Lattice QCD Calculations Research Articles

Transport coefficients and quark-hadron phase transition(s) from PLSM in vanishing and finite magnetic field

In peripheral heavy-ion collisions, localized, short-lived and extremely huge magnetic field can be generated. Its possible influences on the quark-hadron phase transition(s) and the transport properties of the hadronic and partonic matter shall be analysed from the Polyakov linear-sigma model. Our calculations are compared with recent lattice QCD calculations.

Equation of State in Non-Zero Magnetic Field

The Polyakov linear-sigma model (PLSM) and Hadron Resonance Gas (HRG) model are considered to study the hadronic and partonic equation(s) of state, the pressure, and response to finite magnetic field, the magnetization. The results are compared to recent lattice QCD calculations. Both models are in fairly good agreement with the lattice.

η′meson mass from topological charge density correlator in QCD

The flavor-singlet component of the eta prime meson is related to the topological structure of the SU(3) gauge field through the chiral anomaly. We perform a 2+1-flavor lattice QCD calculation and demonstrate that the two-point function of a gluonically defined topological charge density after a short Yang-Mills gradient flow contains the propagation of the eta prime meson, by showing that its mass in the chiral and continuum limit is consistent with the experimental value. The gluonic correlator does not suffer from the contamination of the pion contribution, and the clean signal is obtained at significantly lower numerical cost compared to the conventional method with the quark bilinear operators.

Lattice QCD Calculation of Hadronic Light-by-Light Scattering.

We perform a lattice QCD calculation of the hadronic light-by-light scattering amplitude in a broad kinematical range. At forward kinematics, the results are compared to a phenomenological analysis based on dispersive sum rules for light-by-light scattering. The size of the pion pole contribution is investigated for momenta of typical hadronic size. The presented numerical methods can be used to compute the hadronic light-by-light contribution to the anomalous magnetic moment of the muon. Our calculations are carried out in two-flavor QCD with the pion mass in the range of 270-450MeV and contain so far only the diagrams with fully connected quark lines.

Standard Model Prediction for Direct CP Violation in K→ππ Decay.

We report the first lattice QCD calculation of the complex kaon decay amplitude A_{0} with physical kinematics, using a 32³×64 lattice volume and a single lattice spacing a, with 1/a=1.3784(68) GeV. We find Re(A_{0})=4.66(1.00)(1.26)×10(-7) GeV and Im(A_{0})=-1.90(1.23)(1.08)×10(-11) GeV, where the first error is statistical and the second systematic. The first value is in approximate agreement with the experimental result: Re(A_{0})=3.3201(18)×10(-7) GeV, while the second can be used to compute the direct CP-violating ratio Re(ϵ^{'}/ϵ)=1.38(5.15)(4.59)×10^{-4}, which is 2.1σ below the experimental value 16.6(2.3)×10(-4). The real part of A_{0} is CP conserving and serves as a test of our method while the result for Re(ϵ^{'}/ϵ) provides a new test of the standard model theory of CP violation, one which can be made more accurate with increasing computer capability.

Suppression of Baryon Diffusion and Transport in a Baryon Rich Strongly Coupled Quark-Gluon Plasma.

Five dimensional black hole solutions that describe the QCD crossover transition seen in (2+1)-flavor lattice QCD calculations at zero and nonzero baryon densities are used to obtain predictions for the baryon susceptibility, baryon conductivity, baryon diffusion constant, and thermal conductivity of the strongly coupled quark-gluon plasma in the range of temperatures 130 MeV≤T≤300 MeV and baryon chemical potentials 0≤μ(B)≤400 MeV. Diffusive transport is predicted to be suppressed in this region of the QCD phase diagram, which is consistent with the existence of a critical end point at larger baryon densities. We also calculate the fourth-order baryon susceptibility at zero baryon chemical potential and find quantitative agreement with recent lattice results. The baryon transport coefficients computed in this Letter can be readily implemented in state-of-the-art hydrodynamic codes used to investigate the dense QGP currently produced at RHIC's low energy beam scan.

