Rm Stat Research Articles

Window observable for the hadronic vacuum polarization contribution to the muon g−2 from lattice QCD

Euclidean time windows in the integral representation of the hadronic vacuum polarization contribution to the muon $g-2$ serve to test the consistency of lattice calculations and may help in tracing the origins of a potential tension between lattice and data-driven evaluations. In this paper, we present results for the intermediate time window observable computed using O($a$) improved Wilson fermions at six values of the lattice spacings below 0.1\,fm and pion masses down to the physical value. Using two different sets of improvement coefficients in the definitions of the local and conserved vector currents, we perform a detailed scaling study which results in a fully controlled extrapolation to the continuum limit without any additional treatment of the data, except for the inclusion of finite-volume corrections. To determine the latter, we use a combination of the method of Hansen and Patella and the Meyer-Lellouch-L\"uscher procedure employing the Gounaris-Sakurai parameterization for the pion form factor. We correct our results for isospin-breaking effects via the perturbative expansion of QCD+QED around the isosymmetric theory. Our result at the physical point is $a_\mu^{\mathrm{win}}=(237.30\pm0.79_{\rm stat}\pm1.22_{\rm syst})\times10^{-10}$, where the systematic error includes an estimate of the uncertainty due to the quenched charm quark in our calculation. Our result displays a tension of 3.9$\sigma$ with a recent evaluation of $a_\mu^{\mathrm{win}}$ based on the data-driven method.

Nucleon isovector couplings in Nf=2+1 lattice QCD at the physical point

We present results for the scalar and tensor isovector-couplings ($g_S$ and $g_T$) of the nucleon measured at the physical point ($M_{\pi}=135$ MeV) with a single lattice spacing of $0.085\ \mathrm{fm}$ in 2+1 flavor QCD. Our calculations are carried out with two ensembles of gauge configurations generated by the PACS Collaboration with nonperturbatively ${\cal O}(a)$ improved Wilson quark action and Iwasaki gauge action on $(10.9\ {\rm fm})^4$ and $(5.5\ {\rm fm})^4$ lattices, where the finite-size effect on the nucleon mass was not shown at the level of the statistical precision less than 0.5%. We compute the nucleon three-point correlation functions in the vector, axial, scalar, and tensor channels. We confirm that our previous result of the nucleon axial coupling on the large spatial volume of $(10.9\ {\rm fm})^4$ has no finite-size effect at the level of the statistical precision of 1.9%. For the renormalization, we first renormalize $g_S$ and $g_T$ nonperturbatively using the RI/SMOM$_{(\gamma_\mu)}$ scheme, a variant of Rome-Southampton RI/MOM scheme with reduced systematic errors, as the intermediate scheme. We evaluate our final results at the renormalization scale of 2 GeV in the $\overline{\rm MS}$ scheme through matching procedure between the RI/SMOM$_{(\gamma_\mu)}$ and $\overline{\rm MS}$ schemes with the help of perturbation theory, and then obtain $g_S=0.927(71)_{\rm stat}(22)_{\rm syst}$ and $g_T=1.036(6)_{\rm stat}(20)_{\rm syst}$.

Measurement of the Electric Dipole Moment of ^{171}Yb Atoms in an Optical Dipole Trap.

The permanent electric dipole moment (EDM) of the ^{171}Yb (I=1/2) atom is measured with atoms held in an optical dipole trap. By enabling a cycling transition that is simultaneously spin-selective and spin-preserving, a quantum nondemolition measurement with a spin-detection efficiency of 50% is realized. A systematic effect due to parity mixing induced by a static E field is observed, and is suppressed by averaging between measurements with optical dipole traps in opposite directions. The coherent spin precession time is found to be much longer than 300s. The EDM is determined to be d(^{171}Yb)=(-6.8±5.1_{stat}±1.2_{syst})×10^{-27} e cm, leading to an upper limit of |d(^{171}Yb)|<1.5×10^{-26} e cm (95%C.L.). These measurement techniques can be adapted to search for the EDM of ^{225}Ra.

