摘要
In this article, we assume that there exist the pseudoscalar D■_(s0)~*(2317) and D*■_(s1)~*(2460) molecular states Z1,2 and construct the color singlet-singlet molecule-type interpolating currents to study their masses with the QCD sum rules. In calculations, we consider the contributions of the vacuum condensates up to dimension-10 and use the formulaμ =(M_(X/Y/Z)~2 -(2 Mc)~2)~(1/2) to determine the energy scales of the QCD spectral densities. The numerical results, M_(Z1)=4.61_(-0.08)~(+0.11) GeV and MZ2= 4.60_(-0.06)~(+0.07) GeV, which lie above the D■_(s0)~*(2317) and D*■_(s1)~*(2460) thresholds respectively,indicate that the D■_(s0)~*(2317) and D*■_(s1)~*(2460) are difficult to form bound state molecular states, the Z1,2 are probably resonance states.
In this article, we assume that there exist the pseudoscalar D■_(s0)~*(2317) and D*■_(s1)~*(2460) molecular states Z1,2 and construct the color singlet-singlet molecule-type interpolating currents to study their masses with the QCD sum rules. In calculations, we consider the contributions of the vacuum condensates up to dimension-10 and use the formulaμ =(M_(X/Y/Z)~2 -(2 Mc)~2)~(1/2) to determine the energy scales of the QCD spectral densities. The numerical results, M_(Z1)=4.61_(-0.08)~(+0.11) GeV and MZ2= 4.60_(-0.06)~(+0.07) GeV, which lie above the D■_(s0)~*(2317) and D*■_(s1)~*(2460) thresholds respectively,indicate that the D■_(s0)~*(2317) and D*■_(s1)~*(2460) are difficult to form bound state molecular states, the Z1,2 are probably resonance states.
引文
[1]M.Gell-Mann,Phys.Lett.8(1964)214.
[2]C.Patrignani,et al.,Chin.Phys.C 40(2016)100001.
[3]S.Godfrey and N.Isgur,Phys.Rev.D 32(1985)189.
[4]C.Y.Wong,Phys.Rev.C 69(2004)055202.
[5]C.Meng and K.T.Chao,arXiv:0708.4222[hep-ph];S.H.Lee,K.Morita,and M.Nielsen,Phys.Rev.D 78(2008)076001;S.H.Lee,M.Nielsen,and U.Wiedner,J.Korean Phy.Soc.55(2009)424;J.R.Zhang,Phys.Rev.D 87(2013)116004;J.He and D.Y.Chen,Eur.Phys.J.C 77(2017)398.
[6]L.Maiani,F.Piccinini,A.D.Polosa,and V.Riquer,Phys.Rev.D 71(2005)014028;R.D.Matheus,S.Narison,M.Nielsen,and J.M.Richard,Phys.Rev.D 75(2007)014005;L.Maiani,A.D.Polosa,and V.Riquer,arXiv:0708.3997[hep-ph];Z.G.Wang,Eur.Phys.J.C59(2009)675;J.R.Zhang and M.Q.Huang,Phys.Rev.D 83(2011)036005;Z.G.Wang,Commun.Theor.Phys.66(2016)33.
[7]L.Liu,G.Moir,et al.,J.High Energy Phys.1207(2012)126;C.A.Meyer and E.S.Swanson,Prog.Part.Nucl.Phys.82(2015)21.
[8]N.A.T¨ornqvist,Z.Phys.C 68(1995)647;D.V.Bugg,J.Phys.G 35(2008)075005;D.V.Bugg,Eur.phys.Lett.96(2011)11002.
[9]M.B.Voloshin and L.B.Okun,JETP Lett.23(1976)333;A.De Rujula,H.Georgi,and S.L.Glashow,Phys.Rev.Lett.38(1977)317.
[10]S.K.Choi,et al.,Phys.Rev.Lett.91(2003)262001.
