# M. Laine - University of Bern

## Contact Details

NameM. Laine |
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AffiliationUniversity of Bern |
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CityBern |
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CountrySwitzerland |
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## Pubs By Year |
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## External Links |
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## Pub CategoriesHigh Energy Physics - Phenomenology (45) High Energy Physics - Lattice (26) Cosmology and Nongalactic Astrophysics (3) High Energy Physics - Experiment (2) Nuclear Experiment (2) Nuclear Theory (2) Astrophysics of Galaxies (1) Statistics - Applications (1) Statistics - Methodology (1) Mathematics - Numerical Analysis (1) |

## Publications Authored By M. Laine

Starting from operator equations of motion and making arguments based on a separation of time scales, a set of equations is derived which govern the non-equilibrium time evolution of a GeV-scale sterile neutrino density matrix and active lepton number densities at temperatures T > 130 GeV. The density matrix possesses generation and helicity indices; we demonstrate how helicity permits for a classification of various sources for leptogenesis. The coefficients parametrizing the equations are determined to leading order in Standard Model couplings, accounting for the LPM resummation of 1+n <-> 2+n scatterings and for all 2 <-> 2 scatterings. Read More

Theories with extended Higgs sectors constructed in view of cosmological ramifications (gravitational wave signal, baryogenesis, dark matter) are often faced with conflicting requirements for their couplings; in particular those influencing the strength of a phase transition may be large. Large couplings compromise perturbative studies, as well as the high-temperature expansion that is invoked in dimensionally reduced lattice investigations. With the example of the inert doublet extension of the Standard Model (IDM), we show how a resummed 2-loop effective potential can be computed without a high-T expansion, and use the result to scrutinize its accuracy. Read More

These lecture notes, suitable for a two-semester introductory course or self-study, offer an elementary and self-contained exposition of the basic tools and concepts that are encountered in practical computations in perturbative thermal field theory. Selected applications to heavy ion collision physics and cosmology are outlined in the last chapter. Read More

**Authors:**G. Aarts, J. Aichelin, C. Allton, R. Arnaldi, S. A. Bass, C. Bedda, N. Brambilla, E. Bratkovskaya, P. Braun-Munzinger, G. E. Bruno, T. Dahms, S. K. Das, H. Dembinski, M. Djordjevic, E. G. Ferreiro, A. Frawley, P. -B. Gossiaux, R. Granier de Cassagnac, A. Grelli, M. He, W. Horowitz, G. M. Innocenti, M. Jo, O. Kaczmarek, P. G. Kuijer, M. Laine, M. P. Lombardo, A. Mischke, M. Munhoz, M. Nahrgang, M. Nguyen, A. C. Oliveira da Silva, P. Petreczky, A. Rothkopf, M. Schmelling, E. Scomparin, T. Song, J. Stachel, A. Suaide, L. Tolos, B. Trzeciak, A. Uras, L. van Doremalen, L. Vermunt, S. Vigolo, N. Xu, Z. Ye, H. Zanoli, P. Zhuang

Open and hidden heavy-flavor physics in high-energy nuclear collisions are entering a new and exciting stage towards reaching a clearer understanding of the new experimental results with the possibility to link them directly to the advancement in lattice Quantum Chromo-dynamics (QCD). Recent results from experiments and theoretical developments regarding open and hidden heavy-flavor dynamics have been debated at the Lorentz Workshop "Tomography of the quark-gluon plasma with heavy quarks}, which was held in October 2016 in Leiden, the Netherlands. In this contribution, we summarize identified common understandings and developed strategies for the upcoming five years, which aim at achieving a profound knowledge of the dynamical properties of the quark-gluon plasma. Read More

We consider non-relativistic "dark" particles interacting through gauge boson exchange. At finite temperature, gauge exchange is modified in many ways: virtual corrections lead to Debye screening; real corrections amount to frequent scatterings of the heavy particles on light plasma constituents; mixing angles change. In a certain temperature and energy range, these effects are of order unity. Read More

