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Bounds on neutral current couplings from single pion production
Volume 63B, number 1
PHYSICS LETTERS
5 July 1976
BOUNDS ON NEUTRAL CURRENT COUPLINGS FROM SINGLE PION PRODUCTION ~ G. ECKER and R. FISCHER
Institut ffir TheoretischePhysik, Universitd'tWien,Austria Received 20 April 1976 Assuming a hadronic neutral weak current of the general form J~NC =gv V~ +gAA~ +j / = 0 where V~,A# 3 3 are in the same isotriplets as the corresponding charged currents and j/'~0 is an arbitrary isoscalar current, we investigate the restrictions single pion production cross sections impose on this neutral current.
Although the existing information on the Lorentz structure of neutral currents is by no means conclusive [e.g. 1] we assume that the neutral current is a mixture of vector (V) and axial-vector (A) currents. Moreover, it is assumed that the isospin of the neutral current is at most one and that the 1 = 1 F, A currents are isospin partners of the corresponding charged weak currents. Except for the special case where the neutral current is purely isovector no assumptions are made about the isoscalar neutral current. It will be shown that single pion production leads to constraints which are complementary to the bounds from inclusive scattering [2] and which therefore put additional strong restrictions on the neutral current. Neglecting the Cabibbo angle the Lagrangians for neutrino scattering via charged and neutral weak currents are given by ~?cc=--~£-Th(l+75)v(vl-i2+Al-i2)+h.c.,
,QNC=-~2Fyyh(I+'Y5)V(gvV3+gAA3+jI=O).
(1,2)
The usual isospin analysis leads to the following seven amplitudes for weak single pion production
M I = V 3 + A 3,
M2=V3+A3-V1-A1,
M 4 = 2g V V 3 + 2gAA 3 +gvVl +gAA1 - WO, M 6 =gvV3 +gAA3 - g v V 1 -gAA1 - W0,
M3=V3+A3+2V1+2A1
(3a, b , c )
M 5 =gvV3 +gAA3 - g v V 1 -gAA1 + WO, M 7 = 2gvV 3 +2gAA 3 +gvV1 +gAA1 + WO.
(3d, e) (3f, g)
V3, A 3 (VI, A 1) are isovector amplitudes for the I = 3/2 (I = 1/2) final state, W0 is the isoscalar amplitude and we have neglected the muon mass. The corresponding cross sections are
fd tM212,
(4a, b)
o3-fdo(m+u-n.+)=9fdn.M¢2,
o4 - f do (vp-~ vprt°) = l f d~ lM412,
(4c, d)
os- fdo(vp--,vnlr+)=Zfd lMsl 2,
o6- f do(vn.-,vplr-)=2fcl21M612,
(4e, f)
(4g)
Work supported in part by "Fonds zur F~rderung der wissenschaftlichen Forschung in Osterreich", Projekt Nr. 2787. 59
Volume 63B, number 1
PHYSICS LETTERS
5 July 1976
The integrations in these equations extend over an arbitrary region of phase-space and may also contain an integration over the neutrino spectrum. The charged current amplitudes obey the relation 3M 1 = 2M 2 + M 3
(5)
which implies the well-known triangle inequalities [3] for o I , o 2, o 3 . Similarly, there is a relation for the neutral current amplitudes of the form M 4 +M 5 =M 6 +M 7
(6)
which gives a set of quadrangle inequalities: 2X/2-°4~
X/~5 < 2V~4 +V~6 + 2x/~7,
(7a, b)
V~6 ~<2x/~4 + V~5 + 2x/~7,
2x/'~7 ~<2x/~4 + x/~5 + x/%6.
(7c, d)
These four inequalities are a consequence of the assumption that the isospin of the neutral current is not greater than one. From eqs. (3) one finds IM412 + IM712 = 21 W012 +21(gv - gA)(2V3 + V1) +KA(3M1 -M2)I 2
(8)
IMsI 2 + IM612 =21W012 + 21(gv -gA)(V3 - V1)+gAM212.
