We develop a methodology for the computation of the $K\to \ellν_\ell \ell'^+ \ell'^-$ decay width using lattice QCD and present an exploratory study here. We use a scalar function method to account for the momentum dependence of the decay amplitude and adopt the infinite volume reconstruction method to reduce the systematic errors such as the temporal truncation effects and the finite-volume effects. We then perform a four-body phase-space integral to obtain the decay width. The only remaining technical problem is the possible power-law finite-volume effects associated with the process of $K\toππ\ellν_\ell\to \ellν_\ell \ell'^+ \ell'^-$, where the intermediate state involves multiple hadrons. In this work, we use a gauge ensemble of twisted mass fermion with a pion mass $m_π=352$ MeV and a nearly-physical kaon mass. At this kinematics, the $ππ$ in the intermediate state cannot be on shell simultaneously as $2m_π>m_K$ and the finite-volume effects associated with $ππ$ state are exponentially suppressed. Using the developed methods mentioned above, we calculate the branching ratios for four channels of $K\to \ellν_\ell\ell'^+ \ell'^-$, and obtain the results comparable to the experimental measurements and ChPT predictions. Our work demonstrates the capability of lattice QCD to improve Standard Model prediction in $K\to \ellν_\ell \ell'^+ \ell'^-$ decay width.
We study the hadronic matrix elements describing the $B_s \to D_s\ell \barν_\ell$ decay in and beyond the Standard Model. By using the twisted mass QCD on the lattice with $N_f=2$ dynamical flavors we compute the normalization $\mathscr G_s(1)$ of the form factor dominating $B_s\to D_s \ell \barν_\ell$ in the SM. We also make the first lattice determination of $F_0(q^2)/F_+(q^2)$ and $F_T(q^2)/F_+(q^2)$ near zero recoil (near $q^2_{\rm max}$). We briefly discuss the non-strange case $B \to D\ell \barν_\ell$ as well.
The large radiative production rate for pseudoscalar mesons in the $J/ψ$ radiative decay remains elusive. We present the first lattice QCD calculation of partial decay width of $J/ψ$ radiatively decaying into $η_{(2)}$, the $\mathrm{SU(2)}$ flavor singlet pseudoscalar meson, which confirms QCD $\mathrm{U_A(1)}$ anomaly enhancement to the coupling of gluons with flavor singlet pseudoscalar mesons. The lattice simulation is carried out using $N_f=2$ lattice QCD gauge configurations at the pion mass $m_π \approx 350$ MeV. In particular, the distillation method has been utilized to calculate light…
We show results from calculations in full lattice QCD of the mass, leptonic width and radiative decay rate to eta_c of the J/psi meson. These provide few % tests of QCD. Another (1.5%) test comes from comparison of time-moments of the vector charmonium correlator with results derived from the experimental values of R(e+e- to hadrons) in the charm region.
With the discovery of the doubly heavy $Ξ_{cc}$ baryon, comprehensive studies of the properties of the doubly heavy baryons are started. In the present work, we examine the $Ξ_{bb} \to Σ_b \ell^+ \ell^-$ and $Ξ_{cc} \to Σ_c \ell^+ \ell^-$ decays induced by flavor-changing neutral currents (FCNC) in the framework of the light-cone sum rules. After obtaining the sum rules for the form factors induced by the tensor current, the branching ratios of the relevant transitions are estimated. We found that the branching ratio for the $c \to u$ transition is around five orders smaller than the $b \to d$…
We consider two-loop QCD corrections to the element $Γ_{12}^q$ of the decay matrix in $B_q-\bar{B}_q$ mixing, $q=d,s$, in the leading power of the Heavy Quark Expansion. The calculated contributions involve one current-current and one penguin operator and constitute the next step towards a theory prediction for the width difference $ΔΓ_s$ matching the precise experimental data. We present compact analytic results for all matching coefficients in an expansion in $m_c/m_b$ up to second order. Our new corrections are comparable in size to the current experimental error and slightly increase $ΔΓ_s…
We prove a theorem in QCD stating that in the limit of strong coupling, $g\to\infty$, the observed spectrum of glueballs in QCD is the same of a pure Yang-Mills theory, being mixing effects due to the next-to-leading order. A full effective theory for QCD is obtained and the width of the $σ$ resonance decay is straightforwardly computed. This appears as the lowest glueball state. Vacuum gluon condensate is computed that consistently support studies on the identification of this meson as a glueball.
