# Los Alamos National Laboratory

Delivering science and technology to protect our nation and promote world stability

# Quarterly Progress Reports

Investigating the field of high energy physics through experiments that strengthen our fundamental understanding of matter, energy, space, and time.

## Los Alamos HEP Theory Quarterly Report 2014-03

Tanmoy Bhattacharya, Alexander Friedland, Michael L. Graesser, Rajan Gupta, Emil Mottola, Michael S. Warren

The theory group is active in a number of diverse areas of research. Their primary areas of interest are in physics beyond the Standard Model, cosmology, dark matter, lattice quantum chromodynamics, neutrinos, the fundamentals of quantum field theory and gravity, and particle astrophysics. Generally the questions pursued by this group relate to deep mysteries in our understanding of Nature at the boundaries of the Standard Model and the grammar we use to describe it–quantum field theory and General Relativity. The theory group continues to make advances at the forefront of research in these areas.

### Lattice QCD

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

### Nucleon charges and form-factors

Bhattacharya, Gupta, Yoon and their external collaborators (the PNDME collaboration) finished the reanalysis of the calculation of renormalization constants and quantification of systematic errors in calculations of the matrix elements of scalar and tensor operators to probe new physics at the TeV scale. The revised manuscript (arXiv:1306.5435) with discussions of systematic errors and non-perturbative renormalization were published in Physical Review D. They also performed a first analysis of the extrapolation of lattice data to the physical point with respect to the quark mass, lattice spacing and finite volume. These results were presented by Gupta at Lattice 2014. The collaboration was awarded 20.75 M core hours on clusters at FNAL for FY15 by USQCD. Calculations on cluster and GPU computers at Los Alamos of the largest 643×144 lattices at the weakest coupling are continuing.

Latest References: Physical Review D85:5 (2012054512Physical ReviewD89:9 (2014094502.

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

Bhattacharya, Cirigliano, Gupta and Yoon have made progress on the 1-loop calculations of the mixing and renormalization of novel CP violating operators that contribute to the Neutron Electric Dipole Moment. They have established an operator basis that allows for off-shell renormalization using external fixed momentum states, and a paper describing the one-loop matching between MSbar and a renormalization independent scheme is in progress. The numerical calculations of the relevant matrix elements are being done in collaboration with the RBC group using resources provided by the national USQCD initiative. Bhattacharya, Gupta, and Yoon have made progress on calculation of matrix elements involving disconnected diagrams for the quark electric dipole moment operator using clover fermions on HISQ lattices and preliminary results were presented by Yoon at Lattice 2014.

Latest References: Bhattacharya et al., arXiv:1212.4918arXiv:1403.2445

### Behavior of QCD at finite temperature

Bhattacharya and Gupta carried out the statistical analysis of the entire data set generated by the full HotQCD collaboration to determine the equation of state. They are developing the final analysis tools using the free software package R to make simultaneous fits to data at different points to extrapolate to the continuum limit with full propagation of errors. These results were presented by Bazavov at Quark Matter 2014 and by Bhattacharya at Lattice 2014 conferences. The final paper is being written. Bhattacharya and Gupta also contributed to the analysis and writing of the manuscript on the deconfinement transition and U(1) axial anomaly being prepared for publication in PRL using domain wall fermions.

### Disconnected diagrams and Transverse Momentum Distribution Functions

Bhattacharya, Gupta, Yoon and collaborator Michael Engelhardt at NMSU, are carrying out production runs for calculating matrix elements to evaluate the Sivers function and other transverse momentum distribution functions using computing resources provided by USQCD at JLab. Engelhardt presented these results at Lattice 2014. Bhattacharya, Gupta and Yoon have investigated methods to speed up the calculation of disconnected diagrams and improve the signal. Yoon presented these results at lattice 2014, which included the first results for the quark electric dipole moment operator that contributes to nEDM.