(9)
In order to obtain restrictions on the vector amplitudes we define four additional amplitudes for single pion electroproduction M 8 = 2 V 3 + V 1 - Vo, M 9 = V 3 - V I+V0,
Mlo=V 3-V l-V0,
M l l = 2 V 3 + V I + V 0 , (10a, b , c , d )
where V0 is the isoscalar electromagnetic amplitude. The corresponding cross sections are o8 =
G2 f Q 4 d o ( e - p - o ' e - p l r ° ) = l fd~lMsI2,
87r2t~2
- G2 f Q 4 d o ( e - p -.->e - n T r + ) = 2 f d , IM912, 09 = 87r2o~2
o10
87r2cg2 Q4do (e-n--> e-pTr-) = __c2f
d~2 IM1012,
Oll =8rr2a 2G2 fQ4do(e-n.-+e-nn°)=lfd~21Mlll2
(lla)
(llb)
(1 lc)
(lld)
Q2 is the momentum transfer squared between the leptons and the integrations are as in eqs. (4). From eqs. (10) we obtain the bounds
212V3 + Vl12 < IM812 + IMl112,
21V3 - V112 <~IM912 + IMlo 12.
(12a, b)
1. Isovector-isoscalar neutral current: INC -- O, 1 Eliminating W0 from (8) and (9) we are led to extremize ]M412
6O
+
[M712 _ IMsI 2 _ [M612 = 21(gv - gA)(2 V3 + V1) +gA (3M1 -M2)I 2 _ 21(gv - gA )(V3 - V1) +gAM212' (13)
Volume 63B, number 1
PHYSICS LETTERS
5 July 1976
Using the electroproduction constraints (12) one obtains the following bounds in terms of cross sections 204 + 207 - 05 - 06 ~< [Igv - gA I X/2(o 8 + o 11) + lgA IX/o 1 -- 02 + 03 ] 2 _ [Igv - gA h / d 9 + °l 0 -- IgA IX/-~2] 2 f°r g2 °2 >I (gv - gA)2(°9 + °10)
(14)
2o 4 + 2 o 7 _ 0 5 _ d6 ~< [igv_gAix/2(o8 +o11) + igzlX/Ol _ 02 +03] 2,
f°r g 2 ° 2 <<'(gv - g z ) 2 ( ° 9 +°10) (15) 204 +207 _ 05 _ 06 i> [Ig V _gAIX/2(o8 + o11) _ igA h/Ol _ 02 +03] 2 _ [ig V _ g A I V ~ 9 + Ol 0 + igA IX/~'2] 2 (16) for g2 (o 1 - 02 + 03) i> 2(g V - gA)2(o8 + Oll) 204 + 207 -- o5 - 06 I> - [Igv - gA I X/O9 + o 10 + [gA IX/~"2] 2,
for g 2 ( o l - - o 2 + o3)--.<2(g V -gA)2(o8 +o11). (17)
The inequalities turn into an equality for g v = gA which may be written 2
2 204 + 207 -- 05 -- 06 g v = g.~ Ol _ 202 + 03
(18)
Thus for a V - A isovector neutral current with an arbitrary isoscalar admixture the isovector coupling constant is fixed by the weak pion production cross sections only.
2. Isovector neutral current: INC = 1 In the case of a purely isovector neutral current W0 = 0 which implies 04 = o7,
05 = 06.
(19a, b)
From (8) and (9) using again the electroproduction constraints (12) one obtains the following bounds
4o4 <.[IgV-gAIX/2(o8 +Oll)+lglX/Ol-O2 +O3] 2,
2oS <<.[Igv-gzlx/-o--99 +olo +lgzlx o/-of22]2 (20,21)
4o4 I> [Igv-gAIX/2(o8 + o 1 1 ) - Igz[X/Ol - 02 +03] 2, for g2 (Ol _ 02 +o3)>/2(gv_gA)2(o8 +Oil ) (22) 205/> jig V _ g A I X ~ 9 + Ol 0 _ igA IX~2] 2,
for g2 02 >I (gV - gA )2(09 + °10)"
(23)
For a V - A isovector neutral current [4] these inequalities become two equalities which again do not depend on the electroproduction cross sections 2
2 _
g v = g~4
4o'4
Ol _ 02 + 03
,
g 2 = g 2 = 205 . 02
(24,25)
3. Isoscalar neutral current: INC = 0 For completeness we observe that in the case of a purely isoscalar neutral current 05 = o 6 = 2 o 4 = 2 o 7 .
