## Periodic Reporting for period 2 - SIMDAMA (Strong-interaction matter coupled to electroweak probes and dark matter candidates)

Reporting period: 2019-10-01 to 2021-03-31

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.

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

report

https://www.gauss-centre.eu/results/elementaryparticlephysics/article/baryon-structure-from-lattice-qcd-with-2-1-flavours-of-wilson-quarks/).

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.

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

report

https://www.gauss-centre.eu/results/elementaryparticlephysics/article/baryon-structure-from-lattice-qcd-with-2-1-flavours-of-wilson-quarks/).

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.

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.