Higher precision constraints on the tau $$g-2$$ in LHC photon-initiated production: a full account of hadron dissociation and soft survival effects

We present the first calculation of photon-initiated <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>τ</mml:mi></mml:math> pair production in the presence of non-zero anomalous magnetic ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>a</mml:mi> <mml:mi>τ</mml:mi></mml:msub> </mml:math> ) and/or electric dipole ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>d</mml:mi> <mml:mi>τ</mml:mi></mml:msub> </mml:math> ) moments of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>τ</mml:mi></mml:math> lepton that accounts for the non-trivial interplay between these modifications with the soft survival factor and the possibility of dissociation of the hadron (proton or ion) beam. The impact of these is on general grounds not expected to have a uniform dependence on the value of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>a</mml:mi> <mml:mi>τ</mml:mi></mml:msub> <mml:mo>,</mml:mo> <mml:msub><mml:mi>d</mml:mi> <mml:mi>τ</mml:mi></mml:msub> </mml:mrow> </mml:math> , but in all previous analyses this assumption has been made. We have therefore investigated the importance of these effects in the context of photon-initiated <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>τ</mml:mi></mml:math> pair production in both pp and PbPb collisions. This is in general found to be relatively small, at the percent level in terms of any extracted limits or observations of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>a</mml:mi> <mml:mi>τ</mml:mi></mml:msub> <mml:mo>,</mml:mo> <mml:msub><mml:mi>d</mml:mi> <mml:mi>τ</mml:mi></mml:msub> </mml:mrow> </mml:math> , such that these effects can indeed be safely ignored in existing experimental analyses. However, as the precision of such determinations increases in the future, the relevance of these effects will likewise increase. With this in mind we have made our calculation publicly available in the SuperChic Monte Carlo generator, including the possibility to simulate this process for varying <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>a</mml:mi> <mml:mi>τ</mml:mi></mml:msub> <mml:mo>,</mml:mo> <mml:msub><mml:mi>d</mml:mi> <mml:mi>τ</mml:mi></mml:msub> </mml:mrow> </mml:math> without rerunning.