The TOTEM Experiment will measure the total pp cross-section with the luminosity-independent method and study elastic and diffractive scattering at the LHC. To achieve optimum forward coverage for charged particles emitted by the pp collisions in the interaction point IP5, two tracking telescopes, T1 and T2, will be installed on each side in the pseudorapidity region 3.1 ≤ |η| ≤ 6.5, and Roman Pot stations will be placed at distances of ±147 m and ±220 m from IP5. Being an independent experiment but technically integrated into CMS, TOTEM will first operate in standalone mode to pursue its own physics programme and at a later stage together with CMS for a common physics programme. This article gives a description of the TOTEM apparatus and its performance.

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The TOTEM Experiment at the CERN Large Hadron Collider

In this brief review, a description of the observed evidence for neutrinoless double beta3–5 in the 76Ge experiment in Gran Sasso (Heidelberg–Moscow experiment) which has been operated with 11 kg enriched 76Ge detectors in the period 1990–2003, is provided. Two different methods of pulse shape analysis have been used to select potential 0νββ events from the γ background of the measured spectrum — a selection by a neuronal net approach,3,4,16 and a selection by a new method comparing measured pulses with a library of pulse shapes of point-like events calculated from simulation of the electric field distribution in the detectors (see Refs. 6–8 and 37). The latter method also allows spatial localization of measured events. Both methods lead to selections of events at Qββ with almost no γ-background. The observed line at Qββ is identified as a 0νββ signal. It has a confidence level of more than 6σ.

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The evidence for the observation of 0ν beta beta decay: The identification of 0ν beta beta events from the full spectra.

Current status of the relativistic two nucleon one boson exchange potential

Particle Physics and Introduction to Field Theory

The eikonal approximation for high-energy collisions, long familiar in the theory of potential scattering, is considered from the viewpoint of relativistic quantum field theory. We study, in particular, the Feynman amplitude $M(s, t)$ describing the scattering of two spin-0 particles, $a$ and $b$, interacting by the exchange of spin-0 mesons. We show that if ${M}_{n}(s, t)$, the contribution to $M(s, t)$ arising from all $n\mathrm{th}$-order Feynman diagrams in which exactly $n$ mesons are exchanged between $a$ and $b$, is written in an appropriately symmetrized way, and if the terms in any $a$ or $b$ particle propagator which are quadratic in the internal momenta are then dropped, the resulting expression, ${{M}_{n}}^{\mathrm{eik}}(s, t)$, may be evaluated in closed form, and the sum over $n$, which defines ${M}^{\mathrm{eik}}(s, t)$, may be carried out. The representation of ${M}^{\mathrm{eik}}(s, t)$ found in this way involves the exponential of a function $\ensuremath{\chi}$ of a relative space-time variable $x=({x}^{0}, \mathrm{x})$ and the external momenta; $\ensuremath{\chi}$ is a relativistic generalization of the eikonal ${\ensuremath{\chi}}_{\mathrm{pot}}$ familiar from the theory of high-energy potential scattering. ${M}^{\mathrm{eik}}(s, t)$ is both crossing-symmetric and time-reversal-invariant. In the static limit (${m}_{b}\ensuremath{\rightarrow}\ensuremath{\infty}$), $\ensuremath{\chi}$ tends to ${\ensuremath{\chi}}_{\mathrm{pot}}$ for the appropriate Yukawa potential and ${f}^{\mathrm{eik}}=\ensuremath{-}\frac{{M}^{\mathrm{eik}}}{8\ensuremath{\pi}\ensuremath{\surd}s}$ has a limiting form ${{f}_{\mathrm{pot}}}^{\mathrm{eik}}$, which we also derive directly from the theory of potential scattering; for small scattering angles, ${{f}_{\mathrm{pot}}}^{\mathrm{eik}}$ coincides with the standard result. The amplitude for particle-antiparticle scattering is studied in the same model. It is shown that the eikonal ${\ensuremath{\chi}}_{2}(x)$ associated with the contribution of all annihilation-type diagrams has a logarithmic singularity at $x=0$ whose coefficient is proportional to $\ensuremath{\alpha}(t)+1$, where $\ensuremath{\alpha}(t)$ is the Regge-trajectory function obtained from the asymptotic behavior of the ladder-type diagrams alone. Another connection with Regge behavior is made by showing that the summation of a certain infinite class of radiative corrections to the lowest-order $\ensuremath{\gamma}\ensuremath{-}e$ Compton amplitude gives rise, in our eikonal approximation, to an eikonal $\ensuremath{\chi}(x)$ which has a similar logarithmic singularity with strength $1+\ensuremath{\beta}(t)$; here $\ensuremath{\beta}(t)$ is the trajectory function, introduced less directly in earlier work, which reproduces the major part of the spectrum of positronium on setting $\ensuremath{\beta}(t)=l=n\ensuremath{-}1$. A generalization of a simple algebraic identity used in the derivation of the above results, in the form of an integral representation, permits their extension to the case where one or more particles are off the mass shell. This is illustrated by a computation of an eikonal-type approximation to the Green's function for a relativistic particle moving in an external scalar field and by the summation of an infinite class of contributions to the vertex function in the model referred to above. The possibility of applying an off-shell eikonal approximation to the analysis of production processes is emphasized.

