You are an expert at summarizing long articles. Proceed to summarize the following text: 
the experimental verification of many scalar - isoscalar resonances , @xmath6 , up to the energy of @xmath7 gev @xcite reenforced the idea that the scalar glueball lies among them . however , the remaining open question is which of these scalars - isoscalars is predominantly the glueball.in this paper we address this issue by studying the vacuum phenomenology of scalar - isoscalar states within the framework of the so called extended linear sigma model ( elsm ) @xcite . our numerical calculations of the effective lagrangian ( [ lagrangian ] ) are explicitly done in the case of three quark flavours . for @xmath8 two scalar - isoscalar @xmath5 states exist , the nonstrange @xmath9 and the strange @xmath10 mesons . the scalar glueball @xmath11 is implemented in the elsm from the very beginning as the fluctuation of the dilaton field . we describe @xmath12 as well as the generation of the scale anomaly of the pure yang - mills lagrangian at the quantum level by the usual logarithmic dilaton lagrangian , first introduced in ref . @xcite . due to the same quantum numbers a mixing between the scalar - isoscalar quarkonia and glueball in our model takes place.in this study we focus on the determination of the mixing matrix by using the mass eigenvalues of the scalar - isoscalar states and identify them with the physical masses of the resonances @xmath3 , @xmath4 and @xmath2 @xcite.the outline of this proceeding is as follows : in sec . 2 we present the lagrangian of the extended linear sigma model with a scalar glueball . in sec . 3 we discuss our results and finally in sec . 4 we give a summary as well as an outlook for further research . in order to study the vacuum phenomenology of the scalar - isoscalar resonances @xmath13 and @xmath2 we use the elsm including a scalar glueball @xcite . its compact representation for an optional number of flavours is as follows :    @xmath14\nonumber\\ & -\lambda_{1}(\text{\textrm{tr}}% [ \phi^{\dag}\phi])^{2}+c_{1}(\text{\textrm{det}}\phi^{\dag}-\text{\textrm{det } } \phi)^{2}+\mathrm{tr}[h(\phi^{\dag}+\phi)]\nonumber\\ &   + \text{\textrm{tr}}\left [   \left (   \frac{m_{1}^{2}}{2}\left (   \frac { g}{g_{0}}\right )   ^{2}+\delta\right )   \left(l^{\mu2}+r^{\mu2}\right )   \right ] \nonumber\\ & -\frac{1}{4}\text{\textrm{tr}}\left [ l^{\mu\nu2}+r^{\mu\nu2}\right ]   + \frac{h_{1}}{2}\text{\textrm{tr}% } [ \phi^{\dag}\phi]\text{\textrm{tr}}[l_{\mu}l^{\mu}+r_{\mu}r^{\mu}]\nonumber\\ &   + h_{2}\text{\textrm{tr}}[\phi^{\dag}l_{\mu}l^{\mu}\phi+\phi r_{\mu}r^{\mu } \phi^{\dag}]+2h_{3}\text{\textrm{tr}}[\phi r_{\mu}\phi^{\dag}l^{\mu}]\text { + ... , } \label{lagrangian}\end{aligned}\ ] ]    where @xmath15 and @xmath16the dilaton lagrangian ( [ ldil ] ) describes the scale anomaly of the pure yang - mills sector where the logarithmic term with the energy scale @xmath17 breaks the dilatation symmetry explicitly . the field @xmath12 is the scalar dilaton and after performing the shift @xmath18 a particle with the mass @xmath19 arises which we interpret as the scalar glueball.our model underlies the following symmetries and their several breakings : i ) the global chiral symmetry , @xmath20 , which is broken explicitly due to the quantum effects and the nonvanishing quark masses as well as spontaneously . as a consequence of breaking of the latter one a nonvanishing quark condensate , @xmath21 , arises . ii ) a crucial symmetry in our model is the already mentioned dilatation symmetry or scale invariance , @xmath22 , which is realized at the classical level of the yang - mills sector of qcd , but explicitly broken by the loop corrections . this is known as scale or trace anomaly , respectively and leads to the nonvanishing gluon condensate , @xmath23 . taking into account the dilatation symmetry we can constrain the number of possible terms in our model this implies that in the chiral limit with the exception of the logarithmic term in eq . ( [ ldil ] ) and the term generating the @xmath24 anomaly , all parameters entering in the model are dimensionless . ( note , using the chiral anomaly it was also possible to couple the pseudoscalar glueball to the model , for details and results see refs.