Remote sensing observations are extensively used for analysis of environmental variables. These variables often exhibit spatial correlation, which has to be accounted for in the calibration models used in predictions, either by direct modelling of the dependencies or by allowing for spatially correlated stochastic effects. Another feature in many remote sensing instruments is that the derived predictor variables are highly correlated, which can lead to unnecessary model over-training and at worst, singularities in the estimates. Read More

We estimate the thermal masses and damping rates of active (m < eV) and sterile (M ~ GeV) neutrinos with thermal momenta k ~ 3T at temperatures below the electroweak crossover (5 GeV < T < 160 GeV). These quantities fix the equilibration or "washout" rates of Standard Model lepton number densities. Sterile neutrinos interact via direct scatterings mediated by Yukawa couplings, and via their overlap with active neutrinos. Read More

A two-dimensional tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A Non Uniform Rational Basis Splines (NURBS) curve is used as computational representation of the boundary. Read More

**Authors:**A. Dainese

^{1}, U. A. Wiedemann

^{2}, N. Armesto

^{3}, D. d'Enterria

^{4}, J. M. Jowett

^{5}, J. -P. Lansberg

^{6}, J. G. Milhano

^{7}, C. A. Salgado

^{8}, M. Schaumann

^{9}, M. van Leeuwen

^{10}, J. L. Albacete, A. Andronic, P. Antonioli, L. Apolinario, S. Bass, A. Beraudo, A. Bilandzic, S. Borsanyi, P. Braun-Munzinger, Z. Chen, L. Cunqueiro Mendez, G. S. Denicol, K. J. Eskola, S. Floerchinger, H. Fujii, P. Giubellino, C. Greiner, J. F. Grosse-Oetringhaus, C. -M. Ko, P. Kotko, K. Krajczar, K. Kutak, M. Laine, Y. Liu, M. P. Lombardo, M. Luzum, C. Marquet, S. Masciocchi, V. Okorokov, J. -F. Paquet, H. Paukkunen, E. Petreska, T. Pierog, M. Ploskon, C. Ratti, A. H. Rezaeian, W. Riegler, J. Rojo, C. Roland, A. Rossi, G. P. Salam, S. Sapeta, R. Schicker, C. Schmidt, J. Stachel, J. Uphoff, A. van Hameren, K. Watanabe, B. -W. Xiao, F. Yuan, D. Zaslavsky, K. Zhou, P. Zhuang

**Affiliations:**

^{1}editors,

^{2}editors,

^{3}section editors,

^{4}section editors,

^{5}section editors,

^{6}section editors,

^{7}section editors,

^{8}section editors,

^{9}section editors,

^{10}section editors

The Future Circular Collider (FCC) Study is aimed at assessing the physics potential and the technical feasibility of a new collider with centre-of-mass energies, in the hadron-hadron collision mode, seven times larger than the nominal LHC energies. Operating such machine with heavy ions is an option that is being considered in the accelerator design studies. It would provide, for example, Pb-Pb and p-Pb collisions at sqrt{s_NN} = 39 and 63 TeV, respectively, per nucleon-nucleon collision, with integrated luminosities above 30 nb^-1 per month for Pb-Pb. Read More

We estimate the photon production rate from an SU(3) plasma at temperatures of about 1.1Tc and 1.3Tc. Read More

The co-annihilation rate of heavy particles close to thermal equilibrium, which plays a role in many classic dark matter scenarios, can be "simulated" in QCD by considering the pair annihilation rate of a heavy quark and antiquark at a temperature of a few hundred MeV. We show that the so-called Sommerfeld factors, parameterizing the rate, can be defined and measured non-perturbatively within the NRQCD framework. Lattice measurements indicate a modest suppression in the octet channel, in reasonable agreement with perturbation theory, and a large enhancement in the singlet channel, much above the perturbative prediction. Read More

