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Igor Salom

Publications and source records attributed to Igor Salom.

32 records · Page 2Linked to original sources

DREENA-B framework: first predictions of $R_{AA}$ and $v_2$ within dynamical energy loss formalism in evolving QCD medium

Dynamical energy loss formalism allows generating state-of-the-art suppression predictions in finite size QCD medium, employing a sophisticated model of high-$p_\perp$ parton interactions with QGP. We here report a major step of introducing medium evolution in the formalism though $1+1D$ Bjorken (``B'') expansion, while preserving all complex features of the original dynamical energy loss framework. We use this framework to provide joint $R_{AA}$ and $v_2$ predictions, for the first time within the dynamical energy loss formalism in evolving QCD medium. The predictions are generated for a wide range of observables, i.e. for all types of probes (both light and heavy) and for all centrality regions in both $Pb+Pb$ and $Xe+Xe$ collisions at the LHC. Where experimental data are available, DREENA-B framework leads to a good joint agreement with $v_2$ and $R_{AA}$ data. Such agreement is encouraging, i.e. may lead us closer to resolving $v_2$ puzzle (difficulty of previous models to jointly explain $R_{AA}$ and $v_2$ data), though this still remains to be thoroughly tested by including state-of-the-art medium evolution within DREENA framework. While introducing medium evolution significantly changes $v_2$ predictions, $R_{AA}$ predictions remain robust and moreover in a good agreement with the experimental data; $R_{AA}$ observable is therefore suitable for calibrating parton-medium interaction model, independently from the medium evolution. Finally, for heavy flavor, we observe a strikingly similar signature of the dead-cone effect on both $R_{AA}$ and $v_2$ - we also provide a simple analytical understanding behind this result. Overall, the results presented here indicate that DREENA framework is a reliable tool for QGP tomography.

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To the rescue of Copenhagen interpretation

A recent paper "Single-world interpretations of quantum theory cannot be self-consistent" [arXiv:1604.07422] by D. Frauchiger and R. Renner has attracted a considerable interest of a broader physics audience and shortly elicited a number of replies. In spite of the objections that ensued, we find that significant part of the controversial initial claim has not been refuted - on the contrary, arguments presented both in the initial paper and in the replies seem to leave no longer room for the basic Copenhagen interpretation of quantum mechanics. We revisit the controversy trying to pinpoint the exact phenomenon that lies in its core, pointing out to some aspects of the problem that seem to have been mostly overlooked. Taking all conclusions into account, we here propose novel ways to approach the ostensible paradox, in which the Copenhagen interpretation is naturally preserved. Whereas arguments presented in Frauchiger and Renner paper and the replies that followed revolve over whether Wigner's friend would perceive only one or both of the possible outcomes, we offer the third, pretty obvious solution - namely, that Wigner's friend, in the well known setup, would subjectively perceive {\it none} of the potentially conflicting outcomes. As a side note, we also argue that, contrary to the often stated beliefs, hypothetical real experimental realization of Wigner's friend thought experiment actually would not provide us with any new insight into the quantum mechanics.

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Joint $R_{AA}$ and $v_2$ predictions for $Pb+Pb$ collisions at the LHC within DREENA-C framework

In this paper, we presented our recently developed DREENA-C framework, which is a fully optimized computational suppression procedure based on our state-of-the-art dynamical energy loss formalism in constant temperature finite size QCD medium. With this framework, we for the first time, generated joint $R_{AA}$ and $v_2$ predictions within our dynamical energy loss formalism. The predictions are generated for both light and heavy flavor probes, and different centrality regions in $Pb+Pb$ collisions at the LHC, and compared with the available experimental data. Despite the fact that DREENA-C does not contain medium evolution (to which $v_2$ is largely sensitive) and the fact that other approaches faced difficulties in explaining $v_2$ data, we find that DREENA-C leads to qualitatively good agreement with this data, though quantitatively, the predictions are visibly above the experimental data. Intuitive explanation behind such results is presented, supporting the validity of our model, and it is expected that introduction of evolution in the ongoing improvement of DREENA framework, will lead to better joint agreement with $R_{AA}$ and $v_2$ data, and allow better understanding of the underlying QCD medium.

