arXiv subjects

Rajan Gupta

Publications and source records attributed to Rajan Gupta.

At least 73 records · Page 4Linked to original sources

arXiv2019

Axial Vector Form Factors from Lattice QCD that Satisfy the PCAC Relation

Previous lattice QCD calculations of axial vector and pseudoscalar form factors show significant deviation from the partially conserved axial current (PCAC) relation between them. Since the original correlation functions satisfy PCAC, the observed deviations from the operator identity cast doubt on whether all the systematics in the extraction of form factors from the correlation functions are under control. We identify the problematic systematic as a missed excited state, whose energy as a function of the momentum transfer squared, $Q^2$, is determined from the analysis of the 3-point functions themselves. Its mass is much smaller than those of the excited states previously considered and including it impacts the extraction of all the ground state matrix elements. The form factors extracted using these mass/energy gaps satisfy PCAC and other consistency conditions, and validate the pion-pole dominance hypothesis. We also show that the extraction of the axial charge $g_A$ is very sensitive to the value of the mass gaps of the excited states used and current lattice data do not provide an unambiguous determination of these, unlike the $Q^2 \neq 0$ case. To highlight the differences and improvement between the conventional versus the new analysis strategy, we present a comparison of results obtained on a physical pion mass ensemble at $a\approx 0.0871\,\mathrm{fm}$. With the new strategy, we find $g_A = 1.30(6)$. A very significant improvement over previous lattice results is found for the axial charge radius $r_A = 0.74(6)\,\mathrm{fm}$, extracted using the $z$-expansion to parameterize the $Q^2$ behavior of $G_A(Q^2)$, and $g_P^\ast = 8.06(44)$ obtained using the pion pole-dominance ansatz to fit the $Q^2$ behavior of the induced pseudoscalar form factor $\widetilde{G}_P(Q^2)$.

hep-lat↗

arXiv2019

Machine Learning Estimators for Lattice QCD Observables

A novel technique using machine learning (ML) to reduce the computational cost of evaluating lattice quantum chromodynamics (QCD) observables is presented. The ML is trained on a subset of background gauge field configurations, called the labeled set, to predict an observable $O$ from the values of correlated, but less compute-intensive, observables $\mathbf{X}$ calculated on the full sample. By using a second subset, also part of the labeled set, we estimate the bias in the result predicted by the trained ML algorithm. A reduction in the computational cost by about $7\%-38\%$ is demonstrated for two different lattice QCD calculations using the Boosted decision tree regression ML algorithm: (1) prediction of the nucleon three-point correlation functions that yield isovector charges from the two-point correlation functions, and (2) prediction of the phase acquired by the neutron mass when a small Charge-Parity (CP) violating interaction, the quark chromoelectric dipole moment interaction, is added to QCD, again from the two-point correlation functions calculated without CP violation.

hep-lat↗

arXiv2019

Nucleon Electromagnetic Form Factors in the Continuum Limit from 2+1+1-flavor Lattice QCD

Results are presented for the nucleon isovector electromagnetic form factors using 11 ensembles generated by the MILC collaboration using the 2+1+1-flavors HISQ action. They span 4 lattice spacings $a \sim$ 0.06, 0.09, 0.12 and 0.15~fm and 3 values of $M_π\sim 135, 225$ and 315 MeV. High-statistics estimates are used to perform a simultaneous extrapolation in the lattice spacing, lattice volume and light-quark masses. The $Q^2$ dependence over the range 0.05-1.4 ${\rm GeV}^2$ is investigated using both the $z$-expansion and the dipole form. Final $z$-expansion estimates for the isovector r.m.s. radius are $r_E = 0.769(27)(30)$ fm $r_M = 0.671(48)(76)$ fm and $μ^{p-n} = 3.939(86)(138)$ Bohr magneton. The first error is the combined uncertainty from the leading-order analysis, and the second is an estimate of the additional uncertainty due to using the leading order chiral-continuum-finite-volume fits. The dipole estimates, $r_E = 0.765(11)(8)$ fm, $r_M = 0.704(21)(29)$ fm and $μ^{p-n} = 3.975(84)(125)$, are consistent with those from the $z$-expansion but with smaller errors. Our analysis highlights three points. First, all data from the eleven ensembles and existing lattice data on, or close to, physical mass ensembles from other collaborations collapses more clearly onto a single curve when plotted versus $Q^2/M_N^2$ as compared to $Q^2$ with the scale set by quantities other than $M_N$. The difference between these two analyses is indicative of discretization errors, some of which presumably cancel when the data are plotted versus $Q^2/M_N^2$. Second, the size of the remaining deviation of this common curve from the Kelly curve is small and can be accounted for by statistical and possible systematic uncertainties. Third, to improve lattice estimates, high statistics data for $Q^2 < 0.1$ ${\rm GeV}^2$ are needed.