**Authors:**R. Adhikari, M. Agostini, N. Anh Ky, T. Araki, M. Archidiacono, M. Bahr, J. Baur, J. Behrens, F. Bezrukov, P. S. Bhupal Dev, D. Borah, A. Boyarsky, A. de Gouvea, C. A. de S. Pires, H. J. de Vega, A. G. Dias, P. Di Bari, Z. Djurcic, K. Dolde, H. Dorrer, M. Durero, O. Dragoun, M. Drewes, G. Drexlin, Ch. E. Düllmann, K. Eberhardt, S. Eliseev, C. Enss, N. W. Evans, A. Faessler, P. Filianin, V. Fischer, A. Fleischmann, J. A. Formaggio, J. Franse, F. M. Fraenkle, C. S. Frenk, G. Fuller, L. Gastaldo, A. Garzilli, C. Giunti, F. Glück, M. C. Goodman, M. C. Gonzalez-Garcia, D. Gorbunov, J. Hamann, V. Hannen, S. Hannestad, S. H. Hansen, C. Hassel, J. Heeck, F. Hofmann, T. Houdy, A. Huber, D. Iakubovskyi, A. Ianni, A. Ibarra, R. Jacobsson, T. Jeltema, J. Jochum, S. Kempf, T. Kieck, M. Korzeczek, V. Kornoukhov, T. Lachenmaier, M. Laine, P. Langacker, T. Lasserre, J. Lesgourgues, D. Lhuillier, Y. F. Li, W. Liao, A. W. Long, M. Maltoni, G. Mangano, N. E. Mavromatos, N. Menci, A. Merle, S. Mertens, A. Mirizzi, B. Monreal, A. Nozik, A. Neronov, V. Niro, Y. Novikov, L. Oberauer, E. Otten, N. Palanque-Delabrouille, M. Pallavicini, V. S. Pantuev, E. Papastergis, S. Parke, S. Pascoli, S. Pastor, A. Patwardhan, A. Pilaftsis, D. C. Radford, P. C. -O. Ranitzsch, O. Rest, D. J. Robinson, P. S. Rodrigues da Silva, O. Ruchayskiy, N. G. Sanchez, M. Sasaki, N. Saviano, A. Schneider, F. Schneider, T. Schwetz, S. Schönert, S. Scholl, F. Shankar, R. Shrock, N. Steinbrink, L. Strigari, F. Suekane, B. Suerfu, R. Takahashi, N. Thi Hong Van, I. Tkachev, M. Totzauer, Y. Tsai, C. G. Tully, K. Valerius, J. W. F. Valle, D. Venos, M. Viel, M. Vivier, M. Y. Wang, C. Weinheimer, K. Wendt, L. Winslow, J. Wolf, M. Wurm, Z. Xing, S. Zhou, K. Zuber

We present a comprehensive review of keV-scale sterile neutrino Dark Matter, collecting views and insights from all disciplines involved - cosmology, astrophysics, nuclear, and particle physics - in each case viewed from both theoretical and experimental/observational perspectives. After reviewing the role of active neutrinos in particle physics, astrophysics, and cosmology, we focus on sterile neutrinos in the context of the Dark Matter puzzle. Here, we first review the physics motivation for sterile neutrino Dark Matter, based on challenges and tensions in purely cold Dark Matter scenarios. Read More

The momentum diffusion coefficient of a heavy quark in a hot QCD plasma can be extracted as a transport coefficient related to the correlator of two colour-electric fields dressing a Polyakov loop. We determine the perturbative renormalization factor for a particular lattice discretization of this correlator within Wilson's SU(3) gauge theory, finding a ~12% NLO correction for values of the bare coupling used in the current generation of simulations. The impact of this result on existing lattice determinations is commented upon, and a possibility for non-perturbative renormalization through the gradient flow is pointed out. Read More

We estimate the momentum diffusion coefficient of a heavy quark within a pure SU(3) plasma at a temperature of about 1.5Tc. Large-scale Monte Carlo simulations on a series of lattices extending up to 192^3*48 permit us to carry out a continuum extrapolation of the so-called colour-electric imaginary-time correlator. Read More

