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H. C. Eggers

Publications and source records attributed to H. C. Eggers.

At least 19 recordsLinked to original sources
arXiv2016

Model independent analysis of nearly Lévy correlations

A model-independent method for the analysis of the two-particle short-range correlations is presented, that can be utilized to describe e.g. Bose-Einstein (HBT), dynamical (ridge) or other correlation functions, that have a nearly Lévy or streched exponential shape. For the special case of Lévy exponent alpha = 1, the earlier Laguerre expansions are recovered, for the alpha = 2 special case, a new expansion method is obtained for nearly Gaussian correlation functions. Multi-dimensional Lévy expansions are also introduced and their potential application to analyze rigde correlation data is discussed.

physics.data-an↗
arXiv2015

Bayesian variable selection with spherically symmetric priors

We propose that Bayesian variable selection for linear parametrisations with Gaussian iid likelihoods be based on the spherical symmetry of the diagonalised parameter space. Our r-prior results in closed forms for the evidence for four examples, including the hyper-g prior and the Zellner-Siow prior, which are shown to be special cases. Scenarios of a single variable dispersion parameter and of fixed dispersion are studied, and asymptotic forms comparable to the traditional information criteria are derived. A simulation exercise shows that model comparison based on our r-prior gives good results comparable to or better than current model comparison schemes.

math.ST↗
arXiv2013

Internal cumulants for femtoscopy with fixed charged multiplicity

A detailed understanding of all effects and influences on higher-order correlations is essential. At low charged multiplicity, the effect of a nonpoissonian multiplicity distribution can significantly distort correlations. Evidently, the reference samples with respect to which correlations are measured should yield a null result in the absence of correlations. We show how the careful specification of desired properties necessarily leads to an average-of-multinomials reference sample. The resulting internal cumulants and their averaging over several multiplicities fulfil all requirements of correctly taking into account nonpoissonian multiplicity distributions as well as yielding a null result for uncorrelated fixed-N samples. Various correction factors are shown to be approximations at best. Careful rederivation of statistical variances and covariances within the frequentist approach yields errors for cumulants that differ from those used so far. We finally briefly discuss the implementation of the analysis through a multiple event buffer algorithm.

hep-ex↗
arXiv2007

HBT shape analysis with q-cumulants

Taking up and extending earlier suggestions, we show how two- and threedimensional shapes of second-order HBT correlations can be described in a multivariate Edgeworth expansion around gaussian ellipsoids, with expansion coefficients, identified as the cumulants of pair momentum difference q, acting as shape parameters. Off-diagonal terms dominate both the character and magnitude of shapes. Cumulants can be measured directly and so the shape analysis has no need for fitting.

nucl-th↗
arXiv2005

A class of spatio-temporal and causal stochastic processes, with application to multiscaling and multifractality

We present a general class of spatio-temporal stochastic processes describing the causal evolution of a positive-valued field in space and time. The field construction is based on independently scattered random measures of Levy type whose weighted amplitudes are integrated within a causality cone. General n-point correlations are derived in closed form. As a special case of the general framework, we consider a causal multiscaling process in space and time in more detail. The latter is derived from, and completely specified by, power-law two-point correlations, and gives rise to scaling behaviour of both purely temporal and spatial higher-order correlations. We further establish the connection to classical multifractality and prove the multifractal nature of the coarse-grained field amplitude.

math-ph↗
arXiv2005

Multiparticle correlations in Q-space

We introduce Q-space, the tensor product of an index space with a primary space, to achieve a more general mathematical description of correlations in terms of q-tuples. Topics discussed include the decomposition of Q-space into a sum-variable (location) subspace S plus an orthogonal difference-variable subspace D, and a systematisation of q-tuple size estimation in terms of p-norms. The "GHP sum" prescription for q-tuple size emerges naturally as the 2-norm of difference-space vectors. Maximum- and minimum-size prescriptions are found to be special cases of a continuum of p-sizes.

hep-ph↗
arXiv2005

Multidimensional HBT correlations in proton-antiproton collisions at root(s) = 630 GeV