Partial wave analysis of J/ψ→γη′η′

Using a sample of $(10.09~\pm~0.04)\times10^{9} ~J/\psi$ events collected with the BESIII detector, a partial wave analysis of $J/\psi\to\gamma\eta^{\prime}\eta^{\prime}$ is performed. The masses and widths of the observed resonances and their branching fractions are reported. The main contribution is from $J/\psi\rightarrow\gamma f_0(2020)$ with $f_0(2020)\rightarrow\eta^{\prime}\eta^{\prime}$, which is found with a significance of greater than 25$\sigma$. The product branching fraction ${\cal B}\left(J/\psi\rightarrow\gamma f_0(2020)\right)\cdot{\cal B}\left(f_0(2020)\rightarrow\eta^{\prime}\eta^{\prime}\right)$ is measured to be $(2.63\pm0.06({\rm stat.})^{+0.31}_{-0.46}({\rm syst.}))\times10^{-4}$.

Study of light scalar mesons through Ds+→π0π0e+νe and KS0KS0e+νe decays

Using 6.32~fb$^{-1}$ of $e^+e^-$ collision data recorded by the BESIII detector at center-of-mass energies between $4.178$ to $4.226$~GeV, we present the first measurement of the decay $D_s^+\to f_0(980)e^+\nu_e,\,f_0(980)\to \pi^0\pi^0$. The product branching fraction of $D_s^+\to f_0(980)e^+\nu_e,\,f_0(980)\to \pi^0\pi^0$ is measured to be $(7.9\pm1.4_{\rm stat} \pm0.3_{\rm syst})\times 10^{-4}$, with a statistical significance of $7.8\sigma$. Furthermore, the upper limits on the product branching fractions of $D_s^+\to f_0(500)e^+\nu_e$ with $f_0(500)\to \pi^0\pi^0$ and the branching fraction of $D_s^+\to K_{S}^{0}K_{S}^{0}e^+\nu_e$ are set to be $6.4\times 10^{-4}$ and $3.9\times 10^{-4}$ at 90\% confidence level, respectively. Our results provide valuable inputs to the understanding of the structures of light scalar mesons.

Global Λ -hyperon polarization in Au+Au collisions at sNN=3 GeV

Global hyperon polarization, $\overline{P}_\mathrm{H}$, in Au+Au collisions over a large range of collision energy, $\sqrt{s_\mathrm{NN}}$, was recently measured and successfully reproduced by hydrodynamic and transport models with intense fluid vorticity of the quark-gluon plasma. While na\"{i}ve extrapolation of data trends suggests a large $\overline{P}_\mathrm{H}$ as the collision energy is reduced, the behavior of $\overline{P}_\mathrm{H}$ at small $\sqrt{s_\mathrm{NN}}<7.7$ GeV is unknown. Operating the STAR experiment in fixed-target mode, we measured the polarization of $\Lambda$ hyperons along the direction of global angular momentum in Au+Au collisions at $\sqrt{s_\mathrm{NN}}=3$ GeV. The observation of substantial polarization of $4.91\pm0.81(\rm stat.)\pm0.15(\rm syst.)$% in these collisions may require a reexamination of the viscosity of any fluid created in the collision, of the thermalization timescale of rotational modes, and of hadronic mechanisms to produce global polarization.

Weakly Bound H Dibaryon from SU(3)-Flavor-Symmetric QCD.

We present the first study of baryon-baryon interactions in the continuum limit of lattice QCD, finding unexpectedly large lattice artifacts. Specifically, we determine the binding energy of the H dibaryon at a single quark-mass point. The calculation is performed at six values of the lattice spacing a, using O(a)-improved Wilson fermions at the SU(3)-symmetric point with m_{π}=m_{K}≈420 MeV. Energy levels are extracted by applying a variational method to correlation matrices of bilocal two-baryon interpolating operators computed using the distillation technique. Our analysis employs Lüscher's finite-volume quantization condition to determine the scattering phase shifts from the spectrum and vice versa, both above and below the two-baryon threshold. We perform global fits to the lattice spectra using parametrizations of the phase shift, supplemented by terms describing discretization effects, then extrapolate the lattice spacing to zero. The phase shift and the binding energy determined from it are found to be strongly affected by lattice artifacts. Our estimate of the binding energy in the continuum limit of three-flavor QCD is B_{H}^{SU(3)_{f}}=4.56±1.13_{stat}±0.63_{syst} MeV.

