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very recently , babar collaboration reported the measurement of the baryonic @xmath6 decay @xmath7 and observed a new structure in the @xmath8 invariant mass spectrum at @xmath9 @xcite . for simplicity , one could name the new structure as @xmath0 . soon after the experimental observation , he _ et al . _ have suggested that @xmath0 could be a @xmath1 molecular state from an effective lagrangian calculation @xcite . theoretically , the molecular concept is well and truly not a new topic but with a history . it was put forward nearly 40 years ago in ref . @xcite and was predicted that molecular states have a rich spectroscopy in ref . the possible deuteron - like two - meson bound states were studied in ref . @xcite . in recent years , some of  x " ,  y " , and z " new hadrons are ranked as possible molecular candidates . such as , @xmath10 could be a @xmath11 molecular state @xcite ; @xmath12 is interpreted as a @xmath13 state @xcite ; @xmath14 is proposed to be a @xmath15 @xcite or an @xmath16 state @xcite ; @xmath17 is deciphered as a @xmath18 state @xcite ; @xmath19 and @xmath20 could be @xmath21 and @xmath22 states , respectively @xcite . especially , there already have a lot of works discussing baryon resonances with meson - baryon molecular structures , e.g. @xcite . if molecular states can be completely confirmed by experiment , qcd will be further testified and then one will understand the qcd low - energy behaviors more deeply . therefore , it is interesting to study whether the newly observed @xmath0 state could be a @xmath1 molecular state .    in the real world , quarks are confined inside hadrons and the strong interaction dynamics of hadronic systems is governed by nonperturbative qcd effect completely . many questions concerning dynamics of the quarks and gluons at large distances remain unanswered or understood only at a qualitative level . it is quite difficult to extract hadronic information quantitatively from the basic theory of qcd . the qcd sum rule method @xcite is a nonperturbative formulation firmly based on the first principle of qcd , which has been successfully applied to conventional hadronic systems , i.e. mesons or baryons ( for reviews see @xcite and references therein ) . for multiquark states , there have appeared fruitful results from qcd sum rules these years ( for a review on multiquark qcd sum rules one can see @xcite and references therein ) . in particular for hadrons containing five quarks , some authors began to study light pentaquark states in refs . the application of qcd sum rules to heavy pentaquark states was performed in ref . @xcite for the first time .    in this work , we devote to investigating that whether the newly observed resonance @xmath0 could be a @xmath1 molecular state ( @xmath23 has a quark content @xmath24 ) in the framework of qcd sum rules . as a byproduct , the mass for its bottom counterpart @xmath4 is also predicted on the assumption that it could exist ( @xmath25 has a quark content @xmath26 and one should note that it has not been observed ) . in theory , one could expect that the @xmath25 meson should be assigned the same spin parity @xmath27 as @xmath23 . the rest of the paper is organized as three sections . we discuss qcd sum rules for molecular states in sec . [ sec2 ] utilizing similar techniques as our previous works @xcite . the numerical analysis and discussions are presented in sec . [ sec3 ] , and masses of @xmath1 and @xmath4 molecular states are extracted out . the sec . [ sec4 ] includes a brief summary and outlook . the qcd sum rules for molecular states are constructed from the two - point correlation function @xmath28|0\rangle.\end{aligned}\ ] ] in full theory , the interpolating current for @xmath29 or @xmath25 meson can be found in ref . @xcite , and the one for nucleon @xmath30 has been listed in ref . . one can construct the @xmath1 or @xmath4 molecular state current from meson - baryon type of fields @xmath31 where @xmath32 is heavy quark @xmath33 or @xmath34 , and @xmath35 , @xmath36 , @xmath37 , as well as @xmath38 denote light quarks . the index @xmath39 means matrix transposition , @xmath40 is the charge conjugation matrix , with @xmath41 , @xmath34 , @xmath33 and @xmath42 are color indices . one should note that meson - baryon molecules in the real world are long objects in which the meson and the baryon are far away from each other . the currents in this work and in most of the qcd sum rule works are local and the five field operators here act at the same space - time point . it is a limitation inherent in the qcd sum rule disposal of the hadrons since the bound states are not point particles in a rigorous manner . lorentz covariance implies that the two - point correlation function in eq . ( [ correlator ] ) has the form @xmath43 according to the philosophy of qcd sum