<p>We present a study of the central exclusive production (CEP) of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>η</mi></mrow><mrow><mo>′</mo></mrow></msup><mo stretchy="false">(</mo><mn>958</mn><mo stretchy="false">)</mo></mrow></math> mesons in diffractive proton-proton collisions at high energies. The amplitudes, including pomeron and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mrow><mn>2</mn><mi mathvariant="double-struck">R</mi></mrow></msub></math> reggeon exchanges, are calculated within the tensor-pomeron model. Absorption effects are also taken into account at the amplitude level. We fit some undetermined model parameters (coupling constants and cutoff parameters in form factors) to the WA102 experimental data and then make predictions for the LHC energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msqrt><mrow><mi>s</mi></mrow></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></mrow></math>. Both total cross sections and several differential distributions are presented. For <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi><mo stretchy="false">→</mo><mi>p</mi><mi>p</mi><mi>η</mi></math>, we find an upper limit for the total cross section of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2.5</mn><mtext> </mtext><mtext> </mtext><mi mathvariant="normal">μ</mi><mi mathvariant="normal">b</mi></mrow></math> for pseudorapidity of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> meson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">|</mo><msub><mrow><mi>η</mi></mrow><mrow><mi>M</mi></mrow></msub><mo stretchy="false">|</mo><mo>&lt;</mo><mn>1</mn></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>5.6</mn><mtext> </mtext><mtext> </mtext><mi mathvariant="normal">μ</mi><mi mathvariant="normal">b</mi></mrow></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>&lt;</mo><msub><mrow><mi>η</mi></mrow><mrow><mi>M</mi></mrow></msub><mo>&lt;</mo><mn>5</mn></mrow></math>. For <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi><mo stretchy="false">→</mo><mi>p</mi><mi>p</mi><msup><mi>η</mi><mo>′</mo></msup></math>, we predict the cross section to be in the range of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>0.3</mn><mi>–</mi><mn>0.7</mn><mtext> </mtext><mtext> </mtext><mi mathvariant="normal">μ</mi><mi mathvariant="normal">b</mi></mrow></math> for pseudorapidity of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mo>′</mo></msup></math> meson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>η</mi><mi>M</mi></msub><mo stretchy="false">|</mo><mo>&lt;</mo><mn>1</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>0.9</mn><mi>–</mi><mn>2.1</mn><mtext> </mtext><mtext> </mtext><mi mathvariant="normal">μ</mi><mi mathvariant="normal">b</mi></mrow></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mo>&lt;</mo><msub><mi>η</mi><mi>M</mi></msub><mo>&lt;</mo><mn>5</mn></math>. This opens the possibility to study diffractive production of pseudoscalar mesons in experiments at the LHC. We discuss if there are arguments from SU(3)-flavor symmetry which would forbid pomeron-pomeron fusion giving an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> meson. In our opinion such arguments do not exist. We also consider CEP of the pseudoscalars <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mo>′</mo></msup><mo stretchy="false">(</mo><mn>958</mn><mo stretchy="false">)</mo></math> and the pseudovector meson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1285</mn><mo stretchy="false">)</mo></math> in diffractive proton-proton collisions in a theory with a scalar pomeron. We show that none of these particles can be produced in this way in the scalar-pomeron theory. Thus, experimental observation of any of these particles in the above CEP processes at the LHC would give striking evidence against a scalar character of the pomeron.</p>

Poland

Piotr Lebiedowicz

Germany

Otto Nachtmann

Antoni Szczurek

Central exclusive production of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mo>′</mo></msup></math> mesons in diffractive proton-proton collisions at the LHC within the tensor-pomeron approach

