Volume 196. number I PHYSICS LETTERS B 24 September 1987

RESONANT SUBSTRUCTURE IN Klrn DECAYS OF CHARMED D MESONS *

MARK III Collaboration

J. ADLER, J.J. BECKER, G.T. BLAYLOCK, T. BOLTON, J.S. BROWN, K.O. BUNNELL, T.H. BURNETT, R.E. CASSELL, D. COFFMAN, V. COOK, D.H. COWARD, D.E. DORFAN, G.P. DUBOIS, A.L. DUNCAN, G. EIGEN, K.F. EINSWEILER, B.I. EISENSTEIN, T. FREESE, G. GLADDING, C. GRAB, F. GRANCAGNOLO, R.P. HAMILTON, J. HAUSER, C.A. HEUSCH, D.G. HITLIN, J.M. IZEN, L. KijPKE, A. LI, W.S. LOCKMAN, U. MALLIK, C.G. MATTHEWS, R. MIR, P.M. MOCKETT, R.F. MOZLEY, B. NEMATI, A. ODIAN, L. PARRISH, R. PARTRIDGE, J. PERRIER, D. PITMAN, S.A. PLAETZER, J.D. RICHMAN, H.F.W. SADROZINSKI, M. SCARLATELLA, T.L. SCHALK, R.H. SCHINDLER, A. SEIDEN, C. SIMOPOULOS, A.L. SPADAFORA, I.E. STOCKDALE, W. STOCKHAUSEN, J.J. THALER, W. TOKI, B. TRIPSAS, F. VILLA, S. WASSERBAECH, A. WATTENBERG, A.J. WEINSTEIN, N. WERMES, H.J. WILLUTZKI, D. WISINSKI, W.J. WISNIEWSKI, R. XU and Y. ZHU California Institute of Technology, Pasadena. CA 91125, USA University of California at Santa Crux, Santa Cruz, CA 95064, USA University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA Stanford Linear Accelerator Center, Stanford, CA 94305, USA University of Washington, Seattle, WA 98195. USA

Received 14 July 1987

Dalitz plot analyses of four Knx decays of the Do and D+ mesons are presented. The relative amounts of K*n, Kp and non-

resonant Kax in each decay mode are determined, and isospin amplitudes and phases are derived. These results are compared

with predictions from QCD. The K-x+x+ mode has a non-uniform, non-resonant contribution; attempts to fit this distribution

are described.

The study of pseudoscalar-pseudoscalar (PP) and pseudoscalar-vector (PV) hadronic decays of the D mesons provides information on the mechanisms of heavy quark decay and subsequent hadronization #’ [ 2,3]. The ratios B(D”+K*ono)/B(Do+K*K+) and B(D”+Kopo)IB(Do+K- p’) can distinguish between models which

require the W-exchange diagram [ 41 and those that modify perturbative QCD calculations [ 51. The presence of final state interactions [ 51 can be established. Predictions for the branching fractions of non-resonant decays to three pseudoscalar mesons [6] can be tested once the resonant decays are subtracted. Previous measure- ments [ 71 have been dominated by statistical errors. The Mark III data sample has sufficient statistics in the Cabibbo allowed three-body decays of the D mesons to provide accurate measurements of these branching fractions.

Presented herein are Dalitz plot analyses of four decays of the charmed Do and D+ mesons #2: Do-K-rr +x0, D”+Kontlc-, D++K”rc+nO, and D++K-n+rc+. The data sample consists of an integrated luminosity of 9.3

* Work supported in part by the Department of Energy, under contracts DE-AC03-76SF00515, DE-AC02-76ERO1195, DE-AC03-

8 I ER40050, DE-AM03-76SF00034, and by the National Science Foundation. 41 For a recent review see ref. [ I 1. IL Throughout this paper we adopt the convention that reference to a state also implies reference to its charged conjugate.

