Flavors Of Sea Quarks Research Articles

Semileptonic form factors for Brightarrow D^*ell nu at nonzero recoil from 2+1-flavor lattice QCD

We present the first unquenched lattice-QCD calculation of the form factors for the decay Brightarrow D^*ell nu at nonzero recoil. Our analysis includes 15 MILC ensembles with N_f=2+1 flavors of asqtad sea quarks, with a strange quark mass close to its physical mass. The lattice spacings range from aapprox 0.15 fm down to 0.045 fm, while the ratio between the light- and the strange-quark masses ranges from 0.05 to 0.4. The valence b and c quarks are treated using the Wilson-clover action with the Fermilab interpretation, whereas the light sector employs asqtad staggered fermions. We extrapolate our results to the physical point in the continuum limit using rooted staggered heavy-light meson chiral perturbation theory. Then we apply a model-independent parametrization to extend the form factors to the full kinematic range. With this parametrization we perform a joint lattice-QCD/experiment fit using several experimental datasets to determine the CKM matrix element |V_{cb}|. We obtain left| V_{cb}right| = (38.40 pm 0.68_{text {th}} pm 0.34_{text {exp}} pm 0.18_{text {EM}})times 10^{-3}. The first error is theoretical, the second comes from experiment and the last one includes electromagnetic and electroweak uncertainties, with an overall chi ^2text {/dof} = 126/84, which illustrates the tensions between the experimental data sets, and between theory and experiment. This result is in agreement with previous exclusive determinations, but the tension with the inclusive determination remains. Finally, we integrate the differential decay rate obtained solely from lattice data to predict R(D^*) = 0.265 pm 0.013, which confirms the current tension between theory and experiment.

Form factors of B→πℓν and a determination of |Vub| with Möbius domain-wall fermions

Using a fully relativistic lattice fermion action, we compute the form factors of the semileptonic decay $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\ell}\ensuremath{\nu}$, which is required for the determination of the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{ub}|$. We employ the M\"obius domain-wall fermion formalism for the generation of lattice ensembles with $2+1$ sea quark flavors as well as for the valence heavy and light quarks. We compute the form factors at various values of the lattice spacing and multiple light and heavy quark masses, and extrapolate the results to the physical point. We combine our lattice results with the available experimental data to obtain $|{V}_{ub}|=(3.93\ifmmode\pm\else\textpm\fi{}0.41)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$.

Form factors for the processes Bc+→D0ℓ+νℓ and Bc+→Ds+ℓ+ℓ−(νν¯) from lattice QCD

We present results of the first lattice QCD calculations of the weak matrix elements for the decays $B_c^+ \to D^0 \ell^+ \nu_{\ell}$, $B_c^+ \to D_s^+ \ell^+ \ell^-$ and $B_c^+ \to D_s^+ \nu \overline{\nu}$. Form factors across the entire physical $q^2$ range are then extracted and extrapolated to the continuum limit with physical quark masses. Results are derived from correlation functions computed on MILC Collaboration gauge configurations with three different lattice spacings and including 2+1+1 flavours of sea quarks in the Highly Improved Staggered Quark (HISQ) formalism. HISQ is also used for all of the valence quarks. The uncertainty on the decay widths from our form factors is similar in size to that from the present value for $V_{ub}$. We obtain the ratio $\Gamma (B_{c}^{+} \rightarrow D^0 \mu^{+} \nu_{\mu}) /\left|\eta_{\mathrm{EW}} V_{u b}\right|^{2}=4.43(63) \times 10^{12} \mathrm{~s}^{-1}$. Combining our form factors with those found previously by HPQCD for $B_{c}^{+} \rightarrow J / \psi \mu^{+} \nu_{\mu}$, we find $\left|V_{cb}/V_{ub} \right|^2 \Gamma( B_c^+ \to D^0 \mu^+ \nu_\mu )/\Gamma(B_{c}^{+} \rightarrow J / \psi \mu^{+} \nu_{\mu}) = 0.257(36)_{B_c \to D}(18)_{B_c \to J/\psi}$. We calculate the differential decay widths of $B_c^+ \to D_s^+ \ell^+ \ell^-$ across the full $q^2$ range, and give integrated results in $q^2$ bins that avoid possible effects from charmonium and $u \overline{u}$ resonances. For example, we find that the ratio of differential branching fractions integrated over the range $q^2 = 1 \; \mathrm{GeV}^2 - 6 \; \mathrm{GeV}^2$ for $B_c^+ \to D_s^+ \mu^+ \mu^-$ and $B_{c}^{+} \rightarrow J / \psi \mu^{+} \nu_{\mu}$ is $5.23{\tiny }(73)_{B_c \to D_s}(54)_{B_c \to J/\psi} \times 10^{-6}$. We also give results for the branching fraction of $B_c^+ \to D_s^+ \nu \overline{\nu}$. Prospects for reducing our errors in the future are discussed.