We discuss the reactions <math><mi>π</mi><mi>p</mi><mo>→</mo><mi>π</mi><mi>p</mi></math> and <math><mi>π</mi><mi>p</mi><mo>→</mo><mi>π</mi><mi>p</mi><mi>γ</mi></math> from a general quantum field theory (QFT) point of view, describing these reactions in QCD and lowest relevant order of electromagnetism. We consider the pion-proton elastic scattering both off shell and on shell. The on-shell amplitudes for <math><msup><mi>π</mi><mo>±</mo></msup><mi>p</mi><mo>→</mo><msup><mi>π</mi><mo>±</mo></msup><mi>p</mi></math> scattering are described by two invariant amplitudes, while the off-shell amplitudes contain eight invariant amplitudes. We study the photon emission amplitudes in the soft-photon limit where the center-of-mass photon energy <math><mi>ω</mi><mo>→</mo><mn>0</mn></math>. The Laurent expansion in <math><mi>ω</mi></math> of the <math><msup><mi>π</mi><mo>±</mo></msup><mi>p</mi><mo>→</mo><msup><mi>π</mi><mo>±</mo></msup><mi>p</mi><mi>γ</mi></math> amplitudes is considered and the terms of the orders <math><msup><mi>ω</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> and <math><msup><mi>ω</mi><mn>0</mn></msup></math> are derived. These terms can be expressed by the on-shell invariant amplitudes and their partial derivatives with respect to <math><mi>s</mi></math> and <math><mi>t</mi></math>. The pole term <math><mo>∝</mo><msup><mi>ω</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> in the amplitudes corresponds to Weinberg’s soft-photon theorem and is well known from the literature. We derive the next-to-leading term <math><mo>∝</mo><msup><mi>ω</mi><mn>0</mn></msup></math> using only rigorous methods of QFT. We give the relation of the Laurent series for <math><msup><mi>π</mi><mn>0</mn></msup><mi>p</mi><mo>→</mo><msup><mi>π</mi><mn>0</mn></msup><mi>p</mi><mi>γ</mi></math> and Low’s soft-photon theorem. Our formulas for the amplitudes in the limit <math><mi>ω</mi><mo>→</mo><mn>0</mn></math> are valid for photon momentum <math><mi>k</mi></math> satisfying <math><msup><mi>k</mi><mn>2</mn></msup><mo>≥</mo><mn>0</mn></math>, <math><msup><mi>k</mi><mn>0</mn></msup><mo>=</mo><mi>ω</mi><mo>≥</mo><mn>0</mn></math>, that is, for both real and virtual photons. Here we consider a limit where with <math><mi>ω</mi><mo>→</mo><mn>0</mn></math> we have also <math><msup><mi>k</mi><mn>2</mn></msup><mo>→</mo><mn>0</mn></math>. We discuss the behavior of the corresponding cross sections for <math><msup><mi>π</mi><mo>−</mo></msup><mi>p</mi><mo>→</mo><msup><mi>π</mi><mo>−</mo></msup><mi>p</mi><mi>γ</mi></math> with respect to <math><mi>ω</mi></math> for <math><mi>ω</mi><mo>→</mo><mn>0</mn></math>. We consider cross sections for unpolarized as well as polarized protons in the initial and final states.

Soft-photon theorem for pion-proton elastic scattering revisited

We investigate the photon emission in pion-pion and pion-proton scattering in the soft-photon limit where the photon energy <math><mi>ω</mi><mo>→</mo><mn>0</mn></math>. The expansions of the <math><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup><mo>→</mo><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup><mi>γ</mi></math> and the <math><msup><mi>π</mi><mo>±</mo></msup><mi>p</mi><mo>→</mo><msup><mi>π</mi><mo>±</mo></msup><mi>p</mi><mi>γ</mi></math> amplitudes, satisfying the energy-momentum relations, to the orders <math><msup><mi>ω</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> and <math><msup><mi>ω</mi><mn>0</mn></msup></math> are derived. We show that these terms can be expressed completely in terms of the on-shell amplitudes for <math><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup><mo>→</mo><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math> and <math><msup><mi>π</mi><mo>±</mo></msup><mi>p</mi><mo>→</mo><msup><mi>π</mi><mo>±</mo></msup><mi>p</mi></math>, respectively, and their partial derivatives with respect to <math><mi>s</mi></math> and <math><mi>t</mi></math>. The structure term which is nonsingular for <math><mi>ω</mi><mo>→</mo><mn>0</mn></math> is determined to the order <math><msup><mi>ω</mi><mn>0</mn></msup></math> from the gauge-invariance constraint using the generalized Ward identities for pions and the proton. For the reaction <math><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup><mo>→</mo><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup><mi>γ</mi></math> we discuss in detail the soft-photon theorems in the versions of both Low and Weinberg. We show that these two versions are different and must not be confounded. Weinberg’s version gives the pole term of a Laurent expansion in <math><mi>ω</mi></math> of the amplitude for <math><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup><mo>→</mo><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup><mi>γ</mi></math> around the phase-space point of zero radiation. Low’s version gives an approximate expression for the above amplitude at a fixed phase-space point, corresponding to nonzero radiation. Clearly, the leading and next-to-leading terms in theses two approaches must be, and are indeed, different. We show their relation. We also discuss the expansions of differential cross sections for <math><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup><mo>→</mo><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup><mi>γ</mi></math> with respect to <math><mi>ω</mi></math> for <math><mi>ω</mi><mo>→</mo><mn>0</mn></math>.

