Radiative Corrections to Low-Energy Neutrino-Deuteron Reactions Revisited

0.04 MB·English

by  Takahiro Kubota

Radiative Corrections to Low-Energy
Neutrino-Deuteron Reactions Revisited
Takahiro Kubota
6 DepartmentofPhysics,GraduateSchoolofScience,
0 OsakaUniversity,Toyonaka,Osaka560-0043,Japan
0
2
Abstract. Theone-loopQEDandelectroweakradiativecorrectionstoneutrino-deuteronscattering
n
induced by the neutral current are reexamined, paying a particular attention to the constant term
a
whichhasneverbeentreatedproperlyinliterature.Thisproblemiscloselyrelatedtothedefinition
J
0 of the axial-vectorcoupling constant gA and requires thoroughcalculations of the constant terms
in the chargedcurrentprocesses, too. We find that the radiative corrections to the neutral current
2
induced reactions amount to 1.7 (1.5) per cent enhancement, if the Higgs boson mass is m =
H
3 1.5mZ(mH =5.0mZ)ThisnumberhappenstobeclosetothatgivenbyKurylovetal.,butweargue
v thatthisisaccidental.
1
8
0
This talk is based on the collaboration with Masataka Fukugita [1] (see also [2, 3]),
1
0 and is concerned with radiative corrections to the reactions occurring at the Sudbury
6 Neutrino Observatory (SNO). The observation of the solar neutrinos at SNO has been
0
playing important roles to resolve the solar neutrino problem [4]. The measurement of
/
h neutrino-deuteronscattering
p
-
p n +d −→ e−+p+p, (1)
e
e
h n e+d −→ n e+p+n (2)
:
v
i has now reached the level that radiative corrections should be included in the analyses
X
[5]. The first step toward evaluation of the radiative corrections to (1) and (2) was
r
a taken by Towner [6]. Some subtle problems associated with soft photon emission were
pointed out [7] and have been solved [8] by giving due consideration to the energy-
dependence of the wave function overlap between initial and final states. There has
remained, however, the problem as to the constant terms of the radiative correction, as
remarked by the authors of [8]. They have evaluated the corrections to (1) by assuming
implicitly that the inner correction to the Gamow-Teller part is the same as that to the
Fermitransition.
The transition amplitudes squared of the charged current processes in general are
expressedingeneral on theO(a )levelas
A(b )=(1+d (b )) f2 1+d F h1i2+g2 1+d GT hs i2 , (3)
out V in A in
(cid:2) (cid:0) (cid:1) (cid:0) (cid:1) (cid:3)
where f (≡ 1) and g are the vector and axial-vector coupling constants. The Fermi
V A
and Gamow-Tellermatrix elements are denoted by h1i and hs i, respectively. The outer
correction d (b ) is a function of the electron velocityb and is process-dependent [9].
out
(Seealsoref.[10]foranapproachbasedoneffectivefieldtheory.)Theinnercorrections
d F andd GT areincontrastindependentofchargedcurrentprocessesconsideredandare
in in
universalconstants[11,2].TheFermipartinnercorrectiond F hasbeenknownforlong
in
time[12], whiletheGamow-Tellerpart d GT was calculated onlyrecently [2].
in
The axial-vector coupling constant g˜ usually quoted in literature is extracted from
A
theneutronbetadecay usingtheformula
A(b )=(1+d (b )) 1+d F h1i2f2+hs i2g˜2 . (4)
out in V A
(cid:0) (cid:1)(cid:2) (cid:3)
Thepolarizedneutronbetadecayisalsousedtoextractg˜ insteadofg [3].Therelation
A A
betweeng and g˜ is obviouslygivenby
A A
1+d F
g2 = in g˜2 , (5)
A (cid:18)1+d GT(cid:19) A
in
andthisindicatesg 6=g˜ ,becauseofd F 6=d GTaswasshownbyexplicitcomputationin
A A in in
[2]. This,however,does notcause anypractical problem,sincetherelation between the
“bare"g andthe“redefined"g˜ isuniversal,sofarasweconsideronlychargedcurrent
