Tanmoy Bhattacharya

Michael L. Graesser

Rajan Gupta

Michael S. Warren

#### Lattice QCD

The Los Alamos Lattice QCD team and their collaborators are carrying out precision studies investigating signatures of new physics at the TeV scale, elucidating the structure of the nucleon, and understanding QCD at finite temperature. Progress during this quarter on the four projects being pursued is described below.

**Nucleon charges and form-factors**

The analysis of data of isovector charges using the All-Mode-Averaging (AMA) technique was completed and a manuscript for publication was written as well as the proceedings summarizing this work that was presented at Lattice 2015. They are continuing these clover-on-HISQ calculations on the largest lattices 643×144 lattices at the weakest coupling on the cluster and GPU computers at Los Alamos. Bhattacharya, Gupta and Yoon started clover-on-clover simulations on the Titan computer at Oakridge under the ALCC program. They carried out detailed tests of the efficacy of the variational method using multiple smeared sources versus a 2-state fit with multiple source-sink separations. A manuscript for publication describing these calculations and high precision results is being prepared.

Latest References:

Physical Review D92:9 (2015) 094511

Physical Review D89:9 (2014) 094502

Physical Review D85:5 (2012) 054512

**Matrix elements of novel CP violating operators and nEDM**

Bhattacharya, Cirigliano, Gupta and Yoon finished the 1-loop calculations of the mixing and renormalization of novel CP violating operators of dimension-5 that contribute to the Neutron Electric Dipole Moment. They determined the operator basis that allows for off-shell renormalization using external fixed momentum states. The paper describing the one-loop matching between MSbar and a renormalization independent scheme was completed and paper describing these calculations published in PRD. A second paper with calculations of the quark electric dipole moment (tensor charges of the up, down and strange quarks within the neutron), their contribution to the neutron electric dipole moment and implications for split SUSY models was published in PRL. Bhattacharya, Gupta, and Yoon continue to make progress on calculation of matrix elements involving disconnected diagrams for the quark electric dipole moment operator using the clover-on-HISQ formulation. Bhattacharya presented the first results on the calculation strategy for quark chromo EDM operator at Lattice 2015. The data are being analyzed and the proceedings describing the method and preliminary results was prepared and submitted to the arXiv.

Latest References: Bhattacharya et al.,

Physical Review D92:9 (2015) 114026

Physical Review Letters 112:21 (2015) 212002

arXiv:1502.07325

arXiv:1403.2445

arXiv:1212.4918

**Behavior of QCD at finite temperature**

The HotQCD collaboration is continuing to investigate fluctuations of conserved charges (electric charge, strangness, baryon number) around the transition temperature (140-160 MeV) to investigate the behavior of QCD near the possible critical end-point at finite chemical potential that will be probed by the Beam Energy Scan run II.

Latest References:

Physical Review D90 (2014) 094503

Physical Review Letters113 (2014) 082001

Physical Review D86 (2012) 034509

Physical Review D86 (2012) 094503

Physical Review D85 (2012) 054503

**Disconnected diagrams and Transverse Momentum Distribution Functions**

Bhattacharya, Gupta, Yoon and collaborator Michael Engelhardt at NMSU, are continuing production runs for calculating matrix elements to evaluate the Sivers function and other transverse momentum distribution (TMD) functions using computing resources provided by USQCD at JLab. Results using two different lattice actions to compare and understand systematic errors were presented by Yoon at Lattice 2015. A manuscript with the results for the proceedings was prepared and submitted to the arXiv. A paper comparing estimates for TMDs using clover and domain-wall fermions is being prepared. Bhattacharya, Gupta and Yoon are investigating methods to speed up the calculation of disconnected diagrams and improve the signal.

#### Top Quark, Dark Matter and the LHC

In this quarter, Graesser investigated beyond-the-Standard Model scenarios violating lepton number (Delta L=2) that also contribute to a neutrinoless double-beta decay signal. Specifically, he has been classifying the higher dimension operators that contribute to this process, and constraining their strength using LHC data. At low energies 14 operators (at dimension 9) are known to contribute to a neutrinoless double beta decay. However, when constrained by SU(2)_L x U(1)_Y gauge invariance, only 6 of the 14 operators appear at dimension 9. Continuing to dimension 11, one finds 7 of the remaining operators. To obtain all 14 of the low-energy operators one must go to dimension 13 in an electroweak invariant theory. Since it is unlikely in general for a UV theory to not generate any of the 6 dimension 9 operators in the electroweak invariant theory, these findings indicate that generically one does not expect to generate at the UV scale all of the 14 operators that could appear in principle in the low energy theory. (Although electroweak RGE evolution of these operators will in general populate them all.) Graesser has been constraining these operators using run I LHC data collected at 8 TeV, with preliminary results indicating that such operators must be suppressed by a UV scale of Lambda ~ 1 TeV or larger. Graesser is investigating the competitiveness of these LHC bounds with bounds from the GERDA experiment.