rules , the correlator is evaluated in two ways . phenomenologically , the correlator can be expressed as a dispersion integral over a physical spectral function @xmath44 where @xmath45 is the mass of the hadronic resonance , and @xmath46 gives the coupling of the current to the hadron @xmath47 . in the ope side , short - distance effects are taken care of by wilson coefficients , while long - distance confinement effects are included as power corrections and parameterized in terms of vacuum expectation values of local operators , the so - called condensates . one can write the correlation function in the ope side in terms of a dispersion relation @xmath48 where the spectral density is given by the imaginary part of the correlation function @xmath49 technically , one works at leading order in @xmath50 and considers condensates up to dimension @xmath2 . to keep the heavy - quark mass finite , one can use the momentum - space expression for the heavy - quark propagator @xcite @xmath51\nonumber\\ & & { } -\frac{i}{4}g^{2}t^{a}t^{b}g^{a}_{\alpha\beta}(0)g^{b}_{\mu\nu}(0)\frac{\rlap / p+m_{q}}{(p^{2}-m_{q}^{2})^{5 } } [ \gamma^{\alpha}(\rlap / p+m_{q})\gamma^{\beta}(\rlap / p+m_{q})\gamma^{\mu}(\rlap / p+m_{q})\gamma^{\nu}\\ & & { } + \gamma^{\alpha}(\rlap / p+m_{q})\gamma^{\mu}(\rlap / p+m_{q})\gamma^{\beta}(\rlap / p+m_{q})\gamma^{\nu}+ \gamma^{\alpha}(\rlap / p+m_{q})\gamma^{\mu}(\rlap / p+m_{q})\gamma^{\nu}(\rlap / p+m_{q})\gamma^{\beta}](\rlap / p+m_{q})\nonumber\\ & & { } + \frac{i}{48}g^{3}f^{abc}g^{a}_{\gamma\delta}g^{b}_{\delta\varepsilon}g^{c}_{\varepsilon\gamma}\frac{1}{(p^{2}-m_{q}^{2})^{6}}(\rlap / p+m_{q } ) [ \rlap / p(p^{2}-3m_{q}^{2})+2m_{q}(2p^{2}-m_{q}^{2})](\rlap / p+m_{q}).\nonumber\end{aligned}\ ] ] the light - quark part of the correlation function can be calculated in the coordinate space , with the light - quark propagator @xmath52 which is then fourier - transformed to the momentum space in @xmath53 dimension . the resulting light - quark part is combined with the heavy - quark part before it is dimensionally regularized at @xmath54 . equating the two sides for @xmath55 and assuming quark - hadron duality yield the sum rules , from which masses of hadrons can be determined . after making a borel transform and transferring the continuum contribution to the ope side , the sum rules can be written as @xmath56 @xmath57 where @xmath58 indicates the borel parameter . to eliminate the hadron coupling constant @xmath59 and extract the resonance mass @xmath45 , one can take the derivative of eq . ( [ sumrule1 ] ) with respect to @xmath60 , divide the result by itself and deal with eq . ( [ sumrule2 ] ) in the same way to get @xmath61 @xmath62 where @xmath63 as a matter of fact , many terms of @xmath64 are approximate to zero because they are proportional to light quarks masses in the calculations . thereby , we merely present the spectral densities resulted from @xmath65 here . concretely , they can be written as @xmath66,\nonumber\\ \rho_{2}^{\langle\bar{q}q\rangle^{3}}(s)&=&\frac{m_{q}\langle\bar{q}q\rangle^{3}}{3\cdot2^{4}\pi^{2}}\int_{\lambda}^{1}d\alpha(1-\alpha),\nonumber\\ \rho_{2}^{\langle\bar{q}q\rangle\langle g\bar{q}\sigma\cdot g q\rangle}(s)&=&-\frac{\langle\bar{q}q\rangle\langle g\bar{q}\sigma\cdot g q\rangle}{2^{8}\pi^{4}}s\int_{\lambda}^{1}d\alpha(1-\alpha)^{2},\nonumber\\ \rho_{2}^{\langle g\bar{q}\sigma\cdot g q\rangle\langle g\bar{q}\sigma\cdot g q\rangle}(s)&=&\frac{\langle g\bar{q}\sigma\cdot g q\rangle^{2}}{2^{10}\pi^{4}}\int_{\lambda}^{1}d\alpha(1-\alpha),\nonumber\\ \rho_{2}^{\langle\bar{q}q\rangle\langle g^{2}g^{2}\rangle}(s)&=&\frac{m_{q}\langle\bar{q}q\rangle\langle g^{2}g^{2}\rangle}{3^{2}\cdot2^{13}\pi^{6}}\int_{\lambda}^{1}d\alpha\frac{(1-\alpha)^{2}}{\alpha^{3}}[6\alpha^{2}(\alpha s - m_{q}^{2})+(1-\alpha)^{2}(3\alpha s-4m_{q}^{2})],\nonumber\\ \rho_{2}^{\langle\bar{q}q\rangle\langle g^{3}g^{3}\rangle}(s)&=&-\frac{m_{q}\langle\bar{q}q\rangle\langle g^{3}g^{3}\rangle}{3\cdot2^{14}\pi^{6}}\int_{\lambda}^{1}d\alpha\frac{(1-\alpha)^{4}}{\alpha^{3}},\nonumber\\ \rho_{2}^{\langle g^{2}g^{2}\rangle\langle g\bar{q}\sigma\cdot g q\rangle}(s)&=&-\frac{m_{q}\langle g^{2}g^{2}\rangle\langle g\bar{q}\sigma\cdot g q\rangle}{3\cdot2^{13}\pi^{6}}\int_{\lambda}^{1}d\alpha\frac{(1-\alpha)^{3}}{\alpha^{2}},\nonumber\end{aligned}\ ] ] and @xmath67e^{-m_{q}^{2}/(\alpha m^{2})}\nonumber\\ & & + \frac{m_{q}^{3}\langle g^{2}g^{2}\rangle\langle g\bar{q}\sigma\cdot g q\rangle}{3^{2}\cdot2^{13}\pi^{6}}\int_{0}^{1}d\alpha\frac{(1-\alpha)^{3}}{\alpha^{3}}e^{-m_{q}^{2}/(\alpha m^{2})}\nonumber\\ & & + \frac{m_{q}\langle g\bar{q}\sigma\cdot g q\rangle\langle g^{3}g^{3}\rangle}{3^{2}\cdot2^{14}\pi^{6}}\int_{0}^{1}d\alpha\frac{(1-\alpha)^{3}}{\alpha^{2}}\bigg(\frac{3}{\alpha}-\frac{m_{q}^{2}}{\alpha^{2}m^{2}}\bigg)e^{-m_{q}^{2}/(\alpha m^{2})}\end{aligned}\ ] ] for @xmath1 or @xmath4 state . the lower limit of integration is given by @xmath68 . in this section , the sum rule ( [ sum rule q ] ) is numerically analyzed . the input values are taken as @xmath69 , @xmath70 , @xmath71 , @xmath72 , @xmath73 , @xmath74 , and @xmath75 @xcite .    