Saturday, July 18, 2015

LATTICE 2015, Day Five

In a marked deviation from the "standard programme" of the lattice conference series, Saturday started off with parallel sessions, one of which featured my own talk.

The lunch break was relatively early, therefore, but first we all assembled in the plenary hall for the conference group photo (a new addition to the traditions of the lattice conference), and was followed by afternoon plenary sessions. The first of these was devoted to finite temperature and density, and started with Harvey Meyer giving the review talk on finite-temperature lattice QCD. The thermodynamic properties of QCD are by now relatively well-known: the transition temperature is agreed to be around 155 MeV, chiral symmetry restoration and the deconfinement transition coincide (as well as that can defined in the case of a crossover), and the number of degrees of freedom is compatible with a plasma of quarks and gluons above the transition, but the thermodynamic potentials approach the Stefan-Boltzmann limit only slowly, indicating that there are strong correlations in the medium. Below the transition, the hadron resonance gas model describes the data well. The Columbia plot describing the nature of the transition as a function of the light and strange quark masses is being further solidified: the size of the lower-left hand corner first-order region is being measured, and the nature of the left-hand border (most likely O(4) second-order) is being explored. Beyond these static properties, real-time properties are beginning to be studied through the finite-temperature spectral functions. One interesting point was that there is a difference between the screening masses (spatial correlation lengths) and quasiparticle masses (from the spectral function) in any given channel, which may even tend in opposite directions as functions of the temperature (as seen for the pion channel).

Next, Szabolcs Borsanyi spoke about fluctuations of conserved charges at finite temperature and density. While of course the sum of all outcoming conserved charges in a collision must equal the sum of the ingoing ones, when considering a subvolume of the fireball, this can be best described in the grand canonical ensemble, as charges can move into and out of the subvolume. The quark number susceptibilities are then related to the fluctuating phase of the fermionic determinant. The methods being used to avoid the sign problem include Taylor expansions, fugacity expansions and simulations at imaginary chemical potential, all with their own strengths and weaknesses. Fluctuations can be used as a thermometer to measure the freeze-out temperature.

Lastly, Luigi Scorzato reviewed the Lefschetz thimble, which may be a way out of the sign problem (e.g. at finite chemical potential). The Lefschetz thimble is a higher-dimensional generalization of the concept of steepest-descent integration, in which the integral of eS(z) for complex S(z) is evaluated by finding the stationary points of S and integrating along the curves passing through them along which the imaginary part of S is constant. On such Lefschetz thimbles, a Langevin algorithm can be defined, allowing for a Monte Carlo evaluation of the path integral in terms of Lefschetz thimbles. In quantum-mechanical toy models, this seems to work already, and there appears hope that this might be a way to avoid the sign problem of finite-density QCD.

After the coffee break, the last plenary session turned to physics beyond the Standard Model. Daisuke Kadoh reviewed the progress in putting supersymmetry onto the lattice, which is still a difficult problem due to the fact that the finite differences which replace derivatives on a lattice do not respect the Leibniz rule, introducing SUSY-breaking terms when discretizing. The ways past this are either imposing exact lattice supersymmetries or fine-tuning the theory so as to remove the SUSY-breaking in the continuum limit. Some theories in both two and four dimensions have been simulated successfully, including N=1 Super-Yang-Mills theory in four dimensions. Given that there is no evidence for SUSY in nature, lattice SUSY is of interesting especially for the purpose of verifying the ideas of gauge-dravity duality from the Super-Yang-Mills side, and in one and two dimensions, agreement with the predictions from gauge-gravity duality has been found.

The final plenary speaker was Anna Hasenfratz, who reviewed Beyond-the-Standard-Model calculations in technicolor-like theories. If the Higgs is to be a composite particle, there must be some spontaneously broken symmetry that keeps it light, either a flavour symmetry (pions) or a scale symmetry (dilaton). There are in fact a number of models that have a light scalar particle, but the extrapolation of these theories is rendered difficult by the fact that this scalar is (and for phenomenologically interesting models would have to be) lighter than the (techni-)pion, and thus the usual formalism of chiral perturbation theory may not work. Many models of strong BSM interactions have been and are being studied using a large number of different methods, with not always conclusive results. A point raised towards the end of the talk was that for theories with a conformal IR fixed-point, universality might be violated (and there are some indications that e.g. Wilson and staggered fermions seem to give qualitatively different behaviour for the beta function in such cases).

The conference ended with some well-deserved applause for the organizing team, who really ran the conference very smoothly even in the face of a typhoon. Next year's lattice conference will take place in Southampton (England/UK) from 24th to 30th July 2016. Lattice 2017 will take place in Granada (Spain).

