Semileptonic Form Factors Research Articles

B¯c susceptibilities from fully relativistic lattice QCD

We compute the h¯c (pseudo)scalar, (axial-)vector and (axial-)tensor susceptibilities as a function of u=mc/mh between u=mc/mb and u=0.8 using fully relativistic lattice QCD, employing nonperturbative current renormalization and using the second generation 2+1+1 MILC HISQ gluon field configurations. We include ensembles with a≈0.09, 0.06, 0.045, and 0.033 fm and we are able to reach the physical b-quark on the two finest ensembles. At the physical mh=mb point we find m¯b2χ1+=0.720(34)×10−2, m¯b2χ1−=1.161(54)×10−2, χ0−=2.374(33)×10−2, and χ0+=0.609(14)×10−2. Our results for the (pseudo)scalar, vector, and axial vector are compatible with the expected small size of nonperturbative effects at u=mc/mb. We also give the first nonperturbative determination of the tensor susceptibilities, finding m¯b2χT=0.891(44)×10−2 and m¯b2χAT=0.441(33)×10−2. Our value of m¯b2χAT is in good agreement with the O(αs) perturbation theory, while our result for m¯b2χT is in tension with the O(αs) perturbation theory at the level of 2σ. These results will allow for dispersively bounded parametrizations to be employed using lattice inputs for the full set of h→c semileptonic form factors in future calculations, for heavy-quark masses in the range 1.25×mc≤mh≤mb. Published by the American Physical Society 2024

B→D* and Bs→Ds* vector, axial-vector and tensor form factors for the full q2 range from lattice QCD

We compute the complete set of Standard Model (SM) and tensor B→D*ℓν¯ and Bs→Ds*ℓν¯ semileptonic form factors across the full kinematic range of the decays using second generation MILC nf=2+1+1 highly improved staggered quark (HISQ) gluon field configurations and HISQ valence quarks, with the method. Lattice spacings range from 0.09 to 0.044 fm with pion masses from ≈300 MeV down to the physical value and heavy quark masses ranging between ≈1.5mc and 4.1mc≈0.9mb; currents are normalized nonperturbatively. Using the recent untagged B→D*ℓν¯ℓ data from Belle and Bs→Ds*μν¯μ from LHCb together with our form factors, we determine a model independent value of Vcb=39.03(56)exp(67)latt×10−3, in agreement with previous exclusive determinations and in tension with the most recent inclusive result at the level of 3.6σ. We also observe a ≈1σ tension between the shape of the differential decay rates computed using our form factors and those measured by Belle. We compute a purely theoretical Standard Model value for the ratio of semitauonic and semimuonic decay rates, R(D*)=0.273(15), which we find to be closer to the recent Belle measurement and heavy flavor averaging group average than theory predictions using fits to experimental differential rate data for B→D*ℓν¯ℓ. Determining Vcb from our form factors and the experimental total rate for B→D*ℓν also gives a value in agreement with inclusive results. We also compute the longitudinal polarization fraction for the semitauonic mode, FLD*=0.395(24), which is in tension at the level of 2.2σ with the recent Belle measurement. Our calculation combines B→D* and Bs→Ds* lattice results in a simultaneous chiral continuum extrapolation, maintaining correlations between both modes. We then give results for both B→D* and Bs→Ds*, with the Bs→Ds* results superseding our previous lattice computation. We also give the chiral perturbation theory needed to analyze the tensor form factors. Published by the American Physical Society 2024

