Theoretical Physics Division, Rudjer Bošković Institute, P.O.B.1016 HR Zagreb, Croatia

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1 IRB-TH 1/97 April 1997 Inlusive Charmed-Baryon Deays and Lifetimes arxiv:hep-ph/ v2 11 Jul 1997 Branko Guberina 1 and Blaženka Melić 2 Theoretial Physis Division, Rudjer Bošković Institute, P.O.B.1016 HR Zagreb, Croatia Abstrat We have quantitatively reanalyzed the inlusive harmed-baryon deays. New ingredients are the Voloshin preasymptoti effets in semileptoni deays and the Cabibbo-subleading ontributions to both semileptoni and nonleptoni deays. It has been found that the Cabbibo-subleading Voloshin ontribution essentially improves the theoretial semileptoni branhing ratio of Λ +, in agreement with experiment. The semileptoni branhing ratios for Ξ + and Ω 0 are found to be large, i.e., of the order of 20%. The lifetimes hierarhy is in a good qualitative and even quantitative agreement with experiment exept for the Ξ + lifetime, whih is somewhat smaller than the experimental value. Future measurements, espeially measurements of the semileptoni branhing ratios for Ω 0, Ξ+ and Ξ 0 should be deisive for the hek of this approah. 1 guberina@thphys.irb.hr 2 meli@thphys.irb.hr

2 1. Introdution Weak deays of harmed and bottom hadrons [1-4] are partiularly simple in the limit of infinite heavy quark mass. In reality, hadrons are bound states of heavy quark with light onstituents (light quarks, gluons). The inlusion of soft degrees of freedom generates nonperturbative power orretions, an example of whih is the destrutive Pauli interferene between the spetator light-quark and the light quark in D + meson oming from the deay of the heavy quark [5-7]. Inlusive hadroni deay rates and lifetimes are alulated some time ago[6-9]. It has been found that the overall piture for harmed hadron lifetimes is qualitatively satisfatory. Lifetime hierarhy has been predited for harmed baryons [8,9], in qualitative agreement with present experiments [4]. It has also been shown [6,7] that the Pauli interferene essentially lengthens the lifetime of the D + meson, thus being the main soure of the D 0 D + lifetime differene. The systemati OPE brings in extra operators of dimension 5, namely kineti and hromomagneti operators [10]. Their influene on harmed hadron lifetimes is rather moderate, beause the main ontribution omes from the four-quark operators. Using the urrent quark mass, m 1.4GeV, theresultsfortheharmed familyarequalitatively good[1], provided one assumes that terms of higher dimension in the OPE drive the asymptoti(stati) value of the deay onstant, F meson lose to the smaller value of the physial deay onstant f meson only in meson deays, whereas in baryon deays that is not the ase. In beauty deays, although everything was expeted to work muh better beause of the large b-quark mass, a number of problems has remained unsolved [2,3,11]. In the first plae, it is the disrepany between the measured average semileptoni beauty meson branhing ratio, whih is somewhat smaller than the theoretial predition. Seond, the observed differene of the lifetimes of the Λ b baryon and of the B meson is larger than expeted. In view of these desrepanies, a radial phenomenologial ansatz has been involved [11] with interesting onsequenes for harmed hadron deays. This approah, however, abandons the heavy-quark expansion and loal duality, and requires the introdution [3] of a dominant destrutive interferene in the Ξ + deay and destrutive W-anihilation in D s deays - the requirements that ould hardly be satisfied if the four-quark operators were a dominant soure of preasymptoti effets. Reently, Voloshin has shown [12] that preasymptoti effets are largely present in semileptoni deays of harmed baryons. A signifiant enhanement [3,12] of Γ SL (Ξ ) and Γ SL (Ω ) is expeted relative to Γ SL (Λ ) and Γ SL (D 0 ) in order 1/m 3 owing to the onstrutive Pauli interferene in Γ SL (Ξ,Ω ) among the s-quarks. InthispaperwepresenttheoretialpreditionsontheΛ +,Ξ+,Ξ0 andω0 semileptoni branhing ratios and lifetimes. The lifetimes have already been treated in[8,9]. Here, we extend previous alulations, in whih preasymptoti effets in nonleptoni deay rates were basially attributed to the Cabbibo leading operators of dimension 6. We make extension by inluding Voloshin s preasymptoti effets [12] in inlusive semileptoni deay rates. We alulate and add the Cabibbo subleading ontribu- 1

