High-precision determination of the pi, K, D, and Ds decay constants from lattice QCD

Quark flavor physics and lattice QCD

For a long time, investigation into the weak interactions of quarks has guided us toward understanding the Standard Model we know today. Now in the era of high precision, these studies are still one of the most promising avenues for peering beyond the Standard Model. This is a large-scale endeavour with many tales and many protagonists. In these pages I follow a few threads of a complex story, those passing through the realm of lattice gauge theory.

Hadronic τ Decays as New Physics Probes in the LHC Era

We analyze the sensitivity of hadronic τ decays to nonstandard interactions within the model-independent framework of the standard model effective field theory. Both exclusive and inclusive decays are studied, using the latest lattice data and QCD dispersion relations. We show that there are enough theoretically clean channels to disentangle all the effective couplings contributing to these decays, with the τ→ππν_{τ} channel representing an unexpected powerful new physics probe. We find that the ratios of nonstandard couplings to the Fermi constant are bound at the subpercent level. These bounds are complementary to the ones from electroweak precision observables and pp→τν_{τ} measurements at the LHC. The combination of τ decay and LHC data puts tighter constraints on lepton universality violation in the gauge boson-lepton vertex corrections.

Determination of the Pseudoscalar Decay Constant f_{D_{s}^{+}} via D_{s}^{+}→μ^{+}ν_{μ}

Using a 3.19  fb^{-1} data sample collected at an e^{+}e^{-} center-of-mass energy of E_{cm}=4.178  GeV with the BESIII detector, we measure the branching fraction of the leptonic decay D_{s}^{+}→μ^{+}ν_{μ} to be B_{D_{s}^{+}→μ^{+}ν_{μ}}=(5.49±0.16_{stat}±0.15_{syst})×10^{-3}. Combining our branching fraction with the masses of the D_{s}^{+} and μ^{+} and the lifetime of the D_{s}^{+}, we determine f_{D_{s}^{+}}|V_{cs}|=246.2±3.6_{stat}±3.5_{syst}  MeV. Using the c→s quark mixing matrix element |V_{cs}| determined from a global standard model fit, we evaluate the D_{s}^{+} decay constant f_{D_{s}^{+}}=252.9±3.7_{stat}±3.6_{syst}  MeV. Alternatively, using the value of f_{D_{s}^{+}} calculated by lattice quantum chromodynamics, we find |V_{cs}|=0.985±0.014_{stat}±0.014_{syst}. These values of B_{D_{s}^{+}→μ^{+}ν_{μ}}, f_{D_{s}^{+}}|V_{cs}|, f_{D_{s}^{+}} and |V_{cs}| are each the most precise results to date.

Cabibbo-Kobayashi-Maskawa-favored B decays to a scalar meson and a D meson

In this work, we attempt to study the Cabibbo-Kobayashi-Maskawa-favored [Formula: see text] ("S" denoting the scalar meson) decays within the perturbative QCD approach at the leading order and the leading power. Although the light scalar mesons are widely perceived as primarily the four-quark bound states, in practice it is hard for us to make quantitative predictions based on the four-quark picture for light scalars. Hence, we calculate the decays with light scalars in the two-quark model. For the decays with scalar mesons above 1 GeV, we have explored two possible scenarios, depending on whether the light scalars are treated as the lowest lying [Formula: see text] states or four-quark particles. In total, we calculated the branching fractions of 72 decay modes, and most of them are in the range [Formula: see text]-[Formula: see text], which are measurable in the on-going LHCb experiment and the forthcoming Belle-II experiment. Moreover, since in the standard model these decays occur only through tree operators and have no CP asymmetries, any deviation will be a signal of new physics beyond the standard model. Despite large uncertainties induced by nonperturbative parameters and corrections of high order and high power, our results and discussions will be useful for the on-going LHCb and the forthcoming Belle-II experiments.