Different versions of soft-photon theorems exemplified at leading and next-to-leading terms for pion-pion and pion-proton scattering

In this study, we carry out a non-perturbative approach to a quantum Otto engine, employing an Unruh-DeWitt particle detector to extract work from a quantum Klein-Gordon field in an arbitrary globally hyperbolic curved spacetime. We broaden the scope by considering the field in any quasi-free state, which includes vacuum, thermal, and squeezed states. A key aspect of our method is the instantaneous interaction between the detector and the field, which enables a thorough non-perturbative analysis. We demonstrate that the detector can successfully extract positive work from the quantum Otto cycle, even when two isochoric processes occur instantaneously, provided the detector in the second isochoric process receives a signal from the first interaction. This signaling allows the detector to release heat into the field, thereby the thermodynamic cycle is completed. As a demonstration, we consider a detector at rest in flat spacetime and compute the work extracted from the Minkowski vacuum state.

Japan

Kensuke Gallock-Yoshimura

Relativistic quantum Otto engine: instant work extraction from a quantum field

We evaluate the cross section for diffractive bremsstrahlung of a single photon in the <math><mi>p</mi><mi>p</mi><mo>→</mo><mi>p</mi><mi>p</mi><mi>γ</mi></math> reaction at high energies and at forward photon rapidities. Several differential distributions, for instance, in y, <math><msub><mrow><mi>k</mi></mrow><mrow><mo>⊥</mo></mrow></msub></math> and ω, the rapidity, the absolute value of the transverse momentum, and the energy of the photon, respectively, are presented. We compare the results for our standard approach, based on QFT and the tensor-pomeron model, with two versions of soft-photon-approximations, SPA1 and SPA2, where the radiative amplitudes contain only the leading terms proportional to <math><msup><mrow><mi>ω</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. The SPA1, which does not have the correct energy-momentum relations, performs surprisingly well in the kinematic range considered. We discuss also azimuthal correlations between outgoing particles. The azimuthal distributions are not isotropic and are different for our standard model and SPAs. We discuss also the possibility of a measurement of two-photon-bremsstrahlung in the <math><mi>p</mi><mi>p</mi><mo>→</mo><mi>p</mi><mi>p</mi><mi>γ</mi><mi>γ</mi></math> reaction. In our calculations we impose a cut on the relative energy loss (<math><mn>0.02</mn><mo>&lt;</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>&lt;</mo><mn>0.1</mn></math>, <math><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></math>) of the protons where measurements by the ATLAS Forward Proton (AFP) detectors are possible. The AFP requirement for both diffractively scattered protons and one forward photon (measured at LHCf) reduces the cross section for <math><mi>p</mi><mi>p</mi><mo>→</mo><mi>p</mi><mi>p</mi><mi>γ</mi></math> almost to zero. On the other hand, much less cross-section reduction occurs for <math><mi>p</mi><mi>p</mi><mo>→</mo><mi>p</mi><mi>p</mi><mi>γ</mi><mi>γ</mi></math> when photons are emitted in opposite sides of the ATLAS interaction point and can be measured by two different arms of LHCf. For the SPA1 ansatz we find <math><mi>σ</mi><mo>(</mo><mi>p</mi><mi>p</mi><mo>→</mo><mi>p</mi><mi>p</mi><mi>γ</mi><mi>γ</mi><mo>)</mo><mo>≃</mo><mn>0.03</mn></math> nb at <math><msqrt><mrow><mi>s</mi></mrow></msqrt><mo>=</mo><mn>13</mn></math> TeV and with the cuts <math><mn>0.02</mn><mo>&lt;</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>&lt;</mo><mn>0.1</mn></math>, <math><mn>8.5</mn><mo>&lt;</mo><msub><mrow><mi>y</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>&lt;</mo><mn>9</mn></math>, <math><mo>−</mo><mn>9</mn><mo>&lt;</mo><msub><mrow><mi>y</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>&lt;</mo><mo>−</mo><mn>8.5</mn></math>. Our predictions can be verified by ATLAS and LHCf combined experiments. We discuss also the role of the <math><mi>p</mi><mi>p</mi><mo>→</mo><mi>p</mi><mi>p</mi><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup></math> background for single photon production.