Bc→Bs(d) form factors from lattice QCD

We present results of the first lattice QCD calculations of $B_c \to B_s$ and $B_c \to B_d$ weak matrix elements. Form factors across the entire physical $q^2$ range are then extracted and extrapolated to the physical-continuum limit before combining with CKM matrix elements to predict the semileptonic decay rates $\Gamma(B_c^+ \to B_s^0 \overline{\ell} \nu_{\ell}) = 26.2(1.2) \times 10^9 \,\text{s}^{-1}$ and $\Gamma(B_c^+ \to B^0 \overline{\ell} \nu_{\ell}) = 1.65(10) \times 10^9 \,\text{s}^{-1}$. The lattice QCD uncertainty is comparable to the CKM uncertainty here. Results are derived from correlation functions computed on MILC Collaboration gauge configurations with a range of lattice spacings including 2+1+1 flavours of dynamical sea quarks in the Highly Improved Staggered Quark (HISQ) formalism. HISQ is also used for the propagators of the valence light, strange, and charm quarks. Two different formalisms are employed for the bottom quark: non-relativistic QCD (NRQCD) and heavy-HISQ. Checking agreement between these two approaches is an important test of our strategies for heavy quarks on the lattice. From chained fits of NRQCD and heavy-HISQ data, we obtain the differential decay rates $d\Gamma/ d q^2$ as well as integrated values for comparison to future experimental results.

Lattice QCD Matrix Elements for the B_{s}^{0}-B[over ¯]_{s}^{0} Width Difference beyond Leading Order.

Predicting the B_{s}^{0}-B[over ¯]_{s}^{0} width difference ΔΓ_{s} relies on the heavy quark expansion and on hadronic matrix elements of ΔB=2 operators. We present the first lattice QCD results for matrix elements of the dimension-7 operators R_{2,3} and linear combinations R[over ˜]_{2,3} using nonrelativistic QCD for the bottom quark and a highly improved staggered quark (HISQ) action for the strange quark. Computations use MILC Collaboration ensembles of gauge field configurations with 2+1+1 flavors of sea quarks with the HISQ discretization, including lattices with physically light up or down quark masses. We discuss features unique to calculating matrix elements of these operators and analyze uncertainties from series truncation, discretization, and quark mass dependence. Finally we report the first standard model determination of ΔΓ_{s} using lattice QCD results for all hadronic matrix elements through O(1/m_{b}). The main result of our calculations yields the 1/m_{b} contribution ΔΓ_{1/m_{b}}=-0.022(10) ps^{-1}. Adding this to the leading order contribution, the standard model prediction is ΔΓ_{s}=0.092(14) ps^{-1}.