3 tions sine it was laimed in the literature [13] that they might be important in some ases owing to the statistial fators. We show that the onstrutive Pauli interferene, whih appears in the semileptoni Λ + deay at Cabbibo subleading level, is welome beause it enhanes the theoretial value whih is otherwise too small. Finally, we show that the inlusion of Voloshin s large preasymptoti effets in semileptoni deays does not destroy qualitative hierarhy of lifetimes, but improves it both qualitatively and quantitatively. 2. Preasymptoti effets in inlusive deays The inlusive deay width of a hadron H, of the mass M H, ontaining a quark an be written using the optial theorem as Γ(H f) = 1 2M H 2Im H ˆT H, (1) i.e. as the forward matrix element of the imaginary part of the transition operator ˆT ˆT = i d 4 xt{l eff (x),l eff (0)}. (2) The effetive weak Lagrangian L eff (x) is given [1,3] as a sum of the semileptoni and nonleptoni part L eff = L SL eff +L NL eff. (3) In the following we assume that the energy release in the deay of a quark is large enough so that momenta flowing through internal lines are also large and therefore justify the operator produt expansion of the loal operator (2). The result, widely disussed in the literature [1-3] is given by Γ(H f) = G2 Fm 5 1 { f 192π 3 V 2 2M 3 H H + f H g s σ µν G µν H 5 H + i f 6 H (Γ i q)(qγ i ) H m 3 +O(1/m 4 )+...}. m 2 (4) Here f 3 and f 5 are oeffiient funtions whih depend on the partiular final state. The oeffiients f 3 are known at one-loop order and oeffiients f 5 at tree level [10]. Let us alulate the semi-leptoni deay rates first. The main ontribution is expeted to ome from the quark deay-type diagrams. When orretions O(m 2 ) are inluded, the ontribution takes the form Γ de SL (H ) = G2 F 192π 3m5 (1 1 µ 2 π(h ) m 2 2 µ 2 G(H ) )F m 2 1 (x). (5) 2

4 Here µ 2 π (H ) and µ 2 G (H ) parametrize the matrix elements of the kineti energy and the hromo-magneti operators, respetively. They an be determined from the spetrum of harmed heavy hadrons [14,15]. It turns out that only µ 2 G(Ω 0 ) is different from zero. There is also the ontribution of the dimension five operator Γ G SL(H ) = G2 F 192π ( 2 µ2 G (H ) )F 3m5 2 (x). (6) We have inluded in the above expressions the phase spae orretions F 1 (x) and F 2 (x) [16]. The semileptoni rate, as it has been shown by Voloshin [12], gets important and large ontributions due to the preasymptoti effets. The result is given by m 2 Γ SL = G2 F 12π m2 (4 κ 1) ψ(0) 2. (7) Here, ψ(0) is the baryon wave funtion at the origin and κ is a orretion due to the hybrid renormalization of the effetive Lagrangian. Hybrid renormalization is neessary sine ψ(0) 2 is usually estimated in the effetive quark models whih are expeted to make sense at the typial hadroni sales, µ = GeV. Therefore, it is neessary to evolve the effetive Lagrangian from m down to the sale µ. Total semileptoni rate is given by where Γ SL (H ) = Γ de SL(H )+Γ G SL(H )+Γ Voloshin SL (H ), (8) Γ Voloshin SL (Λ + ) = s2 ΓSL, Γ Voloshin SL (Ξ + ) = ξ2 ΓSL, Γ Voloshin SL (Ξ 0 ) = (ξ 2 +s 2 ) Γ SL, Γ Voloshin SL (Ω 0 ) = 10 3 ξ2 ΓSL. (9) Here s 2 and 2 are abbreviations for sin 2 θ and os 2 θ, and θ is the Cabibbo angle. We have kept the Cabibbo-suppressed ontributions beause the preasymptoti effets are expeted to be very large, and, therefore they might be a signifiant orretion to Γ de SL(H ). Also, we have introdued the parameter ξ whih is the ratio of the matrix elements of the operators ( L γ µ s L )( s L γ µ L ) and ( L γ µ q L )( q L γ µ L ), where q is d or u quark. SU(3) symmetry-breaking effets, measured by ξ are not expeted to exeed 30%. It is very diffiult to reliably estimate the value of ξ, although ertain hints an be made using different hadroni models. For example, the hadroni models used in [9] would suggest ξ > 1, but in view of the fat that we lak reliable models suh a onlusion might be premature. We shall not rely on suh estimates in later disussions, but prefer to treat ξ as a fitting parameter. So far, only semileptoni branhing ratio of Λ + has been measured with reasonable auray BR(Λ + ex) = (4.5±1.7)%. (10) 3