in order to ensure the quality of qcd sum rule analysis , it is known that one can analyze the ope convergence and the pole contribution dominance to determine the conventional borel window for @xmath58 in the standard qcd sum rule approach : on the one hand , the lower constraint for @xmath76 is obtained by considering that the perturbative contribution should be larger than each condensate contribution to have a good convergence in the ope side ; on the other hand , the upper bound for @xmath76 is obtained by the consideration that the pole contribution should be larger than the continuum state contributions . meanwhile , the threshold @xmath77 is not arbitrary but characterizes the beginning of continuum states . therefore , one naturally expects to find conventional borel windows for studied states to make qcd sum rules work commendably . however , things go contrary to one s wishes in some cases and it may be difficult to find a conventional work window rigidly satisfying both of two rules , which has been discussed in some works ( e.g. refs . @xcite ) . referring to the present work , there also arises some similar problem . concretely , some condensates are very large and play an important role in the ope side , which makes the standard ope convergence ( i.e. the perturbative at least larger than each condensate contribution ) happen only at very large values of @xmath58 . the consequence is that it is difficult to find a conventional borel window where both the ope converges well ( the perturbative at least larger than each condensate contribution ) and the pole dominates over the continuum .    to obtain some useful hadronic information from qcd sum rules , one could try releasing the rigid convergence criterion of the perturbative contribution larger than each condensate contribution in some case . the comparison between pole and continuum contributions from sum rule ( [ sumrule2 ] ) for @xmath1 state for @xmath78 is shown in the left panel of fig . 1 , and its ope convergence by comparing the perturbative with other condensate contributions is shown in the right panel . not too bad for the present plight , there are four main condensates ( i.e. @xmath79 , @xmath80 , @xmath81 , and @xmath82 ) and they could cancel out each other to some extent since they have different signs . besides , most of other condensates calculated are very small and almost negligible . thus , one could try releasing the rigid ope convergence criterion ( i.e. the perturbative larger than each condensate contribution ) and restrict the ratio of the perturbative to the  total ope contribution " ( the sum of the perturbative and other condensates calculated ) at least larger than one half , for example @xmath83 or more . in other words , here we consider the perturbative dominating over the sum of condensates instead of the perturbative larger than each condensate . furthermore , it is also very important that we have examined that condensates higher than dimension @xmath2 are quite small and the ratio of the perturbative to the  total ope contribution " does not change much even adding them ( in the total ope contribution ) , which means that condensates higher than dimension @xmath2 could not radically influence the character of ope convergence here . all the above factors bring that the ratio of the perturbative to the  total ope contribution " can be bigger than @xmath83 at relatively low values of @xmath76 in this work . by way of parenthesis , one could also visually see that there exist very stable plateaus from the borel curves for the @xmath1 state shown in fig . = 5.8truecm=5.8truecm    = 5.8truecm    = 5.8truecm    all in all , to test the ope convergence , we have considered the ratio of the perturbative to the  total ope contribution " instead of the ratio of the perturbative to each condensate contribution . this treatment is not freewheeling but has some definite constraints ( i.e. there are merely few important condensates and they could cancel out each other to some extent ; other condensates are almost negligible ) . in this sense , one could expect that the ope convergence is still under control . we must truthfully admit that it is not a so good ope convergence as the conventional case , but then one could find a comparatively reasonable work window and extract the hadronic information from qcd sum rules reliably . thus , we choose some transition range @xmath84 as a compromise borel window and take the continuum thresholds as @xmath85 , and arrive at @xmath86 for @xmath1 state . considering the uncertainty rooting in the variation of quark masses and condensates , we gain @xmath87 ( the first error reflects the uncertainty due to variation of @xmath77 and @xmath76 , and the second error resulted from the variation of qcd parameters ) or @xmath3 for @xmath1 state .    