(26)
The Gargamelle results [5] for neutrino and antineutrino scattering on complex nuclei have recently been shown to be inconsistent with a purely isoscalar neutral current. It will become clear from the discussion below that the ANL data [6] do not favour this possibility (gv = gA = 0), either. Since we are not going to estimate nuclear corrections in this letter our only source of information concerning 61
Volume 63B, number 1
PHYSICS LETTERS
5 July 1976
Table 1 ANL data [6, 7] for weak single pion production. Cross sections are defined in eqs. (4). Ratio Exp.
o 2/o I 0.37 -+ 0.10
o3/ol
a 4/o 1
as/o 1
0.37 ± 0.09
0.40 ± 0.22
0.13 ± 0.06
o 6/ol 0.07 ± 0.03
weak pion production are the ANL bubble chamber experiments [6, 7] on hydrogen and deuterium. Table 1 summarizes the data we have used. As for the electroproduction cross sections we have applied the narrow-width approximation [8] and used data from DESY [9] and CEA [10] to o b t a i n upper b o u n d s for a 8 + Oll and 09 + o10 in the energy range o f the A N L n e u t r i n o beam. Allowing for a p p r o x i m a t e l y 25% b a c k g r o u n d we estimate (09 +olO)/O 1 ~<0.15.
(08 + o11)/o 1 ~<0.19,
(27a, b)
In the derivation o f our results we assumed that all cross sections are k n o w n . However, 07 = o(vn --> v n n ° ) has n o t yet b e e n measured. Therefore we have used the isospin constraints (7) to b o u n d "o7 , i.e.
\
\
gA
\ \ \
\
gA \
\
\
4
\
\
\ \
\
\
\ \
\
\
\
\
\
\\ fl
\ \
ff
\ 2
j I f f
\
\
\ \
ff
\
111
3
'
'gv
gv
\ \
f
\
\\
\ \
-2
-3
\
\ \
\ \
\
\ \
-4
\ \
"2
\
\
\
\
\
\
\
\ \
\
\ \
\
Fig. 1. Constraints from single pion production for g v , gA in the presence of an isoscalar neutral current, as determined from the data in table 1 and the estimates (27). Dotted lines are given by g24o2 = ( g v - g A ) 2 ( a 9 + °1o). Allowed values lie outside the three regions bounded by full lines.
62
\
\
Fig. 2. Constraints for gv, gA from both inclusive scattering and single pion production. Data for inclusive scattering are from ref. [13] (R = 0.25,/~ = 0.36,r = 0.34). Dotted lines as in fig. 1. Allowed regions are shaded.
Volume 63B, number 1
PHYSICS LETTERS
5 July 1976
2x/~-7 ~>max(2x/~-~4 - x/-~-5- x/~6, V ~ 5 - 2x/~-~4- q~6,x/'~6 - 2,v~4 - x/-~5,0),
(28a)
2X/~-7 ~<2X~4 +X/~5 +x/~6.
(28b)
For the ANL data the maximum in (28a) is given by 2V~4 - x/~5 - x/~6. Putting all the information together we obtain the curves shown in fig. 1, where the allowed values ofg V, gA lie outside the three regions bounded by hyperbolas and straight lines. In order to appreciate the relevance of the bounds let us include the information from inclusive scattering. The important point is that inclusive scattering yields upper bounds [2, 11 ] on gv and gA, while single pion production gives essentially lower bounds in the gv, gA plane. In fig. 2 the constraints from both types of experiments are shown. A thorough discussion of the allowed regions is impossible without taking the experimental errors into account. The main sources of error are the large error for o 4 and the fact that 07 is unknown. The bounds are less sensitive to the errors in the charged current and electromagnetic cross sections. Generally speaking, the neutral current cross sections determine the scale of the regions in fig. 1 while the charged current and electromagnetic cross sections determine their shape. The present values for 04, 05, o 6 are also compatible with a purely isovector neutral current. The constraints in the absence of an isoscalar current are shown graphically in fig. 3 where gv, gA must lie outside the two polygons. \\\\
~
gA
.2\ .-,
g,
\' Fig. 3. Constraints for g V, gA from single pion production for a purely isovector neutral current. Data and dotted lines as in fig. I. Allowed region is outside the two polygons (full lines).
63
Volume 63B, number 1
PHYSICS LETTERS
5 July 1976
Even without using the inclusive cross sections we find that single pion production does not favour the AdlerTuan model [4], since from eq. (24) g2v = g 2 = 1.60 + 0.92
(29a)
while (25) gives
g2v=g2" 0.54 + 0 . 3 1 .