The putative recent indication of an unidentified 3.55 keV X-ray line in certain astrophysical sources is taken as a motivation for an improved theoretical computation of the cosmological abundance of 7.1 keV sterile neutrinos. Read More

Because of physical processes ranging from microscopic particle collisions to macroscopic hydrodynamic fluctuations, any plasma in thermal equilibrium emits gravitational waves. For the largest wavelengths the emission rate is proportional to the shear viscosity of the plasma. In the Standard Model at T > 160 GeV, the shear viscosity is dominated by the most weakly interacting particles, right-handed leptons, and is relatively large. Read More

We explore a method developed in statistical physics which has been argued to have exponentially small finite-volume effects, in order to determine the critical temperature Tc of pure SU(3) gauge theory close to the continuum limit. The method allows us to estimate the critical coupling betac of the Wilson action for temporal extents up to Nt ~ 20 with < 0.1% uncertainties. Read More

Even though the Standard Model with a Higgs mass mH = 125 GeV possesses no bulk phase transition, its thermodynamics still experiences a "soft point" at temperatures around T = 160 GeV, with a deviation from ideal gas thermodynamics. Such a deviation may have an effect on precision computations of weakly interacting dark matter relic abundances if their mass is in the few TeV range, or on leptogenesis scenarios operating in this temperature range. By making use of results from lattice simulations based on a dimensionally reduced effective field theory, we estimate the relevant thermodynamic functions across the crossover. Read More

NLO and LPM-resummed computations of thermal dilepton production from a hot QCD plasma are reviewed. An interpolation applicable for all positive photon invariant masses is presented, and possibilities for comparisons with lattice and experimental data are pointed out. Read More

The production rate of right-handed neutrinos from a Standard Model plasma at a temperature above a hundred GeV has previously been evaluated up to NLO in Standard Model couplings (g ~ 2/3) in relativistic (M ~ pi T) and non-relativistic regimes (M >> pi T), and up to LO in an ultrarelativistic regime (M < gT). The last result necessitates an all-orders resummation of the loop expansion, accounting for multiple soft scatterings of the nearly light-like particles participating in 1 <-> 2 reactions. In this paper we suggest how the regimes can be interpolated into a result applicable for any right-handed neutrino mass and at all temperatures above 160 GeV. Read More

In the range of temperatures reached in future heavy ion collision experiments, hadronic pair annihilations and creations of charm quarks may take place within the lifetime of the plasma. As a result, charm quarks may increase the bulk viscosity affecting the early stages of hydrodynamic expansion. Assuming thermalization, we estimate the charm contribution to bulk viscosity within the same effective kinetic theory framework in which the light parton contribution has been computed previously. Read More

Static and non-static thermal screening states that couple to the conserved vector current are investigated in the high-temperature phase of QCD. Their masses and couplings to the current are determined at weak coupling, as well as using two-flavor lattice QCD simulations. A consistent picture emerges from the comparison, providing evidence that non-static Matsubara modes can indeed be treated perturbatively. Read More

Strict next-to-leading order (NLO) results for the dilepton production rate from a QCD plasma at temperatures above a few hundred MeV suffer from a breakdown of the loop expansion in the regime of soft invariant masses M^2 << (pi T)^2. In this regime an LPM resummation is needed for obtaining the correct leading-order result. We show how to construct an interpolation between the hard NLO and the leading-order LPM expression. Read More

Thermal screening masses related to the conserved vector current are determined for the case that the current carries a non-zero Matsubara frequency, both in a weak-coupling approach and through lattice QCD. We point out that such screening masses are sensitive to the same infrared physics as light-cone real-time rates. In particular, on the perturbative side, the inhomogeneous Schrodinger equation determining screening correlators is shown to have the same general form as the equation implementing LPM resummation for the soft-dilepton and photon production rates from a hot QCD plasma. Read More