5 By inspetion of Eq.(9) one notes that exept for Λ +, all baryons reeive potentially large Voloshin s ontributions at the Cabibbo-leading level. Therefore, one expets, as pointed by Voloshin [12], signifiantly larger semileptoni ratio for Ξ +, Ξ 0 and Ω 0. Besides, theontributiontoλ+ semileptonibranhing ratio,althoughcabbibosuppressed by sin 2 θ, might be an important orretion to the deay diagram. This is welome, sine the deay diagram is not large enough to explain the experimental branhing ratio [16]. The alulation of the nonleptoni deay rate losely follows the semileptoni ones. The lepton pair is substituted by a quark pair, and Wilson oeffiients ± hange their values beause of the renormalization. The ontributions oming from the -quark deay-type diagrams (inluding O(m 2 ) orretions) and from the dimension five operator are of the form Γ de NL(H ) = G2 F 192π ( 2 3m )(1 1 µ 2 π (H ) m 2 2 µ 2 G (H ) )F m 2 1 (x), Γ G NL (H ) = G2 F 192π 3m3 ( )µ2 G (H ). (11) The dominant ontribution is expeted to ome from the preasymptoti effets. They are given as Γ ex = G2 F 2π m2 [ (1 κ)( )] ψ(0) 2, Γ int = G2 F 2π m2 [ 1 2 +(2 + ) 1 6 (1 κ)( )] ψ(0) 2, Γ int + = G2 F 2π m2 [ 1 2 +(2 + + ) 1 6 (1 κ)( )] ψ(0) 2. (12) The result of the alulation of the nonleptoni rates is Γ NL (Λ + ) = Γde NL (Λ+ )+2 Γ ex +Γ int +s2 Γ int +, Γ NL (Ξ + ) = Γde NL (Ξ+ )+ξs2 Γ ex +Γ int +ξ2 Γ int +, Γ NL (Ξ 0 ) = Γ de NL(Ξ )+( 2 +ξs 2 )Γ ex +(ξ 2 +s 2 )Γ int +, Γ NL (Ω 0 ) = Γde NL (Ω0 )+ΓG NL (Ω0 )+ξs210 3 Γex +ξ Γint +. (13) Here we have not taken into aount mass orretions, beause they are ompletely negligible. By inspetion of the results one sees that Cabibbo suppressed ontribution only slightly hanges the overall results. The right pattern depends on the value of m and ψ(0) 2. However, for κ = 1, Γ int + is always larger than Γint holds even if hybrid logarithms are taken into aount. Therefore, the Γ int. This onlusion + will dominate the nonleptoni Ξ + deay rate, as far as ξ 1. Sine experimentally Ξ + has the largest lifetime this rate should be relatively small. For the determination of the baryon wave funtion we use estimates of the referenes [9,1], i.e the relation for the ratio of the squares of the meson and baryon wave 4