Isovector and isoscalar tensor charges of the nucleon from lattice QCD

We present results for the iso-vector and flavor diagonal tensor charges $g^{u-d}_T$, $g^{u}_T$, $g^{d}_T$, and $g^{s}_T$ needed to probe novel tensor interactions at the TeV scale in neutron and nuclear $\beta$-decays and the contribution of the quark electric dipole moment (EDM) to the neutron EDM. The lattice QCD calculations were done using nine ensembles of gauge configurations generated by the MILC collaboration using the HISQ action with 2+1+1 dynamical flavors. These ensembles span three lattice spacings $a \approx 0.06, 0.09$ and $0.12 $ fm and three quark masses corresponding to the pion masses $M_\pi \approx 130, 220$ and $310 $ MeV. Using estimates from these ensembles, we quantify all systematic uncertainties and perform a simultaneous extrapolation in the lattice spacing, volume and light quark masses for the connected contributions. The final estimates of the connected nucleon (proton) tensor charge for the iso-vector combination is $g_T^{u-d} = 1.020(76) $ in the $\bar{\text{MS}}$ scheme at $2$ GeV. The additional disconnected quark loop contributions needed for the flavor-diagonal matrix elements are calculated using a stochastic estimator employing the truncated solver method with the all-mode-averaging technique. We find that the size of the disconnected contribution is smaller than the statistical error in the connected contribution. This allows us to bound the disconnected contribution and include it as an additional uncertainty in the flavor-diagonal charges. After a continuum extrapolation, we find $g_T^{u} = 0.774(66) $, $g_T^{d} = -0.233(28) $ and $g_T^{u+d} = 0.541(67) $. The strangeness tensor charge, that can make a significant contribution to the neutron EDM due to the large ratio $m_s/m_{u,d}$, is $g_T^{s}=0.008(9)$ in the continuum limit.

K + → π + ν ν ¯ $$ {K}^{+}\to {\pi}^{+}\nu \overline{\nu} $$ and K L → π 0 ν ν ¯ $$ {K}_L\to {\pi}^0\nu \overline{\nu} $$ in the Standard Model: status and perspectives

In view of the recent start of the NA62 experiment at CERN that is expected to measure the $K^+\to\pi^+\nu\bar\nu$ branching ratio with a precision of 10%, we summarise the present status of this promising decay within the Standard Model (SM). We do likewise for the closely related $K_L\to\pi^0\nu\bar\nu$, which will be measured by the KOTO experiment around 2020. As the perturbative QCD and electroweak corrections in both decays are under full control, the dominant uncertainties within the SM presently originate from the CKM parameters $V_{cb}$, $V_{ub}$ and $\gamma$. We show this dependence with the help of analytic expressions as well as accurate interpolating formulae. Unfortunately a clarification of the discrepancies between inclusive and exclusive determinations of $V_{cb}$ and $V_{ub}$ from tree-level decays will likely require results from the Belle II experiment available at the end of this decade. Thus we investigate whether higher precision on both branching ratios is achievable by determining $V_{cb}$, $V_{ub}$ and $\gamma$ by means of other observables that are already precisely measured. In this context $\varepsilon_K$ and $\Delta M_{s,d}$, together with the expected progress in QCD lattice calculations will play a prominent role. We find $\mathcal{B}(K^+\to\pi^+\nu\bar\nu) = (9.11\pm 0.72) \times 10^{-11}$ and $\mathcal{B}(K_L\to\pi^0\nu\bar\nu) = (3.00\pm 0.30) \times 10^{-11}$, which is more precise than using averages of the present tree-level values of $V_{cb}$, $V_{ub}$ and $\gamma$. Furthermore, we point out the correlation between $\mathcal{B}(K^+\to\pi^+\nu\bar\nu)$, $\overline{\mathcal{B}}(B_s\to\mu^+\mu^-)$ and $\gamma$ within the SM, that is only very weakly dependent on other CKM parameters. Finally, we also update the ratio $\varepsilon'/\varepsilon$ in the SM and present its correlation with $K_L\to\pi^0\nu\bar\nu$.