Friday, July 17, 2015

LATTICE 2015, Days Three and Four

Due to the one-day shift of the entire conference programme relative to other years, Thursday instead of Wednesday was the short day. In the morning, there were parallel sessions. The most remarkable thing to be reported from those (from my point of view) is that MILC are generating a=0.03 fm lattices now, which handily beats the record for the finest lattice spacing; they are observing some problems with the tunnelling of the topological charge at such fine lattices, but appear hopeful that they can be useful.

After the lunch break, excursions were offered. I took the trip to Himeji to see Himeji Castle, a very remarkable five-story wooden building that due to its white exterior is also known the "White Heron Castle". During the trip, typhoon Nangka approached, so the rains cut our enjoyment of the castle park a bit short (though seeing koi in a pond with the rain falling into it had a certain special appeal to it, the enjoyment of which I in my Western ignorance suppose might be considered a form of Japanese wabi aesthetics).

As the typhoon resolved into a rainstorm, the programme wasn't cancelled or changed, and so today's plenary programme started with a talk on some formal developments in QFT by Mithat Ünsal, who reviewed trans-series, Lefschetz thimbles, and Borel summability as different sides of the same coin. I'm far too ignorant of these more formal field theory topics to do them justice, so I won't try a detailed summary. Essentially, it appears that the expansion of certain theories around the saddle points corresponding to instantons is determined by their expansion around the trivial vacuum, and the ambiguities arising in the Borel resummation of perturbative series when the Borel transform has a pole on the positive real axis can in some way be connected to this phenomenon, which may allow for a way to resolve the ambiguities.

Next, Francesco Sannino spoke about the "bright, dark, and safe" sides of the lattice. The bright side referred to the study of visible matter, in particular to the study of technicolor models as a way of implementing the spontaneous breaking of electroweak symmetry, without the need for a fundamental scalar introducing numerous tunable parameters, and with the added benefits of removing the hierarchy problem and the problem of φ4 triviality. The dark side referred to the study of dark matter in the context of composite dark matter theories, where one should remember that if the visible 5% of the mass of the universe require three gauge groups for their description, the remaining 95% are unlikely to be described by a single dark matter particle and a homogeneous dark energy. The safe side referred to the very current idea of asymptotic safety, which is of interest especially in quantum gravity, but might also apply to some extension of the Standard Model, making it valid at all energy scales.

After the coffee break, the traditional experimental talk was given by Toru Iijima of the Belle II collaboration. The Belle II detector is now beginning commissioning at the upcoming SuperKEKB accelerator, which will greatly improved luminosity to allow for precise tests of the Standard Model in the flavour sector. In this, Belle II will be complementary to LHCb, because it will have far lower backgrounds allowing for precision measurements of rare processes, while not being able to access as high energies. Most of the measurements planned at Belle II will require lattice inputs to interpret, so there is a challenge to our community to come up with sufficiently precise and reliable predictions for all required flavour observables. Besides quark flavour physics, Belle II will also search for lepton flavour violation in τ decays, try to improve the phenomenological prediction for (g-2)μ by measuring the cross section for e+e- -> hadrons more precisely, and search for exotic charmonium- and bottomonium-like states.

Closely related was the next talk, a review of progress in heavy flavour physics on the lattice given by Carlos Pena. While simulations of relativistic b quarks at the physical mass will become a possibility in the not-too-distant future, for the time being heavy-quark physics is still dominated by the use of effective theories (HQET and NRQCD) and methods based either on appropriate extrapolations from the charm quark mass region, or on the Fermilab formalism, which is sort of in-between. For the leptonic decay constants of heavy-light mesons, there are now results from all formalisms, which generally agree very well with each other, indicating good reliability. For the semileptonic form factors, there has been a lot of development recently, but to obtain precision at the 1% level, good control of all systematics is needed, and this includes the momentum-dependence of the form factors. The z-expansion, and extended versions thereof allowing for simultaneous extrapolation in the pion mass and lattice spacing, has the advantage of allowing for a test of its convergence properties by checking the unitarity bound on its coefficients.

After the coffee break, there were parallel sessions again. In the evening, the conference banquet took place. Interestingly, the (excelleent) food was not Japanese, but European (albeit with a slight Japanese twist in seasoning and presentation).

Wednesday, July 15, 2015

LATTICE 2015, Day Two

Hello again from Lattice 2015 in Kobe. Today's first plenary session began with a review talk on hadronic structure calculations on the lattice given by James Zanotti. James did an excellent job summarizing the manifold activities in this core area of lattice QCD, which is also of crucial phenomenological importance given situations such as the proton radius puzzle. It is now generally agreed that excited-state effects are one of the more important issues facing hadron structure calculations, especially in the nucleon sector, and that these (possibly together with finite-volume effects) are likely responsible for the observed discrepancies between theory and experiment for quantities such as the axial charge of the nucleon. Many groups are studying the charges and form factors of the nucleon, and some have moved on to more complicated quantities, such as transverse momentum distributions. Newer ideas in the field include the use of the Feynman-Hellmann theorem to access quantities that are difficult to access through the traditional three-point-over-two-point ratio method, such as form factors at very high momentum transfer, and quantities with disconnected diagrams (such as nucleon strangeness form factors).