hep-lat↗

arXiv2019

Lattice QCD and Neutrino-Nucleus Scattering

This document is one of a series of whitepapers from the USQCD collaboration. Here, we discuss opportunities for lattice QCD in neutrino-oscillation physics, which inevitably entails nucleon and nuclear structure. In addition to discussing pertinent lattice-QCD calculations of nucleon and nuclear matrix elements, the interplay with models of nuclei is discussed. This program of lattice- QCD calculations is relevant to current and upcoming neutrino experiments, becoming increasingly important on the timescale of LBNF/DUNE and HyperK.

hep-lat↗

arXiv2019

Lattice QCD calculations of the quark and gluon contributions to the proton spin

A review of the calculations of the proton's spin using lattice QCD is presented. Results for the three contributions, the quark contribution $\sum_{q=u,d,s,c} (\frac{1}{2} {Δq})$, the total angular momentum of the quarks $J_q$ and of the gluons $J_g$, and the orbital angular momentum of the quarks are discussed. The best measured is the the quark contribution $\sum_{q=u,d,s,c} (\frac{1}{2} {Δq})$, and its analysis is used to discuss the relative merits of calculations by the PNDME, ETMC and $χ$QCD collaborations and the level of control over systematic errors achieved in each. The result by the PNMDE collaboration, $\sum_{q=u,d,s} \left[ \frac{1}{2} {Δq} \right] = 0.143(31)(36) $, is consistent with the COMPASS analysis $0.13 < \frac{1}{2} ΔΣ< 0.18$. Results for $J_q$ and $J_g$ by the ETMC collaborations are also consistent with phenomenology. Lastly, I review first results from the LHPC collaboration for the calculation of the orbital angular momentum of the quarks. With much larger computing resources anticipated over the next five years, high precision results for all three will become available and provide a detailed description of their relative contributions to the nucleon spin.

hep-lat↗

arXiv2019

Present and future prospects for lattice QCD calculations of matrix elements for nEDM

A status report on the calculations of the contribution of four CP violating operators, the $Θ$-term, the quark EDM, the chromo EDM and the Weinberg operator to the neutron EDM are presented. At this time, there exit precise physical results only for the quark EDM operator by the PNDME collaboration. First results showing signal in the contributions of the $Θ$-term and the connected part of the chromo EDM operator have been presented. The challenge of divergent mixing in the chromo EDM and Weinberg operators has motivated calculations in the gradient flow scheme. While there has been steady progress, the challenges remaining are large. Results with $O(50\%)$ uncertainty with control over all systematic errors can be expected for the $Θ$-term over the next five years. Prediction of a timeline for progress on the chromo EDM and the Weinberg operators will depend on when the renormalization and divergent mixing of these operators is brought under control. The most optimistic scenario is that the gradient flow scheme provides a solution to the numerical signal and mixing problems for both the gluonic and quark operators.

hep-lat↗

arXiv2018

Updates on Nucleon Form Factors from Clover-on-HISQ Lattice Formulation

Updates on results for the electric, magnetic and axial vector form factors are presented. The data analyzed cover high statistics measurements on 11 ensembles generated with 2+1+1 flavors of HISQ fermions by the MILC collaboration. The data cover the range $0.057\;\mathrm{fm} < a < 0.15\;\mathrm{fm}$ in lattice spacing, $135\;\mathrm{MeV} < M_π< 320\;\mathrm{MeV}$ in the pion mass and $3.3 < M_πL < 5.5 $ in the lattice size. Fits to control excited-state contamination use up to 3-states in the spectral decomposition of the 3-point functions. The simultaneous chiral-continuum-finite-volume fits include leading order corrections in each of the three variables.

