Friday, March 27, 2015

Workshop "Fundamental Parameters from Lattice QCD" at MITP (upcoming deadline)

Recent years have seen a significant increase in the overall accuracy of lattice QCD calculations of various hadronic observables. Results for quark and hadron masses, decay constants, form factors, the strong coupling constant and many other quantities are becoming increasingly important for testing the validity of the Standard Model. Prominent examples include calculations of Standard Model parameters, such as quark masses and the strong coupling constant, as well as the determination of CKM matrix elements, which is based on a variety of input quantities from experiment and theory. In order to make lattice QCD calculations more accessible to the entire particle physics community, several initiatives and working groups have sprung up, which collect the available lattice results and produce global averages.

The scientific programme "Fundamental Parameters from Lattice QCD" at the Mainz Institute of Theoretical Physics (MITP) is designed to bring together lattice practitioners with members of the phenomenological and experimental communities who are using lattice estimates as input for phenomenological studies. In addition to sharing the expertise among several communities, the aim of the programme is to identify key quantities which allow for tests of the CKM paradigm with greater accuracy and to discuss the procedures in order to arrive at more reliable global estimates.

The deadline for registration is Tuesday, 31 March 2015.

Thursday, March 12, 2015

QNP 2015, Day Five

Apologies for the delay in posting this. Travel and jetlag kept me from attending to it earlier.

The first talk today was by Guy de Teramond, who described applications of light-front superconformal quantum mechanics to hadronic physics. I have to admit that I couldn't fully take in all the details, but as far as I understood an isomorphy between AdS2 and the conformal group in one dimension can be used to derive a form of the light-front Hamiltonian for mesons from an AdS/QCD correspondence, in which the dilaton field is fixed to be φ(z)=1/2 z2 by the requirement of conformal invariance, and a similar construction in the superconformal case leads to a light-front Hamiltonian for baryons. A relationship between the Regge trajectories for mesons and baryons can then be interpreted as a form of supersymmetry in this framework.

Next was Beatriz Gay Ducati with a review of the pheonomenology of heavy quarks in nuclear matter, a topic where there are still many open issues. The photoproduction of quarkonia on nucleons and nuclei allows to probe the gluon distribution, since the dominant production process is photon-gluon fusion, but to be able to interpret the data, many nuclear matter effects need to be understood.

After the coffee break, this was followed by a talk by Hrayr Matevosyan on transverse momentum distributions (TMDs), which are complementary to GPDs in the sense of being obtained by integrating out other variables starting from the full Wigner distributions. Here, again, there are many open issues, such as the Sivers, Collins or Boer-Mulders effects.

The next speaker was Raju Venugopalan, who spoke about two outstanding problems in QCD at high parton densities, namely the question of how the systems created in heavy-ion collisions thermalise, and the phenomenon of "the ridge" in proton-nucleus collisions, which would seem to suggest hydrodynamic behaviour in a system that is too small to be understood as a liquid. Both problems may have to do with the structure of the dense initial state, which is theorised to be a colour-glass condensate or "glasma", and the way in which it evolves into a more dilute system.

After the lunch break, Sonny Mantry reviewed some recent advances made in applying Soft-Collinear Effective Theory (SCET) to a range of questions in strong-interaction physics. SCET is the effective field theory obtained when QCD fluctuations around a hard particle momentum are considered to be small and a corresponding expansion (analogous to the 1/m expansion in HQET) is made. SCET has been successfully applied to many different problems; an interesting and important one is the problem of relating the "Monte Carlo mass" usually quoted for the top quark to the top quark mass in a more well-defined scheme such as MSbar.

The last talk in the plenary programme was a review of the Electron-Ion Collider (EIC) project by Zein-Eddine Meziani. By combining the precision obtainable using an electron beam with the access to the gluon-dominated regime provided by a havy ion beam, as well as the ability to study the nucleon spin using a polarised nucleon beam, the EIC will enable a much more in-depth study of many of the still unresolved questions in QCD, such as the nucleon spin structure and colour distributions. There are currently two competing designs, the eRHIC at Brookhaven, and the MEIC at Jefferson Lab.

Before the conference closed, Michel Garçon announced that the next conference of the series (QNP 2018) will be held in Japan (either in Tsukuba or in Mito, Ibaraki prefecture). The local organising committee and conference office staff received some well-deserved applause for a very smoothly-run conference, and the scientific part of the conference programme was adjourned.

