The recent measurements of the elastic cross section by the TOTEM Collaboration together with the first estimations of the inelastic cross sections by other LHC detectors are used to test the simplest version of the geometrical model of the proton-proton scattering. We show that the description found for lower energy data, with the modest adjustment of the model parameter extrapolation, could be, in principle, used to describe the LHC measurement and to predict the cross sections in very high energy cosmic ray domain. However, the shape of the first elastic dip in the elastic differential scattering cross section suggests that ratio of the real to the imaginary part of the elastic amplitude is falling rather fast and the analysis of the elastic cross section fraction suggests that the geometrical picture of the proton-proton collision should be modified considerably when entering the ultra high-energy domain.
The predictions of a model which was tuned in 2013 to describe the elastic and diffractive $pp$- and/or $p\bar p$-data at collider energies up to 7 TeV are compared with the new 13 TeV TOTEM results. The possibility of an odd-signature Odderon exchange contribution is discussed.
We analyse the recent LHC data at 7 and 8 TeV for pp elastic scattering with special attention for the structure of the real part, which is shown to be crucial to describe the differential cross section in the forward region. We determine accurately the position of the zero of the real amplitude, which corresponds to the zero of a theorem by A. Martin.
We analyse the 13 TeV TOTEM data on elastic proton-proton scattering through a thorough statistical analysis, and obtain that $ρ=0.096\pm 0.006$ and $σ_{tot}=(107.5\pm 1.5)$ mb. Theoretical errors could lower the cross section by about 2 mb and increase $ρ$ by about 0.002. We also show that these results do not imply the existence of an odderon at $t=0$.
We analyse the recent LHC data at 7 and 8 TeV for pp elastic scattering with special attention for the structure of the real part, which is shown to be crucial to describe the differential cross section in the forward region. We determine accurately the position of the zero of the real amplitude, which corresponds to the zero of a theorem by A. Martin.
Recent measurements of the differential cross sections in the forward region of pp elastic scattering at 7 and 8 TeV show precise form of the $t$ dependence. We propose a detailed analysis of these measurements including the structures of the real and imaginary parts of the scattering amplitude. A good description is achieved, confirming in all experiments the existence of a zero in the real part in the forward region close to the origin, in agreement with the prediction of a theorem by A. Martin, with important role in the observed form of $dσ/dt$. Universal value for the position of this zer…
Using a unified analytic representation for the elastic scattering amplitudes of pp scattering valid for all energy region, the behavior of observables in the LHC collisions in the range $\sqrt{s}$= 2.76 - 14 TeV is discussed. Similarly to the case of 7 TeV data, the proposed amplitudes give excellent description of the preliminary 8 TeV data. We discuss the expected energy dependence of the observable quantities, and present predictions for the experiments at 2.76, 13 and 14 TeV.
We study high energy $\small{\rm{pp}}$ and $\small{\rm{\bar {p}p}}$ elastic scattering in the TeV region based on an effective field theory model of the proton. We phenomenologically investigate the main processes underlying elastic scattering and quantitatively describe the measured elastic d$\smallσ$/dt at energies 7.0 TeV (LHC $\small{\rm{pp}}$), 1.96 TeV (Tevatron $\small{\rm{\bar {p}p}}$), and 0.630 TeV (SPS $\small{\rm{\bar {p}p}}$). Finally, we give our prediction for $\small{\rm{pp}}$ elastic d$\smallσ$/dt at 14 TeV that will be measured by the TOTEM Collaboration.
Using a unified analytic representation for the elastic scattering amplitudes of pp scattering valid for all high energy region, the behavior of observables in the LHC collisions in the range $\sqrt{s}$ = 2.76 - 14 TeV is discussed. Similarly to the case of 7 TeV data, the proposed amplitudes give excellent description of the preliminary 8 TeV data. We discuss the expected energy dependence of the observable quantities, and present predictions for the experiments at 2.76, 13 and 14 TeV.
