Photon and dilepton emission anisotropy for a magnetized quark-gluon plasma

We study the higher-order anisotropy coefficients <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>v</a:mi><a:mn>4</a:mn></a:msub></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>v</c:mi><c:mn>6</c:mn></c:msub></c:math> in the photon and dilepton emission from a hot magnetized quark-gluon plasma. Together with the earlier predictions for <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>v</e:mi><e:mn>2</e:mn></e:msub></e:math>, these results show a distinctive pattern of the anisotropy coefficients in several kinematic regimes. In the case of photon emission, nonzero coefficients <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>v</g:mi><g:mi>n</g:mi></g:msub></g:math> (with even <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>n</i:mi></i:math>) have opposite signs at small and large values of the transverse momentum (i.e., <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>k</k:mi><k:mi>T</k:mi></k:msub><k:mo>≲</k:mo><k:msqrt><k:mrow><k:mo stretchy="false">|</k:mo><k:mi>e</k:mi><k:mi>B</k:mi><k:mo stretchy="false">|</k:mo></k:mrow></k:msqrt></k:math> and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>k</o:mi><o:mi>T</o:mi></o:msub><o:mo>≳</o:mo><o:msqrt><o:mrow><o:mo stretchy="false">|</o:mo><o:mi>e</o:mi><o:mi>B</o:mi><o:mo stretchy="false">|</o:mo></o:mrow></o:msqrt></o:math>, respectively). Additionally, the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>v</s:mi><s:mi>n</s:mi></s:msub></s:math> signs alternate with increasing <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>n</u:mi></u:math>, and their approximate values decrease as <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mn>1</w:mn><w:mo>/</w:mo><w:msup><w:mi>n</w:mi><w:mn>2</w:mn></w:msup></w:math> in magnitude. The anisotropy of dilepton emission is well pronounced only at large transverse momenta and small invariant masses (i.e., when <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mi>k</y:mi><y:mi>T</y:mi></y:msub><y:mo>≳</y:mo><y:msqrt><y:mrow><y:mo stretchy="false">|</y:mo><y:mi>e</y:mi><y:mi>B</y:mi><y:mo stretchy="false">|</y:mo></y:mrow></y:msqrt></y:math> and <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>M</cb:mi><cb:mo>≲</cb:mo><cb:msqrt><cb:mrow><cb:mo stretchy="false">|</cb:mo><cb:mi>e</cb:mi><cb:mi>B</cb:mi><cb:mo stretchy="false">|</cb:mo></cb:mrow></cb:msqrt></cb:math>). The corresponding <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msub><gb:mi>v</gb:mi><gb:mn>4</gb:mn></gb:msub></gb:math> and <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:msub><ib:mi>v</ib:mi><ib:mn>6</ib:mn></ib:msub></ib:math> coefficients are of the same magnitude and show a similar alternating sign pattern with increasing <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mi>n</kb:mi></kb:math> as in the photon emission.