Erratum: Study of the Dalitz decay J/ψ→e+e−η [Phys. Rev. D 99 , 012006 (2019)

We report corrected results on a study of the electromagnetic Dalitz decay $J/\psi \to e^+e^- \eta$ and search for di-electron decays of a light dark gauge boson ($\gamma'$) in $J/\psi \to \gamma' \eta$ with the two $\eta$ decay modes $\eta \rightarrow \gamma \gamma$ and $\eta \rightarrow \pi^+\pi^-\pi^0$, using $(1310.6\pm 7.0)\times10^6$ $J/\psi$ events collected with the BESIII detector. In particular we update the measurement of the pole mass of the transition form factor (TFF) of $J/\psi \to e^+e^- \eta$ to be $\Lambda = 2.56 \pm 0.04({\rm stat}) \pm 0.03({\rm syst})$ GeV/$c^2$. The branching fraction of $J/\psi \to e^+e^-\eta$ and the kinetic-mixing strength between the Standard Model photon and $\gamma'$ are also updated after taking the corrected $\Lambda$ value into account. The measured branching fraction of $J/\psi \to e^+e^- \eta$ is updated to be $(1.42 \pm 0.04({\rm stat}) \pm 0.07 ({\rm syst}))\times 10^{-5}$, where the first and second uncertainties are statistical and systematic, respectively.

Study of the decay Ds+→π+π+π−η and observation of the W -annihilation decay Ds+→a0(980)+ρ0

The decay $D^{+}_{s}\rightarrow \pi^{+}\pi^{+}\pi^{-}\eta$ is observed for the first time, using $e^+e^-$ collision data corresponding to an integrated luminosity of 6.32 fb$^{-1}$, collected by the BESIII detector at center-of-mass energies between 4.178 and 4.226 GeV. The absolute branching fraction for this decay is measured to be $\mathcal{B}(D^+_s \to \pi^+ \pi^+ \pi^- \eta) = (3.12\pm0.13_{\rm stat.}\pm0.09_{\rm syst.})$%. The first amplitude analysis of this decay reveals the sub-structures in $D^{+}_{s}\rightarrow \pi^{+}\pi^{+}\pi^{-}\eta$ and determines the relative fractions and the phases among these sub-structures. The dominant intermediate process is $D^{+}_{s}\rightarrow a_1(1260)^+ \eta, a_1(1260)^+ \rightarrow \rho(770)^0\pi^+$ with a branching fraction of $(1.73 \pm 0.14_{\rm stat.} \pm 0.08_{\rm syst.})$%. We also observe the W-annihilation process $D^{+}_{s}\rightarrow a_0(980)^+\rho(770)^0$, $a_0(980)^+ \to \pi^+ \eta$ with a branching fraction of $(0.21\pm0.08_{\rm stat.}\pm0.05_{\rm syst.})$%, which is larger than the branching fractions of other measured pure W-annihilation decays by one order of magnitude.

Light meson spectroscopy from Dalitz plot analyses of ηc decays to η′K+K− , η′π+π− , and ηπ+π− produced in two-photon interactions

We study the processes $\gamma \gamma \to \eta_c \to \eta' K^+ K^-$, $\eta' \pi^+ \pi^-$, and $\eta \pi^+ \pi^-$ using a data sample of 519 $fb^{-1}$ recorded with the BaBar detector operating at the SLAC PEP-II asymmetric-energy $e^+e^-$ collider at center-of-mass energies at and near the $\Upsilon(nS)$ ($n = 2,3,4$) resonances. This is the first observation of the decay $\eta_c \to \eta' K^+ K^-$ and we measure the branching fraction $\Gamma(\eta_c \to \eta' K^+ K^-)/(\Gamma(\eta_c \to \eta' \pi^+ \pi^-)=0.644\pm 0.039_{\rm stat}\pm 0.032_{\rm sys}$. Significant interference is observed between $\gamma \gamma \to \eta_c\to \eta \pi^+ \pi^-$ and the non-resonant two-photon process $\gamma \gamma \to \eta \pi^+ \pi^-$. A Dalitz plot analysis is performed of $\eta_c$ decays to $\eta' K^+ K^-$, $\eta' \pi^+ \pi^-$, and $\eta \pi^+ \pi^-$. Combined with our previous analysis of $\eta_c \to K \bar K \pi$, we measure the $K^*_0(1430)$ parameters and the ratio between its $\eta' K$ and $\pi K$ couplings. The decay $\eta_c \to \eta' \pi^+ \pi^-$ is dominated by the $f_0(2100)$ resonance, also observed in $J/\psi$ radiative decays. A new $a_0(1700) \to \eta \pi$ resonance is observed in the $\eta_c \to \eta \pi^+ \pi^-$ channel. We also compare $\eta_c$ decays to $\eta$ and $\eta'$ final states in association with scalar mesons as they relate to the identification of the scalar glueball.

