Global analysis o pa i y- iola ing asymme y da a o elas ic
elec on sca e ing
R. González-Jiménez,1J. A. Caballe o,1and T. W. Donnelly2
1Depa amen o de Física A ómica, Molecula y Nuclea , Uni e sidad de Se illa, 41080 Se illa, Spain
2Cen e o Theo e ical Physics, Labo a o y o Nuclea Science and Depa men o Physics,
Massachuse s Ins i u e o Technology, Camb idge, Massachuse s 02139, USA
(Recei ed 20 Ma ch 2014; published 1 Augus 2014)
We pe o m a s a is ical analysis o he ull se o pa i y- iola ing asymme y da a o elas ic elec on
sca e ing including he mos ecen high p ecision measu emen om Q-weak. Gi en he basis o he
p esen analysis, ou es ima es appea o a o nonze o ec o s angeness, speci ically, posi i e (nega i e)
alues o he elec ic (magne ic) s ange o m ac o s. We also p o ide an accu a e es ima e o he axial-
ec o nucleon o m ac o a ze o momen um ans e , Gep
Að0Þ. Ou s udy shows Gep
Að0Þ o be impo an ly
educed wi h espec o he cu en ly accep ed alue. We also ind ou analysis o da a o be compa ible wi h
he S anda d Model alues o he weak cha ges o he p o on and neu on.
DOI: 10.1103/PhysRe D.90.033002 PACS numbe s: 12.15.-y, 14.20.Dh, 14.65.B , 25.30.B
O e he yea s pa i y- iola ing (PV) elec on sca e ing
has p o ided a g ea deal o p ecise in o ma ion on he
s uc u e o he nucleon. A a ie y o expe imen s unning
on di e en a ge s, om hyd ogen o hea ie sys ems
wi h emphasis on deu e ium and helium, ha e added
s ong cons ain s on he elec oweak o m ac o s.
Mo eo e , he high p ecision eached by he mos ecen
expe imen s [1,2] will se e as a es o he S anda d
Model (SM) p o iding a signi ican cons ain on non-
pe u ba i e QCD e ec s.
The Q-weak Collabo a ion has ecen ly de e mined he
weak cha ge o he p o on co esponding o he analysis o
app oxima ely 4% o he da a collec ed in he expe imen
[2]. The main objec i e o he Q-weak expe imen is o
p o ide a alue o sin2θWwi h a 0.3% p ecision, ha is, he
weak cha ge o he p o on o 4%. This ex emely small
unce ain y will p o ide a signi ican es o he SM. In [2] a
global i o da a aken o hyd ogen, deu e ium and helium
a ge s up o jQ2j¼0.6ðGeV=cÞ2was also done p o iding
some es ima es o he weak neu al cu en (WNC)
couplings. These esul s a e compa ible wi h he ones
ob ained in p e ious analyses pe o med by Young and
collabo a o s [3,4]. Howe e , he use o da a only up o
jQ2j¼0.6ðGeV=cÞ2[in he case o [3] only da a o
jQ2j<0.3ðGeV=cÞ2we e conside ed], in addi ion o
pa icula assump ions o he Q2expansion o he o m
ac o s, ha e con inced us o he necessi y o a new and
mo e comple e analysis o he p ocess. Mo eo e , when
such high le els o p ecision a e he goal, mixing da a
o elas ic sca e ing on he p o on and 4He wi h hose
co esponding o he quasielas ic (QE) p ocess, make i
di icul o disen angle e ec s due o he nucleon s uc u e
om o he s di ec ly linked o inal s a e in e ac ions, o -
shell e ec s, ew-body nuclea s uc u e, e c. Acco dingly,
in his wo k we es ic ou sel es o elas ic elec on
sca e ing p ocesses, and make use o all a ailable da a
in he li e a u e wi h no es ic ion on he Q2 ange
conside ed.