As it was still in the afternoon, I went with some colleagues to visit La Sebastiana, the house of Pablo Neruda in Valparaíso, taking one of the city's famous ascensores down (although up might have been more convenient, as the streets get very steep) before walking back to Viña del Mar along the sea coast.

The next day, there was an organised excursion to a vineyard in the Casablanca valley, where we got to taste some very good Chilean wines (some of the them matured in traditional clay vats) and liqueurs with a very pleasant lunch.

I got to spend another day in Valparaíso before travelling back (a happily uneventful, if again rather long trip).

Friday, March 06, 2015

QNP 2015, Day Four

The first talk today was a review of experimental results in light-baryon spectroscopy by Volker Credé. While much progress has been made in this field, in particular in the design of so-called complete experiments, which as far as I understand measure multiple observables to unambiguously extract a complete description of the amplitudes for a certain process, there still seem to be surprisingly many unknowns. In particular, the fits to pion photoproduction in doubly-polarised processes seem to disagree strongly between different descriptions (such as MAID).

Next was Derek Leinweber with a review of light hadron spectroscopy from the lattice. The de facto standard method in this field is the variational method (GEVP), although there are some notable differences in how precisely different groups apply it (e.g. solving the GEVP at many times and fitting the eigenvalues vs. forming projected correlators with the eigenvectors of the GEVP solved at a single time -- there are proofs of good properties for the former that don't exist for the latter). The way in which the basis of operators for the GEVP is build is also quite different as used by different groups, ranging from simply using different levels of quark field smearing to intricate group-theoretic constructions of multi-site operators. There are also attempts to determine how much information can be extracted from a given set of correlators, e.g. recently by the Cyprus/Athens group using Monte Carlo simulations to probe the space of fitting parameters (a loosely related older idea based on evolutionary fits wasn't mentioned).

This was followed by a talk by Susan Gardner about testing fundamental symmetries with quarks. While we know that there must be physics beyond the Standard Model (because the SM does not explain dark matter, nor does it provide enough CP violation to explain the observed baryon asymmetry), there is so far no direct evidence of any BSM particle. Low-energy tests of the SM fall into two broad categories: null tests (where the SM predicts an exact null result, as for violations of B-L) and precision tests (where the SM prediction can be calculated to very high accuracy, as for (g-2)μ). Null tests play an important role in so far as they can be used to impose a lower limit for the BSM mass scale, but many of them are atomic or nuclear tests, which have complicated theory errors. The currently largest tensions indicating a possible failure of the Standard Model to describe all observations are the proton radius puzzle, and (g-2)μ. A possible explanation of either or both of those in terms of a "dark photon" is on the verge of being ruled out, however, since most of the relevant part of the mass/coupling plane has already been excluded by dark photon searches, and the rest of it will soon be (or else the dark photon will be discovered). Other tests in the hadronic sector, which seem to be less advanced so far, are the search for non-(V-A) terms in β-decays, and the search for neutron-antineutron oscillations.

After the coffee break and the official conference photo, Isaac Vidaña took the audience on a "half-hour walk through the physics of neutron stars". Neutron stars are both almost-black holes (whose gravitation must be described in General Relativity) and extremely massive nuclei (whose internal dynamics must be described using QCD). Observations of binary pulsars allow to determine the masses of neutron stars, which are found to range up to at least two solar masses. However, the Tolman-Oppenheimer-Volkov equations for the stability of neutron stars lead to a maximum mass for a neutron star that depends on the equation of state of the nuclear medium. The observed masses severely constrain the equation of state and in particular seem to exclude models in which hyperons play an important role; however, it seems to be generally agreed that hyperons must play an important role in neutron stars, leading to a "hyperon puzzle", the solution of which will require an improved understanding of the structure and interactions of hyperons.

The last plenary speaker of the day was Stanley Brodsky with the newest developments from light-front holography. The light-front approach, which has in the past been very successful in (1+1)-dimensional QCD, is based on the front form of the Hamiltonian formalism, in which a light-like, rather than a timelike, direction is chosen as the normal defining the Cauchy surfaces on which initial data are specified. In the light-front Hamiltonian approach, the vacuum of QCD is trivial and the Hilbert space can be constructed as a straightforward Fock space. With some additional ansätze taken from AdS/CFT ideas, QCD is reduced to a Schrödinger-like equation for the light-cone wavefunctions, from which observables are extracted. Apparently, all known observations are described perfectly in this approach, but (as for the Dyson-Schwinger or straight AdS/QCD approaches) I do not understand how systematic errors are supposed to be quantified.

