Bottomonium production in heavy-ion collisions at STAR

Bottomonium measurements provide unique insight into hot and cold nuclear matter effects present in the medium that is formed in high-energy heavy-ion collisions. Recent STAR results show that in $\sqrt{s_{NN}}$ = 200 GeV central Au+Au collisions the $\Upsilon$(1S) state is suppressed more than if only cold nuclear matter effects were present, and the excited state yields are consistent with a complete suppression. In 2012, STAR also collected 263.4 $\mu$b$^{-1}$ high-energy-electron triggered data in U+U collisions at $\sqrt{s_{NN}}$= 193 GeV. Central U+U collisions, with an estimated 20% higher energy density than in central Au+Au data, extend the $\Upsilon$(1S+2S+3S) and Upsilon(1S) nuclear modification trends observed in Au+Au towards higher number of participant nucleons, and confirm the suppression of the $\Upsilon$(1S) state. We see a hint with 1.8 sigma significance that the $\Upsilon$(2S+3S) excited states are not completely suppressed in U+U collisions. These data support the sequential in-medium quarkonium dissociation picture and favor models with a strong $q\bar{q}$ binding.Comment: Proceedings of the Hard Probes International Conference 2015, Montreal, Canada. 4 pages, 5 figure

Neutral pion production in Au+Au collisions at RHIC

New results from the 2010 RHIC low energy program show a substantial suppression of neutral pions in central Au+Au collisions at both sqrt{s_NN}=39 and 62.4 GeV c.m.s. energies. At high pT the 62.4 GeV and 200 GeV data follow the same suppression pattern. On the other hand, otherwise successful pQCD predictions do not describe the 39 GeV data. These observations indicate that initial state effects may play a dominant role at smaller c.m.s. energies and at lower pT . The azimuthal dependence of the nuclear modification factor R_AA is strongly correlated with the (approximately elliptical) geometry of the overlap region. The dependence of R_AA on the reaction plane, determined up to pT=20 GeV/c from 2007 high-luminosity sqrt{s_NN}=200 GeV Au+Au data provides great selectivity among theories, and favours the ASW scenario with AdS/CFT correspondence over the pQCD-based models.Comment: Accepted for the Proceedings of Hard Probe 2012, Cagliary, Italy (4 pages, 4 figures

Production of Quarkonia at RHIC

The production of different quarkonium states provides unique insight to the hot and cold nuclear matter effects in the strongly interacting medium that is formed in high energy heavy ion collisions. While LHC explores the energy frontier, RHIC has a broad physics program to explore the nuclear modification at different energies in a wide range of systems. Some of the most interesting recent results on $J/\psi$ and $\Upsilon$ production in p+p, d+Au and A+A collisions from PHENIX and STAR are summarized in this work.Comment: Writeup of the talk on the "Joint Wigner-CCNU High-Energy Heavy-Ion Balaton Workshop 2015", Tihany, Hungary. To be published in the Gribov 85 memorial issue "Exploring Quantum Field Theory". 8 pages, 8 figure

Bond dimension witnesses and the structure of homogeneous matrix product states

For the past twenty years, Matrix Product States (MPS) have been widely used in solid state physics to approximate the ground state of one-dimensional spin chains. In this paper, we study homogeneous MPS (hMPS), or MPS constructed via site-independent tensors and a boundary condition. Exploiting a connection with the theory of matrix algebras, we derive two structural properties shared by all hMPS, namely: a) there exist local operators which annihilate all hMPS of a given bond dimension; and b) there exist local operators which, when applied over any hMPS of a given bond dimension, decouple (cut) the particles where they act from the spin chain while at the same time join (glue) the two loose ends back again into a hMPS. Armed with these tools, we show how to systematically derive `bond dimension witnesses', or 2-local operators whose expectation value allows us to lower bound the bond dimension of the underlying hMPS. We extend some of these results to the ansatz of Projected Entangled Pairs States (PEPS). As a bonus, we use our insight on the structure of hMPS to: a) derive some theoretical limitations on the use of hMPS and hPEPS for ground state energy computations; b) show how to decrease the complexity and boost the speed of convergence of the semidefinite programming hierarchies described in [Phys. Rev. Lett. 115, 020501 (2015)] for the characterization of finite-dimensional quantum correlations.Comment: Accepted for publication in Quantum. We still do not acknowledge support from the European Research Counci

Combinatorial tangle Floer homology

In this paper we extend the idea of bordered Floer homology to knots and links in $S^3$: Using a specific Heegaard diagram, we construct gluable combinatorial invariants of tangles in $S^3$, $D^3$ and $I\times S^2$. The special case of $S^3$ gives back a stabilized version of knot Floer homology.Comment: 106 pages, 44 figure