The rates for lepton number washout in extensions of the Standard Model containing right-handed neutrinos are key ingredients in scenarios for baryogenesis through leptogenesis. We relate these rates to real-time correlation functions at finite temperature, without making use of any particle approximations. The relations are valid to quadratic order in neutrino Yukawa couplings and to all orders in Standard Model couplings. Read More

**Affiliations:**

^{1}University of Bern,

^{2}University of Bielefeld and DESY,

^{3}University of Helsinki

We study the strength of the electroweak phase transition in models with two light Higgs doublets and a light SU(3)_c triplet by means of lattice simulations in a dimensionally reduced effective theory. In the parameter region considered the transition on the lattice is significantly stronger than indicated by a 2-loop perturbative analysis. Within some ultraviolet uncertainties, the finding applies to MSSM with a Higgs mass m_h approximately 126 GeV and shows that the parameter region useful for electroweak baryogenesis is enlarged. Read More

The analytic continuation needed for the extraction of transport coefficients necessitates in principle a continuous function of the Euclidean time variable. We report on progress towards achieving the continuum limit for 2-point correlator measurements in thermal SU(3) gauge theory, with specific attention paid to scale setting. In particular, we improve upon the determination of the critical lattice coupling and the critical temperature of pure SU(3) gauge theory, estimating r0*Tc ~ 0. Read More

We present NLO results for thermal imaginary-time correlators in the vector and scalar channels as a function of the quark mass. The range of quark masses for which a non-relativistic approximation works in the temperature range considered is estimated, and charm quarks turn out to be a borderline case. Comparing with simulation data from fine lattices, we find good agreement in the vector channel but a substantial discrepancy in the scalar one. Read More

After reviewing how simulations employing classical lattice gauge theory permit to test a conjectured Euclideanization property of a light-cone Wilson loop in a thermal non-Abelian plasma, we show how Euclidean data can in turn be used to estimate the transverse collision kernel, C(k_perp), characterizing the broadening of a high-energy jet. First results, based on data produced recently by Panero et al, suggest that C(k_perp) is enhanced over the known NLO result in a soft regime k_perp < a few T. The shape of k_perp^3 C(k_perp) is consistent with a Gaussian at small k_perp. Read More

The vector channel spectral function and the dilepton production rate from a QCD plasma at a temperature above a few hundred MeV are evaluated up to next-to-leading order (NLO) including their dependence on a non-zero momentum with respect to the heat bath. The invariant mass of the virtual photon is taken to be in the range K^2 ~ (pi T)^2 ~ (1 GeV)^2, generalizing previous NLO results valid for K^2 >> (pi T)^2. In the opposite regime 0 < K^2 << (pi T)^2 the loop expansion breaks down, but agrees nevertheless in order of magnitude with a previous result obtained through resummations. Read More

The bulk viscosity of thermalized QCD matter at temperatures above a few hundred MeV could be significantly influenced by charm quarks because their contribution arises four perturbative orders before purely gluonic effects. In an attempt to clarify the challenges of a lattice study, we determine the relevant imaginary-time correlator (of massive scalar densities) up to NLO in perturbation theory, and compare with existing data. We find discrepancies much larger than in the vector channel; this may hint, apart from the importance of taking a continuum limit, to larger non-perturbative effects in the scalar channel. Read More

The production rate of right-handed neutrinos from a Standard Model plasma at a temperature above a hundred GeV is evaluated up to NLO in Standard Model couplings. The results apply in the so-called relativistic regime, referring parametrically to a mass M ~ pi T, generalizing thereby previous NLO results which only apply in the non-relativistic regime M >> pi T. The non-relativistic expansion is observed to converge for M > 15 T, but the smallness of any loop corrections allows it to be used in practice already for M > 4 T. Read More

The transverse broadening of an energetic jet passing through a non-Abelian plasma is believed to be described by the thermal expectation value of a light-cone Wilson loop. In this exploratory study, we measure the light-cone Wilson loop with classical lattice gauge theory simulations. We observe, as suggested by previous studies, that there are strong interactions already at short transverse distances, which may lead to more efficient jet quenching than in leading-order perturbation theory. Read More

