Flavors Of Dynamical Quarks Research Articles

Mass sensitivity of the three-flavor chiral phase transition

The mass sensitivity of the chiral phase transition of QCD with and without axial $U_A(1)$-symmetry breaking at vanishing and finite quark chemical potential is investigated. To focus on the low-energy sector of QCD, a quark-meson model with three dynamical quark flavors is employed. Non-perturbative quantum fluctuations are taken into account with the functional renormalization group. The inherent ambiguities in fixing the low-energy model parameters away from the physical mass point and their consequences for spontaneous chiral symmetry breaking are discussed in detail and a heuristic parameter fixing scheme motivated by chiral perturbation theory is proposed. The influence of vacuum and thermal fluctuations of quarks and mesons on the order of the chiral phase transition is additionally assessed with a mean-field analysis.

The I = 1 pion–pion scattering amplitude and timelike pion form factor from Nf = 2 + 1 lattice QCD

The elastic I=1p-wave ππ scattering amplitude is calculated together with the isovector timelike pion form factor using lattice QCD with Nf=2+1 dynamical quark flavors. Wilson clover ensembles generated by the Coordinated Lattice Simulations (CLS) initiative are employed at four lattice spacings down to a=0.05fm, several pion masses down to mπ=200MeV, and spatial volumes of extent L=3.1–5.5fm. The set of measurements on these ensembles, which is publicly available, enables an investigation of systematic errors due to the finite lattice spacing and spatial volume. The ππ scattering amplitude is fit on each ensemble by a Breit–Wigner resonance lineshape, while the form factor is described better by a thrice-subtracted dispersion relation than the Gounaris–Sakurai parametrization.

Determination of ΛMS¯(nf=2) and analytic parametrization of the static quark-antiquark potential

While lattice QCD allows for reliable results at small momentum transfers (large quark separations), perturbative QCD is restricted to large momentum transfers (small quark separations). The latter is determined up to a reference momentum scale $\Lambda$, which is to be provided from outside, e.g. from experiment or lattice QCD simulations. In this article, we extract $\Lambda_{\overline{\textrm{MS}}}$ for QCD with $n_f=2$ dynamical quark flavors by matching the perturbative static quark-antiquark potential in momentum space to lattice results in the intermediate momentum regime, where both approaches are expected to be applicable. In a second step, we combine the lattice and the perturbative results to provide a complete analytic parameterization of the static quark-antiquark potential in position space up to the string breaking scale. As an exemplary phenomenological application of our all-distances potential we compute the bottomonium spectrum in the static limit.

Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD

We calculate the up-, down-, strange-, charm-, and bottom-quark masses using the MILC highly improved staggered-quark ensembles with four flavors of dynamical quarks. We use ensembles at six lattice spacings ranging from $a\ensuremath{\approx}0.15$ to 0.03 fm and with both physical and unphysical values of the two light and the strange sea-quark masses. We use a new method based on heavy-quark effective theory (HQET) to extract quark masses from heavy-light pseudoscalar meson masses. Combining our analysis with our separate determination of ratios of light-quark masses we present masses of the up, down, strange, charm, and bottom quarks. Our results for the $\overline{\mathrm{MS}}$-renormalized masses are ${m}_{u}(2\text{ }\text{ }\mathrm{GeV})=\phantom{\rule{0ex}{0ex}}2.130(41)\text{ }\text{ }\mathrm{MeV}$, ${m}_{d}(2\text{ }\text{ }\mathrm{GeV})=4.675(56)\text{ }\text{ }\mathrm{MeV}$, ${m}_{s}(2\text{ }\text{ }\mathrm{GeV})=92.47(69)\text{ }\text{ }\mathrm{MeV}$, ${m}_{c}(3\text{ }\text{ }\mathrm{GeV})=\phantom{\rule{0ex}{0ex}}983.7(5.6)\text{ }\text{ }\mathrm{MeV}$, and ${m}_{c}({m}_{c})=1273(10)\text{ }\text{ }\mathrm{MeV}$, with four active flavors; and ${m}_{b}({m}_{b})=4195(14)\text{ }\text{ }\mathrm{MeV}$ with five active flavors. We also obtain ratios of quark masses ${m}_{c}/{m}_{s}=11.783(25)$, ${m}_{b}/{m}_{s}=53.94(12)$, and ${m}_{b}/{m}_{c}=4.578(8)$. The result for ${m}_{c}$ matches the precision of the most precise calculation to date, and the other masses and all quoted ratios are the most precise to date. Moreover, these results are the first with a perturbative accuracy of ${\ensuremath{\alpha}}_{s}^{4}$. As byproducts of our method, we obtain the matrix elements of HQET operators with dimension 4 and 5: ${\overline{\mathrm{\ensuremath{\Lambda}}}}_{\mathrm{MRS}}=555(31)\text{ }\text{ }\mathrm{MeV}$ in the minimal renormalon-subtracted (MRS) scheme, ${\ensuremath{\mu}}_{\ensuremath{\pi}}^{2}=0.05(22)\text{ }\text{ }{\mathrm{GeV}}^{2}$, and ${\ensuremath{\mu}}_{G}^{2}({m}_{b})=0.38(2)\text{ }\text{ }{\mathrm{GeV}}^{2}$. The MRS scheme [Phys. Rev. D 97, 034503 (2018)] is the key new aspect of our method.

