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 27, 2015

## 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 Ω

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.

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 Ω

_{ccc}) 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.

Labels:
conferences

## 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)

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).

_{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).

Labels:
conferences

## Wednesday, February 18, 2015

### Perspectives and Challenges in Lattice Gauge Theory, Day Three

Today's first talk was given by Rainer Sommer, who presented two effective field theories for heavy quarks. The first one was non-perturbatively matched HQET, which has been the subject of a long-running effort by the ALPHA collaboration. This programme is now reaping its first dividends in the form of very reliable fully non-perturbative results for B physics observables. Currently, the form factors for B->πlν decays, which are very important for determining the CKM matrix element V

After tea, we had a session focussed on algorithms and machines. The first speaker was Andreas Frommer speaking about multigrid solvers for the Dirac equation in lattice QCD. A multigrid solver consists of a smoother and a coarse-grid correction. For the smoother for the Dirac equation, the Schwartz Alternating Procedure (SAP) is a natural choice, whereas for the coarse-grid correction, aggregate-based interpolation (essentially the same idea as Lüscher-style inexact deflation) can be used. The resulting multigrid algorithm is very similar to the domain-decomposed algorithm used in the DD-HMC and openQCD codes, but generalises to more than two levels, which may lead to better performance. Applications to the overlap operator were presented.

Next, Stephan Solbrig presented the QPACE2 project, which aims to build a supercomputer based on Intel Knight's Corner (Xeon Phi) cards as processors, where each node consists of four Xeon Phis linked to each other, a weak host CPU used only for booting, and to an Infiniband card via a PCIe switch. The whole system uses hot water cooling, building on experience gathered in the iDataCool project. The 512bit wide registes of the Xeon Phi necessitate several programming tricks such as site fusing to make optimal use of computing resources; the resulting code seems to scale almost perfectly as long as there are sufficient numbers of domains to keep all nodes busy. An interesting side note was that apparently there are extremophile bacteria that thrive in the copper pipes of water-cooled computer clusters.

Pushan Majumdar rounded off the session with a talk about QCD on GPUs. The special programming model of GPUs (small amount of memory per core, restrictions on branching, CPU/GPU data transfer as a bottleneck) makes programming GPUs challenging. The OpenACC compiler standard, which aims to offload the burden of dealing with GPU particulars onto the compiler vendor, may offer a possibility to easily port OpenMP-based code written for CPUs on GPUs, and Pushan showed some worked examples of Fortran 90 OpenMP code adapted for OpenACC.

After lunch, I had to retire to my room for a little (let me hasten to add that the truly excellent lunch provided by the extremely hospitable TIFR is definitely absolutely blameless in this), and thus missed the afternoon's first two talks, catching only the end of Jyotirmoy Maiti's talk about exploring the spectrum of the pure SU(3) gauge theory using the Wilson flow.

Gunnar Bali closed the day's proceeding with a very nice colloquium talk for a larger scientific audience, summarising the Standard Model and lattice QCD in an accessible manner for non-experts before proceeding to present recent results on the sea quark content and spin structure of the proton.

_{ub}(currently subject to some significant tension between inclusive and exclusive determinations) are in the final stages of analysis. The other effective theory was QCD with N_{f}<6 flavours -- which is of course technically an effective theory where the heavy quarks have been integrated out! Rainer presented a new factorisation formula that relates the mass of a light hadron in the theory with a heavy quark to that of the same hadron in a theory in which the heavy quark is massless by a factor dependent on the hadron and a universal perturbative factor. The factorisation formula has been tested for gluonic observables in the pure gauge theory matched to the two-flavour theory.After tea, we had a session focussed on algorithms and machines. The first speaker was Andreas Frommer speaking about multigrid solvers for the Dirac equation in lattice QCD. A multigrid solver consists of a smoother and a coarse-grid correction. For the smoother for the Dirac equation, the Schwartz Alternating Procedure (SAP) is a natural choice, whereas for the coarse-grid correction, aggregate-based interpolation (essentially the same idea as Lüscher-style inexact deflation) can be used. The resulting multigrid algorithm is very similar to the domain-decomposed algorithm used in the DD-HMC and openQCD codes, but generalises to more than two levels, which may lead to better performance. Applications to the overlap operator were presented.

