Investigating the two-pion exchange of the double charm <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>D</mml:mi> <mml:msup> <mml:mi>D</mml:mi> <mml:mo>*</mml:mo> </mml:msup> </mml:math> chiral interactions and <mm

Under chiral effective field theory, we study the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>S</a:mi> </a:math> -wave <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>D</c:mi> <c:msup> <c:mi>D</c:mi> <c:mo>*</c:mo> </c:msup> </c:math> interactions up to second chiral order at one-loop level, which contain full contact, one-pion-exchange (OPE) and two-pion-exchange (TPE) contributions. Here, we adopt a new subtraction scheme of the two-particle-reducible contributions and attempt different regularization schemes uniquely for the TPE contributions since they are highly divergent on the momentum transfer. Under these schemes, we conclude that, in the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>I</e:mi> <e:mo>=</e:mo> <e:mn>0</e:mn> </e:math> channel, the TPE contribution is repulsive, then the competition between this powerful repulsing TPE and the other two (contact and OPE) results in a quite weak attraction. This explains why <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>T</g:mi> <g:mrow> <g:mi>c</g:mi> <g:mi>c</g:mi> </g:mrow> </g:msub> </g:math> has an extremely small binding energy if treated as the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>I</i:mi> <i:mo>=</i:mo> <i:mn>0</i:mn> </i:math> <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>D</k:mi> <k:msup> <k:mi>D</k:mi> <k:mo>*</k:mo> </k:msup> </k:math> bound state. This feature resembles that of hidden charm <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>D</m:mi> <m:msup> <m:mover accent="true"> <m:mi>D</m:mi> <m:mo stretchy="false">¯</m:mo> </m:mover> <m:mo>*</m:mo> </m:msup> </m:math> as we investigated in previous work [], which also interpreted the extremely near-threshold phenomenon of <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>X</q:mi> <q:mo stretchy="false">(</q:mo> <q:mn>3872</q:mn> <q:mo stretchy="false">)</q:mo> </q:math> . In addition, we also solve the Bethe-Salpeter equation with the chiral interactions for a consistency check.