论文标题
Quarkonia的Quark的平均速度及其功率$ v^n $
Average speed and its powers $v^n$ of a heavy quark in quarkonia
论文作者
论文摘要
夸克中沉重的夸克的典型速度是一个广泛使用的数量，在本文中，基于相对论的伯特 - 盐分方程方法，我们计算了平均值$ {\ overline {| \ boldSymbol {q} | $ s $ wave或$ p $ wave quarkonium休息框架中的重夸克，其中$ \ boldsymbol {q} $和$ \ boldsymbol {v} $是三维动量和速度，$ n = 1,2,3,4 $。对于$ j/ψ$中的符号夸克，我们获得了$ v_ {j/ψ} = 0.46 $，$ v^2_ {j/ψ} = 0.26 $，$ v^3_ {j/ψ} = 0.18 $ $ v_ {υ（1s）} = 0.24 $，$ v^2_ {υ（1s）} = 0.072 $，$ v^3_ {υ（1S）} = 0.025 $，和$ v^4_ {υ（1S）} = 0.010 $。值表明$ {v^n}> {v^{n_1}}} \ cdot {v^{n_2}} $，其中$ n_1+n_2 = n $，对于所有Charmonia和Botesonia都是正确的。我们的结果还表明，如果我们在炭系统中进行{速度}扩展，但对底部的{速度}扩展不良。基于$ v^n $值和以下获得的关系$ v^n_ {4s}> v^n_ {3S}> v^n_ {2s}> v^n_ {1s} $，$ v^n_ {4p}> v^n_ $ v^n_ {mp}> v^n_ {ms} $（$ n，m = 1,2,3,4 $），我们得出的结论是，高度兴奋的Quarkonia具有比相应低兴奋和基础状态的相对论更正更大的相对论校正，并且在Charmonium System中有较大的相对论校正。
The typical velocity of a heavy quark in a quarkonium is a widely used quantity, in this paper, based on the relativistic Bethe-Salpeter equation method, we calculate the average values ${\overline{|\boldsymbol{q}|^n}}$ and $ \overline{|\boldsymbol{v}|^n}\equiv v^n$ of a heavy quark in a $S$ wave or $P$ wave quarkonium rest frame, where $\boldsymbol{q}$ and $\boldsymbol{v}$ are the three dimensional momentum and velocity, $n=1,2,3,4$. For a charm quark in $J/ψ$, we obtained $v_{J/ψ}=0.46$, $v^2_{J/ψ}=0.26$, $v^3_{J/ψ}=0.18$, and $v^4_{J/ψ}=0.14$, for a bottom quark in $Υ(1S)$, $v_{Υ(1S)}=0.24$, $v^2_{Υ(1S)}=0.072$, $v^3_{Υ(1S)}=0.025$, and $v^4_{Υ(1S)}=0.010$. The values indicate that ${v^n} >{v^{n_1}}\cdot{v^{n_2}}$, where $n_1+n_2=n$, which is correct for all the charmonia and bottomonia. Our results also show the poor convergence if we make the {speed} expansion in charmonium system, but good for bottomonium. Based on the $v^n$ values and the following obtained relations $v^n_{4S} > v^n_{3S}> v^n_{2S}>v^n_{1S}$, $v^n_{4P} > v^n_{3P}> v^n_{2P}>v^n_{1P}$ and $v^n_{mP}>v^n_{mS}$ ($n,m=1,2,3,4$), we conclude that highly excited quarkonia have larger relativistic corrections than those of the corresponding low excited and ground states, and there are large relativistic corrections in charmonium system.
