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S1242S1242

High Precision Mass High Precision Mass Measurements of Superallowed T=2 Measurements of Superallowed T=2

Nuclear Beta Decay EmittersNuclear Beta Decay Emitters

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Quarks in the SM

Coupling to Higgs field ΦT=(Φ1 Φ2):

after symmetry breaking: mass term weak ≠ mass eigenstates:

interaction Lagrangian quarks - W+ and W-

chuLGdLG RjiuijRji

dij . Yukawa

coupling

LLL dDd '

RRR dDd 'LLL uUu '

RRR uUu '

WdDUugchWdug LiLLLiLiLi ''..

__

tbtstd

cbcscd

ubusud

LL

VVV

VVV

VVV

DUVCabibbo–Kobayashi–Maskawa matrix: - decay

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Vud measurements

J. Hardy, CIPANP 2009

superallowed 0+→ 0+ decays most precise way to extract Vud

due to J = T = L = S = 0:• pure Fermi decay (only vector part)• transition between isobaric analog states• only total Isospin Ladder Operator T± alters wave-function for T = 1:

2

22

2

22 2)(

g

GFM

g

GM VV

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ft- values, corrected Ft-value and Vud

Combination to ft-values (T=1):

corrected Ft value:

V

R … transition indep.R and NS ….transition dep.

c … isospin symmetry breaking (tans. dep.)

Corrections: small ( about a few %), BUT dominating uncertainty

const2 2

VG

Kft f … phase space integral (dep. on Q-

value)

t … „partial halflife“ (dep on. BR and T½ )

K … numerical constant const

)1(2)1)(1(

2

VRV

CNSR G

KftFt

F

Vud G

GV

Experimental Input

}radiative corrections

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Tests of Fundamental Symmetries I

J. Hardy & I.S. TownerJ. Hardy & I.S. Towner W. J. Marciano et al.

1) CVC 2) Scalar Currents

3) |Vud |2

/= 0.28J. Hardy & I.S. Towner, Phys. Rev. C 79, 055502 (2009)

)13(0011.0V

s

c

c

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5) Coupling Universality:

GF (|Vud|2 + |Vus|2 + |Vub|2 ) = G = G

e.g. Z boson in SO(10)

implies: M(Z)> 750 GeV at 95% CL

Tests of Fundamental Symmetries II

4) CKM: basis transformation weak ↔ mass eigenstates

Unitarity test of 1st row:

|Vud|2 + |Vus|2 + |Vub|2 = 1 SM= 0.99995(61) Experiment

J. Hardy & I.S. Towner, Phys. Rev. C 79, 055502 (2009)0.9491(4) 0.0508(4)

B. Tschirhart , CIPANP 2009

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T&H’s c: use W+-spin, not isospin +

new c – calculations (including core orbitals)I.S. Towner & J. C. Hardy, Phys. Rev. C77, 025501 (2008)

Developments for cJ.C. Hardy and I.S. Towner, Phys. Rev. C66, 035501 (2002 )

Phys. Rev. C71, 055501 (2005)W. E. Ormond and B. A. Brown, Phys. Rev. C52, 2455 (1995)

Nucl. Phys. A 440, 274 (1985)

G.A. Miller & A. Schwenk, Phys. Rev. C 78, 035501 (2008)

N. Auerbach, Phys. Rev. C 79, 035502 (2009)

J. C. Hardy & I.S. Towner, Phys. Rev. C 79, 055502 (2009)

New approach to c (Coulomb force treated by perturbation theory)

results lower than T&H

New Hartree-Fock (same model space as Woods-Saxon with core orbitals)

H. Liang et al., Phys. Rev. C, 064316 (2009)

c accessed via self-consistent RPA in relativistic framework

/= 1.0-1.1

implementedimplemented

differentlydifferently

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c : comparisons between models

T&H (2005) ↔ O&B

T&H (2008) ↔ Perturbation theory T&H (2008) ↔ RPA

T&H: WS (2008) ↔ HF (2009)

