Inclusive ηp and ηn charged-current neutrino reactions below 6 GeV

Volume 66B, number 3

PHYSICS LETTERS

INCLUSIVE

vp AND vn CHARGED-CURRENT REACTIONS

31 January 1977

NEUTRINO

BELOW 6 GeV*

S.J. BARISH 1 , M. DERRICK, T. DOMBECK 2 , L.G. HYMAN, B. MUSGRAVE, P. SCHREINER, R. SINGER, M. SZCZEKOWSKI 3 Argonne National Laboratory, Argonne, Illinois 60439, USA

and V.E. BARNES, D.D. CARMONY, E. F E R N A N D E Z and A.F. G A R F I N K E L Purdue University, Lafayette, Indiana 47907, USA

Received 3 November 1976 Results are presented of a study of inclusive vp and un interactions from threshold to 6 GeV. The data show a rapid approach to the distributions expected in the naive quark-parton model. The charged-current u deuteron total cross section is fit by the expression OT(vd) = (0.76 +-0.03) × 10-3a E v cm 2 per GeV per nucleon. For E v > 1.5 GeV, we measure aT(vn)/oT(~p) = (2.02 -+0.23). The distributions in the scaling variables x and y are given and discussed.

The interactions o f high energy neutrinos with complex nuclei have been actively studied in recent years, and the results for neutrino energies up to 30 GeV agree well with the quark-patton model (QPM) [ 1]. By using large cryogenic bubble chambers, these experiments are being extended to reactions on elementary proton and neutron targets. We have previously reported studies o f exclusive final states resulting from exposures o f the Argonne 12-foot H 2 and D 2 filled bubble chamber to the v beam at the Zero Gradient Synchrotron [2]. In this paper, we present results o f an inclusive study o f vp and vn interactions from threshold up to 6 GeV neutrino energy [3]. The data come from 360,000 (9000,000) pictures taken with a hydrogen (deuterium) fill of the bubble chamber yielding a total o f about 1500 v-induced charged-current events. Table 1 lists the reactions we have considered and the number o f events assigned to each channel. The identification o f the constrained reactions ((1), (4), * Work supported by the U.S. Energy Research and Development Administration. 1 Present Address: Carnegie-Mellon University, Pittsburg, PA 15213, USA. 2 Present Address: University of Maryland, College Park, Maryland 20742, USA. a On leave of absence from Institute for Nuclear Research, Warsaw, Poland, USA.

(8), (13), and (16)) is quite straightforward. In the 4- and 5-prong final states, multiple neutrals are negligible, and those 4- and 5-sprong events which do not give a constrained fit are assumed to have either a missing neutron or 7r0, depending on whether there is an identified proton in the final state. The resulting 0constraint solution determines the energy o f the event as well as all the other kinematic quantities o f interest. The separation and v energy measurement for the events with multiple neutrals and the single pion production reactions (9) and (10), induced b y the higher energy neutrinos, is more difficult. We solve this problem in a statistical way b y utilizing the constrained charged-current events and assuming the constrained and unconstrained events, with the same number o f pions, have similar distributions in the kinematic variables [4] ¢. The assignment of most o f the events as having come from a neutron or proton target is straightforward. The only difficulty comes from the possible confusion between vn interactions with proton spectators o f high m o m e n t u m and the vp interactions giving a low m o m e n t u m recoil proton. We define all protons o f * Since we are studying the inclusive cross sections, possible errors coming from cross talk between channels such as (9) and (11) are not important, although the errors given in table 1 do include this systematic effect. 291

Volume 66B, number 3

PHYSICS LETTERS

Table 1 Exclusive channels contributing to the inclusive reactions v + p ~ # - + X++ and v+ n-+ ~-+ X + Reaction

3 l January 1977 F

[

T

[

(Q)