037O-2693/87/S 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

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Volume 196, number 1 PHYSICS LETTERS B 24 September 1987

pb-~ collected on the peak o f the tg (3770) resonance with the Mark III detector [ 8] at SPEAR. Cand ida te D--. Kn n decays are selected with the procedure used in an earl ier analysis of D meson branching

fract ions [9] . Pairs of D mesons are p roduced in the decay o f the t~ (3770) , with each D carrying the beam energy. This "beam cons t ra in t" is imposed when calculating the invar iant mass o f the Knr~ system. In decay modes involving n° 's , constraints on the },~ invar iant mass and the K r ~ ° energy are s imul taneously appl ied [ 10]. These constraints significantly improve the mass resolut ion of the Kr~n system and provide rejection of background from incorrect part icle associat ions and non-charm hadron product ion. Events with a beam-con- s trained mass within 5 MeV/c 2 (3 MeV/c 2 in the case o f K-re +n +) o f the nominal D mass are selected for further study. The resolution of the invariant mass squared of the particle pairs used in the Dali tz plots is ~ 0.015 ( GeV/c 2) 2.

The fract ions o f PV and non-resonant three-body cont r ibut ions to each decay mode are de te rmined by fit t ing the Dal i tz plot d is t r ibut ions to a coherent sum of ampl i tudes using a max imum- l ike l ihood method. The three- body ampl i tude A3b is assumed to be constant over the Dal i tz plot. Relat ivis t ic Bre i t -Wigner ampl i tudes (BW) , which include the vector decay matr ix e lements and mass-dependent widths [! 1 ], are used to parameter ize the K* and p decays. The l ikel ihood functions (L~g) are expressed as double differentials in the Dal i tz plot variables rn~,~,,2 mKn,2. They take the following forms for the K n+r~°, I~°n+Tt-, I~°rt+n°, andK-rc+Tt+ Dal i tz plots, respectively:

"~tgsig +0= Ill exp( i0 , )A3b q-f2 exp(iO2) BWo. +f3 exp(i#3) BWK.- +f4 exp(iO4) BWe,.o 12 , (1)

~s°~ - - = If5 exp(i#5) A3b +f6 exp(i~6) BWpo +f7 exp(iO7) BW~:. 12

+ If5 exp(i¢5)A3b +f6 exp(iO6) BWoo +f7 exp(iO7) BWK.+ 12 , (2)

~0.+0 ~,~ = IA exp(iO8)A3b-fir9 exp(iO9) BW~+ +f~o exp(iO~o) BWn.o [2 (3)

~ ,g+ + = If~ exp(iO~ ) A3b -}-f12 exp(iO~2) B3b +f~3 exp(iO13) BWK~o -[-f13 exp(i~13) BW¢,~o 12 , (4)

where f are the coefficients for each cont r ibu t ion to the Dal i tz plot and the 0, are the relat ive phases ~3. The K n +n + Dal i tz plot contains a non-uniform, non-resonant cont r ibut ion parameter ized by a function B30 to be discussed below. The l ike l ihood functions, including detect ion efficiency, are normal ized across the Dal i tz plot using Monte Carlo Knr~ events generated according to three-body phase space, and subjected to the same analysis as the data.

The d is t r ibut ion of background events under the D signal in each mode is parameter ized by adding a term to the l ikel ihood funct ion which describes the var ia t ion o f the background across the Dal i tz plots. The back- ground term is de te rmined by fit t ing a sample o f background events with beam-cons t ra ined mass between 1.82 and 1.85 GeV/c 2 to a two-dimensional cubic po lynomia l ~4. The background samples show no evidence of res- onant substructure in any of the decay modes. A fit to the beam-cons t ra ined mass d is t r ibut ion de termines the rat io of background to signal in the event sample used in the Dal i tz plot analyses.

The fit results are presented in table 1 ~s and i l lustrated in figs. 1-4. Our def ini t ion o f the branching frac- t ion ~6 implies that the fract ions o f events f rom each componen t will not always sum to one because the inter-

~3 One ¢~ in each expression is fixed at zero. ~4 The mass scale is adjusted up to the D mass. ~5 The three-body branching fractions B(D--,Knn ) are taken from ref. [ 12]. Comparisons between D o and D ÷ decay modes use the

values ao~ =(5.8+0.5+0.6) nb and aD,,=(4.2_+0.6_+0.3) nb, from this source. The value ofB(D°-~f4°n+n ) is taken from ref. [ 1 ], and scaled by the new value of aD,~.

