D→KlνD \rightarrow Kl{\nu} semileptonic decay using lattice QCD with HISQ at physical pion masses

The quark flavor sector of the Standard Model is a fertile ground to look for new physics effects through a unitarity test of the Cabbibo-Kobayashi-Maskawa (CKM) matrix. We present a lattice QCD calculation of the scalar and the vector form factors (over a large $q^2$ region including $q^2 = 0$) associated with the $D \rightarrow Kl{\nu}$ semi-leptonic decay. This calculation will then allow us to determine the central CKM matrix element, $V_{cs}$ in the Standard Model, by comparing the lattice QCD results for the form factors and the experimental decay rate. This form factor calculation has been performed on the $N_f =2+1+1$ MILC HISQ ensembles with the physical light quark masses.Comment: Proceedings for the 35th International Symposium on Lattice Field Theory (Lattice 2017), 8 pages, 5 figure

Precision tests of the standard model using lattice QCD

The Standard Model of particle physics successfully describes the fundamental particles and their interactions, but suffers from a few critical limitations which raise the intriguing possibility of new physics beyond it. My dissertation focuses on the study of the phenomenologically important quantities in the Standard Model, particularly, involving the high precision first principle calculations in the low-energy ($\sim1$GeV) regime of Quantum Chromodynamics (QCD), the $SU(3)$ component of the Standard Model. In this regime, since the QCD coupling becomes strong and the quarks and the gluons are confined to bound states called hadrons, a perturbative expansion in the coupling constant is not possible. However, the introduction of a four-dimensional Euclidean space-time lattice allows for an ab-initio treatment of QCD and provides a powerful tool - lattice QCD to study the low energy dynamics of the hadrons using numerical simulations. I have used existing methods of lattice QCD and developed new methods to study the pseudoscalar and the vector mesons (quark-antiquark hadrons) made of valence light (up and down), strange and charm quarks which are important final states in a number of decay processes that are studied in experiments and are sensitive to new physics. From the large time exponential behaviour of the meson correlators generated on lattice, I have extracted the masses and the decay constants (annihilation amplitude) of the mesons. My results include the most accurate lattice QCD calculation to date of the properties of the vector mesons $\phi$ and $\rho$. In lattice QCD calculations, the systematic uncertainty coming from the renormalisation constants relating the lattice results to the continuum results can be crucial and therefore has been determined precisely. Subsequently, we realised that our methods can also be extended to the calculation of the hadronic vacuum polarisation (HVP) contribution to the anomalous magnetic moment of the muon, $a_\mu$. The anomalous magnetic moment of the muon, shows a large discrepancy ($\sim3\sigma$) between theoretical and experimental results, putting the Standard Model to one of its most stringent tests. To complement the plans for a four-fold improvement in its experimental uncertainty, this project aims to improve the dominant contributions in the theoretical uncertainty coming from the hadronic vacuum polarisation to $\sim1\%$. I with my collaborators have developed a new lattice QCD method to calculate the HVP, making a significant progress over previous calculations by achieving an unprecedented precision ($\sim2\%$) in the HVP. The quark flavour sector of the Standard Model is also a fertile ground to test any new physics effect through the Unitarity test of the Cabbibo-Kobayashi-Maskawa (CKM) matrix. Therefore, my aim was to perform a lattice QCD calculation of the scalar and the vector form factors (over a large $q^2$ region including $q^2=0$) associated with the $D\rightarrow Kl\nu$ semi-leptonic decay. The central CKM matrix element, $V_{cs}$ in the Standard Model, is then calculated by comparing the lattice QCD results for the form factors and the experimental decay rate. For my research I have used publicly avalilable MILC HISQ configurations with dynamical up, down, strange and charm quarks. For most of my calculations I have used HISQ valence quarks except for the renormalisation of currents where for the comparison between different lattice formalisms I have also used the clover valence quarks

Estimate of the hadronic vacuum polarization disconnected contribution to the anomalous magnetic moment of the muon from lattice QCD