D(s)− mesons semileptonic form factors in four-flavor holographic QCD

We investigate semileptonic form factors of a D(s) meson from a modified soft-wall 4-flavor holographic model. The model successfully reproduces the masses and decay constants of various mesons, including ρ, K*, D*, Ds*, a1, K1, f1, D1, Ds1, π, K, η, D, and Ds. Moreover, we study the semileptonic decay processes D+→(π,K,η)l+νl and Ds+→(K,η)l+νl, associated with the vector meson exchange, as well as D(s)+→Kl+νl, associated with the vector and axial vector meson exchange. The form factors f+(q2) for D→π and D(s)→K decays agree excellently with experimental and lattice data, outperforming other theoretical approaches. The f+(q2) form factor for D+→η is compatible with experimental data, while a slight discrepancy is observed for Ds+→η at large q2. Additionally, we predict the vector form factors V(q2) and A1(q2) for D→K and Ds→K decays, respectively. The results agree well with other approaches and lattice data at maximum recoil (q2=0). Published by the American Physical Society 2024

Kaon semileptonic form factors at the physical quark masses on large volumes in Nf = 2 + 1 lattice QCD

We present our results for the kaon semileptonic form factors calculated by using two sets of the PACS10 configuration, whose physical volumes are more than (10 fm)4 at the physical light and strange quark masses in the Nf = 2+1 lattice QCD. The configurations were generated using the Iwasaki gauge action and Nf = 2 + 1 stout-smeared clover quark action. The form factors near zero momentum transfer q 2 can be calculated thanks to the large volume. Using our data, a q 2 interpolation and continuum extrapolation are carried out simultaneously. The value of |Vus | is determined using the result of the form factors at q 2 = 0 in the continuum limit. Our result of |Vus| is compared with the one determined from the CKM matrix unitarity and with those determined using recent lattice results.

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.

Exclusive determinations of vert V_{cb} vert and R(D^{*}) through unitarity

In this work we apply the Dispersive Matrix (DM) method of Di Carlo et al. (Phys Rev D 104:054502, 2021) and Martinelli et al. (Phys Rev D 105:034503, 2022) to the lattice computations of the Form Factors (FFs) entering the semileptonic B rightarrow D^* ell nu _ell decays, recently produced by the FNAL/MILC Collaborations (Fermilab Lattice, MILC collaboration, Semileptonic form factors for B rightarrow D^*ell nu at nonzero recoil from 2 + 1-flavor lattice QCD. arXiv:2105.14019) at small, but non-vanishing values of the recoil variable (w-1). Thanks to the DM method we obtain the FFs in the whole kinematical range accessible to the decay in a completely model-independent and non-perturbative way, implementing exactly both unitarity and kinematical constraints. Using our theoretical bands of the FFs we extract vert V_{cb} vert from the experimental data and compute the theoretical value of R(D^*). Our final result for vert V_{cb} vert reads vert V_{cb} vert = (41.3 pm 1.7) cdot 10^{-3}, compatible with the most recent inclusive estimate at the 0.5sigma level. Moreover, we obtain the pure theoretical value R(D^*) = 0.275 pm 0.008, which is compatible with the experimental world average at the sim 1.3 sigma level.

(Semi-) leptonic D(s) decays at BESIII

BESIII has collected 2.93fb−1 and 6.32fb−1 of e+e− collision data samples at the center-of-mass energies 3.773 and 4.178–4.226 GeV, respectively. We report recent measurements of the (semi-) leptonic decays Ds→ℓ+νℓ (ℓ=μ,τ) and D(s)→Xℓ+νℓ [X=η,K1(1270) or denotes generic decays, and ℓ=e,μ]. The decay constant fDs+, the semileptonic form factor f+η(0) and the CKM matrix elements |Vcd(s)| are determined precisely. These results are important to verify the theoretical calculations of fDs+ and f+η(0), and the unitarity of the CKM matrix. Precision tests of lepton-flavor universality with (semi-) leptonic D(s) decays are also performed.

