Proceedings of The 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022)
The Hamiltonian formalism for lattice gauge theories has experienced a resurgence of interest in ... more The Hamiltonian formalism for lattice gauge theories has experienced a resurgence of interest in recent years due to its relevance for quantum simulation, a major goal of which is the solution of sign problems in QCD. The particular formulation of the Hamiltonian formalism is itself an important design decision, where factors to consider include (non)locality of the degrees of freedom, (non)Abelian constraints, and computational costs associated with simulating the Hamiltonian. This work represents a key step toward understanding the costs and benefits associated with the loop-string-hadron (LSH) formulation of lattice gauge theories by generalizing the original SU(2) construction to SU(3) (in 1+1 D). We show that the SU(3) LSH construction is indeed a straightforward generalization of its SU(2) counterpart with all salient theoretical features left intact-particularly the conversion of SU(3) Clebsch-Gordan coefficients into explicit functions of LSH number operators. The validity of the LSH approach is underscored by demonstrating numerical agreement with the better-known purely-fermionic formulation of the theory (with open boundary conditions).
Lattice quantum chromodynamics (LQCD) has the promise of constraining low-energy constants (LECs)... more Lattice quantum chromodynamics (LQCD) has the promise of constraining low-energy constants (LECs) of nuclear effective field theories (EFTs) from first-principles calculations that incorporate the dynamics of quarks and gluons. Given the Euclidean and finite-volume nature of LQCD outputs, complex mappings are developed in recent years to obtain the Minkowski and infinite-volume counterparts of LQCD observables. In particular, as LQCD is moving toward computing a set of important few-nucleon matrix elements at the physical values of the quark masses, it is important to investigate whether the anticipated precision of LQCD spectra and matrix elements will be sufficient to guarantee tighter constraints on the relevant LECs than those already obtained from phenomenology, considering the non-trivial mappings involved. With a focus on the leading-order LECs of the pionless EFT, L 1,A and g N N ν , which parametrize, respectively, the strength of the isovector axial two-body current in a single-β decay (and other related processes such pp fusion), and of the isotensor contact two-body operator in the neutrinoless double-β decay within the light neutrino exchange scenario, the expected uncertainty on future extractions of L 1,A and g N N ν are examined using synthetic data at the physical values of the quark masses. It is observed that achieving small uncertainties in L 1,A will be challenging, and (sub)percent-level precision in the twonucleon spectra and matrix elements is essential in reducing the uncertainty on this LEC compared to the existing constraints. On the other hand, the short-distance coupling of the neutrinoless double-β decay, g N N ν , is shown to be less sensitive to uncertainties on both LQCD energies and the matrix element, and can likely be constrained with percent-level precision in the upcoming LQCD calculations.
Lattice quantum chromodynamics (LQCD) has the promise of constraining low-energy constants (LECs)... more Lattice quantum chromodynamics (LQCD) has the promise of constraining low-energy constants (LECs) of nuclear effective field theories (EFTs) from first-principles calculations that incorporate the dynamics of quarks and gluons. Given the Euclidean and finite-volume nature of LQCD outputs, complex mappings are developed in recent years to obtain the Minkowski and infinite-volume counterparts of LQCD observables. In particular, as LQCD is moving toward computing a set of important few-nucleon matrix elements at the physical values of the quark masses, it is important to investigate whether the anticipated precision of LQCD spectra and matrix elements will be sufficient to guarantee tighter constraints on the relevant LECs than those already obtained from phenomenology, considering the non-trivial mappings involved. With a focus on the leading-order LECs of the pionless EFT, L1,A and g ν , which parametrize, respectively, the strength of the isovector axial two-body current in a single...
ongoing search for neutrinoless double β process (0νββ) is crucial for determining the Majorana n... more ongoing search for neutrinoless double β process (0νββ) is crucial for determining the Majorana nature of neutrinos. To relate the rate of these processes with the underlying standard model and beyond standard model interactions, the corresponding nuclear matrix elements must be constrained reliably from theory. As an effort in that direction, we present here a way to constrain the two-neutrino β decay amplitude, a process closely related to 0νββ, using lattice quantum chromodynamics (LQCD). The Minkowski infinite volume amplitude of two-hadrons with two-weak current insertions is constructed in the pionless effective field theory at the next-to-leading order. A formalism is then provided to constrain this two-hadron amplitude using a LQCD four-point correlation function in Euclidean and finite-volume spacetime, similar to the work done earlier for single hadron amplitudes. This formalism can be extended to allow the determination of the important 0νββ decay amplitude with LQCD input in upcoming years.