### Neutrinoless double β decay and the LHC

The idea here is to explore what kinds of BSM physics can give rise to a neutrinoless double $\beta$ decay signal, that is not in the form of a Majorana neutrino mass. If at the scale of an 0νββ experiment the only effect of BSM physics—other than a possible Majorana neutrino mass—occurs through higher-dimension operators, then one can enumerate all the leading order possibilities. For a 0νββ signal the leading-order operators are dimension 9 and involve 4 quarks and two same-signed leptons. Graesser initiated a collaboration with Vincenzo Cirigliano (Los Alamos NP), Mark Wise (Caltech) and Yue Zhang (Caltech) to create renormalizable models that have a non-Majorana mass 0νββ signal. Preliminary estimates indicate that the scale suppressing these higher dimension operators can be O(TeV) and still give an appreciable signal in 0νββ. This estimate therefore suggests that constraints from LHC and LEP may be important. They will investigate constraints on these models from the LHC arising from same-signed dilepton and leptoquark searches, as well as those bounds from LEP and the LHC on 4-Fermi contact operators.

### Precision Cosmology Simulations

On April 18--19, 2014, Warren ran the ds14a cosmological simulation using the 2HOT code with 1,073,741,824,000 (102403) particles on 12,288 nodes (196,608 CPU cores and 12,288 NVIDIA K20x GPUs) of the Titan system at Oak Ridge National Laboratory. This is one of the largest computations ever performed in any field of science. The simulation was of a cubical region of space 8,000 Mpc/h across; a region large enough to contain the entire visible Universe older than 2.8 billion years in a light cone to a redshift of 2.3 for an observer at the center of the simulation volume. The simulation carried out 3.14×1020 floating point operations (0.3 zettaflops). We saved 16 particle dumps totaling 540 Terabytes. Had we attempted the same calculation with a simple O(N2) algorithm, it would have taken about ten million times as many operations and approximately 37 thousand years on the same hardware to obtain the answer. During the initial stages of the simulation, a single timestep required about 110 seconds, for a performance of 5.9 Petaflops.

### Fermion Pairing and the Scalar Boson of the 2D Conformal Anomaly

With D. Blaschke (recipient of an APART fellowship of the Austrian Academy of Sciences) and R. Carballo-Rubio (a Ph. D. student at the Univ. of Granada, Spain, who visited LANL through a CSIC grant from Spain) we have analyzed the phenomenon of fermion pairing into an effective boson, which is associated with anomalies and the anomalous commutators of currents bilinear in the fermion fields. A well-known example is the chiral bosonization of the Schwinger model, determined by the axial current anomaly of massless Dirac fermions in two spacetime dimensions. We showed by both functional and Fock space operator methods that a similar bosonized description applies to the 2D conformal trace anomaly of the fermion stress tensor. For both the chiral and conformal anomalies, correlation functions involving anomalous currents,jμ5 o Tμν of massless fermions exhibit a massless boson 1/k2 pole, and the associated spectral functions obey a UV finite sum rule, becoming δ-functions in the massless limit. In both cases the corresponding effective action of the anomaly is non-local, but may be expressed in a local form by the introduction of a new bosonic field, which becomes a bona fide propagating quantum field in its own right. In both cases this is expressed in Fock space by the anomalous Schwinger commutators of currents becoming the canonical commutation relations of the corresponding boson, which has a operator realization as a coherent superposition of massless fermion pairs, and which saturate the intermediate state sums in quantum correlation functions of fermion currents. Further consequences of this mapping of fermion pairs to bosons are that the Casimir energy of fermions on a finite spatial interval [0,L] can be described as a coherent scalar condensation of pairs, and by an algebraic identity the one-loop correlation functions of arbitrary numbers of fermion stress tensors ⟨TTT…⟩may be expressed as a combinatoric sum of purely linear tree diagrams of the scalar boson. This paper is now ready for submission to JHEP.

During this quarter the following invited talks were given:

• “New Horizons in Gravity: Dark Energy and Condensate Stars,” Univ. of Texas, Austin, TX, April 15, 2014.
• “The Instability of the de Sitter Vacuum,” Univ. of Texas, Austin, TX, April 17, 2014.
• “New Horizons in Gravity: Dark Energy and Condensate Stars,” Univ. of California, Berkeley, CA, May 21, 2014.

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