Leading-twist parton distribution amplitudes of S-wave heavy-quarkonia
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- 作者：Minghui Ding<sup>asup><sup> ; sup><sup>bsup> ; Fei Gao<sup>asup><sup> ; sup><sup>bsup> ; Lei Chang<sup>csup> ; Yu-Xin Liu<sup>asup><sup> ; sup><sup>bsup><sup> ; sup><sup>dsup><sup> ; sup><sup>yxliu@pku.edu.cn" class="auth_mail" title="E-mail the corresponding authorsup> ; Craig D. Roberts<sup>esup><sup> ; sup><sup>cdroberts@anl.gov" class="auth_mail" title="E-mail the corresponding authorsup>
- 关键词：Heavy quarkonia ; Hard exclusive processes ; Parton distribution amplitudes ; Dyson&ndash ; Schwinger equations ; Confinement ; Non-relativistic quantum chromodynamics
- 刊名：Physics Letters B
- 出版年：2016
- 出版时间：10 February 2016
- 年：2016
- 卷：753
- 期：Complete
- 页码：330-335
- 全文大小：440 K
文摘
The leading-twist parton distribution amplitudes (PDAs) of ground-state <span id="mmlsi1" class="mathmlsrc">source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315009351&_mathId=si1.gif&_user=111111111&_pii=S0370269315009351&_rdoc=1&_issn=03702693&md5=63b13cf3691fdf926548b56afb73e4b0">![]()
ss="imgLazyJSB inlineImage" height="15" width="22" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0370269315009351-si1.gif">script>![]()
style="vertical-align:bottom" width="22" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0370269315009351-si1.gif"> script><span class="mathContainer hidden"><span class="mathCode">span>span>span> and <span id="mmlsi2" class="mathmlsrc">source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315009351&_mathId=si2.gif&_user=111111111&_pii=S0370269315009351&_rdoc=1&_issn=03702693&md5=57c6131b4f9fde60977011b8cb83c041">![]()
ss="imgLazyJSB inlineImage" height="15" width="22" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0370269315009351-si2.gif">script>![]()
style="vertical-align:bottom" width="22" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0370269315009351-si2.gif"> script><span class="mathContainer hidden"><span class="mathCode">span>span>span><span id="mmlsi3" class="mathmlsrc">source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315009351&_mathId=si3.gif&_user=111111111&_pii=S0370269315009351&_rdoc=1&_issn=03702693&md5=f0671c8e930d0b3b894241497ac2921e">![]()
ss="imgLazyJSB inlineImage" height="11" width="15" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0370269315009351-si3.gif">script>![]()
style="vertical-align:bottom" width="15" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0370269315009351-si3.gif"> script><span class="mathContainer hidden"><span class="mathCode">span>span>span>- and <span id="mmlsi4" class="mathmlsrc">source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315009351&_mathId=si4.gif&_user=111111111&_pii=S0370269315009351&_rdoc=1&_issn=03702693&md5=0bd1cc37009bc8b19468e065496f2bdc">![]()
ss="imgLazyJSB inlineImage" height="14" width="16" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0370269315009351-si4.gif">script>![]()
style="vertical-align:bottom" width="16" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0370269315009351-si4.gif"> script><span class="mathContainer hidden"><span class="mathCode">span>span>span>-quarkonia are calculated using a symmetry-preserving continuum treatment of the meson bound-state problem which unifies the properties of these heavy-quark systems with those of light-quark bound-states, including QCD's Goldstone modes. Analysing the evolution of <span id="mmlsi1" class="mathmlsrc">source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315009351&_mathId=si1.gif&_user=111111111&_pii=S0370269315009351&_rdoc=1&_issn=03702693&md5=63b13cf3691fdf926548b56afb73e4b0">![]()
ss="imgLazyJSB inlineImage" height="15" width="22" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0370269315009351-si1.gif">script>![]()
style="vertical-align:bottom" width="22" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0370269315009351-si1.gif"> script><span class="mathContainer hidden"><span class="mathCode">span>span>span> and <span id="mmlsi2" class="mathmlsrc">source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315009351&_mathId=si2.gif&_user=111111111&_pii=S0370269315009351&_rdoc=1&_issn=03702693&md5=57c6131b4f9fde60977011b8cb83c041">![]()
ss="imgLazyJSB inlineImage" height="15" width="22" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0370269315009351-si2.gif">script>![]()
style="vertical-align:bottom" width="22" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0370269315009351-si2.gif"> script><span class="mathContainer hidden"><span class="mathCode">span>span>span> PDAs with current-quark mass, <span id="mmlsi5" class="mathmlsrc">source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315009351&_mathId=si5.gif&_user=111111111&_pii=S0370269315009351&_rdoc=1&_issn=03702693&md5=46520fff853c42fee0244ad5bc1178e2">![]()
