Constraints on the odderon amplitude in the CGC framework

Abstract

In this manuscript we analyzed the elastic $pp$ and $p\bar{p}$ cross-section in the Color Glass Condensate framework, treating them as a dilute-dense system, and derived the phenomenological constraints (upper bounds) on the odderon-mediated part of the dipole scattering amplitude $\mathcal{O}(Y,\,\boldsymbol{r},\,\boldsymbol{b})$. For our analysis we used the experimental data available from TOTEM-D0 and ISR collaborations and construct an observable defined as a combination of the cross-sections which allows us to suppress possible uncertainties associated with charge-parity even part of the amplitude. We analyzed two phenomenological parametrizations of odderons and demonstrated that after minor adjustments to the global normalization, they can describe the experimental data reasonably well, although due to large experimental uncertainties the odderon amplitude remains loosely constrained. Our results indicate that existing data provide limited sensitivity to the odderon and emphasize the need for improved precision and complementary observables.

Figures (5)

• Figure 1: (Color online) Left: Comparison of the wave functions (\ref{['eq:dIgauss']}) and (\ref{['LFWFb']}). Right: comparison of the $x$-integrated wave functions (\ref{['eq:dIgauss']}) and (\ref{['LFWFb']}). See the text for more details.
• Figure 2: (Color online) The predictions for the odderon-mediated observable $\Sigma$ with parametrization (\ref{['eq:oddben']}) and the wave functions (\ref{['eq:dIgauss']},\ref{['LFWFb']}), respectively (all curves nearly coincide with the photon-only contribution $\Sigma_{\gamma}$). The points with error bars (“ experimental data” for the observable $\Sigma$) were derived from ISR Breakstone:1985 and D0-TOTEM experimental data in Martynov:2017zjzD0:2020tigD0:2012erdTOTEM:2018psk as explained in the text. For ISR, the systematic and statistic errors were added in quadrature. The solid black curve $\Sigma_{\gamma}(t)$ corresponds to the energy-independent contribution of the $t$-channel photon exchange, whereas $\Sigma_{\mathbb{O}}(t)$ is the energy-dependent contribution of the odderon. The quoted values of $\chi^{2}/N$ in the column “ All” of the table correspond to the global analysis (TOTEM-D0 and ISR), whereas columns “ ISR” and “ Totem-D0” take into account only the data from these collaborations. The first row in the table gives values for the photon-only contribution, whereas the last two rows take into account odderons using the wave functions (\ref{['eq:dIgauss']}) and (\ref{['LFWFb']}), respectively.
• Figure 3: (Color online) The predictions for the odderon-mediated observable $\Sigma$ with parametrization (\ref{['eq:oddben']}). The upper row corresponds to the global fit, the central row corresponds to the fit of ISR data only, and the last row includes only TOTEM-D0 data into the fit (see text for details). The left and right columns correspond to the wave functions (\ref{['eq:dIgauss']},\ref{['LFWFb']}), respectively. The points with errorbars (“ experimental data” for the observable $\Sigma$) were derived from ISR Breakstone:1985 and D0-TOTEM experimental data in Martynov:2017zjzD0:2020tigD0:2012erdTOTEM:2018psk. The values of $\lambda$ (together with errors) and the corresponding $\chi^{2}/{\rm d.o.f.}$ are shown in the lower right corner. The quoted values of $\chi^{2}/{\rm d.o.f.}$ correspond only to the points that were taken into account during the fit and should not be confused with a global goodness-of-fit metrics (see the text for more details). The values of $\chi^{2}/{\rm d.o.f.}$ shown in the last two plots exceed $\chi^{2}/N$ shown in the last column of the inline table in the Figure (\ref{['fig:odderon_Benic-1']}) only due to the difference of divisors; the corresponding $\chi^{2}/N=1.92$ for TOTEM-D0 fit. The colored bands show the uncertainty of the fit (95% confidence level).
• Figure 4: (Color online) The predictions for the odderon-mediated observable $\Sigma$ with parametrization (\ref{['OddHatta_b']}) and the profiles $S_{i}(b)$ from the Table \ref{['tab:profiles']} ($m$ is a profile-dependent constant). The left and right columns correspond to the wave functions (\ref{['eq:dIgauss']},\ref{['LFWFb']}), respectively. The quoted values of $\chi^{2}/{\rm d.o.f.}$ correspond to the global fit; the fit of ISR-only data decreases $\chi^{2}/{\rm d.o.f.}$, however yields nearly the same values of $\lambda$. The points with error bars (“ experimental data” for the observable $\Sigma$) were derived from ISR Breakstone:1985 and D0-TOTEM experimental data in Martynov:2017zjzD0:2020tigD0:2012erdTOTEM:2018psk.
• Figure 5: The predictions for the odderon-mediated observable $\Sigma$ with parametrization (\ref{['OddHatta_b']}) and profile (\ref{['eq:Linear']}). The left and right columns correspond to the wave functions (\ref{['eq:dIgauss']},\ref{['LFWFb']}), respectively. The points with error bars (“ experimental” data) for the observable $\Sigma$ were derived from ISR Breakstone:1985 and D0-TOTEM experimental data in Martynov:2017zjzD0:2020tigD0:2012erdTOTEM:2018psk. The quoted values of $\chi^{2}/{\rm d.o.f.}$ correspond to the global fit; the fit of ISR-only data decreases $\chi^{2}/{\rm d.o.f.}$ , however yields nearly the same values of $\lambda_{n}$.