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EXPERIMENTAL TEST OF THE PARTIALLY CONSERVED AXIAL VECTOR CURRENT

HYPOTHESIS

J.-L. Masnou

To cite this version:

J.-L. Masnou. EXPERIMENTAL TEST OF THE PARTIALLY CONSERVED AXIAL VEC- TOR CURRENT HYPOTHESIS. Journal de Physique Colloques, 1971, 32 (C3), pp.C3-117-C3-121.

�10.1051/jphyscol:1971318�. �jpa-00214599�

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JOURNAL DE PHYSIQUE Colloque C3, supplgment au no 10, Tome 32, Octobre 1971, page C3-117

EXPERIMENTAL TEST OF THE PARTIALLY CONSERVED AXIAL VECTOR CURRENT HYPOTHESIS (*)

J.-L. MASNOU

Laboratoire de PAcctltrateur Lintaire. Facultt des Sciences d'Orsay, 91, Orsay

RCsum6. - L'hypothkse de la conservation partielle du courant axial (PCAC) peut &tre vQifiCe dans les interactions inelastiques des neutrinos, p o u ~ les faibles valeurs de q2, carre du quadrivecteur de transfert leptonique. Elle relie en effet la section efficace diffkrentielle de I'interaction

L la section efficace n+ + a + P pour la m&me masse hadronique MD dans les deux reactions. Cette etude montre que les resultats experimentaux sont compatibles a un ecart standard avec les predic- tions de PCAC, pour q2 < 0,12 (GeV/c)z. Nous montrons en particulier que la correction due a la composante transverse du courant faible, estimbe I'aide du modkle a dominance vectorielle, est importante.

Abstract. - The partially conserved axial current hypothesis (PCAC) can be checked in the inelastic neutrino inteiactions for small values of q2, square of the leptonic transfer quadrivector. It relates the differential cross section for the reaction v, + a + p- + /3 to the cross section

n+ + a + P for the same hadronic mass Mn in both reactions. This study shows that the experi- mental results are in agreement to one standard deviation with PCAC's predictions, for

q 2 < 0.12 GeV/c. We show especially that the correction due to the transverse component of the weak current, estimated by the vector dominance model, is important.

Introduction. - S. Adler [I] has proposed an experimental test of PCAC based on the study of high energy inelastic neutrino interactions with O,, -- 0

where O,, is the angle between the outgoing lepton and the incident neutrino. We have already published [3]

the results of PCAC's test with these kinematical conditions, and shown that the experimental and theoretical results are in agreement for

q2 5 0.10 (GeV/c)' .

C. A. Piketty and L. Stodolsky [2] have then proved that this test is possible without cut on O,,.

We shall show in this paper the experimental results we have obtained with these new kinematical condi- tions. We shall see also how the vector dominance model (VDM) gives an estimation of the contribution of the transverse component of the weak current.

Suppose that the angle O,, between the emerging pCL- and the incident neutrino is zero (parallel configura- tion). If the vector current is conserved (CVC) and if PCAC is true, the square of the matrix element of the neutrino interaction, averaged over the spin of the p - , is proportional to the square of the matrix element of the reaction n f + a + p , for the same mass M p of the ,8 system in both reactions.

Adler's theorem has been generalized by C . A.

Piketty and L. Stodolsky [2]. They have expanded the neutrino cross section using q2 instead of a,,,

and shown that if CVC and PCAC are true and when q2 -+ 0, Adler's relation is valid without cut on %,,. Nevertheless, it is necessary t o sum over the impulsions and polarizations of /3 system and on spins of initial and final particles. PCAC leads then to the following expression :

d20 G2 1 2 191

I. Theory of PCAC9s Test. - The Adler's theorem I = _ - g ~ n ox+ -- X

can be expressed as follows : dq2 dv e2-+o 2 n 2 v v

Let us consider the inelastic interaction

v , + a - , , u - + P

.

E(l - m i + q 2 ) -

4 EE' where j? is the hadronic system with mass Mg # M,. - m2 v

-- +

(*) Cet article recouvre en partie la these de doctorat d'Etat es

d 2 0 .

