IL NUOVO CIMENTO VoL. 43 A, N. 4 21 Febbraio 1978

Weak Production of Charmed Baryons (*).

J. ~I%OYLA:ND and :F. ~AVNDAL

Institute of Physics, University of Oslo - Oslo 3, Norway

(rieevuto il I6 Novembre 1977)

Summary.---Differential and integrated cross-sections for neutrino pro- duction of the three lowest charmed baryons are calculated in a rela- tivistic quark model.

1 . - I n t r o d u c t i o n .

The discovery of the b-particles with their special interact ions could most convincingly be explained by the existence of a fourth, heavy quark.

As stressed by GLAsgow, [LIOPOULOS and MAIA~I (1), such a quark was needed in theories for the weak interaction. I t carried a new q u a n t u m number , charm.

I f this quark wus the same as the one which made up the b-particles, then as a direct consequence one should be able to produce charmed hudrons in neutr ino- induced reuctions. The corresponding cross-sections could be calculated f rom

the GII~[ (1) charged weak current

(1.1) J~(x) ---- ~ ( x ) y ~ ( 1 - ~'~)do(x ) -]- ~(x)~,~(1- ~'5)so(x),

where d o and s c are the Cabibbo-rota ted down- and s t range-quark fields

(1.2) d c - - d c o s 0 + s s in0 ,

s o = s c o s 0 - - d s i n 0

(*) To speed up publication, the authors of this paper have agreed to not receive the proofs for correction. (1) S. L. GLis~ow, J. ILIOrOVLOS and L. ~¢IAIANI: Phys. Rev. D, 2, 1285 (1970).

634

WEAK PRODUCTION OF CHARMED :BARYONS 635

with s i n 3 0 _ "~ 1/18. F r o m this general s t ructure it follows tha t the cross-

section for the weak process

(1.3) vv-[-n -~ [z-q-C + ,

where C + is a charmed baryon, is smaller by a factor tg30 compared with the s tandard reaction

(1.4) ~ q - n ~ ~ - d - P ,

which has at high energies a cross-section a--~ 10 -33 em 3. If we ignore possible mass effects, the cross-section for (1.3) then becomes a _ ~ 5.10 -40 cm 3.

I n spite of the ra ther small cross-section, this process offered an obvious method of producing <( naked ~) charm. An actual calculation of the cross-

sections for the product ion of the three lowest conjectured charmed baryons was, therefore, clone immedia te ly af ter the ~ discovery by using the relativistic quark model (3). This model had previously given ve ry good results for weak product ion of nucleon resonances (3), bu t could not be used s t ra ight away for

charm production, since the masses of the charmed baryons were not known

at tha t time. For the same reason, the ordinary electromagnetic-dipole form factor for

the nucleon was used for the weak ~ -+ C transi t ion. This ra ther poor choice forced the differential cross-sections down at large m o m e n t u m transfers and

resulted in correspondingly small, in tegrated product ion cross-sections. This defect was pointed out by Sm~OCK and LEE (8) who did a similar cal-

culation within the f ramework of the isobar model. They obtained results in quali tative agreement with the previous calculation. However , their more

reasonable choice of t ransi t ion form factors gave cross-sections which nu-

merically were an order of magni tude larger. Since the discovery of (( hidden )> charm in the ~-particles, much experi-

menta l work has been done to observe hadrons with (( naked )) charm. So far this has been most successful in e+e - colliding-beam experiments in which one

first saw the charmed D-mesons with masses a round 1870 MeV (4). A charmed ant ibaryon of mass 2260 MeV has been photoproduced together with evidence

for a similar an t iba ryon state of mass ~ 2500 MeV (5).

(3) J. FINJORD and F. RAYNDAL: Phys. ~Lett., 58 B, 61 (1975). (3) R. E. SHROCK and B. W. LEE: Phys. Rev. D, 13, 2539 (1976). (4) For a review of charmed mesons, see B. H. WIIK: in Proceedings o] the X V I I I International Con]erenee on High-Energy Physics (Tbilisi, 1976). (5) B. KNAPP, W. LEE, P. LEUNG, S. D. SMITH, A. WIJANGCO, J. KNAUER, D. YOUNT, J. BRONSTEIN, 1~. COLEMAN, G. GLADDING, M. GOODMAN, M. GORMLE¥, R. ]-~¢[ESSNER, T. 0'HALLORAN, J . SARRACINO, A. WATTElqBERG, M. BINKLEY, I. GAINES and J. PEOPLES: Phys. Rev. Lett., 37, 882 (1976).

