Three-body universality in the <i>B</i> meson sector

Abstract The charged exotic mesons Z b (10610) and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>Z</mml:mi> <mml:mi>b</mml:mi> <mml:mo>′</mml:mo> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:mn>10650</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> observed by the Belle collaboration in 2011 are very close to the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> <mml:mover accent="true"> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> <mml:msup> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> </mml:math> thresholds, respectively. This suggests their interpretation as shallow hadronic molecules of B and B ∗ mesons. Using the masses of the Z b (10610) and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>Z</mml:mi> <mml:mi>b</mml:mi> <mml:mo>′</mml:mo> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:mn>10650</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> as input, we rule out the possibility for universal bound states of three B and B ∗ mesons arising from the Efimov effect based on their spin-isospin structure. As a consequence, we can predict the phase shifts for the scattering of B and B ∗ mesons off the exotic mesons Z b (10610) and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>Z</mml:mi> <mml:mi>b</mml:mi> <mml:mo>′</mml:mo> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:mn>10650</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> to leading order in a non-relativistic effective field theory with contact interactions based on two-body information alone.