Charmed-particle production in right-handed charmed current

L]~TTER]~ AL INUOVO CIMENTO VOL. 17, N. 4 25 S e t t e m b r e 1976

Charmed-Particle Production in Right-Handed Charmed Current.

J . iV[AHAI~AN A

Ins t i tu te o/ Phys ics , Bhubaneswar - 751007 Orissa, I n d i a

L. P. SINGtt

Depar tment o] Phys ics , Utkal Universi ty , Bhubaneswar - 751004 Orissa, I n d i a

( r icevuto il 16 Giugno 1976)

Recen t ly , D~ RUJULA, GI~ORGI a n d GLAStIOW (1,2) (DGG) h a v e sugges ted a new fo rm of weak c u r r e n t in order to p r ov i de a sa t i s fac to ry e x p l a n a t i o n of t h e h i = �89 ru le a n d t h e a n o m a l o u s s t r e n g t h of n o n l e p t o n i c decays of had rons . The h a d r o n i c p a r t of t h e modif ied cha rged weak c u r r e n t is

(1) J ~ = g ~ 7 ~ ( 1 - 4 - 7 5 ) ( n c o s O + ~ s i n O ) - i - ~ ' ? ~ ( 1 - i - y ~ ) ( ~ c o s O - - n s i n O ) - i - ~ ' y ~ ( 1 - - y 5 ) n .

The las t t e r m in eq. (1) ha s t h e V + A s t r u c t u r e whereas t h e res t of t h e e q u a t i o n is t h e f ami l i a r V - - A weak c u r r e n t of GLASHOW, ILIOPOLOUS a n d MAIANI w i t h c h a r m e d qua rk . BARGER et al. (a) h a v e successful ly exp l a ined va r ious aspects of F N A L h igh- ene rgy n e u t r i n o s c a t t e r i n g d a t a in t h e f r a m e w o r k of q u a r k - p a r t o n mode l us ing D G G cu r r en t .

The pu rpose of th i s no t e is to p r e s en t ye t a n o t h e r imp l i ca t i on of t h e modif ied c h a r m c u r r e n t in t h e p r o d u c t i o n of c h a r m e d mesons . I t is b a s e d on t he obse rva t i on t h a t t h e absence of t h e Cab ibbo suppress ion in t h e V + A t e r m enhances ce r t a in cross-sect ions for t h e p r o d u c t i o n of c h a r m e d pseudosca la r a n d vec to r mesons. These processes shou ld be obse rved in h i g h - e n e r g y n e u t r i n o sca t te r iugs . The de ta i l s of t h e p r e sen t ca lcu la t ion wil l be p u b l i s h e d as a s epa ra t e paper .

W e a s sume t h a t Regge p h e n o m e n o l o g y p lays an i m p o r t a n t role in u n d e r s t a n d i n g t he i n t e r a c t i o n of c u r r e n t w i t h h a d r o n s a t h i g h energies (4,5). T h u s we use ful l powers of Regge pole to s t u d y t h e inc lus ive r eac t i on ~ § a n d t h e diffrac- t i v e process v §

(1) -~. DE I~UJULA, ]:I. GEOROI and S. L. GLASnOW: Phys. Rev. Left., 35, 69 (1975); 1~. N. MOHAPATRA considered the possibility of V+A current in the context of CP violation, Phys. Rev. 39, 6, 2093 (1972) (~) A. DE RUJULA, H. GEORGI and S. L. GLASHOW; Harvard preprint. In this article, new fundamental quarks and leptons arc introduced and theory is made rcnormalizablc. Phenomenological implications of this model is under investigation and will be published in a separate article. (3) V. BAROER, T. WEILER and R. J. N. PHILLIPS: Phys. Rev. Left., 35, 692 (1975). (*) Z. F. Ezxwx and J. 1VIAHARANA: Phys. Rev. D, 9, 2164 (197~). (~) J. MAHARANA and L. P. SINGH: Phys. Rev. D (to be published).