The PV asymme y (APV) in he case o elas ic elec on-
p o on (ep) sca e ing may be w i en as ollows [5]:
APV
ep ¼A0
2G½aAðεGp
E~
Gp
EþτGp
M~
Gp
MÞ
−aVffiffiffiffiffiffiffiffiffiffiffiffi
1−ε2
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
τð1þτÞ
pGp
MGep
A;ð1Þ
whe e τ≡jQ2j=ð4M2Þand G≡εðGp
EÞ2þτðGp
MÞ2wi h M
he nucleon mass and Gp
E;M he elec omagne ic (EM) o m
ac o s o he p o on. The e m A0de e mines he scale o
he PVasymme y and is gi en by A0¼GFjQ2j=ð2ffiffiffi
2
pπαÞ
wi h GF he Fe mi coupling and α he ine s uc u e
cons an . Finally, aV¼−1þ4sin2θWand aA¼−1a e
he ec o and axial- ec o WNC elec on couplings,
and we ha e in oduced he kinema ical ac o ε¼½1þ
2τð1þτÞ an2θe=2−1which depends on he sca e ing
angle θe.
Assuming cha ge symme y, he WNC o m ac o s can
be w i en as ollows:
~
Gp
E;MðQ2Þ¼ξp
VGp
E;M þξn
VGn
E;M þξð0Þ
VGs
E;M
Gep
AðQ2Þ¼ξT¼1
AG3
AþξT¼0
AG8
Aþξð0Þ
AGs
A;
whe e Gs
E;M a e he elec ic (E) and magne ic (M) s ange
o m ac o s and G3;8;s
Aa e he iso ec o (3), isoscala (8)
and s ange (s) con ibu ions o he axial- ec o o m ac o
o he p o on (Gep
A). The ξcoe icien s ep esen he WNC
e ec i e coupling cons an s ha a e gi en in e ms o he
weak mixing angle (θW) and adia i e co ec ions (see [5,6]
o explici exp essions).
In his wo k we also conside he da a ob ained by he
HAPPEX Collabo a ion on elas ic e-4He sca e ing. In his
PHYSICAL REVIEW D 90, 033002 (2014)
1550-7998=2014=90(3)=033002(5) 033002-1 © 2014 Ame ican Physical Socie y
case he PVasymme y in ol es he a io o he wo nuclea
monopole o m ac o s: he EM and he WNC ones. Hence,
nuclea e ec s also play a ole in he desc ip ion o he
p ocess— o discussions o how such e ec s a ise, see
[7–9]. I can be shown ha he use o one-body ope a o s
(leading-o de app oxima ion) and he assump ion ha
isospin mixing can be igno ed o he 4He g ound s a e
yield o he a io o nuclea o m ac o s simply a a io o
single-nucleon o m ac o s. The la e poin was i s
discussed in [7] and hen e isi ed in a la e s udy [10]
(see, especially, Fig. 2in ha e e ence). Wi hin he con ex
o he app oaches discussed he e, he e ec s o isospin
mixing in 4He we e ypically ound o be mo e han an
o de o magni ude smalle han he e ec s om s ange-
ness con en in he nucleon, in con as o he expec a ions
o hea ie nuclei [8,9]. This issue is no comple ely closed,
howe e , as o he app oaches ind somewha la ge e ec s
om isospin mixing [11]. In u u e expe imen al s udies,
p e e ably a low momen um ans e s, using a a ie y o
N¼Znuclei i should be possible o add ess his p oblem
mo e de ini i ely; o his s udy we con inue o make he
abo e assump ions, in which case he PVelas ic asymme y
can be w i en in he o m [6]
APV
eHe ¼−
A0
2ðξp
Vþξn
VÞþ2ξð0Þ
VGs
E
Gp
EþGn
E:ð2Þ
Thus, hese da a a e also sensi i e o he WNC nucleon
s uc u e, and hey gi e in o ma ion ha complemen s wha
is ob ained h ough elas ic ep sca e ing.
In a ecen s udy [5] we showed ha a jQ2j¼
1ðGeV=cÞ2( he cu en limi o asymme y da a) he
dispe sion in APV due o he use o di e en p esc ip ions
o he EM o m ac o s (some o hem accoun ing o
wo-pho on exchange con ibu ions) was ∼3% in he e y
o wa d limi (θe¼5°) ge ing much smalle o la ge
angles and lowe jQ2j. The impac o hese unce ain ies
a he pa icula Q-weak kinema ical condi ions has been
explo ed in de ail in [5]. The e o e, in he p esen wo k we
neglec he unce ain ies associa ed wi h he pa icula
desc ip ion o he EM nucleon o m ac o s. On he
con a y, APV is highly sensi i e o he elec ic and
magne ic s ange o m ac o s Gs
E;MðQ2Þand o he axial-
ec o one Gep
AðQ2Þ. In he la e adia i e co ec ions can
in oduce e y s ong e ec s. In his wo k we pe o m a
global i o he i e pa ame e s: ξp
V,ξn
V,ρs,μs( hese wo
linked o he elec ic and magne ic s ange o m ac o s [6])
and he axial- ec o o m ac o a ze o momen um ans e :
Gep
A≡Gep
Að0Þ. Ou p edic ions, based on a s a is ical
analysis o he ull se o PV asymme y da a o elas ic
ep sca e ing (SAMPLE [12], HAPPEX [13–16],PVA4
[17–19],G0[20,21] and Q-weak [2]) as well as he wo PV
elas ic e-4He da a (HAPPEX [15,22]), a e compa ed wi h
all p e ious analyses p esen ed in he li e a u e.