Lattice quantum chromodynamics (LQCD) has the promise of constraining low-energy constants (LECs)... more Lattice quantum chromodynamics (LQCD) has the promise of constraining low-energy constants (LECs) of nuclear effective field theories (EFTs) from first-principles calculations that incorporate the dynamics of quarks and gluons. Given the Euclidean and finite-volume nature of LQCD outputs, complex mappings are developed in recent years to obtain the Minkowski and infinite-volume counterparts of LQCD observables. In particular, as LQCD is moving toward computing a set of important few-nucleon matrix elements at the physical values of the quark masses, it is important to investigate whether the anticipated precision of LQCD spectra and matrix elements will be sufficient to guarantee tighter constraints on the relevant LECs than those already obtained from phenomenology, considering the non-trivial mappings involved. With a focus on the leading-order LECs of the pionless EFT, L 1,A and g N N ν , which parametrize, respectively, the strength of the isovector axial two-body current in a single-β decay (and other related processes such pp fusion), and of the isotensor contact two-body operator in the neutrinoless double-β decay within the light neutrino exchange scenario, the expected uncertainty on future extractions of L 1,A and g N N ν are examined using synthetic data at the physical values of the quark masses. It is observed that achieving small uncertainties in L 1,A will be challenging, and (sub)percent-level precision in the twonucleon spectra and matrix elements is essential in reducing the uncertainty on this LEC compared to the existing constraints. On the other hand, the short-distance coupling of the neutrinoless double-β decay, g N N ν , is shown to be less sensitive to uncertainties on both LQCD energies and the matrix element, and can likely be constrained with percent-level precision in the upcoming LQCD calculations.
Lattice quantum chromodynamics (LQCD) has the promise of constraining low-energy constants (LECs)... more Lattice quantum chromodynamics (LQCD) has the promise of constraining low-energy constants (LECs) of nuclear effective field theories (EFTs) from first-principles calculations that incorporate the dynamics of quarks and gluons. Given the Euclidean and finite-volume nature of LQCD outputs, complex mappings are developed in recent years to obtain the Minkowski and infinite-volume counterparts of LQCD observables. In particular, as LQCD is moving toward computing a set of important few-nucleon matrix elements at the physical values of the quark masses, it is important to investigate whether the anticipated precision of LQCD spectra and matrix elements will be sufficient to guarantee tighter constraints on the relevant LECs than those already obtained from phenomenology, considering the non-trivial mappings involved. With a focus on the leading-order LECs of the pionless EFT, L1,A and g ν , which parametrize, respectively, the strength of the isovector axial two-body current in a single...
ongoing search for neutrinoless double β process (0νββ) is crucial for determining the Majorana n... more ongoing search for neutrinoless double β process (0νββ) is crucial for determining the Majorana nature of neutrinos. To relate the rate of these processes with the underlying standard model and beyond standard model interactions, the corresponding nuclear matrix elements must be constrained reliably from theory. As an effort in that direction, we present here a way to constrain the two-neutrino β decay amplitude, a process closely related to 0νββ, using lattice quantum chromodynamics (LQCD). The Minkowski infinite volume amplitude of two-hadrons with two-weak current insertions is constructed in the pionless effective field theory at the next-to-leading order. A formalism is then provided to constrain this two-hadron amplitude using a LQCD four-point correlation function in Euclidean and finite-volume spacetime, similar to the work done earlier for single hadron amplitudes. This formalism can be extended to allow the determination of the important 0νββ decay amplitude with LQCD input in upcoming years.
The thermodynamics of quantum chromodynamics at low temperatures and in sufficiently strong magne... more The thermodynamics of quantum chromodynamics at low temperatures and in sufficiently strong magnetic fields is governed by neutral pions. We analyze the interacting system of neutral pions and photons at zero baryon chemical potential using effective field theory. As a consequence of the axial anomaly and the external magnetic field, the pions and photons mix with one another. The resulting spectrum contains one usual, relativistic photon state, and two nonrelativistic modes, one of which is gapless and the other gapped. Furthermore, we calculate the leading, one-loop contribution to the pressure of the system. In the chiral limit, a closed analytic expression for the pressure exists, which features an unusual scaling with temperature and magnetic field, T 3 B/f π , at low temperatures, T B/f π. Finally, we determine the pion decay rate as a function of the magnetic field at the tree level. The result is affected by a competition of the anisotropic kinematics and the enlarged phase space due to the anomalous mass of the neutral pion. In the chiral limit, the decay rate scales as B 3 /f 5 π .
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