@xcite).iii ) our model is also in agreement with discrete symmetries of qcd e.g. parity @xmath25 and charge conjugation @xmath26.the multiplet of the ordinary scalar and pseudoscalar mesons in the case of @xmath8 , containing the two out of three bare scalar - isoscalar states @xmath27 and @xmath28 , reads @xcite :    @xmath29{ccc}% \frac{(\sigma_{n}+a_{0}^{0})+i(\eta_{n}+\pi^{0})}{\sqrt{2 } } & a_{0}^{+}% + i\pi^{+ } & k_{0}^{\star+}+ik^{+}\\ a_{0}^{-}+i\pi^{- } & \frac{(\sigma_{n}-a_{0}^{0})+i(\eta_{n}-\pi^{0})}% { \sqrt{2 } } & k_{0}^{\star0}+ik^{0}\\ k_{0}^{\star-}+ik^{- } & \bar{k}_{0}^{\star0}+i\bar{k}^{0 } & \sigma_{s}+i\eta_{s}% \end{array } \right ) . \label{phimatex}%\ ] ]    the explicit form of the left - handed and the right - handed ( axial)vector mesons multiplets , @xmath30 and @xmath31 can be found in ref . @xcite . a reasonable approach to study the scalar - isoscalar sector of the elsm with a scalar glueball is to use the values of the global fit performed in ref . @xcite and only to determine the additional three free parameters which enter in this sector . two of them arise directly from the dilaton lagrangian ( [ ldil ] ) , namely the bare mass of the scalar glueball @xmath32 and the energy scale @xmath17 . the third one is @xmath33 which couples the ordinary ( pseudo)scalar mesons and was in ref . @xcite only determined as a part of combination.in order to obtain the numerical values of the corresponding parameters we use the bare masses of the scalar - isoscalar states and the experimental masses of the resonances @xmath1 and @xmath2 . accordingly we consider the potential of the corresponding states in the matrix representation :    @xmath34{ccc}% m_{\sigma_{n}}^{2 } & z_{g\sigma_{n } } & z_{\sigma_{s}\sigma_{n}}\\ z_{g\sigma_{n } } & m_{g}^{2 } & z_{g\sigma_{s}}\\ z_{\sigma_{s}\sigma_{n } } & z_{g\sigma_{s } } & m_{\sigma_{s}}^{2}% \end{array } \right ) \left ( \begin{array } [ c]{c}% \sigma_{n}\\ g\\ \sigma_{s}% \end{array } \right)\label{pot}.%\ ] ]    the corresponding bare mass equations are :    @xmath35    @xmath36    @xmath37    after diagonalization of the bare mass matrix ( see eq . ( [ pot ] ) ) we obtain the matrix containing the physical masses of the scalar - isoscalar states , @xmath38 , where @xmath39 is the mixing matrix which transforms the bare states into the physical ones and vice versa :    @xmath40{c}% f_{0}(1370)\\ f_{0}(1710)\\ f_{0}(1500)% \end{array } \right)=b \left ( \begin{array } [ c]{c}% \sigma_{n}\equiv\left(\bar{u}u+\bar{d}d\right ) /\sqrt{2}\\ g\equiv gg\\ \sigma_{s}\equiv\bar{s}s\\ \end{array } \right )   \text { .}\label{trafo}%\ ] ]    the numerical values of the free parameters are presented in table [ table1 ] . they have been obtained by requiring that the three following masses of the scalar - isoscalar states @xcite hold : @xmath41 mev , @xmath42 mev and @xmath43 mev . [ c]|c|c|c|parameter & value + @xmath33 & @xmath44 + @xmath32 & @xmath45 [ mev ] + @xmath17 & @xmath46 [ mev ] +    the numerical solution of the mixing matrix reads :    @xmath47{ccc}% 0.92 & -0.39 & 0.05\\ -0.33 & -0.83 & -0.45\\ -0.22 & -0.40 & 0.89% \end{array } \right ) \text { .