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Status of c

• T&H: currently best calculations– Wood Saxon & Hartree-Fock – same model space– good agreement with each other and

CVC

• 4 other descriptions– 3 with numerical results

– disagree with T&H (all lower c )

– but all need improvements

benchmark models / check c – assume CVC– use

– compare with experiment

– new cases or/and cases with large c

Tz= - 1

Tz= 0

|Vud|2

}

NScR

Ftft

11

superallowed T=2 superallowed T=2 casescases

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• new system → wider range for tests of c

• T=2 allows systematic check of c

• c expected to be larger:

roc

cmcc

example: 32Ar → 32Clcalculation based on HF (B.A. Brown) c

cm = 0.6 %

cro = 1.4 %

configuration mixing

with other 0+

radial overlap• radial wavefn altered by Coulomb• enhanced near proton drip lineT=1

T=2

Superallowed T=2 Decays

M. Bhattacharya et al.,Phys. Rev. C 77, 065503 (2008)

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Exp. Challenges for T = 2

• short half-lives ( down to 40 ms ) challenge for high precision mass measurements

• -delayed proton emission

M. Bhattacharya et al.,Phys. Rev. C 77, 065503 (2008)

→ feasible with HCI at TITAN

→ feasible: 32Ar

BR=22.71(11)(11)

ft (32Ar)=1552(12)

c (exp)= 2.1 ± 0.8 %

c (th. )= 2.0 ± 0.4 %

Note: used m.e.(31S) + their Sp measurement:

m.e.(32Cl)=-13337.0 ± 1.6 keV

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Proposed MeasurementsIsoto

peHalf-life

Present m

[keV]

m TITAN (A+) [keV] q

TITAN HCIm [keV]

E*[keV

]

comment

Mg-20

90 ms27 1.865 10

He-like 0.186

request stage 2

Na-20

448 ms6.66 1.864 9

He-like 0.207

13 request stage 2

Si-24 140 ms 19.47 2.237 12 He-like 0.186 ?

Al-24 2.053 s 2.78 2.236 11 He-like 0.203 6 proposal S1191

S-28125 ms 160 2.609 14 He-like 0.186

requires development

P-28270 ms 3.32 2.607 13 He-like 0.201 21

requires development

Ar-32 98 ms1.8 2.981 16 He-like 0.186

requires development

Cl-32 298 ms6.59 2.979 15 He-like 0.199

0.4 requires development

Ca-36

102 ms40 3.353 10

Ne-like 0.335

feasible, request stage 2

K-36 342 ms0.39 3.352 9

Ne-like 0.372 8

request stage 2

Ti-4053 ms 160 3.725 12 Ne-like 0.310

requires development

Sc-40182 ms 2.83 3.724 11 Ne-like 0.339

8 requires development

Cr-44 53 ms 50 4.097 14 Ne-like 0.293requires

development

V-44 111 ms 121 4.096 13 Ne-like 0.315 ? ?

Ti-43 509 ms 6.90 4.002 12 Ne-like 0.334requires

development

Fe-48 44 ms 70 4.469 16 Ne-like 0.279requires

development

Mn-48 158 ms 112 4.468 15 Ne-like 0.298

0.9 requires development

Ni-52 38 ms 84 4.842 18 Ne-like 0.269requires

development

Co-52 115 ms 65 4.840 17 Ne-like 0.28530 requires

development

Isotope Target Source Yield [ions / sec]

Mg-20 SiC TRILIS 240

Na-20 SiC Re surface 1.7▪108

Isotope Target Source Yield [ions / sec]

Ca-36 TiC TRILIS feasible (M. Dombsky)

K-36 TiC Re surface 2.9▪105

Request for each pair:1 shift setup + calibration5 shifts measurement

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Impact of Measurements

• BR measurements are planned

• require >10 ions/sec

contributions to uncertainty of ft-value:

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Test of IMME Quintets

C. Yazidjian et al., Phys. Rev. C 76, 024308 (2007)A. Gade et al., 76, 024317 (2007)

A = 20 A = 36

20Mg

M.E. [keV]

E* [keV]

0+ 17570(27)

2+ 19168(29) 1598(10)

Check for cubic term:

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Summary• Vud most precisely determined via superallowed 0+→ 0+ nuclear

decays• CKM unitarity test: σud ≈ σus

• isospin symmetry breaking corrections c

– current calculations (T&H) in great agreement with CVC– many new theoretical descriptions (in development)– systematic discrepancies between models– experimental data to benchmark models (extreme cases i.p.

