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Register a new userGlobal Conservation Laws and Femtoscopy of Small Systems
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It is important to understand, in detail, two-pion correlations measured in p+p and d+A collisions. In particular, one wishes to understand the femtoscopic correlations, in order to compare to similar measurements in heavy ion collisions. However, in the low-multiplicity final states of these systems, global conservation laws generate significant N-body correlations which project onto the two-pion space in non-trivial ways and complicate the femtoscopic analysis. We discuss a formalism to calculate and account for these correlations in collisions dominated by a single particle species (e.g. pions). We also discuss effects on two-particle correlations between non-identical particles, the understanding of which may be important in the study of femtoscopic space-time asymmetries.
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It is increasingly important to understand, in detail, two-pion correlations measured in p+p and d+A collisions. In particular, one wishes to understand the femtoscopic correlations, in order to compare to similar measurements in heavy ion collisions. However, in the low-multiplicity final states of these systems, global conservation laws generate significant N-body correlations which project onto the two-pion space in non-trivial ways and complicate the femtoscopic analysis. We discuss a model-independent formalism to calculate and account for these correlations in measurements.
The basic principles of the correlation femtoscopy, including its correspondence to the Hanbury Brown and Twiss intensity interferometry, are re-examined. The main subject of the paper is an analysis of the correlation femtoscopy when the source size is as small as the order of the uncertainty limit. It is about 1 fm for the current high energy experiments. Then the standard femtoscopy model of random sources is inapplicable. The uncertainty principle leads to the partial indistinguishability and coherence of closely located emitters that affect the observed femtoscopy scales. In thermal systems the role of corresponding coherent length is taken by the thermal de Broglie wavelength that also defines the size of a single emitter. The formalism of partially coherent phases in the amplitudes of closely located individual emitters is used for the quantitative analysis. The general approach is illustrated analytically for the case of the Gaussian approximation for emitting sources. A reduction of the interferometry radii and a suppression of the Bose-Einstein correlation functions for small sources due to the uncertainty principle are found. There is a positive correlation between the source size and the intercept of the correlation function. The peculiarities of the non-femtoscopic correlations caused by minijets and fluctuations of the initial states of the systems formed in $pp$ and $e^+e^-$ collisions are also analyzed. The factorization property for the contributions of femtoscopic and non-femtoscopic correlations into complete correlation function is observed in numerical calculations in a wide range of the model parameters.
The study of fluctuations of particle multiplicities in relativistic heavy-ion reactions has drawn much attention in recent years, because they have been proposed as a probe for underlying dynamics and possible formation of quark-gluon plasma. Thus, it is of uttermost importance to describe the baseline of statistical fluctuations in the hadron gas phase in a correct way. We have performed a comprehensive study of multiplicity distributions in the full ideal hadron-resonance gas in different ensembles, namely grand-canonical, canonical and microcanonical, using two different methods: asymptotic expansions and full Monte Carlo simulations. The method based on asymptotic expansion allows a quick numerical calculation of dispersions in the hadron gas with three conserved charges at primary hadron level, while the Monte-Carlo simulation is suitable to study the effect of resonance decays. Even though mean multiplicities converge to the same values, major differences in fluctuations for these ensembles persist in the thermodynamic limit, as pointed out in recent studies. We observe that this difference is ultimately related to the non-additivity of the variances in the ensembles with exact conservation of extensive quantities.
In this report we present the first quantitative determination of the correlations between baryons and anti-baryons induced by local baryon number conservation. This is important in view of the many experimental studies aiming at probing the phase structure of strongly interacting matter. We confront our results with the recent measurements of net-proton fluctuations reported by the CERN ALICE experiment. The role of local baryon number conservation is found to be small on the level of second cumulants.
One dimensional systems sometimes show pathologically slow decay of currents. This robustness can be traced to the fact that an integrable model is nearby in parameter space. In integrable models some part of the current can be conserved, explaining this slow decay. Unfortunately, although this conservation law is formally anticipated, in practice it has been difficult to find in concrete cases, such as the Heisenberg model. We investigate this issue both analytically and numerically and find that the appropriate conservation law can be a non-analytic combination of the known local conservation laws and hence is invisible to elementary assumptions.
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