Next, Stephan Solbrig presented the QPACE2 project, which aims to build a supercomputer based on Intel Knight's Corner (Xeon Phi) cards as processors, where each node consists of four Xeon Phis linked to each other, a weak host CPU used only for booting, and to an Infiniband card via a PCIe switch. The whole system uses hot water cooling, building on experience gathered in the iDataCool project. The 512bit wide registes of the Xeon Phi necessitate several programming tricks such as site fusing to make optimal use of computing resources; the resulting code seems to scale almost perfectly as long as there are sufficient numbers of domains to keep all nodes busy. An interesting side note was that apparently there are extremophile bacteria that thrive in the copper pipes of water-cooled computer clusters.

Pushan Majumdar rounded off the session with a talk about QCD on GPUs. The special programming model of GPUs (small amount of memory per core, restrictions on branching, CPU/GPU data transfer as a bottleneck) makes programming GPUs challenging. The OpenACC compiler standard, which aims to offload the burden of dealing with GPU particulars onto the compiler vendor, may offer a possibility to easily port OpenMP-based code written for CPUs on GPUs, and Pushan showed some worked examples of Fortran 90 OpenMP code adapted for OpenACC.

After lunch, I had to retire to my room for a little (let me hasten to add that the truly excellent lunch provided by the extremely hospitable TIFR is definitely absolutely blameless in this), and thus missed the afternoon's first two talks, catching only the end of Jyotirmoy Maiti's talk about exploring the spectrum of the pure SU(3) gauge theory using the Wilson flow.

Gunnar Bali closed the day's proceeding with a very nice colloquium talk for a larger scientific audience, summarising the Standard Model and lattice QCD in an accessible manner for non-experts before proceeding to present recent results on the sea quark content and spin structure of the proton.

Labels:
conferences

## Tuesday, February 17, 2015

### Perspectives and Challenges in Lattice Gauge Theory, Day Two

Today's first session started with a talk by Wolfgang Söldner, who reviewed the new CLS simulations using 2+1 flavours of dynamical fermions with open boundary conditions in the time direction to avoid the freezing of topology at small lattice spacing. Besides the new kind of boundary conditions, these simulations use a number of novel tricks, such as twisted mass reweighting, to make the simulations more stable at light pion masses. First studies of the topology and of the scale setting look promising, and there will likely be some interesting first physics results at the lattice conference in Kobe.

After the tea break, Asit Kumar De talked about lattice gauge theory with equivariant gauge fixing. This is an attempt to evade the Neuberger 0/0 problem with BRST invariance on a lattice by leaving a subgroup of the gauge group unfixed. As a result, on gets four-ghost interactions in the gauge fixed action (this seems to be a general feature of theories trying to extend BRST symmetry; the Curci-Ferrari model for massive gauge fields also has such an interaction).

This was followed Mughda Sarkar speaking about simulations of the gauge-fixed compact U(1) gauge theory. Apparently, the added parameters of the gauge fixing part appear to allow for changing the nature of the phase transition between strong and weak coupling from first to second order, although I didn't quite understand how that is compatible with the idea of having all gauge-invariant quantities be unaffected by the gauge fixing.

After lunch, we had an excursion to the island of Elephanta, where there are some great temples carved out of the rock. Today was a festival of Shiva, so admission was free (otherwise the price structure is quite interesting: र10 for Indians, र250 for foreigners), and there were many people on the island and in the caves. The site is certainly well worth the visit, although many of the statues have been damaged quite severely in the past.

