Coulomb artifacts and bottomonium hyperfine splitting in lattice NRQCD

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By studying an explicit analytical solution of the Schrödinger equation with the Coulomb potential on the lattice we demonstrate a breakdown of perturbative matching for the description of the Coulomb artifacts in lattice NRQCD, which leads to a large systematic error in the predictions for the heavy quarkonium spectrum. The breakdown is a result of a fine interplay between the short and long distance effects specific to the lattice regularization of NRQCD. We show how the problem can be solved by matching the lattice and continuum results for the solution of the full Schrödinger equation without the expansion in the Coulomb interaction.

Section: Analytical Solution Of the Coulomb Problem On The Latticesupporting

confidence: 78%

Section: Jhep12(2017)007mentioning

confidence: 87%

Section: Perturbative and Schrödinger Matching Of Four-quark Operatorsmentioning

confidence: 99%

Section: Perturbative and Schrödinger Matching Of Four-quark Operatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Coulomb artifacts and breakdown of perturbative matching in lattice NRQCD

Penin

Rayyan

2017

Self Cite

Point-particle effective field theory II: relativistic effects and Coulomb/inverse-square competition

Burgess

Hayman

Rummel

et al. 2017

We apply point-particle effective field theory (PPEFT) to compute the leading shifts due to finite-sized source effects in the Coulomb bound energy levels of a relativistic spinless charged particle. This is the analogue for spinless electrons of calculating the contribution of the charge-radius of the source to these levels, and our calculation disagrees with standard calculations in several ways. Most notably we find there are two effective interactions with the same dimension that contribute to leading order in the nuclear size, one of which captures the standard charge-radius contribution. The other effective operator is a contact interaction whose leading contribution to δE arises linearly (rather than quadratically) in the small length scale, , characterizing the finite-size effects, and is suppressed by (Zα) 5 . We argue that standard calculations miss the contributions of this second operator because they err in their choice of boundary conditions at the source for the wave-function of the orbiting particle. PPEFT predicts how this boundary condition depends on the source's charge radius, as well as on the orbiting particle's mass. Its contribution turns out to be crucial if the charge radius satisfies (Zα) 2 a B , where a B is the Bohr radius, because then relativistic effects become important for the boundary condition. We show how the problem is equivalent to solving the Schrödinger equation with competing Coulomb, inverse-square and delta-function potentials, which we solve explicitly. A similar enhancement is not predicted for the hyperfine structure, due to its spin-dependence. We show how the charge-radius effectively runs due to classical renormalization effects, and why the resulting RG flow is central to predicting the size of the energy shifts (and is responsible for its being linear in the source size). We discuss how this flow is relevant to systems having much larger-than-geometric cross sections, such as those with large scattering lengths and perhaps also catalysis of reactions through scattering with monopoles. Experimental observation of these effects would require more precise measurement of energy levels for mesonic atoms than are now possible.

Point-particle effective field theory III: relativistic fermions and the Dirac equation

Burgess¹,

Hayman²,

Rummel³

et al. 2017

We formulate point-particle effective field theory (PPEFT) for relativistic spinhalf fermions interacting with a massive, charged finite-sized source using a first-quantized effective field theory for the heavy compact object and a second-quantized language for the lighter fermion with which it interacts. This description shows how to determine the near-source boundary condition for the Dirac field in terms of the relevant physical properties of the source, and reduces to the standard choices in the limit of a point source. Using a first-quantized effective description is appropriate when the compact object is sufficiently heavy, and is simpler than (though equivalent to) the effective theory that treats the compact source in a second-quantized way. As an application we use the PPEFT to parameterize the leading energy shift for the bound energy levels due to finite-sized source effects in a model-independent way, allowing these effects to be fit in precision measurements. Besides capturing finite-source-size effects, the PPEFT treatment also efficiently captures how other short-distance source interactions can shift bound-state energy levels, such as due to vacuum polarization (through the Uehling potential) or strong interactions for Coulomb bound states of hadrons, or any hypothetical new short-range forces sourced by nuclei.