6 funtions whih is derived using the onstituent quark model developed by De Rujula et al. [17]. There appear effetive quark masses, m 1.5GeV, m u 0.35GeV and quarks are bound by a nonrelativisti potential whih is modified by hyperfine interations. Following the approah of Ref.[1], in the expression for the baryoni wave funtion we shall use the stati value F D instead of the physial deay onstant f D for the reasons given below. This leads to ψ Λ+ (0) 2 = 3(M Σ + M Λ + ) µ 2 G (D) m u ( 1 12 M DF 2 D κ 4/9 ). (14) The importane of the value of ψ Λ+ (0) 2 is obvious sine the differenes in deay widths/lifetimes are presumably generated mostly by the operators of dimension 6 (four-quark operators) and are therefore proportional to FD/m 2 2, whih indeed vanishes as 1/m 3, sine F D behaves as m 1/2 for m. It has been argued [1], on a more intuitive basis, that in order to be onsistent, one should use the stati value F D in the alulations of the baryon deay. For meson deays, however, one should assume that the role of higher dimension terms is not negligible, and onsequently, the physial (measured) onstant f D should be used in alulations. These arguments [1] are based on the fat that in meson deays one uses the fatorization whih neessarily brings into game the physial deay onstant f D, whereas in baryon deays this is not the ase. Sine there is no proof of this ansatz, one should take it as an attempt to disentangle the overall normalization of the mesoni matrix elements from the baryoni ones. In fat, it is known from previous alulations that, for example, the destrutive Pauli interferene in the D + meson deay has reasonable values when the bag model wave funtions are used [6], while the harmed baryon hierarhy was qualitatively well desribed by using nonrelativisti quark models [9]. In other words, in order to ahieve agreement with experimental data, different normalization of matrix elements had to be used for meson and baryon deays. 3. Semileptoni branhing ratios and lifetime hierarhy - results and disussions Our hoie of entral values of parameters roughly follows the set of values of Blok and Shifman [1]. ForΛ QCD = 300MeV, the Wilson oeffiients are + = 0.734, = Our entral value for the harmed quark mass is m = 1.4GeV. However, in Table 1. we show the results for m = 1.35GeV for omparison. There is a 5

7 RESULTS (ξ = 1, Λ QCD = 300MeV,µ = 1GeV) EXP. DATA m = 1.4GeV m = 1.35GeV [4] Lifetimes in units s τ(λ + ) ±0.12 τ(ξ + ) ±0.70 τ(ξ 0 ) ±0.23 τ(ω 0 ) ±0.20 Lifetime ratios τ(ξ + )/τ(λ + ) ±0.35 τ(ξ 0 )/τ(λ+ ) ±0.11 τ(ω 0 )/τ(λ+ ) ±0.09 τ(ξ + )/τ(ξ 0 ) ±1.10 Semileptoni deay rates in units ps 1 Γ SL (Λ + ) ±0.085 Γ SL (Ξ + ) Γ SL (Ξ 0 ) Γ SL (Ω 0 ) Semileptoni branhing ratios in % BR SL (Λ + ) ±1.7 BR SL (Ξ + ) BR SL (Ξ 0 ) BR SL (Ω 0 ) Table 1: Preditions for semileptoni branhing ratios and lifetimes of harmed baryons given for two values of the harmed quark mass m. ontroversy [15] over the value of µ 2 π, whih varies in the range [2] µ 2 π(b) λ 1 = (0.3±0.2)GeV 2. (15) In our alulations we use the lower value, µ 2 π = 0.1GeV 2. However, we also hek that the larger value µ 2 π = 0.5GeV 2 only slightly hanges the result in semileptoni branhing ratios, but has almost no effet on lifetimes. The hromomagneti operator ontributes only to Ω 0 deays [1]; we use the value µ 2 G(Ω 0 ) = 0.182GeV 2. (16) Following [1], we use the following input to obtain the entral value in Eq.(14): F D = 400MeV, m u = 350MeV, M Σ M Λ + = 400MeV (stati value) and M D = 1870MeV. For µ 2 G(D), we use the value µ 2 G(D) = 0.4GeV 2. Then, for κ = 1, Eq.(14) gives our entral value for the baryon wave funtion ψ Λ+ (0) 2 µ=m = GeV 3. (17) 6

