Next-to-leading-order time-like rho electromagnetic form factors in $${k_{\textrm{T}}}$$ factorization

Abstract We calculate the time-like $$\rho $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ρ</mml:mi> </mml:math> electromagnetic (EM) form factor in the $$k_T$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>T</mml:mi> </mml:msub> </mml:math> factorization formalism by including the next-to-leading-order (NLO) corrections of the leading-twist and sub-leading twist contributions. It’s observed that the NLO correction to the magnitude of the LO leading-twist form factor is lower than $$30\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>30</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> at large invariant mass squared $$Q^2 &gt; 30 \,\text {GeV}^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>Q</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>&gt;</mml:mo> <mml:mn>30</mml:mn> <mml:mspace/> <mml:msup> <mml:mtext>GeV</mml:mtext> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> . It is found that the $$\rho $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ρ</mml:mi> </mml:math> meson EM form factor is dominated by twist-3 contribution instead of by twist-2 one because of the end-point enhancement. The theoretical predictions of the moduli of three helicity amplitudes and total cross section are analyzed at $$\sqrt{s}=10.58$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> <mml:mo>=</mml:mo> <mml:mn>10.58</mml:mn> </mml:mrow> </mml:math> GeV, which are consistent with measurements from BABAR Collaboration.