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Does the T = 1 State Exist in the c cbar Meson?

Does the T = 1 State Exist in the c cbar Meson?. Hiroshi Noya Institute of Physics, Hosei University at Tama Machida, Tokyo 194-0298, Japan e-mail : hiroshinoya@yahoo.com and Hiroshi Nakamura Department of Physics and Mathematics College of Science and Engineering Aoyamagakuin University

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Does the T = 1 State Exist in the c cbar Meson?

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  1. Does the T = 1 State Exist in the c cbar Meson? Hiroshi Noya Institute of Physics, Hosei University at Tama Machida, Tokyo 194-0298, Japan e-mail : hiroshinoya@yahoo.com and Hiroshi Nakamura Department of Physics and Mathematics College of Science and Engineering Aoyamagakuin University Fuchinobe, Sagamihara Kanagawa 229-8558, Japan

  2. The mass formula for the Diquark Cluster Model is based on the harmonic oscillator shell model. The mass formula is the following. M = m n T + M(1p1/2)n(1p1/2) + M(1p3/2)n(1p3/2) + M(1d3/2)n(1d3/2) + M(2s1/2)n(2s1/2) + Δ0(nΦ0 + nΦ0) + Δ1(nΦ1 + nΦ1) + Σ ΔTS . The total quark number is n T = k + h where k is a number of quark and h is a number of antiquark

  3. The unit are MeV. * Lambdac

  4. The Unit are Mev.

  5. The u or d quark - quark interaction in the s state diquark cluster is for the spin 0 is Δ0= a - 3/4b, and for the spin 1 is Δ1= a + 1/4b, and a = 186 MeV, b = 195 MeV. The case of s and u or d quark, the s state interaction parameter a is the same but b is bs = (m/ms) b. The c quark mass mc =1646 MeV and the parameter ac= 38.2 MeV is obtained by Λc and X(3845) mass and the acs = -34.7 MeV is obtained by X(4140). The n - c quark – quark interaction case, b is bc = (m/mc) b and the s - c quark – quark interaction case, b is bcs = (m2/mc ms) b.

  6. The quark - quark interaction parameters for the p state in the diquark cluster are Δ00 = Δ11 =Δ01 = 0, Δ10 = - 60 MeV for u or d quark. And Δs 1/2 0 = -19 MeV, Δs 1/2 1 = 0 in the p state diquark cluster if s quark includes one . And Δc 1/2 0 = - 5.5 MeV, Δc 1/2 1 = 0 in the p state diquark cluster if c quark includes one . The first suffix of Δ t s presents an isospin or flavor and second one is a spin, respectively. No any free parameters remain in this calculation for u, d , s and c quarks.

  7. Concluding Remarks. The mass, the spin and the parity calculations, X series of c cbar meson are the four quark states except for X(3872). 2. X(4050), X(4250) and X(4430) states have isospin 1 state in our calculation, if the isospin 1 is observed, these states are sure four quark states. 3. Not only of X(4140) and X(4350) but also several c s cbar sbar mesons will be exist from our calculated results. We are very much interested in future experimental results . Thank you !

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