arXiv subjects

Rajan Gupta

Publications and source records attributed to Rajan Gupta.

At least 91 records · Page 5Linked to original sources

arXiv2017

Axial Vector Form Factors of the Nucleon from Lattice QCD

We present results for the form factors of the isovector axial vector current in the nucleon state using large scale simulations of lattice QCD. The calculations were done using eight ensembles of gauge configurations generated by the MILC collaboration using the HISQ action with 2+1+1 dynamical flavors. These ensembles span three lattice spacings $a \approx 0.06, 0.09$ and $0.12$ fm and light-quark masses corresponding to the pion masses $M_π\approx 135, 225$ and $310$ MeV. High-statistics estimates allow us to quantify systematic uncertainties in the extraction of $G_A(Q^2)$ and the induced pseudoscalar form factor $\tilde{G}_P(Q^2)$. We perform a simultaneous extrapolation in the lattice spacing, lattice volume and light-quark masses of the axial charge radius $r_A$ data to obtain physical estimates. Using the dipole ansatz to fit the $Q^2$ behavior we obtain $r_A|_{\rm dipole} = 0.49(3)$ fm, which corresponds to ${\cal M}_A = 1.39(9)$ GeV, and is consistent with ${\cal M}_A = 1.35(17)$ GeV obtained by the miniBooNE collaboration. The estimate obtained using the $z$-expansion is $r_A|_{z-{\rm expansion}} = 0.46(6)$ fm, and the combined result is $r_A|_{\rm combined} = 0.48(4)$ fm. Analysis of the induced pseudoscalar form factor $\tilde{G}_P(Q^2)$ yields low estimates for $g_P^\ast$ and $g_{π{\rm NN}}$ compared to their phenomenological values. To understand these, we analyze the partially conserved axial current (PCAC) relation by also calculating the pseudoscalar form factor. We find that these low values are due to large deviations in the PCAC relation between the three form factors and from the pion-pole dominance hypothesis.

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arXiv2017

Nucleon Transverse Momentum-dependent Parton Distributions in Lattice QCD: Renormalization Patterns and Discretization Effects

Lattice QCD calculations of transverse momentum-dependent parton distribution functions (TMDs) in nucleons are presented, based on the evaluation of nucleon matrix elements of quark bilocal operators with a staple-shaped gauge connection. Both time-reversal odd effects, namely, the generalized Sivers and Boer-Mulders transverse momentum shifts, as well as time-reversal even effects, namely, the generalized transversity and one of the generalized worm-gear shifts are studied. Results are obtained on two different $n_f = 2+1$ flavor ensembles with approximately matching pion masses but very different discretization schemes: domain-wall fermions (DWF) with lattice spacing $a=0.084$ fm and pion mass 297 MeV, and Wilson-clover fermions with $a=0.114$ fm and pion mass 317 MeV. Comparison of the results on the two ensembles yields insight into the length scales at which lattice discretization errors are small, and into the extent to which the renormalization pattern obeyed by the continuum QCD TMD operator continues to apply in the lattice formulation. For the studied TMD observables, the results are found to be consistent between the two ensembles at sufficiently large separation of the quark fields within the operator, whereas deviations are observed in the local limit and in the case of a straight link gauge connection, which is relevant to the studies of parton distribution functions. Furthermore, the lattice estimates of the generalized Sivers shift obtained here are confronted with, and are seen to tend towards, a phenomenological estimate extracted from experimental data.

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arXiv2017

Nucleon Charges from 2+1+1-flavor HISQ and 2+1-flavor clover lattices

Precise estimates of the nucleon charges $g_A$, $g_S$ and $g_T$ are needed in many phenomenological analyses of SM and BSM physics. In this talk, we present results from two sets of calculations using clover fermions on 9 ensembles of 2+1+1-flavor HISQ and 4 ensembles of 2+1-flavor clover lattices. We show that high statistics can be obtained cost-effectively using the truncated solver method with bias correction and the coherent source sequential propagator technique. By performing simulations at 4--5 values of the source-sink separation $t_{\rm sep}$, we demonstrate control over excited-state contamination using 2- and 3-state fits. Using the high-precision 2+1+1-flavor data, we perform a simultaneous fit in $a$, $M_π$ and $M_πL$ to obtain our final results for the charges.