First Measurement of the Absolute Branching Fraction of Λ→pμ^{-}ν[over ¯]_{μ}.

The absolute branching fraction of Λ→pμ^{-}ν[over ¯]_{μ} is reported for the first time based on an e^{+}e^{-} annihilation sample of 10×10^{9} J/ψ events collected with the BESIII detector at sqrt[s]=3.097 GeV. The branching fraction is determined to be B(Λ→pμ^{-}ν[over ¯]_{μ})=[1.48±0.21(stat)±0.08(syst)]×10^{-4}, which is improved by about 30% in precision over the previous indirect measurements. Combining this result with the world average of B(Λ→pe^{-}ν[over ¯]_{e}), we obtain the ratio {[Γ(Λ→pμ^{-}ν[over ¯]_{μ})]/[Γ(Λ→pe^{-}ν[over ¯]_{e})]} to be 0.178±0.028, which agrees with the standard model prediction assuming lepton flavor universality. The asymmetry of the branching fractions of Λ→pμ^{-}ν[over ¯]_{μ} and Λ[over ¯]→p[over ¯]μ^{+}ν_{μ} is also determined, and no evidence for CP violation is found.

Amplitude analysis and branching fraction measurement of Ds+→K−K+π+π0

The first amplitude analysis of the decay $D_s^+\to K^-K^+\pi^+\pi^0$ is presented using the data samples, corresponding to an integrated luminosity of 6.32 fb$^{-1}$, collected with the BESIII detector at $e^+e^-$ center-of-mass energies between 4.178 and 4.226 GeV. More than 3000 events selected with a purity of 97.5\% are used to perform the amplitude analysis, and nine components are found necessary to describe the data. Relative fractions and phases of the intermediate decays are determined. With the detection efficiency estimated by the results of the amplitude analysis, the branching fraction of $D_s^+\to K^-K^+\pi^+\pi^0$ decay is measured to be $(5.42\pm0.10_{\rm stat.}\pm0.17_{\rm syst.})\%$.

Amplitude analysis and branching-fraction measurement of Ds+→KS0K−π+π+

Using 6.32 fb$^{-1}$ of $e^+e^-$ collision data collected by the BESIII detector at the center-of-mass energies between 4.178 and 4.226 GeV,~an amplitude analysis of the $D^{+}_{s}\rightarrow K^{0}_{S}K^{-}\pi^{+}\pi^{+}$ decays is performed for the first time to determine the intermediate-resonant contributions. The dominant component is the $D_s^+ \to K^*(892)^+\overline{K}^*(892)^0$ decay with a fraction of $(40.6\pm2.9_{\rm stat}\pm4.9_{\rm sys})$%. Our results of the amplitude analysis are used to obtain a more precise measurement of the branching fraction of the $D^{+}_{s}\rightarrow K^{0}_{S}K^{-}\pi^{+}\pi^{+}$ decay, which is determined to be $(1.46\pm0.05_{\rm stat}\pm0.05_{\rm sys}$)%.

Measurements of the branching fractions ofΛc+→pηandΛc+→pπ0decays at Belle

We report measurements of the branching fractions of singly Cabibbo-suppressed decays $\Lambda_c^+ \to p \eta$ and $\Lambda_c^+ \to p \pi^0$ using the full Belle data sample corresponding to an integrated luminosity of 980.6 $\rm fb^{-1}$. The data were collected by the Belle detector at the KEKB $e^{+}$$e^{-}$ asymmetric-energy collider. A clear $\Lambda_c^+$ signal is seen in the invariant mass distribution of $p \eta$. The signal yield of the $\Lambda_c^+ \to p \eta$ process is $7734 \pm 263$; from this, we measure the ratio of branching fractions ${\cal B}(\Lambda_c^+ \to p \eta)/{\cal B}(\Lambda_c^+ \to p K^- \pi^+) = (2.258 \pm 0. 077(\rm stat. ) \pm 0.136(\rm syst. ))\times 10^{-2}$, from which we infer the branching fraction ${\cal B}(\Lambda_c^+ \to p \eta) = (1.42 \pm 0.05(\rm stat.) \pm 0.11(\rm syst.)) \times 10^{-3}$. In addition, no significant signal for $\Lambda_c^+ \to p \pi^0$ is found so an upper limit on the branching fraction of ${\cal B}(\Lambda_c^+ \to p \pi^0)<8.0 \times 10^{-5}$ at 90\% credibility level is set, more than three times better than the best current upper limit.