After the tea break, Asit Kumar De talked about lattice gauge theory with equivariant gauge fixing. This is an attempt to evade the Neuberger 0/0 problem with BRST invariance on a lattice by leaving a subgroup of the gauge group unfixed. As a result, on gets four-ghost interactions in the gauge fixed action (this seems to be a general feature of theories trying to extend BRST symmetry; the Curci-Ferrari model for massive gauge fields also has such an interaction).

This was followed Mughda Sarkar speaking about simulations of the gauge-fixed compact U(1) gauge theory. Apparently, the added parameters of the gauge fixing part appear to allow for changing the nature of the phase transition between strong and weak coupling from first to second order, although I didn't quite understand how that is compatible with the idea of having all gauge-invariant quantities be unaffected by the gauge fixing.

After lunch, we had an excursion to the island of Elephanta, where there are some great temples carved out of the rock. Today was a festival of Shiva, so admission was free (otherwise the price structure is quite interesting: र10 for Indians, र250 for foreigners), and there were many people on the island and in the caves. The site is certainly well worth the visit, although many of the statues have been damaged quite severely in the past.

Labels:
conferences

## Monday, February 16, 2015

### Perspectives and Challenges in Lattice Gauge Theory, Day One

Hello from Mumbai, where I'm attending the workshop "Perspectives and Challenges in Lattice Gauge Theory" at the Tata Institute for Fundamental Research. I arrived on Sunday at an early hour, and had some opportunity to see some of the sights of Mumbai while trying to get acclimatized and jetlag-free.

Today was the first day of the workshop, which started with a talk by Gergely Endrődi on the magnetic response of isospin-asymmetric QCD matter. This is relevant both for heavy-ion collisions and for the astrophysics of neutron stars, where in both cases strong magnetic fields interact with nuclear matter that has more neutrons than protons. From analytical calculations it is known that free quarks would form a paramagnetic state of matter, whereas pions would yield diamagnetism. As QCD matter at low energies should be mostly a hadron gas, and at high temperatures a quark-gluon plasma, the expectation would be that the behaviour of QCD at zero chemical potential changes from diamagnetic to paramagnetic as the temperature increases. On the other hand, at zero temperature and non-zero isospin chemical potential, at small isospin chemical potential the magnetic susceptibility vanishes (by the "Silver Blaze" effect), before suddenly going negative from pion condensation when the chemical potential exceeds half the pion mass, and again going positive as the chemical potential is increased further. Lattice simulations confirm this overall picture, although the susceptibility remains finite at μ

After the coffee break, it was my turn to talk about recent work we have done at Mainz regarding the importance of excited-state effects on nucleon form factors. Briefly summarised, the splitting to the first excited state (nucleon+pion P-wave, or nucleon+2 pions S-wave) gets very small in the chiral regime, but the errors on the nucleon two- and three-point functions grow exponentially as the source-sink separation is increased, making it very hard to find a Euclidean time region of both clean ground-state signal and reasonable statistical precision. Treating the excited states using different methods (summation method and explicit two-state fits) yields indications hinting that the current discrepancy between the nucleon charge radius obtained from lattice simulations and experiment may be due mostly to excited-state effects.

This was followed by Andreas Schäfer speaking about much more ambitious hadron structure observables, namely Transverse Momentum Distributions (TMDs), Parton Distribution Functions (PDFs) and Generalised Parton Distributions (GPDs). Knowledge of these is important to clarify systematics for some of the LHC measurements, so lattice results could certainly have a huge impact here, but the necessary calculations appear quite involved.

After the lunch break, Stefan Dürr reviewed some of the newer inhabitants of the fermion zoo, namely firstly the Brillouin fermions obtained by replacing the standard discretisation of the Laplacian in the Wilson action with its Brillouin discretisation, and the symmetric derivative with its isotropic alternative, and secondly the staggered Wilson fermions of Adams (Adams fermions). In particular for heavier quark masses, the Brillouin fermions seem to do much better than standard Wilson fermions, including by giving a much more continuum-like dispersion relation.