Under the influence of standardly used description of Coulomb-hadronic interference proposed by West and Yennie the protons have been interpreted as transparent objects; elastic events have been interpreted as more central than inelastic ones. It is known that using more general eikonal model the measured elastic data may be interpreted also very differently; elastic processes being more peripheral than inelastic ones. The most ample elastic data set measured at ISR energy of 52.8 GeV have been recently reanalyzed with the help of the eikonal model and new results obtained. The impact of recen…
A precise analysis of the pp elastic scattering data at 7 TeV in terms of its amplitudes is performed as an extension of previous studies for lower energies. Slopes $B_{R}$ and $B_{I}$ of the real and imaginary amplitudes are independent quantities, and a proper expression for the Coulomb phase is used. The real and imaginary amplitudes are fully disentangled, consistently with forward dispersion relations for amplitudes and for slopes. We present analytic expressions for the amplitudes that cover all $t$ range completely, while values of total cross section $σ$, ratio $ρ$, $B_{I}$ and $B_{R}$…
The Bialas-Bzdak model of elastic proton-proton scattering is generalized to the case when the real part of the parton-parton level forward scattering amplitude is non-vanishing. Such a generalization enables the model to describe well the dip region of the differential cross-section of elastic scattering at the ISR energies, and improves significantly the ability of the model to describe also the recent TOTEM data at sqrt{s} = 7 TeV LHC energy. Within this framework, both the increase of the total cross-section, as well as the decrease of the location of the dip with increasing colliding ener…
The data on p$\mathrm{\bar p}$ elastic scattering at 1.8 and 1.96 TeV are analysed in terms of real and imaginary amplitudes, in a treatment with high accuracy, covering the whole t-range and satisfying the expectation of dispersion relation for amplitudes and for slopes. A method is introduced for determination of the total cross section and the other forward scattering parameters and to check compatibility of E-710, CDF and the recent D0 data. Slopes $B_R$ and $ B_I$ of the real and imaginary amplitudes, treated as independent quantities, influence the amplitudes in the whole t-range and are…
With analytical representation for the pp scattering amplitudes introduced and tested at lower energies, a description of high precision is given of the $dσ/dt$ data at $\sqrt{s}$= 13 TeV for all values of the momentum transfer, with explicit identification of the real and imaginary parts. In both $t$ and $b$ coordinates the amplitudes have terms identified as of non-perturbative and perturbative nature, with distinction of their influences in forward and large $|t|$ ranges and in central and peripheral regions respectively. In the forward range, the role of the Coulomb-nuclear interference ph…
In 1970, on purely theoretical grounds, all total hadronic total cross sections were predicted to increase without limit for higher and higher energies. This was contrary to the conventional belief at that time. In 1978, an accurate phenomenological model was formulated for the case of proton-proton and antiproton-proton interactions. The parameters for this model were slightly improved in 1984 using the additional available experimental data. Since then, for thirty years these parameters have not changed. This development, including especially the difficult task of formulating this phenomenol…
Final results of a detailed analysis of p+p elastic scattering data are presented, utilizing the quark-diquark model of protons in a form proposed by Bialas and Bzdak. The differential cross-section of elastic proton-proton collisions is analyzed in a detailed and systematic manner at small momentum transfers, starting from the energy range of CERN ISR at $ \sqrt{s}= 23.5 $ GeV, including also recent TOTEM data at the present LHC energies at $\sqrt{s} = 7$ TeV. These studies confirm the picture that the size of proton increases systematically with increasing energies, while the size of the con…
The measurement of the total $pp$ cross section and its various sub-components (elastic, inelastic and diffractive) is a very powerful tool to understand the proton macro structure and fundamental QCD dynamics. In this contribution I first provide a theoretical introduction to the topic, then a summary of the experimental techniques and finally I review the new results from AUGER and LHC experiments.
We parametrize TOTEM data for the elastic differential pp cross section at sqrt(s)=7 TeV in terms of two exponentials with a relative phase. We employ two previously derived sum rules for pp elastic scattering amplitude in impact parameter space to check whether asymptotia has been reached at the LHC. A detailed study of the TOTEM data for the elastic differential cross section at sqrt(s)=7 TeV is made and it is shown that, within errors, the asymptotic sum rules are satisfied at LHC. We propose to use this parametrization to study forthcoming higher energy data.
Expected precisions of measurements of the elastic scattering cross sections are estimated for $μ^+ μ^+$ and $μ^+ e^-$ colliders, which are recently proposed as future realistic possibilities ($μ$TRISTAN). Comparing with contributions from possible new physics represented by higher dimensional operators, we find that the measurements at a TeV energy $μ^+μ^+$ collider can probe the scale of new physics up to $O(100)$~TeV. A $μ^+ e^-$ collider for the Higgs boson factory can also improve the electroweak precision test.
The TOTEM Collaboration has measured the differential cross section of elastic proton-proton scattering $\mathrm{d}σ/\mathrm{d}|t|$ at $\sqrt{s} = 2.76$, 7, 8, and 13 TeV. It is observed that all $\mathrm{d}σ/\mathrm{d}|t|$ data points vary in the same way as a function of the center-of-mass energy in the so-called "dip" and "bump" regions. These features hint at possible universal properties of elastic scattering. Based on these empirical observations, and taking inspiration from saturation models, we propose a simple scaling law for proton-proton elastic scattering at LHC energies. We find t…
We discuss discrimination of the scattering mechanisms on the basis of functional dependencies of the large-$t$ elastic scattering suggested by the recent data from the TOTEM experiment. It is shown that Orear exponent is in a better agreement with the data than the power-like dependence used by the TOTEM. This implies that the collective dynamics is dominating over the point-like mechanism related to the scattering of the proton constituents.
