Tue·Aug 24, 2021Tuesday·August 24, 2021

1. 01*

   A novel method to evaluate real-time path integral for scalar ${\varphi }^4$ theory

   Shinji Takeda🇯🇵

   We present a new scheme which numerically evaluates the real-time path integral for ${\varphi }^4$ real scalar field theory in a lattice version of the closed-time formalism. First step of the scheme is to rewrite the path integral in an explicitly convergent form by applying Cauchy's integral theorem to each scalar field. In the step an integration path for the scalar field is deformed on a complex plane such that the ${\varphi }^4$ term becomes a damping factor in the path integral. Secondly the integrations of the complexified scalar fields are discretized by the Gauss-Hermite quadrature and then the path integral turns out to be a multiple sum. Finally in order to efficiently evaluate the summation we apply information compression technique using the singular value decomposition to the discretized path integral, then a tensor network representation for the path integral is obtained after integrating the discretized fields. As a demonstration, by using the resulting tensor network we numerically evaluate the time-correlator in 1+1 dimensional system. For confirmation, we compare our result with the exact one at small spatial volume. Furthermore, we show the correlator in relatively large volume using a coarse-graining scheme and verify that the result is stable against changes of a truncation order for the coarse-graining scheme.

   hep-latPoS(2022)·6 citations
2. 02*

   Investigating new type of doubly-charmed molecular tetraquarks composed of the charmed meson in $H$-doublet and the charmed meson in $T$-doublet

   Fu-Lai Wang🇨🇳 · Xiang Liu🇨🇳

   Stimulated by the newly reported doubly-charmed tetraquark state $T_{cc}^{+}$ by LHCb, we carry out a systematic investigation of the $S$-wave interactions between the charmed meson ($D,D^{\ast }$) in $H$-doublet and the charmed meson ($D_1,D_2^{\ast }$) in $T$-doublet by adopting the one-boson-exchange model. Both the $S$-$D$ wave mixing effect and the coupled channel effect are taken into account. By performing a quantitative calculation, we suggest that the $S$-wave $D^{\ast }{D}_1$ states with $I(J^P)=0(0^{-},1^{-})$ and the $S$-wave $D^{\ast }{D}_2^{\ast }$ state with $I(J^P)=0(1^{-})$ should be viewed as the most promising candidates of the doubly-charmed molecular tetraquark states, and the $S$-wave $D{D}_1$ state with $I(J^P)=0(1^{-})$, the $S$-wave $D{D}_2^{\ast }$ state with $I(J^P)=0(2^{-})$, and the $S$-wave $D^{\ast }{D}_2^{\ast }$ state with $I(J^P)=0(2^{-})$ are the possible doubly-charmed molecular tetraquark candidates. With the accumulation of experimental data at Run III and after High-Luminosity-LHC upgrade, these predicted doubly-charmed molecular tetraquark states can be accessible at LHCb in the near future.

   ↳ hep-phhep-exhep-latPRD(2021)·33 citations
3. 03*

   Fidelity and entanglement entropy for infinite-order phase transitions

   Jin Zhang🇺🇸

   We study the fidelity and the entanglement entropy for the ground states of quantum systems that have infinite-order quantum phase transitions. In particular, we consider the quantum O(2) model with a spin-$S$ truncation, where there is an infinite-order Gaussian (IOG) transition for $S=1$ and there are Berezinskii-Kosterlitz-Thouless (BKT) transitions for $S\ge 2$. We show that the height of the peak in the fidelity susceptibility (${\chi }_F$) converges to a finite thermodynamic value as a power law of $1/L$ for the IOG transition and as $1/\ln (L)$ for BKT transitions. The peak position of ${\chi }_F$ resides inside the gapped phase for both the IOG transition and BKT transitions. On the other hand, the derivative of the block entanglement entropy with respect to the coupling constant ($S_{vN}^{\prime }$) has a peak height that diverges as ${\ln }^2(L)$ [${\ln }^3(L)$] for $S=1$ ($S\ge 2$) and can be used to locate both kinds of transitions accurately. We include higher-order corrections for finite-size scalings and crosscheck the results with the value of the central charge $c=1$. The crossing point of ${\chi }_F$ between different system sizes is at the IOG point for $S=1$ but is inside the gapped phase for $S\ge 2$, while those of $S_{vN}^{\prime }$ are at the phase-transition points for all $S$ truncations. Our work elaborates how to use the finite-size scaling of ${\chi }_F$ or $S_{vN}^{\prime }$ to detect infinite-order quantum phase transitions and discusses the efficiency and accuracy of the two methods.

   ↳ quant-phcond-mat.quant-gascond-mat.str-elhep-latPRB(2021)·12 citations
4. 04*

   A novel determination of the $B_c$ lifetime

   Jason Aebischer🇺🇸 · Benjamín Grinstein🇺🇸

   To reduce the current theory uncertainties a novel way to determine the $B_c$ lifetime, ${\tau }_{B_c}$, is proposed. Taking the difference of the $B_c$, and $B$ and $D$ meson decay rates eliminates the leading contributions from the calculation, which exhibit large scale and scheme dependence. The uncertainties in the proposed determination of ${\tau }_{B_c}$ are analyzed and improvements are proposed. The method predicts a value of ${\tau }_{B_c}$ in tension with the experimental determination. Several explanations are considered, including underestimation of uncertainties, duality violation and new physics. We discuss quantitative evidence that our method is vitiated by duality violation in the large mass OPE used to calculate nonleptonic decay rates of $B$ and $D$ mesons.

   ↳ hep-phhep-exhep-latPLB(2022)·19 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.