After a more technical talk on simulating the Gross-Neveu model with Boriçi-Creutz fermions by Jinshu Goswami, Kalman Szabo gave a colloquium for a more general audience explaining the origin of mass from QCD, electromagnetism and the Higgs effect (which is roughly the order of importance for ordinary matter), and how to determine the proton-neutron mass difference (which is after all of great anthropic significance, since an even slightly smaller value would leave hydrogen atoms unstable under inverse β-decay, whereas a somewhat larger value would create too much of a bottleneck in the creation of heavier elements) on the lattice. The lattice results are certainly impressive both in terms of the theoretical and computational effort needed to obtain them and in the accuracy with which they reproduce the experimentally-known situation.

Today was the first day of the workshop, which started with a talk by Gergely Endrődi on the magnetic response of isospin-asymmetric QCD matter. This is relevant both for heavy-ion collisions and for the astrophysics of neutron stars, where in both cases strong magnetic fields interact with nuclear matter that has more neutrons than protons. From analytical calculations it is known that free quarks would form a paramagnetic state of matter, whereas pions would yield diamagnetism. As QCD matter at low energies should be mostly a hadron gas, and at high temperatures a quark-gluon plasma, the expectation would be that the behaviour of QCD at zero chemical potential changes from diamagnetic to paramagnetic as the temperature increases. On the other hand, at zero temperature and non-zero isospin chemical potential, at small isospin chemical potential the magnetic susceptibility vanishes (by the "Silver Blaze" effect), before suddenly going negative from pion condensation when the chemical potential exceeds half the pion mass, and again going positive as the chemical potential is increased further. Lattice simulations confirm this overall picture, although the susceptibility remains finite at μ

_{I}=1/2 m_{π}since the pions already start to melt rather than to condense into a superconductor).After the coffee break, it was my turn to talk about recent work we have done at Mainz regarding the importance of excited-state effects on nucleon form factors. Briefly summarised, the splitting to the first excited state (nucleon+pion P-wave, or nucleon+2 pions S-wave) gets very small in the chiral regime, but the errors on the nucleon two- and three-point functions grow exponentially as the source-sink separation is increased, making it very hard to find a Euclidean time region of both clean ground-state signal and reasonable statistical precision. Treating the excited states using different methods (summation method and explicit two-state fits) yields indications hinting that the current discrepancy between the nucleon charge radius obtained from lattice simulations and experiment may be due mostly to excited-state effects.

This was followed by Andreas Schäfer speaking about much more ambitious hadron structure observables, namely Transverse Momentum Distributions (TMDs), Parton Distribution Functions (PDFs) and Generalised Parton Distributions (GPDs). Knowledge of these is important to clarify systematics for some of the LHC measurements, so lattice results could certainly have a huge impact here, but the necessary calculations appear quite involved.

After the lunch break, Stefan Dürr reviewed some of the newer inhabitants of the fermion zoo, namely firstly the Brillouin fermions obtained by replacing the standard discretisation of the Laplacian in the Wilson action with its Brillouin discretisation, and the symmetric derivative with its isotropic alternative, and secondly the staggered Wilson fermions of Adams (Adams fermions). In particular for heavier quark masses, the Brillouin fermions seem to do much better than standard Wilson fermions, including by giving a much more continuum-like dispersion relation.

After a more technical talk on simulating the Gross-Neveu model with Boriçi-Creutz fermions by Jinshu Goswami, Kalman Szabo gave a colloquium for a more general audience explaining the origin of mass from QCD, electromagnetism and the Higgs effect (which is roughly the order of importance for ordinary matter), and how to determine the proton-neutron mass difference (which is after all of great anthropic significance, since an even slightly smaller value would leave hydrogen atoms unstable under inverse β-decay, whereas a somewhat larger value would create too much of a bottleneck in the creation of heavier elements) on the lattice. The lattice results are certainly impressive both in terms of the theoretical and computational effort needed to obtain them and in the accuracy with which they reproduce the experimentally-known situation.

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