Coordinate Bethe Ansatz for Spin s XXX Model Crampé, Nicolas; Eric Ragoucy, ,; Alonzi, Ludovic
Symmetry, integrability and geometry, methods and applications,
01/2011, Letnik:
7
Journal Article
Recenzirano
Odprti dostop
We compute the eigenfunctions and eigenvalues of the periodic integrable spin s XXX model using the coordinate Bethe ansatz. To do so, we compute explicitly the Hamiltonian of the model. These ...results generalize what has been obtained for spin 1/2 and spin 1 chains.
Allowed charged \(\pi\) meson decays are characterized by simple dynamics, few available decay channels, mainly into leptons, and extremely well controlled radiative and loop corrections. In that ...sense, pion decays represent a veritable triumph of the standard model (SM) of elementary particles and interactions. This relative theoretical simplicity makes charged pion decays a sensitive means for testing the underlying symmetries and the universality of weak fermion couplings, as well as for studying pion structure and chiral dynamics. Even after considerable recent improvements, experimental precision is lagging far behind that of the theoretical description for pion decays. We review the current state of experimental study of the pion electronic decay \(\pi^+ \to e^+\nu_e(\gamma)\), or \(\pi_{e2(\gamma)}\), where the \((\gamma)\) indicates inclusion and explicit treatment of radiative decay events. We briefly review the limits on non-SM processes arising from the present level of experimental precision in \(\pi_{e2(\gamma)}\) decays. Focusing on the PEN experiment at the Paul Scherrer Institute (PSI), Switzerland, we examine the prospects for further improvement in the near term.
The electromagnetic calorimeter for the new muon (g-2) experiment at Fermilab will consist of arrays of PbF2 Cherenkov crystals read out by large-area silicon photo-multiplier (SiPM) sensors. We ...report here on measurements and simulations using 2.0 -- 4.5 GeV electrons with a 28-element prototype array. All data were obtained using fast waveform digitizers to accurately capture signal pulse shapes versus energy, impact position, angle, and crystal wrapping. The SiPMs were gain matched using a laser-based calibration system, which also provided a stabilization procedure that allowed gain correction to a level of 1e-4 per hour. After accounting for longitudinal fluctuation losses, those crystals wrapped in a white, diffusive wrapping exhibited an energy resolution sigma/E of (3.4 +- 0.1) % per sqrt(E/GeV), while those wrapped in a black, absorptive wrapping had (4.6 +- 0.3) % per sqrt(E/GeV). The white-wrapped crystals---having nearly twice the total light collection---display a generally wider and impact-position-dependent pulse shape owing to the dynamics of the light propagation, in comparison to the black-wrapped crystals, which have a narrower pulse shape that is insensitive to impact position.
Building on the rare pion and muon decay results of the PIBETA experiment, the PEN collaboration has undertaken a precise measurement of B_{\pi e2} = R^\pi_{e/\mu}, the \pi^+ -> e^+\nu(\gamma) decay ...branching ratio, at the Paul Scherrer Institute, to reduce the present 40\times experimental precision lag behind theory to ~ 6-7\times. Because of large helicity suppression, R^\pi_{e/\mu} is uniquely sensitive to contributions from non-(V-A) physics, making this decay a particularly suitable subject of study. Even at current precision, the experimental value of B_{\pi e2} provides the most accurate test of lepton universality available. During runs in 2008-10, PEN has accumulated over 2\times 10^7 \pi_{e2} events; a comprehensive maximum-likelihood analysis is currently under way. The new data will also lead to improved precision of the earlier PIBETA results on radiative \pi and \mu decays.
Precision measurements in neutron beta decay serve to determine the coupling constants of beta decay and allow for several stringent tests of the standard model. This paper discusses the design and ...the expected performance of the Nab spectrometer.