Latest References:

Physics Letters B749 (2014) 293

arXiv:1311.2028

Physical Review Letters111 (2013) 121802

JHEP 1302(2013) 046

JHEP 1210(2012) 025

Physics Letters B714 (2012) 267

Physics Review D85 (2012) 054512

arXiv:1107.2666

JHEP 1110(2011) 110

#### Precision Cosmology Simulations

The "Dark Sky Simulations: Early Data Release" paper by Skillman & Warren et al. (arXiv:1407.2600) is the first published N-body simulation results with over a trillion particles. The the data and analysis software made publicly available at http://darksky.slac.stanford.edu. Analysis of a higher resolution simulation on Titan at Oak Ridge with (10240**3) particles and 1/h Gpc box is underway. The calculation involves one zettaflops integrated and will generate one petabyte of data. It will be the highest resolution cosmological simulation of dark matter, mass function, power spectrum, galaxy halo merger history.

#### Lattice QCD

The Los Alamos Lattice QCD team and their collaborators are carrying out precision studies investigating signatures of new physics at the TeV scale, elucidating the structure of the nucleon, and understanding QCD at finite temperature. Progress during this quarter on the four projects being pursued is described below.

**Nucleon charges and form-factors**

The analysis of data of isovector charges using the All-Mode-Averaging (AMA) technique was completed and all the analysis and cross-checks for the manuscript for publication were completed. These these clover-on-HISQ calculations are continuing on the largest lattices 643 X 144643X144 lattices at the weakest coupling on the cluster and GPU computers at Los Alamos. Very significant progress on the clover-on-clover simulations on the Titan computer at Oakridge under the ALCC program was made. A manuscript with detailed tests of the efficacy of the variational method using multiple smeared sources versus a 2-state fit with multiple source-sink separations was prepared and submitted for publication. Gupta completed and submitted manuscript to the proceedings of lattice 2016 describing the clover-on-HISQ results. A proposal for a comprehensive suite of calculations of the hadron structure was prepared and submitted to the USQCD allocation committee.

Latest References:

arXiv:1602.07737

arXiv:1601.01730

Physical Review D92:9 (2015) 094511

Physical Review D89:9 (2014) 094502

Physical Review D85:5 (2012) 054512

**Matrix elements of novel CP violating operators and nEDM**

The paper with the 1-loop calculations of the mixing and renormalization of novel CP violating operators of dimension-5 that contribute to the Neutron Electric Dipole Moment was published in PRD. In this paper Bhattacharya, Cirigliano, Gupta and Yoon calculate the operator basis that allows for off-shell renormalization using external fixed momentum states. The paper describing the one-loop matching between MSbar and a renormalization independent scheme was completed and paper describing these calculations published in PRD. A second paper with calculations of the quark electric dipole moment (tensor charges of the up, down and strange quarks within the neutron), their contribution to the neutron electric dipole moment and implications for split SUSY models was published in PRL. Bhattacharya, Gupta, and Yoon continue to make progress on calculation of matrix elements involving disconnected diagrams for the quark electric dipole moment operator using the clover-on-HISQ formulation. Bhattacharya prepared and submitted the manuscript (proceedings of Lattice 2015) on the first results on the calculation strategy for quark chromo EDM operator and preliminary results to the arXiv.

Latest References: Bhattacharya et al.,

arXiv:1601.02264

Physical Review D92:9 (2015) 114026

Physical Review Letters 112:21 (2015) 212002

arXiv:1502.07325

arXiv:1403.2445

arXiv:1212.4918

**Behavior of QCD at finite temperature**

The HotQCD collaboration is continuing to investigate fluctuations of conserved charges (electric charge, strangness, baryon number) around the transition temperature (140-160 MeV) to investigate the behavior of QCD near the possible critical end-point at finite chemical potential that will be probed by the Beam Energy Scan run II.