Employing the QCD factorization formalism we compute $B_{u}^{-} \to γ^{\ast} \, \ell \, \bar ν_{\ell}$ form factors with an off-shell photon state possessing the virtuality of order $m_b \, Λ_{\rm QCD}$ and $m_b^2$, respectively, at next-to-leading order in QCD. Perturbative resummation for the enhanced logarithms of $m_b / Λ_{\rm QCD}$ in the resulting factorization formulae is subsequently accomplished at next-to-leading logarithmic accuracy with the renormalization-group technique in momentum space. In particular, we derive the soft-collinear factorization formulae for a variety of the subl…
The rare decays $B^0 \to K^{*0} μ^+ μ^-$ and $B_s \to ϕμ^+ μ^-$ 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 $B_s \to ϕ$ form factors; we also determine the form factors relevant for the tree-level decays $B_s \to K^* \ell ν$. 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…
The tree-level $b\rightarrow c{\ell}\barν_{\ell}$ based hadronic transitions have been on the focus of much attention since recording significant deviations of the experimental data, on the ratios of the branching fractions in $ τ$ and $ e-μ$ channels of the semileptonic $ B \rightarrow D $ transition, from the SM predictions by BaBar Collaboration in 2012. It can be of great importance to look whether similar discrepancies take place in the semileptonic baryonic $Λ_{b}\rightarrow Λ_{c}{\ell}\barν_{\ell}$ decay channel or not. In this accordance we estimate the decay width as well as the ratio…
Inclusive P-wave Quarkonium Decay Widths from Lattice QCD and pNRQCD
Technical University of Munich（慕尼黑工业大学）；University of Southern Denmark（南丹麦大学）；RWTH Aachen University（亚琛工业大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of California, Berkeley（加州大学伯克利分校）
A method suitable for extracting resonance parameters of unstable baryons in lattice QCD is examined. The method is applied to the strong decay of the Delta to a pion-nucleon state, extracting the pi-N - Delta coupling constant and Delta decay width.
We present the first lattice QCD determination of the $Λ_b \to Λ^*(1520)$ vector, axial vector, and tensor form factors that are relevant for the rare decays $Λ_b \to Λ^*(1520)\ell^+\ell^-$. The lattice calculation is performed in the $Λ^*(1520)$ rest frame with nonzero $Λ_b$ momenta, and is limited to the high-$q^2$ region. An interpolating field with covariant derivatives is used to obtain good overlap with the $Λ^*(1520)$. The analysis treats the $Λ^*(1520)$ as a stable particle, which is expected to be a reasonable approximation for this narrow resonance. A domain-wall action is used for t…
Using $(2+1)$-flavor lattice QCD, we compute the 10 form factors describing the $Λ_b \to Λ$ matrix elements of the $b \to s$ vector, axial vector, and tensor currents. The calculation is based on gauge field ensembles generated by the RBC and UKQCD Collaborations with a domain-wall action for the $u$, $d$, and $s$ quarks and the Iwasaki gauge action. The $b$ quark is implemented using an anisotropic clover action, tuned nonperturbatively to the physical point, and the currents are renormalized with a mostly nonperturbative method. We perform simultaneous chiral, continuum, and kinematic extrap…
We deliver an exploratory lattice QCD examination of the $K^\ast(892)$ meson decay width with the help of the p-wave scattering phase $δ_1$ of pion-kaon ($πK$) system in the isospin $I=1/2$ channel, which are extracted by the modified Rummukainen-Gottlieb formula for two-particle system with arbitrary mass, and it clearly reveals the entity of a resonance at a mass around $K^\ast(892)$ meson mass. The effective range formula is applied to describe the energy dependence of the scattering phase and we obtain the effective $K^\ast \to πK$ coupling constant as $g_{K^\ast πK} = 6.38(78)$, and subse…
Measurements of the $Λ_b \to p \ell^- \barν_\ell$ and $Λ_b \to Λ_c \ell^- \barν_\ell$ decay rates can be used to determine the magnitudes of the CKM matrix elements $V_{ub}$ and $V_{cb}$, provided that the relevant hadronic form factors are known. Here we present a precise calculation of these form factors using lattice QCD with 2+1 flavors of dynamical domain-wall fermions. The $b$ and $c$ quarks are implemented with relativistic heavy-quark actions, allowing us to work directly at the physical heavy-quark masses. The lattice computation is performed for six different pion masses and two diff…