A A
processes[11, 13]. Thus theanalysisof(1)in [5]need notbecorrected essentially.
If we consider neutral current processes such as (2), however, we have to be more
careful about the finite radiative corrections to the axial-vector coupling constant. The
reaction(2)is purelyoftheGamow-Tellertypeand itsamplitudesquared iswritten as
B(b )=(1+D GT)g2hs i2 , (6)
in A
where D GT is the O(a ) radiative corrections. Using the relation (5), we see that (6) is
in
expressedintermsofg˜ as
A
1+d F
B(b )=(1+D GT) in g˜2hs i2 . (7)
in (cid:18)1+d GT(cid:19) A
in
In [1], we have extracted D GT on the bases of the work of Marciano and Sirlin [14]
in
andhavefound
D GT = 0.0192 for m =1.5m , (8)
in H Z
D GT = 0.0173 for m =5.0m . (9)
in H Z
Combiningtheseresults withthepreviouscalculationoftheinnercorrections [2]
d F =0.0237, d GT =0.0262, (10)
in in
wefind thatthecrosssectionof(2)is enhanced bythefactor
1+d F
1+D GT in =1.017 for m =1.5m ,
in (cid:18)1+d GT(cid:19) H Z
(cid:0) (cid:1) in
1+d F
1+D GT in =1.015 for m =5.0m . (11)
in (cid:18)1+d GT(cid:19) H Z
(cid:0) (cid:1) in
Notethatthisisratherclosetothenumbergivenin[8]andthattheanalysisof(2)in[5]
using [8] need not be altered basically. We should, however, like to emphasize that the
approximateagreementofourresults(11)withthatof[8]issimplyduetoanaccidental
cancellation of errors of the latter, between those caused by putative identification of
constant terms for the Fermi and Gamow-Teller transitions for the charged current
reactions and minor errors in their treatment of the constant terms for neutral current
inducedreactions.
Throughout the present work, the so-called one-body impulse approximation is used
and the effect of the spectator nucleon is not included. See ref. [15] in this connection
for an approach based on heavy-baryon chiral perturbation theory. We note as a final
remarkthattheconstanttermfortheradiativecorrectiontotheratioofneutraltocharged
current reaction(after theusualoutercorrection[8, 9]forthecharged current reaction )
is−0.6%,whichmaybecomparedwiththeclaimederror(0.5%)ofnuclearcalculations
fortheratio oftreelevelcrosssections[16].
ACKNOWLEDGMENTS
The author would like to express his sincere thanks to Professor Masataka Fukugitafor
stimulating discussions, fruitful collaboration and a careful reading of this manuscript.
This work is supported in part by the Grant in Aid from the Ministry of Education and
JSPS.
REFERENCES
1. M.FukugitaandT.Kubota,Phys.Rev.D72,071301(2005).
2. M.FukugitaandT.Kubota,ActaPhysicaPolonicaB35,1687(2004).
3. M.FukugitaandT.Kubota,Phys.Lett.B598,67(2004).
4. J.N.Bahcall,“NeutrinoAstrophysics"(CambridgeUniversityPress,1989).
5. B.Aharmimetal.(SNOCollaboration),arXiv:nucl-ex/0502021.
6. I.S.Towner,Phys.Rev. C58,1288(1998).
7. J.F.BeacomandS.J.Parke,Phys.Rev.D64,091302(2001).
8. A.Kurylov,M.J.Ramsey-MusolfandP.Vogel,Phys.Rev. C65,055501(2002);C67,035502(2003).
9. T.KinoshitaandA.Sirlin,Phys.Rev.113,1652(1959);P.Vogel,Phys.Rev.D29,1918(1984);S.A.
Fayans,Yad.Fiz.42,929(1985)[Sov.J.Nucl.Phys.42,590(1985)].
10. S.Andoetal.,Phys.Lett.B595,250(2004).
11. A.Sirlin,Phys.Rev.164,1767(1967);seealsoE.S.Abers,D.A.Dicus,R.E.NortonandH.R.Quinn,
Phys.Rev.167,1461(1968).
12. W.J.MarcianoandA.Sirlin,Phys.Rev.Lett.56,22(1986).
13. V.Gudkov,J.NeutronRes. 13,39(2005);V. Gudkovetal.,J. Res. Natl.Inst.Stand.Technol.110,
315(2005).
14. W.J.MarcianoandA.Sirlin,Phys.Rev.D22,2695(1980).
15. S.Andoetal.,Phys.Lett.B555,49(2003).
16. S.Nakamura,T.Sato,V.GudkovandK.Kubodera,Phys.Rev.C63,034617(2001);S.Nakamuraet
al.,Nucl.Phys.A707,561(2002).