123

124 j . 5IAHARANA and L. P. SI:NGH

i) , + p - ~ - + D + + a n y t h i n g : I t follows from the quark s t ructure of D + tha t ~o is exchanged in the t-channel of the process J ~ + p ~ D + + a n y t h i n g . Hence one expects a narrow forward peak for small Itl in the current f ragmenta t ion region. The k inemat ica l variables are defined as follows (see fig. la)) .

(2) s = (p + ~/p, t = ( q - - k ) z , M~ = (p + q + k p .

a) b)

F i g . 1. - a) D i a g r a m f o r V ~ + p - 4 D + + X t h r o u g h ~ e x c h a n g e , b) D i f f r a c t i v e p r o d u c t i o n of D *+ on p r o t o n t a r g e t .

Here q is the four m o m e n t a of the current with QZ = --q~. The region of our in teres t is s-~large, MZ-~large, !t I small and q2 fixed. We consider Reggeized pion exchange instead of an e lementary pion exchange. I t follows tha t only vector current cont r ibutes to this procesu. Thus the inclusive cross-section is

d~ 1 (3) S d t d M ~ -- 64~s l<~OD+i~[o>l~ ' r~( - -o :~( t ) ) .

�9 2 2 I1 + exp [*~zc~(t)]l ~= , (M~, t ) .

The mat r ix e lement (.n~ is parametr ized similar to the Kta form factor in the following form (a,v):

o 2 (4) <~~ = qM+(o)(1 § ,~ + q-/m=)

In wri t ing eq. (4) we have neglected the coa t r ibu t ion of ]_(q2) which is known to be small (s) in case of K+ - , =~ I t should be noted, however, t ha t eq. (4) corresponds to the assumpt ion t ha t the form factor is a smooth funct ion of q~ and it can he extra- polated from timelike to spacelike region.

In the kinemat ical region of our in teres t

(5) fi~,:, ( 3I~, t) ~ ~li;~a~, ( Mg , t) , Mx~ --->large

where ~ D ( M ~ , t) is the pro ton Reggeon to ta l cross-section.

(s) I-I. BRAIy.N ~, ~ . COR.NVEL$~E.W, ]~. Iff. ~J[ARTX'N', O. EI~RIQITEZ, S. NATALI, F . I~O~A~O, D . BERTRA/~D, ~ L CSEJTHEy-~JARTI~, J . LESIO.NrNE, p . RENTO~, P . VILALN*, D . C, C U ~ D Y, T . I . PEDERSEN, D . "~VALDREN P h y s . Le t t . , 47 B, 182 (1973) . ( :) S. L , GLAStIOW, J . ILLIOPOULOS a n 4 L . ~IAI.~NTt: P h y s . ROY. D , 2, 1258 (1970)- F o r a r o v i c w a l ld d e t a i l e d r e f e r e n c e s s e e ~i . K . GAILLARD, ]3. \V. L ~ E UP.4 J . L . I~OSNER: RgV. Mod . P h y s . , 47, 277 (1975) .

CHARMED-PARTICLE PRODUCTIO~ IN RIGHT-HANDED CHARMED CURRENT 125

I t is reasonable to assume a~=p = o'=0~ for small values of It]. Furthermore, exact

isospin invariance in strong interaction implies a=0p---- (%+~ + a=-~)/2. Therefore eq. (4) reduces to

do" (6) s - -

dt d.M = 6,~ r ~ ( - c<,,(t))ls'+(O)l ~ I1 + ~ + q~/~n&l"-

�9 [ s \ 2 ~ ( t ) - i �9 ( 1 - - sm 0)~ / - -~ / 11 + exp [i:~=(t)]l~(a=+,~ + ~=-~,)/2.

\m~l

Notice that eq. (6) does not contain any free parameter if/+(0) and 4+ are taken from the Kt3 decay processes. Thus if s and 21/2 are chosen to be large enough such tha t s / M ~ l a r g e and a=p(M~) ~ constan then the inclusive cross-section is fixed completely. Indeed, if charmed mesons exist then observation of the above inclusive process will pro- vide a test for DGG weak current. We have used 0 ~ 15 ~ ]+(0) = 0.212/sinO, 2+ = 0.027, Q 2 = 2 , s = 100, M ~ = 2 0 , ( % + p + % - ~ ) / 2 = 2 5 m b and ~ ( t ) = a ' ( t - - m ~ ) with ~'= = 0.9 GeV -2. We find that the cross-section (see fig. 2a)) corresponding to eq. (6) is of the order of mb/GeV 2 which is quite appreciable.