Review of lattice results concerning low-energy particle physics: Flavour Lattice Averaging Group (FLAG)

We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the determination of the light-quark masses, the form factor [Formula: see text], arising in the semileptonic [Formula: see text] transition at zero momentum transfer, as well as the decay constant ratio [Formula: see text] and its consequences for the CKM matrix elements [Formula: see text] and [Formula: see text]. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of [Formula: see text] and [Formula: see text] Chiral Perturbation Theory. We review the determination of the [Formula: see text] parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. The latter quantities are an addition compared to the previous review. For the heavy-quark sector, we provide results for [Formula: see text] and [Formula: see text] (also new compared to the previous review), as well as those for D- and B-meson-decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. Finally, we review the status of lattice determinations of the strong coupling constant [Formula: see text].

Determination of |V(us)|| from a lattice QCD calculation of the K → πℓν semileptonic 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)|.

Study of X(3872) from effective field theory with pion-exchange interaction

We study DD[over ¯]* (D*D[over ¯]) scattering in the framework of unitarized heavy meson chiral perturbation theory with pion exchange and a contact interaction. 3S1-3D1 mixing effects are taken into account. A loosely bound state X(3872), with the pole position being Mpole}=(3871.70-i0.39)  MeV, is found. The result is not sensitive to the strength of the contact interaction. Our calculation provides a theoretical confirmation of the existence of the 1++ state X(3872). The light quark mass dependence of the pole position indicates it has a predominately DD[over ¯]* (D*D[over ¯]) molecular nature. When the π mass is larger than 142 MeV, the pole disappears, which makes impossible the lattice simulation of this state at large quark mass.

Leptonic-decay-constant ratio f(K+)/f(π+) from lattice QCD with physical light quarks

A calculation of the ratio of leptonic decay constants f(K+)/f(π+) makes possible a precise determination of the ratio of Cabibbo-Kobayashi-Maskawa (CKM) matrix elements |V(us)|/|V(ud)| in the standard model, and places a stringent constraint on the scale of new physics that would lead to deviations from unitarity in the first row of the CKM matrix. We compute f(K+)/f(π+) numerically in unquenched lattice QCD using gauge-field ensembles recently generated that include four flavors of dynamical quarks: up, down, strange, and charm. We analyze data at four lattice spacings a ≈ 0.06, 0.09, 0.12, and 0.15 fm with simulated pion masses down to the physical value 135 MeV. We obtain f(K+)/f(π+) = 1.1947(26)(37), where the errors are statistical and total systematic, respectively. This is our first physics result from our N(f) = 2+1+1 ensembles, and the first calculation of f(K+)/f(π+) from lattice-QCD simulations at the physical point. Our result is the most precise lattice-QCD determination of f(K+)/f(π+), with an error comparable to the current world average. When combined with experimental measurements of the leptonic branching fractions, it leads to a precise determination of |V(us)|/|V(ud)| = 0.2309(9)(4) where the errors are theoretical and experimental, respectively.

OPE, charm-quark mass, and decay constants of D and Ds mesons from QCD sum rules

We present a sum-rule extraction of the decay constants of the charmed mesons D and Ds from the two-point correlator of pseudoscalar currents. First, we compare the perturbative expansion for the correlator and the decay constant performed in terms of the pole and the running MS¯ masses of the charm quark. The perturbative expansion in terms of the pole mass shows no signs of convergence whereas reorganizing this very expansion in terms of the MS¯ mass leads to a distinct hierarchy of the perturbative expansion. Furthermore, the decay constants extracted from the pole-mass correlator turn out to be considerably smaller than those obtained by means of the MS¯-mass correlator. Second, making use of the OPE in terms of the MS¯ mass, we determine the decay constants of both D and Ds mesons with an emphasis on the uncertainties in these quantities related both to the input QCD parameters and to the limited accuracy of the method of sum rules.