Nonfactorizable charming loops in FCNC B decays versus B -decay semileptonic form factors

We compare a nonfactorizable charming-loop correction to an exclusive FCNC $B$ decay given in terms of the three-particle Bethe-Salpeter amplitude (3BS) of the $B$ meson, $⟨0|\overline{q}(x){G}_{\ensuremath{\mu}\ensuremath{\nu}}(z)b(0)|B(p)⟩$, with the corresponding correction to the $B$-meson semileptonic form factor. In spite of certain similarities, these two corrections are shown to have substantial differences: the form-factor correction is dominated by the collinear light-cone configuration of 3BS (${z}_{\ensuremath{\mu}}=u{x}_{\ensuremath{\mu}}$, $0<u<1$, ${x}^{2}=0$); in contrast, the FCNC amplitude is dominated by a different configuration with noncollinear arguments [${x}^{2}=0$, ${z}^{2}=0$, but $(x\ensuremath{-}z{)}^{2}\ensuremath{\ne}0$ (i.e., ${z}_{\ensuremath{\mu}}\ensuremath{\ne}u{x}_{\ensuremath{\mu}}$)].

Improvement of heavy-heavy and heavy-light currents with the Oktay-Kronfeld action

The Cabibbo-Kobayashi-Maskawa matrix elements $|{V}_{cb}|$ and $|{V}_{ub}|$ can be obtained by combining data from the experiments with lattice QCD results for the semileptonic form factors for the $\overline{B}\ensuremath{\rightarrow}{D}^{*}\ensuremath{\ell}\overline{\ensuremath{\nu}}$ and $\overline{B}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\ell}\overline{\ensuremath{\nu}}$ decays. It is highly desirable to use the Oktay-Kronfeld (OK) action for the form factor calculation on the lattice, since the OK action is designed to reduce the heavy quark discretization error down to the $\mathcal{O}({a}^{4}{\mathrm{\ensuremath{\Lambda}}}^{4})\ensuremath{\simeq}\mathcal{O}({\mathrm{\ensuremath{\Lambda}}}^{4}/(2{m}_{Q}{)}^{4})$ level in the power counting rules of the heavy quark effective theory (HQET). Here, we present a matching calculation to improve heavy-heavy and heavy-light currents up to the ${\ensuremath{\lambda}}^{3}$ order in HQET, the same level of improvement as the OK action. Our final results for the improved currents are being used in a lattice QCD calculation of the semileptonic form factors for the $\overline{B}\ensuremath{\rightarrow}{D}^{*}\ensuremath{\ell}\overline{\ensuremath{\nu}}$ and $\overline{B}\ensuremath{\rightarrow}D\ensuremath{\ell}\overline{\ensuremath{\nu}}$ decays.

Latest results on rare kaon decays from the NA48/2 experiment @CERN

The NA48/2 experiment at CERN reports the first observation of the [Formula: see text] decay from an exposure of [Formula: see text] charged kaon decays recorded in 2003–2004. A sample of 4919 candidates with 4.9% background contamination allows the determination of the branching ratio in the full kinematic region. The study of the kinematic space shows evidence for a structure-dependent contribution in agreement with predictions based on chiral perturbation theory. Several [Formula: see text]- and [Formula: see text]-violating asymmetries are also evaluated. The most precise measurement of the charged kaon semi-leptonic form factors obtained by NA48/2 with 4.4 million [Formula: see text] and 2.3 million [Formula: see text] events collected in 2004 will also be presented.

Semileptonic decays of heavy mesons with artificial neural networks

Experimental checks of the second row unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix involve extractions of the matrix element $V_{cd}$, which may be obtained from semileptonic decay rates of $D$ to $\pi$. These decay rates are proportional to hadronic form factors which parameterize how the quark $c \to d$ transition is realized in $D \to \pi$ meson decays. The form factors can not yet be analytically computed over the whole range of available momentum transfer $q^2$, but can be parameterized with a varying degree of model dependency. We propose using artificial neural networks trained from experimental pseudo-data to predict the shape of these form factors with a prescribed uncertainty. We comment on the parameters of several commonly-used model parameterizations of semileptonic form factors. We extract shape parameters and use unitarity to bound the form factor at a given $q^2$, which then allows us to bound the CKM matrix element $|V_{cd}|$.