In the afternoon there were parallel talks. An interesting contribution was given by Mainz PhD student Franziska Hagelstein, who demonstrated how even a very small non-monotonicity in the electric form factor at low Q2 (where there are no ep scattering data) could explain the difference between the muonic and electronic hydrogen results for the proton radius.

The conference banquet took place in the evening at a very nice restaurant, and fun was had over cocktails and an excellent dinner.

Thursday, March 05, 2015

QNP 2015, Day Three

Today began with a talk by Mikhail Voloshin on QCD sum rules and heavy-quark states. The idea of exploiting quark-hadron duality to link perturbatively calculable current-current correlators to hadronic obervables and extract mesonic decay constants or quark masses is quite old, but has received a boost in recent years with the advent of three- and four-loop perturbative calculations in particularly from Chetyrkin and collaborators, which have also been used in conjunction with lattice results, e.g. by the HPQCD collaboration.

A review of hadron spectroscopy at B factories (including LHCb) by Roberto Mussa followed. The charmonium and bottomonium spectra are now measured to great detail, with recent additions being 1D and 3P states, and more states are also being discovered in the heavy-light (where the Bc(2S) has recently been discovered at ATLAS) and heavy-quark baryon (where the most recent discovery was the Ξb) sectors, and many more transitions being discovered and studied.

The next speaker was Raphaël Dupré, who spoke about colour propagation and neutralisation in strongly interacting systems. The idea here appears to be that in hadronisation processes, quarks first loose energy by radiating gluons and thus turn into colourless pre-hadrons, which then bind into hadrons on a longer timescale, and there seems to be experimental evidence supporting this energy-loss model.

After the coffee break, Javier Castillo reviewed quarkonium suppression and regeneration in heavy-ion collisions. Quarkonia are generally considered important probes of the quark-gluon plasma, because the production of heavy quark-antiquark pairs is a perturbative process that happens at high energies early in the collision, while their binding is non-perturbative and is expected to be suppressed by Debye screening in the coloured plasma. As a consequence, more tightly bound quarkonia, like the Y(1S), can exist at higher temperatures, while the more lightly bound charmonia or Y(3S) states will "melt" at lower temperatures. However, quarkonia can also be regenerated by thermalised heavy quarks rejoining into quarkonia at the phase boundary. Experimental data support the screening picture, with the J/ψ being more suppressed at the LHC than at STAR (because of the higher temperature), the Y(2S) more suppressed than the Y(1S), and transport models with a negligible regeneration component describing the data well. The regeneration component increases at low pT, and the elliptic flow of the charm quarks is inherited by the regenerated J/ψ mesons. Some more difficult to understand effects of the nuclear environment, called Cold Nuclear Matter (CNM) effects are beginning to be seen in the data.

Next was Zoltan Fodor with a talk about Lattice QCD results at zero and finite temperature from the BMW collaboration. By simulating QCD+QED with 1+1+1+1 flavours of dynamical quarks, BMW have been able to determine the isospin splitting of the nucleon and other baryonic systems. This work, which appears set to become a cover story in "Science", had to overcome a number of serious obstacles, in particular long-range autocorrelations (which could cured by a Fourier-accelerated HMC variant) and power-law finite-volume effects (which had to be fitted to results obtained at a range of volumes) introduced by the massless photon. In the finite-temperature regime, the crossover temperature is now generally agreed to be around 150-160 MeV, but the position and even existence of the critical endpoint is still contentious (and any existing results are not yet continuum-extrapolated in any case).

After the lunch break, Yiota Foka gave an overview of heavy-ion results from RHIC and the LHC. The elliptic flow is still found to be in agreement with perfect hydrodynamics, but people are now also studying higher harmonics, as well as the interplay between jets and flow, which provide important constraints on the physics of the quark-gluon plasma. At the LHC, it has been found that it is the mass, and not the valence quark content, that drives the flow behaviour of hadrons, as the φ meson has the same flow behaviour as the proton.

The next speaker was Carl Gagliardi, who reviewed results in nucleon structure from high-energy polarised proton-proton collisions. Proton-proton scattering is complementary to DIS in that it gives access to the gluonic degrees of freedom which are invisible to electrons, and RHIC has a programme of polarised proton collisions to explore the spin structure of the nucleon. Without the RHIC data, the gluon polarisation ΔG is almost unconstrained, but with the RHIC data, it is seen to be clearly positive and contribute about 0.2 to the proton spin. Using W production, it is possible to separate polarised quark and antiquark distributions, and there is more to come in the near future.

