The Primakoff reaction study for pion polarizability measurement at COMPASS

The electromagnetic structure of charged pions can be described by the electric (α_π) and magnetic (β_π) polarizabilities that depend on the rigidity of pion’s internal structure as a composite particle. It is shown that the values of α_π and β_π can be precisely measured via the Primakoff reaction π⁻ + (A, Z) → π⁻ + (A, Z) + γ in the COMPASS experiment at CERN.     

Measurement of electric and magnetic polarizabilities with Primakoff reaction at COMPASS

The COMPASS spectrometer is well suited to perform precise measurements of the pion polarizabilities via the Primakoff reaction π(Z,A)→π+(Z,A)+ψ. The electric\((\bar \alpha _\pi )\) and magnetic\((\bar \beta _\pi )\) polarizabilities characterize the response of the response of the pion quark substructure to the electromagnetic field of the ψ during the πψ scattering. The results of a simulation for the foreseen 2004 setup are presented. The measurement of the pion polarizabilities allows for a test of the chiral perturbation theory (χPT) predictions.     

Cross-sections for low-energy πgamma; reactions

We review the cross-sections for low-energy π^-γ reactions in the framework of chiral perturbation theory. Charged-pion Compton scattering, π^-γ → π^-γ , is considered up to one-loop order where the pion's internal structure enters through the difference of the electric and magnetic pion polarizability, α_π - β_π . The ongoing COMPASS experiment aims at measuring this important structure constant with high statistics using the Primakoff effect. In the same way, the reaction π^-γ → π^-π⁰ serves as a test of the QCD chiral anomaly (via the γ3π -coupling constant F _γ3π . Furthermore, we calculate the total cross-sections for neutral and charged pion-pair production, π^-γ → π^-π⁰π⁰ and π^-γ → π^-π⁺π^- , which are governed by the chiral ππ -interaction. Finally, we investigate the radiative (correction) process π^-γ → π^-γγ and calculate the corresponding two-photon mass spectrum. This information will be useful for analyzing the π^- Primakoff scattering events with photons in the final state.     

New limits on Primakoff production of hybrid mesons

I discuss constraints on properties of isoscalarJ ^PC =1^?+ exotic hybrid mesons, assuming their dominant decay mode is ηπ. This work expands on a similar study by the Rochester-Minnesota-Fermilab collaboration, which excluded ?π as the dominant decay channel for such hybrids. The experimental limits are based on Primakoff production of such states and on a VDM argument relating their radiative widths to their ?π decay modes. Using data on coherent production of ηπ⁺ systems in π⁺ collisions with nuclei, I obtain few percent limits on the ?π branching ratios for hybrid masses ?1.5 GeV.     

COMPASS-II

On December 1st 2010 the proposal of the COMPASS-II Experiment [1] has been approved by the CERN Research Board. After almost ten years of important results achieved by the COMPASS Collaboration in both nucleon spin physics, with the use of muon beam, and hadron spectroscopy, using hadron beams, this second phase offers now a unique chance to address in the very near future newly opened QCD-related challenges, at very moderate upgrade cost, thanks to the versatility of the COMPASS apparatus [2]. This implies mainly study of chiral perturbation theory (ChPT), by measuring the pion polarizability through Primakoff reaction; generalized parton distributions (GPDs), by measuring exclusive deeply virtual compton scattering (DVCS) and hard exclusive meson production (DVMP); transverse momentum dependent parton distributions (TMDs) in single-polarised pion-induced Drell-Yan muon production and in SIDIS on a liquid hydrogen target (in parallel to DVCS). An overview of the COMPASS-II proposal is presented here, with a main focus on the new upcoming investigation of the nucleon structure via the Drell-Yan and DVCS processes.     

