Doron Gazit
Institute for Nuclear Theory
University of Washington, Seattle.

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Motivation.
Interaction of weak probes with nuclei.
Part I: Weak structure of the nucleon.
Part II: Some studies of weak interaction in light
nuclei.
Application to astrophysics.
Summary and outlook.
Doron Gazit - The weak structure
of the nucleon
August 2009
2
The response of a nucleon to an
external weak probe at low
energy
◦ Only the probe is perturbative.
◦ One would like to constrain the nonperturbative response:
 To study the fundamental theory
 To acquire a predictive quality.
Doron Gazit - The weak structure
of the nucleon
August 2009
4
A precision era:
◦ Available accurate
ab-initio methods.
◦ Consistent currents
and potentials from
cPT.
◦ Allow parameter free
calculations with subpercentage accuracy,
with nucleonic dof.
Doron Gazit - The weak structure
of the nucleon
August 2009
5
3 r ˆ a r ˆ  ,a r
ˆ
HW ~   d x j  x J x 
Lepton
current
P“f  E f , Pf
k “2  k 2 , k 2 
Nuclear
current

q0  ,q

W , Z 0
k1  m ,0

Pi“  E i , Pi 

g 
q q
2
M
W ,Z
W  ,Z 0 propagator  2
2
q  MW ,Z
Doron Gazit - The weak structure
of the nucleon
August 2009
g

qM W ,Z M 2
W ,Z
6

The standard model dictates the quark currents:



J  V  A




J0  (1 2sin W )V0  2sin W I  A0
2
Va  q  
a
2
q
Aa  q   5
2
a
2
q
1
I   q  q
2
When sandwiched between nucleonic/nuclear
 states,the strong interaction induces form
factors.
 cPT offers a venue to characterize these form
factors, at low energies.

Doron Gazit - The weak structure
of the nucleon
August 2009
7
Low
energy
EFT
QCD
Nuclear Hamiltonian
Chiral
Lagrangian
Wave
functions
Nöther
current
Weak
current
Nuclear
Matrix
Element
Doron Gazit - JLab Theory seminar
8
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The leading order NNN
forces are at N2LO.
They include 2 new contact
parameters.
No new parameters at
N3LO.
Weinberg, van Kolck, Ordonez, Meissner,Doron
Epelbaum,
Nogga,
Gazit - The weak
structure Bernard, Kaiser,
of the nucleon August 2009
Krebs, Machleidt, Entem…
9
Single nucleon current
1 pion exchange
Contact term
dˆ R
Nucleon-pion
interaction,
NO new
parameters
Contact term

Gårdestig, Phillips, Phys. Rev. Lett. 98, 232301
DG, Quaglioni, Navratil,
Doron Gazit -(2006);
The weak structure
of the
nucleon
10
AugustarXiv:
2009
T.-S.
al, 103,
Phys.102502
Rev. C 67,
055206 (2003); DG
PhD
thesis
0807.0216
Phys. Park
Rev. et
Lett.
(2009).
p'
Second class currents
2


iF
q


M

2


2
 a
N pVa N'  p'  u p'FV q  
 q  FS q q  up
2M N



 2
Weak
Induced
Vector
magnetism
scalar
p
q   p'  p 
2
2

 
G
q
iG
q





P
T

2



a

, 5


N p Aa N'  p'  u p' GA q  
q 
 q  5 u p
2M N
2M N


p

 2

uP    
Induced
Induced
n 
Axial
Pseudoscalar Pseudotensor

Weinberg Phys. Rev., 112, 1375 (1958)
Doron Gazit - The weak structure
of the nucleon

August 2009
11
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The quark currents have a specific behavior
under G-parity Cexp(-iπT2) .
Since isospin is not a symmetry of the strong
force, induced second class currents are allowed
in nuclear reactions.
They are expected to be suppressed by a factor:
md  mu
mn  m p

No experimental evidence for second class
currents!

Doron Gazit - The weak structure
of the nucleon
August 2009
12
Doron Gazit - The weak structure
of the nucleon
August 2009
13

At zero momentum transfer:
1


normalization
of nucleonic w. f .
pV0 q  0 n  FV 0
The fact that FV is not renormalized at low
energies, led to the Conserved Vector Current
hypothesis.