~ ( m ; + q2) 4 ~ ' ( m ; + q2)'

Sciences Physiques soutenue a la Faculte des Sciences d'Orsay le

23 mars 1971, no d'ordre du CNRS : A0 5586. Titre : test de

PCAC dans les interactions de neutrinos de haute 6nergie. dq2 dv '

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971318

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C3-118 J.-L. MASNOU

differential cross section of v, + a -+ p-,+ P.

O Z + : cross section of reaction -nf + a -+ P.

G : weak coupling constant.

E' : p- energy.

E : neutrino energy.

v = E - E' : leptonic energy transfer.

m : p- mass.

4 : (q, iv).

Jn this formula, the second and third terms are due to the direct exchange of a .n+.

We have tried to check expression [I] in the three following ways.

a) By a comparison of the absolute theoretical and experimental number of events.

b) By a comparison of experimental and theoretical distributions in M; and cos O,,.

c) By a comparison of the distributions in number and nature of p system's particles for neutrino and n interactions.

11. The sample of inelastic neutrino interactions. -

We have made a complete kinematical analysis [4]

of the neutrino interactions obtained in the CERN 1967 experiment. T o eliminate the background due to interactions of incoming charged particles and as the neutrino flux is not well known for energy smaller than 1 GeV, we have applied the following cuts :

P, > 1 GeV/c E,,, > 1 GeV .

P, is the projection on the neutrino direction of the sum of impulsions of visible tracks.

E,,, is the sum of kinetic energy of baryons and of total energy of mesons and is, equal to the neutrino energy if all outgoing particles are detected.

With this cuts we have found 393 interactions with a possible p- and a background consisting only of 11 unidentified neutron interactions.

From this sample we have obtained, applying the

cut M; > 1,16 (G~V/C')~, 3 11 inelastic interactions

with a background smaller than 6 elastic interactions.

I t is this sample we have used ,for PCAC's test.

TII. Comparison of experimental and theoretical results. - We shall make this comparison, first neglecting the transverse contribution of the weak current and then taking an estimation of it given by the VDM model.

111. I .TEST OF PCAC NEGLECTING THE TRANSVERSE

CONTRIBUTION. - 111 . l . 1 Comparison of q2 distri- butions. - Due to low statistics, we have integrated the formula (1) over E and v . Figure 1 compares the experimental and theoretical distributions given in

r---

~2 and =4 c1 and c3 c2 and ~3

FIG. 1. - Experimental and theoretical distributions versus 9 2 . The theoretical curves are given by PCAC, neglecting transverse contribution of the weak current. M j > 1.16 (GeV/c)z, E > 1 GeV.

I

C1 : without shadow effect.

C2 : with shadow effect.

Theoretical C3 : CT=+ computed by extrapolation of transition hypothesis : rate of n+ + C( + fi reaction.

C4 : on+ computed by extrapolation of cross sec-

\ tion.

Histograms : See fotonote (1).

a) Computation of a,+ : o,+ is the cross section of a virtual n+. To get it from a,+ for a n f on mass shell, we can extrapolate either the transition rate of the n+ + a -+ p reaction, or the a,+ cross section itself. The corresponding uncertainly is of the order of 25 % if we do n i t make any cut on i.

b) (( Shadow effect )) : In a nucleus, there is a paradox in formula (I). The -n+ cross section should behave as A213 and the neutrino cross section should behave as A. (A is the atomic mass of the target.) For carbon, this effect gives a factor 2.3 between left and right hand sides of (1). The resulting uncer- tainty is of the order of 20 % for propane.

The different theoretical curves drawn on figure I correspond to these uncertainties.

J. S. Bell [6] has shown, using an optical model for the A (1 236) resonance, that the longitudinal component of the weak current is suppressed in nucleus. The transverse component is not changed.

Until now, due to statistics and quasi-elastic events, the experimental results have not yet allowed to confirm this model. Nevertheless, as at low q 2 , the longitudinal component of the weak current is domi- - nant we can assume that there is a shadow effect.

We can also assume that extrapolation of the transi- tion rate gives the best estimation for o,+. So on figure 1, the lowest curve (conditions C2 and C3) is more reasonable.

function 0fq2. (1) For events with several p- candidates

Two theoretical difficulties appear in this test

the p- is ( the negative track with minimum angle --.

of PCAC. the negative track with maximum angle - - - -.