IO0

~

v+n--~-÷

i

q

r

~

(c)

i

:

x +

i

ii

Weighted number of events H2 exposure D2 exposure

/

/ (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17)

up +t~-pn + u p - ~ / p n +(Irr ° ) 1 > 1

up~/Jmr+rr+(mn°)m>O -

÷

÷

-

up-~prrn~r u p ~ - P ~r%r+lr-lr° up -+ ~-nrr+n%r+Ir vp-~-+strangeparticles ~U-P vn~u-plr ° vn--*u-nrr + vn-+u-p(kTr0)k>2 vn--,~-nrc+(Irt°)l>1 vn-~#prrn un~-prr+n-(lrr 0 ) I > 1 vn --, #-nlr%r+Tr-(mnO)m > 0 vn-+/aprr n n z r vn-+ . - + strange particles -

+

-

-

÷

+

-

-

90 ± 11 5+- 3 2+- 1 0 2 -+ l 0 3± 3

267 +- 21 23± 6 12± 4 10± 3 1 -+ 1 0 1± 1 808 ± 40 126 ± 14 81 -+ 10 3 2 -+ 13 29 -+ 12 20± 5 8± 4 3± 2 0 9± 3

L

l

,0t[ (5 0.I z >

t

i,o

+'

•

t

•

.

. . . . .

+'

{d)

~3 t ?+ •

+

21 i

"

I00:

i '.++, :

I

,2!

i

ioi

/I

!

/

/

/

/

•

i ~ 2.0 3.0

4.0

/

m o m e n t u m < 350 MeV/c as spectator protons. Corrections are then made for the misclassification o f events using the observed spectator p r o t o n m o m e n tum distribution in the 3-constraint reaction vd + / - P P s and the observed recoil p r o t o n m o m e n t u m distribution from the identified up events such as vd ~/a-pTr+ns . We make small corrections in each o f the unconstrained channels for events induced by incident neutrons and for neutral-current v events. The neutroninduced background is 1.5% overall and is normalized using the observed events o f the reaction np ~ p p l r - . Fig. l(a, b) shows the distribution o f events in neutrino energy separately for the n e u t r o n and p r o t o n targets. The reactions are d o m i n a t e d by the quasi-elastic (/a- p) and single pion p r o d u c t i o n (~-pTr +) final states, respectively, as shown by the dashed histograms. The total cross section, expressed as the average o f un and vp, is given in fig. l(c). The errors include a systematic flux uncertainty of-+15% folded in with the statistical error. Within errors, the cross section rises linearly with E and can be parameterized as aT(Vd ) = (0.76 -+ 0.03) XVl0 - 38 Eu cm 2 per nucleon per GeV. The o n l y o t h e r u cross section m e a s u r e m e n t in this energy range is f r o m a freon target in Gargamelle [5]. That experiment measured a slope o f 0.74 + 0.02 in the energy range 1 - 9 GeV, so the results o f the two experiments agree. 292

oILL 0

] 1,0 2.0

3.0

4.0

E GeV

5.0

6.0

0L

i

0

l.O

1

~

_.J 5.0

60

E GeV

Fig. 1. (a) Neutrino energy distribution of events of the reaction v + n + ~-+ X÷. (b) Neutrino energy distribution of events of the reaction v + p ~ u- + X~. Note the change of binning at 2 GeV and 3 GeV in both (a) and (b). The dashed histograms represent the ~-p and u-pn ÷ final states, respectively. (c) Total vN cross section measured as the mean of the vn and up cross sections. (d) Total cross section ratio for vn and up interactions as a function of E v. The quasi-elastic events have been removed for the data with open circles. (e) Mean value of the square of the four-momentum transfer as a function of Ev. Since the n e u t r o n has two d o w n quarks and the proton only one, the QPM predicts that the total cross section ratio R = aT(vn)/aw(vP) should be 2.0 if only the three valence quarks contribute. Specific scaling fits to electron, m u o n , and high energy v data predict values in the range 1.56 to 2.34 [6]. The only published value o f 1.5 + 0.3 comes from an old C E R N experiment in a small heavy liquid bubble chamber [7], although preliminary values have also been q u o t e d f r o m more current experiments [8]. Our measured cross section ratio is shown in fig. 1(d) as a f u n c t i o n o f E v. The

