Scattering in the dual regime of Yang-Baxter deformed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn> <mml:mi>N</mml:

We continue to explore the previously suggested dual regime of Yang-Baxter (YB) deformed <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi mathvariant="normal">O</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>2</a:mn> <a:mi>N</a:mi> <a:mo stretchy="false">)</a:mo> </a:math> sigma models, which is a new one-parametric deformation of the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mi mathvariant="normal">O</f:mi> <f:mo stretchy="false">(</f:mo> <f:mn>2</f:mn> <f:mi>N</f:mi> <f:mo stretchy="false">)</f:mo> </f:math> model. It can be obtained from the conventional YB deformed <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi mathvariant="normal">O</k:mi> <k:mo stretchy="false">(</k:mo> <k:mn>2</k:mn> <k:mi>N</k:mi> <k:mo>+</k:mo> <k:mn>2</k:mn> <k:mo stretchy="false">)</k:mo> </k:math> sigma model by freezing two isometries. The scattering matrix in the nondeformed <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mi mathvariant="normal">O</p:mi> <p:mo stretchy="false">(</p:mo> <p:mi>n</p:mi> <p:mo stretchy="false">)</p:mo> </p:math> model is known to coincide with the rational <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msub> <u:mrow> <u:mi mathvariant="fraktur">so</u:mi> </u:mrow> <u:mi>n</u:mi> </u:msub> </u:math> -invariant <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:mi>R</x:mi> </x:math> -matrix. For <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:mi>n</z:mi> <z:mo>=</z:mo> <z:mn>2</z:mn> <z:mi>N</z:mi> </z:math> this rational solution allows for two trigonometric deformations: the usual <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:msubsup> <bb:mi>D</bb:mi> <bb:mi>N</bb:mi> <bb:mrow> <bb:mo stretchy="false">(</bb:mo> <bb:mn>1</bb:mn> <bb:mo stretchy="false">)</bb:mo> </bb:mrow> </bb:msubsup> </bb:math> and the twisted <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:msubsup> <fb:mi>D</fb:mi> <fb:mi>N</fb:mi> <fb:mrow> <fb:mo stretchy="false">(</fb:mo> <fb:mn>2</fb:mn> <fb:mo stretchy="false">)</fb:mo> </fb:mrow> </fb:msubsup> </fb:math> . The usual one is known to coincide with the scattering matrix of the conventional YB- <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"> <jb:mi mathvariant="normal">O</jb:mi> <jb:mo stretchy="false">(</jb:mo> <jb:mn>2</jb:mn> <jb:mi>N</jb:mi> <jb:mo stretchy="false">)</jb:mo> </jb:math> model. A natural question to ask is what sigma model corresponds to the twisted solution. In this work we claim that it is precisely our dual regime of YB- <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"> <ob:mi mathvariant="normal">O</ob:mi> <ob:mo stretchy="false">(</ob:mo> <ob:mn>2</ob:mn> <ob:mi>N</ob:mi> <ob:mo stretchy="false">)</ob:mo> </ob:math> . We find the corresponding unitarizing function <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"> <tb:msub> <tb:mi>F</tb:mi> <tb:mi>N</tb:mi> </tb:msub> <tb:mo stretchy="false">(</tb:mo> <tb:mi>θ</tb:mi> <tb:mo stretchy="false">)</tb:mo> </tb:math> explicitly, and, as a bonus, extract some physical properties of this system using the thermodynamic Bethe ansatz technique.