}\label{bnum}\ ] ]    it turns out that the resonances @xmath3 and @xmath4 are predominantly nonstrange and strange @xmath5 states , and that the resonance @xmath2 is predominantly a scalar glueball . for other results of the mixing matrix @xmath39 using different theoretical models , we refer to refs . @xcite and refs . therein . the solution in eq . [ bnum ] relies only on calculations of masses of the scalar - isoscalar states . in order to give final statements regarding the composition of the @xmath48 resonances evaluation of the corresponding decays is essential . nevertheless , it is astonishing that by increasing the number of flavours in our model , @xmath49 , the phenomenology of the @xmath48 resonances seems to change ( see ref . we have evaluated the numerical values of the mixing matrix @xmath39 by using the masses of the scalar - isoscalar states between @xmath50 and @xmath7 gev within a chiral model , the so called extended linear sigma model with a scalar glueball @xcite . we have found that the resonances @xmath3 and @xmath4 are predominantly nonstrange and strange @xmath5 states , and the resonance @xmath2 is predominantly a scalar glueball.study in progress are calculations of the decay processes appropriate to the solution presented in this work and further search for a solution with the assignment where @xmath4 is predominantly a glueball and @xmath2 predominantly a strange @xmath5 state @xcite . the author thanks f. giacosa , d. parganlija and d. h. rischke for cooperation and useful discussions and acknowledges support from h - qm and hgs - hire . s.  gallas , f.  giacosa and d.  h.  rischke , phys . d * 82 * , 014004 ( 2010 ) [ arxiv:0907.5084 [ hep - ph ] ] ; d.  parganlija , f.  giacosa and d.  h.  rischke , phys . d * 82 * , 054024 ( 2010 ) [ arxiv:1003.4934 [ hep - ph ] ] . c.  rosenzweig , a.  salomone and j.  schechter , phys . d * 24 * , 2545 ( 1981 ) ; a.  salomone , j.  schechter and t.  tudron , phys . d * 23 * , 1143 ( 1981 ) ; c.  rosenzweig , a.  salomone and j.  schechter , nucl . b * 206 * , 12 ( 1982 ) [ erratum - ibid . b * 207 * , 546 ( 1982 ) ] ; h.  gomm and j.  schechter , phys . b * 158 * , 449 ( 1985 ) ; r.  gomm , p.  jain , r.  johnson and j.  schechter , phys . d * 33 * , 801 ( 1986 ) .      c.  amsler and f.  e.  close , phys . d * 53*,295 ( 1996 ) [ arxiv : hep - ph/9507326 ] ; w.  j.  lee and d.  weingarten , phys .  rev . d * 61 * , 014015 ( 2000 ) [ arxiv : hep - lat/9910008 ] ; f.  e.  close and a.  kirk , eur . j.  c * 21 * , 531 ( 2001 ) [ arxiv : hep - ph/0103173 ] ; f.  giacosa , t.  gutsche , v.  e.  lyubovitskij and a.  faessler , phys . d * 72 * , 094006 ( 2005 ) [ arxiv : hep - ph/0509247 ] ; f.  giacosa , t.  gutsche and a.  faessler , phys . c * 71 * , 025202 ( 2005 ) [ arxiv : hep - ph/0408085 ] ; h.  y.  cheng , c.  k.  chua and k.  f.  liu , phys . d * 74 * , 094005 ( 2006 ) [ arxiv : hep - ph/0607206 ] ; v.  mathieu , n.  kochelev and v.  vento , int . j.  mod . e * 18 * , 1 ( 2009 ) [ arxiv:0810.4453 [ hep - ph ] ] . w.  i.  eshraim , s.  janowski , f.  giacosa and d.  h.  rischke , phys . d * 87 * , 054036 ( 2013 ) [ arxiv:1208.6474 [ hep - ph ] ] ; w.  i.  eshraim , s.  janowski , a.  peters , k.  neuschwander and f.  giacosa , acta phys . supp .   * 5 * , 1101 ( 2012 ) [ arxiv:1209.3976 [ hep - ph ] ] ; w.  i.  eshraim and s.  janowski , j.  phys . 426 * , 012018 ( 2013 ) [ arxiv:1211.7323 [ hep - ph ] ] ; w.  i.  eshraim and s.  janowski , arxiv:1301.3345 [ hep - ph ] .
using the @xmath0 extended linear sigma model with the ordinary ( pseudo)scalar and ( axial)vector mesons as well as a scalar glueball , we study the vacuum phenomenology of the scalar - isoscalar resonances @xmath1 and @xmath2 . 
 we present here a solution , based only on the masses and not yet on decays , in which the resonances @xmath3 and @xmath4 are predominantly nonstrange and strange @xmath5 states respectively , and the resonance @xmath2 is predominantly a scalar glueball .