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arXiv2017

Isovector charges of the nucleon from 2+1-flavor QCD with clover fermions

We present high-statistics estimates of the isovector charges of the nucleon from four 2+1-flavor ensembles generated using Wilson-clover fermions with stout smearing and tree-level tadpole improved Symanzik gauge action at lattice spacings $a=0.114$ and $0.080$ fm and with $M_π\approx 315$ and 200 MeV. The truncated solver method with bias correction and the coherent source sequential propagator construction are used to cost-effectively achieve $O(10^5)$ measurements on each ensemble. Using these data, the analysis of two-point correlation functions is extended to include four states in the fits and of three-point functions to three states. Control over excited-state contamination in the calculation of the nucleon mass, the mass gaps between excited states, and in the matrix elements is demonstrated by the consistency of estimates using this multistate analysis of the spectral decomposition of the correlation functions and from simulations of the three-point functions at multiple values of the source-sink separation. The results for all three charges, $g_A$, $g_S$ and $g_T$, are in good agreement with calculations done using the clover-on-HISQ lattice formulation with similar values of the lattice parameters.

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arXiv2017

The Contribution of Novel CP Violating Operators to the nEDM using Lattice QCD

In this talk, we motivate the calculation of the matrix elements of novel CP violating operators, the quark EDM and the quark chromo EDM operators, within the nucleon state using lattice QCD. These matrix elements, combined with the bound on the neutron EDM, would provide stringent constraints on beyond the standard model physics, especially as the next generation of neutron EDM experiments reduce the current bound. We then present our lattice strategy for the calculation of these matrix elements, in particular we describe the use of the Schrödinger source method to reduce the calculation of the 4-point to 3-point functions needed to evaluate the quark chromo EDM contribution. We end with a status report on the quality of the signal obtained in the lattice calculations of the connected contributions to the quark chromo EDM operator and the pseudoscalar operator it mixes with under renormalization.

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arXiv2017

Controlling Excited-State Contamination in Nucleon Matrix Elements

We present a detailed analysis of methods to reduce statistical errors and excited-state contamination in the calculation of matrix elements of quark bilinear operators in nucleon states. All the calculations were done on a 2+1 flavor ensemble with lattices of size $32^3 \times 64$ generated using the rational hybrid Monte Carlo algorithm at $a=0.081$~fm and with $M_π=312$ MeV. The statistical precision of the data is improved using the all-mode-averaging method. We compare two methods for reducing excited-state contamination: a variational analysis and a two-state fit to data at multiple values of the source-sink separation $t_{\rm sep}$. We show that both methods can be tuned to significantly reduce excited-state contamination and discuss their relative advantages and cost-effectiveness. A detailed analysis of the size of source smearing used in the calculation of quark propagators and the range of values of $t_{\rm sep}$ needed to demonstrate convergence of the isovector charges of the nucleon to the $t_{\rm sep} \to \infty $ estimates is presented.

