Wed·Oct 26, 2022Wednesday·October 26, 2022

1. 01*

   Spectral-weight sum rules for the hadronic vacuum polarization

   Diogo Boito🇧🇷 · Maarten Golterman🇺🇸 · Kim Maltman🇨🇦 · Santiago Peris🇪🇸

   We develop a number of sum rules comparing spectral integrals involving judiciously chosen weights to integrals over the corresponding Euclidean two-point function. The applications we have in mind are to the hadronic vacuum polarization that determines the most important hadronic correction $a_{\mu }^{\mathrm{HVP}}$ to the muon anomalous magnetic moment. First, we point out how spectral weights may be chosen that emphasize narrow regions in $\sqrt{s}$, providing a tool to investigate emerging discrepancies between data-driven and lattice determinations of $a_{\mu }^{\mathrm{HVP}}$. Alternatively, for a narrow region around the $\rho$ mass, they may allow for a comparison of the dispersive determination of $a_{\mu }^{\mathrm{HVP}}$ with lattice deteruminations zooming in on the region of the well-known BaBar-KLOE discrepancy. Second, we show how such sum rules can in principle be used for carrying out precision comparisons of hadronic-$\tau$-decay-based data and $e^{+}{e}^{-}\to \text{mbox}hadrons(\gamma )$-based data, where lattice computations can provide the necessary isospin-breaking corrections.

   hep-lathep-phPRD(2023)·25 citations
2. 02*

   Deformations of Boltzmann Distributions

   Bálint Máté🇨🇭 · François Fleuret🇨🇭

   Consider a one-parameter family of Boltzmann distributions $p_t(x)=\frac{1}{Z_t}{e}^{-S_t(x)}$. This work studies the problem of sampling from $p_{t_0}$ by first sampling from $p_{t_1}$ and then applying a transformation ${\Psi }_{t_1}^{t_0}$ so that the transformed samples follow $p_{t_0}$. We derive an equation relating $\Psi$ and the corresponding family of unnormalized log-likelihoods $S_t$. The utility of this idea is demonstrated on the ${\varphi }^4$ lattice field theory by extending its defining action $S_0$ to a family of actions $S_t$ and finding a $\tau$ such that normalizing flows perform better at learning the Boltzmann distribution $p_{\tau }$ than at learning $p_0$.

   hep-latcond-mat.stat-mechcs.LG2 citations
3. 03*

   Massless Schwinger model with a 4-fermi interaction at topological angle $\theta =\pi$

   Dominic Hirtler🇦🇹 · Christof Gattringer🇦🇹

   We study the massless Schwinger model with an additional 4-fermi interaction and a topological term. For topological angle $\theta =\pi$ charge conjugation symmetry is implemented in a non-trivial way and we study the possibility of its spontaneous breaking. For the lattice discretization we use staggered fermions and the Villain action for the gauge fields, where the topological term is an integer and charge conjugation at $\theta =\pi$ is an exact symmetry. The complex action problem is overcome by a suitable worldline/worldsheet representation. We find that as a function of the 4-fermi coupling the system shows a critical point separating a weak coupling phase where charge conjugation symmetry is intact from a strong coupling phase with spontaneously broken charge conjugation symmetry.

   hep-latcond-mat.str-elPoS(2023)·3 citations
4. 04*

   ${\alpha }_s$ from an improved $\tau$ vector isovector spectral function

   Diogo Boito🇧🇷 · Maarten Golterman🇺🇸 · Kim Maltman🇨🇦 · Santiago Peris🇪🇸 · Marcus V. Rodrigues🇧🇷 · Wilder Schaaf🇺🇸

   After discussing difficulties in determining ${\alpha }_s$ from tau decay due to the existence of Duality Violations and the associated asymptotic nature of the OPE, we describe a new determination based on an improved vector isovector spectral function, now based solely on experimental input, obtained by (i) combining ALEPH and OPAL results for $2\pi +4\pi$ and (ii) replacing $K^{-}{K}^0$ and higher-multiplicity exclusive-mode contributions, both previously estimated using Monte Carlo, with new experimental BaBar results for $K^{-}{K}^0$ and results implied by $e^{+}{e}^{-}$ cross sections and CVC for the higher-multiplicity modes. We find ${\alpha }_s(m_{\tau })=0.3077\pm 0.0075$, which corresponds to ${\alpha }_s(m_Z)=0.1171\pm 0.0010$. Finally, we comment on some of the shortcomings in the criticism of our approach by Pich and Rodriguez-Sanchez.

   ↳ hep-phhep-latEPJ Web Conf.(2022)·1 citation
5. 05*

   The gaugino condensate from asymmetric four-torus with twists

   Mohamed M. Anber🇬🇧 · Erich Poppitz🇨🇦

   We calculate the gaugino condensate in $SU(2)$ super Yang-Mills theory on an asymmetric four-torus ${\mathbb{T}}^4$ with 't Hooft's twisted boundary conditions. The ${\mathbb{T}}^4$ asymmetry is controlled by a dimensionless detuning parameter $\Delta$, proportional to $L_3{L}_4-L_1{L}_2$, with $L_i$ denoting the ${\mathbb{T}}^4$ periods. We perform our calculations via a path integral on a ${\mathbb{T}}^4$. Its size is taken much smaller than the inverse strong scale $\Lambda$ and the theory is well inside the semi-classical weak-coupling regime. The instanton background, constructed for $\Delta \ll 1$ in arXiv:hep-th/0007113, has fractional topological charge $Q=\frac{1}{2}$ and supports two gaugino zero modes, yielding a non-vanishing bilinear condensate, which we find to be $\Delta$-independent. Further, the theory has a mixed discrete chiral/$1$-form center anomaly leading to double degeneracy of the energy eigenstates on any size torus with 't Hooft twists. In particular, there are two vacua, $|0⟩$ and $|1⟩$, that are exchanged under chiral transformation. Using this information, the $\Delta$-independence of the condensate, and assuming further that the semi-classical theory is continuously connected to the strongly-coupled large-${\mathbb{T}}^4$ regime, we determine the numerical coefficient of the gaugino condensate: $⟨0|\text{mbox}tr\lambda \lambda |0⟩=|⟨1|\text{mbox}tr\lambda \lambda |1⟩|=32{\pi }^2{\Lambda }^3$, a result equal to twice the known ${\mathbb{R}}^4$ value. We discuss possible loopholes in the continuity approach that may lead to this discrepancy.

   ↳ hep-thhep-lathep-phJHEP(2023)·25 citations

* Reconstructed cohort: no mailing for this day survives in the archive. Papers are grouped by their submission times and arXiv's announcement cut-off, assuming announcement without delay; positions follow identifier order. Validated at ~91% exact-day agreement against the archived era.