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Quarks and Hadrons – and the Spectrum in Between

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Quarks and Hadrons – and the Spectrum in Between Golden Spike Award by the HLRS Steering Committee in 2014 Applications Quarks and Hadrons – and the Spectrum in Between The mass of ordinary matter, due to Lattice QCD, which traditionally uses a protons and neutrons, is described space-time lattice with quarks on the with a precision of about five percent [1] lattice sites and the gluons located by a theory void of any parameters – on the lattice links. In the so-called (massless) Quantum Chromodynamics continuum limit, the lattice spacing (QCD). The remaining percent are due is sent to zero and QCD and the to other parts of the Standard Model continuous space-time are recovered. of Elementary Particle Physics: the Simulations of Lattice QCD require sig- Higgs-Mechanism, which explains the nificant computational resources. As a existence of quark masses, and a per matter of fact, they have been a driving mil effect due to the presence of force of supercomputer development. Electromagnetism. Only at this stage, A large range of special-purpose free parameters are introduced1. Lattice QCD machines, e.g. the com- Mass is thus generated in QCD without puters of the APE family, QPACE, and the need of quark masses, an effect QCDOC among others, have been devel- termed “mass without mass” [2]. oped, the QCDOC being the ancestor of the IBM Blue Gene family of supercom- This mass generation is due to the puters. Over the last decade, these dynamics of the strongly interacting simulations have matured substantially. quarks and gluons, the latter mediating In 2008, the first fully controlled cal- the force like the photon in the case of culation of the particle spectrum [1] Quantum Electrodynamics. However, became available and simpler quantities in contrast to the photons, which are such as masses and decay constants themselves uncharged and thus do not interact (directly) with one another, the 10 gluons themselves carry the strong (color) charge. This is the essential ΔΣ experiment complication in the dynamics of the 8 ΔΞ QCD+QED prediction strong interaction, since it renders the interaction non-linear. Furthermore, 6 Δ due to the uncertainty relation of D quantum physics and relativity, even 4 the number of quarks inside the proton M [MeV] Δ ΔΞ cc or neutron is not fixed: quark anti- Δ quark pairs are created and annihilated 2 N Δ constantly and contribute significantly CG to the overall mass of the particle. 0 So far, the only known way to analyze BMW 2014 HCH QCD at small energies, where its interaction strength is large, is through Figure 1: Mass splittings [3]. The horizontal lines are the experimental values and the grey shaded regions represent the experimental errors than those of our pre- simulations. These simulations are dictions. Our results are shown by red dots with their uncertainties. A blue shaded based on the discretized theory, called region indicates that no experimental results are available or that these results have larger errors. 1 These parameters are a coupling (electro- magnetic charge) and the quark masses Spring 2015 • Vol. 13 No. 1 • inSiDE 29 Applications are now routinely computed to percent Including these effects is, however, precision. non-trivial. The biggest obstacle turns out to be the long ranged nature of Neutron, Proton, and the electrodynamics. Whereas the strong Stability of Matter force is essentially confined inside its In order to increase the precision of "bound-states", the so-called hadrons, the calculations further, one has to ad- the electromagnetic force, falling off dress the largest sources of uncertain- according to the well-known 1/r2 rule, ties, which, in case of the spectrum, is still felt at large distances. This are due to Electrodynamics and the introduces significant finite size ef- difference between the up- and down- fects, which are typically larger than quark masses. Once these effects are the mass splittings one is interested properly included in the simulations, in. In our recent calculation, the cor- one can calculate per mil effects of rect theoretical framework for a treat- the particle spectrum of the Standard ment of these effects was established Model, e.g. the difference between the and the finite-size corrections were proton and the neutron mass. calculated analytically. A new simula- tion algorithm for the Electrodynamics For equal light quark masses, Electro- part of the calculations was developed, dynamics renders the proton slightly which reduced the autocorrelation by heavier, due to energy stored in the three orders of magnitude. Combined electromagnetic field that surrounds with other advanced methods, such it. The light quark mass splitting, con- as the latest multi-level solvers, this versely, increases the neutron mass, allowed us to compute the particle since it contains two of the heavier