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the hadronic decays of @xmath0 mesons have provided us with a good place to study cp violation in particle physics . in particular , the detection of direct cp violation in a decay process requires that there exist at least two contributing amplitudes with different weak and strong phases . the direct cp - violating effect in the @xmath0 system has finally been observed in the @xmath6 decay at the @xmath0-factories @xcite , proving the existence of nontrivial strong phases in @xmath0 decays . it is therefore of consequence to find out the patterns of final - state strong phases for a wider set of decay modes .    since the ckm factors involved in charmed @xmath0 meson decays are purely real to a good approximation , the phases associated with the decay amplitudes thus have the origin of strong interactions . such final - state rescattering effects have been noticed from data in these decays @xcite , and estimated to be at 15 - 20% level @xcite . unfortunately , no satisfactory first - principle calculations can yield such strong phases @xcite . in ref . @xcite , we performed an analysis based upon the experimental data available at that time . a few theoretical and experimental questions are left unanswered . as more decay modes have been observed and others are measured at higher precisions , it becomes possible for us to look at and answer those questions . in this paper , flavor su(3 ) symmetry is employed to relate different amplitudes and strong phases of the same topological type . moreover , we will take a different approach by fitting theoretical parameters to all available branching ratios simultaneously . an advantage of this analysis is that the parameters thus obtained are insensitive to statistical fluctuations of individual modes . this paper is organized as follows . in section  [ sec : decomp ] , we give the amplitude decomposition of modes under flavor su(3 ) symmetry and the current branching ratio data . theoretical parameters involved in our analysis are defined . in section  [ sec : phases ] , we consider three sets of charmed decay modes : @xmath7 , @xmath8 , and @xmath2 , where @xmath3 and @xmath4 denote charmless pseudoscalar and vector mesons , respectively . a summary of our findings is given in section  [ sec : summary ] . in the decomposition of decay amplitudes , relevant meson wave functions are assumed to have the following quark contents , with phases chosen so that isospin multiplets contain no relative signs :    * _ beauty mesons : _ @xmath9 , @xmath10 , @xmath11 . * _ charmed mesons : _ @xmath12 , @xmath13 , @xmath14 , with corresponding phases for vector mesons . * _ pseudoscalar mesons @xmath3 : _ @xmath15 , @xmath16 , @xmath17 , @xmath18 , @xmath19 , @xmath20 , @xmath21 , @xmath22 , @xmath23 , assuming a specific octet - singlet mixing @xcite in the @xmath24 and @xmath25 wave functions . ) * _ vector mesons @xmath4 : _ @xmath26 , @xmath27 , @xmath28 , @xmath29 , @xmath30 , @xmath31 , @xmath32 , @xmath33 , @xmath34 . the amplitudes contributing to the decays discussed here involve only three different topologies @xcite :    1 .   _ tree amplitude @xmath35 : _ this is associated with the transition @xmath36 ( cabibbo - favored ) or @xmath37 ( cabibbo - suppressed ) in which the light ( color - singlet ) quark - antiquark pair is incorporated into one meson , while the charmed quark combines with the spectator antiquark to form the other meson . _ color - suppressed amplitude @xmath38 : _ the transition is the same as in the tree amplitudes , namely @xmath39 or @xmath37 , except that the charmed quark and the @xmath40 combine into one meson while the @xmath41 or @xmath42 quark and the spectator antiquark combine into the other meson . _ exchange amplitude @xmath43 : _ the @xmath44 quark and spectator antiquark exchange a @xmath45 boson to become a @xmath46 pair , which then hadronizes into two mesons by picking up a light quark - antiquark pair out of the vacuum . after factoring out the ckm factors explicitly , we obtain the flavor amplitude decomposition of the charmed @xmath0 decay modes in tables  [ tab : dp ] , [ tab : dstp ] , and [ tab : dv ] . in these tables , we introduce positive @xmath47 s to parameterize the flavor su(3 ) breaking effects . this symmetry is respected between strangeness - conserving and strangeness - changing amplitudes when @xmath47 s are taken to be unity . as we will discuss in the next section , @xmath47 s will be allowed to change in order to test the assumption . using the wolfenstein parameters @xcite , the relevant ckm factors are : @xmath48 none of which contain a weak phase to the order we are concerned with . in the following analysis , we take