Assuming he adia i e co ec ions (RC) o be mildly
dependen on he ene gy, namely, on he pa icula
kinema ics selec ed, he esul s o ou analysis could se e
as a es o hei s eng h. Thus he dispe sion ound in he
alues o ξp
Vand ξn
Vwi h espec o he co esponding ee-
le el esul s (see [6] o de ails) could p o ide in o ma ion
on Rp
Vand Rn
V. Simila ly, he de ia ion in Gep
Að0Þwould
cons ain he RC con ibu ions in he axial cu en as well
as possible e ec s linked o he anapole momen [23–25].
Recen ly a la ge amoun o heo e ical wo k has been
ca ied ou ega ding he ene gy-dependen γZ-box co -
ec ion [26–29]. Ob iously, he esul s o any global
analysis o da a a e a ec ed by he co ec ion associa ed
wi h he γZbox. Howe e , a p esen his co ec ion can
only be applied o a limi ed se o da a: e y o wa d
sca e ing angles. Hence in his wo k we do no in oduce
such co ec ions, so ha all da a a e ea ed consis en ly
in he global analysis. Ou p esen analysis o he weak
cha ges o he p o on and neu on, wi h hei unce ain ies
linked o he pa ame e s ha ha e been es ima ed, is
consis en wi h he s udy epo ed by he Q-weak
Collabo a ion [2], whe e he γZ-box ene gy-dependen
co ec ion was applied. Howe e , some cau ion should
be d awn conce ning his ou come because o he p esen
limi ed analysis o Q-weak da a (only 4% o da a ha e been
conside ed). Once he analysis is ex ended o he 100% o
he Q-weak da a, and aking in o accoun ha ξp
Vis
basically no cons ained by any o he da a, he γZ-box
co ec ion o he Q-weak da a will become c ucial.
Be o e en e ing in o a de ailed discussion o he esul s, a
gene al commen on he i p ocedu e should be made.
Speci ically, he cu en ly accep ed alue o he axial- ec o
o m ac o a Q2¼0, namely, Gep
Að0Þ¼−1.04 0.44
(see [30]), has been included as an addi ional expe imen al
cons ain in he global i . Al hough a signi ican con i-
bu ion o Gep
Acomes om G3
A≡gA¼1.2695 ha is well
de e mined om Gamow-Telle β-decay measu emen s,
adia i e co ec ions can in oduce an impo an unce ain y
in Gep
AðQ2Þ(see discussion in [5]). Hence he e is s ill oom
in he global i p ocedu e o a ia ion o he speci ic alue
o Gep
AðQ2Þ. In summa y, ou analysis akes in o accoun
all 31 expe imen al da a o he PVasymme y a ailable in
he li e a u e plus he es ic ion applied o Gep
Að0Þ.
The Q2dependence in he ec o s ange and axial-
ec o o m ac o s has been aken in hei usual o m [5,6],
namely, dipole (dipole imes τ) o Gs
M(Gs
E) wi h a ec o
mass MV¼0.84 GeV, and dipole shape o he axial o m
ac o wi h he axial mass MA¼1.03 GeV. The GKex
p esc ip ion [31–33] has been used o he EM o m ac o s.