The TOTEM 2.76, 7, 8, and 13 TeV pp elastic differential cross sections are extrapolated using a data-driven approach to obtain the 1.96 TeV pp elastic cross section. A difference with a 3.4$σ$ significance is observed between the extrapolated pp elastic cross section and the D0 p$\bar{\rm p}$ elastic cross section at 1.96 TeV in the region of the diffractive minimum and the second maximum of the pp cross section, providing evidence for colourless C-odd gluonic exchanges, also denoted as odderon. These results are combined with a TOTEM analysis of the same $t$-channel C-odd exchanges based on …
A new measurement of elastic $pp$ scattering at $\sqrt{s} = 13$ TeV with the ATLAS-ALFA detector is presented. The measurement was performed using data recorded in a special run of the LHC with $β^\star = 2.5$ km. The elastic cross-section was measured differentially in the Mandelstam $t$ variable and from a fit to ${\textrm{d}}σ/\textrm{d}t$ the total cross section, the $ρ$-parameter and parameters of the nuclear slope are determined. The results for $σ_{\textrm{tot}}$ and $ρ$ are \begin{equation*} σ_{\textrm{tot}}(pp\rightarrow X) = \mbox{104.7} \; \pm 1.1 \; \mbox{mb} , \; \; ρ= \mbox{0.098…
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 proto…
In supersymmetric theories, cosmic strings produced in the early Universe often have a width of TeV scale, while the tension is much larger. In a scaling regime, an infinite cosmic string releases significant fraction of its energy in the form of string loops. These thick string loops lose their energies efficiently by particle emissions, and hence it may have effects on cosmological observations. We study cosmological implications of string loops with TeV scale width in detail and derive constraints on the tension of the string. Implications on future gravitational wave detectors are also dis…
The distribution of cosmic rays in the Galaxy at energies above few TeVs is still uncertain and this affects the expectations for the diffuse gamma flux produced by hadronic interactions of cosmic rays with the interstellar gas. We show that the TeV gamma-ray sky can provide interesting constraints. Namely, we compare the flux from the galactic plane measured by Argo-YBJ, HESS, HAWC and Milagro with the expected flux due to diffuse emission and point-like and extended sources observed by HESS showing that experimental data can already discriminate among different hyphoteses for cosmic ray dist…
Recent observations have detected extended TeV gamma-ray emission surrounding young and middle-aged pulsars. The morphology of these "TeV halos" requires cosmic-ray diffusion to be locally suppressed by a factor of ~100-1000 compared to the typical interstellar medium. No model currently explains this suppression. We show that cosmic-ray self-confinement can significantly inhibit diffusion near pulsars. The steep cosmic-ray gradient generates Alfven waves that resonantly scatter the same cosmic-ray population, suppressing diffusion within ~20 pc of pulsars younger than ~100 kyr. In this model,…
The AMS-02 has measured the cosmic ray electron (plus positron) spectrum up to ~TeV with an unprecedent precision. The spectrum can be well described by a power law without any obvious features above 10 GeV. The satellite instrument Dark Matter Particle Explorer (DAMPE), which was launched a year ago, will measure the electron spectrum up to 10 TeV with a high energy resolution. The cosmic electrons beyond TeV may be attributed to few local cosmic ray sources, such as supernova remnants. Therefore, spectral features, such as cutoff and bumps, can be expected at high energies. In this work we g…
I show that pair production on sunlight introduces a sizable anisotropy in the cosmic background of TeV gamma-rays. The anisotropy amplitude in the direction of the Sun exceeds the cosmic dipole anisotropy from the motion of the Sun relative to the cosmic rest-frame.