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O(6) algebraic theory of three nonrelativistic quarks bound by spin-independent interactions

We apply the newly developed theory of permutation-symmetric O(6) hyperspherical harmonics to the quantum-mechanical problem of three non-relativistic quarks confined by a spin-independent 3-quark potential. We use our previously derived results to reduce the three-body Schrödinger equation to a set of coupled ordinary differential equations in the hyper-radius $R$ with coupling coefficients expressed entirely in terms of (i) a few interaction-dependent O(6) expansion coefficients and (ii) O(6) hyperspherical harmonics matrix elements, that have been evaluated in our previous paper. This system of equations allows a solution to the eigenvalue problem with homogeneous 3-quark potentials, which class includes a number of standard Ansätze for the confining potentials, such as the Y- and $Δ$-string ones. We present analytic formulae for the $K = 2, 3, 4, 5$ shell states' eigen-energies in homogeneous three-body potentials, which formulae we then apply to the Y- and $Δ$-string, as well as the logarithmic confining potentials. We also present numerical results for power-law pair-wise potentials with the exponent ranging between -1 and +2. In the process we resolve the 25 year-old Taxil and Richard vs. Bowler et al. controversy regarding the ordering of states in the $K = 3$ shell, in favor of the former. Finally, we show the first clear difference between the spectra of $Δ$- and Y-string potentials, which appears in $K \geq 3$ shells. Our results are generally valid, not just for confining potentials, but also for many momentum-independent permutation-symmetric homogenous potentials, that need not be pairwise sums of two-body terms. The potentials that can be treated in this way must be square-integrable under the O(6) hyperangular integral, however, which class does not include the Dirac $δ$-function.

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Permutation-symmetric three-body O(6) hyperspherical harmonics in three spatial dimensions

We have constructed the three-body permutation symmetric O(6) hyperspherical harmonics which can be used to solve the non-relativistic three-body Schr{\" o}dinger equation in three spatial dimensions. We label the states with eigenvalues of the $U(1) \otimes SO(3)_{rot} \subset U(3) \subset O(6)$ chain of algebras and we present the corresponding $K \leq 4$ harmonics. Concrete transformation properties of the harmonics are discussed in some detail.

math-ph↗

Role of the orthogonal group in construction of osp(1|2n) representations

It is well known that the symmetric group has an important role (via Young tableaux formalism) both in labelling of the representations of the unitary group and in construction of the corresponding basis vectors (in the tensor product of the defining representations). We show that orthogonal group has a very similar role in the context of positive energy representations of osp(1|2n,R). In the language of parabose algebra, we essentially solve the long standing problem of reducibility of Green's ansatz representations.

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Generalization of the Gell-Mann formula for sl(n,R) and su(n) algebras

The so called Gell-Mann or decontraction formula is proposed as an algebraic expression inverse to the Inonu-Wigner Lie algebra contraction. It is tailored to express the Lie algebra elements in terms of the corresponding contracted ones. In the case of sl(n,R) and su(n) algebras, contracted w.r.t. so(n) subalgebras, this formula is generally not valid, and applies only in the cases of some algebra representations. A generalization of the Gell-Mann formula for sl(n,R) and su(n) algebras, that is valid for all tensorial, spinorial, (non)unitary representations, is obtained in a group manifold framework of the SO(n) and/or Spin(n) group. The generalized formula is simple, concise and of ample application potentiality. The matrix elements of the SL(n,R)/Spin(n), i.e. SU(n)/SO(n), generators are determined, by making use of the generalized formula, in a closed form for all irreducible representations.