The i p ocedu e consis s in minimizing he χ2 unc ion:
χ2¼½Aexp −A heT½V−1½Aexp −A he;ð3Þ
whe e Aexp con ains all da a and A he akes ca e o he
co esponding heo e ical p edic ions ha depend on he
i e pa ame e s conside ed: ξp
V;ξn
V;ρs;μs;G
ep
A. The e m V
ep esen s he co a iance e o ma ix de ined as
GONZÁLEZ-JIMÉNEZ, CABALLERO, AND DONNELLY PHYSICAL REVIEW D 90, 033002 (2014)
033002-2
Vij ¼ðσunco
iÞ2δij þσco
iσco
jð4Þ
wi h σunco
iand σco
i he unco ela ed and co ela ed unce -
ain ies o he i h measu emen , espec i ely. In his wo k
only co ela ed e o s epo ed by G0 Collabo a ion a e
conside ed.
The esul s o he χ2 i a e summa ized in Table Iwhich
con ains he alues o he i e ee pa ame e s as well as
hei 1σe o s (χ<χ2
MIN þ1). These alues a e in good
ag eemen wi h he SM weak cha ges o he p o on and
neu on [34]:ξp
V¼0.0710 0.0007 and ξn
V¼−0.9890 
0.0007. On he con a y, Gep
Aex ac ed om he i ,
Gep
A¼−0.62 0.41, is signi ican ly lowe han he alue
Gep
A¼−1.04 0.44 gi en in [30]. Howe e , no e ha bo h
esul s a e a ec ed by la ge e o s ha make he wo
p edic ions o e lap. These esul s may e lec impo an
e ec s coming om highe -o de con ibu ions ( adia i e
co ec ions) as well as om al e na i e desc ip ions o
he Q2dependence. The use o he s anda d dipole jQ2j
dependence o he axial o m ac o in oduces a sys em-
a ical unce ain y in he i ha p opaga es in o he speci ic
alue o Gep
Aa jQ2j¼0. O he unc ional dependences
[5] as well as he use o a di e en alue o he axial
mass MA≈1.35 GeV=c as ound by he MiniBooNE
Collabo a ion [35] may lead o sligh ly di e en esul s.
Finally, in spi e o he signi ican e o s associa ed wi h he
s ange o m ac o s, ou global i a o s a la ge-posi i e
s ange cha ge adius ρs(elec ic s angeness), whe eas he
s ange magne ic momen μs ends o be nega i e al hough
s ill being compa ible wi h ze o con ibu ion.
The co ela ion coe icien s be ween pai s o he i e
pa ame e s conside ed in he χ2 i a e gi en in Table II.
No ice he ex emely small co ela ion o he pai
ðξp
V;G
ep
AÞ. This esul suppo s he idea ha a de e mina ion
o he weak cha ge o he p o on is no a ec ed by he la ge
unce ain y in Gep
A. The co ela ion alues be ween ξp
Vand
he h ee emaining pa ame e s, ξn
V,ρsand μs, al hough
ela i ely small, should be aken in o accoun ca e ully i a
high p ecise de e mina ion o he p o on weak cha ge is
desi ed. To conclude, he es o pa ame e s: ξn
V,Gep
A,ρs
and μs, a e e y s ongly co ela ed.
In Fig. 1we show all PV asymme y da a o elas ic
elec on sca e ing compa ed wi h ou heo e ical p edic-
ions (ze o line). The inne e o ba s ep esen he
expe imen al e o s while he ou e ones (in ed) include
he heo e ical unce ain y p o ided by he global i
co esponding o he 1σcon idence le el. The s ong
co ela ion be ween some o he pa ame e s has been aken
in o accoun in o de o de e mine he heo e ical e o .
In Fig. 2we show he 95% con idence con ou s ob ained
in ou analysis ex apola ed o jQ2j¼1ðGeV=cÞ2. The
esul s o ou p esen i ( ed ellipse) a e compa ed wi h
hose om ou p e ious wo k [5] (blue cu e). The
signi ican di e ence in he a eas spanned by he wo
ellipses is due o he di e en app oaches conside ed in
he wo cases. In [5]a global analysis o he ull se o PV
TABLE I. Values o he ee pa ame e s om he global i .
The educed χ2 alue is χ2
MIN=27 ¼1.30.
ξp
Vξn
VGep
A
0.070 0.013 −0.946 0.044 −0.62 0.41
ρsμs
0.92 0.58 −0.26 0.26
TABLE II. Co ela ion coe icien s be ween he ee pa ame e s
o he i .