The last plenary speaker of the day was Craig Roberts, who reviewed the pion and nucleon structure from the point of view of the Dyson-Schwinger equations approach. In this approach, the pion is closely linked to the quark mass function, which comes out of a quark gap equation and describes how the running quark mass at high energies turns into a much larger constituent quark mass at low energies. Landau-gauge gluons also become massive at low energies, and confinement is explained as the splitting of poles into pairs of conjugate complex poles giving an exponentially damped behaviour of the position space propagator. While this approach seems to be able to readily explain every single known experimental result, I do not understand how the systematic errors from the truncation of the infinite tower of DSEs are supposed to be controlled or quantified.

After the coffee break, there were parallel sessions. An interesting parallel talk was given by Johan Bijnens, who has determined the leading logarithms for the nucleon mass (and some other systems) to rather high orders (which also for effective theories can be done using only one-loop integrals from a consistency argument by Weinberg).

Wednesday, March 04, 2015

QNP 2015, Day Two

Hello again from Valparaíso. Today's first speaker was Johan Bijnens with a review of recent results from chiral perturbation theory in the mesonic sector, including recent results for charged pion polarisabilities and for finite-volume corrections to lattice measurements. To allow others to perform their own calculations for their own specific needs (which might include technicolor-like theories, which will generally have different patterns of chiral symmetry breaking, but otherwise work just the same way), Bijnens & Co. have recently published CHIRON, a general two-loop mesonic χPT package. The leading logarithms have been determined to high orders, and it has been found that the speed of convergence depends both on the observable and on whether the leading-order or physical pion decay constant is used.

Next was Boris Grube, who presented some recent results from light-meson spectroscopy. The light mesons are generally expected to be some kind of superpositions of quark-model states, hybrids, glueballs, tetraquark and molecular states, as may be compatible with their quantum numbers in each case. The most complex sector is the 0++ sector of f0 mesons, in which the lightest glueball state should lie. While the γγ width of the f0(1500) appears to be compatible with zero, which would agree with the expectations for a glueball, whereas the f0(1710) has a photonic width more in agreement with being an s-sbar state, in J/ψ -> γ (ηη), which as a gluon-rich process should couple strongly to glueball resonances, little or no f0(1500) is seen, whereas a glueball nature for the f0(1710) would be supported by these results. New data to come from GlueX, and later from PANDA, should help to clarify things.

The next speaker was Paul Sorensen with a talk on the search for the critical point in the QCD phase diagram. The quark-gluon plasma at RHIC is not only a man-made system that is over 300 times hotter than the centre of the Sun, it is also the most perfect fluid known, as it close to saturates the viscosity bound η/s > 1/(4π). Studying it experimentally is quite difficult, however, since one must extrapolate back to a small initial fireball, or "little bang", from correlations between thousands of particle tracks in a detector, not entirely dissimilar from the situation in cosmology, where the properties of the hot big bang (and previous stages) are inferred from angular correlations in the cosmic microwave background. Beam energy scans find indications that the phase transition becomes first-order at higher densities, which would indicate the existence of a critical endpoint, but more statistics and more intermediate energies are needed.

After the coffee break, François-Xavier Girod spoke about Generalised Parton Distributions (GPDs) and deep exclusive processes. GPDs, which reduce to form factors and to parton distributions upon integrating out the unneeded variables in each case, correspond to a three-dimensional image of the nucleon performed in the longitudinal momentum fraction and the transverse impact parameter, and their moments are related to matrix elements of the energy-momentum tensor. Experimentally, they are probed using deeply virtual Compton scattering (DVCS); the 12 GeV upgrade at Jefferson Lab will increase the coverage in both Bjørken-x and Q2, and the planned electron-ion collider is expected to allow probing the sea and gluon GPDs as well.

After the lunch break, there were parallel sessions. I chaired the parallel session on lattice and other perturbative methods, with presentations of lattice results by Eigo Shintani and Tereza Mendes, as well as a number of AdS/QCD-related results by various others.