In the mid-20th century, deinstitutionalization of mental health hospitals in the United States led to a dramatic decline in the availability of centralized institutional services. As a result, a ...result, a significant portion of the inmate population at correctional facilities consists of individuals with serious mental illness. In Charlottesville, VA and surrounding counties, individuals suffering from serious mental illness often depend on local community service providers (CSPs) for treatment after their release from custody, but limited interagency coordination impedes access to treatment. To better understand the characteristics of the population of incarcerated individuals with serious mental illness, data spanning a 30-month period from July 2015 to December 2017 were obtained through research partnerships with criminal justice agencies and CSPs in the Charlottesville area. In order to evaluate who might benefit from mental health services, this paper characterizes the population of inmates who met screening criteria for further mental health evaluation relative to those who did not. In the Albemarle-Charlottesville Regional Jail (ACRJ) booking data, 5,284 unique individuals were identified, of which 3,064 (48%) were screened for serious mental illness. Of those screened, 32% met the screening criteria for further mental health evaluation. For individuals who met the screening criteria, 21% were linked to a local community service provider for further mental health services. Key findings of this study include: *individuals who met the screening criteria for serious mental illness spent a more time in jail during the study period than those who did not meet the criteria. *individuals who stayed more than 30 days for any given booking event were more likely to have met the criteria for serious mental illness, *individuals who returned to custody due to probation violations were more likely to have met the criteria for serious mental illness, *individuals who were returned to custody most frequently and spent the most time in jail were more likely to meet the criteria for serious mental illness. The paper also analyzes the linkages between the criminal justice system and these individuals who require further mental health evaluation and services. These findings help agencies and community stakeholders develop a better understanding of relationships and interactions and establish best practices for enhancing public safety while addressing the needs of individuals suffering from mental illness.
A central problem for organizations with a with a tactical surveillance mission is that of the "quiet agent." The quiet agent problem concerns the real-time detection of a quiet entity moving in the ...midst of other entities, such as a silent person passing through an otherwise noisy crowd. The detection of the quiet agent is made possible by the effect it has on the surrounding agents and environment. In this paper we describe a proof-of-concept machine learning framework that is able to detect quiet agents in closed spaces where audio monitoring is available. Our approach begins by simulating an environment to produce relevant and usable data. The data is then converted into matrix form to be run through a neural network to detect the presence and movement of the quiet agent. The neural network was able to predict the location of the quiet agent with reasonable accuracy. Finally, the framework includes a step where data is normalized and heatmaps are generated, allowing the human eye to follow the quiet agent path.
We report a measurement of two energy-weighted gamma cascade angular distributions from polarized slow neutron capture on the \({}^{35}\)Cl nucleus, one parity-odd correlation proportional to ...\(\vec{s_{n}} \cdot \vec{k_{\gamma}}\) and one parity-even correlation proportional to \(\vec{s_{n}} \cdot \vec{k_{n}} \times \vec{k_{\gamma}}\). A parity violating asymmetry can appear in this reaction due to the weak nucleon-nucleon (NN) interaction which mixes opposite parity S and P-wave levels in the excited compound \(^{36}\)Cl nucleus formed upon slow neutron capture. If parity-violating (PV) and parity-conserving (PC) terms both exist, the measured differential cross section can be related to them via \(\frac{d\sigma}{d\Omega}\propto1+A_{\gamma, PV}\cos\theta+A_{\gamma,PC}\sin\theta\). The PV and PC asymmetries for energy-weighted gamma cascade angular distributions for polarized slow neutron capture on \(^{35}\)Cl averaged over the neutron energies from 2.27~meV to 9.53~meV were measured to be \(A_{\gamma,PV}=(-23.9\pm0.7)\times 10^{-6}\) and \(A_{\gamma,PC}=(0.1\pm0.7)\times 10^{-6}\). These results are consistent with previous experimental results. Systematic errors were quantified and shown to be small compared to the statistical error. These asymmetries in the angular distributions of the gamma rays emitted from the capture of polarized neutrons in \(^{35}\)Cl were used to verify the operation and data analysis procedures for the NPDGamma experiment which measured the parity-odd asymmetry in the angular distribution of gammas from polarized slow neutron capture on protons.
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