ξn
VGep
Aρsμs
ξp
V−0.191 0.0469 0.262 0.162
ξn
V0.392 0.552 −0.775
Gep
A0.711 −0.749
ρs−0.870
0.1 1
|Q2| (GeV/c)2
(Aexp - A heo) / A0
HAPPEX 4He
Qweak
HAPPEXa
SAMPLE
HAPPEXb
G0- o wa d
G0-backwa d
HAPPEXIII
PVA4-145ª
PVA4-35.5ª
HAPPEX99
-0.1
-0.05
0
0.05
0.1
FIG. 1 (colo online). Full se o PV asymme y expe imen al
da a o elas ic elec on sca e ing. The da a a e no malized by
sub ac ing ou heo e ical asymme y and di iding by A0.
-1 -0.5 00.5 11.5
GM
s
-0.1
-0.05
0
0.05
0.1
GE
s
This wo k (95%)
Young e al. (95%)
Liu e al. (95%)
Phys. Rep. (95%)
Leinwebe e al.
Doi e al.
|Q2|=0.1 (GeV/c)2
FIG. 2 (colo online). 95% con idence le el cons ain ellipses
in he plane Gs
E-Gs
Ma jQ2j¼0.1ðGeV=cÞ2: ed ↔ his wo k,
g een ↔[3],b own↔[30], blue ↔[5]. Black and o ange
c osses a e he heo e ical p edic ions p esen ed in [36,37] and
[38], espec i ely.
GLOBAL ANALYSIS OF PARITY-VIOLATING ASYMMETRY …PHYSICAL REVIEW D 90, 033002 (2014)
033002-3
asymme y da a, including only ep sca e ing, was pe -
o med (28 da a) aking only ρsand μsas ee pa ame e s
(see [5] o de ails). On he con a y, he ed ellipse
co esponds o he p edic ions ob ained by simul aneously
i ing i e pa ame e s. This la ge numbe o ee pa am-
e e s explains he signi ican inc ease in he a ea. No e ha
he p esen analysis seems o a o posi i e (nega i e)
alues o ρs(μs). Howe e , he case o ze o s angeness,
i.e., ρs¼μs¼0, is s ill inside he 95% con idence le el in
ou p esen analysis ( ed cu e), and only sligh ly ou side
he egion ob ained om ou p e ious s udy (blue).
We also compa e ou p edic ions wi h he s a is ical
analyses o da a pe o med by Liu e al. [30] (b own
ellipse) and Young e al. [3] (g een ellipse). Also shown o
e e ence he heo e ical p edic ions p o ided by Leinwebe
e al. [36,37] (black c oss) and Doi e al. [38] (o ange
c oss). The ellipses co esponding o he wo ks [3,30] a e
he esul s o χ2 i s o he PV asymme y da a o elec on
sca e ing on helium, deu e ium and hyd ogen in he
icini y o jQ2j≈0.1ðGeV=cÞ2. In pa icula , in he wo k
o Liu e al. [30] a o al o 10 da a in he ange 0.091 ≤
jQ2j≤0.136 ðGeV=cÞ2we e employed wi h only wo ee
pa ame e s: he elec ic and magne ic s ange o m ac o s,
Gs
EðjQ2j¼0.1ðGeV=cÞ2Þ,Gs
MðjQ2j¼0.1ðGeV=cÞ2Þ.On
he con a y, in [3] a o al o 19 da a in he ange 0.038 ≤
jQ2j≤0.299 ðGeV=cÞ2we e used. In his case, ou ee
pa ame e s we e conside ed in he i : he wo ec o
s ange o m ac o s and he axial- ec o o m ac o o
he p o on and neu on a ze o momen um ans e ed,
Gep
Að0Þand Gen
Að0Þ.
In Fig. 3we p esen he 95% con idence le el ellipse in
he (μs;G
ep
A) plane. Resul s ha e been ex apola ed o he
kinema ical si ua ion jQ2j¼0.1ðGeV=cÞ2. Ou p edic ion
( ed ellipse) is compa ed wi h he one o Young e al. [3]
(g een ellipse). As shown, ou analysis imp o es signi i-
can ly he p e ious p edic ion (impo an educ ion in he
a ea o he ellipse).
