Narrow Results

We review old and new results on the Fröhlich polaron model. The discussion includes the validity of the (classical) Pekar approximation in the strong coupling limit, quantum corrections to this limit, as well as the divergence of the effective polaron mass.

Lattice QCD at finite temperature T and chemical potential μ is studied analytically in the strong coupling limit with overlap fermions. We start from the first order approximation of lattice action with generalized overlap (GO) fermions to derive an effective free energy written in terms of chiral condensate as a function of T and μ with the use of mean field approximation. We elucidate the phase structure on the (μ, T) plane and discover the tricritical point separating the first and the second order chiral phase transition. Discussion of the doubling problem and higher order terms are given.

We show that a Green function solution can be given for a class of nonhomogeneous nonlinear systems having relevance in quantum field theory. This in turn means that a quantum field theory in the strong coupling limit can be formulated and the spectrum obtained.

An overview is given on key physics, detector and accelerator aspects of the LHeC including its further development with emphasis to its role as the cleanest microscope of parton dynamics and a precision Higgs facility.

Starting from the divergent character of the perturbative expansions in QCD and using the technique of series acceleration by the conformal mappings of the Borel plane, I define a novel, non-power perturbative expansion for the Adler function, which simultaneously implements renormalisation-group summation and has a tamed large-order behaviour. The new expansion functions, which replace the standard powers of the coupling, are singular at the origin of the coupling plane and have divergent perturbative expansions, resembling the expanded function itself. Confronting the new perturbative expansions with the standard ones on specific models investigated recently in the literature, I show that they approximate in an impressive way the exact Adler function and the spectral function moments. Applied to the τ hadronic width, the contour-improved and the renormalisation-group summed non-power expansions in the scheme lead to the prediction , which translates to .

A determination of the strong coupling α_s at rather low energies is possible through the analysis of hadronic decays of the τ lepton. In turn, the low energy necessitates sufficient control over perturbative QCD corrections, the nonperturbative condensate contributions in the framework of the operator product expansion (OPE), as well as corrections going beyond the OPE, the duality violations (DVs). Perturbative QCD uncertainties arise from open questions regarding the renormalization group resummation of the series. The fit quantities are moment integrals of the τ spectral function data in a certain energy window and care should be taken to have good perturbative behavior of those moments as well as control over higher-dimensional operator corrections. Furthermore, all parameters occurring in the theoretical description should be extracted from fits to the data in a self-consistent manner.

Recently, we extracted the strong coupling, ${\alpha }_s(m_{\tau }^2)$, from the revised ALEPH data for non-strange hadronic tau decays. Our analysis is based on a method previously used for the determination of the strong coupling from OPAL data. In our strategy, we employ different moments of the spectral functions both with and without pinching, including duality violations, in order to obtain fully self-consistent analyses that do not rely on untested assumptions (such as the smallness of higher dimension contributions in the operation product expansion (OPE)). Here we discuss the ${\alpha }_s$ values obtained from the ALEPH and the OPAL data, the robustness of the analysis, as well as non-perturbative contributions from DVs and the OPE. We show that, although the ${\alpha }_s$ determination is sound, non-perturbative effects limit the accuracy with which one can extract the strong coupling from tau decay data. Finally, we discuss the compatibility of the data sets and the possibility of a combined analysis.

Using the most recent release of the ALEPH $\tau$ decay data, we present a very detailed phenomenological update of the ${\alpha }_s(m_{\tau }^2)$ determination. We have exploited the sensitivity to the strong coupling in many different ways, exploring several complementary methodologies. All determinations turn out to be in excellent agreement, allowing us to extract a very reliable value of the strong coupling. We find ${\alpha }_s^{(n_f=3)}(m_{\tau }^2)=0.328\pm 0.012$ which implies ${\alpha }_s^{(n_f=5)}(M_Z^2)=0.1197\pm 0.0014$. We critically revise previous work, and point out the problems flawing some recent analyses which claim slightly smaller values.

We review the determination of ${\alpha }_{\mathrm{\text{s}}}$ that follows from comparing at short distances the QCD static energy at three loops and resummation of the next-to-next-to leading logarithms with its determination in 2+1-flavor lattice QCD provided by the HotQCD collaboration. The result that we obtain is ${\alpha }_{\mathrm{\text{s}}}$(1.5 GeV) = 0.336${}_{-0.008}^{+0.012}$, corresponding to ${\alpha }_{\mathrm{\text{s}}}$(M_Z) = 0.1166${}_{-0.0008}^{+0.0012}$. We outline future possible developments.

