There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

http://risa.stanford.edu/teaching/362/particledarkmatter.pdf

Particle dark matter: Evidence, candidates and constraints

Nuclear forces can be systematically derived using effective chiral Lagrangians consistent with the symmetries of QCD. I review the status of the calculations for two- and three-nucleon forces and their applications in few-nucleon systems. I also address issues like the quark mass dependence of the nuclear forces and resonance saturation for four-nucleon operators.

/pdf/modern-theory-of-nuclear-forces-436h635pm0.pdf

Modern theory of nuclear forces

A golden age for heavy-quarkonium physics dawned a decade ago, initiated by the confluence of exciting advances in quantum chromodynamics (QCD) and an explosion of related experimental activity. The early years of this period were chronicled in the Quarkonium Working Group (QWG) CERN Yellow Report (YR) in 2004, which presented a comprehensive review of the status of the field at that time and provided specific recommendations for further progress. However, the broad spectrum of subsequent breakthroughs, surprises, and continuing puzzles could only be partially anticipated. Since the release of the YR, the BESII program concluded only to give birth to BESIII; the B-factories and CLEO-c flourished; quarkonium production and polarization measurements at HERA and the Tevatron matured; and heavy-ion collisions at RHIC have opened a window on the deconfinement regime. All these experiments leave legacies of quality, precision, and unsolved mysteries for quarkonium physics, and therefore beg for continuing investigations at BESIII, the LHC, RHIC, FAIR, the Super Flavor and/or Tau-Charm factories, JLab, the ILC, and beyond. The list of newly found conventional states expanded to include h(c)(1P), chi(c2)(2P), B-c(+), and eta(b)(1S). In addition, the unexpected and still-fascinating X(3872) has been joined by more than a dozen other charmonium- and bottomonium-like "XYZ" states that appear to lie outside the quark model. Many of these still need experimental confirmation. The plethora of new states unleashed a flood of theoretical investigations into new forms of matter such as quark-gluon hybrids, mesonic molecules, and tetraquarks. Measurements of the spectroscopy, decays, production, and in-medium behavior of c (c) over bar, b (b) over bar, and b (c) over bar bound states have been shown to validate some theoretical approaches to QCD and highlight lack of quantitative success for others. Lattice QCD has grown from a tool with computational possibilities to an industrial-strength effort now dependent more on insight and innovation than pure computational power. New effective field theories for the description of quarkonium in different regimes have been developed and brought to a high degree of sophistication, thus enabling precise and solid theoretical predictions. Many expected decays and transitions have either been measured with precision or for the first time, but the confusing patterns of decays, both above and below open-flavor thresholds, endure and have deepened. The intriguing details of quarkonium suppression in heavy-ion collisions that have emerged from RHIC have elevated the importance of separating hot- and cold-nuclear-matter effects in quark-gluon plasma studies. This review systematically addresses all these matters and concludes by prioritizing directions for ongoing and future efforts.

/pdf/heavy-quarkonium-progress-puzzles-and-opportunities-2tru0l8jyp.pdf

Heavy quarkonium: progress, puzzles, and opportunities

The hidden-charm pentaquark and tetraquark states

We construct the Lagrangian for an effective theory of highly energetic quarks with energy Q, interacting with collinear and soft gluons. This theory has two low energy scales, the transverse momentum of the collinear particles, ${p}_{\ensuremath{\perp}},$ and the scale ${p}_{\ensuremath{\perp}}^{2}/Q.$ The heavy to light currents are matched onto operators in the effective theory at one loop and the renormalization group equations for the corresponding Wilson coefficients are solved. This running is used to sum Sudakov logarithms in inclusive $\stackrel{\ensuremath{\rightarrow}}{B}{X}_{s}\ensuremath{\gamma}$ and $\stackrel{\ensuremath{\rightarrow}}{B}{X}_{u}l\overline{\ensuremath{\nu}}$ decays. We also show that the interactions with collinear gluons preserve the relations for the soft part of the form factors for heavy-to-light decays found by Charles et al. [Phys. Rev. D 60, 014001 (1999)], establishing these relations in the large energy limit of QCD.