~6 The branching fraction to a given final state i is defined as the ratio of the partial width to state i in the absence of other decay modes, divided by the total width. With this definition, the fraction of events in each decay mode that are attributed to the ith component of ~s,~ is determined by settingfi equal to its fit value and the otherf to zero and numerically integrating 5gs, g across the Da|itz plot, then dividing by the integral of L,°s~g with all fj's set to their fit value.

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Volume 196, number 1

Table 1 D~Knn fit results.

PHYSICS LETTERS B 24 September 1987

Decay mode Fit fraction Phase a.B a) Branching fraction a) (%) (degrees) (nb) (%)

K-n+n ° 0.76-+0.04"+0.08 13.3"+ 1.2"+ 1.3 K p+ 81 + 3-+ 6 0.0 0.62"+0.02"+0.09 10.8"+0.4"+ 1.7 K*-n + 12"+ 2"+ 3 154"+ 11 0.28"+0.04"+0.08 4.9"+0.7"+ 1.5 I(*°~ ° 13_+2"+ 3 7"+ 7 0.15"+0.02"+0.04 2.6"+0.3"+0.7 non-resonant 9"+2"+ 4 52"+ 9 0.07"+0.02_+0.03 1.2-+0.2-+0.6

IZ°n +rt - 0.37 -+ 0.03 _+ 0.03 6.4 -+ 0.5 "+ 1.0 I~°p ° 12"+ 1 "+ 7 93"+30 0.04"+0.01 "+0.02 0.8"+0.1 "+0.5 K* n + 56"+4"+ 5 0.0 0.31 "+0.02"+0.05 5.3"+0.4"+ 1.0 non-resonant 33 -+ 5 _+ 10 - 0.12 _+ 0.02 _+ 0.04 2.1 _+ 0.3 _+ 0.7

l~On +no 0.42 _+ 0.08 -+ 0.08 10.2 -+ 2.5 -+ 1.6 I~°p + 68_+8"+ 12 0.0 0.29"+0.03"+0.09 6.9"+0.8"+2.3 K,O~+ 19"+6"+ 6 43"+23 0.24"+0.07+0.10 5.9"+ 1.9"+2.5 non-resonant 13 _+ 7 _+ 8 250 -+ 19 0.05 -+ 0.03 _+ 0.04 1.3 -+ 0.7 _+ 0.9

K n+n + 0.39"+0.01 "+0.03 9.1_+ 1.3-+0.4 ~,on+ 13-+ 1 -+ 7 105"+ 8 0.08"+0.01 "+0.04 1.8+_0.2-+ 1.0 non-resonant 79 "+ 7 "+ 15 0.0 0.31 _+ 0.03 _+ 0.10 7.2 _+ 0.6 _+ 1.8

a~ See footnote 5.

f e rence t e rms do no t necessar i ly in tegra te to zero. In each m o d e the best fit requi res coherence be tween all

r e sonan t and non - r e sonan t ampl i tudes , except in the K°n + n - m o d e , where the best fit sl ightly favors incoh-

e rence be tween the r e sonan t con t r i bu t i ons and the non - r e sonan t th ree -body ampl i tude .

