737 research outputs found

### Moments and power corrections of longitudinal and transverse proton structure functions from lattice QCD

We present a simultaneous extraction of the moments of $F_2$ and $F_L$
structure functions of the proton for a range of photon virtuality, $Q^2$. This
is achieved by computing the forward Compton amplitude on the lattice utilizing
the second-order Feynman-Hellmann theorem. Our calculations are performed on
configurations with two different lattice spacings and volumes, all at the
$SU(3)$ symmetric point. We find the moments of $F_{2}$ and $F_{L}$ in good
agreement with experiment. Power corrections turn out to be significant. This
is the first time the $Q^2$ dependence of the lowest moment of $F_2$ has been
quantified.Comment: 14 pages, 11 figures, 2 tables. Version to appear in PR

### Feynman--Hellmann approach to transition matrix elements and quasi-degenerate energy states

The Feynman--Hellmann approach to computing matrix elements in lattice QCD by
first adding a perturbing operator to the action is described using the
transition matrix and the Dyson expansion formalism. This perturbs the energies
in the two-point baryon correlation function, from which the matrix element can
be obtained. In particular at leading order in the perturbation we need to
diagonalise a matrix of near-degenerate energies. While the method is general
for all hadrons, we apply it here to a study of a Sigma to Nucleon baryon
transition vector matrix element.Comment: 50 pages. Minor typos fixed. Published versio

### Feynman-Hellmann approach to transition matrix elements and quasi-degenerate energy states

The Feynman-Hellmann approach to computing matrix elements in lattice QCD by first adding a perturbing operator to the action is described using the transition matrix and the Dyson expansion formalism. This perturbs the energies in the two-point baryon correlation function, from which the matrix element can be obtained. In particular at leading order in the perturbation we need to diagonalise a matrix of near-degenerate energies. While the method is general for all hadrons, we apply it here to a study of a Sigma to Nucleon baryon transition vector matrix element

### Quasi-degenerate baryon energy states, the Feynman-Hellmann theorem and transition matrix elements

The standard method for determining matrix elements in lattice QCD requires the computation of three-point correlation functions. This has the disadvantage of requiring two large time separations: one between the hadron source and operator and the other from the operator to the hadron sink. Here we consider an alternative formalism, based on the Dyson expansion leading to the Feynman-Hellmann theorem, which only requires the computation of two-point correlation functions. Both the cases of degenerate energy levels and quasi-degenerate energy levels which correspond to diagonal and transition matrix elements respectively can be considered in this formalism. As an example numerical results for the Sigma to Nucleon vector transition matrix element are presented

### Weak decay constants of the pseudoscalar mesons from lattice QCD+QED

With increasing requirements for greater precision, it becomes essential to describe the effects of isospin breaking induced by both quark masses and electro-magnetic effects. In this work we have performed a lattice analysis of the weak decay constants of the pseudoscalar mesons including such isospin breaking effects, with particular consideration being given to the state mixing of the $\pi^0$, $\eta$ and $\eta^\prime$. We also detail extensions to the non-perturbative RI$^\prime$-MOM renormalization scheme for application to non-degenerate flavour-neutral operators which are permitted to mix, and present initial results. Using flavour-breaking expansions in terms of quark masses and charges we reach decay constant determinations at physical quark masses for all but the $\eta^\prime$, demonstrating in principle how precision determinations of all pseudoscalar decay constants could be reached in lattice QCD with QED and strong isospin-breaking

