Fragmentation functions for gluon into Bc or $$ {B}_c^{\ast } $$ meson
Xu-Chang Zheng, Chao-Hsi Chang, Xing-Gang Wu
Abstract
A bstract In the paper, we calculate the fragmentation functions for g → B c and g → $$ {B}_c^{\ast } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>B</mml:mi> <mml:mi>c</mml:mi> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> . The ultraviolet divergences in the calculation are removed through the renormalization of the operator definition of the fragmentation functions under the modified minimal subtrac- tion scheme. We then obtain the fragmentation functions $$ {D}_{g\to {B}_c} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>D</mml:mi> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>→</mml:mo> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:mrow> </mml:msub> </mml:math> ( z, μ F ) and $$ {D}_{g\to {B}_c^{\ast }} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>D</mml:mi> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>→</mml:mo> <mml:msubsup> <mml:mi>B</mml:mi> <mml:mi>c</mml:mi> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:mrow> </mml:msub> </mml:math> ( z, μ F ), which are presented as figures and fitting functions. The obtained fragmentation functions are complementary to the previous work on the next-to-leading order fragmentation functions for $$ \overline{b} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> → B c ( $$ {B}_c^{\ast } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>B</mml:mi> <mml:mi>c</mml:mi> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> ) and c → B c ( $$ {B}_c^{\ast } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>B</mml:mi> <mml:mi>c</mml:mi> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> ).