Doron Gazit - The weak structure
of the nucleon
August 2009
14

  V 
V ,

 cosC 
CVC hypothesizes:
◦ The vector parts of the charge changing current and the
isovector piece of the electromagnetic curret are three
components of a vector in isospace.
◦ All 3 components are conserved.

Gerstein, Zeldovich, Sov. Phys. JETP 2, 576 (1956)
Feynman, Gell Mann, Phys. Rev. 109, 193 (1958)

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The vector and induced-weak-magnetic form factors
are equal to their electromagnetic counter parts,
including the momentum dependence.
The induced scalar form factor vanishes.
CVC implies that Siegert theorem holds for weak
reactions.
An excellent approximation in the nuclear sector.
◦ According to cPT, CVC holds to 2×10-4.
Doron Gazit - The weak structure
of the nucleon
Kaiser, Phys. Rev. C, 64, 028201 (2001)
August 2009
15


e
e


M  i   f
2
F
0+0+
2

2

 T T  1  TZ Tz  11 C 
Only vector current
contributes.
1
ft ~ 2
FV M F
The nuclear matrix
element:


Towner & Hardy define
“nucleus independent”
half-life:
Ft  ft1 C 1 R 
Superallowed transitions
Doron Gazit - The weak structure
of the nucleon
August 2009
16
Vud  0.97424(22)
Vud  Vus  Vub  0.99995(61)
2
2
2
me Fs FV  (0.0011 0.0013)

Ft  3071.8  0.83 sec
Miller & Schwenk, Phys. Rev. C 78,Doron
035501
(2008).
Gazit - The weak structure
Hardy & Towner, Phys. Rev. C 79, 055502 (2009)
of the nucleon
August 2009
17
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“Needs” a nuclear
correction of 0.72%.
T&H suggest 0.52±0.04%.
An existing NCSM
calculation:
(0+,1)
(1.4645(19)%)
10C
(0+,1) E*=1.7415
EB=15.6988(4) MeV
Caurier et al., Phys. Rev. C 66, 024314(2002)
(98.53(2)%)
(1+,0) E*=0.71835
(3+,0)
10B
EB=12.0507(4) MeV
ft=3041.7±4.3
Doron Gazit - The weak structure
of the nucleon
August 2009
18
Doron Gazit - The weak structure
of the nucleon
August 2009
19

Assuming no second class current.
2

 
G
q


P

2


N p Aa N' p'  u p'GA q  
q  5 a up
2M N



 2

The axial current is not conserved, even in the

chiral
limit.
◦ Partial conservation of the axial current (PCAC):
q2
m2 F
2
2
2M N GA q 
GP q  2 2
G
q


N
2M N
m  q 2
2

The axial constant is renormalized, in a
relativistic manner: gA 1.2695(29)
2


r
A
2
 Oq 4 
GA q 2  gA 
1
q


6



Doron Gazit - The weak structure
Bernard, Elouadrhiri, Meissner, J. Phys. G: Nucl.
Part.
Phys.
of the
nucleon
August28,
2009 R1 (2002).20

Doron Gazit - The weak structure
of the nucleon
August 2009
21
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One can asses the axial constant through
AdS/QCD correspondence – using a conformal
“cousin” theory of QCD which has a gravitational
analogue in 5 dimensions.
A systematic way of including weak interactions
into the AdS/QCD dictionary was recently
proposed.
Using Sakai-Sugimoto model one gets a
parameter free prediction: gA≅1.3.
Calculations of other weak form factors as well
as nucleon forces are underway.
Doron Gazit - The weak structure
of the nucleon
DG, Yee, Phys. Lett. B670, 154 (2008).
August 2009
22

