Volume 58B, number 1 PHYSICS LETTERS 18 August 1975

N E U T R I N O - P R O D U C T I O N O F C H A R M E D B A R Y O N S

J. FINJORD and F. RAVNDAL NORDITA. Blegdamsve] 1 7, DK-2100 Copenhagen, Denmark

Received 29 April 1975

Cross-sections for neutrino-production of the three lowest conjectured charmed baryons are calculated from a • relativistic quark model.

The surprising discovery of the narrow $- or J- resonances [1] has made the actual existence of charmed hadrons more likely [2]. Bjorken and Glashow and Amati et al. [3] were the first to discuss the possibility of a fourth, charmed quark. More recently it has been shown that a fourth quark is required in unified theo- ries of weak and electromagnetic interactions [4] where the charged, weak hadronic current takes the form:

J~(x) = ~u(x)%(1 - 3'5)[$d(x) cos0+ Ss(X)sin 0] (1)

+ ~c(X)3'a( 1 -- 3'5) [~bs(X) cos0 -- ~kd(X) sin 0] .

From this current follows directly that charmed ba- ryons (C) should be produced by incident neutrinos on nuclear targets,

v + N - + # - + C , (2)

with cross-sections of the same order of magnitude as for production of strange baryons (Y) with antineu- trinos [5],

F + N "-"/~+ + Y , (3)

i.e., o ~ 10-40cm 2. In order to find out more detailed properties of

the charmed, final baryon state in eq. (2), we have used a relativistic quark model [6] to calculate the cross- sections for weak production of the three lowest, charmed resonances. This model has previously been found to work quite well for weak production of nu- cleon [7] and strange [8] resonances.

Symmetry-breaking effects due to the large mass of the charmed quark [2J, will be included only by using the physical masses of the charmed baryons in the current matrix elements.

With four quarks, each with spin 1/2, baryons in

the completely symmetric state will belong to the SU(8) representation 120. The SU(4), J / ' ) content of this representation is:

r20 a +~ 120 = ~ S,$- J + ( 2 0 M , { + ) " (4)

Each SU(4) representation contains ordinary SU(3) representations with definite charm. For the symmetric representation 20 S, this content is

(5) 20S=(10, C=0)+(6, C= 1) + (3, C=2) + (1, C=3) .

And for the SU(4) representation with mixed symmetry, 20M, one has:

20 M = (8, C= O) + (6 , C = l ) + (5, C= l ) + (3, C = 2) " ~.6)

Introducing the following notation for the charmed C= 1, non-strange baryons in these multiplets,

(LC=l,JP=½+) : c~, + + +

(6, C = I , J P=½+):C O,C 1,C 1 , (7)

(6'C=I'JP=~+): C~ 0,CI*+'~IO*++ ,

we have five possible reactions:

v + N + - ++ - * v + C I , (8)

-* # - + C~ ++ , (9)

v +N O - * / a - + C 0 , (10)

-* /a -+C~ , (11)

-* # - + C~ + . (12)

The AI = 1/2 property of the charm-changing piece in the weak current in eq. (1), gives immediately the fol- lowing two relations between the cross-sections for these reactions:

o(v+N+-*la-+C+ll+)=2o(v+NO-*la-+C1), (13)

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Voh~me 58B, number 1 PHYSICS LETTERS 18 August 1975

Table 1 Weak production amplitudes for the three lowest charmed C = 1 and non-strange S = 0 baryons.

c ; I÷, : } , / Z . R ÷

cg, J P : ½÷) fo +: } ~ " ¢s + c ) I o - : } ~ . (s - c )

, I - , : } , / ~ . R -

C; f . , = - ½x/2.R ÷ ~6. j e = ½*) Io÷ = + ½ ~ . ~3s - c )

[ o - = + ½, f i" ~3s + c ) f - , = - ½ , f i . n -

Ct + f+3 = -x/~'R÷ (6, JP= }÷) f+~ = -R +

• to+ = -2C fo- = - 2 C f-t = + R -

]'-3 = + x/'3"R-

*+ u - + c~ +) o 0 ' + N + ~ / . t - + C 1 + ) = 2 o ( v + N 0 ~ . (14 )

15

E L)

' O 05

3.5

~ 5 f - -

4 6 8 10 12 lt,. 16 18 20

E(GeV)

Fig. 1. Integrated prod uction cross-section for v + N O --. # - + C~ as function of neutrino energy E. Each curve is labelled by the mass in GeV of the charmed baryon.

We therefore only have to consider neutrino excitation of neutron targets (10), (11) and (12).