When considering NLO corrections to thermal particle production in the "relativistic" regime, in which the invariant mass squared of the produced particle is K^2 ~ (pi T)^2, then the production rate can be expressed as a sum of a few universal "master" spectral functions. Taking the most complicated 2-loop master as an example, a general strategy for obtaining a convergent 2-dimensional integral representation is suggested. The analysis applies both to bosonic and fermionic statistics, and shows that for this master the non-relativistic approximation is only accurate for K^2 > (8 pi T)^2, whereas the zero-momentum approximation works surprisingly well. Read More

We carry out lattice simulations of a cosmological electroweak phase transition for a Higgs mass m_h ~ 126 GeV. The analysis is based on a dimensionally reduced effective theory for an MSSM-like scenario including a relatively light coloured SU(2)-singlet scalar, referred to as a right-handed stop. The non-perturbative transition is stronger than in 2-loop perturbation theory, and may offer a window for electroweak baryogenesis. Read More

The chemical equilibration of heavy quarks in a quark-gluon plasma proceeds via annihilation or pair creation. For temperatures T much below the heavy quark mass M, when kinetically equilibrated heavy quarks move very slowly, the annihilation in the colour singlet channel is enhanced because the quark and antiquark attract each other which increases their probability to meet, whereas the octet contribution is suppressed. This is the so-called Sommerfeld effect. Read More

We present an NLO analysis of the massive vector current correlator at temperatures above a few hundred MeV. The physics of this correlator originates from a transport peak, related to heavy quark diffusion, and from the quark-antiquark threshold, related to quarkonium physics. In the bottom case both can be studied with separate effective theories, but for charm these may not be accurate, so a study within the full theory is needed. Read More

Recently the issue of radiative corrections to leptogenesis has been raised. Considering the "strong washout" regime, in which OPE-techniques permit to streamline the setup, we report the thermal self-energy matrix of heavy right-handed neutrinos at NLO (resummed 2-loop level) in Standard Model couplings. The renormalized expression describes flavour transitions and "inclusive" decays of chemically decoupled right-handed neutrinos. Read More

It has been argued by Caron-Huot that infrared contributions to the jet quenching parameter in hot QCD, denoted by qhat, can be extracted from an analysis of a certain static-potential related observable within the dimensionally reduced effective field theory. Following this philosophy, the order of magnitude of a non-perturbative contribution to qhat from the colour-magnetic scale, g^2T/pi, is estimated. The result is small; it is probably below the parametrically perturbative but in practice slowly convergent contributions from the colour-electric scale, whose all-orders resummation therefore remains an important challenge. Read More

Motivated by indications that heavy (charm and bottom) quarks interact strongly at temperatures generated in heavy ion collision experiments, we suggest a non-perturbative definition of a heavy quark chemical equilibration rate as a transport coefficient. Within leading-order perturbation theory (corresponding to 3-loop level), the definition is argued to reduce to an expression obtained from the Boltzmann equation. Around T ~ 400 MeV, an order-of-magnitude estimate for charm yields a rate Gamma^{-1}_{chem} > 60 fm/c which remains too slow to play a practical role in current experiments. Read More

By subtracting from a recent lattice measurement of the thermal vector-current correlator the known 5-loop vacuum contribution, we demonstrate that the remainder is small and shows no visible short-distance divergence. It can therefore in principle be subjected to model-independent analytic continuation. Testing a particular implementation, we obtain estimates for the flavour-diffusion coefficient (2 pi T D \gsim 0. Read More

We consider the next-to-leading order thermal production rate of heavy right-handed neutrinos in the non-relativistic regime m_top < pi*T << M, where m_top refers to the electroweak scale. Rephrasing the problem in an OPE language and making use of different techniques than a previous analysis by Salvio et al, we confirm the general structure of their result and many of the coefficients. We also extend the analysis to the next order in the non-relativistic expansion, thereby revealing the leading non-trivial momentum dependence, as well as to NNLO in couplings, revealing the leading sensitivity to thermal resummations. Read More