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Validity of the Gell-Mann formula for sl(n,R) and su(n) algebras

The so called Gell-Mann formula, a prescription designed to provide an inverse to the Inonu-Wigner Lie algebra contraction, has a great versatility and potential value. This formula has no general validity as an operator expression. The question of applicability of Gell-Mann's formula to various algebras and their representations was only partially treated. The validity constraints of the Gell-Mann formula for the case of sl(n,R) and su(n) algebras are clarified, and the complete list of representations spaces for which this formula applies is given. Explicit expressions of the sl(n,R) generators matrix elements are obtained, in these cases, by making use of the Gell-Mann formula.

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Generalization of the Gell-Mann formula for sl(5, R) and su(5) algebras

The so called Gell-Mann formula expresses the Lie algebra elements in terms of the corresponding Inonu-Wigner contracted ones. In the case of sl(n, R) and su(n) algebras contracted w.r.t. so(n) subalgebras, the Gell-Mann formula is generally not valid, and applies only in the cases of some algebra representations. A generalization of the Gell-Mann formula for sl(5,R) and su(5) algebras, that is valid for all representations, is obtained in a group manifold framework of the SO(5) and/or Spin(5) group.

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SO(5) Clebsch-Gordan coefficients involving the 14-dimensional representation

Analytic expressions for the Clebsch-Gordan (CG) coefficients of the SO(5) group that involve the 14-dimensional representation can be found in an old paper of M. K. F. Wong. A careful analysis yields that roughly 30% of the coefficients given in that paper are wrong. The correct analytic expressions for all SO(5) group CG coefficients containing the 14-dimensional representation are obtained.

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Parabose algebra as generalized conformal supersymmetry

The form of realistic space-time supersymmetry is fixed, by Haag-Lopuszanski-Sohnius theorem, either to the familiar form of Poincare supersymmetry or, in massless case, to that of conformal supersymmetry. We question necessity for such strict restriction in the context of theories with broken symmetries. In particular, we consider parabose N=4 algebra as an extension of conformal supersymmetry in four dimensions (coinciding with the, so called, generalized conformal supersymmetry). We show that sacrificing of manifest Lorentz covariance leads to interpretation of the generalized conformal supersymmetry as symmetry that contains, on equal footing, two "rotation" groups. It is possible to reduce this large symmetry down to observable one by simply breaking one of these two SU(2) isomorphic groups down to its U(1) subgroup.

hep-th↗

Extension of Conformal (Super)Symmetry using Heisenberg and Parabose operators

In this paper we investigate a particular possibility to extend C(1,3) conformal symmetry using Heisenberg operators, and a related possibility to extend conformal supersymmetry using parabose operators. The symmetry proposed is of a simple mathematical form, as is the form of necessary symmetry breaking that reduces it to the conformal (super)symmetry. It turns out that this extension of conformal superalgebra can be obtained from standard non-extended conformal superalgebra by allowing anticommutators $\{Q_η, Q_ξ\}$ and $\{\bar Q_{\dot η}, \bar Q_{\dot ξ}\}$ to be nonzero operators and then by closing the algebra. In regard of the famous Coleman and Mandula theorem (and related Haag-Lopuszanski-Sohnius theorem), the higher symmetries that we consider do not satisfy the requirement for finite number of particles with masses below any given constant. However, we argue that in the context of theories with broken symmetries, this constraint may be unnecessarily strong.

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Algebraic Approach to the Duality Symmetry

The duality symmetry of free electromagnetic field is analyzed within an algebraic approach. To this end, the conformal $c(1,3)$ algebra generators are expressed as operators quadratic in some abstract operators $κ^α$ and $π_β$ which satisfy Heisenberg algebra relations. It is then shown that the duality generator can also be expressed in this manner. Standard issues regarding duality are considered in such a framework. It is shown that duality generator also generates chiral transformations, and the conflict between duality and manifest Lorentz symmetry is analyzed from the viewpoint of symmetry group greater then conformal, in which duality generator appears as a natural part of an $su(2)$ subalgebra.

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