splittings using the presently available down-quarks compared to one in case resources of the Gauss Centre for of the proton. The interplay between Supercomputing2, JUQUEEN at JSC, these effects has significant implica- Hermit at HLRS, and SuperMUC at LRZ tions for the stability of matter. If the (Fig. 1). neutron-proton mass splitting was about a third of the 0.14% found in From Hadrons to Quark nature, hydrogen atoms would un- Soup dergo inverse beta decay, leaving pre- In the case of the proton and the neu- dominantly neutrons. Even with a value tron, quarks and gluons are confined somewhat larger than 0.05%, Big Bang to the hadron. If we, however, increase Nucleosynthesis (BBN) would have pro- the temperature of the system suf- duced much more helium-4 and far less fciently, both particles will "melt" and hydrogen than it did in our universe. As quarks and gluons behave as free a result, stars would not have ignited particles, forming an exotic state of in the way they did. On the other hand, matter called quark-gluon plasma. a value considerably larger than 0.14% This (rapid) transition from the quark- would result in a much faster beta gluon to the hadronic phase occurred decay for neutrons. This would lead to when the early universe evolved from far less neutrons at the end of the BBN the "quark epoch", lasting from 10-12 epoch and would make the burning of to 10 -6 seconds after the Big Bang, hydrogen in stars and the synthesis of to the following hadron epoch, which heavy elements more difficult. ended when the universe was about 2 see acknowledgements 30 Spring 2015 • Vol. 13 No. 1 • inSiDE Applications Figure 2: (Left) Preliminary results for the charmed EoS. For comparison, we show the HRG result, the Nf = 2 + 1 band, and, at high Temperatures, the HTL result, where the central line marks the HTL expectation for the EoS with the band resulting from (large) varia- tions of the renormalization scale. (Right) Preliminary results for the pressure, errors indicate the Stefan-Boltzmann value. All errors are statistical only. one second old. Present heavy-ion ex- charm quark, which restrict their re- periments (LHC@CERN, RHIC@BNL, gion of applicability to temperatures and the upcoming FAIR@GSI) create, below about 400 MeV. In order to for a brief moment when two heavy reach larger temperatures, we have nuclei collide, the extreme conditions of set up new simulations which take the the early universe, allowing us to study charm quark into account, using an im- this transition and the properties of proved formulation of Lattice QCD. Our the quark-gluon plasma some 13 Billion preliminary results illustrate the impact years later. of the charm quark for temperatures larger than 400 MeV (Fig. 2), and Considerable theoretical effort is invested make contact with both HRG at low attempting to describe these experi- and HTL at large temperatures. The ments, from collision to detector signals. EoS is thus becoming available for the Here, the Equation of State (EoS) of whole temperature region. QCD [4] is a central ingredient for a complete understanding of the experi- Computational Aspects mental findings. At low temperatures, Simulations of Lattice QCD generally the EoS can be calculated using the so- happen in three main phases. In the called "Hadron Resonance Gas" (HRG) first phase, an ensemble is generated model. At high temperatures, pertur- through a Markov process. This phase bative analyses of QCD become pos- is thus usually scaled to a large number sible (e.g. "Hard Thermal Loop" (HTL) of cores, minimizing "wall-clock" time. perturbation theory). The intermediate We have, so far, scaled our production region, from ca. 100 MeV to 1 GeV, code used for the ensemble genera- can be covered systematically through tion up to 1.8 million parallel threads, simulations of Lattice QCD. running at a sustained performance of over 1.6 PFlop/s (Fig. 3). The sec- Presently available Lattice QCD results ond production stage then analyzes for the EoS neglect the effects of the the individual "configurations" that Spring 2015 • Vol. 13 No. 1 • inSiDE 31 Applications constitute an ensemble one by one. early universe transition between, and Since an ensemble can contain 1,000 the properties of matter in, the quark configurations and more, this greatly and the hadron epoch, starting 10-12 reduces the need for scaling to a large seconds after the Big Bang. number of cores. Therefore, we can optimize production at this stage for Acknowledgements efficiency (which reaches up to 70% of We thank all the Members of the the hardware peak flop rate) and queue Budapest-Marseille-Wuppertal and throughput. Physics results are then Wuppertal-Budapest collaborations for extracted in the final step of the cal- the fruitful and enjoyable cooperation. culation, which, with our involved blind analysis procedure [1,3], requires a Our simulations require substantial small compute cluster on its own.
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