Nucleus II Summer School, Tennessee June 2003
p e- g e- p Recoil effects in E&M Hadrons exchange gluons so need to include most general Lorentz-invariant terms in interaction Recoil effects Has to be zero to allow conservation of charge: Anomalous magnetic moment
e+ d ne W u Recoil effects in Weak decays Recoil effects gS and gWM: Conservation of the Vector Current: I=1 form factors in VE&Mare identicalto form factors in VWEAK gT: Second Class Currents: breaking of G-parity gPS: Partial Conservation of the Axial Current (plus pion-pole dominance):
Conservation of the Vector Current: I=1 form factors in VE&Mare identicalto form factors in VWEAK Width of M1 and (e,e’) cross-section determine <gWM> for E&M I=1,Jp=0+ 14O I=1,Jp=0+ I=1,Jp=0+ 14C 14N Shape of beta spectrum, t, determines <gWM> for WEAK Potential for checking CVC at fraction of % level • Garcia and B.A. Brown, • Phys Rev. C 52, 3416 (1995).
gPS: Partial Conservation of the Axial Current (plus pion-pole dominance): Approximation should hold very well : u and d quarks are very light chiral symmetry: V. Bernard et al. Phys. Rev. D 50, 6899 (1994). Measure intensity of m + p =n + n + g Radiative m capture Ordinary m capture
gT: Second Class Currents: breaking of G-parity In 1970’s evidence that (ft)+/(ft)- changed linearly with end-point energy
From Minamisono et al. Phys. Rev. Lett. 80, 4132(1998).
Angular momentum and Rotations Rotating the coordinate system: Invariance: For any rotation: Invariance under rotations imply conservation of J
Isospin Notice n+n, n+p, p+p hadronic interactions are very similar. Use spin formalism to take into account Pauli exclusion principle etc.
Weak Decays of Quarks Once upon a time: Weak interactions needed neutral component to render g sinq = e. m- m+ But the process KL0m+m- could not be observed. Why not?? Z0 s d
Weak Decays of Quarks G.I.M. proposed The neutral weak currents go like: No strangeness-changing Neutral Currents
m- m+ W W d s Weak Decays of Quarks G.I.M. proposed The neutral weak currents go like: n The process KL0m+m- actually goes through this diagram u c
Finding J/Psi confirmed the existence of the c quark and gave validity to the G.I.M. hypothesis
Q 0 -1 +2/3 -1/3 Weak decays in the Standard Model I u e+ ne 1/2 W d 1/2 Ke3 0.220 nm e+ From nuclear 0.974 0.080 ne m CKM matrix: Is it really Unitary?
In order to measure Vud we compare intensities for semi-leptonic to purely leptonic decays e+ d ne Fermi’s Golden rule: t -1 α |<f H i>|2 f(E) Then: |<f I i>|2Vud2 ftm /ftquarks u nm e+ ne m
Example: decay of 14O Level density not high so Isospin config. mixing very small. I=1 Iz=1, Jp=0+ 14O easy to produce and half-life convenient for separating from other radioactivity. 14O (t1/2=70.6 s) I=1 Iz=0, Jp=0+ branch <1% Additional branches so small that beta intensity can almost be obtained directly from 14O half-life 14N Many features contribute to allowing a precise determination of ft
Nuclear weak decays are driven by two currents : Vm and Am. Vm is conserved (in the same sense that the electromagnetic current is conserved). Initially most precise results came from decays for which only Vm can contribute: Jp(Initial nucleus)=0+ Jp(Final nucleus)=0+
From Hardy et al, Nucl. Phys. A509, 429 (1990). Note this range is only 0.5% Nuclear 0+ 0+ decays: 2.3s away from 1
Complication: Isospin symmetry breaking Nuclei do have charge and To understand it we can separate it into effects at two different levels: 1) decaying proton and new-born neutron sample different mean fields. E 2) shell-model configurations are mixed p n
Radiative and isospin breaking corrections have to be taken into account. From Hardy et al, Nucl. Phys. A509, 429 (1990).
The complication of isospin-breaking correctionscan be circumvented by looking at: 1) p+p0 e+n2) n p e-n 1) p+p0 e+n has a very small branch (10-8); 2) n p e-n is a mixed transition (Vm and Am contribute).
Determinnig Vud from neutron b decay • Disadvantage: Vm and Am contribute to this Jp=1/2+ 1/2+ decay. Consequently need to measure 2 quantities with precision. • Advantage: Simplest nuclear decay. No isospin-breaking corrections. Neutron t already well known: need to determine b asymmetry (e- angular distribution) from polarized neutrons.
Beta asymmetry with beam of Cold Neutrons (v 500 m/s) e- vacuum beam pipe neutron momentum neutron spin B field decreases to decrease transverse component of momentum which lowers backscattering Abele et al. Phys. Rev. Lett. 88, 211801 (2002).
Ultra-Cold Neutron Source Layout(LANL) SS UCN Bottle 58Ni coated stainless guide Liquid N2 Flapper valve Be reflector LHe Solid D2 UCN Detector 77 K poly Tungsten Target • Saunders, 2003 • C. Morris et al, PRL 89, 272501
Line C Measurements • Saunders, 2003 • C. Morris et al, PRL 89, 272501 UCN Detector Cold Neutron Detector Proton Beam • Line C results show reduced ( 100) UCN production. • D2 frost on guide windows and walls. • Gravity+Aluminum detector window
Solid D2 in a “windowless” container Grown from a gas phase at 50 mbar Cooled through the triple point • Saunders, 2003 • C. Morris et al, PRL 89, 272501
Neutrons in Magnetic Field In a frame rotating with freq. w:
Neutrons in Magnetic Field Field B1 rotating with freq. w around B0 . In a frame rotating with freq. w: strength of B0 freq. of B1 strength of B1
Neutrons in Magnetic Field In S’ motion is precession around Bewith angular velocity a = -w Be