hep-lat↗

arXiv2018

Update on $B\to D^\ast \ell ν$ form factor at zero-recoil using the Oktay-Kronfeld action

We present an update on the calculation of $\bar{B}\to D^\ast \ell \barν$ semileptonic form factor at zero recoil using the Oktay-Kronfeld bottom and charm quarks on $N_f=2+1+1$ flavor HISQ ensembles generated by the MILC collaboration. Preliminary results are given for two ensembles with $a\approx 0.12$ and $0.09$ fm and $M_π\approx 310$ MeV. Calculations have been done with a number of valence quark masses, and the dependence of the form factor on them is investigated on the $a\approx 0.12$ fm ensemble. The excited state is controlled by using multistate fits to the three-point correlators measured at 4--6 source-sink separations.

hep-lat↗

arXiv2018

Neutron Electric Dipole Moment from Beyond the Standard Model

We present an update on our calculations of the matrix elements of the CP violating quark and gluon chromo-EDM operators, as well as the operators these mix with, such as the QCD Theta-term. Their contribution to the neutron EDM is obtained by extrapolating the $F_3$ form factor of a vector current to zero momentum transfer. The calculation is being done using valence Wilson-clover quarks on HISQ background configurations generated by the MILC collaboration.

hep-lat↗

arXiv2018

Isovector and flavor diagonal charges of the nucleon from 2+1+1 flavor QCD

We present high-statistics results for the isovector and flavor diagonal charges of the proton using 11 ensembles of 2+1+1 flavor HISQ fermions. In the isospin symmetric limit, results for the neutron are given by the $u \leftrightarrow d$ interchange. A chiral-continuum fit with leading order corrections was made to extract the connected and disconnected contributions in the continuum limit and at $M_π=135$ MeV. All results are given in the $\overline{MS}$ scheme at 2 GeV. The isovector charges, $g_A^{u-d} = 1.218(25)(30)$, $g_S^{u-d} = 1.022(80)(60) $ and $g_T^{u-d} = 0.989(32)(10)$, are used to obtain low-energy constraints on novel scalar and tensor interactions, $ε_{S}$ and $ε_{T}$, at the TeV scale. The flavor diagonal axial charges are: $g_A^u \equiv Δu \equiv \langle 1 \rangle_{Δu^+} = 0.777(25)(30)$, $g_A^d \equiv Δd \equiv \langle 1 \rangle_{Δd^+} = -0.438(18)(30)$, and $g_A^s \equiv Δs \equiv \langle 1 \rangle_{Δs^+} = -0.053(8)$. Their sum gives the total quark contribution to the proton spin, $\sum_{q=u,d,s} (\frac{1}{2} Δq) = 0.143(31)(36)$. This result is in good agreement with the recent COMPASS analysis $0.13 < \frac{1}{2} ΔΣ< 0.18$. Implications of results for the flavor diagonal tensor charges, $g_T^u = 0.784(28)(10)$, $g_T^d = -0.204(11)(10)$ and $g_T^s = -0.0027(16)$ for constraining the quark electric dipole moments and their contributions to the neutron electric dipole moment are discussed. These flavor diagonal charges also give the strength of the interaction of dark matter with nucleons via axial and tensor mediators.

