Application of fragmentation function to the indirect production of fully charmed tetraquark

Abstract The indirect production mechanisms of fully charmed tetraquark are analyzed using the NRQCD factorization and Suzuki approach, respectively. The process first produces a heavy charm quark through Higgs, $$W^+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>W</mml:mi> <mml:mo>+</mml:mo> </mml:msup> </mml:math> , or $$Z^0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>Z</mml:mi> <mml:mn>0</mml:mn> </mml:msup> </mml:math> decay, and then the resulting charm quark evolves into an S -wave fully charmed tetraquark state with quantum number $$J^{PC}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>J</mml:mi> <mml:mrow> <mml:mi>PC</mml:mi> </mml:mrow> </mml:msup> </mml:math> , including $$0^{++}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>0</mml:mn> <mml:mrow> <mml:mo>+</mml:mo> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:math> , $$1^{+-}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>+</mml:mo> <mml:mo>-</mml:mo> </mml:mrow> </mml:msup> </mml:math> , and $$2^{++}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo>+</mml:mo> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:math> , via the fragmentation function. While the transverse momentum $$\langle \vec {q}_T^2\rangle $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>⟨</mml:mo> <mml:msubsup> <mml:mover> <mml:mi>q</mml:mi> <mml:mo>→</mml:mo> </mml:mover> <mml:mi>T</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>⟩</mml:mo> </mml:mrow> </mml:math> in Suzuki approach ranges from 2.01 to 299.04 $$\text {GeV}^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mtext>GeV</mml:mtext> <mml:mn>2</mml:mn> </mml:msup> </mml:math> , the numerical results obtained from these two approaches are consistent with each other. The decay widths, branching ratios, and produced events would be predicted at LHC and CEPC, respectively. The corresponding theoretical uncertainty of heavy quark mass $$m_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> and distribution of energy fraction are also presented. The results show that the contribution for the production of $$T_{4c}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mn>4</mml:mn> <mml:mi>c</mml:mi> </mml:mrow> </mml:msub> </mml:math> through $$W^+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>W</mml:mi> <mml:mo>+</mml:mo> </mml:msup> </mml:math> decay channel at LHC is relatively large. At CEPC, a sufficient number of $$T_{4c}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mn>4</mml:mn> <mml:mi>c</mml:mi> </mml:mrow> </mml:msub> </mml:math> events are produced through $$Z^0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>Z</mml:mi> <mml:mn>0</mml:mn> </mml:msup> </mml:math> decays, which is likely to be detected in future experiments.