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The axial current is not conserved!
Thus, its extension to nuclei is not trivial.
Doron Gazit - The weak structure
of the nucleon
August 2009
23
The calculation uses
Idaho N3LO NN
potential,
Combined with N2LO
NNN force.
DG, Quaglioni, Navratil, Phys. Rev. Lett. 103, 102502 (2009)
Doron Gazit - The weak structure
of the nucleon
August 2009
24
Navratil et al., Phys. Rev. Lett. 99, 042501 (2007).
Doron Gazit - The weak structure
of the nucleon
August 2009
25
0.3  c D  0.1

c E  0.220,0.189

Doron Gazit - The weak structure
of the nucleon
August 2009
26
A prediction of
4He
Doron Gazit - JLab Theory seminar
27
•The NNN force has NNN
a negligible
are not effect.
important???
•Specific character of the NN force has minor effect, as long as
it is “state of the art”
•Caliration of cD is robust – depends weakly on the force.
• Is this the origin for the success of EFT*?
Doron Gazit - The weak structure
of the nucleon
August 2009
29
Doron Gazit - The weak structure
of the nucleon
August 2009
30
Phenom.
Hamiltonian
QCD
Low
energy EFT
Chiral Lagrangian
Nöther
current
Solution of
Schrödinger equation
Weak
current
Wave
functions
i Jˆa f
2
T.-S. Park et al, Phys. Rev. C 67, 055206 (2003), M. Rho nucl-th/061003; DG, Nir Barnea,
31
Phys. Rev. Lett. 98, 192501 (2007); O’Connor, DG et al. Phys.PANIC08
Rev. C (2008).



Consistent calculations of weak and strong
effects are possible.
The weak sensitivity of the weak decay to the
NNN force make it an ideal candidate to
constrain the NNN parameters.
The calibration of cD looks robust, whereas the
value of cE will probably change when including
3NF N3LO potential.
Now we’re ready to look at the axial
constant evolution in nuclei.
Doron Gazit - The weak structure
of the nucleon
August 2009
32
Surveys of β-decay rates of nuclei suggest that gA
is gradually suppressed from ~1.27 to 1 (fully utilized A≅40).
b decay of 6He
0+1+:
1
ft ~ 2
gA M A

2
M  i GT  f
2
A


2

gA(q0)=1 in the quark
level.
gA(q0)=1.27 in the
nucleon level.
gA(q0)1 inside
nuclei???
 Vaintraub, Barnea, DG, Phys. Rev. C, 79 065501 (2009).
Doron Gazit - The weak structure
of the nucleon
August 2009
33

This is not surprising:
◦ Axial current is not conserved.
◦ Nucleons interact in nuclei.

However:
◦ A VMC calculation of the β decay 6He(0+)6Li(1+) used
AV18/UIX with phenomenological MEC and found:
 Single nucleon GT strength overestimates by 4% the
experimental strength.
 Adding MEC worsens the discrepancy to 5.4%.

Are the VMC wave functions to blame?
Pervin et al., Phys. Rev. C 76, 064319 (2007).


Are the MEC to blame?
An exotic effect?
Doron Gazit - The weak structure
of the nucleon
2009
Schiavilla and Wiringa, Phys. Rev. C 65,August
054302
(2002).
34



We use the HH method to solve the 6 body
problem, with JISP16 NN potential.
We use fourth order axial MEC calibrated in the
triton.
Very rapid convergence:
E∞(6He)=28.70(13) MeV
Eexp(6He)=29.269 MeV
E∞(6Li)=31.46(5) MeV
Eexp(6Li)=31.995 MeV
GT|LO=2.225(2)
GT=2.198(2)
Doron Gazit - The weak structure
of the nucleon
August 2009
35
OPEC
Contact

|GT|JISP16(6He)=2.198(7)
|GT|exp(6He)=2.161(5)



The contact interaction
that does not exist in
pheno. MEC, has a
opposite sign with
respect to the long
range one.
The final GT is just 1.7%
away from the
experimental one!
MEC brings the theory
closer to experiment!
No dependence on the
cutoff!
Doron Gazit - The weak structure
of the nucleon
August 2009
36



The inclusion of cPT based MEC is helpful, even when
one uses phen. interaction.
The conclusion is that the weak correlations inside
the nucleus can lead to the observed suppression.
RPA surveys of  capture showed that suppression is
needed only in GT channel – consistent with MEC.
Zinner, Langanke, Vogel, Phys. Rev. C 74, 024326 (2006).