Latest References:

Physical Review D90 (2014) 094503

Physical Review Letters113 (2014) 082001

Physical Review D86 (2012) 034509

Physical Review D86 (2012) 094503

Physical Review D85 (2012) 054503

**Disconnected diagrams and Transverse Momentum Distribution Functions**

Bhattacharya, Gupta, Yoon and collaborator Michael Engelhardt at NMSU, are continuing production runs for calculating matrix elements to evaluate the Sivers function and other transverse momentum distribution (TMD) functions using computing resources provided by USQCD at JLab. Results using two different lattice actions to compare and understand systematic errors were presented by Yoon at Lattice 2015. A manuscript with the results for the proceedings was prepared and submitted to the arXiv. A paper comparing estimates for TMDs using clover and domain-wall fermions is being prepared. Bhattacharya, Gupta and Yoon are investigating methods to speed up the calculation of disconnected diagrams and improve the signal.

Latest References:

arXiv:1601.05717

#### Neutrinoless double beta decay

Graesser spent this quarter preparing a paper for submission to the arxiv. This work determines the leading short-distance operators that provide contributions to neutrinoless double beta decay, that are not due to an effective Majorana neutrino mass. These results supersede previous results in the literature which only imposes color and electromagnetic charge invariance of the operators. Graesser's work imposes full electroweak invariance, and the consequences are discussed. This work also sets up a systematic matching of such 4-quark operators to the chiral effective theory, and uses that formalism to determine the leading chiral operators that contribute to the pion-pion coupling. The pion-pion coupling is important for phenomenology since it can lead to an enhanced neutrinoless double beta decay rate compared to induced four-nucleon or pion-and-two-nucleon couplings.

Latest References:

Physics Letters B749 (2014) 293

arXiv:1311.2028

Physical Review Letters111 (2013) 121802

JHEP 1302(2013) 046

JHEP 1210(2012) 025

Physics Letters B714 (2012) 267

Physics Review D85 (2012) 054512

arXiv:1107.2666

JHEP 1110(2011) 110

#### Precision Cosmology Simulations

The "Dark Sky Simulations: Early Data Release" paper by Skillman & Warren et al. (arXiv:1407.2600) is the first published N-body simulation results with over a trillion particles. The the data and analysis software made publicly available at http://darksky.slac.stanford.edu. Analysis of a higher resolution simulation on Titan at Oak Ridge with (10240**3) particles and 1/h Gpc box is underway. The calculation involves one zettaflops integrated and will generate one petabyte of data. It will be the highest resolution cosmological simulation of dark matter, mass function, power spectrum, galaxy halo merger history.

#### Lattice QCD

The Los Alamos Lattice QCD team and their collaborators are carrying out precision studies investigating signatures of new physics at the TeV scale, elucidating the structure of the nucleon, and understanding QCD at finite temperature. Progress during this quarter on the four projects being pursued is described below.

**Nucleon charges and form-factors**

The analysis of data of isovector charges using the All-Mode-Averaging (AMA) technique was completed and submitted for publication. These 2+1+1-flavor clover-on-HISQ calculations are continuing on a second physical mass ensemble of lattices with size 963×192963×192 at 0.06 fm on cluster and GPU computers at Los Alamos and using ERCAP allocations at NERSC. At the same time, the analysis of four ensembles of clover-on-clover simulations on the Titan computer at Oakridge under the ALCC program has been carried out. A manuscript with detailed tests of the efficacy of the variational method using multiple smeared sources versus a 2-state fit with multiple source-sink separations was published. These results were prepared for presentation at Lattice 2016. The analysis of electric, magnetic and axial form factors using 2-state fits has been carried out and these results were also presented at Lattice 2016 by post-doc Yong-Chull Jang. Manuscripts describing these results are being prepared for publication.

Latest References:

arXiv:1606.07049

Physical Review D93:11 (2016) 114506

arXiv:1601.01730

Physical Review D92:9 (2015) 094511

Physical Review D89:9 (2014) 094502

Physical Review D85:5 (2012) 054512

**Matrix elements of novel CP violating operators and nEDM**

First calculations of the matrix elements of the quark chromo electric dipole moment operator were carried out to establish the signal and mixing with the pseudoscalar operator. Results were prepared for presentation at Lattice 2016 by Bhattacharya. Codes to calculate the disconnected diagrams were developed. The formalism for these calculations and new numerical techniques are being developed. The paper with the 1-loop calculations of the mixing and renormalization of novel CP violating operators of dimension-5 that contribute to the Neutron Electric Dipole Moment was published in PRD. In this paper Bhattacharya, Cirigliano, Gupta and Yoon calculate the operator basis that allows for off-shell renormalization using external fixed momentum states. The paper describing the one-loop matching between MSbar and a renormalization independent scheme was completed and paper describing these calculations was also published in PRD. A second paper with calculations of the quark electric dipole moment (tensor charges of the up, down and strange quarks within the neutron), their contribution to the neutron electric dipole moment and implications for split SUSY models was published in PRL.

