Unitarity effects in elastic scattering at the LHC

We study the high-energy behavior of the elastic scattering amplitude using two distinct unitarization schemes: the eikonal and the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>U</a:mi></a:math>-matrix. Our analysis begins with a formalism involving solely Pomerons, incorporating pion-loop insertions in the Pomeron trajectory representing the nearest singularity generated by <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>t</c:mi></c:math>-channel unitarity. Subsequently, we explore a scenario that includes the presence of an Odderon. In our analyses, we explore the tension between the TOTEM and the ATLAS measurements for <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>σ</e:mi><e:mi>tot</e:mi></e:msub></e:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mi>d</g:mi><g:mi>σ</g:mi><g:mo>/</g:mo><g:mi>d</g:mi><g:mi>t</g:mi></g:mrow></g:math> at 7, 8, and 13 TeV and the subsequent implications for the properties of both the Pomeron and Odderon. Our results show that the Odderon phase factor <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:msub><i:mrow><i:mi>ξ</i:mi></i:mrow><i:mrow><i:mi mathvariant="double-struck">O</i:mi></i:mrow></i:msub><i:mo>=</i:mo><i:mo>−</i:mo><i:mn>1</i:mn></i:mrow></i:math> is favored in both unitarization schemes, supporting an Odderon with a phase opposite to that of other crossing-odd components of the scattering amplitude. More interestingly, this specific phase factor stands as the sole one that aligns with results consistent with a nonzero Odderon coupling. Published by the American Physical Society 2024