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style="vertical-align:bottom" width="18" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0370269315009351-si5.gif"> script><span class="mathContainer hidden"><span class="mathCode">span>span>span>, increasing away from the chiral limit, it is found that in all cases there is a value of <span id="mmlsi5" class="mathmlsrc">source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315009351&_mathId=si5.gif&_user=111111111&_pii=S0370269315009351&_rdoc=1&_issn=03702693&md5=46520fff853c42fee0244ad5bc1178e2">![]()
ss="imgLazyJSB inlineImage" height="15" width="18" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0370269315009351-si5.gif">script>![]()
style="vertical-align:bottom" width="18" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0370269315009351-si5.gif"> script><span class="mathContainer hidden"><span class="mathCode">span>span>span> for which the PDA matches the asymptotic form appropriate to QCD's conformal limit and hence is insensitive to changes in renormalisation scale, ζ. This mass lies just above that associated with the s-quark. At current-quark masses associated with heavy-quarkonia, on the other hand, the PDAs are piecewise convex–concave–convex. They are much narrower than the asymptotic distribution on a large domain of ζ ; but nonetheless deviate noticeably from <span id="mmlsi6" class="mathmlsrc">source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315009351&_mathId=si6.gif&_user=111111111&_pii=S0370269315009351&_rdoc=1&_issn=03702693&md5=f11eef21103825ecf98227b8f4c31406">![]()
ss="imgLazyJSB inlineImage" height="17" width="127" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0370269315009351-si6.gif">script>![]()
style="vertical-align:bottom" width="127" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0370269315009351-si6.gif"> script><span class="mathContainer hidden"><span class="mathCode">span>span>span>, which is the result in the static-quark limit. There are also material differences between <span id="mmlsi1" class="mathmlsrc">source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315009351&_mathId=si1.gif&_user=111111111&_pii=S0370269315009351&_rdoc=1&_issn=03702693&md5=63b13cf3691fdf926548b56afb73e4b0">![]()
ss="imgLazyJSB inlineImage" height="15" width="22" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0370269315009351-si1.gif">script>![]()
style="vertical-align:bottom" width="22" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0370269315009351-si1.gif"> script><span class="mathContainer hidden"><span class="mathCode">span>span>span> and <span id="mmlsi2" class="mathmlsrc">source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315009351&_mathId=si2.gif&_user=111111111&_pii=S0370269315009351&_rdoc=1&_issn=03702693&md5=57c6131b4f9fde60977011b8cb83c041">![]()
ss="imgLazyJSB inlineImage" height="15" width="22" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0370269315009351-si2.gif">script>![]()
style="vertical-align:bottom" width="22" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0370269315009351-si2.gif"> script><span class="mathContainer hidden"><span class="mathCode">span>span>span> PDAs, and between the PDAs for different vector-meson polarisations, which vanish slowly with increasing ζ . An analysis of moments of the root-mean-square relative-velocity, <span id="mmlsi7" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315009351&_mathId=si7.gif&_user=111111111&_pii=S0370269315009351&_rdoc=1&_issn=03702693&md5=111dcad601dc315fa21cc69cf6a0e481" title="Click to view the MathML source">〈v<sup>2msup>〉span><span class="mathContainer hidden"><span class="mathCode">span>span>span>, in <span id="mmlsi1" class="mathmlsrc">source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315009351&_mathId=si1.gif&_user=111111111&_pii=S0370269315009351&_rdoc=1&_issn=03702693&md5=63b13cf3691fdf926548b56afb73e4b0">![]()
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ss="imgLazyJSB inlineImage" height="15" width="22" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0370269315009351-si2.gif">script>![]()
style="vertical-align:bottom" width="22" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0370269315009351-si2.gif"> script><span class="mathContainer hidden"><span class="mathCode">span>span>span> systems reveals that <span id="mmlsi118" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269315009351&_mathId=si118.gif&_user=111111111&_pii=S0370269315009351&_rdoc=1&_issn=03702693&md5=0ddd6ca29d3eae2185773a7ee561c4ef" title="Click to view the MathML source">〈v<sup>4sup>〉span><span class="mathContainer hidden"><span class="mathCode">span>span>span>-contributions may be needed in order to obtain a reliable estimate of matrix elements using such an expansion, especially for processes involving heavy pseudoscalar quarkonia.