In this paper, we review recent progress on relativistic hydrodynamics in (2 + 1) dimensions with an external magnetic field. We discuss the formalism allowing for momentum loss due to the explicit and spontaneous breaking of translation invariance by scalar operators. We also compare to some results from the gauge/gravity correspondence.

The problem of the strong-coupling regime is considered in the scalar superrenormalizable field theory . By using the Gaussian transform, we have found an optimal representation within which the exact strong-coupling behavior of the free energy is already obtained in the leading-order approximation. Within this representation, the interaction becomes slower as the bare coupling constant grows, so the higher-order corrections can be systematically estimated by using a modified perturbation scheme. The next-to-leading terms give rise in insignificant corrections for finite coupling. The regularization procedure regroups the initial counterterms so that the divergencies are exactly removed in final expressions. The main idea is demonstrated in the simplest examples of a plain quartic integral and the anharmonic oscillator.

This is a review of the status and outstanding issues in attempts to construct chiral lattice gauge theories by decoupling the mirror fermions from a vectorlike theory. In the first half, we explain why studying nonperturbative chiral gauge dynamics may be of interest, enumerate the problems that a lattice formulation of chiral gauge theories must overcome, and briefly review our current knowledge. We then discuss the motivation and idea of mirror–fermion decoupling and illustrate the desired features of the decoupling dynamics by a simple solvable toy model. The role of exact chiral symmetries and matching of 't Hooft anomalies on the lattice is also explained. The second, more technical, half of the paper is devoted to a discussion of the known and unknown features of mirror-decoupling dynamics formulated with Ginsparg–Wilson fermions. We end by pointing out possible directions for future studies.

We consider an imaginary time functional integral formulation of a two-flavor, 3+1 lattice QCD model with Wilson's action and in the strong coupling regime (with a small hopping parameter, κ > 0, and a much smaller plaquette coupling, , so that the quarks and glueballs are heavy). The model has local SU(3)_c gauge and global SU(2)_f flavor symmetries, and incorporates the corresponding part of the eightfold way particles: baryons (mesons) of asymptotic mass ≈-3 ln κ(≈-2 ln κ). We search for pentaquark states as meson–baryon bound states in the energy–momentum spectrum of the model, using a lattice Bethe–Salpeter equation. This equation is solved within a ladder approximation, given by the lowest nonvanishing order in κ and β of the Bethe–Salpeter kernel. It includes order κ² contributions with a exchange potential together with a contribution that is a local-in-space, energy-dependent potential. The attractive or repulsive nature of the exchange interaction depends on the spin of the meson–baryon states. The Bethe–Salpeter equation presents integrable singularities, forcing the couplings to be above a threshold value for the meson and the baryon to bind in a pentaquark. We analyzed all the total isospin sectors, I = 1/2, 3/2, 5/2, for the system. For all I, the net attraction resulting from the two sources of interaction is not strong enough for the meson and the baryon to bind. Thus, within our approximation, these pentaquark states are not present up to near the free meson–baryon energy threshold of ≈-5 ln κ. This result is to be contrasted with the spinless case for which our method detects meson–baryon bound states, as well as for Yukawa effective baryon and meson field models. A physical interpretation of our results emerges from an approximate correspondence between meson–baryon bound states and negative energy states of a one-particle lattice Schrödinger Hamiltonian.

We determine two-baryon bound states in a 3+1 lattice QCD model with improved Wilson action and two flavors. We work in the strong coupling regime: small hopping parameter κ > 0 and much smaller plaquette coupling β > 0. In this regime, it is known that the low-lying energy–momentum spectrum is comprised of baryons and mesons with asymptotic masses -3 ln κ and -2 ln κ, respectively. We show that the dominant baryon–baryon interaction is an order κ² space-range-one -exchange potential. We also show that this interaction has an important and novel isospin–spin interchange symmetry relating the various possible bound states, and then governing the two-baryon spectral structure. Letting S(I) denote the total spin (total isospin) of the two-baryon bound states, S, I = 0, 1, 2, 3, we find bound states with asymptotic binding energy κ²/4, for I+S = 1, 3, and 4 (here, with I = S = 2); κ²/12, for I+S = 0, 2, 4 and 3 (here, with I = 1, 2). In particular, we show that the two-baryon spectrum contains deuteron (I = 0), diproton (I = 1) and dineutron (I = 1)-like bound states. Using the isospin–spin symmetry, we can circumvent the lack of spin symmetry of the lattice action and show they all have the same asymptotic binding energy, namely κ²/4. Our analysis uses convenient two and four-baryon correlations, their spectral representations and a lattice Bethe–Salpeter equation, which is solved in a ladder approximation. For the isospin, spin part of the interaction, we obtain a permanent representation which describes the interaction of the individual spins and isospins of the quarks of one baryon with those of the other baryon.