We analyse second moments $R_2$ of like-sign pion pairs in the two-dimensional $(q_L,q_T)$ and three-dimensional $(q_O,q_S,q_L)$ decompositions of the three-momentum difference. Conventional fit parametrisations such as gaussian, exponential, power-law and Edgeworth fail miserably, while more elaborate ones such as Levy do well but fail to yield a unique best-fit solution. A two-component model using a hard cut to separate small- and large-scale parts appears possible but not compelling. In all cases, the data exhibits a strong and hitherto unexplained peak at small momentum differences which exceeds current fits.

hep-ex↗
arXiv2001

Experimental correlation analysis: foundations and practice

Commonalities and differences in correlation analysis in terms of phase space, conditioning and uncorrelatedness are discussed. The Poisson process is not generally appropriate as reference distribution for normalisation and cumulants, so that generalised statistics in terms of arbitrarily defined reference processes must be employed. Consideration of the sampling hierarchy leads us to a classification of current event-by-event observables.

hep-ex↗
arXiv2000

Cumulant ratios in fully developed turbulence

In the context of random multiplicative cascade processes, we derive analytical solutions for one- and two-point cumulants with restored translational invariance. On taking ratios of cumulants in ln epsilon, geometrical effects due to spatial averaging cancel out. These ratios can successfully distinguish between splitting functions while multifractal scaling exponents and multiplier distributions cannot.

hep-ph↗
arXiv2000

Multiplicity dependence of Bose-Einstein correlations in antiproton-proton reactions: a discussion of possible origins

The observed pronounced multiplicity dependence of correlation functions in hadron-hadron reactions and in particular of Bose-Einstein correlations provides information about underlying physics. We discuss in this contribution several interpretations, giving special attention to the string model for Bose-Einstein correlations of Andersson and Hofmann, as well as the core-halo picture of Csorgo, Lorstad and Zimanyi.

hep-ph↗
arXiv1998

Multiplicity Dependence of Like-Sign and Opposite-Sign Correlations in $\bar{p}p$ Reactions

Discussions about Bose-Einstein correlations between decay products of coproduced W-bosons again raise the question about the behaviour of correlations if several strings are produced. This is studied by the multiplicity dependence of correlation functions of particle pairs with like-sign and opposite-sign charge in $\bar{p}p$ reactions at $\sqrt{s} = 630$ GeV.

hep-ex↗
arXiv1997

A sensitive test for models of Bose-Einstein correlations

Accurate and sensitive measurements of higher order cumulants open up new approaches to pion interferometry. It is now possible to test whether a given theoretical prediction can consistently match cumulants of both second and third order. Our consistency test utilizes a new technique combining theoretically predicted functions with experimentally determined weights in a quasi-Monte Carlo approach. Testing a general quantum statistics-based framework of Bose-Einstein correlations with this technique, we find that predictions for third order cumulants differ significantly from UA1 data. This discrepancy may point the way to more detailed dynamical information.

hep-ph↗
arXiv1996

Pion interferometry with higher-order cumulants

We have measured second- and third-order cumulants in UA1 data ($\bar pp$ collisions at 630 GeV/c). Rather than quoting numerical values for source parameters, we have used these in three checks to test the ``quantum statistics'' theory for consistency over these cumulants. In the process, we have found a method for folding theoretical correlation functions with experimental one-particle distributions. Our preliminary results appear to indicate that, for the specific tests performed, the data contradicts the theory.

hep-ph↗
arXiv1996

Dileptons from bremsstrahlung: going beyond the soft photon approximation

The traditional calculation of dilepton yields from bremsstrahlung relies on the assumption that electromagnetic and strong processes factorize. We argue that this assumption, embodied by the soft photon approximation, cannot hold true for invariant mass spectra on very general grounds. Deriving a formula for the dilepton cross section for pion-pion scattering that does not rely on such factorization, we formulate the problem exactly in terms of three-particle phase space invariants. Using a simple one boson exchange model for comparison, we find that dilepton cross sections and yields are generally overestimated by the soft photon approximation by factors 2--8. In extreme cases, overestimation up to a factor 40 is possible.

hep-ph↗