T=2)• T=2 cases in experimental reach: NEW NUCLEONIC SYSTEM

– BR measurements feasible (32Ar done + other in preparation)– masses: HCI on short lived isotopes with TITAN

propose high precision mass measurements on superallowed emitters:

20Mg, 24Si, 28S, 32Ar, 36Ca, 40Ti, 44Cr, 48Fe, and 52Nirequest 1 shift setup + 5 shifts measurement for each case

measurements also important for tests of IMME (i.p. 20Mg, 36Ca)

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S1242 collaborationTRIUMF: M. Brodeur, T. Brunner, S. Ettenauer, A. Gallant, A. Lapierre, S.

Triambak, P.P.J. Delheij, J. Dilling

University of Washington: A. Garcia, C. Wrede

Texas A&M University: D.G. Melconian

University of Manitoba: G. Gwinner

NSCL: R. Ringle

TITAN collaboration

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Details on new Details on new c c descriptionsdescriptions

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isospin operator +c

T&H: W-spin operator

M&S: • W-spin formalism loses SM isospin commutation relations• radial quantum numbers not necessarily the same• separation model dependent• correct SM +

• complete formalism developed to calculate c

aar ,

,

ba

• because proton and neutron states are not the same

• but assumes radial quantum numbers are the same

roc

cmcc

G.A. Miller & A. Schwenk, Phys. Rev. C 78, 035501 (2008)

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Wood-Saxon ↔ Hartree Fock

nucleus with Z+1 protonsCoulomb term in proton wavefunction:• Wood Saxon:

• Hartree Fock:

J. C. Hardy & I.S. Towner, Phys. Rev. C 79, 055502 (2009)

r

ZeRrV CC

2

)(

r

eZr

rr

erdrV rdir

C

2

11

2

13 )1(

)()(

3/1

113

2

)(3

2

3)(

rrd

erV ex

C

difficult to calculateexactly in Skyrme HF

T&H: 1) calculate single HF for A-1 nucleus →

2) use proton mean field for proton wf →

3) use neutron mean field for neutron wf →

in agreement with T&H’s Wood-Saxon

e.g.:33S34Cl34S

different than O&B

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new calculations c

self consistent RPA build on• relativistic Hartree with

– DD-ME1 , DD-ME2 – NL3 , TM1

• relativistic Hartree-Fock with – PKO1 , PKO2 , PKO3 – PKO1 but Coulomb

exchange term turned off

Conclusions:Conclusions:1) RHF+RPA (without C-Ex) = RH+RPA

proper treatment of Coulomb field is essential for c

2) more investigations required (e.g. proper n-p mass difference, isoscaler and isovector pairing, deformation)

H. Liang et al., Phys. Rev. C, 064316 (2009)

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new calculations c II

Perturbation Theory:

• charge independent Hamiltonian H0

• treat Coulomb force perturbatively

details:

• VC: uniformly charged sphere

• off diagonal matrix elements

largest elements for giant isovector monopole states (IVMS)

• wave function for PT: gs (H0) + IVMS

N. Auerbach, Phys. Rev. C 79, 035502 (2009)

213/2

1

418

A

Vc

nitrR

ZenV

izic )(0

20 2

3

2

z-comp. of isovector monopole operator

isospin impurity

num. factor (model dep.)

symm. potential strength

Model characteristics:• includes collectivity• pure isospin formulation• BUT: equivalent to W-spin • uncertainties in model parameters• neglects non-Coulomb charge dep. int.