puzzle and hairpin diagrampuzzle and hairpin diagram

7
IL NUOVO CIMENTO VOL. 100 A, N. 5 Novembre 1988 D~176 Puzzle and Hairpin Diagram(*). XIAO-YUAN LI and XUE-OJAN LI Center of Theoretical Physics, CCAST (World Laboratory) Institute of Theoretical Physics, Academia Sinica, P.O. Box 2735 - Beijing, China PING WANG Institute of High Energy Physics, Academia Sinica, P.O. Box 918(4) - Beijing, China (ricevuto il 5 Aprile 1988) Summary. -- A possible way to solve the D~ ~0~ puzzle is suggested. By assuming the external W-emission diagram dominance and the substantial contribution of the hairpin diagram, a good phenomenology of DO and D § decays including D~ ~0~ and K~ is reproduced. A negligible D~ ~ but relative large branching ratios of D~ +--* o~ + and ~' are predicted. PACS 13.25 - Hadronic decays of mesons. Recently the decay D~ ~0~ has been observed in several experiments (~) with a branching ratio ~ 1%, and this situation has attracted the attention of a number of theorists (~). Originally it was proposed that certain decays of D o and (*) To speed up publication, the authors of this paper have agreed to not receive the proofs for correction. C) H. ALBRECHT et al. (ARGUS): Phys. Left. B, 158, 525 (1985); C. BEBAC et al. (CLEO): Phys. Rev. Left., 56, 1893 (1986); R. M. BALTUSArrISet al. (MARK III): Phys. Rev. Lea., 56, 2136 (1936). (2) L. L. CHAU and H. Y. CHENG: Phys. Rev. Lett., 56, 1665 (1986). (3) D. FAKIROVand B. STECH: Nucl. Phys. B, 133, 315 (1978); M. BAUER and B. STECH: Phys. Lett. B, 152, 380 (1985). (4) M. BAUER, B. STECH and M. WIRBEL: Heidelberg preprint HD-THEP-86-19 (1986). (5) A. J. BURAS, J. M. GERARD and R. ROCKL: Nucl. Phys. B, 268, 16 (1986). (e) U. BAUR, A. J. BURAS, J. M. GERARDand R. ROCKL: Phys. Lea. B, 175, 377 (1986). (7) j . F. DONOGHUE: Phys. Rev. D, 33, 1516 (1986). 693

Upload: xiao-yuan-li

Post on 22-Aug-2016

224 views

Category:

Documents


3 download

TRANSCRIPT

Page 1: puzzle and hairpin diagrampuzzle and hairpin diagram

IL NUOVO CIMENTO VOL. 100 A, N. 5 Novembre 1988

D~176 Puzzle and Hairpin Diagram(*).

XIAO-YUAN LI and XUE-OJAN LI

Center of Theoretical Physics, CCAST (World Laboratory) Institute of Theoretical Physics, Academia Sinica, P.O. Box 2735 - Beijing, China

PING WANG

Institute of High Energy Physics, Academia Sinica, P.O. Box 918(4) - Beijing, China

(ricevuto il 5 Aprile 1988)

Summary. - - A possible way to solve the D~ ~0~ puzzle is suggested. By assuming the external W-emission diagram dominance and the substantial contribution of the hairpin diagram, a good phenomenology of D O and D § decays including D~ ~0~ and K~ is reproduced. A negligible D ~ ~ but relative large branching ratios of D~ +--* o~ + and ~ ' are predicted.

PACS 13.25 - Hadronic decays of mesons.

Recent ly the decay D~ ~ 0 ~ has been observed in several exper iments (~) with a branching ratio ~ 1%, and this situation has a t t rac ted the at tent ion of a number of theoris ts (~). Originally it was proposed that certain decays of D o and

(*) To speed up publication, the authors of this paper have agreed to not receive the proofs for correction. C) H. ALBRECHT et al. (ARGUS): Phys. Left. B, 158, 525 (1985); C. BEBAC et al. (CLEO): Phys. Rev. Left., 56, 1893 (1986); R. M. BALTUSArrIS et al. (MARK III): Phys. Rev. Lea., 56, 2136 (1936). (2) L. L. CHAU and H. Y. CHENG: Phys. Rev. Lett., 56, 1665 (1986). (3) D. FAKIROV and B. STECH: Nucl. Phys. B, 133, 315 (1978); M. BAUER and B. STECH: Phys. Lett. B, 152, 380 (1985). (4) M. BAUER, B. STECH and M. WIRBEL: Heidelberg preprint HD-THEP-86-19 (1986). (5) A. J. BURAS, J. M. GERARD and R. ROCKL: Nucl. Phys. B, 268, 16 (1986). (e) U. BAUR, A. J. BURAS, J. M. GERARD and R. ROCKL: Phys. Lea. B, 175, 377 (1986). (7) j . F. DONOGHUE: Phys. Rev. D, 33, 1516 (1986).