(29b)
An extended version of this work will be contained in a forthcoming publication where in addition the following topics will be treated in detail: investigation o f models o f the Salam-Weinberg type [ 12] and a treatment o f the constraints which follow from neutrino and antineutrin0 cross sections together. We want to thank Professor A. Bartl for information on the electroproduction cross sections. One of us (R.F. is grateful to Professor H. Pietschmann and the Institute for Theoretical Physics o f the University of Vienna for their kind hospitality.
References [1] J.J. Sakurai, CERN preprint TH 2099 (1975). [2] G. Rajasekaran and K.V.L. Sarma, Phys. Lett. 55B (1975) 201; M. Gourdin, Proc. of the 14th Schladming Winter School, ed. P. Urban, Springer (Wien-New York, 1975). [3] C.H. Llewellyn Smith, Phys. Reports 3C (1972) 261. [4] S.L. Adler and S.F. Tuan, Phys. Rev. D l l (1975) 129. [5] G.H. Bertrand Coremans et al. (Gargamelle collaboration), Phys. Lett. 61B (1976) 207. [6] L.G. Hyman, Proc. of La physique du neutrino a haute energie, Ecole Polytechnique, Paris (1975). [7] S.J. Barish et ai., Phys. Rev. Lett. 36 (1976) 179. [8] H.F. Jones and M.D. Scadron, Ann. Phys. (N.Y.) 81 (1973) 1. [9] S. Galster et al., Phys. Rev. D5 (1972) 519; M. K~Sbberlinget al., DESY preprint 74•32. [10] K.M. Hanson, Proc. Intern. Symp. on Lepton and photon interactions at high energies, Stanford (1975). [11] L.M. Sehgal, ANL Report ANL-HEP-PR-75-45. [12] A. Salam, Proc. 8th Nobel Symposium, eds. N. Svartholm, Almqvist and Wiksell (Stockholm, 1968); S. Weinberg, Phys. Rev. Lett. 19 (1967) 1264. [13] A. Bodek, Rencontre de Moriond, Flaine (1976).
64
PHYSICS LETTERS
5 July 1976
BOUNDS ON NEUTRAL CURRENT COUPLINGS FROM SINGLE PION PRODUCTION ~ G. ECKER and R. FISCHER
Institut ffir TheoretischePhysik, Universitd'tWien,Austria Received 20 April 1976 Assuming a hadronic neutral weak current of the general form J~NC =gv V~ +gAA~ +j / = 0 where V~,A# 3 3 are in the same isotriplets as the corresponding charged currents and j/'~0 is an arbitrary isoscalar current, we investigate the restrictions single pion production cross sections impose on this neutral current.
Although the existing information on the Lorentz structure of neutral currents is by no means conclusive [e.g. 1] we assume that the neutral current is a mixture of vector (V) and axial-vector (A) currents. Moreover, it is assumed that the isospin of the neutral current is at most one and that the 1 = 1 F, A currents are isospin partners of the corresponding charged weak currents. Except for the special case where the neutral current is purely isovector no assumptions are made about the isoscalar neutral current. It will be shown that single pion production leads to constraints which are complementary to the bounds from inclusive scattering [2] and which therefore put additional strong restrictions on the neutral current. Neglecting the Cabibbo angle the Lagrangians for neutrino scattering via charged and neutral weak currents are given by ~?cc=--~£-Th(l+75)v(vl-i2+Al-i2)+h.c.,
,QNC=-~2Fyyh(I+'Y5)V(gvV3+gAA3+jI=O).
(1,2)
The usual isospin analysis leads to the following seven amplitudes for weak single pion production
M I = V 3 + A 3,
M2=V3+A3-V1-A1,
M 4 = 2g V V 3 + 2gAA 3 +gvVl +gAA1 - WO, M 6 =gvV3 +gAA3 - g v V 1 -gAA1 - W0,
M3=V3+A3+2V1+2A1
(3a, b , c )
M 5 =gvV3 +gAA3 - g v V 1 -gAA1 + WO, M 7 = 2gvV 3 +2gAA 3 +gvV1 +gAA1 + WO.