Light quark masses in {N_mathrm{f}=2+1} lattice QCD with Wilson fermions

We present a lattice QCD determination of light quark masses with three sea-quark flavours (N_mathrm{f}=2+1). Bare quark masses are known from PCAC relations in the framework of CLS lattice computations with a non-perturbatively improved Wilson-Clover action and a tree-level Symanzik improved gauge action. They are fully non-perturbatively improved, including the recently computed Symanzik counter-term b_{mathrm{A}} - b_{mathrm{P}}. The mass renormalisation at hadronic scales and the renormalisation group running over a wide range of scales are known non-perturbatively in the Schrödinger functional scheme. In the present paper we perform detailed extrapolations to the physical point, obtaining (for the four-flavour theory) m_{mathrm{u}/mathrm{d}}(2~mathrm{GeV})= 3.54(12)(9)~mathrm{MeV} and m_{mathrm{s}}(2~mathrm{GeV}) = 95.7(2.5)(2.4)~mathrm{MeV} in the overline{mathrm{MS}} scheme. For the mass ratio we have m_{mathrm{s}}/m_{mathrm{u}/mathrm{d}}= 27.0(1.0)(0.4). The RGI values in the three-flavour theory are M_{mathrm{u}/mathrm{d}}= 4.70(15)(12)~mathrm{MeV} and M_{mathrm{s}}= 127.0(3.1)(3.2)~mathrm{MeV}.

Renormalizing vector currents in lattice QCD using momentum-subtraction schemes

We examine the renormalisation of flavour-diagonal vector currents in lattice QCD with the aim of understanding and quantifying the systematic errors from nonperturbative artefacts associated with the use of intermediate momentum-subtraction schemes. Our study uses the Highly Improved Staggered Quark (HISQ) action on gluon field configurations that include $n_f=2+1+1$ flavours of sea quarks, but our results have applicability to other quark actions. Renormalisation schemes that make use of the exact lattice vector Ward-Takahashi identity for the conserved current also have renormalisation factors, $Z_V$, for nonconserved vector currents that are free of contamination by nonperturbative condensates. We show this by explicit comparison of two such schemes: that of the vector form factor at zero momentum transfer and the RI-SMOM momentum-subtraction scheme. The two determinations of $Z_V$ differ only by discretisation effects (for any value of momentum-transfer in the RI-SMOM case). The RI$^{\prime}$-MOM scheme, although widely used, does not share this property. We show that $Z_V$ determined in the standard way in this scheme has $\mathcal{O}(1\%)$ nonperturbative contamination that limits its accuracy. Instead we define an RI$^{\prime}$-MOM $Z_V$ from a ratio of local to conserved vector current vertex functions and show that this $Z_V$ is a safe one to use in lattice QCD calculations. We also perform a first study of vector current renormalisation with the inclusion of quenched QED effects on the lattice using the RI-SMOM scheme.

Domain wall fermion QCD with the exact one flavor algorithm

Lattice QCD calculations including the effects of one or more non-degenerate sea quark flavors are conventionally performed using the Rational Hybrid Monte Carlo (RHMC) algorithm, which computes the square root of the determinant of $\mathscr{D}^{\dagger} \mathscr{D}$, where $\mathscr{D}$ is the Dirac operator. The special case of two degenerate quark flavors with the same mass is described directly by the determinant of $\mathscr{D}^{\dagger} \mathscr{D}$ --- in particular, no square root is necessary --- enabling a variety of algorithmic developments, which have driven down the cost of simulating the light (up and down) quarks in the isospin-symmetric limit of equal masses. As a result, the relative cost of single quark flavors --- such as the strange or charm --- computed with RHMC has become more expensive. This problem is even more severe in the context of our measurements of the $\Delta I = 1/2$ $K \rightarrow \pi \pi$ matrix elements on lattice ensembles with $G$-parity boundary conditions, since $G$-parity is associated with a doubling of the number of quark flavors described by $\mathscr{D}$, and thus RHMC is needed for the isospin-symmetric light quarks as well. In this paper we report on our implementation of the exact one flavor algorithm (EOFA) introduced by the TWQCD collaboration for simulations including single flavors of domain wall quarks. We have developed a new preconditioner for the EOFA Dirac equation, which both reduces the cost of solving the Dirac equation and allows us to re-use the bulk of our existing high-performance code. Coupling these improvements with careful tuning of our integrator, the time per accepted trajectory in the production of our 2+1 flavor $G$-parity ensembles with physical pion and kaon masses has been decreased by a factor of 4.2.

