The origin of mass. Update, October 2013. Page: 3 of 5
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The origin of mass. Update, October 2013.
Peter Boyle*, Michael L Buchofft, Norman Christ, Taku Izubuchi , Chulwoo Jung5, Zhongjie Lint,
Thomas C. Luut, Robert Mawhinney, Chris Schroedert, Ron Soltzt, Pavlos Vranast, Joseph Wasemt, Hantao Yin$
*SUPA, School of Physics, The University of Edinburgh, Edinburgh EH9 3JZ, UK
tPhysical Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
1Physics Department, Columbia University, New York, NY 10027, USA
5Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USAAbstract-Since our April Gordon Bell Prize submission we
have proceeded to the exploration of the order of the QCD phase
transition as the constituent quark masses are varied to even
lower values. This is significant to the understanding of QCD as
well as to a possible cosmic transition that could have created
composite dark matter. Here we report a time-to-solution over
the previous-state-of-the-art that is approximately a factor of 2
better than our April submission and was made possible because
of our algorithms. This is approximately 400 times better than
the previous state of the art. This opens a new area of research
that was previously out of reach. Here we provide first physics
results from simulations on the LLNL BlueGene/Q systems. We
also show that the factor of 400 is robust and obtainable on the
full LLNL BlueGene/Q system.
Category: Scalability and Time to solution
I. BACKGROUND
The phase diagram of the QCD thermal transition as a
function of the mass of the up and down quark masses (set
to be equal here since they are nearly equal in nature; x axis)
and the strange quark mass (y axis) is shown in Figure 1.
The diamond indicates the physical point where these quarks
have their experimentally measured values. At that point the
transition is a crossover from the quark gluon plasma to
the stable nuclear matter of today. This diagram is referred
as the Columbia phase diagram [1]. The remaining three
quarks(charm, top, and bottom) are considerably heavier and
do not affect the order of the transition. If dark matter is
composite and governed by a similar theory as QCD then its
cosmic thermal transition would correspond to a point in a
similar plot.
The upper right part of the phase diagram corresponding
to large quark masses is well established by early numerical
simulations of Lattice QCD. This is easy to simulate because
the heavy quark masses directly set the lowest eigenvalues of
the Dirac matrix to large values making its inversion very fast.
The bottom right and top left are similarly well understood.
The bottom left of this diagram is the most important phys-
ically. Not only does it contain the physical point (diamond)
but also is expected to have a richer phase structure consisting
of second order phase transition lines, a tricritical point and
a first order phase transition region. That phase structure is
important since it affects the more detailed properties of the
nearby physical point (diamond) as well as it indicates the
sensitivity on the quark masses.Ne2
PURE
GAUGE
Ne1Fig. 1. The phase diagram of the QCD thermal transition as a function of
the quark masses, Columbia phase diagram [1], from [2].
The problem is that although we now know that the physical
point is in the crossover region the rest of the bottom left is
largely a theoretical conjecture. In addition, the lines shown are
schematic. Even if the conjecture proves to be right we do not
know to which values of the quark masses they correspond.
For example how close is the physical point to the second
order line? Or how small should the quark masses be to
enter the first order transition region? These questions can
only be answered using Lattice QCD simulations. But this
has been impossible over the past nearly 40 years because the
corresponding quark masses are small demanding very large
lattices and having very ill-conditioned matrices that have been
prohibitive to invert. In addition that region demands firm
control over chiral symmetry, a fundamental ingredient that
ensures the pions have equal masses. This is spoiled by the
lattice and could not be faithfully addressed until the advent
of Domain Wall Fermions that add additional computational
costs. It is this problem that for the first time we are able
to investigate. Because of our time-to-solution speedup we
estimate that on LLNL BG/Q Sequoia type resources it would
take about half a year to complete this project. Just a few years
ago this project would have taken 200 years to complete.nd 2 order 1st
2 order Z(2) order
0(4)
physical point N3
Smt
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1st 2 order
rder(2)
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Boyle, P.; Buchoff, M.; Christ, N.; Izubuchi, T.; Jung, C.; Lin, Z. et al. The origin of mass. Update, October 2013., article, October 2, 2013; Livermore, California. (https://digital.library.unt.edu/ark:/67531/metadc871669/m1/3/: accessed March 28, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.