TeV and Superheavy Mass-Scale Particles from Supersymmetric Topological Defects, the Extragalactic Gamma-ray Background, and the Highest Energy Cosmic Rays
Modern models of high energy elastic hadron-hadron scattering predict an oscillation character of differential cross sections at the LHC energy of 14 TeV and at a sufficiently high momentum transfer. The Totem collaboration did not see the oscillations at 7 TeV. According to some predictions, the oscillations are weak at 7 TeV in the studied 4-momentum transfer range (|t|< 2.5 GeV$^2$). They may be beyond the range of the experiment. But a direct extension of the Totem collaboration data on the pp-scattering at 7 TeV above |t|\sim 2.5 GeV$^2$ contradicts previous measurements. Thus the collabo…
The latest IceCube data suggest that the all-flavor cosmic neutrino flux may be as large as 10^-7 GeV/cm^2/s/sr around 30 TeV. We show that, if sources of the TeV-PeV neutrinos are transparent to gamma rays with respect to two-photon annihilation, strong tensions with the isotropic diffuse gamma-ray background measured by Fermi are unavoidable, independently of the production mechanism. We further show that, if the IceCube neutrinos have a photohadronic (pgamma) origin, the sources are expected to be opaque to 1-100 GeV gamma rays. With these general multimessenger arguments, we find that the …
Measurements of cosmic ray electron+positron spectrum above 10 TeV with ground-based experiments is challenging because of the difficulty of rejection of hadronic extensive air shower background. We study the efficiency of rejection of the hadronic background with water Cherenkov detector array supplemented by muon detection layer. We show that addition of a continuous muon detection layer to the experimental setup allows to achieve a ~ 1e-5 rejection factor for hadronic background at 10 TeV and enables measurement of electron spectrum in 10-100 TeV energy range. We show that measurements of e…
Several cosmic-ray observatories have provided a high accuracy map of the sky at TeV--PeV energies. The data reveals an O(0.1%) deficit from north galactic directions that peaks at 10 TeV and then evolves with the energy, together with other anisotropies at smaller angular scales. Using Boltzmann's equation we derive expressions for the cosmic-ray flux that fit most of these features. The anisotropies depend on the local interstellar magnetic field B_{IS}, on the average galactic field B_{R} in our vicinity, and on the distribution of dominant cosmic-ray sources. We show that the initial dipol…
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 t…
The unitarity condition unambigously requires the Orear region to appear in between the diffraction cone at low transferred momenta and hard parton scattering regime at high transferred momenta in hadron elastic scattering. It originates from rescattering of the diffraction cone processes. It is shown that such region has been observed in the differential cross section of the elastic pp-scattering at \sqrt s=7 TeV. The Orear region is described by exponential decrease with the scattering angle and imposed on it damped oscillations. They explain the steepening at the end of the diffraction cone…
Recently published and preliminary results of the TOTEM experiment are presented, emphasizing a recent discovery of a non-exponential behaviour of the differential cross-section of elastic proton-proton scattering, that TOTEM measured with an unprecedented precision at the centre-of-mass energy $\sqrt{s}$ = 8 TeV based on a high-statistics data sample obtained with the $β_* = 90$ m optics of CERN LHC. Both the statistical and systematic uncertainties remained below 1%, except for the t-independent contribution from the overall normalisation. This measurement allowed TOTEM to exclude a purely e…
Observations have shown that spatially extended "TeV halos" are a common (and potentially generic) feature surrounding young and middle-aged pulsars. However, their morphology is not understood. They are larger than the "compact" region where the stellar remnant dominates the properties of the interstellar medium, but smaller than expected in models of cosmic-ray diffusion through the standard interstellar medium. Several explanations have been proposed, but all have shortcomings. Here, we revisit a class of models where the cosmic-ray gradient produced by the central source induces a streamin…
Several experiments have reported regions in the TeV sky with an excess of cosmic rays. Here we consider the possibility that the excess cosmic rays are coming from dark matter annihilation in nearby subhalos. We provide motivation for dark matter as the source of the excess and show that dark matter annihilations can naturally produce the cosmic ray anisotropy without the need for exotic dark matter models. We show that viable dark matter explanations of the cosmic ray excess are consistent with current measurements of antiprotons, positrons, and gamma-rays. Additionally, we show that the dar…
We report the analysis of the $10-1000$ TeV large-scale sidereal anisotropy of Galactic cosmic rays (GCRs) with the data collected by the Tibet Air Shower Array from October, 1995 to February, 2010. In this analysis, we improve the energy estimate and extend the declination range down to $-30^{\circ}$. We find that the anisotropy maps above 100 TeV are distinct from that at multi-TeV band. The so-called "tail-in" and "loss-cone" features identified at low energies get less significant and a new component appears at $\sim100$ TeV. The spatial distribution of the GCR intensity with an excess (7.…
Constraining the behavior of cosmic ray data observed at Earth requires a precise understanding of how the cosmic rays propagate in the interstellar medium. The interstellar medium is not homogeneous; although turbulent magnetic fields dominate over large scales, small coherent regions of magnetic field exist on scales relevant to particle propagation in the nearby Galaxy. Guided propagation through a coherent field is significantly different from random particle diffusion and could be the explanation of spatial anisotropies in the observed cosmic rays. We present a Monte Carlo code to propaga…
Predicting Proton-Air Cross Sections at sqrt s ~30 TeV, using Accelerator and Cosmic Ray Data
我们使用高能量的预测QCD启发的参数化的所有加速器数据的前向质子-质子和反质子-质子散射振幅，随着格劳伯理论，预测质子-空气截面在能量接近\sqrt s \approx 30 TeV。质子-质子截面的参数化结合了解析性和么正性，并要求渐近质子是软部分子的黑色圆盘。通过与p-air宇宙线测量结果的比较，我们的分析结果在包容粒子产生截面的约束。
