Lattice study of scattering phase shifts for <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> and <mml:math xmlns:mml="http://www.w3

We investigate the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>S</a:mi> </a:math> - and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>P</c:mi> </c:math> -wave phase shifts for the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>D</e:mi> <e:msup> <e:mi>D</e:mi> <e:mo>*</e:mo> </e:msup> </e:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>B</g:mi> <g:msup> <g:mi>B</g:mi> <g:mo>*</g:mo> </g:msup> </g:math> scatterings using Lüscher’s finite-size method under twisted boundary conditions to search for doubly charmed tetraquarks <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msubsup> <i:mi>T</i:mi> <i:mrow> <i:mi>c</i:mi> <i:mi>c</i:mi> </i:mrow> <i:mo>+</i:mo> </i:msubsup> </i:math> and doubly bottomed tetraquarks <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msubsup> <k:mi>T</k:mi> <k:mrow> <k:mi>b</k:mi> <k:mi>b</k:mi> </k:mrow> <k:mo>−</k:mo> </k:msubsup> </k:math> as the hadronic bound states. The <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msubsup> <m:mi>T</m:mi> <m:mrow> <m:mi>c</m:mi> <m:mi>c</m:mi> </m:mrow> <m:mo>+</m:mo> </m:msubsup> </m:math> state was observed as a peak just below the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>D</o:mi> <o:msup> <o:mi>D</o:mi> <o:mo>*</o:mo> </o:msup> </o:math> threshold by LHCb Collaboration, while the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msubsup> <q:mi>T</q:mi> <q:mrow> <q:mi>b</q:mi> <q:mi>b</q:mi> </q:mrow> <q:mo>−</q:mo> </q:msubsup> </q:math> state is a theoretically predicted tetraquark state having heavier quark flavors <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mrow> <s:mi>b</s:mi> <s:mi>b</s:mi> <s:mover accent="true"> <s:mrow> <s:mi>u</s:mi> </s:mrow> <s:mrow> <s:mo stretchy="false">¯</s:mo> </s:mrow> </s:mover> <s:mover accent="true"> <s:mrow> <s:mi>d</s:mi> </s:mrow> <s:mrow> <s:mo stretchy="false">¯</s:mo> </s:mrow> </s:mover> </s:mrow> </s:math> . Lüscher’s finite-size method is one of the well-established methods for calculating the scattering phase shifts between two hadrons in lattice QCD simulations. Several studies have used simulations under the periodic boundary condition to determine the scattering phase shifts at a few discrete momenta for the <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mi>D</y:mi> <y:msup> <y:mi>D</y:mi> <y:mo>*</y:mo> </y:msup> </y:math> system. However, the scattering phase shift has not been investigated for the <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mi>B</ab:mi> <ab:msup> <ab:mi>B</ab:mi> <ab:mo>*</ab:mo> </ab:msup> </ab:math> system. In this study, we investigate <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mi>S</cb:mi> </cb:math> - and <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:mi>P</eb:mi> </eb:math> -wave scattering phase shifts for the <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:mi>D</gb:mi> <gb:msup> <gb:mi>D</gb:mi> <gb:mo>*</gb:mo> </gb:msup> </gb:math> and <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:mi>B</ib:mi> <ib:msup> <ib:mi>B</ib:mi> <ib:mo>*</ib:mo> </ib:msup> </ib:math> systems in both <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:mi>I</kb:mi> <kb:mo>=</kb:mo> <kb:mn>0</kb:mn> </kb:math> and <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"> <mb:mi>I</mb:mi> <mb:mo>=</mb:mo> <mb:mn>1</mb:mn> </mb:math> channels under several types of partially twisted boundary conditions. The use of the partially twisted boundary conditions enables us to obtain the scattering phase shift at any momentum by continuously varying the twisting angle. It also allows us to easily access the <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"> <ob:mi>P</ob:mi> </ob:math> -wave scattering phase shifts through the mixing of <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"> <qb:mi>S</qb:mi> </qb:math> and <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"> <sb:mi>P</sb:mi> </sb:math> waves, which is induced by the imposed boundary conditions. The <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"> <ub:mrow> <ub:mn>2</ub:mn> <ub:mo>+</ub:mo> <ub:mn>1</ub:mn> </ub:mrow> </ub:math> flavor PACS-CS gauge ensembles at <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"> <wb:msub> <wb:mi>m</wb:mi> <wb:mi>π</wb:mi> </wb:msub> <wb:mo>=</wb:mo> <wb:mn>295</wb:mn> </wb:math> , 411, and 569 MeV are used. For charm and bottom quarks, the relativistic heavy quark action is adopted to reduce the lattice discretization artifacts due to the heavy quark mass. We discuss the emergence of a shallow bound state with a binding energy of <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"> <yb:mi mathvariant="script">O</yb:mi> <yb:mo stretchy="false">(</yb:mo> <yb:mn>100</yb:mn> <yb:mo stretchy="false">)</yb:mo> <yb:mtext> </yb:mtext> <yb:mtext> </yb:mtext> <yb:mi>keV</yb:mi> </yb:math> at the physical pion mass in the <dc:math xmlns:dc="http://www.w3.org/1998/Math/MathML" display="inline"> <dc:mi>B</dc:mi> <dc:msup> <dc:mi>B</dc:mi> <dc:mo>*</dc:mo> </dc:msup> </dc:math> system, which has the quantum number <fc:math xmlns:fc="http:/