Calculation of B → D*lv form factor at zero recoil using the Oktay-Kronfeld action

We present the first preliminary results for the semileptonic form factor hA1 (w = 1)/ρAj at zero recoil for the B → D*lv decay using lattice QCD with four flavors of sea quarks. We use the HISQ staggered action for the light valence and sea quarks (the MILC HISQ configurations), and the Oktay-Kronfeld (OK) action for the heavy valence quarks.

B → D*lv at non-zero recoil

We present preliminary results from our analysis of the form factors for the B → D*lv decay at non-zero recoil. Our analysis includes 15 MILC asqtad ensembles with Nf = 2 + 1 flavors of sea quarks and lattice spacings ranging from a ≈ 0.15 fm down to 0.045 fm. The valence light quarks employ the asqtad action, whereas the heavy quarks are treated using the Fermilab action. We conclude with a discussion of future plans and phenomenological implications. When combined with experimental measurements of the decay rate, our calculation will enable a determination of the CKM matrix element |Vcb|.

Lattice simulations withNf=2+1improved Wilson fermions at a fixed strange quark mass

The explicit breaking of chiral symmetry of the Wilson fermion action results in additive quark mass renormalization. Moreover, flavour singlet and non-singlet scalar currents acquire different renormalization constants with respect to continuum regularization schemes. This complicates keeping the renormalized strange quark mass fixed when varying the light quark mass in simulations with $N_f=2+1$ sea quark flavours. Here we present and validate our strategy within the CLS (Coordinated Lattice Simulations) effort to achieve this in simulations with non-perturbatively order-$a$ improved Wilson fermions. We also determine various combinations of renormalization constants and improvement coefficients.

Nucleon structure functions and longitudinal spin asymmetries in the chiral quark constituent model

We have analysed the phenomenological dependence of the spin independent ($F_1^{p,n}$ and $F_2^{p,n}$) and the spin dependent ($g_1^{p,n}$) structure functions of the nucleon on the the Bjorken scaling variable $x$ using the unpolarized distribution functions of the quarks $q(x)$ and the polarized distribution functions of the quarks $\Delta q(x)$ respectively. The chiral constituent quark model ($\chi$CQM), which is known to provide a satisfactory explanation of the proton spin crisis and related issues in the nonperturbative regime, has been used to compute explicitly the valence and sea quark flavor distribution functions of $p$ and $n$. In light of the improved precision of the world data, the $p$ and $n$ longitudinal spin asymmetries ($A_1^p(x)$ and $A_1^n(x)$) have been calculated. The implication of the presence of the sea quarks has been discussed for ratio of polarized to unpolarized quark distribution functions for up and down quarks in the $p$ and $n$ $\frac{\Delta u^p(x)}{u^p(x)}$, $\frac{\Delta d^p(x)}{d^p(x)}$, $\frac{\Delta u^n(x)}{u^n(x)}$, and $\frac{\Delta d^n(x)}{d^n(x)}$. The ratio of the $n$ and $p$ structure functions $R^{np}(x)=\frac{F_2^n(x)}{F_2^p(x)}$ has also been presented. The results have been compared with the recent available experimental observations. The results on the spin sum rule have also been included and compared with data and other recent approaches.

Finite volume for three-flavour Partially Quenched Chiral Perturbation Theory through NNLO in the meson sector

We present a calculation of the finite volume corrections to meson masses and decay constants in three flavour Partially Quenched Chiral Perturbation Theory (PQChPT) through two-loop order in the chiral expansion for the flavour-charged (or off-diagonal) pseudoscalar mesons. The analytical results are obtained for three sea quark flavours with one, two or three different masses. We reproduce the known infinite volume results and the finite volume results in the unquenched case. The calculation has been performed using the supersymmetric formulation of PQChPT as well as with a quark-flow technique. Partial analytical results can be found in the appendices. Some examples of cases relevant to lattice QCD are studied numerically. Numerical programs for all results are available as part of the CHIRON package.