on account of the difficulty encountered in finding a conventional borel window , one may suppose the nonexistence of @xmath88 molecule itself . as one possibility , the assumption of its nonexistence indeed should be drawn attention . however , in the present work , we are inclined to make a premise that the @xmath88 molecular state could exist and then study whether it could act as one potential explanation of @xmath0 in view of two mian points : i ) the possibility for the existence of @xmath1 molecule and the molecular interpretation of @xmath0 are not entirely fabricated without any grounds . by an effective lagrangian calculation @xcite , _ found that @xmath29 and nucleon can form a loosely bound state with the small binding energy , and @xmath0 can be well explained as the @xmath1 molecular hadron , which is supported by both the analysis of the mass spectrum and the study of its dominant decay channel . moreover , the observed @xmath89 can also be reasonably described . ii ) we believe the present result from qcd sum rules could provide another support to the @xmath1 explanation to @xmath0 . certainly , we must confess to a weakness that it is difficult to find the conventional borel window in the present case . just as we have stated above , one could try releasing the rigid ope convergence criterion and eventually find the ope convergence is still under control in the present case . although it is not a so good ope convergence as the conventional case , one could find a comparatively reasonable work window and safely extract the hadronic information from qcd sum rules .    there comes forth the same problem for @xmath4 as the above case for @xmath1 , and we treat it similarly . the mass of @xmath4 state as a function of @xmath76 from sum rule ( [ sum rule q ] ) is shown in fig . 3 . graphically , one can see there have very stable plateaus for borel curves . we choose a compromise borel window @xmath90 and take @xmath91 for @xmath4 state . in the work windows , we obtain @xmath92 for @xmath4 state . varying input values of quark masses and condensates , we attain @xmath93 ( the first error reflects the uncertainty due to variation of @xmath77 and @xmath76 , and the second error resulted from the variation of qcd parameters ) or @xmath5 for @xmath4 state . assuming the newly observed structure @xmath0 by babar collaboration as a @xmath1 molecular state , we calculate its mass value in the framework of qcd sum rules . technically , contributions of operators up to dimension @xmath2 are included in the ope . we find that it is difficult to find the conventional ope convergence in this work . via trying releasing the rigid ope convergence criterion , one could find that the ope convergence is still under control in the present work and the final numerical result for @xmath1 state is @xmath3 , which coincides with the experimental value @xmath9 . in view of that the conventional ope convergence is not obtained here , thus only weak conclusions can be drawn regarding the explanation of @xmath0 in terms of a @xmath1 molecular state . meanwhile , one should note that the @xmath88 molecular state is just one possible theoretical interpretation of @xmath0 and there may have some other different explanations for its configuration . one could expect that contributions from both future experimental observations and theoretical analysis will further reveal the nature structure of @xmath0 . additionally , we have also studied the bottom counterpart @xmath4 state and predicted its mass to be @xmath5 . by analogy with @xmath1 state , this bottom counterpart state could be searched in the @xmath94 invariant mass spectrum in future experiments . k.  p.  khemchandani , a.  martnez  torres , and e.  oset , eur . j. a * 37 * , 233 ( 2008 ) ; 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we present a qcd sum rule analysis for the newly observed resonance @xmath0 by assuming it as a @xmath1 molecular state . 
 technically , contributions of operators up to dimension @xmath2 are included in the operator product expansion ( ope ) . 
 we find that it is difficult to find the conventional ope convergence in this work . by trying releasing the rigid ope convergence criterion 
 , one could find that the ope convergence is still under control in the present work and the numerical result for @xmath1 state is @xmath3 , which is in agreement with the experimental data of @xmath0 . in view of 
 that the conventional ope convergence is not obtained here , thus only weak conclusions can be drawn regarding the explanation of @xmath0 in terms of a @xmath1 molecular state . as a byproduct , the mass for the bottom counterpart @xmath4 state is predicted to be @xmath5 .