arXiv subjects
Publications and source records attributed to I. Szanyi.
The Lévy $α$-stable generalization of the ReBB model of elastic proton-proton and proton-antiproton scattering is presented. The motivation for the future use of this model in describing experimental data is discussed.
Evaluating the H(x, s; pp) scaling function of elastic proton-proton (pp) collisions from recent TOTEM data at sqrt(s) = 8 TeV and comparing it with the same function of elastic proton-antiproton (pp-) data of the D0 collaboration at sqrt(s) = 1.96 TeV, we find, from this comparison alone, an at least 3.79 sigma {\signal} of Odderon exchange. If we combine this model independently obtained result with that of a similar analysis but using TOTEM elastic pp scattering data at sqrt(s) = 7 TeV, which resulted in an at least 6.26 σ signal, the combined significance of Odderon exchange increases to at least 7.08 σ, model independently. Further combinations of various datasets in the TeV energy range are detailed in the manuscript
A simple Lévy-$α$ stable (SL) model is used to describe the data on elastic $pp$ and $p\bar p$ scattering at low-$|t|$ from SPS energies up to LHC energies. The SL model is demonstrated to describe the data with a strong non-exponential feature in a statistically acceptable manner. The energy dependence of the parameters of the model is determined and analyzed. The Lévy $α$ parameter of the model has an energy-independent value of 1.959 $\pm$ 0.002 following from the strong non-exponential behavior of the data. We strengthen the conclusion that the discrepancy between TOTEM and ATLAS elastic $pp$ differential cross section measurements arises only in the normalization and not in the shape of the distribution of the data as a function of $t$. We find that the slope parameter has different values for $pp$ and $p\bar p$ elastic scattering at LHC energies. This may be the effect of the odderon exchange or the jump in the energy dependence of the slope parameter in the energy interval 3 GeV $\lesssim \sqrt s \lesssim$ 4 GeV.
It is known that the Real Extended Bialas-Bzdak (ReBB) model describes the proton-proton ($pp$) and proton-antiproton ($p\bar p$) differential cross-section data in a statistically non-excludible way,\linebreak i.e., with a confidence level greater than or equal to 0.1\% in the center of mass energy range \linebreak 546 GeV $\leq\sqrt{s}\leq$ 8 TeV and in the squared four-momentum transfer range 0.37 GeV$^2$ $\leq -t\leq$ 1.2 GeV$^2$. Considering, instead of Gaussian, a more general Lévy $α$-stable shape for the parton distributions of the constituent quark and diquark inside the proton and for the relative separation between them, a generalized description of data is obtained, where the ReBB model corresponds to the $α=$ 2 special case. Extending the model to $α<$ 2, we conjecture that the validity of the model can be extended to a wider kinematic range, in particular, to lower values of the four-momentum transfer $-t$. We present the formal Lévy $α$-stable generalization of the Bialas-Bzdak model and show that a simplified version of this model can be successfully fitted, with $α<$ 2, to the non-exponential, low $-t$ differential cross-section data of elastic proton-proton scattering at $\sqrt{s} =$ 8 TeV.
We complete the model-independent analysis of the scaling properties of the differential cross section of elastic proton-proton cross sections, including new TOTEM data published in 2022 at $\sqrt{s} = 8$ TeV. We separate the signal and the background region with a new gating method. In the signal region, we find that the statistical significance of Odderon exchange from the combined 7.0 and 8.0 TeV $pp$ data of TOTEM and the 1.96 TeV $p\bar{p}$ data of D0 is at least 7.32$σ$. In the background region, the scaling functions of elastic proton-proton data at 7 and 8 TeV and that of elastic proton-antiproton scattering data at 1.96 TeV agree with a statistical significance not larger than 1.93$σ$.
The Real Extended Bialas-Bzdak (ReBB) model study is extended to the 8 TeV $pp$ TOTEM elastic differential cross section data. The analysis shows that the ReBB model describes the $pp$ and $p\bar{p}$ differential cross section data in the limited $0.37 \leq -t \leq 1.2$ GeV$^2$ and $1.96 \leq \sqrt{s} \leq 8$ TeV kinematic region, in a statistically acceptable manner. In this kinematic region a greater than 30 $σ$ model-dependent Odderon signal is observed by comparing the $pp$ and ReBB extrapolated $p\bar{p}$ differential cross sections. Thus, in practical terms, within the framework of the ReBB model, Odderon exchange is not a probability, but a certainty.