Spectroscopy of A=9 hyperlithium with the (e,e′K+) reaction

Missing mass spectroscopy with the $(e,e^{\prime}K^{+})$ reaction was performed at Jefferson Laboratory's Hall C for the neutron rich $\Lambda$ hypernucleus $^{9}_{\Lambda}{\rm Li}$. The ground state energy was obtained to be $B_{\Lambda}^{\rm g.s.}=8.84\pm0.17^{\rm stat.}\pm0.15^{\rm sys.}~{\rm MeV}$ by using shell model calculations of a cross section ratio and an energy separation of the spin doublet states ($3/2^{+}_1$ and $5/2^{+}_1$). In addition, peaks that are considered to be states of [$^{8}{\rm Li}(3^{+})\otimes s_{\Lambda}=3/2^{+}_{2}, 1/2^{+}$] and [$^{8}{\rm Li}(1^{+})\otimes s_{\Lambda}=5/2^{+}_{2}, 7/2^{+}$] were observed at $E_{\Lambda}({\rm no.~2})=1.74\pm0.27^{\rm stat.}\pm0.11^{\rm sys.}~{\rm MeV}$ and $E_{\Lambda}({\rm no.~3})=3.30\pm0.24^{\rm stat.}\pm0.11^{\rm sys.}~{\rm MeV}$, respectively. The $E_{\Lambda}({\rm no.~3})$ is larger than shell model predictions by a few hundred keV, and the difference would indicate that a ${\rm ^{5}He}+t$ structure is more developed for the $3^{+}$ state than those for the $2^{+}$ and $1^{+}$ states in a core nucleus $^{8}{\rm Li}$ as a cluster model calculation suggests.

Measurement of branching fraction and search for CP violation in B→ϕϕK

We report the measurement of branching fractions and $CP$-violation asymmetries in $B\to \phi \phi K$ decays based on a $711\,{\rm fb}^{-1}$ data sample containing $772\times 10^6$ $B\bar{B}$ events. The data were recorded at the $\Upsilon (4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. For $B^+ \to \phi \phi K^+$, the branching fraction and $CP$-violation asymmetry measured below the $\eta_{c}$ threshold ($m_{\phi\phi}<2.85\,{\rm GeV}/c^2$) are $[3.43^{\,+\,0.48}_{\,-\,0.46}({\rm stat})\pm 0.22({\rm syst})] \times10^{-6}$ and $-0.02\pm0.11({\rm stat})\pm0.01({\rm syst})$, respectively. Similarly, the branching fraction obtained for $B^0 \to\phi\phi K^0$ below the $\eta_{c}$ threshold is $[3.02^{\,+\,0.75}_{\,-\,0.66} ({\rm stat})\pm \,0.20({\rm syst})]\times10^{-6}$. We also measure the $CP$-violation asymmetry for $B^+ \to\phi\phi K^+$ within the $\eta_{c}$ region ($m_{\phi\phi}\in [2.94,3.02]\,{\rm GeV}/c^2$) to be $+0.12\pm0.12({\rm stat})\pm0.01({\rm syst})$.

Study of the K_{L}→π^{0}νν[over ¯] Decay at the J-PARC KOTO Experiment.

The rare decay K_{L}→π^{0}νν[over ¯] was studied with the dataset taken at the J-PARC KOTO experiment in 2016, 2017, and 2018. With a single event sensitivity of (7.20±0.05_{stat}±0.66_{syst})×10^{-10}, three candidate events were observed in the signal region. After unveiling them, contaminations from K^{±} and scattered K_{L} decays were studied, and the total number of background events was estimated to be 1.22±0.26. We conclude that the number of observed events is statistically consistent with the background expectation. For this dataset, we set an upper limit of 4.9×10^{-9} on the branching fraction of K_{L}→π^{0}νν[over ¯] at the 90%confidence level.