We study the flux tubes produced by static quark-antiquark, quark-quark and quark-gluon charges at finite temperature in pure gauge SU(3) lattice QCD. Our sources are static and our lattice correlators are composed of fundamental and adjoint Polyakov loops. To signal the flux tubes, we compute the square densities of the chromomagnetic and chromoelectric fields with plaquettes, in a gauge invariant framework. We study the existence and non-existence of flux tubes both above and below the deconfinement phase transition temperature Tc. Using the Lagrangian density as a probability distribution, …
We use our lattice QCD computation of the $B_c\rightarrow J/ψ$ form factors to determine the differential decay rate for the semitauonic decay channel and construct the ratio of branching fractions $R(J/ψ) = \mathcal{B}(B_c^- \rightarrow J/ψτ^-\barν_τ)/\mathcal{B}(B_c^- \rightarrow J/ψμ^-\barν_μ)$. We find $R(J/ψ) = 0.2582(38)$ and give an error budget. We also extend the relevant angular observables, which were recently suggested for the study of lepton flavor universality violating effects in $B\rightarrow D^*\ellν$, to $B_c \rightarrow J/ψ\ellν$ and make predictions for their values under d…
We determine the rate for $D_s^* \rightarrow D_s γ$ for the first time from lattice QCD and include the full effect of $u$, $d$ and $s$ sea quarks. The valence quarks are implemented using the Highly Improved Staggered Quark (HISQ) formalism and we normalise the vector current nonperturbatively. We obtain $M(D_s^*)-M(D_s)$ of 148(4) MeV, in good agreement with experiment. The value of the decay constant of the $D_s^*$ we find to be 274(6) MeV, so that $f_{D_s^*}/f_{D_s} = 1.10(2)$. For the radiative decay we find $Γ(D_s^* \rightarrow D_s γ)$ = 0.066(26) keV. Given the experimental branching fr…
Lattice QCD plays an increasing role in reducing theoretical uncertainties in kaon decays. Here we focus on kaon decay channels $K\to \ellν_\ell \ell'^+ \ell'^-$, which are closely related to radiative kaon decays since the lepton pairs $\ell'^+ \ell'^-$ come from virtual photon emission: $K\to \ellν_\ell γ^* \to \ellν_\ell \ell'^+ \ell'^-$. Compared with real photon emission, these channels involve more complicated form factors due to the off-shell photon with possible large momentum transfer, which causes a challenge to lattice-QCD studies. In this work, we introduce a lattice calculation pr…
We present the results of our lattice QCD study of the $πγ\toππ$ process, where the $ρ$ resonance appears as an enhancement in the transition amplitude. We use $N_f=2+1$ clover fermions on a lattice of $L=3.6$ fm and a pion mass of $320$ MeV. Using a combination of forward, stochastic, and sequential propagators, we calculate the two-point and three-point functions that allow us to determine the $πγ\toππ$ matrix elements for several values of the invariant mass $s$ and momentum transfer $q^2$. To fit the $q^2$ and $s$ dependence of the $πγ\toππ$ amplitude, we explore a set of general parametri…
A decay width calculation for a hybrid exotic meson h, with JPC=1-+, is presented for the channel h->pi+a1. This quenched lattice QCD simulation employs Luescher's finite box method. Operators coupling to the h and pi+a1 states are used at various levels of smearing and fuzzing, and at four quark masses. Eigenvalues of the corresponding correlation matrices yield energy spectra that determine scattering phase shifts for a discrete set of relative pi+a1 momenta. Although the phase shift data is sparse, fits to a Breit-Wigner model are attempted, resulting in a decay width of about 60 MeV when a…
Predicting the $B_s^0-\bar{B}_s^0$ 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 $\tilde{R}_{2,3}$ using nonrelativistic QCD for the bottom quark and a highly improved staggered quark (HISQ) action for the strange quark. Computations use MILC ensembles of gauge field configuations with $2+1+1$ flavors of sea quarks with the HISQ discretization, including lattices with physically light up/down quark masses.…
We investigate the effects produced by the three-momentum scale $\sqrt{mΛ_{QCD}}$ in the strong coupling regime of heavy quarkonium. We compute the leading non-vanishing contributions due to this scale to the masses and inclusive decay widths. We find that they may provide leading corrections to the S-wave decay widths but only subleading corrections to the masses.
The standard approach to determine the parameters of a resonance is based on the study of the volume dependence of the energy spectrum. In this work we study a non-linear sigma model coupled to a scalar field in which a resonance emerges. Using an analysis method introduced recently, based on the concept of probability distribution, it is possible to determine the mass and the width of the resonance.