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arXiv2017

Axial, Scalar and Tensor Charges of the Nucleon from 2+1+1-flavor Lattice QCD

We present results for the isovector axial, scalar and tensor charges $g^{u-d}_A$, $g^{u-d}_S$ and $g^{u-d}_T$ of the nucleon needed to probe the Standard Model and novel physics. The axial charge is a fundamental parameter describing the weak interactions of nucleons. The scalar and tensor charges probe novel interactions at the TeV scale in neutron and nuclear $β$-decays, and the flavor-diagonal tensor charges $g^{u}_T$, $g^{d}_T$ and $g^{s}_T$ are needed to quantify the contribution of the quark electric dipole moment (EDM) to the neutron EDM. The 9 ensembles, generated by the MILC Collaboration using the HISQ action with 2+1+1 dynamical flavors, span three lattice spacings $a \approx 0.06, 0.09$ and 0.12 fm and light-quark masses corresponding to the pion masses $M_π\approx 135, 225$ and 315 MeV. High-statistics estimates on five ensembles using the all-mode-averaging method allow us to quantify all systematic uncertainties and perform a simultaneous extrapolation in the lattice spacing, lattice volume and light-quark masses for the connected contributions. Our final estimates, in the $\overline{\text{MS}}$ scheme at 2 GeV, of the isovector charges are $g_A^{u-d} = 1.195(33)(20)$, $g_S^{u-d} = 0.97(12)(6) $ and $g_T^{u-d} = 0.987(51)(20)$. The first error includes statistical and all systematic uncertainties except that due to the extrapolation Ansatz, which is given by the second error estimate. Combining our estimate for $g_S^{u-d}$ with the difference of light quarks masses $(m_d-m_u)^{\rm QCD}=2.67(35)$ MeV given by FLAG, we obtain $(M_N-M_P)^{\rm QCD} = 2.59(49)$ MeV. Estimates of the connected part of the flavor-diagonal tensor charges of the proton are $g^{u}_T=0.792(42)$ and $g^{d}_T=-0.194(14)$. Combining our new estimates with precision low-energy experiments, we update constraints on novel scalar and tensor interactions, $ε_{S,T}$, at the TeV scale.

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arXiv2016

Quark Chromoelectric Dipole Moment Contribution to the Neutron Electric Dipole Moment

The quark chromo-electric dipole moment operator and the pseudo-scalar fermion bilinear with which it mixes under renormalization can both be included in a calculation of the electromagnetic form factor of the nucleon using the Schwinger source method. A preliminary calculation of these operators using clover quarks on HISQ lattices generated by MILC collaboration will be presented showing the quality of the signal in the correlators necessary for calculating the neutron electric dipole moment.

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arXiv2016

Tuning the hopping parameter in the Oktay-Kronfeld action for charm and bottom quarks on a MILC HISQ ensemble

The first step in the calculation of semi-leptonic form factors in the decay of heavy mesons is the tuning of the hopping parameter $κ$ for the charm and bottom quark masses. Results for the Oktay-Kronfeld (OK) action are presented for one $N_f=2+1+1$ HISQ ensemble generated by the MILC collaboration at $a\approx 0.12\,\mathrm{fm}$ and $M_π\approx 310$ MeV. Estimates of hyperfine splitting of heavy-light and heavy-heavy mesons are presented and the inconsistency parameter is evaluated.

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arXiv2016

Algorithms for Disconnected Diagrams in Lattice QCD

Computing disconnected diagrams in Lattice QCD (operator insertion in a quark loop) entails the computationally demanding problem of taking the trace of the all to all quark propagator. We first outline the basic algorithm used to compute a quark loop as well as improvements to this method. Then, we motivate and introduce an algorithm based on the synergy between hierarchical probing and singular value deflation. We present results for the chiral condensate using a 2+1-flavor clover ensemble and compare estimates of the nucleon charges with the basic algorithm.

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arXiv2016

Neutron Electric Dipole Moment from quark Chromoelectric Dipole Moment

The connection between a regularization-independent symmetric momentum substraction (RI-$\tilde{\rm S}$MOM) and the $\overline{\rm MS}$ scheme for the quark chromo EDM operators is discussed. A method for evaluating the neutron EDM from quark chromoEDM is described. A preliminary study of the signal in the matrix element using clover quarks on a highly improved staggered quark (HISQ) ensemble is shown.