The K - n +n + Da l i t z plot has u n i q u e fea tures [ 7 ]. S ince this f inal state con ta ins iden t ica l charged pions, the

Da l i t z p lo t m u s t be fo lded (fig. 4) . A large non - r e sonan t con t r i bu t ion in terferes wi th the K*°n + ampl i tude ,

shif t ing the K* peak to low masses at one end o f the b a n d and to high masses at the o the r end, where the K*

decay m a t r i x e l e m e n t changes sign. T h e n o n - r e s o n a n t con t r i bu t i on is no t d i s t r ibu ted accord ing to phase space,

bu t a ccumula t e s in the reg ion where mzK~, app roaches rn2~2. To a c c o m m o d a t e this d i s t r ibu t ion it is necessary

to add an ad hoc t e r m to the l ike l ihood func t ion . T h e best fit is o b t a i n e d wi th a Bose s y m m e t r i c t e r m o f the

f o r m B3b = I rn ~ , - - m 2 2 I. N o e v i d e n c e is f ound for any k n o w n [13 ] o r hypo thes i zed Kn resonances [o the r

than the K * ( 8 9 2 ) ] , exot ic n +n + states, or non- resonan t P-wave K n or D - w a v e nn ampl i tudes . Since B3b changes

rapid ly in the K *° region, m u c h o f the appa ren t K *° signal is a t t r ibu ted by the fit to in ter ference .

To eva lua te the goodness o f fit, the da ta are b i n n e d in a t w o - d i m e n s i o n a l h i s tog ram and three p ro j ecnons .

The fit results, n o r m a l i z e d to the n u m b e r o f da ta events , are then c o m p a r e d to the b i n n e d data, and a Z 2 is

e v a l u a t e d for each h i s tog ram ~7. The ~2 per degree o f f r e e d o m is close to one for all o f the t w o - d i m e n s i o n a l

h is tograms and projec t ions shown in the figures. N o sys temat ic dev ia t ion be tween the b inned da ta and fit results is obse rved in any reg ion o f the Da l i t z plots.

The sys temat ic errors on the fit f rac t ions are e s t i m a t e d by va ry ing the even t se lec t ion cr i ter ia , the m e t h o d

o f backg round d e t e r m i n a t i o n , the m e t h o d o f e f f ic iency d e t e r m i n a t i o n , and the pa t t e rn o f in te r fe rence be tween con t r ibu t ions . The largest sources o f sys temat ic e r ro r are the n ° r econs t ruc t ion ef f ic iency and the pa r ame te r -

~v The Z 2 measure that we use is defined as Z2= 2Z,niln(n//4), where ni is the number of events in bin i, ,u~ is the number of events predicted by the fit to be in bin i, and the sum is over all bins within the kinematically allowed region of the Dalitz plot. See ref. [ 14].

109

Volume 196, number 1 PHYSICS LETTERS B 24 September 1987

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Fig. 2. The Dalitz plot for D °-, I~°n +n , and the three projections.

ization of the background. In the K - n +n + mode, no systematic error has been included for the parameteri- zat ion of the non-uniform, non-resonant contribution.

Comparisons of PV branching fractions measured in two distinct final states show good agreement for

B ( D ° ~ K * - n +) but poor agreement for B ( D + ~ I~*°n ÷) (see table 1). The discrepancy in the latter mode

suggests that while the l ikelihood function ~ g + ÷ provides a good fit to the data, the form of B3b chosen does

not adequately describe the physics. In the comparisons that follow, the results f rom the fit to the K - n +n ÷ mode will not be used.

110

Volume 196, number 1 PHYSICS LETTERS B 24 September 1987

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Fig. 3. The Dalitz plot for D + -~ l(°n + n °, and the three projections. Fig. 4. The Dalitz plot for D+-,K n+n +, and the three projections.

Recent extensions of the spectator model of D meson decay adequately account for the pattern of PP decays either by the addition of new amplitudes (e.g., W-exchange [4]) or by the modification of the effective coef- ficients of the hadronic matrix elements [ 5 ]. To distinguish between these two corrections to the naive spec- tator picture, their predictions for PV decays may be evaluated against the measurements presented here. Table 2 compares two representative models, those of Kamal [4] (model 1) and of Stech and collaborators [5] (model 2).

Model 2 is favored, suggesting that deviations from the spectator picture arise from non-perturbative con- tributions to the QCD coefficients.

