The weak structure of the nucleon from muon capture on 3He

0.08 MB·English

by  Doron Gazit

The weak structure of the nucleon
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3
0 from muon capture on He
0
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Doron Gazit

n
a Institute for Nuclear Theory, Universityof Washington, Box 351550, 98195, Seattle, WA, USA.
J

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] Abstract
h
-t I use a microscopic calculation of the weak capture process 3He(µ−,νµ)3H, to extract and
l
c constrain the weak form factors of the nucleon, particularly the induced pseudo-scalar, and
u the second-class currents. The induced pseudo-scalar form-factor is found to agree with the
n prediction of chiral perturbation theory. The constraint found on the conservation of vector
[ current (CVC) hypothesisis the tightest todate.

1
v
Key words:
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PACS: 23.40.-s,12.15.-y,27.10.+h,14.20.Dh
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5
0
1. The weak structure of the nucleon is a reflection of the influence of quantum chromo-
0 dynamics(QCD)onrenormalizingthecouplingsofweakprobestothenucleoniccurrent.
9 Thus,itsmeasurementcanbeusedtoconstrainandcheckthetheoryatlowenergies.The
0 structure of the current, transferring momentum qµ, is dictated by Lorentz invariance,
:
v including a part with polar-vector symmetry [1]:
i
X i g
JˆV =F (q2)γ + F (q2)σ qν + s q , (1)
r µ V µ 2M M µν m µ
a N µ
and with axial-vectorsymmetry:
G (q2) g
−JˆA =G (q2)γ γ + P γ q +i t γ σ qν. (2)
µ A µ 5 m 5 µ 2M 5 µν
µ N
Herem andM arethemassesofthemuonandnucleon,respectively.Thefactthatthe
µ N
nucleon has a complex internal structure implies a deviation from the V −A structure,
i.e. F /G 6= 1, and induces non-zero scalar g , pseudo-scalar G , weak-magnetic F ,
V A s P M
and axial-tensor g , form factors. G is well known, mainly from neutron β-decay rate.
t A
Thesimilaritybetweenthestructureoftheweakvectorcurrent,andtheelectro-magnetic
PreprintsubmittedtoElsevier 5January2009
currenthasledtothe CVC hypothesis,whichsuggeststhatthesecurrentsareconnected
via a rotation in isospin space. Implicitly, this entails that the weak vector form-factors
are identical to the electro-magnetic form factors, and that g = 0, as it precedes a
s
term which breaks charge conservation. The latter can be connected to the fact that
the g and g terms have abnormal behavior under G-parity, the combination of charge
s t
conjugation and rotation in isospin space, broken only by the small difference between
the up and down quarks masses. Thus, g and g are highly suppressed [3]. The induced
s t
pseudo-scalar form-factor G is rather poorly known, to an accuracy of about 15% [4],
P
as it vanishes for low-momentum processes.
Theweakprocessinwhichamuoniscapturedbyanucleushasbeenknownasauseful
laboratoryfortestingweakcurrentsinthenucleus,duetotherelativelyhighmomentum
transfer in this process, ~|~q|/c ∼ m , which allows probing of all weak form-factors [2].
µ
In this contribution,I reporta recentuse of the weak capture process3He(µ−,ν )3H, to
µ
extract and constrain the weak form factors of the nucleon [5]. The amazingly accurate
measurement of this decay rate Γexp =1496(4)Hz [6], makes this reaction an ideal test-
site for the weak structure of the nucleon. This, however, necessitates a description of
the problem from its nucleonic degrees of freedom, and its dynamics without any free
parameters. The latter has limited the ability of previous attempts to use the reaction
to constrain the nucleonic weak form-factors [7].
Here,Iuseadifferentapproachtotheproblem,resultinginaparameterfreeevaluation
of the capture rate. First, the bound states of the trinuclei are calculated using realistic
nuclear forces, specifically the nucleon-nucleon Argonne v (AV18) potential [8] com-
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bined with the Urbana-IX (UIX) three nucleon force [9]. The calculation, accomplished