Search for the X(2370) and observation of ηc→ηηη′ in J/ψ→γηηη′

Using a sample of $1.31\times10^{9} ~J/\psi$ events collected with the BESIII detector, we perform a study of $J/\psi\to\gamma\eta\eta\eta^{\prime}$ to search for the $X(2370)$ and $\eta_{c}$ in the $\eta\eta\eta^{\prime}$ invariant mass distribution. No significant signal for the $X(2370)$ is observed, and we set an upper limit for the product branching fraction of ${\cal B}(J/\psi\to\gamma X(2370)\cdot{\cal B}(X(2370)\to\eta\eta\eta^{\prime}) < 9.2\times10^{-6}$ at the 90% confidence level. A clear $\eta_{c}$ signal is observed for the first time, yielding a product branching fraction of ${\cal B}(J/\psi\to \gamma\eta_{c})\cdot{\cal B}(\eta_{c}\to \eta\eta\eta^{\prime}) = (4.86\pm0.62~({\rm stat.})\pm0.45~({\rm sys.}))\times10^{-5}$.

Mellin moments ⟨x⟩ and ⟨x2⟩ for the pion and kaon from lattice QCD

We present a calculation of the pion quark momentum fraction, $\langle x \rangle$, and its third Mellin moment $\langle x^2 \rangle$. We also obtain directly, for the first time, $\langle x \rangle$ and $\langle x^2 \rangle$ for the kaon using local operators. We use an ensemble of two degenerate light, a strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with clover improvement. The quark masses are chosen so that they reproduce a pion mass of about 260 MeV, and a kaon mass of 530 MeV. The lattice spacing of the ensemble is 0.093 fm and the lattice has a spatial extent of 3 fm. We analyze several values of the source-sink time separation within the range of $1.12-2.23$ fm to study and eliminate excited-states contributions. The necessary renormalization functions are calculated non-perturbatively in the RI$'$ scheme, and are converted to the $\overline{\rm MS}$ scheme at a scale of 2 GeV. The final values for the momentum fraction are $\langle x \rangle^\pi_{u^+}=0.261(3)_{\rm stat}(6)_{\rm syst}$, $\langle x \rangle^K_{u^+}=0.246(2)_{\rm stat}(2)_{\rm syst}$, and $\langle x \rangle^K_{s^+}=0.317(2)_{\rm stat}(1)_{\rm syst}$. For the third Mellin moments we find $\langle x^2 \rangle^\pi_{u^+}=0.082(21)_{\rm stat}(17)_{\rm syst}$, $\langle x^2 \rangle^K_{u^+}=0.093(5)_{\rm stat}(3)_{\rm syst}$, and $\langle x^2 \rangle^K_{s^+}=0.134(5)_{\rm stat}(2)_{\rm syst}$. The reported systematic uncertainties are due to excited-state contamination. We also give the ratio $\langle x^2 \rangle/\langle x \rangle$ which is an indication of how quickly the PDFs lose support at large $x$.

Chiral extrapolation of the magnetic polarizability of the neutral pion

The magnetic polarizability of the neutral pion has been calculated in the background magnetic-field formalism of Lattice QCD. In this investigation, the chiral extrapolation of these lattice results is considered in a formalism preserving the exact leading nonanalytic terms of chiral perturbation theory. The $n_f = 2 + 1$ numerical simulations are electro-quenched, such that the virtual sea-quarks of the QCD vacuum do not interact with the background field. To understand the impact of this, we draw on partially quenched chiral perturbation theory and identify the leading contributions of quark-flow connected and disconnected diagrams. While electro-quenching does not impact the leading-loop contribution to the magnetic polarizability, the loops which generate the leading term have yet to be considered in lattice QCD simulations. Lattice QCD results are used to constrain the analytic terms in the chiral expansion and supplementing those with the two-loop result from chiral perturbation theory enables an evaluation of the polarizability at the physical quark mass. The resulting magnetic polarizability of the neutral pion is $\beta_{\pi^0}=3.44(19)^{\rm stat}(37)^{\rm syst}\times 10^{-4}$ fm$^3$, which lies just above the $1 \sigma$ error bound of the experimental measurement.