the central values @xmath49 and @xmath50 quoted by the ckmfitter group @xcite . since only the relative strong phases are physically measurable , we fix the tree ( @xmath35 , @xmath51 , and @xmath52 ) amplitudes to be real and pointing in the positive direction . we then associate the color - suppressed and exchange amplitudes with the corresponding strong phases explicitly as follows : @xmath53    the magnitude of invariant decay amplitude @xmath54 for a decay process @xmath55 is related to its partial width via the following relation : @xmath56 with @xmath57 where @xmath58 are the masses of @xmath59 , respectively . to relate partial widths to branching ratios , we use the world - average lifetimes @xmath60 ps , @xmath61 ps , and @xmath62 ps computed by the heavy flavor averaging group ( hfag ) @xcite . .branching ratios and flavor amplitude decomposition for @xmath63 decays . data are quoted from refs . @xcite [ cols="<,^,^,^,^,^ " , ]     @xmath64 gev can be extracted from the @xmath65 mode using the u - spin symmetry and taking @xmath66 . this is slightly larger than our fit result in scheme 2 . directly from the @xmath67 mode , we have only a poor upper bound of @xmath68 gev on @xmath69 . the observable @xmath70 has the largest contribution to the total @xmath71 . from table [ tab : dv ] , we observe that the area of the triangle formed from the @xmath72 , @xmath73 and @xmath74 decays is very small , while that of the triangle formed from the @xmath75 , @xmath76 and @xmath77 modes is not . this is the reason why the global @xmath78 fits in the @xmath2 sector are not as satisfactory as those in the @xmath7 and @xmath79 sectors .    in ref . @xcite , we noted that @xmath80 extracted from @xmath81 was inconsistent with @xmath82 extracted from a combination of the @xmath83 and @xmath84 modes . currently , the former is @xmath85 gev if we take @xmath86 , and the latter is @xmath87 gev . there is still a discrepancy at the 1.7@xmath88 level , or this discrepancy implies that the su(3 ) breaking factor @xmath89 should be greater than about @xmath90 . a determination of @xmath91 and better measurements of related modes will be very useful in providing further insights into this problem . = 1 ( pink , solid ) and 2.30 ( blue , dotted ) contours on the @xmath92-@xmath93 , @xmath94-@xmath95 , and @xmath95-@xmath93 planes in scheme 3.,title="fig:",height=170 ] = 1 ( pink , solid ) and 2.30 ( blue , dotted ) contours on the @xmath92-@xmath93 , @xmath94-@xmath95 , and @xmath95-@xmath93 planes in scheme 3.,title="fig:",height=170 ] = 1 ( pink , solid ) and 2.30 ( blue , dotted ) contours on the @xmath92-@xmath93 , @xmath94-@xmath95 , and @xmath95-@xmath93 planes in scheme 3.,title="fig:",height=170 ]    in fig .  [ fig : dv2ce ] , we show the @xmath96 and @xmath97 contours on the @xmath92-@xmath93 , @xmath94-@xmath95 , and @xmath95-@xmath93 planes in scheme 3 , respectively . we find that @xmath98 and @xmath99 . we see that the magnitude of @xmath51 is larger than @xmath35 and @xmath52 , resulting in a more hierarchical structure among @xmath100 , @xmath80 and @xmath69 . another result of the large @xmath51 is reflected in the bigger branching ratio prediction for the most dominant @xmath101 mode . as in the @xmath79 sector , the central value of @xmath94 is non - zero , but is still consistent with zero within the 68.3% cl region . the ratio of the two effective wilson coefficients can be extracted as @xmath102 where @xmath98 as obtained from the @xmath78 analysis in scheme 3 . in ref . @xcite , it is estimated that @xmath103 at the 1  @xmath104 level using the data of the @xmath72 , @xmath73 and @xmath105 modes .    finally , we summarize our findings in fig .  [ fig : amps ] . these diagrams are constructed by taking the central values of the fitted parameters in each category using scheme 3 . they illustrate the sizes and relative phases among the tree , color - suppressed , and exchange amplitudes .     decays ; ( b ) : @xmath79 decays ; and ( c ) : @xmath2 decays . [ fig : amps],title="fig:",height=113 ] + ( a ) +   decays ; ( b ) : @xmath79 decays ; and ( c ) : @xmath2 decays . [ fig : amps],title="fig:",height=113 ] + ( b ) +   decays ; ( b ) : @xmath79 decays ; and ( c ) : @xmath2 decays . [ fig : amps],title="fig:",height=113 ] + ( c ) + we have used the @xmath78 fit approach to re - analyze the two - body charmed @xmath0 meson decays in the flavor su(3)-symmetric formalism , taking into account different symmetry breaking schemes as well . in the @xmath7 and @xmath8 decays , there are significant improvement in the @xmath78 minimum between scheme  1 and scheme  2 , but not much between scheme  2 and scheme  3 . this shows that the major su(3 ) breaking effect can be accounted for by the decay constant ratio @xmath106 , as demanded for example by naive factorization . the same feature , however , is not observed in the @xmath2 sector , where the corresponding decay constant ratio is approximately one .    