Charged Kaons semi-leptonic form factors from NA48/2

The NA48/2 experiment collected unprecedent statistics of charged kaon decays in 2003 and 2004. The main purpose of the experiment was to measure direct CP violation in kaon decays to three pions while an extensive physics program was carried out together with the main goal. The huge statistics collected allowed to test with a high accuracy the predictions of low energy QCD theories in several charged kaon decay processes. The precise measurement of the charged kaon semileptonic form factors are reported here, based on data collected in 2004 with a dedicated minimum bias trigger.

Recent QCD results from NA48/2

In 2003 and 2004, the NA48/2 experiment collected an unprecedented statistics of charged kaon decays to measure the CP violation in three pions. An additional extensive physics program has been carried out. In particular, it was possible to verify the predictions of low energy QCD in several processes, with high precision. In this paper we present the precise measurement of the charged kaon semileptonic form factors (FF) and the first observation of the K+ → π+π0e+e− decay. The semileptonic FF are measured on the sample collected in 2004 in a dedicated minimum bias run, to overcome the limitation imposed by the 3 pions triggers, while the first observation of the K+ → π+π0e+e− decay is based on the full sample of data collected in two years.

Recent NA48/2 results on rare kaon decays

NA48/2 results contributing to ChPT testing are presented. A sample of 1663 events of the rare decay $ K^ \pm \to \mu ^ \pm ve^ + e^ - $ has been selected with a minimume+e−effective mass of 140 MeV. The measured model independent decay rate is in agreement with ChPT predictions. The branching ratio of the $ K^ \pm \to \mu ^ \pm ve^ + e^ - $ decay, never observed so far, has been obtained from a sample of about 5000 candidates with less than 6% background, also in agreement with ChPT predictions. In addition, a most precise measurement of the charged kaon semileptonic formfactors has been obtained from 4.4 millionKe3and 2.3 millionKµ3events collected in 2004.

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).

D meson semileptonic form factors in Nf = 3 QCD with Möbius domain-wall quarks

e present our calculation of D → π and D → K semileptonic form factors in Nf = 2 + 1 lattice QCD. We simulate three lattice cutoffs a-1 ≃ 2.5, 3.6 and 4.5 GeV with pion masses as low as 230 MeV. The Möbius domain-wall action is employed for both light and charm quarks. We present our results for the vector and scalar form factors and discuss their dependence on the lattice spacing, light quark masses and momentum transfer.

HQET form factors for Bs → Klv decays beyond leading order

We compute semi-leptonic Bs decay form factors using Heavy Quark Effective Theory on the lattice. To obtain good control of the 1 /mb expansion, one has to take into account not only the leading static order but also the terms arising at O (1/mb): kinetic, spin and current insertions. We show results for these terms calculated through the ratio method, using our prior results for the static order. After combining them with non-perturbative HQET parameters they can be continuum-extrapolated to give the QCD form factor correct up to O (1/[see formula in PDF]) corrections and without O (αs(mb)n) corrections.

Improvement of heavy-heavy current for calculation of B̅ → D(*)lv̅ form factors using Oktay-Kronfeld heavy quarks

The CKM matrix element |Vcb| can be extracted by combining data from experiments with lattice QCD results for the semileptonic form factors for the B̅ → D(*)lv̅ decays. The Oktay-Kronfeld (OK) action was designed to reduce heavy-quark discretization errors to below 1%, or through O(λ3) in HQET power counting. Here we describe recent progress on bottom-to-charm currents improved to the same order in HQET as the OK action, and correct formerly reported results of our matching calculations, in which the operator basis was incomplete.

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.

The B(s) → D(s)lv Decay with Highly Improved Staggered Quarks and NRQCD

We report on progress of a lattice QCD calculation of the B → Dlv and Bs → Dslv semileptonic form factors. We use a relativistic staggered action (HISQ) for light and charm quarks, and an improved non-relativistic (NRQCD) action for bottom, on the second generation MILC ensembles.