Leading hadronic contributions to the running of the electroweak coupling constants from lattice QCD

The quark-connected leading-order hadronic contributions to the running of the electromagnetic fine structure constant, $\alpha_{\rm QED}$, and the weak mixing angle, $\theta_W$, are determined by a four-flavour lattice QCD computation with twisted mass fermions. Full agreement of the results with a phenomenological analysis is observed with an even comparable statistical uncertainty. We show that the uncertainty of the lattice calculation is dominated by systematic effects which then leads to significantly larger errors than obtained by the phenomenological analysis.

Diagonal and off-diagonal quark number susceptibilities at high temperatures

We present continuum extrapolated lattice QCD results for up to fourth-order diagonal and off-diagonal quark number susceptibilities in the high temperature region of 300-700 MeV. Lattice QCD calculations are performed using 2+1 flavors of highly improved staggered quarks with nearly physical quark masses and at four different lattice spacings. Comparisons of our results with recent weak coupling perturbative calculations yield reasonably good agreements for the entire temperature range.

Baryon-strangeness correlation in quark combination models

The baryon-strangeness correlation in the hadronization of the quark matter is studied within the quark combination mechanism. We calculate the correlation coefficient $C_{BS} = -3\big(\langle B S \rangle -\langle B\rangle \langle S\rangle\big)/\big( \langle S^2 \rangle-\langle S \rangle^2 \big)$ of initial hadrons produced from the deconfined free quark system with $C^{(q)}_{BS}=1$. The competition of the production of baryons against that of mesons is the key dynamics that is most relevant to the change of baryon-strangeness correlation during system hadronization. Results of quark combination under the Poisson statistics agree with the statistical model predictions for a hadron resonance gas at vanishing chemical potential but differ from those at relatively large chemical potentials. Results beyond Poisson statistics are also obtained and are compared with calculations of Lattice QCD in the phase boundary, giving the best agreement at temperature $T =163$ MeV. We predict the dependence of the $C_{BS}$ of hadron system on the baryon chemical potential and strangeness. These predictions are expected to be tested by the future Lattice QCD calculations at non-zero chemical potentials and/or by the Beam Energy Scan experiment of STAR Collaboration at RHIC.

Study of dynamics ofD0→K−e+νeandD0→π−e+νedecays

In an analysis of a 2.92 fb(-1) data sample taken at 3.773 GeV with the BESIII detector operated at the BEPCII collider, we measure the absolute decay branching fractions B(D-0 -> K(-)e(+)nu(e)) = (3.505 +/- 0.014 +/- 0.033)% and B(D-0 -> pi(-)e(+)nu(e)) = (0.295 +/- 0.004 +/- 0.003)%. From a study of the differential decay rates we obtain the products of hadronic form factor and the magnitude of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element f(+)(K)(0)vertical bar V-cs vertical bar = 0.7172 +/- 0.0025 +/- 0.0035 and f(+)(pi)(0)vertical bar V-cd vertical bar = 0.1435 +/- 0.0018 +/- 0.0009. Combining these products with the values of vertical bar V-cs(d)vertical bar from the SM constraint fit, we extract the hadronic form factors f(+)(K)(0) = 0.7368 +/- 0.0026 +/- 0.0036 and f(+)(pi)(0) = 0.6372 +/- 0.0080 +/- 0.0044, and their ratio f(+)(pi)(0)/f(+)(K)(0) = 0.8649 +/- 0.0112 +/- 0.0073. These form factors and their ratio are used to test unquenched lattice QCD calculations of the form factors and a light cone sum rule (LCSR) calculation of their ratio. The measured value of f(+)(K(pi))(0)vertical bar V-cs(d)vertical bar and the lattice QCD value for f(+)(K(pi))(0) are used to extract values of the CKM matrix elements of vertical bar V-cs vertical bar = 0.9601 +/- 0.0033 +/- 0.0047 +/- 0.0239 and vertical bar V-cd vertical bar = 0.2155 +/- 0.0027 +/- 0.0014 +/- 0.0094, where the third errors are due to the uncertainties in lattice QCD calculations of the form factors. Using the LCSR value for f(+)(pi)(0)/f(+)(K)(0), we determine the ratio vertical bar V-cd vertical bar/vertical bar V-cs vertical bar = 0.238 +/- 0.004 +/- 0.002 +/- 0.011, where the third error is from the uncertainty in the LCSR normalization. In addition, we measure form factor parameters for three different theoretical models that describe the weak hadronic charged currents for these two semileptonic decays. All of these measurements are the most precise to date.