636 J. FROYLAND a n d F. RAVNDAL

So far no charmed hadron has been identified in neutr ino produc t ion with the possible except ion of the so-called Samios event (6). I t can be unders tood as the weak product ion of a charmed ba ry o n wi th mass 2426 MeV, which then strongly decays into a pion and another cha rmed ba ryon wi th mass equal to 2244 MeV. The two pho toproduced cha rmed states are mos t p robab ly the antiparticles of these two weakly produced states.

On the other hand, there is cer ta inly s trong evidence for neutr ino produc- t ion of charm in the form of dileptons in the final s ta te (7). The t+ results f rom the weak decay of the charmed s ta te in (1.3). This follows direct ly f rom the GIM current (1.1), which also explains the m a n y strange part icles in the same final states (s).

All this new exper imenta l informat ion has made it possible to per form a much be t t e r calculation of the cross-sections for weak produc t ion of charmed baryons. Knowing tha t these will be needed in the fu ture for fu r ther tests of the GIM mechanism and invest igat ions of dileptons due to weak product ion of possible heavy leptons, we here present an improved calculation of these product ion ampli tudes and cross-sections within the same quark model.

2. - C r o s s - s e c t i o n s .

As discussed in ref. (2), the spectroscopy of charmed, nons t range baryons is almost identical to the spectroscopy of s trange, noncharmed baryons. The lowest Z --~ 0 S U 8 mult iple t contains seven C --~ -~ 1 baryons with the fol- lowing spin-pari ty:

(2.1) { J ~ = ½+ for C°(ddc), C+(udc), C++(uuc), C+(udc),

J P = ~+ for C*°(ddc), C*+(udc), C*++(uue).

The lower index gives the isospin of the state. The masses of these baryons have been predic ted b y DE RVXULA, GEOnGI

and GLASHOW (~). They obta ined 2200 1V[eV for the l ightest one, C0 +. This is in ve ry good agreement with the mass of the pho toproduced s ta te with mass

(6) E. G. CAZZOLI, A. M. CHoPs, P. L. CONNOLLY, R. I. LOUTTIT, ~VL J. MURTAGtt, R. B. PALMER, N. P. SAMIOS, T. T. TSO and H. H. WILLIAMS: Phys. Rev. ~Lett., 34, 1125 (1975). (7) A. BENVENUTI, D. CLIVE, W. T. FORD, R. IMLAY, T. Y. LING, A. K. MANN, R. ORR, D. D. REEDE~, C. RUBBIA, R. STEFANSKI, L. SULAK and P. WANDERER: Phys. Bey. ~ett., 35, 1203 (1975). (s) See M. K. GAILLARD: in Proceedings o] the International Neutrino Con]erenee (Aachen, 1976). (9) A. DE RvJVLA, H. GIORGI and S. L. GLASHOW: Phys. Rev. D, 12, 147 (1975).

W E A K P R O D U C T I O N OF C H A R M E D B A R Y O N S 6 3 7

2260 MeV. I f we, therefore, add 60 MeV to the i r predict ions, we find Cd2420) and C*(2480) in addi t ion to 00(2260). These are the masses we will use in the following.

Wi th incident neutr ino beams we can produce all the cha rmed ba ryons wi th posi t ive charge:

(2.2a) v ~ + p --~ ~x--]-C ++

- - ~ r ~ * + + (2.2b) vT-+-P -+ V. -t-~l

(2.3a) vu--~-n --> [~-@C + ,

(2.3b) v~-]-n ---> y.--{-C + ,

-- , + (2.3e) ~ + n --> y. -t-C 1 .