Tuesday, March 03, 2015

QNP 2015, Day One

Hello from Valparaíso, where I continue this year's hectic conference circuit at the 7th International Conference on Quarks and Nuclear Physics (QNP 2015). Except for some minor inconveniences and misunderstandings, the long trip to Valparaíso (via Madrid and Santiago de Chile) went quite smoothly, and so far, I have found Chile a country of bright sunlight and extraordinarily helpful and friendly people.

The first speaker of the conference was Emanuele Nocera, who reviewed nucleon and nuclear parton distributions. The study of parton distributions become necessary because hadrons are really composed not simply of valence quarks, as the quark model would have it, but of an indefinite number of (sea) quarks, antiquarks and gluons, any of which can contribute to the overall momentum and spin of the hadron. In an operator product expansion framework, hadronic scattering amplitudes can then be factorised into Wilson coefficients containing short-distance (perturbative) physics and parton distribution functions containing long-distance (non-perturbative) physics. The evolution of the parton distribution functions (PDFs) with the momentum scale is given by the DGLAP equations containing the perturbatively accessible splitting functions. The PDFs are subject to a number of theoretical constraints, of which the sum rules for the total hadronic momentum and valence quark content are the most prominent. For nuclei, on can assume that a similar factorisation as for hadrons still holds, and that the nuclear PDFs are linear combinations of nucleon PDFs modified by multiplication with a binding factor; however, nuclei exhibit correlations between nucleons, which are not well-described in such an approach. Combining all available data from different sources, global fits to PDFs can be performed using either a standard χ2 fit with a suitable model, or a neural network description. There are far more and better data on nucleon than nuclear PDFs, and for nucleons the amount and quality of the data also differs between unpolarised and polarised PDFs, which are needed to elucidate the "proton spin puzzle".

Next was the first lattice talk of the meeting, given by Huey-Wen Lin, who gave a review of the progress in lattice studies of nucleon structure. I think Huey-Wen gave a very nice example by comparing the computational and algorithmic progress with that in videogames (I'm not an expert there, but I think the examples shown were screenshots of Nethack versus some modern first-person shooter), and went on to explain the importance of controlling all systematic errors, in particular excited-state effects, before reviewing recent results on the tensor, scalar and axial charges and the electromagnetic form factors of the nucleon. As an outlook towards the current frontier, she presented the inclusion of disconnected diagrams and a new idea of obtaining PDFs from the lattice more directly rather than through their moments.

The next speaker was Robert D. McKeown with a review of JLab's Nuclear Science Programme. The CEBAF accelerator has been upgraded to 12 GeV, and a number of experiments (GlueX to search for gluonic excitations, MOLLER to study parity violation in Møller scattering, and SoLID to study SIDIS and PVDIS) are ready to be launched. A number of the planned experiments will be active in areas that I know are also under investigation by experimental colleagues in Mainz, such as a search for the "dark photon" and a study of the running of the Weinberg angle. Longer-term plans at JLab include the design of an electron-ion collider.

After a rather nice lunch, Tomofumi Nagae spoke about the hadron physics programme an J-PARC. In spite of major setbacks by the big earthquake and a later radiation accident, progress is being made. A search for the Θ+ pentaquark did not find a signal (which I personally do not find surprising, since the whole pentaquark episode is probably of more immediate long-term interest to historians and sociologists of science than to particle physicists), but could not completely exclude all of the discovery claims.

This was followed by a take by Jonathan Miller of the MINERνA collaboration presenting their programme of probing nuclei with neutrinos. Major complications include the limited knowledge of the incoming neutrino flux and the fact that final-state interactions on the nuclear side may lead to one process mimicking another one, making the modelling in event generators a key ingredient of understanding the data.

Next was a talk about short-range correlations in nuclei by Or Henn. Nucleons subject to short-range correlations must have high relative momenta, but a low center-of-mass momentum. The experimental studies are based on kicking a proton out of a nucleus with an electron, such that both the momentum transfer (from the incoming and outgoing electron) and the final momentum of the proton are known, and looking for a nucleon with a momentum close to minus the difference between those two (which must be the initial momentum of the knocked-out proton) coming out. The astonishing result is that at high momenta, neutron-proton pairs dominate (meaning that protons, being the minority, have a much larger chance of having high momenta) and are linked by a tensor force. Similar results are known from other two-component Fermi systems, such as ultracold atomic gases (which are of course many, many orders of magnitude less dense than nuclei).