Quark flavor distribution functions for the octet baryons in the chiral quark constituent model

The quark flavor distribution functions of the octet baryons ($N$, $\mathrm{\ensuremath{\Sigma}}$, $\mathrm{\ensuremath{\Xi}}$, and $\mathrm{\ensuremath{\Lambda}}$) have been calculated in the chiral constituent quark model. In particular, the valence and sea quark flavor distribution functions of the scalar density matrix elements of octet baryons have been computed explicitly. The implications of chiral symmetry breaking and SU(3) symmetry breaking have been discussed in detail for the sea quark asymmetries, a fraction of a particular quark (antiquark) present in a baryon, flavor structure functions and the Gottfried integral. The meson-baryon sigma terms ${\ensuremath{\sigma}}_{\ensuremath{\pi}B}$, ${\ensuremath{\sigma}}_{KB}$, and ${\ensuremath{\sigma}}_{\ensuremath{\eta}B}$ for the case of $N$, $\mathrm{\ensuremath{\Sigma}}$, and $\mathrm{\ensuremath{\Xi}}$ baryons have also been calculated. The results have been compared with the recent available experimental observations for the case of $N$, and how the future experiments for $\mathrm{\ensuremath{\Sigma}}$, $\mathrm{\ensuremath{\Xi}}$, and $\mathrm{\ensuremath{\Lambda}}$ can provide important constraints to describe the role of nonvalence (sea) degrees of freedom has been discussed.

Scalar strangeness content of the nucleon and baryon sigma terms

The scalar strangeness content of the nucleon, characterized by the so-called strangeness-nucleon sigma term, is of fundamental importance in understanding its sea-quark flavor structure. We report a determination of the octet baryon sigma terms via the Feynman-Hellmann theorem by analyzing the latest high-statistics $n_f=2+1$ lattice QCD simulations with covariant baryon chiral perturbation theory up to next-to-next-to-next-to-leading order. In particular, we predict $\sigma_{\pi N}=55(1)(4)$ MeV and $\sigma_{sN}=27(27)(4)$ MeV, while the first error is statistical and the second systematic due to different lattice scales. The predicted $\sigma_{sN}$ is consistent with the latest LQCD results and the results based on the next-to-next-to-leading order chiral perturbation theory. Several key factors in determining the sigma terms are systematically taken into account and clarified for the first time, including the effects of lattice scale setting, systematic uncertainties originating from chiral expansion truncations, and constraint of strong-interaction isospin breaking effects.

Update of|Vcb|from theB¯→D*ℓν¯form factor at zero recoil with three-flavor lattice QCD

We compute the zero-recoil form factor for the semileptonic decay $\bar{B}^0\to D^{*+}\ell^-\bar{\nu}$ (and modes related by isospin and charge conjugation) using lattice QCD with three flavors of sea quarks. We use an improved staggered action for the light valence and sea quarks (the MILC \asqtad\ configurations), and the Fermilab action for the heavy quarks. Our calculations incorporate higher statistics, finer lattice spacings, and lighter quark masses than our 2008 work. As a byproduct of tuning the new data set, we obtain the $D_s$ and $B_s$ hyperfine splittings with few-MeV accuracy. For the zero-recoil form factor, we obtain $\mathcal{F}(1)=0.906(4)(12)$, where the first error is statistical and the second is the sum in quadrature of all systematic errors. With the latest HFAG average of experimental results and a cautious treatment of QED effects, we find $|V_{cb}| = (39.04 \pm 0.49_\text{expt} \pm 0.53_\text{QCD} \pm 0.19_\text{QED})\times10^{-3}$. The QCD error is now commensurate with the experimental error.

