Prospects for observing novel photon-induced <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><m

We investigate the production of charged scalar boson pairs <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>H</a:mi><a:mo>−</a:mo></a:msup><a:msup><a:mi>H</a:mi><a:mo>+</a:mo></a:msup></a:math> via photon-photon fusion in proton-proton collisions at the High-Luminosity LHC (HL-LHC), High-Energy LHC (HE-LHC), and Future Circular hadron-hadron Collider (FCC-hh). The analysis is performed within the framework of the Two-Higgs-Doublet Model type-III, which predicts large branching ratios for the decay channel <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>H</c:mi><c:mo>±</c:mo></c:msup><c:mo stretchy="false">→</c:mo><c:msup><c:mi>τ</c:mi><c:mo>±</c:mo></c:msup><c:msub><c:mi>ν</c:mi><c:mi>τ</c:mi></c:msub></c:math>, the focus of this work. Motivated by the current excess of events in <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mrow><f:mi mathvariant="script">B</f:mi><f:mi mathvariant="script">R</f:mi></f:mrow><f:mo stretchy="false">(</f:mo><f:mi>t</f:mi><f:mo stretchy="false">→</f:mo><f:msup><f:mi>H</f:mi><f:mo>±</f:mo></f:msup><f:mi>b</f:mi><f:mo stretchy="false">)</f:mo><f:mo>×</f:mo><f:mrow><f:mi mathvariant="script">B</f:mi><f:mi mathvariant="script">R</f:mi></f:mrow><f:mo stretchy="false">(</f:mo><f:msup><f:mi>H</f:mi><f:mo>±</f:mo></f:msup><f:mo stretchy="false">→</f:mo><f:mi>c</f:mi><f:mi>b</f:mi><f:mo stretchy="false">)</f:mo></f:math> for <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msub><r:mi>M</r:mi><r:msup><r:mi>H</r:mi><r:mo>±</r:mo></r:msup></r:msub><r:mo>=</r:mo><r:mn>130</r:mn><r:mtext> </r:mtext><r:mtext> </r:mtext><r:mi>GeV</r:mi></r:math>, we explore charged Higgs boson masses in the range <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:msub><t:mi>M</t:mi><t:msup><t:mi>H</t:mi><t:mo>±</t:mo></t:msup></t:msub><t:mo>=</t:mo><t:mn>100</t:mn><t:mi>–</t:mi><t:mn>150</t:mn><t:mtext> </t:mtext><t:mtext> </t:mtext><t:mi>GeV</t:mi></t:math>. Using benchmark points (BPs) consistent with current experimental constraints, we evaluate the process <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mi>γ</v:mi><v:mi>γ</v:mi><v:mo stretchy="false">→</v:mo><v:msup><v:mi>H</v:mi><v:mo>−</v:mo></v:msup><v:msup><v:mi>H</v:mi><v:mo>+</v:mo></v:msup><v:mo stretchy="false">→</v:mo><v:mi>τ</v:mi><v:msub><v:mi>ν</v:mi><v:mi>τ</v:mi></v:msub><v:mi>τ</v:mi><v:msub><v:mi>ν</v:mi><v:mi>τ</v:mi></v:msub><v:mo stretchy="false">→</v:mo><v:mi>e</v:mi><v:mi>μ</v:mi><v:mo>+</v:mo><v:msub><v:menclose notation="updiagonalstrike"><v:mi>E</v:mi></v:menclose><v:mi>T</v:mi></v:msub></v:math> and find <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:mo>≳</bb:mo><bb:mn>5</bb:mn><bb:mi>σ</bb:mi></bb:math> across the entire mass range. For the most favored BP with <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:msub><db:mi>M</db:mi><db:msup><db:mi>H</db:mi><db:mo>±</db:mo></db:msup></db:msub><db:mo>=</db:mo><db:mn>130</db:mn><db:mtext> </db:mtext><db:mtext> </db:mtext><db:mi>GeV</db:mi></db:math>, we predict of <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:mn>3</fb:mn><fb:mi>σ</fb:mi></fb:math>, <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:mn>5</hb:mn><hb:mi>σ</hb:mi></hb:math>, <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:mn>8</jb:mn><jb:mi>σ</jb:mi></jb:math> with integrated luminosities of 3000, 2300, and <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"><lb:mn>300</lb:mn><lb:mtext> </lb:mtext><lb:mtext> </lb:mtext><lb:msup><lb:mi>fb</lb:mi><lb:mrow><lb:mo>−</lb:mo><lb:mn>1</lb:mn></lb:mrow></lb:msup></lb:math> at center-of-mass energies of 14 TeV (HL-LHC), 27 TeV (HE-LHC), and 100 TeV (FCC-hh), respectively.