8 RESULTS (m = 1.4GeV,Λ QCD = 300MeV,µ = 1GeV) EXP. DATA ξ = 1 ξ = 0.75 [4] Lifetimes in units s τ(λ + ) ±0.12 τ(ξ + ) ±0.70 τ(ξ 0 ) ±0.23 τ(ω 0 ) ±0.20 e e Semileptoni branhing ratios in % BR SL (Λ + ) ±1.7 BR SL (Ξ + ) BR SL (Ξ 0 ) BR SL (Ω 0 ) Table 2: Preditions for harmed baryons in dependene of the parameter ξ. Our numerial results are presented in Tables 1-2. The left set of numbers in the Tables are numerial results obtained for our entral values disussed before, and for m = 1.4GeV, m s = 150MeV, µ = 1GeV and ξ = 1. The agreement with available experimental data is very good, exept for the lifetime of Ξ +, where theoretially predited value is smaller than in experiment (see Table 1). The same problem with Ξ + persists if one alulates theratio of lifetimes (insuh a way signifiantly reduing the unertainty oming from the wave-funtion value). However, the semileptoni branhing ratio for Λ + is in exellent agreement with the experimental value, showing learly that preasymptoti effets of Voloshin s type, although at the Cabibbo suppressed level, signifiantly improve the theoretial value. For Λ QCD = 200MeV the results are almost not affeted exept the Λ + lifetime whih grows by 20%, beoming so unpleasantly large. However, one should keep in mind that suh modest disrepanes are expeted sine in harmed baryon deays we are far away from the asymptoti limit. In Table 1 we also display results of the alulations for the smaller value of the urrent quark mass, m = 1.35GeV. Again, the results are not very sensitive to this variation, although the agreement with experiment is slightly improved, espeially for Ξ + deays. In Table 2 we have presented the results of alulations for the speifi hoie of the parameter ξ, ξ = 0.75, ompared with the results obtained for ξ = 1. As disussed above, we allow ξ to have a value different from 1, treating it as a free parameter. Fitting ξ roughly to the value needed to bring the Ξ + lifetime into agreement with experiment gives ξ Fitting ξ basially means to fit the onstrutive interferene term Γ int + for Cabibbo favoured deays. The simple fit of one lifetime would of ourse, not make muh progress. However, Γ int + enters also the deay rates of other baryons, Ξ 0 and Ω 0, at the same Cabibbo level. Besides, 7