Eikonal Approximation in Quantum Field Theory

High energy pp and elastic scattering carried out at CERN ISR and SPS Collider and at Fermilab Tevatron are studied first in a model where the nucleon has an outer cloud and an inner core. Elastic scattering is viewed as primarily due to two processes: (a) diffraction scattering originating from cloud–cloud interaction; (b) a hard or large |t| scattering originating from one nucleon core scattering off the other via vector meson ω exchange, while their outer clouds interact independently. For small |t| diffraction dominates, but the hard scattering takes over as |t| increases. The ω-exchange amplitude shows that ω behaves like an elementary vector meson at high energy, contrary to a regge pole behavior. This behavior, however, can be understood in the nonlinear σ-model where ω couples to a topological baryonic current like a gauge boson, and the nucleon is described as a topological soliton. Further investigation shows that the underlying effective field theory model is a gauged Gell-Mann–Levy type linear σ-model that has not only the pion sector and the Wess–Zumino–Witten action of the nonlinear σ-model, but also a quark sector where quarks and antiquarks interact via a scalar field. The scalar field vanishes near the center of the nucleon, but rises sharply at some critical distance to its vacuum value fπ leading to a condensate analogous to a BCS condensate in superconductivity. The nucleon structure that emerges then is that the nucleon has an outer cloud of condensed ground state, an inner core of topological baryonic charge probed by ω, and a still smaller quark-bag containing massless valence quarks. Large |t|pp elastic scattering is attributed to valence quark–quark elastic scattering, which is taken to be due to the hard pomeron (BFKL pomeron with next to leading order corrections). The parameters in the model are determined by requiring that they satisfactorily describe the known asymptotic behavior of σtot(s) and ρ(s), and the measured at , 630 GeV, and 1.8 TeV. The model is then used to predict pp elastic differential cross-section at LHC at and |t| = 0–10 GeV2. Our predicted dσ/dt at 14 TeV is found to be very different from those predicted by the impact-picture model and the eikonalized pomeron–reggeon model. Precise measurement of dσ/dt at LHC by the TOTEM group will be able to distinguish between these models. If our predicted dσ/dt is quantitatively confirmed, then it will indicate that various novel ideas developed to describe the nucleon combine and lead to a unique physical description of its structure.

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NEAR FORWARD pp ELASTIC SCATTERING AT LHC AND NUCLEON STRUCTURE

High energy elastic $p p$ scattering at the Large Hadron Collider (LHC) at c.m. energy 14 TeV is predicted using the asymptotic behavior of $\sigma_{tot}(s)$ and $\rho(s)$ known from dispersion relation calculations and the measured elastic $\bar p p$ differential cross section at $\sqrt{s} = 546 {\rm GeV}$. The effective field theory model underlying the phenomenological analysis describes the nucleon as having an outer cloud of quark-antiquark condensed ground state, an inner core of topological baryonic charge of radius $\simeq 0.44F$ and a still smaller valence quark-bag of radius $\lesssim 0.1 {\rm F}$. The LHC experiment TOTEM (Total and Elastic Measurement), if carried out with sufficient precision from $|t| = 0$ to $|t| > 10 {\rm GeV^2}$, will be able to test this structure of the nucleon.

p p Elastic Scattering at LHC and Nucleon Structure

High energy elastic pp scattering at the Large Hadron Collider (LHC) at c.m. energy 14 TeV is predicted using the asymptotic behavior of σtot(s) and ρ(s) known from dispersion relation calculations and the measured elastic $\bar{p}p$ differential cross-section at $\sqrt{s}=546~{\rm GeV}$. The effective field theory model underlying the phenomenological analysis describes the nucleon as having an outer cloud of quark–antiquark condensed ground state, an inner core of topological baryonic charge of radius ≃ 0.44 F and a still smaller valence quark-bag of radius ≲ 0.1 F. The LHC experiment TOTEM (Total and Elastic Measurement), if carried out with sufficient precision from |t| = 0 to |t| > 10 GeV2, will be able to test this structure of the nucleon.

pp ELASTIC SCATTERING AT LHC AND NUCLEON STRUCTURE

Deep-elastic pp scattering at c.m. energy 14 TeV at LHC in the momentum transfer range 4 GeV2 ≲ |t| ≲ 10 GeV2 is planned to be measured by the TOTEM group. We study this process in a model where the deep-elastic scattering is due to a single hard collision of a valence quark from one proton with a valence quark from the other proton. The hard collision originates from the low-x gluon cloud around one valence quark interacting with that of the other. The low-x gluon cloud can be identified as color glass condensate and has size ≃0.3 F. Our prediction is that pp dσ/dt in the large |t| region decreases smoothly as momentum transfer increases. This is in contrast to the prediction of pp dσ/dt with visible oscillations and smaller cross sections by a large number of other models.

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DEEP-ELASTIC pp SCATTERING AT LHC FROM LOW-x GLUONS

A relativistic eikonal amplitude for the generalized ladder diagrams with radiative corrections to all orders is derived. The connection between this approach and the graphical analysis of infra-red divergence in quantum eleetrodynamics is explicitly exhibited. The discrepancy between the Levy-Sucher formula and that of Schiff is resolved. Inclusion of radiative corrections due to nonsoft mesons at the vertices of a hard interaction is investigated, and the difference with results obtained by other authors is noted.

M. M. Islam

Papers

NEAR FORWARD pp ELASTIC SCATTERING AT LHC AND NUCLEON STRUCTURE

p p Elastic Scattering at LHC and Nucleon Structure

pp ELASTIC SCATTERING AT LHC AND NUCLEON STRUCTURE

DEEP-ELASTIC pp SCATTERING AT LHC FROM LOW-x GLUONS

Relativistic eikonal amplitude and radiative corrections