Analysis of ATLAS pp elastic measurements at $\sqrt{s}$=13 TeV and comparison with TOTEM measurements

TL;DR

The paper analyzes pp elastic scattering at $\sqrt{s}=13$ TeV by ATLAS and TOTEM within the KFK framework, showing that differences in $d\sigma/dt$ and $\sigma_{\rm tot}$ are largely attributable to a common normalization related by the optical theorem. By disentangling the real and imaginary parts of the amplitude with independent slopes and locating zeros (including Martin's zero) in both parts, the study explains why the ATLAS and TOTEM results are qualitatively similar and yields a model-dependent $\rho^{ATLAS}=0.091\pm0.004$. It demonstrates that an effective normalization factor of about $0.88$ aligns the differential cross sections across the measured $|t|$ ranges, and highlights the importance of the $T_R$ and $T_I$ separation for interpreting forward quantities and the dip–bump structure. The work underscores that $\rho$ and related slope parameters are sensitive to the underlying amplitude model, and that genuine incompatibilities between experiments are unlikely once a coherent phenomenological description is employed.

Abstract

A comparative description is made of the measurements at LHC of pp elastic scattering at 13 TeV by the ATLAS and TOTEM Collaborations. In the total and differential cross sections we show that the differences are justified through single numerical factor. It seems that there is no fundamental physical difference, but only a difference of normalization between the two experiments. We study the real and imaginary amplitudes disentangled with the KFK (Kohara-Ferreira-Kodama) model and show that the properties are similar in qualitative aspects for both experiments. The real and imaginary parts have different slopes at the origin and present zeros, with distributions that are common to several models, with three zeros in the real part and one zero in the imaginary amplitude. A zero in the real part, known as Martin's zero, influences the determination of the $ρ$ parameter.

Figures (4)

• Figure 1: Representation of the 79 points of ATLAS measurements of differential cross section of pp elastic scattering at 13 TeV with a function of the KFK model. Fit and plot with statistical errors only.
• Figure 2: Separation of the imaginary and real amplitudes of $d\sigma/dt$ of ATLAS data in the analysis with the KFK model. The symbol RC means superposition of real nuclear and Coulomb amplitudes. In the first plot we show $d\sigma^{RC}/dt$ and $d\sigma^I/dt$, dips indicating their zeros. In the second plot we show the amplitudes. In the real part the first zero is in the cancellation with the negative Coulomb amplitude at $|t|=0.008 \,\hbox{GeV}^2$ . The second real zero is Martin's zero at $|t|=0.205\,\hbox{GeV}^2$. The third real zero is outside the data range at $|t|=0.98\,\hbox{GeV}^2$. The imaginary zero is predicted for $|t|=0.466\,\hbox{GeV}^2$, just after the data. The dip in the differential cross section is predicted for $|t|=0.47\,\hbox{GeV}^2$, also after the end of the data. In the third plot we show the imaginary and real nuclear amplitudes in the range of very small |t|, with their zeros, compared with the behaviour of pure exponentials, with different slopes.
• Figure 3: ATLAS and TOTEM data differ by a factor 0.88 in $d\sigma/t$ that is determined by the square of the ratio of the total cross sections $\sigma^{\rm ATLAS}/\sigma^{\rm TOTEM}=104.7/111.56=0.9385$ that is the ratio of the t=0 imaginary amplitudes. In the first plot a range is chosen to show the precision of the factor 0.88. The second plot includes all 79 points of ATLAS data together with proper junction of TOTEM data of Sets I and II. The fitting function of data ATLAS is given by KFK model, the same used in Figs. (\ref{['ATLAS_13_KFK']},\ref{['amplitudes_ATLAS_13_TeV']}).
• Figure 4: Full ranges of representations of ATLAS and TOTEM data by KFK Model. In the LHS only the TOTEM data and representative curve are shown. In the RHS the comparative lines are shown for the KFK calculation with the parameters for ATLAS and TOTEM data given in Table \ref{['KFK_parameters']}. The dashed line has a fictitious extension for the ATLAS case. The dipper $d\sigma /dt$ shape in the dashed line is due to the proximity of the values of zeros imaginary $Z_I=0.466$ and real $Z_{RC}^{(2)}=0.981$ in ATLAS data as compared to the corresponding zeros in TOTEM data.