Exclusive diffractive bremsstrahlung of one and two photons at forward rapidities: Possibilities for experimental studies in collisions at the LHC

We discuss central-exclusive production (CEP) of photons via different fusion processes in the reaction <math><mi>p</mi><mi>p</mi><mo>→</mo><mi>p</mi><mi>p</mi><mi>γ</mi></math> at high energies, available at RHIC and LHC, within the tensor-Pomeron model. We consider two types of processes, the photoproduction contribution via the photon-Pomeron and photon-Reggeon fusion reactions, and the purely diffractive contribution via the Reggeon-Pomeron and Odderon-Pomeron fusion reactions. We present predictions for the measurements of photons at midrapidity, <math><mo>|</mo><mi>y</mi><mo>|</mo><mo>&lt;</mo><mn>2.5</mn></math>, and at relatively low transverse momentum, <math><mn>0.1</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>&lt;</mo><msub><mi>k</mi><mo>⊥</mo></msub><mo>&lt;</mo><mn>1</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. To check the main results of our study the measurement of the outgoing protons is not necessary. This is of relevance, e.g., for the present version of the ALICE detector at the LHC. Several differential distributions, for instance, in y, <math><msub><mi>k</mi><mo>⊥</mo></msub></math>, and <math><mi>ω</mi></math>, the rapidity, the absolute value of the transverse momentum, and the energy of the photon, respectively, are presented. We show that the photoproduction is an important process in the kinematic region specified above. There it gives a much larger cross section than diffractive bremsstrahlung where the basic <math><mi>p</mi><mi>p</mi><mo>→</mo><mi>p</mi><mi>p</mi></math> reaction is due to strong interaction diffraction. This is remarkable as the CEP cross section is of order <math><msubsup><mi>α</mi><mrow><mi>em</mi></mrow><mn>3</mn></msubsup></math> whereas the bremsstrahlung one is only of order <math><msub><mi>α</mi><mrow><mi>em</mi></mrow></msub></math>. On the other hand, the soft-photon bremsstrahlung is more important than CEP in the forward rapidity range, <math><mo>|</mo><mi>y</mi><mo>|</mo><mo>&gt;</mo><mn>4</mn></math>, and/or at very low <math><msub><mi>k</mi><mo>⊥</mo></msub></math>. We leave it as a challenge for the planned ALICE 3 experiment at the LHC to study these two contributions to soft photon production in <math><mi>p</mi><mi>p</mi></math> collisions. This could shed new light on the so-called “soft photon puzzle” in hadron-hadron collisions.

Central exclusive diffractive production of a single photon in high-energy proton-proton collisions within the tensor-Pomeron approach

The two-tensor-pomeron model proposed previously to describe low x DIS data is applied to real and virtual Compton scattering on a proton. The model includes two tensor pomerons, a soft and a hard one, and tensor reggeons. We include contributions of both transverse and longitudinal virtual photons. We show that this model gives a very good description of experimental data at small Bjorken x on deeply virtual Compton scattering (DVCS) from HERA. The reggeon exchange term is particularly relevant for describing the real-photon-proton scattering measured at lower γp energies at FNAL. We present two fits which differ somewhat in the strength of the hard pomeron contribution. In both fits we find that the interference between soft- and hard-pomeron exchange plays an important role. We find that in DVCS the soft-pomeron contribution is considerable up to <math><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>∼</mo><mn>20</mn></math> GeV$^{2}$. Our model allows to study the transition from the small-<math><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup></math> regime, including the photoproduction (<math><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>0</mn></math>) limit, to the large-<math><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup></math> regime, the DIS limit. We also discuss the ratio of cross sections for longitudinally and transversely polarized virtual photons in <math><msup><mrow><mi>γ</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mi>p</mi><mo>→</mo><mi>γ</mi><mi>p</mi></math> as a function of <math><mo>|</mo><mi>t</mi><mo>|</mo></math> and <math><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup></math>. The ratio <math><mover><mrow><mi>R</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><msup><mrow><mi>W</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mi>t</mi><mo>)</mo><mo>=</mo><mo>(</mo><mi>d</mi><msub><mrow><mi>σ</mi></mrow><mrow><mi>L</mi></mrow></msub><mo>/</mo><mi>d</mi><mi>t</mi><mo>)</mo><mo>/</mo><mo>(</mo><mi>d</mi><msub><mrow><mi>σ</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>/</mo><mi>d</mi><mi>t</mi><mo>)</mo></math> strongly increases with t. Our findings may be checked in future lepton-nucleon scattering experiments in the low-x regime, for instance, at a future Electron-Ion Collider at the BNL (EIC), and, if LHeC is realized, at the LHC.