[11]E.S.Swanson,Phys.Lett.B 588(2004)189;M.Suzuki,Phys.Rev.D 72(2005)114013;M.T.AlFiky,F.Gabbiani,and A.A.Petrov,Phys.Lett.B 640(2006)238;S.Fleming,M.Kusunoki,T.Mehen,and U.van Kolck,Phys.Rev.D 76(2007)034006;E.Braaten,M.Lu,and J.Lee,Phys.Rev.D 76(2007)054010;C.Hanhart,Y.S.Kalashnikova,A.E.Kudryavtsev,and A.V.Nefediev,Phys.Rev.D 76(2007)034007;M.B.Voloshin,Phys.Rev.D 76(2007)014007;P.Colangelo,F.De Fazio,and S.Nicotri,Phys.Lett.B 650(2007)166.
[12]M.Ablikim,et al.,Phys.Rev.Lett.110(2013)252001.
[13]Z.G.Wang and T.Huang,Eur.Phys.J.C 74(2014)2891;Z.G.Wang,Eur.Phys.J.C 74(2014)2963.
[14]Q.Wang,C.Hanhart,and Q.Zhao,Phys.Rev.Lett.111(2013)132003;F.Aceti,M.Bayar,et al.,Phys.Rev.D90(2014)016003.
[15]A.Bondar,et al.,Phys.Rev.Lett.108(2012)122001.
[16]J.R.Zhang,M.Zhong,and M.Q.Huang,Phys.Lett.B704(2011)312.
[17]L.S.Geng,J.X.Lu,M.P.Valderrama,and X.L.Ren,Phys.Rev.D 97(2018)091501.
[18]Z.G.Wang and T.Huang,Eur.Phys.J.C 76(2016)43;Z.G.Wang,Eur.Phys.J.C 76(2016)387;Z.G.Wang and J.X.Zhang,Eur.Phys.J.C 78(2018)503;Z.G.Wang,arXiv:1806.10384[hep-ph].
[19]L.J.Reinders,H.Rubinstein,and S.Yazaki,Phys.Rept.127(1985)1.
[20]Z.G.Wang and T.Huang,Phys.Rev.D 89(2014)054019.
[21]M.A.Shifman,A.I.Vainshtein,and V.I.Zakharov,Nucl.Phys.B 147(1979)385;Nucl.Phys.B 147(1979)448.
[22]P.Colangelo and A.Khodjamirian,At the Frontier of Particle Physics:Handbook of QCD,Vol.3,ed.M.Shifman,World Scientific,Singapore(2001)p.1495.
[23]Z.G.Wang,Chin.Phys.C 41(2017)083103.
[24]Z.G.Wang,Eur.Phys.J.C 74(2014)2874;Z.G.Wang and T.Huang,Nucl.Phys.A 930(2014)63;Z.G.Wang,Commun.Theor.Phys.63(2015)466;Z.G.Wang and Y.F.Tian,Int.J.Mod.Phys.A 30(2015)1550004.
[25]L.Maiani,F.Piccinini,A.D.Polosa,and V.Riquer,Phys.Rev.D 89(2014)114010;M.Nielsen and F.S.Navarra,Mod.Phys.Lett.A 29(2014)1430005;Z.G.Wang,Commun.Theor.Phys.63(2015)325;S.S.Agaev,K.Azizi,and H.Sundu,Phys.Rev.D 96(2017)034026.
[26]Z.G.Wang,Eur.Phys.J.C 77(2017)78.
[27]S.Godfrey and K.Moats,Phys.Rev.D 93(2016)034035.
[28]X.Liu,Z.G.Luo,and S.L.Zhu,Phys.Lett.B 699(2011)341.
[29]M.S.Sanchez,L.S.Geng,J.X.Lu,et al.,Phys.Rev.D98(2018)054001.
[30]Z.G.Wang,Eur.Phys.J.C 75(2015)427.