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Strong-interaction matter coupled to electroweak probes and dark matter candidates

Periodic Reporting for period 3 - SIMDAMA (Strong-interaction matter coupled to electroweak probes and dark matter candidates)

Reporting period: 2021-04-01 to 2022-09-30

After the discovery of the Higgs boson and the non-observation of
particles beyond the Standard Model at the Large Hadron Collider, many
research avenues in particle physics are currently being pursued in
parallel. These include the search for dark matter particles, the
quest to complete the determination of neutrino oscillation parameters
and their absolute mass scale, as well as the intensified search for
deviations between Standard Model predictions and experimental
measurements of precision observables. The current situation and
plans for the future are described in the Physics Briefing Book
(arXiv:1910.11775) which serves as input for the European Strategy
for Particle Physics. While the Standard Model of particle physics
has been enormously successful at predicting observables measured in
collider experiments, it fails to account for gravity, for neutrino
oscillations and for dark matter, which makes up 27 percent of the
energy in the universe.

Of the fields of precision tests of the Standard Model, dark matter
searches and neutrino oscillation experiments, it is presently an open
race as to which one will lead to the most decisive progress in our
understanding of fundamental physics. Project SIMDAMA, based on the
`lattice QCD' framework, aims at enabling a more stringent test of the
Standard Model (SM), contributing to narrowing down the list of
dark-matter candidate particles, and reducing uncertainties in
neutrino detection. In all cases, the complexity of the strong
interaction is a bottleneck in pursuing these research avenues. The
strong-interaction physics is addressed within SIMDAMA using the ab
initio method of lattice QCD. The basic idea of this computational
framework is to discretize space and time and to formulate a lattice
field theory whose renormalized correlation functions converge to the
QCD correlation functions in the limit of zero lattice spacing. In
principle, all physics observables can be extracted from these
correlation functions. The method is numerically very demanding and
requires massively parallel computing resources.
The specific task chosen of testing the SM more stringently
consists in improving its prediction for the anomalous magnetic moment
(g-2) of the muon, which is measured experimentally to sub-ppm level
and has served as a precision observable for decades. The uncertainty
of the SM prediction is entirely dominated by the hadronic
contributions, and SIMDAMA aims at reducing the uncertainty on the
virtual effect of hadronic light-by-light scattering. At this point, a
lattice calculation carried out within SIMDAMA at larger-than-physical
quark masses has been published. It has yielded a result with a
competitive overall precision of 13 percent. The publication [Chao et
al, Eur. Phys. J. C 80 (2020) no.9 869] also contains a
phenomenological estimate of the correction needed to reach a
prediction at physical quark masses. Lattice calculations are ongoing
to directly compute this hadronic contribution at or near physical quark
masses. In addition to this direct calculation of hadronic
light-by-light scattering in (g-2), its single largest contribution,
namely the pion-pole exchange, can be computed separately. Within
SIMDAMA, this contribution was computed with a state-of-the-art
precision of six percent [Gerardin et al, Phys.Rev. D100 (2019) no.3
034520]. A significant amount of computing time was allocated to this
SIMDAMA project within the PRACE programme to further reduce this uncertainty.

In the area of neutrino detection, lattice calculations are underway
to provide a high-quality determination of the nucleon axial form
factor. This is a central input in nuclear calculations of the
neutrino-nucleus interaction, which are needed in order to determine
neutrino fluxes in long-baseline oscillation experiments. New methods
have been developed to perform this calculation (H.B. Meyer et al, PoS
LATTICE2018 (2018), 062). Next, inelastic contributions to
neutrino-nucleon scattering will be studied, which become the dominant
component of the cross-section at the neutrino energies of several GeV
relevant for the DUNE experiment.

In the area of WIMP dark matter detection -- WIMP stands for weakly
interacting massive particle, providing more accurate scalar matrix
elements of the nucleon enables one to reliably translate the
experimental measurement of a WIMP-nucleus cross-section or an
exclusion limit thereof into a value of the coupling of the WIMP
particle to the SM Higgs particle, assuming the former is a scalar
particle. Here too, significant computing resources have been
allocated to perform this challenging calculation (see the online

A further goal of SIMDAMA is to make decisive progress in determining
the spectral functions of the quark-gluon plasma (QGP), the
high-temperature phase of strong-interaction matter. The spectral
functions associated with the electromagnetic current are directly
proportional to the photon emissivity and the rate of dilepton
production. The direct photon and dilepton spectra are central
observables in heavy-ion collision experiments, which study the
properties of the QGP in the lab. Thus, combined with the hydrodynamic
description of the reaction, the spectral functions allow one to make
predictions for these spectra and compare them to experimental
measurements. A second motivation comes from sterile neutrinos as a
dark matter candidate. Through their oscillation into active
neutrinos, their interactions with the QGP are governed by closely
related spectral functions. Hence, under certain conditions the
rate of sterile-neutrino production and therefore their abundance in
the universe are determined by the QGP spectral functions at a
temperature around 200\,MeV.

In the past year, a new quality of lattice calculations has been
achieved to probe the photon emissivity of the QGP (Ce et al,
Phys. Rev. D 102 (2020) no.9 091501). It is the first calculation in
QCD with dynamical quarks to take the continuum limit of the relevant
correlation function, before analyzing it in terms of spectral
functions. The results obtained are in good agreement with the
predictions of weak-coupling calculations, in spite of the temperature
considered being only 250 MeV.

As part of SIMDAMA, a new method has been developed to probe the
photon emission rate (H.B. Meyer, Eur. Phys. J. A 54 (2018) no.11 192). This
method has been implemented and the project has obtained computing
time to be carried out at J\"ulich Supercomputing Centre. The photon
emissivity is now accessible in a physically more transparent way via
a dispersion relation at fixed virtuality.
Concerning the anomalous magnetic moment of the muon, in the past year
the SIMDAMA calculation of the hadronic light-by-light contribution
was only the second lattice QCD calculation to be published, and
achieved a relatively high degree of statistical precision. These two
calculations are consistent with each other and also confirm within
the uncertainties the result obtained by dispersive methods. Until
the end of the SIMDAMA project, further increase in precision and
reliability is expected, mainly by performing the calculation closer
to physical quark masses. In addition, the calculation of the
pion-pole contribution is expected to improve significantly via a
calculation directly at the physical point.

Several publications on nucleon structure, in particular on the axial
form factor and the scalar form factor, relevant respectively for
neutrino detection and scalar WIMP detection, are planned for 2021. A
new analysis technique of lattice data will be used. The axial form
factor will be provided in terms of the coefficients of the so-called
z-expansion, a model-independent way of parametrizing the form factor
at spacelike virtualities. The vector and axial-vector transition form
factors between the nucleon and the delta resonance will be calculated
with a publication expected towards the end of SIMDAMA.

On the front of spectral functions at finite temperature, the plan is
to publish a calculation of the dilepton production rate at a
temperature of 250 MeV, with direct relevance to heavy-ion collisions.
The calculation will be based, similarly to the case of the photon
emissivity published this year, on continuum-limit extrapolated
lattice data in QCD with dynamical quarks. This will also enable a
cross-check of the results obtained this year for the photon
emissivity. Secondly, a global constraint on the photon emissivity
will be obtained in the framework of dispersion relations at fixed
virtuality, which will test for the first time resummed weak-coupling
predictions. Thirdly, a publication is planned in the near future on
the physics of the spectral functions at spacelike virtualities, and
the associated question of the resolution scale at which the quarks
become `visible' inside the quark-gluon plasma.