693

Page 2: puzzle and hairpin diagrampuzzle and hairpin diagram

694 XIAO-YUAN LI, XUE-QIAN LI and PING WANG

D+ mesons, such as D~ K~ Dr--* np, r.%o etc. should be clear signatures for the contributions of W-exchange and annihilation diagram (see fig. 1,2)(8.g). The experimental observation of D~ K~ has led some authors(z'') to put the W-

Fig. 1. - The W-exchange diagram.

Fig. 2. - The W - a n t a t i o n diagram.

exchange diagram into their calculations and an analysis based on quark diagrammatic approach, in fact, has reached the conclusion that the internal W- emission diagram (see fig. 3) is very important and the W-exchange diagram is nonnegligible, but enhancing either the W-exchange or the internal W-emission amplitudes is not sufficient to consistently fit the data (2).

Fig. 3. - The internal W-emission diagram.

On the other hand, by assuming a) the quark decay diagram (see fig. 4) dominance; b) factorization of the QCD-corrected effective weak-interaction Hamiltonian H ~ in products of matrix elements of quark currents; and c) no

Fig. 4. - The external W-emission diagram.

(8) I. I. Y. BIGI and M. FUKUGrrA: Phys. Lea. B, 91, 121 (1986). (9) X. Y. LI: Z. Phys. C, 7, 21 (1980).

Page 3: puzzle and hairpin diagrampuzzle and hairpin diagram

D~176 PUZZLE AND HAIRPIN DIAGRAM 695

colour mismatch (formation of final mesons only by quarks which belong to the same colour singlet currents), a comprehensive framework for describing all two body decay modes of charmed mesons (,.4) have produced reasonable agreement with some twenty D-decay modes C~ However, this factorization approach fails in reproducing the decay D~ ~0 ~ data by at least three orders of magnitude (6), unless through strong-interaction rescattering the quark diagram could lead to final states that mimic nonspectator decays (,.7).

The 1/Nr techniques developed for strong-interaction meson physics (11) have also been applied to weak decays of charmed mesons recently (5). It has been shown that to leading order of 1/Nr the assumptions of factorization and no colour mismatch hold exactly and one arrives essentially at the phenomenologically successful model of factorization approach (3). The large N~ approximation enhances the estimate of the decay D ~ ~o~ considerably, but in order to fully reproduce the data either nonieading terms in 1/Nr expansion have to be included or PCAC has to be strongly violated at large momentum transfer(e). Moreover, one still has to investigate the influence of this enhancement mechanism to other D-* PV channels which are clearly well explained by quark decay diagram only (3). The situation remains unsolved and the decay D~176 puzzle still needs to be explained.

In this paper we would like to suggest an alternative way to solve the DO-* ~04 puzzle. Our observation essentially is the following. The factorization prescription(3,4) works quite well for D decays except D~176 and K~ and the characteristic of these two decay channels is that in the final states they both contain a hadron which has a SU(3) flavour singlet component. However, in the quark diagrammatic approach when a hadron with a SU(3) flavour singlet component, such as ~o, 4, r,', is produced, there is the contribution from an extra quark diagram so-called hairpin diagram('~.'3), which is shown in fig. 5.

Fig. 5. - The hairpin diagram.

C ~ R. H. SCHINDLER: SLAC preprint, SLA-PUB-4135 (1986); D. HITLIN: Caltech preprint, CALT-68-1370 (1986). (11) G. 'T HOOFT: Nucl. Phys. B, 72, 641 (1974); G. ROSSI and G. VENEZlANO: Nucl. Phys. B, 123, 507 (1977); E. WrrrzN: Nucl. Phys. B, 160, 57 (1979). (=) L. L. CHAU: Phys. Rep., 95, 1 (1983). (13) X. Y. LI and S. F. TUAN: DESY preprint, DESY 83-(}78 (1983), unpublished.

Page 4: puzzle and hairpin diagrampuzzle and hairpin diagram

696 XL~O-YUAN U , X U E ~ LI and PING WANG

Furthermore, in the Cabibbo-favoured D--, PV decays, the hairpin diagram only contributes to D~176162 K~ ~ . 0 ~ , and D:--* ~b~ +, ~ + , p+~', while leaving other D O channels and all D + channels unaffected (~s). Therefore by including the contribution of the hairpin diagram instead of large W-exchange and internal W- emission amplitudes(z) we may retain all good results in the factorization approach and at the same time solve the D~ K~ decay pnzzle.

