2026/06/23 by Anonymous, Ulaş Özdem
Physics and Astronomy · #Quantum Chromodynamics and Particle Interactions #Cold Atom Physics and Bose-Einstein Condensates #Pulsars and Gravitational Waves Research
paper · pdf · doi:10.1103/8p4m-zbpb
Probing the internal organization of hidden-charm pentaquarks—including the spin-color correlations that distinguish compact diquark-diquark-antiquark configurations from loosely bound hadronic molecules—requires observables that go beyond mass spectroscopy. We argue that multicurrent QCD light-cone sum rules provide a diagnostic framework for this problem, not only through the expected sensitivity of the magnetic moment to the internal spin structure but, more importantly, through exact analytic relations among the flavor-sector contributions that are enforced by the algebra of the interpolating currents themselves. We identify two such signatures that emerge from our analysis of compact diquark-diquark-antiquark configurations: (i) for any of the four currents considered the light-quark contributions satisfy the exact ratio <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>μ</a:mi> <a:mi>u</a:mi> </a:msub> <a:mo>/</a:mo> <a:msub> <a:mi>μ</a:mi> <a:mi>d</a:mi> </a:msub> <a:mo>=</a:mo> <a:msub> <a:mi>e</a:mi> <a:mi>u</a:mi> </a:msub> <a:mo>/</a:mo> <a:msub> <a:mi>e</a:mi> <a:mi>d</a:mi> </a:msub> <a:mo>=</a:mo> <a:mo>−</a:mo> <a:mn>2</a:mn> </a:math> , reflecting a common Lorentz-color kernel that couples <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>u</c:mi> </c:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>d</e:mi> </e:math> only through their electric charges; and (ii) for the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>J</g:mi> <g:mn>3</g:mn> </g:msub> <g:mo stretchy="false">(</g:mo> <g:mi>x</g:mi> <g:mo stretchy="false">)</g:mo> </g:math> current the charm-quark contribution vanishes identically, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>μ</k:mi> <k:mi>c</k:mi> </k:msub> <k:mo>=</k:mo> <k:mn>0</k:mn> </k:math> , arising not from the pseudoscalar embedding of the charm diquark alone—since the same embedding occurs in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msub> <m:mi>J</m:mi> <m:mn>1</m:mn> </m:msub> <m:mo stretchy="false">(</m:mo> <m:mi>x</m:mi> <m:mo stretchy="false">)</m:mo> </m:math> , which yields a nonzero <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msub> <q:mi>μ</q:mi> <q:mi>c</q:mi> </q:msub> </q:math> —but from the specific Dirac structure associated with the anticharm coupling in the global current, which produces an analytic cancellation in the operator product expansion. We illustrate these signatures through explicit calculations using four independent diquark-diquark-antiquark interpolating currents <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msub> <s:mi>J</s:mi> <s:mn>1</s:mn> </s:msub> <s:mo stretchy="false">(</s:mo> <s:mi>x</s:mi> <s:mo stretchy="false">)</s:mo> <s:mi>–</s:mi> <s:msub> <s:mi>J</s:mi> <s:mn>4</s:mn> </s:msub> <s:mo stretchy="false">(</s:mo> <s:mi>x</s:mi> <s:mo stretchy="false">)</s:mo> </s:math> , assumed to carry <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:msup> <y:mi>J</y:mi> <y:mi>P</y:mi> </y:msup> <y:mo>=</y:mo> <y:msup> <y:mfrac> <y:mn>1</y:mn> <y:mn>2</y:mn> </y:mfrac> <y:mo>−</y:mo> </y:msup> </y:math> , and obtain <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:msub> <ab:mi>μ</ab:mi> <ab:msub> <ab:mi>J</ab:mi> <ab:mn>1</ab:mn> </ab:msub> </ab:msub> <ab:mo>=</ab:mo> <ab:mo>−</ab:mo> <ab:mn>1.3</ab:mn> <ab:msubsup> <ab:mn>5</ab:mn> <ab:mrow> <ab:mo>−</ab:mo> <ab:mn>0.28</ab:mn> </ab:mrow> <ab:mrow> <ab:mo>+</ab:mo> <ab:mn>0.35</ab:mn> </ab:mrow> </ab:msubsup> <ab:msub> <ab:mi>μ</ab:mi> <ab:mi>N</ab:mi> </ab:msub> </ab:math> , <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:msub> <cb:mi>μ</cb:mi> <cb:msub> <cb:mi>J</cb:mi> <cb:mn>2</cb:mn> </cb:msub> </cb:msub> <cb:mo>=</cb:mo> <cb:mn>3.1</cb:mn> <cb:msubsup> <cb:mn>4</cb:mn> <cb:mrow> <cb:mo>−</cb:mo> <cb:mn>0.50</cb:mn> </cb:mrow> <cb:mrow> <cb:mo>+</cb:mo> <cb:mn>0.65</cb:mn> </cb:mrow> </cb:msubsup> <cb:msub> <cb:mi>μ</cb:mi> <cb:mi>N</cb:mi> </cb:msub> </cb:math> , <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:msub> <eb:mi>μ</eb:mi> <eb:msub> <eb:mi>J</eb:mi> <eb:mn>3</eb:mn> </eb:msub> </eb:msub> <eb:mo>=</eb:mo> <eb:mn>1.0</eb:mn> <eb:msubsup> <eb:mn>1</eb:mn> <eb:mrow> <eb:mo>−</eb:mo> <eb:mn>0.20</eb:mn> </eb:mrow> <eb:mrow> <eb:mo>+</eb:mo> <eb:mn>0.25</eb:mn> </eb:mrow> </eb:msubsup> <eb:msub> <eb:mi>μ</eb:mi> <eb:mi>N</eb:mi> </eb:msub> </eb:math> , and <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:msub> <gb:mi>μ</gb:mi> <gb:msub> <gb:mi>J</gb:mi> <gb:mn>4</gb:mn> </gb:msub> </gb:msub> <gb:mo>=</gb:mo> <gb:mo>−</gb:mo> <gb:mn>1.7</gb:mn> <gb:msubsup> <gb:mn>9</gb:mn> <gb:mrow> <gb:mo>−</gb:mo> <gb:mn>0.34</gb:mn> </gb:mrow> <gb:mrow> <gb:mo>+</gb:mo> <gb:mn>0.41</gb:mn> </gb:mrow> </gb:msubsup> <gb:msub> <gb:mi>μ</gb:mi> <gb:mi>N</gb:mi> </gb:msub> </gb:math> . These four predictions are then assigned to the observed