Implementation of general background electromagnetic fields on a periodic hypercubic lattice

Nonuniform background electromagnetic fields, once implemented in lattice quantum chromodynamics calculations of hadronic systems, provide a means to constrain a large class of electromagnetic properties of hadrons and nuclei, from their higher electromagnetic moments and charge radii to their electromagnetic form factors. We show how nonuniform fields can be constructed on a periodic hypercubic lattice under certain conditions and determine the precise form of the background U(1) gauge links that must be imposed on the quantum chromodynamics gauge-field configurations to maintain periodicity. Once supplemented by a set of quantization conditions on the background-field parameters, this construction guarantees that no nonuniformity occurs in the hadronic correlation functions across the boundary of the lattice. The special cases of uniform electric and magnetic fields, a nonuniform electric field that varies linearly in one spatial coordinate (relevant to the determination of quadruple moment and charge radii), nonuniform electric and magnetic fields with given temporal and spatial dependences (relevant to the determination of nucleon spin polarizabilities) and plane-wave electromagnetic fields (relevant to the determination of electromagnetic form factors) are discussed explicitly.

Beyond-Standard-Model Tensor Interaction and Hadron Phenomenology.

We evaluate the impact of recent developments in hadron phenomenology on extracting possible fundamental tensor interactions beyond the standard model. We show that a novel class of observables, including the chiral-odd generalized parton distributions, and the transversity parton distribution function can contribute to the constraints on this quantity. Experimental extractions of the tensor hadronic matrix elements, if sufficiently precise, will provide a, so far, absent testing ground for lattice QCD calculations.

Mass Spectrum of Baryons in a Relativistic Hypercentral Constituent Quark Model

We have investigated the light and strange baryons as a relativistic three-body bound system. Inspired by lattice QCD calculations, we treated the baryons as a spin-independent three-quark system. For this purpose we introduced a spin independent relativistic description for the SU (6) invariant part of the spectrum by presenting the analytical solution of the three-particle Klein-Gordon equation. We carried out calculations within the constituent quark model based on a hypercentral approach, which takes into account three-body force effects and standard two-body potential contributions. Herewith the average energy values of the nonstrange and strange resonances are reproduced. Then we used the generalized Gursey-Radicati mass formula as a SU (6) breaking interaction to describe the splittings within the SU (6)-multiplets and the hyperfine structure of the baryon. The considered SU (6)-invariant potential is the well-known ＂Coulomb-plus-linear＂ potential. The resulting description of the baryon spectrum is fairly good and comparable with the experimental spectrum.

Thermodynamics of strong-interaction matter from lattice QCD

We review results from lattice QCD calculations on the thermodynamics of strong-interaction matter with emphasis on input these calculations can provide to the exploration of the phase diagram and properties of hot and dense matter created in heavy ion experiments. This review is organized in sections as follows: (1) Introduction, (2) QCD thermodynamics on the lattice, (3) QCD phase diagram at high temperature, (4) Bulk thermodynamics, (5) Fluctuations of conserved charges, (6) Transport properties, (7) Open heavy flavors and heavy quarkonia, (8) QCD in external magnetic fields, (9) Summary.