The Real Extended Bialas-Bzdak (ReBB) model is shown here to describe, in the $0.37 \le -t \le 1.2$ GeV$^2$ region, the proton-proton elastic differential cross section data published by the TOTEM Collaboration at LHC at $\sqrt{s} = 8 $ TeV center of mass energy. In this kinematic range, corresponding to the diffractive minimum-maximum region, a model-dependent Odderon signal higher than 18 $σ$ is obtained by comparing the ReBB model prediction for the $p\bar{p}$ elastic differential cross section to this TOTEM measured $pp$ elastic differential cross section data at 8 TeV. However, when combining this signal with the Odderon signals from the ReBB model in the $0.37 \leq -t \leq 1.2$ GeV$^2$ four-momentum-transfer range at $\sqrt{s} = $ 1.96, 2.76 and 7 TeV, it turns out that the combined significance is dominated not by the new 8 TeV but by that of earlier 7 TeV TOTEM data, that carry an even larger Odderon effect. Thus, in any practical terms, within the framework of the ReBB model, the Odderon signal in the limited $0.37 \leq -t \leq 1.2$ GeV$^2$ and $1.96 \leq \sqrt{s} \leq 8$ TeV kinematic region is not a probability, but a certainty. We show also that the $H(x)$ scaling version of the ReBB model works reasonably well at 8 TeV in the $0.37 \le -t \le 0.97$ GeV$^2$ region.
The unitarily extended Bialas-Bzdak model of elastic proton-proton scattering is applied, without modifications, to describe the differential cross-section of elastic proton-antiproton collisions in the TeV energy range, and to extrapolate these differential cross-sections to LHC energies. In this model-dependent study we find that the differential cross-sections of elastic proton-proton collision data at 2.76 and 7 TeV energies differ significantly from the differential cross-section of elastic proton-antiproton collisions extrapolated to these energies. The elastic proton-proton differential cross-sections, extrapolated to 1.96 TeV energy with the help of this extended Bialas-Bzdak model do not differ significantly from that of elastic proton-antiproton collisions, within the theoretical errors of the extrapolation. Taken together these results provide a model-dependent, but statistically significant evidence for a crossing-odd component of the elastic scattering amplitude at the at least 7.08 sigma level. From the reconstructed Odderon and Pomeron amplitudes, we determine the $\sqrt{s}$ dependence of the corresponding total and differential cross-sections.
We study the scaling properties of the differential cross section of elastic proton-proton ($pp$) and proton-antiproton ($p\bar p$) collisions at high energies. We introduce a new scaling function, that scales -- within the experimental errors -- all the ISR data on elastic $pp$ scattering from $\sqrt{s} = 23.5$ to $62.5$ GeV to the same universal curve. We explore the scaling properties of the differential cross-sections of the elastic $pp$ and $p\bar p$ collisions in a limited TeV energy range. Rescaling the TOTEM $pp$ data from $\sqrt{s} = 7$ TeV to $2.76$ and $1.96$ TeV, and comparing it to D0 $p\bar p$ data at $1.96$ TeV, our results provide an evidence for a $t$-channel Odderon exchange at TeV energies, with a significance of at least 6.26$σ$. We complete this work with a model-dependent evaluation of the domain of validity of the new scaling and its violations. We find that the $H(x)$ scaling is valid, model dependently, within $200$ GeV $ \leq \sqrt{s} \leq$ $ 8$ TeV, with a $-t$ range gradually narrowing with decreasing colliding energies.
We provide a statistically significant observation of the elusive Odderon exchange, based on novel and model-independent analysis of the scaling properties of the differential cross sections of elastic $pp$ and $p\bar p$ scattering in the TeV energy range. We report the statistical significance of the observed Odderon signal at the level of 6.26$σ$.
We investigate the scaling properties of elastic scattering data at ISR and LHC energies and find that the significance of an Odderon observation is larger than the discovery threshold of 5$σ$. As an unexpected by-product of these investigations, for certain experimentally relevant cases, we also conjecture the possibility of proton holography with the help of elastic proton-proton scattering.