using the EIHH method [10], yields the experimental binding energies (within 20keV)
and charge radii, and compares well with other ab-initio methods [11]. Second, the dy-
namicsofthecaptureisdescribedusingchiralperturbationtheory(χPT)tofourthorder.
χPTisaneffectivetheoryofQCDatlow-energies,thatallowsasystematicperturbative
expansionoftheQCDLagrangian[12].Bydescribingthedynamicsoftheproblemwithin
χPT, a straight connection to the underlying theory is achieved. Up to fourth order in
χPT, the weak current includes a single nucleon current of the form of Eqs. (1-2). To
this order, CVC holds, and g = 0. The pion form-factor was calculated within χPT
t
[13], to be G (q2 =−0.954m2)=7.99(20). In addition to the single nucleon current, at
P µ
third order in chiral perturbation theory, meson exchange currents appear. Contrary to
oldmodels,the constraintsexertedbythe chiralsymmetrydictatethe structureofthese
currents.To the calculatedorder,they include onlyone unknownparameter,originating
in a contact term of two nucleons, coupled to an external lepton, and calibrated using
the triton β-decay rate. This parameter free, hybrid approach, named EFT*, has had
impressive success in the literature [14].
In principle, the nuclear forces should be derived from the same chiral Lagrangian
as the currents, and to the same order. However, this inconsistency is not expected to
change the results significantly due to two main reasons. First, in a previous study of
the reaction, Marcucci et al. [7] have shown that the capture is essentially independent
ofthe nuclearforce,aslongasitdescribescorrectlythe binding energiesofthe trinuclei.
Second, in a recent calculation of triton decay, within chiral perturbation theory, the
short-rangecorrelationsof weakcharacterwere shownto be disentangledfromthe short
range correlationin the wavefunctions [15]. Thus, only the long range part of the forces
affectthe reaction.This partis similarin the chiralforcesandin the AV18+UIXmodel.
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This fact is apparent in the weak dependence the current calculation has on changing
the χPTcutoff(lessthan0.2%),indicatingthattheneededdegreesoffreedomaretaken
into account.
ThepredictionofthecurrentapproachforthecapturerateisΓ=1499(10) (6) Hz,
NM RC
consistent with the experimental measurement Γexp = 1496(4)Hz. The first theoretical
stat
error is due to the dependence in the nuclear model, including the χPT cutoff depen-
dence, and uncertainties in triton half-life and in the low-energy constants χPT cutoff.
Theseconderrorisduetotheoreticaluncertaintyintheelectroweakradiativecorrections
calculatedfornuclei[16].Theradiativecorrections,whichincreasethedecay-rateby3%,
were not takeninto accountin previousstudies. The resulting constraintonthe induced
pseudoscalar form factor, G (q2 = −0.954m2) = 8.13±0.6, is in very good agreement
P µ
withthe χPT prediction.This shouldbe comparedto the currentexperimentaldetermi-
nation, G (q2 =−0.88m2)=7.3±1.2 [4].
P µ
The axialG-paritybreaking term is constrainedby the calculationto be gt =−0.1±
gA
0.68,comparabletothecurrentexperimentallimit|g |<0.3at90%CL[17],thoughstill
t
far from its theoretical determination, gt =−0.0152(53)[18].
gA
The extracted value for the CVC breaking form factor according to this work is g =
s
−0.005± 0.040. This represents a significant improvement to the current limit g =
s
0.01±0.27 [3].
Summarizing, I have shown that the weak process 3He(µ−,ν )3H, can be used to
µ
get prominent bounds on the weak structure of the nucleon. In particular, the induced
pseudo-scalar form factor is constrained to ±8%, and agrees with χPT prediction[13],
and the CVC hypothesis is confirmed to a new limit |g |<0.045.The calculation shows
s
the potential of nuclear ab initio calculations of weak processes as quantitative tests for
the weak structure of the nucleon, as well as other properties of QCD at low energy.
This work was supported, in part, by DOE grant number DE-FG0200ER41132.
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