We report the first calculation using physical light-quark masses of the electromagnetic form factor $V(z)$ describing the long-distance contributions to the $K^+\toπ^+\ell^+\ell^-$ decay amplitude. The calculation is performed on a 2+1 flavor domain wall fermion ensemble with inverse lattice spacing $a^{-1}=1.730(4)$GeV. We implement a Glashow-Iliopoulos-Maiani cancellation by extrapolating to the physical charm-quark mass from three below-charm masses. We obtain $V(z=0.013(2))=-0.87(4.44)$, achieving a bound for the value. The large statistical error arises from stochastically estimated quar…
We present HPQCD's improved scalar, vector and tensor form factors for $B \to K$ semileptonic decays, using the heavy-HISQ formalism for more accurate normalisation of the weak currents. Working with masses close to the physical $b$ on the finest ensemble and including three ensembles with physical light quarks, we cover the full physical $q^2$ range with good precision. Our uncertainties at $q^2=0$ are a factor of three better than earlier work. We compare Standard Model observables using our form factors to experimental measurements for the rare flavour changing neutral current processes $B …
We report on our calculation of the B \to D^(*) \ell νform factors in 2+1 flavor lattice QCD. The Möbius domain-wall action is employed for light, strange, charm and bottom quarks. At lattice cutoffs 1/a \sim 2.4, 3.6 and 4.5 GeV, we simulate bottom quark masses up to 0.7/a to control discretization errors. The pion mass is as low as 230 MeV. We extrapolate the form factors to the continuum limit and physical quark masses, and make a comparison with recent phenomenological analyses.
The first lattice QCD calculation of the form factors governing $Λ_c \to Λ\ell^+ ν_\ell$ decays is reported. The calculation was performed with two different lattice spacings and includes one ensemble with a pion mass of 139(2) MeV. The resulting predictions for the $Λ_c \to Λe^+ ν_e$ and $Λ_c \to Λμ^+ ν_μ$ decay rates divided by $|V_{cs}|^2$ are $0.2007(71)(74)\:{\rm ps}^{-1}$ and $0.1945(69)(72)\:{\rm ps}^{-1}$, respectively, where the two uncertainties are statistical and systematic. Taking the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ from a global fit and the $Λ_c$ lifetime from…
Inclusive semileptonic $D_s\to X_s\ell\barν$ decays from lattice QCD: continuum and chiral extrapolation
High Energy Accelerator Research Organization (KEK)（高能加速器研究机构）；PRISMA++ Cluster of Excellence & Institut für Kernphysik, Johannes-Gutenberg-Universität Mainz（美因茨约翰内斯·古腾堡大学 PRISMA++ 卓越集群与核物理研究所）；School of Physics and Astronomy, University of Southampton（南安普顿大学物理与天文学院）；STAG Research Center, University of Southampton（南安普顿大学 STAG 研究中心）；School of High Energy Accelerator Science, SOKENDAI (The Graduate University for Advanced Studies)（高级研究院（SOKENDAI）高能加速器科学学校）；RIKEN Center for Computational Science (R-CCS)（理化学研究所计算科学中心）；CERN, Theoretical Physics Department（欧洲核子研究中心理论物理部）
We present a lattice QCD calculation of the $ρ$ meson decay width via the $P$-wave scattering phase shift for the I=1 two-pion system. Our calculation uses full QCD gauge configurations for $N_f=2$ flavors generated using a renormalization group improved gauge action and an improved Wilson fermion action on a $12^3\times24$ lattice at $m_π/m_ρ=0.41$ and the lattice spacing $1/a=0.92 {\rm GeV}$. The phase shift calculated with the use of the finite size formula for the two-pion system in the moving frame shows a behavior consistent with the existence of a resonance at a mass close to the vector…
We present results from quenched lattice QCD for the form factors for the decay $B\toρlν$. The calculations are performed using a nonperturbatively improved action and operators at two values of the lattice spacing. The bottom quark mass is reached by extrapolation from simulations performed with heavy quark masses around the charm mass. Our primary result is for the partially integrated decay rate $Γ_{PI}$ over the range $12.7\gev^2 < q^2 < 18.2\gev^2$: Γ_PI = (4.9^{+12}_{-10}{+0}_{-14}) X 10^12 s^-1
