Strangeonium spectrum with screening effects and interpretation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>h</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>1911</mml

Motivated by two new states <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>h</a:mi><a:mn>1</a:mn></a:msub><a:mo stretchy="false">(</a:mo><a:mn>1911</a:mn><a:mo stretchy="false">)</a:mo></a:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>X</e:mi><e:mo stretchy="false">(</e:mo><e:mn>2300</e:mn><e:mo stretchy="false">)</e:mo></e:math> observed by BESIII, we have investigated the mass spectrum and the strong decay properties of the strangeonium mesons within the modified Godfrey-Isgur model by considering the screening effects. We have determined the free parameters using the masses and widths of the well-established <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>s</i:mi><i:mover accent="true"><i:mi>s</i:mi><i:mo stretchy="false">¯</i:mo></i:mover></i:math> states <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>ϕ</m:mi><m:mo stretchy="false">(</m:mo><m:mn>1020</m:mn><m:mo stretchy="false">)</m:mo></m:math>, <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>ϕ</q:mi><q:mo stretchy="false">(</q:mo><q:mn>1680</q:mn><q:mo stretchy="false">)</q:mo></q:math>, <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi>h</u:mi><u:mn>1</u:mn></u:msub><u:mo stretchy="false">(</u:mo><u:mn>1415</u:mn><u:mo stretchy="false">)</u:mo></u:math>, <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msubsup><y:mi>f</y:mi><y:mn>2</y:mn><y:mo>′</y:mo></y:msubsup><y:mo stretchy="false">(</y:mo><y:mn>1525</y:mn><y:mo stretchy="false">)</y:mo></y:math>, and <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msub><cb:mi>ϕ</cb:mi><cb:mn>3</cb:mn></cb:msub><cb:mo stretchy="false">(</cb:mo><cb:mn>1850</cb:mn><cb:mo stretchy="false">)</cb:mo></cb:math>. According to our results, <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msub><gb:mi>h</gb:mi><gb:mn>1</gb:mn></gb:msub><gb:mo stretchy="false">(</gb:mo><gb:mn>1911</gb:mn><gb:mo stretchy="false">)</gb:mo></gb:math> and <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mi>X</kb:mi><kb:mo stretchy="false">(</kb:mo><kb:mn>2300</kb:mn><kb:mo stretchy="false">)</kb:mo></kb:math> could be well explained as <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:msub><ob:mi>h</ob:mi><ob:mn>1</ob:mn></ob:msub><ob:mo stretchy="false">(</ob:mo><ob:msup><ob:mn>2</ob:mn><ob:mn>1</ob:mn></ob:msup><ob:msub><ob:mi>P</ob:mi><ob:mn>1</ob:mn></ob:msub><ob:mo stretchy="false">)</ob:mo></ob:math> and <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:msub><sb:mi>h</sb:mi><sb:mn>1</sb:mn></sb:msub><sb:mo stretchy="false">(</sb:mo><sb:msup><sb:mn>3</sb:mn><sb:mn>1</sb:mn></sb:msup><sb:msub><sb:mi>P</sb:mi><sb:mn>1</sb:mn></sb:msub><sb:mo stretchy="false">)</sb:mo></sb:math> <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"><wb:mi>s</wb:mi><wb:mover accent="true"><wb:mi>s</wb:mi><wb:mo stretchy="false">¯</wb:mo></wb:mover></wb:math> states, respectively. Meanwhile, the possible assignments of <ac:math xmlns:ac="http://www.w3.org/1998/Math/MathML" display="inline"><ac:mi>X</ac:mi><ac:mo stretchy="false">(</ac:mo><ac:mn>2000</ac:mn><ac:mo stretchy="false">)</ac:mo></ac:math>, <ec:math xmlns:ec="http://www.w3.org/1998/Math/MathML" display="inline"><ec:msub><ec:mi>η</ec:mi><ec:mn>2</ec:mn></ec:msub><ec:mo stretchy="false">(</ec:mo><ec:mn>1870</ec:mn><ec:mo stretchy="false">)</ec:mo></ec:math>, and <ic:math xmlns:ic="http://www.w3.org/1998/Math/MathML" display="inline"><ic:mi>ϕ</ic:mi><ic:mo stretchy="false">(</ic:mo><ic:mn>2170</ic:mn><ic:mo stretchy="false">)</ic:mo></ic:math> as <mc:math xmlns:mc="http://www.w3.org/1998/Math/MathML" display="inline"><mc:msup><mc:mn>3</mc:mn><mc:mn>3</mc:mn></mc:msup><mc:msub><mc:mi>S</mc:mi><mc:mn>1</mc:mn></mc:msub></mc:math>, <oc:math xmlns:oc="http://www.w3.org/1998/Math/MathML" display="inline"><oc:msup><oc:mn>1</oc:mn><oc:mn>1</oc:mn></oc:msup><oc:msub><oc:mi>D</oc:mi><oc:mn>2</oc:mn></oc:msub></oc:math>, and <qc:math xmlns:qc="http://www.w3.org/1998/Math/MathML" display="inline"><qc:msup><qc:mn>2</qc:mn><qc:mn>3</qc:mn></qc:msup><qc:msub><qc:mi>D</qc:mi><qc:mn>1</qc:mn></qc:msub></qc:math> are also discussed. Furthermore, the masses and widths of the <sc:math xmlns:sc="http://www.w3.org/1998/Math/MathML" display="inline"><sc:mn>2</sc:mn><sc:mi>S</sc:mi></sc:math>, <uc:math xmlns:uc="http://www.w3.org/1998/Math/MathML" display="inline"><uc:mn>3</uc:mn><uc:mi>S</uc:mi></uc:math>, <wc:math xmlns:wc="http://www.w3.org/1998/Math/MathML" display="inline"><wc:mn>1</wc:mn><wc:mi>P</wc:mi></wc:math>, <yc:math xmlns:yc="http://www.w3.org/1998/Math/MathML" display="inline"><yc:mn>2</yc:mn><yc:mi>P</yc:mi></yc:math>, <ad:math xmlns:ad="http://www.w3.org/1998/Math/MathML" display="inline"><ad:mn>3</ad:mn><ad:mi>P</ad:mi></ad:math>, <cd:math xmlns:cd="http://www.w3.org/1998/Math/MathML" display="inline"><cd:mn>1</cd:mn><cd:mi>D</cd:mi></cd:math>, and <ed:math xmlns:ed="http://www.w3.org/1998/Math/MathML" display="inline"><ed:mn>2</ed:mn><ed:mi>D</ed:mi></ed:math> <gd:math xmlns:gd="http://www.w3.org/1998/Math/MathML" display="inline"><gd:mi>s</gd:mi><gd:mover accent="true"><gd:mi>s</gd:mi><gd:mo stretchy="false">¯</gd:mo></gd:mover></gd:math> states are also given and compared with various theoretical predictions, which will be helpful for the observations and confirmations of these states in the future.