 Award ID(s):
 1820860
 NSFPAR ID:
 10297318
 Date Published:
 Journal Name:
 International Journal of Modern Physics A
 Volume:
 35
 Issue:
 24
 ISSN:
 0217751X
 Page Range / eLocation ID:
 2030013
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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New LHCb Collaboration results on pentaquarks with hidden charm 1 are discussed. These results fit nicely in the hadrocharmonium pentaquark scenario.[Formula: see text] In the new data the old LHCb pentaquark [Formula: see text] splits into two states [Formula: see text] and [Formula: see text]. We interpret these two almost degenerated hadrocharmonium states with [Formula: see text] and [Formula: see text], as a result of hyperfine splitting between hadrocharmonium states predicted in Ref. 2. It arises due to QCD multipole interaction between colorsinglet hadrocharmonium constituents. We improve the theoretical estimate of hyperfine splitting[Formula: see text] that is compatible with the experimental data. The new [Formula: see text] state finds a natural explanation as a bound state of [Formula: see text] and a nucleon, with [Formula: see text], [Formula: see text] and binding energy 42 MeV. As a bound state of a spin[Formula: see text] meson and a nucleon, hadrocharmonium pentaquark [Formula: see text] does not experience hyperfine splitting. We find a series of hadrocharmonium states in the vicinity of the wide [Formula: see text] pentaquark that can explain its apparently large decay width. We compare the hadrocharmonium and molecular pentaquark scenarios and discuss their relative advantages and drawbacks.more » « less

We study the dynamics of the unicritical polynomial family [Formula: see text]. The [Formula: see text]values for which [Formula: see text] has a strictly preperiodic postcritical orbit are called Misiurewicz parameters, and they are the roots of Misiurewicz polynomials. The arithmetic properties of these special parameters have found applications in both arithmetic and complex dynamics. In this paper, we investigate some new such properties. In particular, when [Formula: see text] is a prime power and [Formula: see text] is a Misiurewicz parameter, we prove certain arithmetic relations between the points in the postcritical orbit of [Formula: see text]. We also consider the algebraic integers obtained by evaluating a Misiurewicz polynomial at a different Misiurewicz parameter, and we ask when these algebraic integers are algebraic units. This question naturally arises from some results recently proven by Buff, Epstein, and Koch and by the second author. We propose a conjectural answer to this question, which we prove in many cases.

null (Ed.)We prove the Marchenko–Pastur law for the eigenvalues of [Formula: see text] sample covariance matrices in two new situations where the data does not have independent coordinates. In the first scenario — the blockindependent model — the [Formula: see text] coordinates of the data are partitioned into blocks in such a way that the entries in different blocks are independent, but the entries from the same block may be dependent. In the second scenario — the random tensor model — the data is the homogeneous random tensor of order [Formula: see text], i.e. the coordinates of the data are all [Formula: see text] different products of [Formula: see text] variables chosen from a set of [Formula: see text] independent random variables. We show that Marchenko–Pastur law holds for the blockindependent model as long as the size of the largest block is [Formula: see text], and for the random tensor model as long as [Formula: see text]. Our main technical tools are new concentration inequalities for quadratic forms in random variables with blockindependent coordinates, and for random tensors.more » « less

We collect from several sources some of the most important results on the forward and backward limits of points under real and complex rational functions, and in particular real and complex Newton maps, in one variable and we provide numerical evidence that the dynamics of Newton maps [Formula: see text] associated to real polynomial maps [Formula: see text] with no complex roots has a complexity comparable with that of complex Newton maps in one variable. In particular such a map [Formula: see text] has no wandering domain, almost every point under [Formula: see text] is asymptotic to a fixed point and there is some nonempty open set of points whose [Formula: see text]limit equals the set of nonregular points of the Julia set of [Formula: see text]. The first two points were proved by B. Barna in the real onedimensional case.more » « less

null (Ed.)Let [Formula: see text] be a convex function satisfying [Formula: see text], [Formula: see text] for [Formula: see text], and [Formula: see text]. Consider the unique entropy admissible (i.e. Kružkov) solution [Formula: see text] of the scalar, 1d Cauchy problem [Formula: see text], [Formula: see text]. For compactly supported data [Formula: see text] with bounded [Formula: see text]variation, we realize the solution [Formula: see text] as a limit of fronttracking approximations and show that the [Formula: see text]variation of (the right continuous version of) [Formula: see text] is nonincreasing in time. We also establish the natural timecontinuity estimate [Formula: see text] for [Formula: see text], where [Formula: see text] depends on [Formula: see text]. Finally, according to a theorem of Goffman–Moran–Waterman, any regulated function of compact support has bounded [Formula: see text]variation for some [Formula: see text]. As a corollary we thus have: if [Formula: see text] is a regulated function, so is [Formula: see text] for all [Formula: see text].more » « less