Latest References: Bhattacharya et al.,

arXiv:1601.02264

Physical Review D92:9 (2015) 114026

Physical Review Letters 112:21 (2015) 212002

arXiv:1502.07325

arXiv:1403.2445

arXiv:1212.4918

**Behavior of QCD at finite temperature**

The HotQCD collaboration is continuing to investigate fluctuations of conserved charges (electric charge, strangness, baryon number) around the transition temperature (140–160 MeV) to investigate the behavior of QCD near the possible critical end-point at finite chemical potential that will be probed by the Beam Energy Scan run II.

Latest References:

Physical Review D90 (2014) 094503

Physical Review Letters 113 (2014) 082001

Physical Review D86 (2012) 034509

Physical Review D86 (2012) 094503

Physical Review D85 (2012) 054503

**Disconnected diagrams and Transverse Momentum Distribution Functions**

A manuscript with the results for the Sivers and Boer-Mulders shift, the transversity and the generalized worm-gear shift for two different fermion discretization schemes is being prepared. Bhattacharya, Gupta, Yoon and collaborator Michael Engelhardt at NMSU are continuing production runs for calculating matrix elements to evaluate the Sivers function and other transverse momentum distribution (TMD) functions using computing resources provided by USQCD at JLab. Bhattacharya, Gupta and Yoon are also investigating methods to speed up the calculation of disconnected diagrams and improve the signal.

Latest References:

arXiv:1601.05717

#### Neutrinoless double beta decay

Graesser submitted a preprint to the arXiv during this quarter, in which he investigates possible Beyond the Standard Model contributions to neutrinoless double beta decay. These can appear in the form of higher dimension operators, where the scale is very roughly O(TeV) to be consistent with the null results from the GERDA experiment. A discovery of neutrinoless double-β decay would be profound, providing the first direct experimental evidence of overall lepton number violating processes. While a natural explanation is provided by an effective Majorana neutrino mass, in this preprint other new physics interpretations are carefully evaluated. At low--energies such new physics could manifest itself in the form of color and SU(2)L×U(1)Y invariant higher dimension operators. In this preprint Graesser determines a complete set of electroweak invariant dimension--9 operators, and this analysis supersedes those that only impose U(1)em invariance. Imposing electroweak invariance implies: 1) a significantly reduced set of leading order operators compared to only imposing U(1)em invariance; and 2) other collider signatures. Prior to imposing electroweak invariance there are 32 dimension-9 operators, which is reduced to 15 electroweak invariant operators at leading order in the expansion in the Higgs vacuum expectation value. Graesser establishes a systematic analysis of the hadronic realization of the 4-quark operators using chiral perturbation theory, and applies it to determine which of these operators have long-distance pion enhancements at leading order in the chiral expansion. Operators that vanish or are negligible at lowest chiral order are found to have non-zero two-pion couplings at NNLO chiral order. He also finds at dimension--11 and dimension--13, the electroweak invariant operators that after electroweak symmetry breaking produce the remaining ΔL=2 operators that would appear at dimension--9 if only U(1)em is imposed.

Latest References:

arXiv:1606.04549

Physics Letters B749 (2014) 293

arXiv:1311.2028

Physical Review Letters111 (2013) 121802

JHEP 1302(2013) 046

JHEP 1210(2012) 025

Physics Letters B714 (2012) 267

Physics Review D85 (2012) 054512

arXiv:1107.2666

JHEP 1110(2011) 110

#### Precision Cosmology Simulations

The "Dark Sky Simulations: Early Data Release" paper by Skillman & Warren et al. (arXiv:1407.2600) is the first published N-body simulation results with over a trillion particles. The the data and analysis software made publicly available at http://darksky.slac.stanford.edu. Analysis of a higher resolution simulation on Titan at Oak Ridge with (10240**3) particles and 1/h Gpc box is underway. The calculation involves one zettaflops integrated and will generate one petabyte of data. It will be the highest resolution cosmological simulation of dark matter, mass function, power spectrum, galaxy halo merger history.