The A I = ½ p r o p e r t y of the charm-chang ing piece in the weak cur ren t (1.1) gives the following relat ions be tween the cross-sections for these reac t ions :

(2.4)

(2.5)

a(v~-nt-p --~ ~ - + C ++) = 2a(,J~+n -+ ~z-+C+),

( r ( ,~+p -+ ~--t-C~ ++) --- 2a (v~+n --~ ~-+C~ '+) .

We, therefore, only have to consider the first three react ions, (2.2a), (2.2b) and (2.3a).

The differential cross-sections for these neut r ino- induced react ions h a v e the general fo rm (lo)

G 2 d 2d° 21i ,2)] ( ~ . 6 ) ~ (u~lt+I ~ + .

Here we have i n t roduced / o , ]+ and ]_ for the m a t r i x e lements of the charm- changing weak cur rent corresponding to scalar, r ight- and l e f t -handed polar- izations. A com m on fac tor of sin 0 has been t a k e n out of these ampl i tudes a n d combined wi th the weak-coupl ing cons tan t G to give G, ~ G sin 0. Q* are the space components of the 4 - m o m e n t u m t rans fe r q, in the res t s y s t e m of the cha rmed ba ryon , g~ ---~ v *~ - - Q*~. The pure ly k inemat ica l fac tors u and v are given b y

1 (2.7) u ---= ~ (E + E ' -t- Q) ,

1 (2.8) v = ~ (E + E ' - - Q ) ,

(lo) F. RAVNDAL: 2g@OVO Cimento, 18A, 385 (1973).

6 3 8 J . F R O T L A N D ~ n ~ F. R A V N D A L

where E is the incident neutr ino energy in the labora tory system. The final muon energy is E ' = E - - v in the same sys tem in which also q 2 = v~_ Q2.

:Now the calculation of the t ransi t ion ampli tudes ]o and ]+ follows straight- forwardly from the s tandard formalism developed in ref. (~0). I f we notice

tha t the wave functions of the charmed baryons are identical with those of the corresponding hyperons, all the amplitudes can be t aken directly f rom the calculation of weak product ion cross-sections for strange baryons (1~). In this

TABLE I. -- Matrix elements o] the weak current between a neutron and a positively charged charmed baryon.

Co+(2260) ]+~ = ~ ~/6R +

/o+= { V ~ ( s ' + c )

/o- = 23 V~ (s - c)

] - 1 = ~ V ~ R -

C+(2420) /+1 = -- ½ ~/~R+

fo+ = + ½ "X/2 (3S - - C)

/ o -= + ~ / ~ ( 3 8 + c)

/-1 = - - ½ V ~ R -

c~+(24so) /+~ = - - VSR+

] +1 ~ - - / ¢ +

/o+ = -- 2C

/ o - = - 2 c

/ -1= + R -

way we find the transit ion amplitudes given in table I. They involve the kine-

matical factors

/~ __ q2 F v* (2.9) S - - 6 M 2 Q , ~ (3Mm + q 2 - - m 2) -~ 6 M Q . 2 ( M ~ - - , m ~) ,

Z F (2.].0) C - - 6MQ* ( M 2 - m 2 ) '

(2.11) R ~ = - - (R~ ± R A) ,

where

(2.12) 10 ~= V ~ F Q * M + m

( M + m) 2 - - q2

(11) j , FINJORD and F. RAV~DAL: Nucl. Phys., 106B, 228 (1976).

W:EAK P R O D U C T I O N OF C H A R M E D B A R Y O N S 639

a n d

(2d3) RA = Z T ~ M ~ % / 2 ( + m ) .