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EXPERIMENTAL TEST OF THE PARTIALLY CONSERVED In neutrino interactions with several p- candidates,

there is an ambiguity on the value of q2. So we have a - 15 % uncertainty on the number of inelastic events with low q2 value. An other uncertainty comes from the f 15 % error on neutrino flux.

Nevertheless, table I shows that we find experimental and theoretical results in agreement to one standard deviation for q2 < 0.12 (GeV/c)'. Beyond this value, the experimental number of events is higher than the number predicted by PCAC.

FIG. 3. - Experimental and theoretical distributions versus cos B,, q 2 < 0.12 (GeV/c)Z, E > 1 GeV, M j > 1 .16 (GeV/c2)2.

The theoretical curve is normalised to the observed number of events.

TABLE I

C1 : without slzadow effect

Histograms : See footnote (1).

Hypothesis

q 2 < 0.12 0.12 < q 2 < 0.20

(GeV/c)' (GeVlc)' standard deviation, corresponding to the average of the Experimental 26 - 6 31 f 7

- - - experimental error on M;.

C2 : with shadow effect

C3 : extrapolation of transition rate to compute on+

C1 and C3 22.9 + 3.5 14.2 + 2.2 We find experimental and theoretical results in 'heore- c1 and C4 29.5 4.4 20.3 + 3.0 agreement with PCAC to one standard deviation. We ical

C2 and C3 18.7 f 2.7 .5 I .8 notice on table I1 that the number of neutrino events C2andC4 23.1f 3.5 15.9 + 2.4 with M; > 2 (Gev/c2)' is higher than predicted.

C4 : extrapolation of cross section

The number of events with q2 < 0.12 ( G ~ V / C ) ~ is too

TABLE I1 low to be sensitive to the theoretical uncertainties

discussed above. ~ 8 2 < 2 (GeV/c2)' > 2 (GeV/c2)'

- - -

111.1 .2 Comparison of M; and cos O,, distributions.

-We keep now the neutrino interactions with Experimental 14 f 4 12 f 5

q2 < 0.12 (GeV/c)'. On figures 2 and 3, we have Theoretical nor-

compared the M; and cos Op, distributions. The theore- malized 18.8 7.2

FIG. 2. - Experimental and theoretical distributions versus M j q z < 0.12 (GeV/c)z, E > 1 GeV, Mi; > 1.16 (GeV/cz)? The theoretical curve, computed neglecting the transverse contribu- tion of the weak current has been convoluted to a gaussian of width 0.70 (GeV/cz)%nd normalized to the observed number of events.

Histograms : See footnote (1).

I11 . l . 3 Comparison of multiplicities for P system. - For this comparison we have made an analysis of n+

interactions in propane. Pictures were taken in the Ecole Polytechnique bubble chamber BP 3 in 1967 at Saclay. We have computed a mean percentage of n + interactions according to the number of outgoing pions, by ponderation over the theoretical M; distri- bution. We have excluded coherent interactions on carbon nucleus 151. Table I11 gives results in the A (1 236) resonance region. We do not find a big absorp- tion of n + in the carbon in this region. Nevertheless we find too many neutrino events without outgoing charged pion. From q2 distributions, we have found that no more that 10 % of these events come from the background of elastic events. Since we shall see that the transverse contribution may be important, we shall not conclude on the validity of PCAC from these results on multiplicities.

tical distributions are normalized to the observed

(1) For events with several p- candidates number of events. The distribution in M; has also been

the p- is ( the negative track with minimum angle --.

convoluted to a gaussian curve with 0.35 (GeV/c2)' the negative track with maximum angle - - - -.

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J.-L. MASNOU

TABLE I11

q2 < 0.12 (GeV/c)', M; < 2 (GeV/c2)'

Number of n" 0 1 > 1

- - - -

Interactions Target = C,H,

1 0.19 f 0.05 0.77 f 0.05 0.04 f 0.04

n+ + a 3 P Target = unbound nucleons 0.16 0.83 0.01

Interactions v + a -, ,u- + f3 0.36 -1- 0.13 0.64 f 0.13 0

111.2 TEST OF PCAC WITH CORRECTIONS ESTIMATED BY THE VECTOR DOMINANCE MODEL (2). - The neutrino interaction has been described by C. A. Piketty and L. Stodolsky using VDM, with +, A: and n + exchange for vector and axial current.