An Effective field theory for collinear and soft gluons: Heavy to light decays

We construct an effective field theory valid for processes in which highly energetic light-like particles interact with collinear and soft degrees of freedom, using the decay $\stackrel{\ensuremath{\rightarrow}}{B}{X}_{s}\ensuremath{\gamma}$ near the end point of the photon spectrum, ${x=2E}_{\ensuremath{\gamma}}{/m}_{b}\ensuremath{\rightarrow}1,$ as an example. Below the scale $\ensuremath{\mu}{=m}_{b}$ both soft and collinear degrees of freedom are included in the effective theory, while below the scale $\ensuremath{\mu}{=m}_{b}\sqrt{x\ensuremath{-}y},$ where $1\ensuremath{-}y$ is the light cone momentum fraction of the b quark in the B meson, we match onto a theory of bilocal operators. We show that at one loop large logarithms cancel in the matching conditions, and that we recover the well-known renormalization group equations that sum leading Sudakov logarithms.

Summing Sudakov logarithms in B-->X s γ in effective field theory

In this paper we show how gauge symmetries in an effective theory can be used to simplify proofs of factorization formulas in highly energetic hadronic processes. We use the soft-collinear effective theory, generalized to deal with back-to-back jets of collinear particles. Our proofs do not depend on the choice of a particular gauge, and the formalism is applicable to both exclusive and inclusive factorization. As examples we treat the $\ensuremath{\pi}\ensuremath{-}\ensuremath{\gamma}$ form factor $(\ensuremath{\gamma}{\ensuremath{\gamma}}^{*}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}),$ light meson form factors $({\ensuremath{\gamma}}^{*}\stackrel{\ensuremath{\rightarrow}}{M}M),$ as well as deep inelastic scattering ${(e}^{\ensuremath{-}}\stackrel{\ensuremath{\rightarrow}}{p}{e}^{\ensuremath{-}}X),$ the Drell-Yan process $(p\overline{p}\ensuremath{\rightarrow}{\mathrm{Xl}}^{+}{l}^{\ensuremath{-}}),$ and deeply virtual Compton scattering $({\ensuremath{\gamma}}^{*}\stackrel{\ensuremath{\rightarrow}}{p}{\ensuremath{\gamma}}^{(*)}p).$

Hard scattering factorization from effective field theory

The production rate of prompt {psi}{prime}`s at large transverse momentum at the Fermilab Tevatron is larger than theoretical expectations by about a factor of 30. As a solution to this puzzle, we suggest that the dominant {psi}{prime} production mechanism is the fragmentation of a gluon into a {ital c{bar c}} pair in a pointlike color-octet {ital S}-wave state, which subsequently evolves nonperturbatively into a {psi}{prime} plus light hadrons. This contribution to the fragmentation function is enhanced by a short-distance factor of 1/{alpha}{sup 2}{sub {ital s}}, which may compensate for its suppression by {ital v}{sup 4}, where {ital v} is the relative momentum of the charm quark in the {psi}{prime}.

Color-Octet Fragmentation and the psi ' Surplus at the Fermilab Tevatron.

We construct jet observables for energetic top quarks that can be used to determine a short-distance top quark mass from reconstruction in e+e- collisions with accuracy better than LambdaQCD. Using a sequence of effective field theories we connect the production energy, mass, and top width scales, Q>>m>>Gamma, for the top jet cross section, and derive a QCD factorization theorem for the top invariant mass spectrum. Our analysis accounts for alphas corrections from the production and mass scales, corrections due to constraints in defining invariant masses, nonperturbative corrections from the cross talk between the jets, and alphas corrections to the Breit-Wigner line shape. This paper mainly focuses on deriving the factorization theorem for hemisphere invariant mass distributions and other event shapes in e+e- collisions applicable at a future linear collider. We show that the invariant mass distribution is not a simple Breit-Wigner function involving the top width. Even at leading order it is shifted and broadened by nonperturbative soft QCD effects. We predict that the invariant mass peak position increases linearly with Q/m due to these nonperturbative effects. They are encoded in terms of a universal soft function that also describes soft effects for massless dijet events. In a future paper we compute alphas corrections to the jet invariant mass spectrum, including a summation of large logarithms between the scales Q, m, and Gamma.

/pdf/jets-from-massive-unstable-particles-top-mass-determination-2sd88u6u8q.pdf

Sean Fleming

Papers

An Effective field theory for collinear and soft gluons: Heavy to light decays

Summing Sudakov logarithms in B-->X s γ in effective field theory

Hard scattering factorization from effective field theory

Color-Octet Fragmentation and the psi ' Surplus at the Fermilab Tevatron.

Jets from massive unstable particles: Top-mass determination