Tensor form factor of D→π(K)ℓν and D→π(K)ℓℓ decays with Nf=2+1+1 twisted-mass fermions

We present the first lattice Nf=2+1+1 determination of the tensor form factor $f_T^{D \pi(K)}(q^2)$ corresponding to the semileptonic and rare $D \to \pi(K)$ decays as a function of the squared 4-momentum transfer $q^2$. Together with our recent determination of the vector and scalar form factors we complete the set of hadronic matrix elements regulating the semileptonic and rare $D \to \pi(K)$ transitions within and beyond the Standard Model, when a non-zero tensor coupling is possible. Our analysis is based on the gauge configurations produced by ETMC with Nf=2+1+1 flavors of dynamical quarks, which include in the sea, besides two light mass-degenerate quarks, also the strange and charm quarks with masses close to their physical values. We simulated at three different values of the lattice spacing and with pion masses as small as 220 MeV. The matrix elements of the tensor current are determined for plenty of kinematical conditions in which parent and child mesons are either moving or at rest. As in the case of the vector and scalar form factors, Lorentz symmetry breaking due to hypercubic effects is clearly observed also in the data for the tensor form factor and included in the decomposition of the current matrix elements in terms of additional form factors. After the extrapolations to the physical pion mass and to the continuum and infinite volume limits we determine the tensor form factor in the whole kinematical region accessible in the experiments. A set of synthetic data points, representing our results for $f_T^{D \pi(K)}(q^2)$ for several selected values of $q^2$, is provided and the corresponding covariance matrix is also available. At zero four-momentum transfer we get $f_T^{D \pi}(0) = 0.506 (79)$ and $f_T^{D K}(0) = 0.687 (54)$, which correspond to $f_T^{D \pi}(0)/f_+^{D \pi}(0) = 0.827 (114)$ and $f_T^{D K}(0)/f_+^{D K}(0)= 0.898 (50)$.

Extraction of |V_{cd}| and |V_{cs}| from experimental decay rates using lattice QCD D rightarrow pi (K) ell nu form factors