Lattice QCD calculation of form factors describing the rare decaysB→K*ℓ+ℓ−andBs→ϕℓ+ℓ−

The rare decays $B^0 \to K^{*0} \mu^+ \mu^-$ and $B_s \to \phi \mu^+ \mu^-$ are now being observed with enough precision to test Standard Model predictions. A full understanding of these decays requires accurate determinations of the corresponding hadronic form factors. Here we present results of lattice QCD calculations of the $B \to K^*$ and $B_s \to \phi$ form factors; we also determine the form factors relevant for the tree-level decays $B_s \to K^* \ell \nu$. We use full-QCD configurations including 2+1 flavors of sea quarks using an improved staggered action, and we employ lattice non-relativistic QCD to describe the bottom quark.

Determination of|Vus|from a Lattice QCD Calculation of theK→πℓνSemileptonic Form Factor with Physical Quark Masses

We calculate the kaon semileptonic form factor f+(0) from lattice QCD, working, for the first time, at the physical light-quark masses. We use gauge configurations generated by the MILC Collaboration with Nf = 2 + 1 + 1 flavors of sea quarks, which incorporate the effects of dynamical charm quarks as well as those of up, down, and strange. We employ data at three lattice spacings to extrapolate to the continuum limit. Our result, f+(0) = 0.9704(32), where the error is the total statistical plus systematic uncertainty added in quadrature, is the most precise determination to date. Combining our result with the latest experimental measurements of K semileptonic decays, one obtains the Cabibbo-Kobayashi-Maskawa matrix element |V(us)| = 0.22290(74)(52), where the first error is from f+(0) and the second one is from experiment. In the first-row test of Cabibbo-Kobayashi-Maskawa unitarity, the error stemming from |V(us)| is now comparable to that from |V(ud)|.

Direct determination of the strange and light quark condensates from full lattice QCD

We determine the strange quark condensate from lattice QCD for the first time and compare its value to that of the light quark and chiral condensates. The results come from a direct calculation of the expectation value of the trace of the quark propagator followed by subtraction of the appropriate perturbative contribution, derived here, to convert the non-normal-ordered $m\overline{\ensuremath{\psi}}\ensuremath{\psi}$ to the $\overline{\mathrm{MS}}$ scheme at a fixed scale. This is then a well-defined physical ``nonperturbative'' condensate that can be used in the operator product expansion of current-current correlators. The perturbative subtraction is calculated through $\mathcal{O}({\ensuremath{\alpha}}_{s})$ and estimates of higher order terms are included through fitting results at multiple lattice spacing values. The gluon field configurations used are ``second generation'' ensembles from the MILC collaboration that include $2+1+1$ flavors of sea quarks implemented with the highly improved staggered quark action and including $u/d$ sea quarks down to physical masses. Our results are $⟨\overline{s}s{⟩}^{\overline{\mathrm{MS}}}(2\text{ }\text{ }\mathrm{GeV})=\ensuremath{-}(290(15)\text{ }\text{ }\mathrm{MeV}{)}^{3}$, $⟨\overline{l}l{⟩}^{\overline{\mathrm{MS}}}(2\text{ }\text{ }\mathrm{GeV})=\ensuremath{-}(283(2)\text{ }\text{ }\mathrm{MeV}{)}^{3}$, where $l$ is a light quark with mass equal to the average of the $u$ and $d$ quarks. The strange to light quark condensate ratio is 1.08(16). The light quark condensate is significantly larger than the chiral condensate in line with expectations from chiral analyses. We discuss the implications of these results for other calculations.

Masses of Mesons with Charm Valence Quarks from 2+1+1 Flavor Twisted Mass Lattice QCD

We present preliminary results of an ongoing lattice QCD computation of the spectrum of $D$ mesons and $D_s$ mesons and of charmonium using 2+1+1 flavors of twisted mass sea and valence quarks.