Two-pion exchange potential and the πN\pi N amplitude

We discuss the two-pion exchange potential which emerges from a box diagram with one nucleon (the spectator) restricted to its mass shell, and the other nucleon line replaced by a subtracted, covariant $\pi N$ scattering amplitude which includes $\Delta$, Roper, and $D_{13}$ isobars, as well as contact terms and off-shell (non-pole) dressed nucleon terms. The $\pi N$ amplitude satisfies chiral symmetry constraints and fits $\pi N$ data below $\sim$ 700 MeV pion energy. We find that this TPE potential can be well approximated by the exchange of an effective sigma and delta meson, with parameters close to the ones used in one-boson-exchange models that fit $NN$ data below the pion production threshold.Comment: 9 pages (RevTex) and 7 postscript figures, in one uuencoded gzipped tar fil

Gauging the three-nucleon spectator equation

We derive relativistic three-dimensional integral equations describing the interaction of the three-nucleon system with an external electromagnetic field. Our equations are unitary, gauge invariant, and they conserve charge. This has been achieved by applying the recently introduced gauging of equations method to the three-nucleon spectator equations where spectator nucleons are always on mass shell. As a result, the external photon is attached to all possible places in the strong interaction model, so that current and charge conservation are implemented in the theoretically correct fashion. Explicit expressions are given for the three-nucleon bound state electromagnetic current, as well as the transition currents for the scattering processes \gamma He3 -> NNN, Nd -> \gamma Nd, and \gamma He3 -> Nd. As a result, a unified covariant three-dimensional description of the NNN-\gamma NNN system is achieved.Comment: 23 pages, REVTeX, epsf, 4 Postscript figure

Enumerative aspects of the Gross-Siebert program

We present enumerative aspects of the Gross-Siebert program in this introductory survey. After sketching the program's main themes and goals, we review the basic definitions and results of logarithmic and tropical geometry. We give examples and a proof for counting algebraic curves via tropical curves. To illustrate an application of tropical geometry and the Gross-Siebert program to mirror symmetry, we discuss the mirror symmetry of the projective plane.Comment: A version of these notes will appear as a chapter in an upcoming Fields Institute volume. 81 page

Gauging the spectator equations

We show how to derive relativistic, unitary, gauge invariant, and charge conserving three-dimensional scattering equations for a system of hadrons interacting with an electromagnetic field. In the method proposed, the spectator equations describing the strong interactions of the hadrons are gauged using our recently introduced gauging of equations method. A key ingredient in our model is the on-mass-shell particle propagator. We discuss how to gauge this on-mass-shell propagator so that both the Ward-Takahashi and Ward identities are satisfied. We then demonstrate our gauging procedure by deriving the gauge-invariant three-dimensional expression for the deuteron photodisintegration amplitude within the spectator approach.Comment: 17 pages, REVTeX, epsf, 1 Postscript figur

Quantum backreaction in dilute Bose-Einstein condensates

For many physical systems which can be approximated by a classical background field plus small (linearized) quantum fluctuations, a fundamental question concerns the correct description of the backreaction of the quantum fluctuations onto the dynamics of the classical background. We investigate this problem for the example of dilute atomic/molecular Bose-Einstein condensates, for which the microscopic dynamical behavior is under control. It turns out that the effective-action technique does not yield the correct result in general and that the knowledge of the pseudo-energy-momentum tensor ${<\hat T_{\mu\nu}>}$ is not sufficient to describe quantum backreaction.Comment: 8 pages of RevTex4; extended discussion with additional sections, to be published in Physical Review

Interaction of pulses in nonlinear Schroedinger model

The interaction of two rectangular pulses in nonlinear Schroedinger model is studied by solving the appropriate Zakharov-Shabat system. It is shown that two real pulses may result in appearance of moving solitons. Different limiting cases, such as a single pulse with a phase jump, a single chirped pulse, in-phase and out-of-phase pulses, and pulses with frequency separation, are analyzed. The thresholds of creation of new solitons and multi-soliton states are found.Comment: 9 pages, 7 figures. Accepted to Phys. Rev. E, 200

Branching ratio and CP asymmetry of Bs→π+π−B_s \to \pi^+ \pi^- decays in the perturbative QCD approach

In this paper, we calculate the decay rate and CP asymmetry of the $B_s \to \pi^+\pi^-$ decay in perturbative QCD approach with Sudakov resummation. Since none of the quarks in final states is the same as those of the initial $B_s$ meson, this decay can occur only via annihilation diagrams in the standard model. Besides the current-current operators, the contributions from the QCD and electroweak penguin operators are also taken into account. We find that (a) the branching ratio is about $4 \times 10^{-7}$; (b) the penguin diagrams dominate the total contribution; and (c) the direct CP asymmetry is small in size: no more than $3$; but the mixing-induced CP asymmetry can be as large as ten percent testable in the near future LHC-b experiments.Comment: 12 pages, 4 figures included, RevTe

PR-box correlations have no classical limit

One of Yakir Aharonov's endlessly captivating physics ideas is the conjecture that two axioms, namely relativistic causality ("no superluminal signalling") and nonlocality, so nearly contradict each other that a unique theory - quantum mechanics - reconciles them. But superquantum (or "PR-box") correlations imply that quantum mechanics is not the most nonlocal theory (in the sense of nonlocal correlations) consistent with relativistic causality. Let us consider supplementing these two axioms with a minimal third axiom: there exists a classical limit in which macroscopic observables commute. That is, just as quantum mechanics has a classical limit, so must any generalization of quantum mechanics. In this classical limit, PR-box correlations violate relativistic causality. Generalized to all stronger-than-quantum bipartite correlations, this result is a derivation of Tsirelson's bound without assuming quantum mechanics.Comment: for a video of this talk at the Aharonov-80 Conference in 2012 at Chapman University, see quantum.chapman.edu/talk-10, published in Quantum Theory: A Two-Time Success Story (Yakir Aharonov Festschrift), eds. D. C. Struppa and J. M. Tollaksen (New York: Springer), 2013, pp. 205-21

Interacting Open Wilson Lines in Noncommutative Field Theories

In noncommutative field theories, it was known that one-loop effective action describes propagation of non-interacting open Wilson lines, obeying the flying dipole's relation. We show that two-loop effective action describes cubic interaction among `closed string' states created by open Wilson lines. Taking d-dimensional noncommutative [\Phi^3] theory as the simplest setup, we compute nonplanar contribution at low-energy and large noncommutativity limit. We find that the contribution is expressible in a remarkably simple cubic interaction involving scalar open Wilson lines only and nothing else. We show that the interaction is purely geometrical and noncommutative in nature, depending only on sizes of each open Wilson line.Comment: v1: 27 pages, Latex, 7 .eps figures v2: minor wording change + reference adde