Deeply virtual Compton scattering in the tensor-pomeron approach

We introduce a new model of relativistic quantum analogue of the classical Otto engine in the presence of a perfectly reflecting boundary. A single qubit acts as the working substance interacting with a massless quantum scalar field, with the boundary obeying the Dirichlet condition. The quantum vacuum serves as a thermal bath through the Unruh effect. We observe that the response function of the qubit gets significantly modified by the presence of the reflecting boundary. From the structure of the correlation function, we find that three different cases emerge, namely, the intermediate boundary regime, the near boundary regime, and the far boundary regime. As expected, the correlation in the far boundary regime approaches that of the Unruh quantum Otto engine (UQOE) when the reflecting boundary goes to infinity. The effect of the reflecting boundary is manifested through the reduction of the critical excitation probability of the qubit and the work output of the engine. Inspite of the reduced work output, the efficiency of the engine remains unaltered even in the presence of the boundary.

India

Arnab Mukherjee

Sunandan Gangopadhyay

A. Majumdar

Unruh quantum Otto engine in the presence of a reflecting boundary

We discuss diffractive processes in proton-proton collisions at small momentum transfers without and with photon radiation. We consider the soft exclusive reactions <math><mi>p</mi><mi>p</mi><mo>→</mo><mi>p</mi><mi>p</mi></math>, <math><mi>p</mi><mover><mi>p</mi><mo>¯</mo></mover><mo>→</mo><mi>p</mi><mover><mi>p</mi><mo>¯</mo></mover></math>, and <math><mi>p</mi><mi>p</mi><mo>→</mo><mi>p</mi><mi>p</mi><mi>γ</mi></math> within the tensor-Pomeron and vector-odderon approach. We compare our results with the data for <math><mi>p</mi><mi>p</mi></math> and <math><mi>p</mi><mover><mi>p</mi><mo>¯</mo></mover></math> total cross sections, for the ratio of real to imaginary parts of the forward scattering amplitude, and for the elastic <math><mi>p</mi><mi>p</mi></math> cross sections, especially those from TOTEM. To describe the low-energy data more accurately, the secondary reggeons must be included. We write down the amplitudes for the photon bremsstrahlung in high-energy proton-proton collisions using the tensor-Pomeron model. These results are relevant for the c.m. energies presently available at the Relativistic Heavy Ion Collider and at the LHC. We present predictions for the proposed measurements of soft photons with the planned future upgrade of the ALICE experiment at the LHC. We investigate the limits of applicability of the soft-photon approximation (SPA) based on Low’s theorem. The corresponding SPA results are compared to those obtained from our complete model. The regions of phase space are given quantitatively where SPA and our complete tensor-Pomeron results are close to each other. As an example, let <math><msub><mi>k</mi><mo>⊥</mo></msub></math>, <math><mi>y</mi></math>, and <math><mi>ω</mi></math>, be the absolute value of the transverse momentum, the rapidity, and the energy of the photon, respectively, in the overall c.m. system. For the region <math><mn>1</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>&lt;</mo><msub><mi>k</mi><mo>⊥</mo></msub><mo>&lt;</mo><mn>100</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> and <math><mrow><mn>3.5</mn><mo>&lt;</mo><mo>|</mo><mi>y</mi><mo>|</mo><mo>&lt;</mo><mn>5.0</mn></mrow></math>, we find that the SPA Ansatz with only the pole terms <math><mo>∝</mo><msup><mi>ω</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> agrees at the percent level with our complete model result up to <math><mi>ω</mi><mo>≅</mo><mn>2</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>.

Soft-photon radiation in high-energy proton-proton collisions within the tensor-Pomeron approach: Bremsstrahlung

Uniformly accelerated frame mimics a thermal bath whose temperature is proportional to the proper acceleration. Using this phenomenon we give a detailed construction of an Otto cycle between two energy eigenstates of a system, consists of two entangled qubits. In the isochoric stages the thermal bath is being provided via the vacuum fluctuations of the background field for a monopole interaction by accelerating them. We find that making of Otto cycle is possible when one qubit is accelerating in the right Rindler wedge and other one is moving in the left Rindler wedge; i.e. in anti-parallel motion, with the initial composite state is a non-maximally entangled one. However, the efficiency greater than that of the usual single qubit quantum Otto engine is not possible. We provide values of the available parameters which make Otto cycle possible. On the other hand, Otto cycle is not possible if one considers the non-maximally entangled state for parallel motion. Moreover, for both initial symmetric and anti-symmetric Bell states we do not find any possibility of the cycle for qubits’ parallel and anti-parallel motion.