The transverse structure of the QCD string

The characterization of the transverse structure of the QCD string is discussed. We formulate a conjecture as to how the stress-energy tensor of the underlying gauge theory couples to the string degrees of freedom. A consequence of the conjecture is that the energy density and the longitudinal-stress operators measure the distribution of the transverse position of the string, to leading order in the string fluctuations, whereas the transverse-stress operator does not. We interpret recent numerical measurements of the transverse size of the confining string and show that the difference of the energy and longitudinal-stress operators is the appropriate probe to use when comparing with the next-to-leading order string prediction. Secondly we derive the constraints imposed by open-closed string duality on the transverse structure of the string. We show that a total of three independent `gravitational' form factors characterize the transverse profile of the closed string, and obtain the interpretation of recent effective string theory calculations: the square radius of a closed string of length \beta, defined from the slope of its gravitational form factor, is given by (d-1)/(2\pi\sigma)\log(\beta/(4r_0)) in d space dimensions. This is to be compared with the well-known result that the width of the open-string at mid-point grows as (d-1)/(2\pi\sigma) log(r/r_0). We also obtain predictions for transition form factors among closed-string states.Comment: 21 pages, 1 figur

Unifying Requirements and Code: an Example

Requirements and code, in conventional software engineering wisdom, belong to entirely different worlds. Is it possible to unify these two worlds? A unified framework could help make software easier to change and reuse. To explore the feasibility of such an approach, the case study reported here takes a classic example from the requirements engineering literature and describes it using a programming language framework to express both domain and machine properties. The paper describes the solution, discusses its benefits and limitations, and assesses its scalability.Comment: 13 pages; 7 figures; to appear in Ershov Informatics Conference, PSI, Kazan, Russia (LNCS), 201

Density, short-range order and the quark-gluon plasma

We study the thermal part of the energy density spatial correlator in the quark-gluon plasma. We describe its qualitative form at high temperatures. We then calculate it out to distances approx. 1.5/T in SU(3) gauge theory lattice simulations for the range of temperatures 0.9<= T/T_c<= 2.2. The vacuum-subtracted correlator exhibits non-monotonic behavior, and is almost conformal by 2T_c. Its broad maximum at r approx. 0.6/T suggests a dense medium with only weak short-range order, similar to a non-relativistic fluid near the liquid-gas phase transition, where eta/s is minimal.Comment: 4 pages, 4 figure

Lattice Gauge Theory Sum Rule for the Shear Channel

An exact expression is derived for the $(\omega,p)=0$ thermal correlator of shear stress in SU($N_c$) lattice gauge theory. I remove a logarithmic divergence by taking a suitable linear combination of the shear correlator and the correlator of the energy density. The operator product expansion shows that the same linear combination has a finite limit when $\omega\to\infty$. It follows that the vacuum-subtracted shear spectral function vanishes at large frequencies at least as fast as $\alpha_s^2(\omega)$ and obeys a sum rule. The trace anomaly makes a potential contribution to the spectral sum rule which remains to be fully calculated, but which I estimate to be numerically small for $T\gtrsim 3T_c$. By contrast with the bulk channel, the shear channel spectral density is then overall enhanced as compared to the spectral density in vacuo.Comment: 11 pages, no figure

Cutoff Effects on Energy-Momentum Tensor Correlators in Lattice Gauge Theory

We investigate the discretization errors affecting correlators of the energy-momentum tensor $T_{\mu\nu}$ at finite temperature in SU($N_c$) gauge theory with the Wilson action and two different discretizations of $T_{\mu\nu}$. We do so by using lattice perturbation theory and non-perturbative Monte-Carlo simulations. These correlators, which are functions of Euclidean time $x_0$ and spatial momentum ${\bf p}$, are the starting point for a lattice study of the transport properties of the gluon plasma. We find that the correlator of the energy $\int d^3x T_{00}$ has much larger discretization errors than the correlator of momentum $\int d^3x T_{0k}$. Secondly, the shear and diagonal stress correlators ($T_{12}$ and $T_{kk}$) require \Nt\geq 8 for the $Tx_0={1/2}$ point to be in the scaling region and the cutoff effect to be less than 10%. We then show that their discretization errors on an anisotropic lattice with \as/\at=2 are comparable to those on the isotropic lattice with the same temporal lattice spacing. Finally, we also study finite ${\bf p}$ correlators.Comment: 16 pages, 5 figure

Lattice QCD and the two-photon decay of the neutral pion

Two-photon decays probe the structure of mesons and represent an important contribution to hadronic light-by-light scattering. For the neutral pion, the decay amplitude tests the effects of the chiral anomaly; for a heavy quarkonium state, it measures the magnitude of its wavefunction at the origin. We rederive the expression of the decay amplitude in terms of a Euclidean correlation function starting from the theory defined on the torus. The derivation shows that for timelike photons the approach to the infinite-volume decay amplitude is exponential in the periodic box size.Comment: 18 pages, no figure

Top Quark Production

Recent measurements of top quark pair and single top production are presented. The results include inclusive cross sections as well as studies of differential distributions. Evidence for single top quark production in association with a W-boson in the final state is reported for the first time. Calculations in perturbative QCD up to approximate next-to-next-to-leading order show very good agreement with the data.Comment: Physics in Collision, Slovakia, 2012 PSNUM 0