in our analysis , the fit results are generally consistent with those extracted from individual modes . we have found that the color - suppressed amplitudes are enhanced in the @xmath7 and @xmath79 sectors , but not in the @xmath2 sector . this strongly suggests that non - factorizable effects or final - state rescattering effects can not be neglected in the former two sectors .    in the @xmath2 sector , it is observed that the cabibbo - suppressed @xmath107 yields a @xmath80 that exceeds the bound @xmath108 given by a combination of the @xmath109 and @xmath110 branching ratios at @xmath111 level , or @xmath89 should be greater than about @xmath90 . we urge the measurement of @xmath112 for a direct determination of the exchange amplitude , which may provide a possible solution to this problem . finally we note that the exchange diagrams are at least an order of magnitude smaller than the dominant tree topologies in these decays . consequently , it is difficult to determine their phases , particularly in the @xmath79 and @xmath2 sectors , unless data precision can be significantly improved in the future . c. would like to thank the hospitality of the national center for theoretical sciences in taiwan and the institute of theoretical physics at univ .  of oregon during his visit where part of this work was initiated and carried out . this research was supported in part by the national science council of taiwan , r.o.c .  under grant no . nsc 95 - 2112-m-008 - 008 . 99 b.  aubert _ et al . _ [ babar collaboration ] , phys . lett .   * 93 * , 131801 ( 2004 ) [ arxiv : hep - ex/0407057 ] . y.  chao _ et al . _ [ belle collaboration ] , phys . lett .   * 93 * , 191802 ( 2004 ) [ arxiv : hep - ex/0408100 ] ; k.  abe _ et al . _ , arxiv : hep - ex/0507045 . h.  y.  cheng , phys .  rev . d * 65 * , 094012 ( 2002 ) [ arxiv : hep - ph/0108096 ] . c.  k.  chua , w.  s.  hou and k.  c.  yang , phys .  rev . d * 65 * , 096007 ( 2002 ) [ arxiv : hep - ph/0112148 ] ; c.  k.  chua and w.  s.  hou , phys . d * 72 * , 036002 ( 2005 ) [ arxiv : hep - ph/0504084 ] . fayyazuddin , jhep * 0209 * , 055 ( 2002 ) [ arxiv : hep - ph/0206164 ] ; phys . d * 70 * , 114018 ( 2004 ) [ arxiv : hep - ph/0402189 ] . l.  wolfenstein , phys .  rev . d * 69 * , 016006 ( 2004 ) [ arxiv : hep - ph/0309166 ] ; arxiv : hep - ph/0407344 . c.  w.  chiang and j.  l.  rosner , phys . d * 67 * , 074013 ( 2003 ) [ arxiv : hep - ph/0212274 ] . l.  l.  chau , h.  y.  cheng , w.  k.  sze , h.  yao and b.  tseng , phys . d * 43 * , 2176 ( 1991 ) [ erratum - ibid . d * 58 * , 019902 ( 1998 ) ] . m.  gronau and j.  l.  rosner , phys . d * 53 * , 2516 ( 1996 ) [ arxiv : hep - ph/9509325 ] ; a.  s.  dighe , m.  gronau and j.  l.  rosner , phys . b * 367 * , 357 ( 1996 ) [ erratum - ibid . b * 377 * , 325 ( 1996 ) ] [ arxiv : hep - ph/9509428 ] . d.  zeppenfeld , z.  phys . c * 8 * , 77 ( 1981 ) ; m.  j.  savage and m.  b.  wise , phys . d * 39 * , 3346 ( 1989 ) [ erratum - ibid . d * 40 * , 3127 ( 1989 ) ] ; m.  gronau , o.  f.  hernandez , d.  london and j.  l.  rosner , phys . d * 50 * , 4529 ( 1994 ) [ hep - ph/9404283 ] ; m.  gronau , o.  f.  hernandez , d.  london and j.  l.  rosner , phys .  rev . d * 52 * , 6356 ( 1995 ) [ arxiv : hep - ph/9504326 ] ; m.  gronau , o.  f.  hernandez , d.  london and j.  l.  rosner , phys . d * 52 * , 6374 ( 1995 ) [ hep - ph/9504327 ] . l.  wolfenstein , phys . lett .   * 51 * , 1945 ( 1983 ) . j.  charles _ et al . _ [ ckmfitter group ] , eur . j.  c * 41 * , 1 ( 2005 ) [ arxiv : hep - ph/0406184 ] . updated results may be found on web site http://ckmfitter.in2p3.fr/. updated results and references are tabulated periodically by the heavy flavor averaging group : http://www.slac.stanford.edu/xorg/hfag/rare . w.  m.  yao _ et al . _ [ particle data group ] , j.  phys . g * 33 * , 1 ( 2006 ) . 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the charmed @xmath0 decays , @xmath1 and @xmath2 , are re - analyzed using the latest experimental data , where @xmath3 and @xmath4 denote the pseudoscalar meson and vector meson , respectively . 
 we perform global fits under the assumption of flavor su(3 ) symmetry . 
 the size of the decay amplitudes and the strong phases between the topologically distinct amplitudes are studied . 
 predictions of the related @xmath5 decay rates are made based upon the fitted results . 
 we also note a serious su(3 ) symmetry breaking or inconsistency in the @xmath2 sector . 
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