Next was a review of progress in light flavour physics by Andreas Jüttner, who likewise gave an excellent overview of this also phenomenologically very important core field. Besides the "standard" quantities, such as the leptonic pion and kaon decay constants and the semileptonic K-to-pi form factors, more difficult light-flavour quantities are now being calculated, including the bag parameter BK and other quantities related to both Standard Model and BSM neutral kaon mixing, which require the incorporation of long-distance effects, including those from charm quarks. Given the emergence of lattice ensembles at the physical pion mass, the analysis strategies of groups are beginning to change, with the importance of global ChPT fits receding. Nevertheless, the lattice remains important in determining the low-energy constants of Chiral Perturbation Theory. Some groups are also using newer theoretical developments to study quantities once believed to be outside the purview of lattice QCD, such as final-state photon corrections to meson decays, or the timelike pion form factor.

After the coffee break, the Ken Wilson Award for Excellence in Lattice Field Theory was announced. The award goes to Stefan Meinel for his substantial and timely contributions to our understanding of the physics of the bottom quark using lattice QCD. In his acceptance talk, Stefan reviewed his recent work on determining |Vub|/|Vcb| from decays of Λb baryons measured by the LHCb collaboration. There has long been a discrepancy between the inclusive and exclusive (from B -> πlν) determinations of Vub, which might conceivably be due to a new (BSM) right-handed coupling. Since LHCb measures the decay widths for Λb to both pμν and Λcμν, combining these with lattice determinations of the corresponding Λb form factors allows for a precise determination of |Vub|/|Vcb|. The results agree well with the exclusive determination from B -> πlν, and fully agree with CKM unitarity. There are, however, still other channels (such as b -> sμ+μ- and b -> cτν) in which there is still potential for new physics, and LHCb measurements are pending.

This was followed by a talk by Maxwell T. Hansen (now a postdoc at Mainz) on three-body observables from lattice QCD. The well-known Lüscher method relates two-body scattering amplitudes to the two-body energy levels in a finite volume. The basic steps in the derivation are to express the full momentum-space propagator in terms of a skeleton expansion involving the two-particle irreducible Bethe-Salpeter kernel, to express the difference between the two-particle reducible loops in finite and infinite volume in terms of two-particle cuts, and to reorganize the skeleton expansion by the number of cuts to reveal that the poles of the propagator (i.e. the energy levels) in finite volume are related to the scattering matrix. For three-particle systems, the skeleton expansion becomes more complicated, since there can now be situations involving two-particle interactions and a spectator particle, and intermediate lines can go on-shell between different two-particle interactions. Treating a number of other technical issues such as cusps, Max and collaborators have been able to derive a Lüscher-like formula three-body scattering in the case of scalar particles with a Z2 symmetry forbidding 2-to-3 couplings. Various generalizations remain to be explored.

The day's plenary programme ended with a talk on the Standard Model prediction for direct CP violation in K-> ππ decays by Christopher Kelly. This has been an enormous effort by the RBC/UKQCD collaboration, who have shown that the ΔI=1/2 rule comes from low-energy QCD by way of strong cancellations between the dominant contributions, and have determined ε' from the lattice for the first time. This required the generation of ensembles with an unusual set of boundary conditions (G-parity boundary conditions on the quarks, requiring complex conjugation boundary conditions on the gauge fields) in space to enforce a moving pion ground state, as well as the precise evaluation of difficult disconnected diagrams using low modes and stochastic estimators, and treatment of finite-volume effects in the Lellouch-Lüscher formalism. Putting all of this together with the non-perturbative renormalization (in the RI-sMOM scheme) of ten operators in the electroweak Hamiltonian gives a result which currently still has three times the experimental error, but is systematically improvable, with better-than-experimental precision expected in maybe five years.

In the afternoon there were parallel sessions again, and in the evening, the poster session took place. Food ran out early, but it was pleasant to see free-form smearing begin improved upon and used to very good effect by Randy Lewis, Richard Woloshyn and students.

Tuesday, July 14, 2015

LATTICE 2015, Day One

Hello from Kobe, where I am attending the Lattice 2015 conference. The trip here was uneventful, as was the jetlag-day.

The conference started yesterday evening with a reception in the Kobe Animal Kingdom (there were no animals when we were there, though, with the exception of some fish in a pond and some cats in a cage, but there were lot of plants).