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arXiv2016

Nucleon Charges, Form-factors and Neutron EDM

We present an update of our analysis of statistical and systematic errors in the calculation of iso-vector scalar, axial and tensor charges of the nucleon. The calculations are done using $N_f=2+1+1$ flavor HISQ ensembles generated by the MILC Collaboration at three values of the lattice spacing ($a=0.12,\ 0.09,$ and $0.06$ fm) and three values of the quark mass ($M_π\approx 310,\ 220$ and $130$ MeV); and clover fermions for calculating the correlation functions, i.e., we use a clover-on-HISQ lattice formulation. The all-mode-averaging method allows us to increase the statistics by a factor of eight for the same computational cost leading to a better understanding of and control over excited state contamination. Our current results, after extrapolation to the continuum limit and physical pion mass are $g_A^{u-d} = 1.21(3)$, $g_T^{u-d} = 1.005(59)$ and $g_S^{u-d} = 0.95(12) $. Further checks of control over all systematic errors, especially in $g_A^{u-d}$, are still being performed. Using results for the flavor-diagonal charges, $g_T^{u} $, $g_T^{d} $ and $g_T^{s}$, we analyze contributions of the quark electric dipole moment to the neutron EDM and the consequences for split SUSY model.

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arXiv2016

Iso-vector and Iso-scalar Tensor Charges of the Nucleon from Lattice QCD

We present results for the iso-vector and flavor diagonal tensor charges $g^{u-d}_T$, $g^{u}_T$, $g^{d}_T$, and $g^{s}_T$ needed to probe novel tensor interactions at the TeV scale in neutron and nuclear $β$-decays and the contribution of the quark electric dipole moment (EDM) to the neutron EDM. The lattice QCD calculations were done using nine ensembles of gauge configurations generated by the MILC collaboration using the HISQ action with 2+1+1 dynamical flavors. These ensembles span three lattice spacings $a \approx 0.06, 0.09$ and $0.12 $ fm and three quark masses corresponding to the pion masses $M_π\approx 130, 220$ and $310 $ MeV. Using estimates from these ensembles, we quantify all systematic uncertainties and perform a simultaneous extrapolation in the lattice spacing, volume and light quark masses for the connected contributions. The final estimates of the connected nucleon (proton) tensor charge for the iso-vector combination is $g_T^{u-d} = 1.020(76) $ in the $\bar{\text{MS}}$ scheme at $2$ GeV. The additional disconnected quark loop contributions needed for the flavor-diagonal matrix elements are calculated using a stochastic estimator employing the truncated solver method with the all-mode-averaging technique. We find that the size of the disconnected contribution is smaller than the statistical error in the connected contribution. This allows us to bound the disconnected contribution and include it as an additional uncertainty in the flavor-diagonal charges. After a continuum extrapolation, we find $g_T^{u} = 0.774(66) $, $g_T^{d} = -0.233(28) $ and $g_T^{u+d} = 0.541(67) $. The strangeness tensor charge, that can make a significant contribution to the neutron EDM due to the large ratio $m_s/m_{u,d}$, is $g_T^{s}=0.008(9)$ in the continuum limit.

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arXiv2016

Neutron Electric Dipole Moment and Tensor Charges from Lattice QCD

We present Lattice QCD results on the neutron tensor charges including, for the first time, a simultaneous extrapolation in the lattice spacing, volume, and light quark masses to the physical point in the continuum limit. We find that the "disconnected" contribution is smaller than the statistical error in the "connected" contribution. Our estimates in the $\bar{\text{MS}}$ scheme at $2$ GeV, including all systematics, are $g_T^{d-u}=1.020(76)$, $g_T^d = 0.774(66)$, $g_T^u = - 0.233(28)$, and $g_T^s = 0.008(9)$. The flavor diagonal charges determine the size of the neutron electric dipole moment (EDM) induced by quark EDMs that are generated in many new scenarios of CP-violation beyond the Standard Model (BSM). We use our results to derive model-independent bounds on the EDMs of light quarks and update the EDM phenomenology in split Supersymmetry with gaugino mass unification, finding a stringent upper bound of $d_n < 4 \times 10^{-28} \, e$ cm for the neutron EDM in this scenario.