A few more words may be necessary. The hairpin diagram is a kind of diagram which is thought to be suppressed by 0ZI rule (~') and in the large Nc expansion, it is not of the leading order, not fully factorizable, difficult to calculate and consequently it was believed that the hairpin should be neglected(6). However, as is well known, the nonleptonic decays involve a complicated interplay between the weak current-current interaction and strong interactions, to which our current knowledge is not on a solid ground. On the other hand, as we shall show, by assuming that due to some unknown mechanism the hairpin diagram contributes substantially, together with the quark decay diagram, we cannot only produce a good phenomenology for the observed D O and D § nonleptonlc decays, but also give predictions which are distinguishable from those of others (,,6) and this can be tested in the D: decay experiments.

With the hard ghon corrections, the effective Hamiltonian for Cabibbo- favoured charm nonleptonlc decays may be written as C 5)

(1) 2 He~ = Gv COS 0r [C1 (~l)L (SC)L -b C 2 (Sd)L (UC)L "~" h . c . ] ,

where (~d)L = fir~(1 -- rs)d and C1, C2 are the OPE coefficients (~e). As the first- order approximation, we drop those colour-suppressed diagrams as well as the W-exchange and annihilation diagrams. Therefore in our framework, only the external W-emission and the hairpin diagrams are to be considered. They are disposed in fig. 6, where the wry lines denote the charged current and the dashed lines represent the effective neutral current corresponding to the second term in eq. (1). We have

(2) {: ~ C1 a'~ hd oc CI,

0r C2 b' oc C2 hc 0r C2.

The hairpin diagram hc contributes to D ~ ~ and r ~ whereas h d to D:--* ~b~ + and o)~ +. The dependence of the decay amplitudes on these diagrams is

(14) j . IIZUKA: Prog. Theor. Phys. Suppl., 37-38, 21 (1966); S. OKUBO: Phys. Lea. B, 5, 165 (1963); G. ZWEIG: CERN report, CERN 8419frH412 (1964), unpublished. (19 M. K. GAILLARD and B. W. LEE: Phys. Rev. Left., 33, 108 (1974); G. ALTARELLI and L. MAIANI: Phys. Lett. B, 52, 351 (1974); W. BERNRF.UTHER: Z. Phys. C, 29, 245 (1985). (]9 K. WILSON: Phys. Rev., 178, 1499 (1969).

Page 5: puzzle and hairpin diagrampuzzle and hairpin diagram

D ~ 1 7 6 PUZZLE AND HAIRPIN DIAGRAM 697

,< ) . / < ) . ,<)v _ _ / I / / -

)v a) b) h i ) b l)

%)o,, %1: Fig. 6. - The d iagrams responsible for D--~ PV decays.

TABLE I. - Cabibbo-favoured D - * P V decay amplitudes in terms of the diagrams in fig. 6.

D + decays Amplitudes

K * ~ + a' + b' p+"~o a + b

D O decays r eK ~

K * - ~+ K , % 0

p+ K :Ko

(1/2) h~ (1/V~)(b + h J

a ' - (1/3Xa' + b')(1 - exp [/AK..J)

(1/V~)[b'- (2/3Xa' + b'X1 -exp [/3,~.j)] a - (1/3Xa + b)(1 - exp [/A#z])

( l fV~)[b - (2/3)(a + b)(1 - exp [/ZIoK])]

D~ + decays § 0

p0 ~+ 0

K *+ K ~ b ~ , o K + b'

: ~~ (2t~) a 4~ + a ' + (1/2)h d

co~ + ( 1 / 3 ~ ) a d

2 ~' (1/V~)(a + h~)

A common factor co~#r is abbreviated and the absolute value is to be understood. _ x.. x*, d ~ K = # ~ - - * ~ . *~" is the phase shiR of K* for 1=1/2 final state. * ~ ' , *m * ~ are defined similarly.

46 - II Nuovo Ciraenlo A.

Page 6: puzzle and hairpin diagrampuzzle and hairpin diagram

698 XlAO-YUAN LI, XUE-QIAN LI and PING WANG

listed in table I, where the final-state interaction is taken into account. Here we have made a rough estimate of these diagrams from the experimental data. For simplicity, we only take the following central values of the data C'~~

~D +) = 9.2 "10-13S,

Br(DO__> ~ o ) = 0.7%,

Br(DO__> ~ . o no) = 2.1%,

Br(D ~ ~+ K-) = 13.7%,

Br(D + __> p+ ~o) = 12.2%.