The quark-line disconnected diagram is a potentially important ingredient in lattice QCD calculations of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon. It is also a notoriously difficult one to evaluate. Here, for the first time, we give an estimate of this contribution based on lattice QCD results that have a statistically significant signal, albeit at one value of the lattice spacing and an unphysically heavy value of the u/d quark mass. We use HPQCD’s method of determining the anomalous magnetic moment by reconstructing the Adler function from time moments of the current-current correlator at zero spatial momentum. Our results lead to a total (including u, d and s quarks) quark-line disconnected contribution to aμ of −0.15% of the u/d hadronic vacuum polarization contribution with an uncertainty which is 1% of that contribution

Nonperturbative tests of the renormalization of mixed clover-staggered currents in lattice QCD

The Fermilab Lattice and MILC collaborations have shown in one-loop lattice QCD perturbation theory that the renormalization constants of vector and axial-vector mixed clover-asqtad currents are closely related to the product of those for clover-clover and asqtad-asqtad (local) vector currents. To be useful for future higher precision calculations this relationship must be valid beyond one-loop and very general. We test its validity nonperturbatively using clover and Highly Improved Staggered (HISQ) strange quarks, utilising the absolute normalization of the HISQ temporal axial current. We find that the renormalization of the mixed current differs from the square root of the product of the pure HISQ and pure clover currents by 2−3%. We also compare discretization errors between the clover and HISQ formalisms

Nonperturbative comparison of clover and highly improved staggered quarks in lattice QCD and the properties of the ϕ meson

We compare correlators for pseudoscalar and vector mesons made from valence strange quarks using the clover quark and highly improved staggered quark (HISQ) formalisms in full lattice QCD. We use fully nonperturbative methods to normalize vector and axial vector current operators made from HISQ quarks, clover quarks and from combining HISQ and clover fields. This allows us to test expectations for the renormalization factors based on perturbative QCD, with implications for the error budget of lattice QCD calculations of the matrix elements of clover-staggered b-light weak currents, as well as further HISQ calculations of the hadronic vacuum polarization.We also compare the approach to the (same) continuum limit in clover and HISQ formalisms for the mass and decay constant of the ϕ meson. Our final results for these parameters, using single-meson correlators and allowing an uncertainty for the neglect of quark-line disconnected diagrams are: Mϕ ¼ 1.023ð6Þ GeV and fϕ ¼ 0.238ð3Þ GeV in good agreement with experiment. The results come from calculations in the HISQ formalism using gluon fields that include the effect of u, d, s and c quarks in the sea with three lattice spacing values and mu=d values going down to the physical point

The hadronic vacuum polarization contribution to aμa_{\mu} from full lattice QCD

We determine the contribution to the anomalous magnetic moment of the muon from the $\alpha^2_{\mathrm{QED}}$ hadronic vacuum polarization diagram using full lattice QCD and including $u/d$ quarks with physical masses for the first time. We use gluon field configurations that include $u$, $d$, $s$ and $c$ quarks in the sea at multiple values of the lattice spacing, multiple $u/d$ masses and multiple volumes that allow us to include an analysis of finite-volume effects. We obtain a result for $a_{\mu}^{\mathrm{HVP,LO}}$ of $667(6)(12)$, where the first error is from the lattice calculation and the second includes systematic errors from missing QED and isospin-breaking effects and from quark-line disconnected diagrams. Our result implies a discrepancy between the experimental determination of $a_{\mu}$ and the Standard Model of 3$\sigma$.Comment: 14 pages, 10 figures. Discussion of method extended with additional tests and figures added. Typographical errors correcte

Higher-order hadronic-vacuum-polarization contribution to the muon g-2 from lattice QCD

We introduce a new method for calculating the ${\rm O}(\alpha^3)$ hadronic-vacuum-polarization contribution to the muon anomalous magnetic moment from ${ab-initio}$ lattice QCD. We first derive expressions suitable for computing the higher-order contributions either from the renormalized vacuum polarization function $\hat\Pi(q^2)$, or directly from the lattice vector-current correlator in Euclidean space. We then demonstrate the approach using previously-published results for the Taylor coefficients of $\hat\Pi(q^2)$ that were obtained on four-flavor QCD gauge-field configurations with physical light-quark masses. We obtain $10^{10} a_\mu^{\rm HVP,HO} = -9.3(1.3)$, in agreement with, but with a larger uncertainty than, determinations from $e^+e^- \to {\rm hadrons}$ data plus dispersion relations.Comment: Expanded and clarified discussion and revised Figure 4. Results unchanged. 11 pages, 5 tables, 5 figures. Version accepted to Physical Review