Measurements of charged current lepton universality and |Vus| using tau lepton decays to e- ν(e) ν(τ), μ- ν(μ) ν(τ), π- ν(τ), and K- ν(τ)

Using 467  fb(-1) of e+e- annihilation data collected with the BABAR detector, we measure (B(τ- → μ- ν(μ) ν(τ)))/(B(τ- → e- ν(e) ν(τ))) =(0.9796±0.0016±0.0036), (B(τ- → π- ν(τ)))/(B(τ- → e- ν(e) ν(τ))) = (0.5945±0.0014±0.0061), and (B(τ- → K- ν(τ)))/(B(τ- → e- ν(e) ν(τ))) = (0.03882±0.00032±0.00057), where the uncertainties are statistical and systematic, respectively. From these precision τ measurements, we test the standard model assumption of μ-e and τ-μ charge current lepton universality and provide determinations of |Vus| experimentally independent of the decay of a kaon.

Precise charm to strange mass ratio and light quark masses from full lattice QCD

By using a single formalism to handle charm, strange, and light valence quarks in full lattice QCD for the first time, we are able to determine ratios of quark masses to 1%. For m(c)/m(s) we obtain 11.85(16), an order of magnitude more precise than the current PDG average. Combined with 1% determinations of the charm quark mass now possible this gives m(s)(2 GeV)=92.4(1.5) MeV. The MILC result for m(s)/m(l)=27.2(3) yields m(l)(2 GeV)=3.40(7) MeV for the average of u and d quark masses.

Prediction of the B{c}{*} mass in full lattice QCD

By using the highly improved staggered quark formalism to handle charm, strange, and light valence quarks in full lattice QCD, and NRQCD to handle bottom valence quarks, we are able to determine accurately ratios of the B meson vector-pseudoscalar mass splittings, in particular, [m(B{c}{*})-m(B{c})]/[m(B{s}{*})-m(B{s})]. We find this ratio to be 1.15(15), showing the "light" quark mass dependence of this splitting to be very small. Hence we predict m(B{c}{*})=6.330(7)(2)(6) GeV, where the first two errors are from the lattice calculation and the third from existing experiment. This is the most accurate prediction of a gold-plated hadron mass from lattice QCD to date.

Accumulating evidence for nonstandard leptonic decays of Ds mesons

The measured rate for D{s}{+}-->l+nu decays, where l is a muon or tau, is larger than the standard model prediction, which relies on lattice QCD, at the 3.8sigma level. We discuss how robust the theoretical prediction is, and we show that the discrepancy with experiment may be explained by a charged Higgs boson or a leptoquark.

Measurement of B(Ds{+}-->mu+nu(mu))

We present a measurement of the branching fraction B(D{s}{+}-->mu{+}nu{mu}) using a 548 fb{-1} data sample collected by the Belle experiment at the KEKB e{+}e{-} collider. The D{s} momentum is determined by reconstruction of the system recoiling against DKgammaX in events of the type e{+}e{-}-->D{s}{*}DKX, D{s}{*}-->D{s}gamma, where X represents additional pions or photons from fragmentation. This full-reconstruction method provides high resolution in the neutrino momentum and thus good background separation, equivalent to that achieved by experiments at the tau-charm factories. We obtain the branching fraction B(D{s}{+}-->mu{+}nu{mu})=[6.44+/-0.76(stat)+/-0.57(syst)]x10{-3}, implying a D{s} decay constant of f{D{s}}=[275+/-16(stat)+/-12(syst)] MeV.

Measurement of the absolute branching fraction of Ds+ --> tau+ nutau decay

Using a sample of tagged D(s)(+) decays collected near the D(s)(*+/-)D(s)(-/+) peak production energy in e(+)e(-) collisions with the CLEO-c detector, we study the leptonic decay D(s)(+)-->tau(+)nu(tau) via the decay channel tau(+)-->e(+)nu(e)nu(tau). We measure B(D(s)(+)-->tau(+)nu(tau))=(6.17+/-0.71+/-0.34)%, where the first error is statistical and the second systematic. Combining this result with our measurements of D(s)(+)-->mu(+)nu(mu) and D(s)(+)-->tau(+)nu(tau) (via tau(+)-->pi(+)nu(tau)), we determine f(D(s))=(274+/-10+/-5) MeV.