Today, the scientific programme began with the first plenary session. After a welcome address by Akira Ukawa, who reminded us of the previous lattice meetings held in Japan and the tremendous progress the field has made in the intervening twelve years, Leonardo Giusti gave the first plenary talk, speaking about recent progress on chiral symmetry breaking. Lattice results have confirmed the proportionality of the square of the pion mass to the quark mass (i.e. the Gell-Mann-Oakes-Renner (GMOR) relation, a hallmark of chiral symmetry breaking) very accurately for a long time. Another relation involving the chiral condensate is the Banks-Casher relation, which relates it to the eigenvalue density of the Dirac operator at zero. It can be shown that the eigenvalue density is renormalizable, and that thus the mode number in a given interval is renormalization-group invariant. Two recent lattice studies, one with twisted-mass fermions and one with O(a)-improved Wilson fermions, confirm the Banks-Casher relation, with the chiral condensates found agreeing very well with those inferred from GMOR. Another relation is the Witten-Veneziano relation, which relates the η' mass to the topological susceptibility, thus explaining how precisely the η' is not a Goldstone boson. The topological charge on the lattice can be defined through the index of the Neuberger operator or through chain of spectral porjectors, but a recently invented and much cheaper definition is through the topological charge density at finite flow time in Lüscher's Wilson flow formalism. The renormalization properties of the Wilson flow allow for a derivation of the universality of the topological susceptibility, and numerical tests using all three definitions indeed agree within errors in the continuum limit. Higher cumulants determined in the Wilson flow formalism agree with large-Nc predictions in pure Yang-Mills, and the suppression of the topological susceptibility in QCD relative to the pure Yang-Mills case is in line with expectations (which in principle can be considered an a posteriori determination of Nf in agreement with the value used in simulations).

The next speaker was Yu Nakayama, who talked about a related topic, namely the determination of the chiral phase transition in QCD from the conformal bootstrap. The chiral phase transition can be studied in the framework of a Landau effective theory in three dimensions. While the mean-field theory predicts a second-order phase transition in the O(4) universality class, one-loop perturbation theory in 4-ε dimensions predicts a first-order phase transition at ε=1. Making use of the conformal symmetry of the effective theory, one can apply the conformal bootstrap method, which combines an OPE with crossing relations to obtain results for critical exponents, and the results from this method suggest that the phase transition is in fact of second order. This also agrees with many lattice studies, but others disagree. The role of the anomalously broken U(1)A symmetry in this analysis appears to be unclear.

After the coffee break, Tatsumi Aoyama, a long-time collaborator in the heroic efforts of Kinoshita to calculate the four- and five-loop QED contributions to the electron and muon anomalous moments, gave a plenary talk on the determination of the QED contribution to lepton (g-2). For likely readers of this blog, the importance of (g-2) is unlikely to require an explanation: the current 3σ tension between theory and experiment for (g-2)μ is the strongest hint of physics beyond the Standard Model so far, and since the largest uncertainties on the theory side are hadronic, lattice QCD is challenged to either resolve the tension or improve the accuracy of the predictions to the point where the tension becomes an unambiguous, albeit indirect, discovery of new physics. The QED calculations are on the face of it simpler, being straightforward Feynman diagram evaluations. However, the number of Feynman diagrams grows so quickly at higher orders that automated methods are required. In fact, in a first step, the number of Feynman diagrams is reduced by using the Ward-Takahashi identity to relate the vertex diagrams relevant to (g-2) to self-energy diagrams, which are then subjected to an automated renormalization procedure using the Zimmermann forest formula. In a similar way, infrared divergences are subtracted using a more complicated "annotated forest"-formula (there are two kinds of IR subtractions needed, so the subdiagrams in a forest need to be labelled with the kind of subtraction). The resulting UV- and IR-finite integrands are then integrated using VEGAS in Feynman parameter space. In order to maintain the required precision, quadruple-precision floating-point numbers (or an emulation thereof) must be used. Whether these methods could cope with the six-loop QED contribution is not clear, but with the current and projected experimental errors, that contribution will not be required for the foreseeable future, anyway.

This was followed by another (g-2)-related plenary, with Taku Izubichi speaking about the determination of anomalous magnetic moments and nucleon electric dipole moments in QCD. In particular the anomalous magnetic moment has become such an active topic recently that the time barely sufficed to review all of the activity in this field, which ranges from different approaches to parameterizing the momentum dependence of the hadronic vacuum polarization, through clever schemes to reduce the noise by subtracting zero-momentum contributions, to new ways of extracting the vacuum polarization through the use of background magnetic fields, as well as simulations of QCD+QED on the lattice. Among the most important problems are finite-volume effects.

After the lunch break, there were parallel sessions in the afternoon. I got to chair the first session on hadron structure, which was devoted to determinations of hadronic contributions to (g-2)μ.

After the coffee break, there were more parallel sessions, another complete one of which was devoted to (g-2) and closely-related topics. A talk deserving to be highlighted was given by Jeremy Green, who spoke about the first direct calculation of the hadronic light-to-light scattering amplitude from lattice QCD.