We present a determination of the Cabibbo–Kobayashi–Maskawa matrix elements |V_{cd}| and |V_{cs}| obtained by combining the momentum dependence of the semileptonic vector form factors f_+^{D rightarrow pi }(q^2) and f_+^{D rightarrow K}(q^2), recently determined from lattice QCD simulations, with the differential rates measured for the semileptonic D rightarrow pi ell nu and D rightarrow K ell nu decays. Our analysis is based on the results for the semileptonic form factors produced by the European Twisted Mass Collaboration with N_f = 2 + 1 + 1 flavors of dynamical quarks in the whole range of values of the squared 4-momentum transfer accessible in the experiments. The statistical and systematic correlations between the lattice data as well as those present in the experimental data are properly taken into account. With respect to the standard procedure based on the use of only the vector form factor at zero 4-momentum transfer, we obtain more precise and consistent results: |V_{cd} |= 0.2341 ~ (74) and |V_{cs} |= 0.970 ~ (33). The second-row CKM unitarity is fulfilled within the current uncertainties: |V_{cd}|^2 + |V_{cs}|^2 + |V_{cb}|^2 = 0.996 ~ (64). Moreover, using for the first time hadronic inputs determined from first principles, we have calculated the ratio of the semileptonic D rightarrow pi (K) decay rates into muons and electrons, which represent a test of lepton universality within the SM, obtaining in the isospin-symmetric limit of QCD: mathcal{{R}}_{LU}^{Dpi } = 0.985~(2) and mathcal{{R}}_{LU}^{DK} = 0.975~(1).

Effects of nonequilibrated topological charge distributions on pseudoscalar meson masses and decay constants

We study the effects of failure to equilibrate the squared topological charge $Q^2$ on lattice calculations of pseudoscalar masses and decay constants. The analysis is based on chiral perturbation theory calculations of the dependence of these quantities on the QCD vacuum angle $\theta$. For the light-light partially quenched case, we rederive the known chiral perturbation theory results of Aoki and Fukaya, but using the nonperturbatively-valid chiral theory worked out by Golterman, Sharpe and Singleton, and by Sharpe and Shoresh. We then extend these calculations to heavy-light mesons. Results when staggered taste-violations are important are also presented. The derived $Q^2$ dependence is compared to that of simulations using the MILC collaboration's ensembles of lattices with four flavors of HISQ dynamical quarks. We find agreement, albeit with large statistical errors. These results can be used to correct for the leading effects of unequilibrated $Q^2$, or to make estimates of the systematic error coming from the failure to equilibrate $Q^2$. In an appendix, we show that the partially quenched chiral theory may be extended beyond a lower bound on valence masses discovered by Sharpe and Shoresh. Subtleties occurring when a sea-quark mass vanishes are discussed in another appendix.

Topological susceptibility of QCD with dynamical Möbius domain-wall fermions

We compute the topological susceptibility $\chi_t$ of lattice QCD with $2+1$ dynamical quark flavors described by the M\"obius domain wall fermion. Violation of chiral symmetry as measured by the residual mass is kept at $\sim$1 MeV or smaller. We measure the fluctuation of the topological charge density in a `slab' sub-volume of the simulated lattice using the method proposed by Bietenholz {\it et al.} The quark mass dependence of $\chi_t$ is consistent with the prediction of chiral perturbation theory, from which the chiral condensate is extracted as $\Sigma^{\overline{\rm MS}} (\mbox{2GeV}) = [274(13)(29)\mbox{MeV}]^3$, where the first error is statistical and the second one is systematic. Combining the results for the pion mass $M_\pi$ and decay constant $F_\pi$, we obtain $\chi_t = 0.229(03)(13)M_\pi^2F_\pi^2$ at the physical point.

Instanton liquid properties from lattice QCD

We examined the instanton contribution to the QCD configurations generated from lattice QCD for NF = 0, NF = 2 + 1 and NF = 2 + 1 + 1 dynamical quark flavors from two different and complementary approaches. First via the use of Gradient flow, we computed instanton liquid properties using an algorithm to localize instantons in the gauge field configurations and studied their evolution with flow time. Then, the analysis of the running at low momenta of gluon Green’s functions serves as an independent confirmation of the instanton density which can also be derived without the use of the Gradient flow.