#### Lattice QCD

**Nucleon charges and form-factors**

The analysis of data of isovector charges using the 2+1-flavor clover-on-clover lattice QCD formulation was completed and a manuscript for publication was prepared. The four ensembles of clover-on-clover were simulated on the Titan computer at Oakridge under the ALCC program. The clover-on-clover calculation has the advantage of being based on a unitary lattice formulation, and provides an important check on the 2+1+1-flavor clover-on-HISQ calculations. We are continuing the analysis of a second physical mass HISQ ensemble with lattice size 963 ×192 at 0.06 fm on cluster and GPU computers at Los Alamos and using ERCAP allocations at NERSC. Proceedings of talks given at Lattice 2016 were prepared for publication. The analysis of electric, magnetic and axial form factors using 2-state fits has been carried out and these results were also presented at Lattice 2016 by post-doc Yong-Chull Jang. Manuscripts describing these results are being prepared for publication.

Recent References:

Physical Review D94:5 (2016) 054508

Physical Review D93:11 (2016) 114506

arXiv:1601.01730

Physical Review D92:9 (2015) 094511

Physical Review D89:9 (2014) 094502

Physical Review D85:5 (2012) 054512

**Matrix elements of novel CP violating operators and nEDM**

Calculations of the matrix elements of the quark chromo electric dipole moment operator and mixing with the pseudoscalar operator are ongoing. The formalism for these calculations and new numerical techniques are being developed. Status of results were presented at Lattice 2016 by Bhattacharya. Codes to calculate the disconnected diagrams and the reweighting factor were developed. The paper with the 1-loop calculations of the mixing and renormalization of novel CP violating operators of dimension-5 that contribute to the Neutron Electric Dipole Moment was published in PRD. In this paper Bhattacharya, Cirigliano, Gupta and Yoon calculate the operator basis that allows for off-shell renormalization using external fixed momentum states. The paper describing the one-loop matching between MSbar and a renormalization independent scheme was completed and paper describing these calculations was also published in PRD. A second paper with calculations of the quark electric dipole moment (tensor charges of the up, down and strange quarks within the neutron), their contribution to the neutron electric dipole moment and implications for split SUSY models was published in PRL.

Latest References: Bhattacharya et al.,

arXiv:1601.02264

Physical Review D92:9 (2015) 114026

Physical Review Letters 112:21 (2015) 212002

arXiv:1502.07325

arXiv:1403.2445

arXiv:1212.4918

**Disconnected diagrams and Transverse Momentum Distribution Functions**

A manuscript with the results for the Sivers and Boer-Mulders shift, the transversity and the generalized worm-gear shift for two different fermion discretization schemes is being prepared. Bhattacharya, Gupta, Yoon and collaborator Michael Engelhardt at NMSU are continuing production runs for calculating matrix elements to evaluate the Sivers function and other transverse momentum distribution (TMD) functions using computing resources provided by USQCD at JLab. Gupta and Yoon, in collaboration with Gambhir, Orginos and Stathopoulos at William and Mary are developing methods to speed up the calculation of disconnected diagrams and improve the signal.

Latest References:

arXiv:1611.01193

arXiv:1601.05717

**Behavior of QCD at finite temperature**

The HotQCD collaboration is continuing to investigate fluctuations of conserved charges (electric charge, strangness, baryon number) around the transition temperature (140–160 MeV) to investigate the behavior of QCD near the possible critical end-point at finite chemical potential that will be probed by the Beam Energy Scan run II.

Latest References:

Physical Review D90 (2014) 094503

Physical Review Letters 113 (2014) 082001

Physical Review D86 (2012) 034509

Physical Review D86 (2012) 094503

Physical Review D85 (2012) 054503

#### Dark Matter and LHC Physics

In this quarter Graesser worked on a number of ongoing projects. He and Yue Zhang (Northwestern U.) are investigating the phenomenological implications of scenario of dark matter in which the dark matter is light, i.e., less than a GeV, and the mediator is a pseudo-scalar. That the mediator is a pseudo-scalar leads to a qualitatively different phenomenology than previously discussed in the literature. Graesser and Shashank Shalgar (Los Alamos) are investigating the impact that interactions between dark matter and either photons or neutrinos can have on the dark matter power spectrum and the cosmic microwave background. Graesser is also working on a number of projects using 8 and 13 TeV LHC data to constrain models of TeV scale physics. These projects includes studying models having light stops and models that lead at low-energies to novel signatures of neutrinoless double beta decay. Graesser is also collaborating with Tuhin Roy (TATA Institute, Mumbai, India) on a new method to improve the sensitivity of the LHC to new TeV-scale physics.

Latest References:

arXiv:1606.04549

Physics Letters B749 (2014) 293

arXiv:1311.2028

Physical Review Letters111 (2013) 121802

JHEP 1302(2013) 046

JHEP 1210(2012) 025

Physics Letters B714 (2012) 267

Physics Review D85 (2012) 054512

arXiv:1107.2666

JHEP 1110(2011) 110