9 µ = 0.5 GeV µ = 0.7 GeV µ = 1.0 GeV µ = 0.5 GeV µ = 0.7 GeV µ = 1.0 GeV τ(λ + ) ps τ(ξ +) ps ψ(0) 2 µ=m GeV ψ(0) 2 µ=m GeV 3 Figure 1: Lifetimes of Λ + and Ξ + as a funtion of the square of the baryon wave funtion ψ(0) 2, given for three values of the hybrid renormalization point µ. The shaded areas are the experimentally allowed regions. The dot-dashed vertial line is avalueof ψ(0) 2 usedintables1to2. Theresultsareobtainedusingm = 1.4GeV, Λ QCD = 300MeV, µ 2 π = 0.1GeV 2. the same fator ξ enters Voloshin s ontributions to semileptoni deay rates, again at the same Cabibbo level. Therefore, any trivial fit to Ξ + ould at the same time worsen the results for other partiles. However, interestingly enough, here this is not the ase. Although the fit ξ = 0.75 brings the Ξ + lifetime into perfet agreement between theory and experiment, it does not spoil the agreement between theory and experiment for both semileptoni BR s and lifetimes of other partiles. Next we study the dependene of lifetimes on the square of the baryon wave funtion ψ(0) 2 and show the results in Fig.1 and 2. We vary the value ψ(0) 2 inside a fator of 2 in the range 0.018GeV 3 ψ Λ+ (0) 2 µ=m 0.034GeV 3, (18) with a entral value given by (17). It is interesting to note that the lifetimes of Λ + and Ξ + are very sensitive to the value of ψ Λ+ (0) 2, Fig.1. On the other hand, the other deays are not so sensitive, and are onsistent with experiment even for the lower value of ψ Λ+ (0) 2 given in (18), Fig.2. Therefore, one ould easily bring the lifetimes of Ξ +, Ξ0 and Ω 0 to agreement with experiment simply by using a smaller value of ψλ+ (0) 2. This would enlarge the Λ + lifetime and introdue a desrepany between theory and experiments. However, our analysis of lifetimes, as disussed above, shows that the Ξ + lifetime exhibits a peuliar behavior - strong µ-dependene and strong ψ(0) 2 - dependene. Furthermore, the entral value of ψ Λ+ (0) 2, given in (36), gives a good 8

10 µ = 0.5 GeV µ = 0.7 GeV µ = 1.0 GeV µ = 0.5 GeV µ = 0.7 GeV µ = 1.0 GeV τ(ξ 0 ) ps τ(ω 0) ps ψ(0) 2 µ=m GeV ψ(0) 2 µ=m GeV 3 Figure 2: Lifetimes of Ξ 0 and Ω0 as a funtion of the square of the baryon wave funtion ψ(0) 2 given for three values of the hybrid renormalization point µ. The shaded areas are the experimentally allowed regions. The dash-dotted vertial line is avalueof ψ(0) 2 usedintables1to2. Theresultsareobtainedusingm = 1.4GeV, Λ QCD = 300MeV, µ 2 π = 0.1GeV 2, µ 2 G (Ω0 ) = 0.182GeV 2. semileptoni branhing ratio of Λ +, whih we disuss next. As disussed in the preeding setion, baryons reeive Voloshin s large interferene ontributions at the Cabibbo leading level. Their role is obvious from Table 1, where a ertain hierarhy of semileptoni BR s is strongly pronouned: BR SL (Λ + ) < BR SL (Ξ 0 ) < BR SL (Ω 0 ) < BR SL (Ξ + ). (19) It is in the numerial range from 4.5 to 25 perent. We onsider predition (19) as a ruial test of the approah presented here, for the following reasons: Voloshin s interferene effets, being proportional to ψ(0) 2 are neessarily large, beause one needs a large ψ(0) 2 in order to reprodue experimental values of lifetimes. If one finds experimentally that all semileptoni BR s are of the order of BR SL (Λ + ), this will mean that the interferene effet in semileptoni deays is negligible, and that, therefore, the preasymptoti effets in (12) are unlikely to be responsible for the experimentally evident hierarhy of lifetimes. In addition to this very lear predition, Voloshin s interferene effet helps to improve the theoretial value of the Λ + semileptoni branhing ratio. It appears at the Cabibbo suppressed level and ats as a orretion to the main ontribution oming from the deay diagram. It has been known for a long time that the quark deay mehanism annot explain the semileptoni branhing ratio of Λ +, if one uses the urrent quark mass m 1.4GeV in (5). An effetive mass of the order GeV is atually needed [1-3,11]. 9