D → π and D → K semileptonic form factors with Nf = 2 + 1 + 1 twisted mass fermions

We present a lattice determination of the vector and scalar form factors of the D → π(K)lv semileptonic decays, which are relevant for the extraction of the CKM matrix elements |Vcd| and |Vcs| from experimental data. Our analysis is based on the gauge configurations produced by the European Twisted Mass Collaboration with Nf = 2 + 1 +1 flavors of dynamical quarks. We simulated at three different values of the lattice spacing and with pion masses as small as 210 MeV. The matrix elements of both vector and scalar currents are determined for a plenty of kinematical conditions in which parent and child mesons are either moving or at rest. Lorentz symmetry breaking due to hypercubic effects is clearly observed in the data and included in the decomposition of the current matrix elements in terms of additional form factors. After the extrapolations to the physical pion mass and to the continuum limit the vector and scalar form factors are determined in the whole kinematical region from q2 = 0 up to [see formula in PDF] accessible in the experiments, obtaining a good overall agreement with experiments, except in the region at high values of q2 where some deviations are visible.

Tensor form factor for the D → π(K) transitions with Twisted Mass fermions.

We present a preliminary lattice calculation of the D → π and D → K tensor form factors fT (q2) as a function of the squared 4-momentum transfer q2. ETMC recently computed the vector and scalar form factors f+(q2) and f0(q2) describing D → π(K)lv semileptonic decays analyzing the vector current and the scalar density. The study of the weak tensor current, which is directly related to the tensor form factor, completes the set of hadronic matrix element regulating the transition between these two pseudoscalar mesons within and beyond the Standard Model where a non-zero tensor coupling is possible. Our analysis is based on the gauge configurations produced by the European Twisted Mass Collaboration with Nf = 2 + 1 + 1 flavors of dynamical quarks. We simulated at three different values of the lattice spacing and with pion masses as small as 210 MeV and with the valence heavy quark in the mass range from ≃ 0.7 mc to ≃ 1.2mc. The matrix element of the tensor current are determined for a plethora of kinematical conditions in which parent and child mesons are either moving or at rest. As for the vector and scalar form factors, Lorentz symmetry breaking due to hypercubic effects is clearly observed in the data. We will present preliminary results on the removal of such hypercubic lattice effects.

Towards a holographic quark matter crystal

We construct the gravity dual of d = 4, mathcal{N}=4 , SU(Nc) super Yang-Mills theory, coupled to Nf flavors of dynamical quarks, at non-zero temperature T and nonzero quark density Nq. The supergravity solutions possess a regular horizon if T > 0 and include the backreaction of Nc color D3-branes and Nf flavor D7-branes with Nq units of electric flux on their worldvolume. At zero temperature the solutions interpolate between a Landau pole singularity in the ultraviolet and a Lifshitz geometry in the infrared. At high temperature the thermodynamics is directly sensitive to the Landau pole, whereas at low temperature it is not, as expected from effective field theory. At low temperature and sufficiently high charge density we find thermodynamic and dynamic instabilities towards the spontaneous breaking of translation invariance.