hep-lat↗

arXiv2018

Isovector Charges of the Nucleon from 2+1+1-flavor Lattice QCD

We present high statistics results for the isovector charges $g^{u-d}_A$, $g^{u-d}_S$ and $g^{u-d}_T$ of the nucleon. Calculations were carried out on eleven ensembles of gauge configurations generated by the MILC collaboration using highly improved staggered quarks (HISQ) action with 2+1+1 dynamical flavors. These ensembles span four lattice spacings $a \approx$ 0.06, 0.09, 0.12 and 0.15 fm and light-quark masses corresponding to $M_π\approx$ 135, 225 and 315 MeV. Excited-state contamination in the nucleon 3-point correlation functions is controlled by including up to three-states in the spectral decomposition. Remaining systematic uncertainties associated with lattice discretization, lattice volume and light-quark masses are controlled using a simultaneous fit in these three variables. Our final estimates of the isovector charges in the $\overline{\text{MS}}$ scheme at 2 GeV are $g_A^{u-d} = 1.218(25)(30)$, $g_S^{u-d} = 1.022(80)(60) $ and $g_T^{u-d} = 0.989(32)(10)$. The first error includes statistical and all systematic uncertainties except that due to the extrapolation ansatz, which is given by the second error estimate. We provide a detailed comparison with the recent result of $g_A^{u-d} = 1.271(13)$ by the CalLat collaboration and argue that our error estimate is more realistic. Combining our estimate for $g_S^{u-d}$ with the difference of light quarks masses $(m_d-m_u)^{\rm QCD}=2.572(66)$ MeV given by the MILC/Fermilab/TUMQCD collaboration for 2+1+1-flavor theory, we obtain $(M_N-M_P)^{\rm QCD} = 2.63(27)$ MeV. We update the low-energy constraints on novel scalar and tensor interactions, $ε_{S}$ and $ε_{T}$, at the TeV scale by combining our new estimates for $g^{u-d}_S$ and $g^{u-d}_T$ with precision low-energy nuclear experiments, and find them comparable to those from the ATLAS and the CMS experiments at the LHC.

hep-lat↗

arXiv2018

Flavor diagonal tensor charges of the nucleon from 2+1+1 flavor lattice QCD

We present state-of-the-art results for the matrix elements of flavor diagonal tensor operators within the nucleon state. The calculation of the dominant connected contribution is done using eleven ensembles of gauge configurations generated by the MILC Collaboration using the highly improved staggered quark (HISQ) action with 2+1+1 dynamical flavors. The calculation of the disconnected contributions is done using seven (six) ensembles for the strange (light) quarks. These high-statistics simulations allowed us to address various systematic uncertainties. A simultaneous fit in the lattice spacing and the light-quark mass is used to extract the tensor charges in the continuum limit and at $M_π=135$ MeV. Results for the proton in the $\overline{MS}$ scheme at 2~GeV are: $g_T^u = 0.784(28)(10)$, $g_T^d = -0.204(11)(10)$ and $g_T^s = -0.0027(16)$. Implications of these results for constraining the quark electric dipole moments and their contributions to the neutron electric dipole moment are discussed.

hep-lat↗

arXiv2018

Quark contribution to the proton spin from 2+1+1-flavor lattice QCD

We present the first chiral-continuum extrapolated up, down and strange quark spin contribution to the proton spin using lattice QCD. For the connected contributions, we use eleven ensembles of 2+1+1-flavor of Highly Improved Staggered Quarks (HISQ) generated by the MILC Collaboration. They cover four lattice spacings $a \approx \{0.15,0.12,0.09,0.06\}$ fm and three pion masses, $M_π\approx \{315,220,135\}$ MeV, of which two are at the physical pion mass. The disconnected strange calculations are done on seven of these ensembles, covering the four lattice spacings but only one with the physical pion mass. The disconnected light quark calculation was done on six ensembles at two values of $M_π\approx \{315,220\}$ MeV. High-statistics estimates on each ensemble for all three quantities allow us to quantify systematic uncertainties and perform a simultaneous chiral-continuum extrapolation in the lattice spacing and the light-quark mass. Our final results are $Δu \equiv \langle 1 \rangle_{Δu^+} = 0.777(25)(30)$, $Δd \equiv \langle 1 \rangle_{Δd^+} = -0.438(18)(30)$, and $Δs \equiv \langle 1 \rangle_{Δs^+} = -0.053(8)$, adding up to a total quark contribution to proton spin of $\sum_{q=u,d,s} (\frac{1}{2} Δq) = 0.143(31)(36)$. The second error is the systematic uncertainty associated with the chiral-continuum extrapolation. These results are obtained without model assumptions and are in good agreement with the recent COMPASS analysis $0.13 < \frac{1}{2} ΔΣ< 0.18$, and with the $Δq$ obtained from various global analyses of polarized beam or target data.