Bottomonium mesons and strategies for their observation

The $B$-factories and Large Hadron Collider experiments have demonstrated the ability to observe and measure the properties of bottomonium mesons. In order to discover missing states it is useful to know their properties to develop a successful search strategy. To this end we calculate the masses and decay properties of excited bottomonium states. We use the relativized quark model to calculate the masses and wavefunctions and the $^3P_0$ quark-pair creation model to calculate decay widths to open bottom. We also summarize results for radiative transitions, annihilation decays, hadronic transitions and production cross sections which are used to develop strategies to find these states. We find that the $b\bar{b}$ system has a rich spectroscopy that we expect to be substantially extended by the LHC and $e^+e^-$ experiments in the near future. Some of the most promising possibilities at the LHC are observing the $\chi_{b(1,2)}(3P)$, $\chi_{b(1,2)}(4P)$ and $\eta_b(3S)$ states in $\gamma \mu^+\mu^-$ final states that proceed via radiative transitions through $\Upsilon(nS)$ intermediate states and $1^3D_J$ and $2^3D_J$ into $\gamma\gamma \mu^+\mu^-$ final states proceeding via $1^3P_J\to 1^3S_1$ and $2^3P_J\to 2^3S_1$ intermediate states respectively. Some of the most interesting possibilities in $e^+e^-$ collisions are studying the $1^3D_J$ states via $4\gamma$ cascades starting with the $\Upsilon (3S)$ and the $3^3P_J$ states in $\gamma\gamma\mu^+ \mu^-$ final states starting with the $\Upsilon (4S)$ and proceeding via $\Upsilon (nS)$ intermediate states. Completing the bottomonium spectrum is an important validation of lattice QCD calculations and a test of our understanding of bottomonium states in the context of the quark model.

Ab initio Calculation of the np→dγ Radiative Capture Process.

Lattice QCD calculations of two-nucleon systems are used to isolate the short-distance two-body electromagnetic contributions to the radiative capture process np→dγ, and the photo-disintegration processes γ^{(*)}d→np. In nuclear potential models, such contributions are described by phenomenological meson-exchange currents, while in the present work, they are determined directly from the quark and gluon interactions of QCD. Calculations of neutron-proton energy levels in multiple background magnetic fields are performed at two values of the quark masses, corresponding to pion masses of m_{π}~450 and 806 MeV, and are combined with pionless nuclear effective field theory to determine the amplitudes for these low-energy inelastic processes. At m_{π}~806 MeV, using only lattice QCD inputs, a cross section σ^{806 MeV}~17 mb is found at an incident neutron speed of v=2,200 m/s. Extrapolating the short-distance contribution to the physical pion mass and combining the result with phenomenological scattering information and one-body couplings, a cross section of σ^{lqcd}(np→dγ)=334.9(+5.2-5.4) mb is obtained at the same incident neutron speed, consistent with the experimental value of σ^{expt}(np→dγ)=334.2(0.5) mb.

B→Dlνform factors at nonzero recoil and extraction of|Vcb|

We present a lattice QCD calculation of the $B \rightarrow D l \nu$ semileptonic decay form factors $f_+(q^2)$ and $f_0(q^2)$ for the entire physical $q^2$ range. Non-relativistic QCD (NRQCD) bottom quarks and Highly Improved Staggered Quark (HISQ) charm and light quarks are employed together with $N_f = 2+1$ MILC gauge configurations. A joint fit to our lattice and BaBar experimental data allows an extraction of the CKM matrix element $|V_{cb}|$. We also determine the phenomenologically interesting ratio $R(D) = {\cal B}(B \rightarrow D \tau \nu_\tau) / {\cal B}(B \rightarrow D l \nu_l)$ ($l = e, \mu$). We find $|V_{cb}|_{excl.}^{B \rightarrow D} = 0.0402(17)(13)$, where the first error consists of the lattice simulation errors and the experimental statistical error and the second error is the experimental systematic error. For the branching fraction ratio we find $R(D) = 0.300(8)$.

Factorization for radiative heavy quarkonium decays into scalar Glueball

We establish the factorization formula for scalar Glueball production through radiative decays of vector states of heavy quarkonia, e.g. $J/\psi$, $\psi(2S)$ and $\Upsilon(nS)$, where the Glueball mass is much less than the parent heavy quarkonium mass. The factorization is demonstrated explicitly at one-loop level through the next-to-leading order (NLO) corrections to the hard kernel, the non-relativistic QCD (NRQCD) long-distance matrix element (LDMEs) of the heavy quarkonium, and the light-cone distribution amplitude (LCDA) of scalar Glueball. The factorization provides a comprehensive theoretical approach to investigate Glueball production in the radiative decays of vector states of heavy quarkonia and to determine the physic nature of Glueball. We discuss the scale evolution equation of LCDA for scalar Glueball. In the end, we extract the value of the decay constant of Scalar Glueball from Lattice QCD calculation and analyze the mixing effect among $f_0(1370)$, $f_0(1500)$ and $f_0(1710)$.