10

10 r ~ 1

o

.s

10 -T

�9 / 0 ~ 2

0 1.2

I

\ \

\

i 014 i \ O i I

l el ~GeV)2J

Fig. 2. - D o t t e d l ine is t he inc lus ive cross-sect ion s(da/dt d~/~) for V V + p - ~ D ++x . Solid cu rv e is for t he d i f f rac t ive process J ~ + p - - * D * + §

ii) Diffraction production of D*+: We consider the process J ~ + p - ~ D * + + p incorporating SU 4 scheme. I t has been argued by INA~I (s) and also by GAILLARD, JACKSON and NANOPOULOS (9) that the hypothesis of vector-meson dominance for elec- tromagnetic current can be generalized for the charged and neutral weak current as

(7) i 2 (OIJffJ V~) = s~mv~/gv~

(s) T. IN~r Phys. Let t . ,56B, 291 (1975). (0) M. ]~. GAILLARD, S. A. JACKSON a n d D. V. NANOPOLLOS: C E R N p rep r in t , T H . 2049.

126 J. MAHARANA and L. e. 8INGH

I t follows from GVMD hypothesis (s,9) tha t ,

, A v , da da (Ji T p--~D *+ + p) (D*+p--~ D*+p)

2 2 where Av, = mv,/(mv, + Q~) was in t roduced to consider the effect of off-mass shell cur- rent , carrying momen tun l q with Q ~ = - - q 2 . Following the prescript ion of INAMI (s) to in t roduce effective S U 4 breaking mechanism for the coupling of the poineron, we get

(9) da AD,+ ~ m a / 1 - - sin O\ 2 da ~ i ( D * ~ p - + D * + p ) = 4A;~( 1 - 7 2 ( t ) ) ' m D . ( cos0~s0 ) ~ ( P + P - > P + P ) "

Here y.,(t)= ( 1-- ~1(t))( 1-- ~sc(t)) -~ with as(t) = 0.5 -- 0.9t and ~Jc(t) = - - 3.8 + 0.5t(da/dt) (pp--~ pp) is parametr ized as

da a~(Op) (10) d t (PP-~ ~p) = 1--6~- exp [bt].

Thus eq. (9) takes the form,

t2 da a~(,~p) A D. m~ (1 -- 72(t))2( 1 - s i n 0 - exp[b t ] . (11) d~ - ( D * p - + D * p ) - 64,~ A~ ?f~D $ [ COS0

The cross-section for the above process is shown in fig. 2 b), with m D ~ 2.2 GeV, Q~ = 0.25, aT(?p) = 26 mb and b - 6 GeV -~. Notice tha t in case of GIM charm current (9) ( 1 - sin 0) 2 will be replaced by sin 2 0 and thus the cross-section will bc reduced by one order of magni tude . We feel tha t this process provides another cri terion to test DGG mode l for weak current .

We conclude this note with the following remarks ;

i) The inclusive process V ~ W p ~ D + + X will show a sharp forward peak due to the ~0 exchange. The magni tude of the cross-section depends crucial ly on the form of the hadronic weak current . We emphasize tha t eq. (6) conta ins no free pa ramete r once Dt3 form factor is fixed. There seems to be exper imenta l evidence (10) for charmed hadrons at FNAL. Observat ion of D § inclusive cross-sections will provide a check for present invest igat ion.

ii) Sinfilarly, diffractive product ion of D*+ will provide ano ther test for the DGG model. In this case we have restr ic ted ourselves to ra ther low Q2 where VMD is expected to give bet ter results.

iii) An enlarged version of the present inves t igat ion together wi th the effect of neu t ra l cur rent (2) in other charmed-meson product ion will be publ ished elsewhere.

We arc thankfu l to members of high-energy physics group at the Ins t i t u t e of Physics and Vani Vihar. We are grateful to Dr. D. P. RoY for encouragements and useful communica t ions .

(~0) D. P. RoY: private communication.