After the coffee break, Heinz Clement spoke about dibaryons, specifically about the recently discovered d*(2380) resonance, which taking all experimental results into account may be interpreted as a ΔΔ bound state

The last talk of the day was by André Walker-Loud, who reviewed the study of nucleon-nucleon interactions and nuclear structure on the lattice, starting with a very nice review of the motivations behind such studies, namely the facts that big-bang nucleosynthesis is very strongly dependent on the deuterium binding energy and the proton-neutron mass difference, and this fine-tuning problem needs to be understood from first principles. Besides, currently the best chance for discovering BSM physics seems once more to lie with low-energy high-precision experiments, and dark matter searches require good knowledge of nuclear structure to control their systematics. Scattering phase shifts are being studied through the Lüscher formula. Current state-of-the-art studies of bound multi-hadron systems are related to dibaryons, in particular the question of the existence of the H-dibaryon at the physical pion mass (note that the dineutron, certainly unbound in the real world, becomes bound at heavy enough pion masses), and three- and four-nucleon systems are beginning to become treatable, although the signal-to-noise problem gets worse as more baryons are added to a correlation function, and the number of contractions grows rapidly. Going beyond masses and binding energies, the new California Lattice Collaboration (CalLat) has preliminary results for hadronic parity violation in the two-nucleon system, albeit at a pion mass of 800 MeV.

Friday, February 27, 2015

Back from Mumbai

On Saturday, my last day in Mumbai, a group of colleagues rented a car with a driver to take a trip to Sanjay Gandhi National Park and visit the Kanheri caves, a Buddhist site consisting of a large number of rather simple monastic cells and some worship and assembly halls with ornate reliefs and inscriptions, all carved out out of solid rock (some of the cell entrances seem to have been restored using steel-reinforced concrete, though).

On the way back, we stopped at Mani Bhavan, where Mahatma Gandhi lived from 1917 to 1934, and which is now a museum dedicated to his live and legacy.

In the night, I flew back to Frankfurt, where the temperature was much lower than in Mumbai; in fact, on Monday there was snow.

Friday, February 20, 2015

Perspectives and Challenges in Lattice Gauge Theory, Day Five

Today's programme started with a talk by Santanu Mondal on baryons in the sextet gauge model, which is a technicolor-style SU(3) gauge theory with a doublet of technifermions in the sextet (two index symmetric) representation, and a minimal candidate for a technicolor-like model with an IR almost-fixed point. Using staggered fermions, he found that when setting the scale by putting the technipion's decay constant to the value derived from identifying the Higgs vacuum expectation value as the technicondensate, the baryons had masses in excess of 3 TeV, heavy enough to not yet have been discovered by the LHC, but to be within reach of the next run. However, the anomaly cancellation condition when embedding the theory into the Standard Model of the electroweak interactions requires charge assignments such that the lightest technibaryon (which would be a stable particle) would have a fractional electrical charge of 1/2, and while the cosmological relic density can be made small enough to evade detection, the technibaryons produced by the cosmic rays in the Earth's atmosphere should have been able to accumulate (there currently appear to be no specific experimental exclusions for charge-1/2 particles though).

Next was Nilmani Mathur speaking about mixed action simulations using overlap valence quarks on the MILC HISQ ensembles (which include the radiative corrections to the lattice gluon action from the quarks). Tuning the charm quark mass via the kinetic rather than rest mass of charmonium, the right charmonium hyperfine splitting is found, as well as generally correct charmonium spectra. Heavy-quark baryons (up to and including the Ωccc) have also been simulated, with results in good agreement with experimental ones where the latter exist. The mixed-action effects appear to be mild small in mixed-action χPT, and only half as large as those for domain-wall valence fermions on an asqtad sea.

In a brief note, Gunnar Bali encouraged the participants of the workshop to seek out opportunities for Indo-German research collaboration, of which there are still only a limited number of instances.

After the tea break, there were two more theoretical talks, both of them set in the framework of Hamiltonian lattice gauge theory: Indrakshi Raychowdhury presented a loop formulation of SU(2) lattice gauge theory based on the prepotential formalism, where both the gauge links and their conjugate electrical fields are constructed from harmonic oscillator variables living on the sites using the Schwinger construction. By some ingenious rearrangements in terms of "fusion variables", a representation of the perturbative series for Hamiltonian lattice gauge theory purely in terms of integer-valued quantum numbers in a geometric-combinatorial construction was derived.