As shown in ref. [7] the differential cross-section for any of these neutrino reactions can be written in the general form: (15)

dq2d° -G212uv[ f0124 (~ .22 ) ( u 2 1 f + 1 2 + ° 2 [ f 4 7 r -12) 1 "

The matrix elements of the charm-changing piece of the weak current give the production amplitudes f0 , f _ and f+ corresponding to scalar, right-handed and left-handed polarizations. A common factor of sin 0 where 0 is the Cabibbo angle, has been taken out of these amplitudes and combined instead with the weak coupling constant G to give G s = G sin 0. Other kine- matical variables like u and v are defined in ref. [7].

In order to calculate these amplitudes, we use the fact that the SU(8) wavefunctions for the three lowest charmed and nonstrange baryons have exactly the same form in terms of c, u and d quarks as the SU(6) wavefunctions for the three lowest hyperons in terms of s, u and d quarks. More explicitly:

[C~(c, u, d), 3,½+1 = [A0(1115)(s-*c,u, d), 8 ,½+], +

[Cl(C, u, d), 6,½ +] = [zO(1193) (s- .c , u, d), 8,½+1,

[C p(c, u, d), 6,-} + ] - [Z*0(1385)(s-*c,u,d), I0,}+].

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The weak production amplitudes for these charmed baryons will therefore be identical to the amplitudes for weak production of the corresponding hyperon. Only the resonance masses have to be changed. The latter amplitudes are given in ref. [8] and are repro- duced here in table 1. The notation is the same as in ref. [7].

Having the amplitudes, it is straight-forward to cal- culate the differential cross-sections from eq. (15). Here we only give the integrated cross-sections. In fig. 1 this is given for the isosinglet C; while cross-

. - + ~-t- section for the two so tnp le t members C 1 and C 1 are presented in fig. 2. Each curve has been labelled by the mass used for the charmed baryon. We have considered masses ranging from 1.5 GeV up to 4 GeV.

From these two figures and eqs. (13) and (14) it is clear that the dominant contribution to production on nuclear targets comes from the spin 1/2 charmed baryon C~ and spin 3/2 c '*++ ~ l . Both have cross-sections which rise very rapidly to their asymptotic values just above production threshold. These are still very small, around 1% of the total neutrino cross-section at the lowest energies.

Since several events of weak product ion of hyperons which have cross-sections of roughly the same size [8], have been observed [5], one should also expect to see

Volume 58B, number 1 PHYSICS LETTERS 18 August 1975

0.5 1.5

0 t,

u 3 03 '2

"b 0.2

01

2 4 6 8 10 12 1/. 16 18 20

E{GeV)

Fig. 2. Integrated production cross-section for u + N ° ~ p - + C~ (broken lines) and l,+ N ° ~ ja- + C~ '+ (solid lines) as func- tions of neutrino energy E. Each curve is labelled by the mass of the charmed baryon in GeV.

charmed baryon production at existing CERN and Brookhaven energies. Through weak decays, they will show up as strageness S = - 1 final states [2]. A signal of that kind could be indicative of charmed baryon production. However, it could also result from ordinary associated production where one of the strange particles, probably a K 0, escapes detection or it could be due to antineutrino contamination of the incident neutrino beam.

Should the produced charmed baryon decay via a weak leptonic mode, the final state will contain, in addition to the strangeness S = - 1 hadrons, a lepton pair. The negative lepton comes from the primary re- action, eq. (2), while the positive antilepton comes from the weak decay [9].

References

[1] J.J. Aubert et al., Phys. Rev. Letters 33 (1974) 1404; J.E. Augustin et al., Phys. Rev. Letters 33 (1974) 1406; G.S. Abrams et al., Phys. Rev. Letters 33 (1974) 1453.

[2] M.K. Gaillard, B.W. Lee and J.L. Rosner, FNAL preprint FERMILAB-Pub-74/86-THY; A. De Rfjula and S.L. Glashow, Phys. Rev. Letters 34 (1975) 46.

[3] J.D. Bjorken and S.L. Glashow, Phys. Letters 11 (1964) 255; D. Amati, H. Bacry, J. Nuyts and J. Prentki, Phys. Letters 11 (1964) 190.

[4] S.L. Glashow, J. Uiopoulos and L. Maiani, Phys. Rev. D2 (1970) 1285.

[5] T. Eichten et al., Phys. Letters 40B (1972) 593. [6] R.P. Feynman, M. Kislinger and F. Ravndal, Phys. Rev.

D3 (1971) 2706. [7] F. Ravndal, Nuovo Cimento 18A (1973) 385. [8] J. Finjord and F. Ravndal, in preparation. [9] A. Benvenuti et al., Phys. Rev. Letters 34 (1975) 419.

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