H e r e m is t h e t a r g e t n u c l e o n m a s s a n d M is t h e c h a r m e d - b a r y o n mass . As

in ref . (10), t h e n o r m a l i z a t i o n c o n s t a n t Z ----- 0.74 is n e c e s s a r y in o r d e r to g e t

t h e co r r ec t a x i a l v e c t o r c o u p l i n g c o n s t a n t gA = 1.23 for t h e nuc l eon . T is

a n ove ra l l f o r m f ac to r . F o r w e a k a n d e l e c t r o m a g n e t i c t r a n s i t i o n s b e t w e e n

n u c l e o n s i t was chosen so t h a t i t r e p r o d u c e s t h e co r r ec t d ipo le f o r m f a c t o r

(2.14) F(,N~--> ,N') - - ( 1 - - q2/lm")½ ( 1 - q2/0.71)2 '

w h e r e q2 is m e a s u r e d in un i t s of (GeV) 2. F o r a t r a n s i t i o n b e t w e e n a n u c l e o n

a n d a c h a r m e d b a r y o n w i t h m o r e t h a n t w i c e t h e n u c l e o n mass , t h e r e is l i t t l e

r e a s o n to e x p e c t t h e s a m e b e h a v i o u r of t h e c o r r e s p o n d i n g f o r m f a c to r .

. F o l l o w i n g t h e a r g u m e n t s of S h r o e k a n d Lee , we t a k e t h e a t t i t u d e t h a t

t h e c h a r a c t e r i s t i c m a s s 0.71 (GeV) 2 in t h e e l a s t i c f o r m f a c t o r (2.9) is in some

w a y se t b y t h e m a s s e s of t h e o r d i n a r y v e c t o r m e s o n s p a n d o~. W i t h a c h a r m e d

v e c t o r m e s o n D* w i t h a m a s s n e a r 2 G e V (4) we wi l l t h e r e f o r e a s s u m e for t h e

i n e l a s t i c t r a n s i t i o n f o r m f a c t o r

(2.15) F ( ~ - ~ c ) = (1 - q2/(M + m)2)~

This wi l l o b v i o u s l y g ive l a r g e r c ro s s - sec t i ons for l a r g e r m o m e n t u m t r a n s f e r s .

The k i n e m a t i c a l f u n c t i o n S in eq. (2.9) is seen to i n c l u d e a t e r m p r o p o r t i o n a l

to t h e m a s s d i f fe rence M 2 - - m 2. I t was n o t p r e v i o u s l y i n c l u d e d , s ince t h e w e a k

v e c t o r c u r r e n t s we re t a k e n to b e a p p r o x i m a t e l y conse rved . F o r t h e c h a r m -

c h a n g i n g r e a c t i o n s u n d e r c o n s i d e r a t i o n s h e r e i t m u s t be i n c l u d e d . I t g ives

a s i zab le c o n t r i b u t i o n to t h e d i f f e r e n t i a l c ro s s - sec t i ons in t h e f o r w a r d d i r e c t i o n

w h e r e t h e t r a n s v e r s e a m p l i t u d e s do n o t c o n t r i b u t e .

3 . - R e s u l t s .

The d i f f e r e n t i a l c ros s - sec t ions for i n c i d e n t n e u t r i n o e n e r g y E = 20 GeV

a r e s h o w n in fig. 1. F o r c o m p a r i s o n we h a v e a lso i n c l u d e d t h e r e s u l t s of S h r o c k

a n d Lee for t w o of t h e r e s o n a n c e s . F o r t h e C+(2260), we o b t a i n a l m o s t t h e s a m e

c ross - sec t ion , whi l e for t h e C++(2420) ou r v a l u e s a r e s m a l l e r b y r o u g h l y a f a c t o r

of two .

~40 J, FROTLAED and F. RAVNDAL

The i n t e g r a t e d c ross - sec t ions a r e p l o t t e d in fig. 2 as f u n c t i o n s of t h e e n e r g y E .

As n o t e d f i rs t b y FZNJO~]D a n d t~AVNDAL (3), t h e C+(2260) comes o u t w i t h t h e

l a rge s t c ross - sec t ion , g ~ 2 0 . 1 0 -4° c m ~ u b o v e t h r e s h o l d . T h e C++(2420) s h o u l d

101

10 o

A

~EuEIO (

! o

10 ¢

~ " - . I I I I I I

\ \ \

c t *~ " -

I I I I I I 2 4 6 - q 2 [(GeV)2]

Fig. 1. - Differential cross-sections for the weak product ion of the three lowest charmed baryons a t ~n incident neutrino energy E = 20 GeV. Dot ted lines ~re obta ined from (~).