The importance of final state interactions is emphasized in both models. This is observed in the data as phase shifts between isospin amplitudes. The isospin amplitudes A~/2, A3/2 and phase shifts 61/2, 63/2 have been defined,

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Volume 196, number 1

Table 2 Decay width ratios compared with theory.

PHYSICS LETTERS B 24 September 1987

Ratio This experiment Model 1 [4] Model 2 [5]

/-'( D°~ K*°lt°)/l" (D °-, K*-Tt + ) 0.50 + 0.07 + 0.15 0.124-0.271 0.43 F(D°-d~.°9 °)/F (D°-oK p+ ) 0.07 + 0.01 _+ 0.04 0.036-0.135 0.08

for example , in ref. [ 2 ]. F r o m table 1, the ra t io o f i sospin amp l i t udes is d e t e r m i n e d to be

D ~ I~P:

D--,I~*rc;

D~I~ .E:

IAI/2/A3/2 [ = 3.12 +0 .40 ,

lAIn~A3~21 = 3.22 + 0 . 9 7 ,

IA ln /A3n l = 3.67 +0 .27 ,

~1/2 - ~ 3 / 2 = ( 0 + 2 6 ) ° ,

6~1/2 --~3/2 = ( 8 4 + 13) ° ,

~1/2 --~3/2 = (77 + 11 ) ° ,

where the last set is d e r i v e d f r o m ref. [ 10 ]. T h e ex is tence o f i sospin a m p l i t u d e phase shifts ind ica tes s izeable

f inal state in t e rac t ions in the I(Tr and I~*n modes .

We grateful ly acknowledge the effor ts o f the S P E A R staff. We also wish to thank I.I .Y. Bigi, H. Haber , T.

Banks, and M. Peskin for useful discussions. Th i s w o r k was suppor t ed in par t by the U S N a t i o n a l Science Foun-

da t ion and the U S D e p a r t m e n t o f Energy unde r contracts No. DE-AC03-76SF00515 , No. DE-AC02-76ER01195 ,

No . D E - A C 0 3 - 8 I ER40050 , and No. D E - A M 0 3 - 7 6 S F 0 0 0 3 4 .

References

[ 1 ] R. Schindler, in: High energy electron-positron physics (World Scientific, Singapore) SLAC-PUB-4135 (1986), to be published. [ 2 ] R. Rtickl, Habilitationschrift Universit~it MiJnchen ( 1983). [3] L.L. Chau, Phys. Rep. 95 (1983) 1;

L.L. Chau and H.Y. Cheng, Phys. Rev. Lett. 56 (1986) 1655. [4] A.N. Kamal, SLAC-PUB-3443 (1984), unpublished; Phys. Rev. D 33 (1986) 1344. [5] D. Fakirov and B. Stech, Nucl. Phys. B 133 (1978) 315;

M. Bauer and B. Stech, Phys. Lett. B 152 (1985) 380; M. Bauer, B. Stech and M. Wirbel, Z. Phys. C 34 (1987) 103.

[6] H.Y. Cheng, Z. Phys. C 32 (1986) 243. [7] J.E. Wiss et al., Phys. Rev. Lett. 37 (1976) 1531;

R.H. Schindler et al., Phys. Rev. D 24 (1981) 78. [8] D. Bernstein et al., Nucl. Instrum. Methods 226 (1984) 301. [9] R.M. Baltrusaitis et al., Phys. Rev. Lett. 56 (1986) 2140.

[ 10] J. Hauser, Ph.D. thesis, California Institute of Technology, CALT-68-1275 (1985). [ 11 ] J.D. Jackson, Nuovo Cimento 34 (1964) 1644;

J. Blatt and V. Weisskopf, Theoretical nuclear physics (Wiley, New York, 1952 ) p. 358. [ 12] J. Adler et al., SLAC-PUB-4291, submitted to Phys. Rev. Lett. [ 13 ] M. Aguilar-Benitez et al., Review of particle properties, Phys. Lett. B 170 (1986) 1, and references therein. l 14 ] S. Baker and R.D. Cousins, Nucl. Instrum. Methods 221 (1984) 437.

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