V o l u m e 66B, n u m b e r 3

I00

PHYSICS LETTERS

31 January 1977

(o)

(o)

- -

i

20-

80 _-

15-

__

1/0

'

•

15

6O I0-

-I0

I

5

? 0

~"

i

l

I

i

t

0.2

0.4

0.6

0.8

1.0

z

~

y

-

0 40-

I

I

I

I

80

l
o

,. 3 0 -

60

2
40

m 20I,---

2
>

5

10-

-

20

I

0 0

0.2

0.4

0.6 Y

0.8

1.0

Fig. 2. The distribution in the energy sharing variable y = ( E u - E # ) / E v for ud interactions for (a) 1 < E u < 2 GeV and (b) 2 < E v < 6 GeV. The quasi-elastic events vn --, #-p

are s h o w n dashed.

40-

I

i

I

(c)

--71

120

30- _ ~ _ ~

//d

Ev~3 GeV 90

20

~- 60

I0

30

0

open circles show the ratio with the quasi-elastic events removed. We use only the deuterium data in this plot so the measurement is independent o f the flux. After a strong fall at low energies, where the quasi-elastic events dominate, the ratio levels off at about 2. For E v > 1.5 GeV, we measure R = 2.02 +- 0.23 for all the data and 1.20 +- 0.15 and rising with increasing energy if the quasi-elastic events are removed. Our results show that the value expected in the QPM is approached quickly. A second check on this precocious scaling can be made by looking at the mean square four-momentum transfer between the leptons, (Q2), as a function of E v. As seen in fig. l (e), (Q2) rises with E v and, using all the data, the best linear fit is (Q2) ___(0.05 -+ 0.02) + (0.31 + 0.03) E v with 0.75 GeV gives (Q2) = (0.11 -+ 0.04) + (0.26 + 0 . 0 3 ) E v as shown on fig. l(e). This fit is in agreement with that obtained in the Gargamelle [5] experiment where (Q2) = (0.12 + 0.03) + (0.23 -+ 0 . 0 1 ) E v represented the data with E v > 1 GeV. The finite intercept presumably arises from the v energy thresholds for the quasi-elastic and single-pion production channels. The slopes also agree fairly well with

I

0

I

i

I

I

0.2

0.4

0.6

0.8

I.O

X

Fig. 3. distributions in the x variable (x = Q 2 / 2 M ( E v - E # ) ) . (a) Comparison of the x distributions for ~ interactions (full histogram) with that for vn interactions (dashed histogram) with that for un interactions (dashed histogram) for the present experiment with 2 < E u < 6 GeV. Co) x distributions for interactions with the two energy selections 1 < E v < 2 GeV (dashed histogram) and 2 < E v < 6 GeV (full histogram). (c) Comparison o f t h e vdx distribution for 2 < E v < 6 GeV with m e a n v energy 3.20 GeV (full histogram) with wp interaction at a m e a n energy of ~ 3 0 GeV (dashed histogram). In (a), (b), and (c), the ordinate scale for the full (dashed) histogram is on the left (right). The two distributions in each o f (a), (b), and (c) are normalized to equal areas.

0.18 -+ 0.01 measured in the high energy vp experiment at Fermilab [9], even though our data are dominated by a few exclusive channels and hence by the vector and axial vector nucleon form factors [2]. With our spectrum and the observed cross sections, the mean energy of the events in the 2 to 6 GeV neutrino energy range is 3.20 GeV, and the mean charged hadron multiplicities are 2.29 -+ 0.06 and 1.29 + 0.05 for up and vn interactions, respectively. The mean hadronic mass, W, is 1.6 GeV. The vp multiplicity is in good agreement with extrapolations of the W de293