be p r o d u c e d w i t h a m u c h s m a l l e r c r o s s - s e c t i o n ~___ 4 . 1 0 -4° c m 2. F o r t h e

C*++(2480), we o b t a i n ~ _ ~ 6 . 1 0 - 4 0 c m ~. N o c o m p a r i s o n c a n in th i s case b e

m a d e w i t h S h r o c k a n d Lee . Th is is d u e t o t h e i r u se of t h e i s o b a r f o r m a l i s m

which g ives a c ross - sec t ion i n c r e a s i n g w i t h e n e r g y fo r th i s p a r t i c u l a r r e s o n a n c e

w i t h sp in J = ~. I n t h e q u a r k m o d e l n o such p r o b l e m ar i ses , s ince b o t h t h e

J - - - - ½ a n d J ~ ~ r e s o n a n c e s h a v e a5 = 0.

W E A K 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 ~ l

101

E u .

I o

b

I I i I I I

J

I0

C{ ++

C++

I I I I 10°0 20 30 E(GeV)

Fig. 2. - Total cross-sections for the weak production of the three lowest charmed baryons as functions of the incident neutrino energy E.

4 . - Discussion.

Recent ly AWLS, Z, XOBAYASIII and K 6 ~ , n (12) h a v e calcula ted the same product ion cross-sections in a nonrela t iv is t ic qua rk mode l wi th somewha t different assumpt ions abou t the crucial t rans i t ion fo rm factors. They calculate to t a l cross-sections which are in rough agreement wi th our results. Their cross- section for the C ++ is, however , larger t h a n for the v 1~*++, jus t the opposi te of wha t we have found. I n a more recent calculat ion (la) using essential ly the same qua rk model , the i r resul ts get sl ightly modified and now agree ve ry well wi th wha t we have presented here and wi th the results of Shroek and Lee.

Three independent calculat ions give therefore essential ly the same cross- sections for weak produc t ion of cha rmed baryons . Hopefu l ly the expe r imen ta l s i tuat ion will improve so m u c h t h a t a compar ison wi th da ta can be made . High-s ta t is t ics exper iments could even check finer detai ls of the p roduc t ion process like densi ty matr ices . These follow direct ly f r o m the ampl i tudes in tab le Z as expla ined in ref. (10) and reflect direct ly the conjectured V - - A s t ruc ture of the cha rmed piece of the GIlV[ current .

(12) C . A V I L E Z , T. KOBAYASHI and J. G. KORNER: Phys. Lett., 66 B, 147 (1977). (13) C. AvIT.Ez, T. KOBAYASHI and J. G. KSRNER: DESY prcprint (1977).

41 - I I Nuovo Gimento A.

642 J. FROYLAND aHd F. RAVNDAL

F i n a l l y i t s h o u l d b e s a id t h a t t h e s a m e q u a r k m o d e l o b v i o u s l y m a k e s i t

p o s s i b l e to c a l c u l a t e t h e i nve r se of t h e r e a c t i o n s c o n s i d e r e d he re , n a m e l y semi-

l e p t o n i c d e c a y s of c h a r m e d b a r y o n s . T h e s e p a r t i a l w i d t h s wi l l b e of some

i m p o r t a n c e fo r t h e u n d e r s t a n d i n g of t h e d i m u o n e v e n t s r e s u l t i n g f r o m n e u t r i n o -

i n d u c e d p r o d u c t i o n of c h a r m .

• R I A S S U N T 0 (*)

Si calcolano le sezioni d 'ur to differenziali e in tegra te per la produzione da par te del neutrino dei t re pifi bassi barioni incanta t i in un modello a quark relativistico.

(*) Traduzione a cura della Redazione.

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Pe3ioMe (*). - - B paMi<ax peTI~ITHBIdCTCKO~ MOJIeJ'ltI KBapKoB BblqHCJ/~IIOTC~I ~rlqbqbe- peHtIHanbab~e a mtTerpanbHbIe nonepe~rmIe ce~teHrla p o ~ e a H ~ Tpex HIIalIIIIX o~apoBaa- rmtx 6ap~oaoB B pe3y~sxaTe B3aldMO~e-~CTBH~ He~Tpn~o.

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