Lastly, Sreeraj T.P. presented a derivation of an analogy between the Gauss constraint in Hamiltonian lattice gauge theory and the condition of equal "angular impulses" in the SU(2) x SU(2) description of the SO(4) symmetry of the Coulomb potential to derive a description of the Hilbert space of SU(2) lattice gauge theory in terms of hydrogen atom (n,l,m) variables located on the plaquettes subject only to the global constraint of vanishing total angular momentum, from where a variational ansatz for the ground state can be constructed.

The workshop closed with some well-deserved applause for the organisers and all of the supporting technical and administrative staff, who have ensured that this workshop ran very smoothly indeed. Another excellent lunch (I understand that our lunches have been a kind of culinary journey through India, starting out in the north on Monday and ending in Kerala today) concluded the very interesting workshop.

I will keep the small subset of my readers whom it may interest updated about my impressions from an excursion planned for tomorrow and my trip back.

Thursday, February 19, 2015

Perspectives and Challenges in Lattice Gauge Theory, Day Four

Today was dedicated to topics and issues related to finite temperature and density. The first speaker of the morning was Prasad Hegde, who talked about the QCD phase diagram. While the general shape of the Columbia plot seems to be fairly well-established, there is now a lot of controversy over the details. For example, the two-flavour chiral limit seems to be well-described by either the O(4) or O(2) universality class, it isn't currently possible to exclude that it might be Z(2), and while the three-flavour transition appears to be known to be Z(2), simulations with staggered and Wilson quarks give disagreeing results for its features. Another topic that gets a lot of attention is the question of U(1)A restoration; of course, U(1)A is broken by the axial anomaly, which arises from the path integral measure and is present at all temperatures, so it cannot be expected to be restored in the same sense that chiral symmetry is, but it might be that as the temperature gets larger, the influence of the anomaly on the Dirac eigenvalue spectrum gets outvoted by the temporal boundary conditions, so that the symmetry violation might disappear from the correlation functions of interest. However, numerical studies using domain-wall fermions suggest that this is not the case. Finally, the equation of state can be obtained from stout or HISQ smearing with very similar results and appears well-described by a hadron resonance gas at low T, and to match reasonably well to perturbation theory at high T.

The next speaker was Saumen Datta speaking on studies of the QCD plasma using lattice correlators. While the short time extent of finite-temperature lattices makes it hard to say much about the spectrum without the use of techniques such as the Maximum Entropy Method, correlators in the spatial directions can be readily used to obtain screening masses. Studies of the spectral function of bottomonium in the Fermilab formalism suggest that the Y(1S) survives up to at least twice the critical temperature.

Sorendu Gupta spoke next about the equation of state in dense QCD. Using the Taylor expansion (which was apparently first invented in the 14th-15th century by the Indian mathematician Madhava) method together with Padé approximants to reconstruct the function from the truncated series, it is found that the statistical errors on the reconstruction blow up as one nears the suspected critical point. This can be understood as a specific instance of the "no-free-lunch theorem", because a direct simulation (were it possible) would suffer from critical slowing down as the critical point is approached, which would likewise lead to large statistical errors from a fixed number of configurations.

The last talk before lunch was Bastian Brandt with an investigation of an alternative formulation of pure gauge theory using auxiliary bosonic fields in an attempt to render the QCD action amenable to a dual description that might allow to avoid the sign problem at finite baryon chemical potential. The alternative formulation appears to describe exactly the same physics as the standard Wilson gauge action at least for SU(2) in 3D, and in 2D and/or in certain limits, its a continuum limit is in fact known to be Yang-Mills theory. However, when fermions are introduced, the dual formulation still suffers from a sign problem, but it is hoped that any trick that might avoid this sign problem would then also avoid the finite-μ one.

After lunch, there were two non-lattice talks. The first one was given by Gautam Mandal, who spoke about thermalisation in integrable models and conformal field theories. In CFTs, it can be shown that for certain initial states, the expectation value of an operator equilibrates to a certain "thermal" expectation value, and a generalisation to integrable models, where the "thermal" density operator includes chemical potentials for all (infinitely many) conserved charges, can also be given.

The last talk of the day was a very lively presentation of the fluid-gravity correspondence by Shiraz Minwalla, who described how gravity in Anti-deSitter space asymptotically goes over to Navier-Stokes hydrodynamics in some sense.

In the evening, the conference banquet took place on the roof terrace of a very nice restaurant serving very good European-inspired cuisine and Indian red wine (also rather nice -- apparently the art of winemaking has recently been adapted to the Indian climate, e.g. the growing season is during the cool season, and this seems to work quite well).