Increasing average period lengths by switching of robust chaos maps in finite precision

The direct measurement of the gluon polarization in the nucleon at the COMPASS experiment is discussed. Three complementary analyses are considered. All of them study ΔG/G using method based on selection of events originating from the Photon Gluon Fusion process. Most precise preliminary value of ΔG/G is obtained from the high p _T pair channel for the Q ² < 1 (GeV/c)² region: ΔG/G = 0.016 ± 0.058 (stat.) ± 0.055 (syst.). on behalf of the COMPASS collaboration     

Spin physics with COMPASS

COMPASS is a fixed target experiment at CERN studying nucleon spin structure in polarised deep inelastic muon nucleon scattering and hadron spectroscopy using hadron beams. The main goal of the COMPASS spin physics program is the measurement of the helicity contribution of the gluons to the nucleon spin, ΔG. This quantity is accessible via the photon-gluon-fusion process which can be selected by open charm production or production of hadron pairs with large transverse momenta. The spin physics program of COMPASS includes also measurements with a transversely polarised target. These allow to measure the transverse structure function.COMPASS has up to now successfully finished three runs with a muon beam of 160 GeV and a longitudinally polarized⁶LiD target in the years 2002, 2003 and 2004. An overview of the physics addressed by the muon program, with an emphasis on the ΔG/G measurement will be presented. The status of the analysis of the highpt hadron pairs, open charm, longitudinal and transverse asymmetries will be reviewed.     

Density isomerism and the Primakoff effect

We show that the decay width for π⁰→2γ in nuclear matter could be used as a signal for phase transitions in nuclear matter. The decay width of the π⁰ is experimentally measured using pion photoproduction off heavy nuclei by observing the Primakoff peak in the differential cross sections. We present calculations for the differential cross section with corrections to the γ?γ?π⁰ vertex arising from the nuclear medium within the nuclear radius when the medium is in the abnormal matter phase.     

Configuration mixing and total muon capture rates

We modify the Primakoff closure approximation to get independence on the mean neutrino energy and energy weighted sum rules are used for the corrective terms. A near model - independent discussion is then possible, and the total rates are shown to be a very sensitive tool to investigate configuration mixing of the target. Wild discrepancies with experiment would arise if the limit of pure jj or LS couplings are used for ¹²C, whereas the Cohen-Kurath wave function gives a very good result.     

SU(4) breaking,allowed transitions and total muon capture rates in nuclei

We study muon capture rates in light nuclei and show that one can evaluate them in a model-independent way by correcting the Primakoff closure approximation to the first order in the neutrino energy dependence. In this framework the interplay between the existence of allowed transitions and SU(4) breaking is analyzed. In the correction to the first order in the neutrino energy dependence by a sum rule, Majorana and SU(4) breaking potentials are taken into account. The method is also applied to single multipolar transitions, in particular for the dipole transitions. General considerations are illustrated for ⁶Li and ¹²C by explicit calculations. The stability of the results varying the mean neutrino energy allows the use of capture rates as a very sensitive tool to investigate the configuration mixing of the target because we connect the corrective term to spectroscopic information using directly the matrix elements of the effective potentials.     

Internal ionization in 41Ca

The internal ionization accompanying the first-forbidden unique electron-capture decay of ⁴¹Ca was investigated. The integrated probability of electron ejection with energy greater than 38keV was found to be (0.17 ± 0.02) × 10⁻⁵ per K-capture. In this energy range, the measured spectrum of ejected electrons is fairly close to predictions of the simple theory of Primakoff and Porter, and of the relativistic theory of Mukoyama et al. By a model-dependent extrapolation of this spectrum toward low energies, the total probability of internal ionization in ⁴¹Ca was estimated and compared with relevant experimental results for other isotopes.     

Polarised Drell-Yan measurements at COMPASS-II

The spin structure of the nucleon and its Parton Distribution Functions (PDFs) are important topics studied by the COMPASS experiment at CERN. So far, the transverse momentum dependent PDFs (TMD PDFs) of the proton and deuteron have been studied in Semi-Inclusive Deep Inelastic Scattering (SIDIS). The Drell-Yan (DY) process is a complementary way to access the TMD PDFs, using a transversely polarised target. Studying the angular distributions of dimuons from the DY events produced in the collisions of a π^? beam with 190 GeV/c momentum off a transversely polarised proton target (NH₃) we are able to extract the azimuthal spin asymmetries, which are generated by 4 out of the 8 TMD PDFs needed to describe the nucleon structure at leading order QCD. The expected sign change in Sivers and Boer-Mulders functions when accessed from DY and SIDIS will be checked [1]. The opportunity to study, in the same experiment, the TMD PDFs from both SIDIS and DY processes is unique at COMPASS. The COMPASS II Proposal [2] was approved by CERN including one year for polarised DY measurements; the beginning of the DY data taking is scheduled for 2014. The feasibility of the measurement was proven by several beam tests performed so far.     

