Spin alignment of vector mesons in high energy $pp$ collisions

The spin alignment of vector mesons produced in high energy reactions is determined by the spin-dependent fragmentation function $D_{1LL}(z,{\mu }_f)$ that is shown to be independent of the polarization of the fragmenting quark. In this paper, we extract the spin-dependent fragmentation function $D_{1LL}(z,{\mu }_f)$ from data on the spin alignment of $K^{*0}$ in $e^{+}{e}^{-}$ annihilation at the large electron-position collider (LEP) in two different scenarios and apply them to make predictions in $pp$ collisions. We make detailed analysis of contributions from different subprocesses and show that the spin alignment should be quite significant also in high energy $pp$ collisions.

Figure 1

The ${\chi }^2$ plot in scenario I with AKK08 and DHESS parametrizations. Here, as well as in all figures in the following of this paper, $K^{*0}$ denotes the sum of $K^{*0}$ and ${\overline{K}}^{*0}$.

Figure 2

The spin alignments of $K^{*0}$ and ${\rho }^0$ in $e^{+}{e}^{-}\to VX$ at the $Z$-pole calculated in scenario I with AKK08 and DHESS unpolarized FFs compared with experimental data [1, 2]. In the calculations, we have chosen the center-of-mass energy of $e^{+}{e}^{-}$ as the factorization scale.

Figure 3

The ratio of the spin-dependent fragmentation function $D_{1LL}(z,{\mu }_f)$ to that of the corresponding spin-averaged $D_1(z,{\mu }_f)$ at different scales in scenario I with AKK08 FFs.

Figure 4

The spin-dependent fragmentation function $D_{1LL}(z,{\mu }_f)$ at different scales in scenario I with AKK08 FFs.

Figure 5

The ${\chi }^2$ plot in scenario II with AKK08 and DHESS parametrizations.

Figure 6

The spin alignment of $K^{*0}$ (left panel) and that of ${\rho }^0$ (right panel) in $e^{+}{e}^{-}\to VX$ at the $Z$-pole calculated in scenario II with AKK08 and DHESS FFs compared with experimental data [1, 2].

Figure 7

The ratio of the spin-dependent fragmentation function $D_{1LL}(z,{\mu }_f)$ to that of the corresponding spin-averaged $D_1(z,{\mu }_f)$ at different scales in scenario II with AKK08 FFs.

Figure 8

The spin-dependent fragmentation function $D_{1LL}(z,{\mu }_f)$ at different scales in scenario II with AKK08 FFs.

Figure 9

Fractional contributions $R_c^{\text{jet}}(y,p_T)$ to jet production from different flavors of quarks/antiquarks and gluon at $|y|<0.5$ as functions of $p_T$ in $pp$ collisions at RHIC energy $\sqrt{s}=200\mathrm{GeV}$ (left) and LHC energy $\sqrt{s}=5.02\mathrm{TeV}$ (right).

Figure 10

Fractional contributions $R_c^{\mathrm{V}}(y,p_T)$ to the production of $K^{*0}$ from different flavors of quarks/antiquarks and gluon at $|y|<0.5$ as functions of $p_T$ in $pp$ collisions at RHIC energy $\sqrt{s}=200\mathrm{GeV}$ (left) and LHC energy $\sqrt{s}=5.02\mathrm{TeV}$ (right) obtained with AKK08 and DHESS FFs, respectively.

Figure 11

Fractional contributions $R_c^{\text{jet}}(y,p_T)$ to jet production from different flavors of quarks/antiquarks and gluon as functions of $x_F$ in $pp$ collisions at RHIC energy $\sqrt{s}=200\mathrm{GeV}$ with $p_T\ge 5\mathrm{GeV}$ (left) and LHC energy $\sqrt{s}=5.02\mathrm{TeV}$ $p_T\ge 10\mathrm{GeV}$ (right).

Figure 12

Fractional contributions $R_c^{\mathrm{V}}(y,p_T)$ to the production of $K^{*0}$ from different flavors of quarks/antiquarks and gluon as functions of $x_F$ in $pp$ collisions at RHIC energy $\sqrt{s}=200\mathrm{GeV}$ with $p_T\ge 5\mathrm{GeV}$ (left) and LHC energy $\sqrt{s}=5.02\mathrm{TeV}$ with $p_T\ge 10\mathrm{GeV}$ (right) obtained with AKK08 and DHESS FFs, respectively.

Figure 13

Spin alignments of vector mesons in $pp$ collisions at RHIC energy $\sqrt{s}=200\mathrm{GeV}$ for $K^{*0}$ and ${\rho }^0$ in two rapidity regions as functions of $p_T$.

Figure 14

Spin alignments of vector mesons in $pp$ collisions at the LHC energy $\sqrt{s}=5.02\mathrm{TeV}$ for $K^{*0}$ and ${\rho }^0$ in two rapidity regions as functions of $p_T$.

Figure 15

Spin alignments of vector mesons in $pp$ collisions at the RHIC energy $\sqrt{s}=200\mathrm{GeV}$ for $K^{*0}$ and ${\rho }^0$ at $p_T>5\mathrm{GeV}$ as functions of $x_F$.

Figure 16

Spin alignments of vector mesons in $pp$ collisions at the LHC energy $\sqrt{s}=5.02\mathrm{TeV}$ for $K^{*0}$ and ${\rho }^0$ at $p_T>10\mathrm{GeV}$ as functions of $x_F$.