Scalar and vector form factors of D→π(K)ℓν decays with Nf=2+1+1 twisted fermions

We present a lattice determination of the vector and scalar form factors of the $D\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\ell}\ensuremath{\nu}$ and $D\ensuremath{\rightarrow}K\ensuremath{\ell}\ensuremath{\nu}$ semileptonic decays, which are relevant for the extraction of the CKM matrix elements $|{V}_{cd}|$ and $|{V}_{cs}|$ from experimental data. Our analysis is based on the gauge configurations produced by the European Twisted Mass Collaboration with ${N}_{f}=2+1+1$ flavors of dynamical quarks, at three different values of the lattice spacing ($a\ensuremath{\simeq}0.062,0.082,0.089\text{ }\text{ }\mathrm{fm}$) and with pion masses as small as 210 MeV. Quark momenta are injected on the lattice using nonperiodic boundary conditions. The matrix elements of both vector and scalar currents are determined for plenty of kinematical conditions in which parent and child mesons are either moving or at rest. Lorentz symmetry breaking due to hypercubic effects is clearly observed in the data and included in the decomposition of the current matrix elements in terms of additional form factors. After the extrapolations to the physical pion mass and to the continuum limit, we determine the vector and scalar form factors in the whole kinematical region from ${q}^{2}=0$ up to ${q}_{\mathrm{max}}^{2}=({M}_{D}\ensuremath{-}{M}_{\ensuremath{\pi}(K)}{)}^{2}$ accessible in the experiments, obtaining a good overall agreement with experiments, except in the region at high values of ${q}^{2}$ where some deviations are visible. A set of synthetic data points, representing our results for ${f}_{+}^{D\ensuremath{\pi}(K)}({q}^{2})$ and ${f}_{0}^{D\ensuremath{\pi}(K)}({q}^{2})$ for several selected values of ${q}^{2}$, is provided and also the corresponding covariance matrix is available. At zero four-momentum transfer, we get ${f}_{+}^{D\ensuremath{\rightarrow}\ensuremath{\pi}}(0)=0.612(35)$ and ${f}_{+}^{D\ensuremath{\rightarrow}K}(0)=0.765(31)$. Using the experimental averages for $|{V}_{cd}|{f}_{+}^{D\ensuremath{\rightarrow}\ensuremath{\pi}}(0)$ and $|{V}_{cs}|{f}_{+}^{D\ensuremath{\rightarrow}K}(0)$, we extract $|{V}_{cd}|=0.2330(137)$ and $|{V}_{cs}|=0.945(38)$, respectively. The second row of the CKM matrix is found to be in agreement with unitarity within the current uncertainties: $|{V}_{cd}{|}^{2}+|{V}_{cs}{|}^{2}+|{V}_{cb}{|}^{2}=0.949(78)$.

Fluctuation-induced modifications of the phase structure in ( 2+1 )-flavor QCD

The low-energy sector of QCD with $N_f = 2\!+\!1$ dynamical quark flavors at non-vanishing chemical potential and temperature is studied with a non-perturbative functional renormalization group method. The analysis is performed in different truncations in order to explore fluctuation-induced modifications of the quark-meson correlations as well as quark and meson propagators on the chiral phase transition of QCD. Depending on the chosen truncation significant quantitative implications on the phase transition are found. In the chirally symmetric phase, the quark flavor composition of the pseudoscalar $(\eta,\eta^{\prime})$-meson complex turns out to be drastically sensitive to fluctuation-induced modifications in the presence of the axial $U(1)_A$ anomaly. This has important phenomenological consequences for the assignment of chiral partners to these mesons.

Inclusive semi-leptonic B meson decay structure functions from lattice QCD

We propose a method to non-perturbatively calculate the forward-scattering matrix elements relevant to inclusive semi-leptonic B meson decays. Corresponding hadronic structure functions at unphysical kinematics are accessible through lattice QCD calculation of four-point correlation functions. The unphysical kinematical point may be reached by analytic continuation from the physical differential decay rate. A numerical test is performed for the B_s -> X_c l nu mode in the zero-recoil limit. We use lattice ensembles generated with 2+1 dynamical quark flavors. The valence charm quark mass is tuned to its physical value, while the bottom quark mass is varied in the range (1.56-2.44)m_c. From the numerical results we can identify the contributions of the ground state D_s^(*) meson as well as those of excited states or continuum states.

Mass of thebquark andB-meson decay constants fromNf=2+1+1twisted-mass lattice QCD

We present precise lattice computations for the b-quark mass, the quark mass ratios mb/mc and mb/ms as well as the leptonic B-decay constants. We employ gauge configurations with four dynamical quark flavors, up/down, strange and charm, at three values of the lattice spacing (a ~ 0.06 - 0.09 fm) and for pion masses as low as 210 MeV. Interpolation in the heavy quark mass to the bottom quark point is performed using ratios of physical quantities computed at nearby quark masses exploiting the fact that these ratios are exactly known in the static quark mass limit. Our results are also extrapolated to the physical pion mass and to the continuum limit and read: mb(MSbar, mb) = 4.26(10) GeV, mb/mc = 4.42(8), mb/ms = 51.4(1.4), fBs = 229(5) MeV, fB = 193(6) MeV, fBs/fB = 1.184(25) and (fBs/fB)/(fK/fpi) = 0.997(17).