11 µ = 0.5 GeV µ = 0.7 GeV µ = 1.0 GeV µ = 0.5 GeV µ = 0.7 GeV µ = 1.0 GeV Γ sl (Λ + ) ps ) ps -1 Γ sl (Λ ψ(0) 2 µ=m GeV ψ(0) 2 µ=m GeV 3 Figure 3: Semileptoni Λ + -deay rate for three values of the hybrid renormalization point µ is given as a funtion of the square of the baryon wave funtion ψ(0) 2. On the left piture finite α s -ontributions are not inluded. The vertial dot-dashed line denotes the entral value in (17). The shaded area is the experimentally allowed region. denotes the semileptoni deay rate without Voloshin s ontributions. The other parameter values used are m = 1.4GeV, Λ QCD = 300MeV, µ 2 π = 0.1GeV 2. In Fig.3 we show the semileptoni branhing ratio for Λ + as a funtion of ψ(0) 2, fortwoases, namelywithandwithoutfiniteα s -orretions. Itisquitelearthatthe interferene effet is welome, beause it brings the theoretial value lose to experiment. In all alulations, presented in Tables 1-2, the finite α s -orretions have not been taken into aount beause they are not known for all kinds of preasymptoti ontribution. However, the right figure in Fig.3 shows the semileptoni branhing ratio with finite α s -orretions inluded. Obviously, without the interferene effet the theoretial value is outside the experimentally allowed region. 4. Conlusions In this paper we have performed an analysis of inlusive semileptoni branhing ratios and lifetimes for the harmed baryon family. New ingredients in this analysis are the inlusion of preasymptoti effets in semileptoni deays and the inlusion of Cabibbo suppressed ontributions. In the alulations we have used the input parameters determined by QCD, thus following the approah of Blok and Shifman [1], i.e. we have avoided the introdution of effetive parameters, suh as effetive 10

12 harmed quark mass, effetive hadron mass instead of quark mass, et. In this way we have tried to test quark-hadron duality using our present knowledge of OPE and QCD up to the level of introduing the baryon wave funtion, ψ Λ+ (0) as a measure of the strength of the dominant preasymptoti effets. Having fixed the harmed quark mass to be approximately m 1.4GeV, the semileptoni branhing ratios and lifetimes of harmed baryons depend essentially on the square of the baryon wave funtion, ψ Λ+ (0) 2, whih, in spirit of the above onsiderations may be regarded as a fitting parameter. It is a pleasent disovery that a rough fit of ψ Λ+ (0) 2 agrees very well with the Blok-Shifman estimate [1]. Our analysis leads to the following onlusions: i) The inlusion of Voloshin s large preasymptoti effets leads to following preditions: The semileptoni branhing ratios of Ξ +, Ξ 0, and Ω 0 are signifiantly larger than the semileptoni branhing ratios of Λ + with a hierarhy already given in Eq.(19): BR SL (Λ + ) < BR SL(Ξ 0 ) < BR SL(Ω 0 ) < BR SL(Ξ + ). The inlusion of the Cabibbo suppresed interferene effet in the semileptoni deay rate of Λ + enhanes it and brings the branhing ratio to agreement with experiment. ii) The hange in semileptoni deay rates whih is due to interferene effets signifiantly helps to obtain very good qualitative and even quantitive results for the lifetimes with the same hierarhy τ(ω 0 ) < τ(ξ 0 ) < τ(λ + ) < τ(ξ + ), (20) as predited in [8,9]. The predited lifetime of Ξ + appears to be somewhat smaller than the experimental value. We do not onsider that as a problem, sine we are far away from the asymptoti limit and it would be premature to expet that higher order terms in OPE are really negligible. iii) Conerning the results as obtained and shown in Tables 1-2, one may onlude that quark-hadron duality works suprisingly well for the harmed baryon family. After ompletion of this work we have learned of a reent paper of Cheng [18] where Voloshin s type of orretions were onsidered in a different ontext, in a more phenomenologial way, introduing the effetive harmed-quark mass, substitution of the universal quark mass by the partiular physial hadron mass, et. We believe that our results, ompared with the results of Cheng [18], are more onsistent and more reliable. Aknowledgement This work was supported by the Ministry of Siene and Tehnology of the Republi of Croatia under the ontrat Nr

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