### Constraining beyond the Standard Model nucleon isovector charges

At the TeV scale, low-energy precision observations of neutron
characteristics provide unique probes of novel physics. Precision studies of
neutron decay observables are susceptible to beyond the Standard Model (BSM)
tensor and scalar interactions, while the neutron electric dipole moment,
$d_n$, also has high sensitivity to new BSM CP-violating interactions. To fully
utilise the potential of future experimental neutron physics programs, matrix
elements of appropriate low-energy effective operators within neutron states
must be precisely calculated. We present results from the QCDSF/UKQCD/CSSM
collaboration for the isovector charges $g_T,~g_A$ and $g_S$ using lattice QCD
methods and the Feynman-Hellmann theorem. We use a flavour symmetry breaking
method to systematically approach the physical quark mass using ensembles that
span five lattice spacings and multiple volumes. We extend this existing
flavour breaking expansion to also account for lattice spacing and finite
volume effects in order to quantify all systematic uncertainties. Our final
estimates of the isovector charges are
$g_T~=~1.009(20)_{\text{stat}}(03)_{\text{sys}},~g_A=1.246(69)_{\text{stat}}(05)_{\text{sys}}$
and $g_S~=~1.06(10)_{\text{stat}}(03)_{\text{sys}}$ renormalised, where
appropriate, at $\mu=2~\text{GeV}$ in the $\overline{\text{MS}}$ scheme.Comment: 16 pages, 11 figures, 6 table

### Quasi-degenerate baryon energy states, the Feynman-Hellmann theorem and transition matrix elements

The standard method for determining matrix elements in lattice QCD requires the computation of three-point correlation functions. This has the disadvantage of requiring two large time separations: one between the hadron source and operator and the other from the operator to the hadron sink. Here we consider an alternative formalism, based on the Dyson expansion leading to the Feynman-Hellmann theorem, which only requires the computation of two-point correlation functions. Both the cases of degenerate energy levels and quasi-degenerate energy levels which correspond to diagonal and transition matrix elements respectively can be considered in this formalism. As an example numerical results for the Sigma to Nucleon vector transition matrix element are presented

### Constraining beyond the Standard Model nucleon isovector charges

At the TeV scale, low-energy precision observations of neutron characteristics provide unique probes of novel physics. Precision studies of neutron decay observables are susceptible to beyond the Standard Model (BSM) tensor and scalar interactions, while the neutron electric dipole moment, $d_n$, also has high sensitivity to new BSM CP-violating interactions. To fully utilise the potential of future experimental neutron physics programs, matrix elements of appropriate low-energy effective operators within neutron states must be precisely calculated. We present results from the QCDSF/UKQCD/CSSM collaboration for the isovector charges $g_T,~g_A$ and $g_S$ using lattice QCD methods and the Feynman-Hellmann theorem. We use a flavour symmetry breaking method to systematically approach the physical quark mass using ensembles that span five lattice spacings and multiple volumes. We extend this existing flavour breaking expansion to also account for lattice spacing and finite volume effects in order to quantify all systematic uncertainties. Our final estimates of the isovector charges are $g_T~=~1.009(20)_{\text{stat}}(03)_{\text{sys}},~g_A=1.246(69)_{\text{stat}}(05)_{\text{sys}}$ and $g_S~=~1.06(10)_{\text{stat}}(03)_{\text{sys}}$ renormalised, where appropriate, at $\mu=2~\text{GeV}$ in the $\overline{\text{MS}}$ scheme

### Measurements of $SU(3)_f$ symmetry breaking in $B$ meson decay constants

We present updates from QCDSF/UKQCD/CSSM on the $SU(3)_f$ breaking in $B$ meson decay constants. The $b$-quarks are generated with an anisotropic clover-improved action, and are tuned to match properties of the physical $B$ and $B^*$ mesons. Configurations are generated with $\overline{m}=(1/3)(2m_l+m_s)$ kept constant to control symmetry breaking effects. Various sources of systematic uncertainty will be discussed, including those from continuum extrapolations and extrapolations to the physical point. We also present new efforts to calculate $f_B$ and $f_{B_s}$ using weighted averages across multiple time fitting regions. The use of an automated weighted averaging technique over multiple fitting ranges allows for timely tuning of the $b$-quark and reduces the impact of systematic errors from fitting range biases in calculations of $f_B$ and $f_{B_s}

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