Instanton-dyon ensemble with two dynamical quarks: The chiral symmetry breaking

This is the second paper of the series aimed at understanding the ensemble of instanton-dyons, now with two flavors of light dynamical quarks. The partition function is appended by the fermionic factor, $(det T)^{N_f}$ and Dirac eigenvalue spectra at small values are derived from the numerical simulation of 64 and 128 dyons. Those spectra show clear chiral symmetry breaking pattern at high dyon density.

Three-dimensional super Yang-Mills with compressible quark matter

We construct the gravity dual of three-dimensional, $SU(N_{\textrm{c}})$ super Yang-Mills theory with $N_{\textrm{f}}$ flavors of dynamical quarks in the presence of a non-zero quark density $N_{\textrm{q}}$. The supergravity solutions include the backreaction of $N_{\textrm{c}}$ color D2-branes and $N_{\textrm{f}}$ flavor D6-branes with $N_{\textrm{q}}$ units of electric flux on their worldvolume. For massless quarks, the solutions depend non-trivially only on the dimensionless combination $\rho=N_{\textrm{c}}^2 N_{\textrm{q}} / \lambda^2 N_{\textrm{f}}^4$, with $\lambda=g_{\textrm{YM}}^2 N_{\textrm{c}}$ the 't Hooft coupling, and describe renormalization group flows between the super Yang-Mills theory in the ultraviolet and a non-relativistic theory in the infrared. The latter is dual to a hyperscaling-violating, Lifshitz-like geometry with dynamical and hyperscaling-violating exponents $z=5$ and $\theta=1$, respectively. If $\rho \ll 1$ then at intermediate energies there is also an approximate AdS$_4$ region, dual to a conformal Chern-Simons-Matter theory, in which the flow exhibits quasi-conformal dynamics. At zero temperature we compute the chemical potential and the equation of state and extract the speed of sound. At low temperature we compute the entropy density and extract the number of low-energy degrees of freedom. For quarks of non-zero mass $M_{\textrm{q}}$ the physics depends non-trivially on $\rho$ and $M_{\textrm{q}} N_{\textrm{c}}/\lambda N_{\textrm{f}}$.

Baryon effects on the location of QCD’s critical end point

The location of the critical end point of QCD has been determined in previous studies of ${N}_{f}=2+1$ and ${N}_{f}=2+1+1$ dynamical quark flavors using a (truncated) set of Dyson-Schwinger equations for the quark and gluon propagators of Landau-gauge QCD. A source for systematic errors in these calculations has been the omission of terms in the quark-gluon interaction that can be parametrized in terms of baryonic degrees of freedom. These have a potentially large dependence on chemical potential and therefore may affect the location of the critical end point. In this exploratory study we estimate the effects of these contributions, both in the vacuum and at finite temperature and chemical potential. We find only a small influence of baryonic contributions on the location of the critical end point. We estimate the robustness of this result by parameterizing further dependencies on chemical potential.

BBinteractions with static bottom quarks from lattice QCD

The isospin, spin and parity dependent potential of a pair of $B$ mesons is computed using Wilson twisted mass lattice QCD with two flavours of degenerate dynamical quarks. The $B$ meson is addressed in the static-light approximation, i.e.\ the $b$ quarks are infinitely heavy. From the results of the $B\,B$ meson-meson potentials, a simple rule can be deduced stating which isospin, spin and parity combinations correspond to attractive and which to repulsive forces. We provide fits to the ground state potentials in the attractive channels and discuss the potentials in the repulsive and excited channels. The attractive channels are most important since they can possibly lead to a bound four-quark state, i.e.\ a $\bar{b}\bar{b}ud$ tetraquark. Using these attractive potentials in the Schr\"odinger equation, we find indication for such a tetraquark state of two static bottom antiquarks and two light $u/d$ quarks with mass extrapolated down to the physical value.