cPT estimation for the suppression of gA in infinite
nuclear matter:
◦ gA/gA~+8% - +13% due to long range MEC.
◦ gA/gA~-28% due to contact interaction.
◦ gA/gA~-15% - -20% total.
Park, Jung, Min, Phys. Lett. B409, 26 (1997).
Doron Gazit - The weak structure
of the nucleon
August 2009
37
 capture on 3He
DG, Phys. Lett. B666, 472 (2008).
Doron Gazit - The weak structure
of the nucleon
August 2009
38




In QCD, the induced pseudoscalar form factor gP
depends on the axial form factor.
Adler, Dothan and Wolfenstein: GP q2  4M2N gN F2   2 MN2 rA2
m  q
HBcPT verified this result and connected it to
QCD, as well as allowed corrections to the
formula.

3
A comparison to experiment needs higher
momentum than b decays –  capture.
gP q 
2
m
2M N
GP q 2 
Adler, Dothan, Phys. Rev. 151, 1257 (1966).
Bernard, Kaiser, Meissner, Phys. Rev.
D 50, 6899 (1994),
Doron Gazit - The weak structure
of the nucleon August 2009
Kaiser, Phys. Rev. C 67, 027002 (2003).
39

e
aB 
e
e
Zm c

me e
aB
m
~1/ 207




 free  2.197019(21) 106 sec




Since  is close to the atom 2so the capture
3 4
probability is bigger: Z  1S 0 ~ m me  Z
.
The rates become comparable for Z~10.
In proton, 0.16% branching ratio of OMC.

Doron Gazit - The weak structure
of the nucleon
August 2009
40


The branching ration is very small (10-8 in
hydrogen).
Doron Gazit - The weak structure
of the nucleon
August 2009
41


Due to the huge effects of the nuclear structure,
studying the weak structure of the nucleon in
muon capture processes has reduced to the
proton.
Studies of OMC and RMC on hydrogen are hard:
◦ Depend on the transition rate between ortho- and
para-hydrogen.
◦ Have small branching ratios.
Doron Gazit - The weak structure
of the nucleon
August 2009
42

expr
g
The MuCap result: P  7.3  1.2
is consistent with cPT prediction: gP  8.26  0.23


but with far bigger uncertainty.
The RMC result clearly deserves
more work,

though probably in the atomic side.
gPexpr  12.8  1.1

More information is needed from other nuclei.

RMC: G. Jonkmans et al., Phys.
Rev. Lett. 77, 4512 (1996)
Doron Gazit - The weak structure
of the 99,
nucleon
August 2009 (2007).
OMC: V. A. Andreev et al., Phys. Rev. Lett.
0322002
43

For the (exclusive) process 3He(,) 3H
an incredible measurement ( 0.3%) exists:
  3 He    +t  1496  4 Hz
stat

ab-initio calculations, based on
phenomenological MEC or  excitation:

◦ Congleton
and Truhlik [PRC, 53, 956 (1996)]: 150232
Hz.
◦ Marcucci et. al. [PRC, 66, 054003(2002)]: 14844 Hz.

The main critique – too much freedom, without
microscopic origin.
◦ Did not include radiative corrections increase the cross
section by 3.00.4%.
Ackerbauer Doron
et al
, Phys.
Lett.
B417, 224 (1998).
Gazit
- The weak
structure
Czarnecki, Marciano, Sirlin, Phys. ofRev.
Lett
99, 032003
the nucleon August
2009
44


Using the EIHH method to solve for the wave
functions, with AV18/UIX potential:
 =1499(2) (3)NM (5)t (6)RC 1499 16 Hz





Only free parameter calibrated using triton halflife.
To be compared with: EXP 1496  4 Hz
The dependence on the nuclear model is
negligible.
The role of MEC ~ 12%! (compare to the 2% in
triton b decay
where it was calibrated).
This allows to constrain the weak structure of the
nucleon.
Doron Gazit - The weak structure
of the nucleon
August 2009
45
Form Factor
This work
Pseudo-scalar 8.13±0.5
gP(q2=-0.954m2)
Induced scalar
meFS/FV
Induced
pseudotensor GT
Theoretical
estimation
7.99±0.2
(HBcPT)
Experimental
gP(q2=-0.88m2)=
7.3±1.1
(0.5±2)×10-4
-
gt
 0.1(0.68)
gA
gt
 0.0152(53)
gA
gt
 0.36 at 90%
gA
QCD sum rules
-0.0011±0.0013
(Towner & Hardy)