For low values of q2, PCAC gives the value of the axial longitudinal cross-section. The vector longitu- dinal cross section is of the order of q4 and can be neglected for low q2. The transverse cross section is given by :

By CVC and chiral symmetry, one can take :

where g,, and g,,, are the weak coupling constants of p+ and A: ;

M p and MA, are respectively the p and A , masses ; o;+ and are the transverse cross sections of p and A,+ ;

a (y + a -+ p) is the photoproduction cross section of a y with energy given by : E, = v :

a = - 1 137 '

If we take M, = MA,, we get the following general expression for inelastic neutrino interactions at low q2 :

Figure 4 shows the experimental and theoretical distributions given by formula (2). We have computed

ox+ by extrapolation of transition rate of n + + a -+ P

reaction, assuming shadow effect. We have taken a target with independent nucleons for photoproduction cross section and assumed E, = v for the energy of the photon.

FIG. 4. - Experimental and theoretical distributions versus q z assuming shadow effect. a,+ is computed by extrapolation of transition rate. M j > 1.16 (GeV/c2)2, E > 1 GeV : (a) PCAC without any correction ; (/3) PCAC + corrections due t o direct x+ exchange ; (y) PCAC + corrections due to direct z+ exchange

+ transverse current contribution (VDM). Dashed region cor- responds to f 15 % uncertainty on the neutrino flux.

Histograms : See footnote (1).

We see on figure 4 and table IV that the transverse contribution is of the order of 40 %

for q2 < 0.12 (GeV/c)'. It is - 10 % if we take q2 < 0.02 (GeVIc)'.

TABLE IV

q2 < 0.12 0.12 < q2 < 0.20 (GeVlc) (GeV/c)'

Experimental 26 + 6 31 4 7

- -

Theoretical

PCAC without cor-

rection 20.2 +_ 3.0 12.2 + 1.8

PCAC + n+

exchange 18.7 +_ 2.7 11.5 t 1.8 PCAC + VDM + .n+

exchange 34.2 + 5.1 28.7 & 4.2

(1) For events with several p- candidates

the p- is ( the negative track with minimum angle --.

the negative track with maximum angle - - - -.

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EXPERIMENTAL TEST OF THE PARTIALLY CONSERVED C3-121

We find that the experimental and theoretical results are in agreement to one standard deviation for q2 < 0.12 (GeVIc)', PCAC + VDM gives also a good prediction for 0.12 < q2 < 0.20 (GeV/c)'.

The transverse contribution has no sensitive effect on M; and cos O,, distributions so that results are still in agreement to one standard deviation with PCAC + VDM.

Conclusion. - We have shown that the experimental results on inelastic neutrino interactions are in agree- ment within one standard deviation with PCAC, taking

account for corrections estimated by VDM. For a more precise test of PCAC, the cut q2 = 0.02 (GeV/c)' is necessary if one wants to reduce the transverse contribution to 10 %. To reduce the uncertainty for - computation of on+, it is necessary to take v % Jq2.

To suppress the uncertainty due to shadow effect, the PCAC's test should be made on hydrogen. However, in hydrogen bubble chambers, the uncertainty due to events with several p- candidates will subsist.

I thank Mr. J. Six and Mrs. C. A. Piketty for many stimulating discussions.

References

[I] ADLER (S. L.), Phys. Rev., 1964,135,963. [5] FIORINI (E.), Some (( nuclear u considerations based on [2] PIKETTY (C. A.), STODOLSKY (L.), Nucl. PFzys., 1970, the zf interactions on propane, Internal report,

B 15, 571. INFN, Milano, 1968.

[3] BONETTI ( S . V.) et a]., Lettere a1 Nuovo Cimento, S6rie I , [6] BELL (J. S.), LLEWELLYN SMITH (C. H.), Th. 1198,

2, 877. CERN, 1970.

[4] MASNOU (J. L.), Thbe d'Etat, Universitk de Paris, 1971.

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