We review physical scenarios in different vacua of 𝒩 = 2 supersymmetric QCD deformed by the mass term μ for the adjoint matter. This deformation breaks supersymmetry down to 𝒩 = 1 and, at large μ, the theory flows to 𝒩 = 1 QCD. We focus on dynamical scenarios which can serve as prototypes of what we observe in real-world QCD. The so-called r = N vacuum is especially promising in this perspective. In this vacuum an "instead-of-confinement" phase was identified previously, which is qualitatively close to the conventional QCD confinement: the quarks and gauge bosons screened at weak coupling, at strong coupling evolve into monopole–antimonopole pairs confined by non-Abelian strings. We review genesis of this picture.

SU(N_c) lattice gauge theories with N_f flavors of massless staggered fermions are studied in the presence of quark chemical potential μ. A recent exact result that in the strong coupling limit (vanishing inverse gauge coupling β) and for sufficiently large μ the theory is in a chiral symmetric phase is here extended into the finite gauge coupling region. These and similar results are obtained by means of a cluster expansion which combines a fermion spacelike hopping expansion and a strong coupling plaquette expansion. The cluster expansion is shown to converge for sufficiently large μ and small β at any temperature T. All expectations of chirally noninvariant local fermion operators vanish identically, or, equivalently, their correlations cluster exponentially within the expansion. This implies the absence of spontaneous breaking of (any part of) the global chiral symmetries in the theory. The resulting phase at low T may be described as a "quarkyonic" matter phase. There is thus absence of any superfluidity or color superconductivity in this strong coupling regime. Implications for the phase diagram of SU(N_c) theories in the region of large chemical potential are discussed.

We present a summary of results from studies of quantum chromodynamics at the Fermilab Tevatron collider by the CDF and the D0 experiments. These include Run II results for the time period up to the end of Summer 2014. A brief description of Run I results is also given. This review covers a wide spectrum of topics, and includes measurements with jet and vector boson final states in the hard (perturbative) energy regime, as well as studies of soft physics such as diffractive and elastic scatterings, underlying and minimum bias events, hadron fragmentation, and multiple parton interactions.

Jet production at hadron colliders provides powerful constraints on the parton distribution functions (PDFs) of the proton, in particular on the gluon PDF. Jet production can also be used to extract the QCD coupling ${\alpha }_s(Q)$ and to test its running with the momentum transfer up to the TeV region. In this review, I summarize the information on PDFs and the strong coupling that has been provided by Run I LHC jet data. First of all, I discuss why jet production is directly sensitive to the gluon and quark PDFs at large-x, and then review the state-of-the-art perturbative calculations for jet production at hadron colliders and the corresponding fast calculations required for PDF fitting. Then I present the results of various recent studies on the impact on PDFs, in particular the gluon, that have been performed using as input jet measurements from ATLAS and CMS. I also review the available determinations of the strong coupling constant based on ATLAS and CMS jet data, with emphasis on the fact that LHC jet data provides, for the first time, a direct test of the ${\alpha }_s(Q)$ running at the TeV scale. I conclude with a brief outlook on possible future developments.

Quantum Chromodynamics predicts that the strong coupling strength ${\alpha }_{\mathrm{\text{s}}}$ decreases with increasing energy or momentum transfer, and vanishes at asymptotically high energies. The history and the status of experimental tests of asymptotic freedom are summarised in this review.

Efficient cluster algorithms have recently been discovered to solve strong coupling lattice QCD with staggered fermions in the chiral limit from first principles. This allows us for the first time to uncover the universal properties close to chiral phase transitions and make connections with chiral perturbation theory. In this article we will review some of the recent progress and outline some possible directions for future work.