hep-lat↗

arXiv2018

Parton distributions and lattice QCD calculations: a community white paper

In the framework of quantum chromodynamics (QCD), parton distribution functions (PDFs) quantify how the momentum and spin of a hadron are divided among its quark and gluon constituents. Two main approaches exist to determine PDFs. The first approach, based on QCD factorization theorems, realizes a QCD analysis of a suitable set of hard-scattering measurements, often using a variety of hadronic observables. The second approach, based on first-principle operator definitions of PDFs, uses lattice QCD to compute directly some PDF-related quantities, such as their moments. Motivated by recent progress in both approaches, in this document we present an overview of lattice-QCD and global-analysis techniques used to determine unpolarized and polarized proton PDFs and their moments. We provide benchmark numbers to validate present and future lattice-QCD calculations and we illustrate how they could be used to reduce the PDF uncertainties in current unpolarized and polarized global analyses. This document represents a first step towards establishing a common language between the two communities, to foster dialogue and to further improve our knowledge of PDFs.

hep-ph↗

arXiv2018

Isovector and flavor-diagonal charges of the nucleon

We present an update on the status of the calculations of isovector and flavor-diagonal charges of the nucleon. The calculations of the isovector charges are being done using ten $2+1+1$-flavor HISQ ensembles generated by the MILC collaboration covering the range of lattice spacings $a \approx$ 0.12, 0.09, 0.06 fm and pion masses $M_π\approx$ 310, 220, 130 MeV. Excited-states contamination is controlled by using four-state fits to two-point correlators and three-states fits to the three-point correlators. The calculations of the disconnected diagrams needed to estimate flavor-diagonal charges are being done on a subset of six ensembles using the stocastic method. Final results are obtained using a simultaneous fit in $M_π^2$, the lattice spacing $a$ and the finite volume parameter $M_πL$ keeping only the leading order corrections.

hep-lat↗

arXiv2018

Nucleon Axial and Electromagnetic Form Factors

We present results for the isovector axial, induced pseudoscalar, electric, and magnetic form factors of the nucleon. The calculations were done using $2+1+1$-flavor HISQ ensembles generated by the MILC collaboration with lattice spacings $a \approx$ 0.12, 0.09, 0.06$\mathrm{fm}$ and pion masses $M_π\approx$ 310, 220, 130$\mathrm{MeV}$. Excited-states contamination is controlled by using four-state fits to two-point correlators and by comparing two- versus three-states in three-point correlators. The $Q^2$ behavior is analyzed using the model independent z-expansion and the dipole ansatz. Final results for the charge radii and magnetic moment are obtained using a simultaneous fit in $M_π$, lattice spacing $a$ and finite volume.

hep-lat↗

arXiv2017

Neutron Electric Dipole Moment on the Lattice

For the neutron to have an electric dipole moment (EDM), the theory of nature must have T, or equivalently CP, violation. Neutron EDM is a very good probe of novel CP violation in beyond the standard model physics. To leverage the connection between measured neutron EDM and novel mechanism of CP violation, one requires the calculation of matrix elements for CP violating operators, for which lattice QCD provides a first principle method. In this paper, we review the status of recent lattice QCD calculations of the contributions of the QCD $Θ$-term, the quark EDM term, and the quark chromo-EDM term to the neutron EDM.

hep-lat↗

arXiv2017

Calculation of $\bar B \rightarrow D^\ast \ell \bar ν$ form factor at zero recoil using the Oktay-Kronfeld action

We present the first preliminary results for the semileptonic form factor $h_{A_1}(w=1)/ρ_{A_j}$ at zero recoil for the $\bar B \rightarrow D^\ast \ell \bar ν$ 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.

hep-lat↗