(3d, e) (3f, g)
V3, A 3 (VI, A 1) are isovector amplitudes for the I = 3/2 (I = 1/2) final state, W0 is the isoscalar amplitude and we have neglected the muon mass. The corresponding cross sections are
fd tM212,
(4a, b)
o3-fdo(m+u-n.+)=9fdn.M¢2,
o4 - f do (vp-~ vprt°) = l f d~ lM412,
(4c, d)
os- fdo(vp--,vnlr+)=Zfd lMsl 2,
o6- f do(vn.-,vplr-)=2fcl21M612,
(4e, f)
(4g)
Work supported in part by "Fonds zur F~rderung der wissenschaftlichen Forschung in Osterreich", Projekt Nr. 2787. 59
Volume 63B, number 1
PHYSICS LETTERS
5 July 1976
The integrations in these equations extend over an arbitrary region of phase-space and may also contain an integration over the neutrino spectrum. The charged current amplitudes obey the relation 3M 1 = 2M 2 + M 3
(5)
which implies the well-known triangle inequalities [3] for o I , o 2, o 3 . Similarly, there is a relation for the neutral current amplitudes of the form M 4 +M 5 =M 6 +M 7
(6)
which gives a set of quadrangle inequalities: 2X/2-°4~
X/~5 < 2V~4 +V~6 + 2x/~7,
(7a, b)
V~6 ~<2x/~4 + V~5 + 2x/~7,
2x/'~7 ~<2x/~4 + x/~5 + x/%6.
(7c, d)
These four inequalities are a consequence of the assumption that the isospin of the neutral current is not greater than one. From eqs. (3) one finds IM412 + IM712 = 21 W012 +21(gv - gA)(2V3 + V1) +KA(3M1 -M2)I 2
(8)
IMsI 2 + IM612 =21W012 + 21(gv -gA)(V3 - V1)+gAM212.
(9)
In order to obtain restrictions on the vector amplitudes we define four additional amplitudes for single pion electroproduction M 8 = 2 V 3 + V 1 - Vo, M 9 = V 3 - V I+V0,
Mlo=V 3-V l-V0,
M l l = 2 V 3 + V I + V 0 , (10a, b , c , d )
where V0 is the isoscalar electromagnetic amplitude. The corresponding cross sections are o8 =
G2 f Q 4 d o ( e - p - o ' e - p l r ° ) = l fd~lMsI2,
87r2t~2
- G2 f Q 4 d o ( e - p -.->e - n T r + ) = 2 f d , IM912, 09 = 87r2o~2
o10
87r2cg2 Q4do (e-n--> e-pTr-) = __c2f
d~2 IM1012,
Oll =8rr2a 2G2 fQ4do(e-n.-+e-nn°)=lfd~21Mlll2
(lla)
(llb)
(1 lc)
(lld)
Q2 is the momentum transfer squared between the leptons and the integrations are as in eqs. (4). From eqs. (10) we obtain the bounds
212V3 + Vl12 < IM812 + IMl112,
21V3 - V112 <~IM912 + IMlo 12.
(12a, b)
1. Isovector-isoscalar neutral current: INC -- O, 1 Eliminating W0 from (8) and (9) we are led to extremize ]M412
6O
+
[M712 _ IMsI 2 _ [M612 = 21(gv - gA)(2 V3 + V1) +gA (3M1 -M2)I 2 _ 21(gv - gA )(V3 - V1) +gAM212' (13)
Volume 63B, number 1
PHYSICS LETTERS
5 July 1976
Using the electroproduction constraints (12) one obtains the following bounds in terms of cross sections 204 + 207 - 05 - 06 ~< [Igv - gA I X/2(o 8 + o 11) + lgA IX/o 1 -- 02 + 03 ] 2 _ [Igv - gA h / d 9 + °l 0 -- IgA IX/-~2] 2 f°r g2 °2 >I (gv - gA)2(°9 + °10)
(14)
2o 4 + 2 o 7 _ 0 5 _ d6 ~< [igv_gAix/2(o8 +o11) + igzlX/Ol _ 02 +03] 2,
f°r g 2 ° 2 <<'(gv - g z ) 2 ( ° 9 +°10) (15) 204 +207 _ 05 _ 06 i> [Ig V _gAIX/2(o8 + o11) _ igA h/Ol _ 02 +03] 2 _ [ig V _ g A I V ~ 9 + Ol 0 + igA IX/~'2] 2 (16) for g2 (o 1 - 02 + 03) i> 2(g V - gA)2(o8 + Oll) 204 + 207 -- o5 - 06 I> - [Igv - gA I X/O9 + o 10 + [gA IX/~"2] 2,
for g 2 ( o l - - o 2 + o3)--.<2(g V -gA)2(o8 +o11). (17)
The inequalities turn into an equality for g v = gA which may be written 2
2 204 + 207 -- 05 -- 06 g v = g.~ Ol _ 202 + 03
(18)
Thus for a V - A isovector neutral current with an arbitrary isoscalar admixture the isovector coupling constant is fixed by the weak pion production cross sections only.