Volume 66B, number 3

PHYSICS LETTERS

pendence seen in the higher energy data [10]. The distributions in the scaling variable y = (E v - E ~ ) / E v are shown in fig. 2 for vd interactions and the energy selections (a) 1 < E v < 2 GeV and (b) 2 < E v < 6 GeV. The y distribution is somewhat different in the two energy ranges, and is flatter for the higher energy selection, in agreement with the scaling prediction beyond the resonance region. For a low energy experiment, the kinematic restrictions on y are important and favor the central y range. The contribution from the quasi-elastic channel vn ~ / a - p is shown shaded. Since the y distribution measures the inelasticity, the higher multiplicity events populate the larger y values [4]. The distributions in the other scaling variable x = Q2/2M(Ev - E u ) , where M i s the nucleon mass, are shown in fig. 3. In this case since the quasi-elastic events have a singular distribution peaked at x = 1, we do not include them in the plots. In fig. 3(a) we show the x distribution for the 2 < E v < 6 GeV selection separately for n and p targets The distributions agree well, so that at the present statistical level, our results do not show evidence for a leading quark in the nucleon. The x distributions for vd interactions with the two energy selections 1 <~E v < 2 GeV (dashed histogram) and 2 < E v < 6 GeV (full histogram) are shown in fig. 3(b). As the energy increases, the x distribution becomes sharper with an increase in the region x < 0.2 and a decrease at larger x values. Fig. 3(c) compares the x distribution measured in this experiment for our higher energy selections with the Fermilab vp data at a mean energy about ten times higher. The shrinkage seen within our own data is observed to continue, albeit more slowly, as E v is increased. This behavior is qualitatively similar to the nature of the scaling violations claimed in the electron and

294

31 January 1977

muon inclusive data from SLAC and Fermilab [ 11 ]. These experiments show the type of scaling violation predicted by the asymptotically-flee gauge theories [ 12]. This similarity is remarkable considering that our data are in the resonance region. We would like to thank D.H. Perkins for stimulating discussions on the topics of this Letter.

References [ 1] See, for example, F. Scuilli, High energy neutrino processes, in: Particles and fields 1975, eds. H.J. Lubatti and P.M. Mockett (University of Washington). [2] W.A. Mann et al., Phys. Rev. Letters 31 (1973) 844; S.J. Barish et al., Phys. Rev. Letters 36 (1976) 179. [3] The neutrino flux for this experiment is given in S.J. Barish et al., Phys. Rev. Letters 33 (1974) 1446. [4] M. Derrick, Charged-current v and ~ interactions in hydrogen and deuterium, ANL-HEP-CP-76-42,to be published in Proceedings of the 1976 Aachen v Conference. [5 ] T. Eichten et al., Phys. Lett. 46B (1973) 274. [6] A. De Rujula et al., Rev. Mod. Plays. 46 (1974) 391; V. Barger and R. Phillips, Nucl. Phys. B73 0974) 269; R. McElhaney and S.F. Tuan, Nucl. Phys. B72 (1974) 487. [7] G. Myatt and D.H. Perkins, Phys. Lett. 34B (1971) 524. [8] See, for example, the review by D.H. Perkins, in: Proc. 1975 Lepton and photon conference, Stanford, p. 571. [9] J.P. Berge et al., Phys. Rev. Lett. 36 (1976) 639. [10] J.W. Chapman et al., Phys. Rev. Lett. 36 (1976) 124. [11 ] H.L. Anderson et al., Measurement of nucleon structure functions in muon deep inelastic scattering at 100 and 150 GeV/c, paper presented at Tbilisi Conference. [12] H.D. Politzer, Phys. Reports 14C (1974) 129; Wu-KiTung, Phys. Rev. Lett. 35 (1975) 490; Porter W. Johnson and Wu-KiTung, Comparison of asymptotically-free theories with high energy deep inelastic scattering data, liT preprint (1976); G. Altarelli et al., Phys. Lett. 63B (1976) 183.