To conclude, we apply ou analysis o he de e mina ion
o he WNC e ec i e couplings. Thus, we build he
95% con idence le el con ou in he plane ðC1u−C1d;
C1uþC1dÞ. This is shown in Fig. 4by he ed ellipse. Ou
p edic ion is also compa ed wi h p e ious analyses gi en
in he li e a u e: blue ellipse [5], g een illed ellipse [4], and
b own ellipse [2]. The yellow one is he esul o combining
he cons ain s coming om ou p esen analysis ( ed
ellipse) wi h hose om A omic PV in Cesium (APV-Cs)
expe imen s (magen a ho izon al band, see [34,39,40] o
de ails). Likewise, he cyan ellipse is he esul o he
combined analysis p esen ed in [2].
This combined analysis allows us o ge a mo e accu a e
de e mina ion o he WNC qua k coupling cons an s:
C1u¼−0.186 0.006,C1d¼0.338 0.006 wi h a co -
ela ion coe icien −0.966. Simila ly, he weak cha ges
o he p o on and neu on esul : ξp
V¼0.070 0.013
and ξn
V¼−0.978 0.012 wi h a co ela ion coe icien
−0.716. Ou esul s a e in excellen ag eemen wi h he
S anda d Model p edic ions [34]:ξp
V¼0.0710 0.0007,
ξn
V¼−0.9890 0.0007 [C1u¼−0.1885 0.0002,C1d¼
0.3415 0.0002].
Summa izing, we ha e p esen ed a comple e s a is ical
analysis o all PV asymme y da a a ailable o elas ic
sca e ing [41] on he p o on and on 4He. The χ2 es is
based on he simul aneous i o i e ee pa ame e s ha a e
shown o be s ongly co ela ed in mos o he cases. This
esul may indica e ha some cau ion should be exe cised
when conside ing p e ious analyses ha a e based on a
educed numbe o pa ame e s. Ou new s udy seems o
a o ec o s angeness di e en om ze o. This is
consis en wi h ou p e ious indings [5]. Mo eo e , a
s iking esul in ou analysis is he unexpec edly lowe
alue o Gep
A. Howe e , he axial- ec o o m ac o is
-3 -2 -1 0 1 2 3
GA
ep
-1.5
-1
-0.5
0
0.5
1
1.5
GM
s
Young e al. (PVES, 95%)
This wo k (95%)
|Q2|=0.1 (GeV/c)2
FIG. 3 (colo online). 95% con idence le el cons ain ellipse in
he plane Gs
M-Gep
Aa jQ2j¼0.1ðGeV=cÞ2: ed ↔ his wo k,
g een ↔[3].
-0.6 -0.55 -0.5 -0.45 -0.4
C1u - C1d
0.12
0.14
0.16
0.18
C1u + C1d
APV Cs
Young e al. (PVES, 1σ)
Qweak Collab. (PVES, 95%)
Phys. Rep. (PVep, 95.45%)
This wo k (95%)
APV Cs + This wo k
APV Cs + Qweak Collab.
S anda d Model
FIG. 4 (colo online). Con idence le el ellipses om di e en
wo ks: ed ↔ his wo k, blue ↔[5], g een illed ↔[4], b own ↔
[2]. The magen a ho izon al band ep esen s he cons ain om
133Cs APV esul [39] (ex ac ed om [2]). The yellow (cyan)
ellipse is he esul o combining he analysis o his wo k
(Q-weak Collab a ion [2]) and he 133Cs APV esul . The
S anda d Model p edic ion is also ep esen ed as e e ence
(black c oss).
GONZÁLEZ-JIMÉNEZ, CABALLERO, AND DONNELLY PHYSICAL REVIEW D 90, 033002 (2014)
033002-4
known o be highly sensi i e o adia i e co ec ions ha
could explain his esul . In any case, mo e s udies a e
needed and ou p edic ion could simply be conside ed
as a signal o possible al e na i e desc ip ions o he Q2
dependence o Gep
A. Finally, ou esul s a e in acco dance
wi h he weak cha ges o p o on and neu on p o ided by
he S anda d Model.
This wo k was pa ially suppo ed by DGI (Spain):
FIS2011-28738-C02-01, by he Jun a de Andalucía
(FQM-160) and he Spanish Consolide -Ingenio 2000
p og ammed CPAN, and in pa (T. W. D.) by U.S.
Depa men o Ene gy unde coope a i e ag eemen DE-
FC02-94ER40818. R. G. J. acknowledges inancial help
om VPPI-US (Uni e sidad de Se illa).
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GLOBAL ANALYSIS OF PARITY-VIOLATING ASYMMETRY …PHYSICAL REVIEW D 90, 033002 (2014)
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