New target transverse spin dependent azimuthal asymmetries from COMPASS experiment

In general, eight target transverse spin-dependent azimuthal modulations are allowed in semi inclusive deep inelastic scattering of polarized leptons on a transversely polarized target. In the QCD parton model four of these asymmetries can be interpreted within the leading order approach. Two of them, namely Collins and Sivers effects were already measured by HERMES and COMPASS experiments. Other two leading twist and remaining four azimuthal asymmetries which can be interpreted as twist-three contributions have been measured for the first time in COMPASS using a 160 GeV/c longitudinally polarized (P _l }~ −0.8) muon beam and a transversely polarized ⁶LiD target. We present here the preliminary results from the 2002–2004 data. on behalf of the COMPASS collaboration     

Collins and Sivers asymmetries on the deuteron from COMPASS

COMPASS, a fixed target experiment on the SPS M2 beamline at CERN, has started to collect physics data from Autumn 2002 on a polarized ⁶LiD target. This target can be both longitudinally and transversely polarized with respect to the polarized 160 GeV/c μ⁺ beam. In 2002, 2003 and 2004, 20% of the beam-time was spent in the transverse configuration, allowing the measurement of transverse spin effects. Here the results for the Collins and Sivers asymmetries for charged hadrons, extracted from the 2003–2004 data are presented. on behalf of the COMPASS collaboration     

η − η′ photoproduction and the axial isoscalar neutral current coupling

We show that coherentη andη′ photoproduction by means of the Primakoff Effect on the proton depends on the strange component of the neutral axial current coupling. We construct polarization asymmetries that are sensitive to this coupling through theγ?Z interference. Theη′ is not a Goldstone boson of a spontaneously broken chiral symmetry, but a phenomenological analysis of theη andη′ production through chiral perturbation theory allows to calculate the observables of interest. The polarized proton or polarized photon asymmetries are predicted to be close to 10^?4 for ?q ²～0.1?0.5 GeV².     

Neutron-neutron interaction and muon capture by deutron

The reaction μ⁻ + d → 2n + v_μ is studied in the non-relativistic approximation using the Primakoff weak interaction Hamiltonian including relativistic corrections. The neutron-neutron interaction is treated (a) by the Om?es-Muskhelishvili equation, (b) in a potential model, (c) using the Bethe-Longmire procedure. Influence of D-state admixture in deutron upon the transition rates and neutron spectrum is investigated.     

Holstein–Primakoff (H-P) Approach to Determine the Optical Response of Hybrid Optomechanical System Containing Multiple Quantum Dots

A theoretical model is presented to study the hybrid optomechanical system comprising an ensemble of N number of quantum dots (QDs). Utilizing the Holstein–Primakoff (H-P) transformation formalism, the calculations become easily scalable. The bistability in this hybrid optomechanical system is studied in the presence of third order nonlinear χ⁽³⁾ medium using the H-P transformation method and to verify the results, numerical method has also been utilized. It is also demonstrated that the system's parameters may be tuned to alter the bistability phenomenon and absorption spectrum's response, which exhibits both positive and negative absorption (emission). This alternative approach (H-P transform) is demonstrated to solve analytically the system containing multiple QDs in an elegant manner.     

μCR42β: Muon capture rates for double-beta decay

Gamma-rays following nuclear capture of negative muons in enriched ⁴⁸Ti, ⁷⁶Se, ¹⁰⁶Cd, as well as natural Se and Cd targets were measured. Time evolution of several gamma-lines allowed to deduce the total μ-capture rates in Ti, Se and Cd isotopes, which are compared to the Primakoff estimate. The data on the partial μ-capture rates will be used for more precise calculation of the 2β-NMEs of ⁴⁸Ca, ⁷⁶Se and ¹⁰⁶Cd. Presented by V. Egorov at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’05), Corfu, Greece, September 26–29, 2005. Partly supported by the Russian Foundation for Basic Research (grant 06-02-16587).