2. Isovector neutral current: INC = 1 In the case of a purely isovector neutral current W0 = 0 which implies 04 = o7,
05 = 06.
(19a, b)
From (8) and (9) using again the electroproduction constraints (12) one obtains the following bounds
4o4 <.[IgV-gAIX/2(o8 +Oll)+lglX/Ol-O2 +O3] 2,
2oS <<.[Igv-gzlx/-o--99 +olo +lgzlx o/-of22]2 (20,21)
4o4 I> [Igv-gAIX/2(o8 + o 1 1 ) - Igz[X/Ol - 02 +03] 2, for g2 (Ol _ 02 +o3)>/2(gv_gA)2(o8 +Oil ) (22) 205/> jig V _ g A I X ~ 9 + Ol 0 _ igA IX~2] 2,
for g2 02 >I (gV - gA )2(09 + °10)"
(23)
For a V - A isovector neutral current [4] these inequalities become two equalities which again do not depend on the electroproduction cross sections 2
2 _
g v = g~4
4o'4
Ol _ 02 + 03
,
g 2 = g 2 = 205 . 02
(24,25)
3. Isoscalar neutral current: INC = 0 For completeness we observe that in the case of a purely isoscalar neutral current 05 = o 6 = 2 o 4 = 2 o 7 .
(26)
The Gargamelle results [5] for neutrino and antineutrino scattering on complex nuclei have recently been shown to be inconsistent with a purely isoscalar neutral current. It will become clear from the discussion below that the ANL data [6] do not favour this possibility (gv = gA = 0), either. Since we are not going to estimate nuclear corrections in this letter our only source of information concerning 61
Volume 63B, number 1
PHYSICS LETTERS
5 July 1976
Table 1 ANL data [6, 7] for weak single pion production. Cross sections are defined in eqs. (4). Ratio Exp.
o 2/o I 0.37 -+ 0.10
o3/ol
a 4/o 1
as/o 1
0.37 ± 0.09
0.40 ± 0.22
0.13 ± 0.06
o 6/ol 0.07 ± 0.03
weak pion production are the ANL bubble chamber experiments [6, 7] on hydrogen and deuterium. Table 1 summarizes the data we have used. As for the electroproduction cross sections we have applied the narrow-width approximation [8] and used data from DESY [9] and CEA [10] to o b t a i n upper b o u n d s for a 8 + Oll and 09 + o10 in the energy range o f the A N L n e u t r i n o beam. Allowing for a p p r o x i m a t e l y 25% b a c k g r o u n d we estimate (09 +olO)/O 1 ~<0.15.
(08 + o11)/o 1 ~<0.19,
(27a, b)
In the derivation o f our results we assumed that all cross sections are k n o w n . However, 07 = o(vn --> v n n ° ) has n o t yet b e e n measured. Therefore we have used the isospin constraints (7) to b o u n d "o7 , i.e.
\
\
gA
\ \ \
\
gA \
\
\
4
\
\
\ \
\
\
\ \
\
\
\
\
\
\\ fl
\ \
ff
\ 2
j I f f
\
\
\ \
ff
\
111
3
'
'gv
gv
\ \
f
\
\\
\ \
-2
-3
\
\ \
\ \
\
\ \
-4
\ \
"2
\
\
\
\
\
\
\
\ \
\
\ \
\
Fig. 1. Constraints from single pion production for g v , gA in the presence of an isoscalar neutral current, as determined from the data in table 1 and the estimates (27). Dotted lines are given by g24o2 = ( g v - g A ) 2 ( a 9 + °1o). Allowed values lie outside the three regions bounded by full lines.