~(D ~ = 4.3" 10-13s,

Br(DO__. polo) = 1.3%,

Br(D~ K*- ~§ = 7.3%,

Br(D +_._) ~ . o ~+) = 3.0%,

By fitting these data, we obtain

(3) ]he] - 2.8- 10 -e ,

(4) lal --~ 3.2.10 -6 , b/a ~- - 0.35, AsK = 24 ~

and

(5) la'l -~ 2.7 �9 10 -6 , b ' / a ' - - - 0 . 5 7 , ZlK~ ---- 52 ~ ,

where A~x = $ ~ - $]~, $#2 and $ ~ are the final-state phase shift of pK-strong interaction with isospin I = 3/2 and I = 1/2, respectively. The A K'~ has a similar definition.

With the above values of b and he, but with an unknown phase between them, we get Br (D~176 compared with the measured value (3.8 + 1.5)%. Similarly with b' , a ' and hc and employing the experimental data r(D:)=3.85"10-13sC~ we get Br(D: -o K *~ K+) = 2.8% vs . (4.8+2.4)% experimental and B r ( D : - * 4 ~ + ) = ( 2 . 3 - 8 ) % vs. (3.3+1.4)% experimental. From eq. (2), we have

(6) b/a -- C2/C1, b ' /a ' ~- C2/C1.

The QCD calculation gives (15) at the mass scale of charm quark mass

(7) C1 -- 1.21, C2 -~ - 0.42, C2/C1 ~ - 0 . 3 5 .

The fitted values of b/a and b ' /a ' in (4) and (5) are reasonably consistent with the ratio in (7).

The above results indicate that our assumptions are consistent with all the existing experimental data and the hairpin diagram has a large amplitude.

Page 7: puzzle and hairpin diagrampuzzle and hairpin diagram

D~176 P U Z Z L E A N D H A I R P I N DIAGRAM

TABLE II. - Comparison of different predictions of D+~ decays.

699

D [ decays ref. p) ref. (D ours

~0=+ 0.5% 10% 0 ~+ ~0 0.5% 0 ~+ 2.8% (2 + 8)% Oj-/~ + 3 0 ~

Whether the hairpin diagram does play an essential role can be tested in D: decays. We predict that Df--*p= is negligible and from (2), we have hd=(C~/C2)" he so the hairpin diagram has even bigger contributions to D + decays than to D ~ We anticipate a large branching ratio of D~ + -* ~ + . The ratio DO__. pon, may also be large, although we cannot calculate its value because we do not have the information on the amplitude of h~ shown in fig. 6. The comparison of our predictions with others is in table II.

In conclusion, the importance of the hairpin diagram is a possible way to explain why the factorization work~ to all the measured D-decay channels but DO__. ~o~ and o~ ~0. From our point, the two types of diagrams, i.e. the external W-emission diagram and the hairpin diagram together can meet all the existing data. The measurements of D: decays will provide a clear-cut test for this assumption.

�9 RIASSUNTO (*)

Si suggerisce un possibile metodo per risolvere il problema D~176 Assumendo la dominaa~ del diagranuna di emissione di W esterna e il sostanziale contributo del diagramma ad U, si riproduee tma buona fenomenologia dei decadimenti di D O e D* ehe ineludono D~176 e K~ Si prevedono un traseurabi]e D~ ma rapporti tra probabilit~ di deeadimento relativamente grandi per D~*-* cot, + e p~'.

(*) Traduzione a cura della Redazione.

llpo~eMns DO--, ~o~ a ~tilaarpam~a wlna ~mma.~ma,~.

Pe~lOMr - - Ilpc~aaracxc~ nO3MO~lmbn~ cnoco5 p e m e ~ n p o 6 a e ~ i D~176 Ilpe:~noaaraa llO~mTawrHocrs :~arpau~l snenmero RcnycKamm W H cymecalemmn~ egaa~ ~Harpam~ ~na ,,mmulsra~,~, ~cnpoa3Bo~-rcs cl~enouenoaonea pacna.aon D O n D +, agaioqa.q D~176 a K~ IIpe~acza3hmaayrca npene6pezo~o MaJIBg BepOYlTHOC'rb DO--* p~, no OTnOCaTeahno 6ohnme ovnomemla nevaett aaa D + -oo~ ~ n p~'.

(*) l'lepeae(}e~o peOaKu, ue~.