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arXiv2015

Disconnected Quark Loop Contributions to Nucleon Structure

We calculate the disconnected contribution to isoscalar nucleon charges for scalar, axial and tensor channels of light and strange quarks. The calculation has been done with the Clover valence quarks on the MILC $N_f=2+1+1$ HISQ lattices whose light quark masses corresponding to the pion masses of 305 MeV and 217 MeV at $a \approx 0.12$ fm and 312 MeV at $a \approx 0.09$ fm. All-mode-averaging technique is used for the evaluation two-point functions. Disconnected quark loops are estimated by using the truncated solver method with Gaussian random noise sources. Contamination from the excited states is removed by fitting the results of various source-sink separations and operator insertions to the formula including up to the first excited state, simultaneously.

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arXiv2015

Precision calculations of nucleon charges $g_A$, $g_S$, $g_T$

We present a detailed analysis of statistical and systematic errors in the calculation of matrix elements of iso-vector scalar, axial and tensor charges between a neutron and a proton state. These analyses are being done on dynamical $N_f=2+1+1$ HISQ configurations generated by the MILC Collaboration using valence clover fermions. Using ensembles at three values of the lattice spacing ($a=0.12,\ 0.09,$ and $0.06$ fm) and three values of the quark mass ($M_π\approx 310,\ 220$ and $130$ MeV) we find that the estimates of the tensor charge are stable and it can be extracted with $5\%$ precision with O(10,000) measurements. We also find that higher statistics are needed to resolve the various uncertainties in the calculation of $g_A$ and improve the signal in $g_S$, which with present data has large errors. A brief status report on the mixing and renormalization of novel operators contributing to nEDM is also given.

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arXiv2014

The equation of state in (2+1)-flavor QCD

We present results for the equation of state in (2+1)-flavor QCD using the highly improved staggered quark action and lattices with temporal extent $N_τ=6,~8,~10$, and $12$. We show that these data can be reliably extrapolated to the continuum limit and obtain a number of thermodynamic quantities and the speed of sound in the temperature range $(130-400)$ MeV. We compare our results with previous calculations, and provide an analytic parameterization of the pressure, from which other thermodynamic quantities can be calculated, for use in phenomenology. We show that the energy density in the crossover region, $145~ {\rm MeV} \leq T \leq 163$ MeV, defined by the chiral transition, is $ε_c=(0.18-0.5)~{\rm GeV}/{\rm fm}^3$, $i.e.$, $(1.2-3.1)\ ε_{\rm nuclear}$. At high temperatures, we compare our results with resummed and dimensionally reduced perturbation theory calculations. As a byproduct of our analyses, we obtain the values of the scale parameters $r_0$ from the static quark potential and $w_0$ from the gradient flow.

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arXiv2014

Nucleon Charges and Electromagnetic Form Factors from 2+1+1-Flavor Lattice QCD

We present lattice-QCD results on the nucleon isovector axial, scalar and tensor charges, the isovector electromagnetic Dirac and Pauli form factors, and the connected parts of the isoscalar charges. The calculations have been done using two ensembles of HISQ lattices generated by the MILC Collaboration with 2+1+1 dynamical flavors at a lattice spacing of 0.12 fm and with light-quark masses corresponding to pions with masses 310 and 220 MeV. We perform a systematic study including excited-state degrees of freedom and examine the dependence of the extracted nucleon matrix elements on source-sink separation. This study demonstrates with high-statistics data that including excited-state contributions and generating data at multiple separations is necessary to remove contamination that would otherwise lead to systematic error. We also determine the renormalization constants of the associated quark bilinear operators in the RI-sMOM scheme and make comparisons of our renormalized results with previous dynamical-lattice calculations.

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