H. Shiomi, J. Korean Phys. Soc. 29 (1996) S378.

Doron Gazit - The weak structure
of the nucleon
August 2009
46


Few body nuclear physics acts as a pivot between
QCD and heavy nuclei.
The current precision era in few-body nuclear
physics provides an opportunity to study the
weak structure of the nucleon:
◦ Using precision measurements of weak interactions in
nuclei one can constrain the bare form factors, as well
as their “evolution” inside nuclei, without free
parameters.
◦ Constraints on strong properties are possible.
◦ In particular, the upcoming MuSun measurement of 
capture on the deutron will enable:
to calibrate the 3NF at the 2-body level!
Doron Gazit - The weak structure
of the nucleon
August 2009
47
◦ Going to heavier nuclei, mainly A=6-8 and A=10, within cPT,
should be a holy grail, as it will open the door to new
constraints of CVC and second class currents.



Microscopic understanding of weak reactions
validates cross-sections predicted for astrophysics,
which are out of reach experimentally.
Using AdS/QCD for the calculation of weak couplings
of the nucleon seems like a good approximation!
Open questions:
◦ Role of  excitations in weak reactions within cPT?
◦ Role of a1?
◦ How far can we go in momentum transfer within cPT?
Doron Gazit - The weak structure
of the nucleon
August 2009
48
Doron Gazit - The weak structure
of the nucleon
August 2009
49

Available methods for solving
exactly the Schrödinger
equation for few body
systems, from their nucleonic
degrees of freedom.




HH
NCSM
GFMC
FY
ab-initio calculations





High precision nuclear
interaction, phenomenological
or cPT based.
Consistent microscopic
approach for the construction
of (meson exchange) currents
in the nucleus.
HBcPT
Allows parameter free calculations of nuclear wave functions
and low-energy reaction rates, with sub-percentage
accuracy.
Allows extraction of the weak structure of the nucleon from
the strongly-correlated nuclear wave function.
Offers a hint on the in-medium evolution of the weak
structure.
Doron Gazit - The weak structure
of the nucleon
August 2009
50

Contrary to the vector coupling, the axial
constant is renormalized.
◦ Had the quarks were non-relativistic:
rr
gA    5 /3
◦ The deviation is a reflection of the relativistic dynamics
of the u and d quarks in the nucleon.


Thus, its numerical
calculation is a test for our

understanding of QCD.
Still, experiment provides the most accurate
result.
gA 1.2695(29)
2


r
A
2
 Oq 4 
GA q 2  gA 
1
q

 - The weak structure
Doron
Gazit
6

 of the nucleon
August 2009
51


2


r
A
4
q 2 

O
q
momentum: GA q2  gA 1



6


At finite
From neutrino scattering:
rA2  0.666  0.014 fm 2




From pion-electroproduction:
rA2  0.639  0.010 fm 2

This axial radius discrepancy was solved in
Baryon cPT, which allowed including finite pion
mass in thepion-electroproduction.
The “radius” measured in pionelectroproduction:
rA2
 elec.
 rA2 
3  12 
1 2 
2 
64F   
Doron Gazit - The weak structure
Bernard, Kaiser, Meissner, Phys. Rev. Lett. 691,
877
(1992).
of the
nucleon
August 2009
52


Schindler et al. have
included a1 in their
manifestly Lorentz
invariant cPT.
They showed that it
has an effect only at
higher energy.
Doron Gazit - The weak structure
Schindler et al, Phys. Rev. C, 75, 025202 (2007)
of the nucleon
August 2009
53



FV(q0)=1 in the quark
level.
FV(q0)=1 in the nucleon
level.
FV(q0)=1 inside nuclei.
Renormalization of gV(q0)





gA(q0)=1 in the quark
level.
gA(q0)=1.27 in the
nucleon level.
gA(q0)1 inside
nuclei???
Renormalization of gA(q0)
“Restoration of axial symmetry”.
The implications are immense, e.g., weak
reaction rates in supernovae.
Doron Gazit - The weak structure
of the nucleon
August 2009
54