We report on a lattice investigation of heavy quark diffusion within pure SU(3) plasma above the deconfinement transition, with the quarks treated to leading order in the heavy mass expansion. Using a multilevel algorithm, several volumes and lattice spacings, as well as tree-level improvement and perturbative renormalization, we measure the relevant "colour-electric" Euclidean correlator, finding that it clearly exceeds its perturbative counterpart. Even without analytic continuation, this suggests that at temperatures just above the critical one, non-perturbative interactions felt by the heavy quarks are stronger than within the weak-coupling expansion. Read More

Some of the modifications that a thermal medium, of the type generated in heavy ion collision experiments at the LHC, may impose on the properties of hadrons, are reviewed. The focus is on hadrons containing at least one heavy quark (charm or bottom or their antiparticles). Read More

Motivated by applications in thermal QCD and cosmology, we elaborate on a general method for computing next-to-leading order spectral functions for composite operators at vanishing spatial momentum, accounting for real, virtual as well as thermal corrections. As an example, we compute these functions (together with the corresponding imaginary-time correlators which can be compared with lattice simulations) for scalar and pseudoscalar densities in pure Yang-Mills theory. Our results may turn out to be helpful in non-perturbative estimates of the corresponding transport coefficients, which are the bulk viscosity in the scalar channel and the rate of anomalous chirality violation in the pseudoscalar channel. Read More

By making use of a non-perturbative definition of a momentum diffusion coefficient as well as Heavy Meson Chiral Perturbation Theory, we investigate the Brownian motion and kinetic equilibration of heavy quark flavours deep in the confined phase. It appears that the momentum diffusion coefficient can be expressed in terms of known low-energy constants; it increases rapidly at temperatures above 50 MeV, behaving as ~ T^7/F_pi^4 for m_pi / pi << T << F_pi, where m_pi and F_pi are the pion mass and decay constant, respectively. The early increase may suggest a broad peak in kappa/T^3 around the QCD crossover. Read More

Some time ago, Cuniberti et al have proposed a novel method for analytically continuing thermal imaginary-time correlators to real time, which requires no model input and should be applicable with finite-precision data as well. Given that these assertions go against common wisdom, we report on a naive test of the method with an idealized example. We do encounter two problems, which we spell out in detail; this implies that systematic errors are difficult to quantify. Read More

Lattice measurements of spatial correlation functions of the operators FF and FF-dual in thermal SU(3) gauge theory have revealed a clear difference between the two channels at "intermediate" distances, x ~ 1/(pi T). This is at odds with the AdS/CFT limit which predicts the results to coincide. On the other hand, an OPE analysis at short distances (x << 1/(pi T)) as well as effective theory methods at long distances (x >> 1/(pi T)) suggest differences. Read More

Inspired by recent lattice measurements, we determine the short-distance (a << r << 1/pi T) as well as large-frequency (1/a >> omega >> pi T) asymptotics of scalar (trace anomaly) and pseudoscalar (topological charge density) correlators at 2-loop order in hot Yang-Mills theory. The results are expressed in the form of an Operator Product Expansion. We confirm and refine the determination of a number of Wilson coefficients; however some discrepancies with recent literature are detected as well, and employing the correct values might help, on the qualitative level, to understand some of the features observed in the lattice measurements. Read More

This pedagogically intended lecture, one of four under the header "Basics of thermal QCD", reviews an interesting relationship, originally pointed out by Bodeker, that exists between the bulk viscosity of Yang-Mills theory (of possible relevance to the hydrodynamics of heavy ion collision experiments) and the decay rate of scalar fields coupled very weakly to a heat bath (appearing in some particle physics inspired cosmological scenarios). This topic serves, furthermore, as a platform on which a number of generic thermal field theory concepts are illustrated. The other three lectures (on the QCD equation of state and the rates of elastic as well as inelastic processes experienced by heavy quarks) are recapitulated in brief encyclopedic form. Read More