We calculate the mass difference between the $Υ$ and $η_b$ and the $Υ$ leptonic width from lattice QCD using the Highly Improved Staggered Quark formalism for the $b$ quark and including $u$, $d$, $s$ and $c$ quarks in the sea. We have results for lattices with lattice spacing as low as 0.03 fm and multiple heavy quark masses, enabling us to map out the heavy quark mass dependence and determine values at the $b$ quark mass. Our results are: $M_Υ -M_{η_b} = 57.5(2.3)(1.0) \,\mathrm{MeV}$ (where the second uncertainty comes from neglect of quark-line disconnected correlation functions) and decay…
We calculate the J/ψ mass, leptonic width and radiative decay rate to γη_c from lattice QCD including u, d and s quarks in the sea for the first time. We use the Highly Improved Staggered Quark formalism and nonperturbatively normalised vector currents for the leptonic and radiative decay rates. Our results are: M_{J/ψ} -M_{η_c} = 116.5(3.2) MeV; Γ(J/ψ to e^+e^-) = 5.48(16) keV; Γ(J/ψ to γη_c) = 2.49(19) keV. The first two are in good agreement with experiment, with Γ(J/ψ to e^+e^-) providing a test of a decay matrix element in QCD, independent of CKM uncertainties, to 2%. At the same time res…
We determine the decay rate to leptons of the ground-state $Υ$ meson and its first radial excitation in lattice QCD for the first time. We use radiatively-improved NRQCD for the $b$ quarks and include $u$, $d$, $s$ and $c$ quarks in the sea with $u/d$ masses down to their physical values. We find $Γ(Υ\rightarrow e^+e^-)$ = 1.19(11) keV and $Γ(Υ^{\prime} \rightarrow e^+e^-)$ = 0.69(9) keV, both in good agreement with experiment. The decay constants we obtain are included in a summary plot of meson decay constants from lattice QCD given in the Conclusions. We also test time-moments of the vector…
We update the lattice calculation of the $B\toπ$ semileptonic form factors, which have important applications to the CKM matrix element $|V_{ub}|$ and the $B\toπ\ell^+\ell^-$ rare decay. We use MILC asqtad ensembles with $N_f=2+1$ sea quarks and over a range of lattice spacings $a \approx 0.045$--$0.12$ fm. We perform a combined chiral and continuum extrapolation of our lattice data using SU(2) staggered chiral perturbation theory in the hard pion limit. To extend the results for the form factors to the full kinematic range, we take a functional approach to parameterize the form factors using …
We present a direct lattice QCD calculation of the $κ$ meson decay width with the s-wave scattering phase shift for the isospin $I=1/2$ pion-kaon ($πK$) system. We employ a special finite size formula, which is the extension of the Rummukainen-Gottlieb formula for the $πK$ system in the moving frame, to calculate the scattering phase, which indicates a resonance around $κ$ meson mass. Through the effective range formula, we extract the effective $κ\to πK$ coupling constant $g_{κπK} = 4.54(76)$ GeV and decay width $Γ= 293 \pm 101$ MeV. Our simulations are done with the MILC gauge configurations…
Charmonium properties at high temperatures from lattice QCD
Fakultät für Physik, Universität Bielefeld（比勒费尔德大学物理系）；Physics Department, Brookhaven National Laboratory（布鲁克海文国家实验室物理系）；Institut für Kernphysik, Technische Universität Darmstadt（达姆施塔特工业大学核物理研究所）；Werner-Heisenberg-Gymnasium Bad Dürkheim（巴特迪尔凯姆维尔纳·海森堡中学）
We perform a lattice QCD study of the $ρ$ meson decay from the $N_f=2+1$ full QCD configurations generated with a renormalization group improved gauge action and a non-perturbatively $O(a)$-improved Wilson fermion action. The resonance parameters, the effective $ρ\toππ$ coupling constant and the resonance mass, are estimated from the $P$-wave scattering phase shift for the isospin I=1 two-pion system. The finite size formulas are employed to calculate the phase shift from the energy on the lattice. Our calculations are carried out at two quark masses, $m_π=410\,{\rm MeV}$ ($m_π/m_ρ=0.46$) and …
We calculate the $B \to D^{(*)} \ell ν$ form factors in 2+1 flavor relativistic lattice QCD by employing the Möbius domain-wall action for all quark flavors. Our simulations are carried out at lattice cut-offs $a^{-1} \sim 2.5$, 3.6 and 4.5 GeV with the bottom quark masses up to 0.7 $a^{-1}$ to control discretization effects. We extrapolate the form factors to the continuum limit and physical quark masses, and discuss systematic uncertainties of the form factors.