62
\
\
Fig. 2. Constraints for gv, gA from both inclusive scattering and single pion production. Data for inclusive scattering are from ref. [13] (R = 0.25,/~ = 0.36,r = 0.34). Dotted lines as in fig. 1. Allowed regions are shaded.
Volume 63B, number 1
PHYSICS LETTERS
5 July 1976
2x/~-7 ~>max(2x/~-~4 - x/-~-5- x/~6, V ~ 5 - 2x/~-~4- q~6,x/'~6 - 2,v~4 - x/-~5,0),
(28a)
2X/~-7 ~<2X~4 +X/~5 +x/~6.
(28b)
For the ANL data the maximum in (28a) is given by 2V~4 - x/~5 - x/~6. Putting all the information together we obtain the curves shown in fig. 1, where the allowed values ofg V, gA lie outside the three regions bounded by hyperbolas and straight lines. In order to appreciate the relevance of the bounds let us include the information from inclusive scattering. The important point is that inclusive scattering yields upper bounds [2, 11 ] on gv and gA, while single pion production gives essentially lower bounds in the gv, gA plane. In fig. 2 the constraints from both types of experiments are shown. A thorough discussion of the allowed regions is impossible without taking the experimental errors into account. The main sources of error are the large error for o 4 and the fact that 07 is unknown. The bounds are less sensitive to the errors in the charged current and electromagnetic cross sections. Generally speaking, the neutral current cross sections determine the scale of the regions in fig. 1 while the charged current and electromagnetic cross sections determine their shape. The present values for 04, 05, o 6 are also compatible with a purely isovector neutral current. The constraints in the absence of an isoscalar current are shown graphically in fig. 3 where gv, gA must lie outside the two polygons. \\\\
~
gA
.2\ .-,
g,
\' Fig. 3. Constraints for g V, gA from single pion production for a purely isovector neutral current. Data and dotted lines as in fig. I. Allowed region is outside the two polygons (full lines).
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Volume 63B, number 1
PHYSICS LETTERS
5 July 1976
Even without using the inclusive cross sections we find that single pion production does not favour the AdlerTuan model [4], since from eq. (24) g2v = g 2 = 1.60 + 0.92
(29a)
while (25) gives
g2v=g2" 0.54 + 0 . 3 1 .
(29b)
An extended version of this work will be contained in a forthcoming publication where in addition the following topics will be treated in detail: investigation o f models o f the Salam-Weinberg type [ 12] and a treatment o f the constraints which follow from neutrino and antineutrin0 cross sections together. We want to thank Professor A. Bartl for information on the electroproduction cross sections. One of us (R.F. is grateful to Professor H. Pietschmann and the Institute for Theoretical Physics o f the University of Vienna for their kind hospitality.
References [1] J.J. Sakurai, CERN preprint TH 2099 (1975). [2] G. Rajasekaran and K.V.L. Sarma, Phys. Lett. 55B (1975) 201; M. Gourdin, Proc. of the 14th Schladming Winter School, ed. P. Urban, Springer (Wien-New York, 1975). [3] C.H. Llewellyn Smith, Phys. Reports 3C (1972) 261. [4] S.L. Adler and S.F. Tuan, Phys. Rev. D l l (1975) 129. [5] G.H. Bertrand Coremans et al. (Gargamelle collaboration), Phys. Lett. 61B (1976) 207. [6] L.G. Hyman, Proc. of La physique du neutrino a haute energie, Ecole Polytechnique, Paris (1975). [7] S.J. Barish et ai., Phys. Rev. Lett. 36 (1976) 179. [8] H.F. Jones and M.D. Scadron, Ann. Phys. (N.Y.) 81 (1973) 1. [9] S. Galster et al., Phys. Rev. D5 (1972) 519; M. K~Sbberlinget al., DESY preprint 74•32. [10] K.M. Hanson, Proc. Intern. Symp. on Lepton and photon interactions at high energies, Stanford (1975). [11] L.M. Sehgal, ANL Report ANL-HEP-PR-75-45. [12] A. Salam, Proc. 8th Nobel Symposium, eds. N. Svartholm, Almqvist and Wiksell (Stockholm, 1968); S. Weinberg, Phys. Rev. Lett. 19 (1967) 1264. [13] A. Bodek, Rencontre de Moriond, Flaine (1976).
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