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Register a new userHadronic Form Factors: Combining QCD Calculations with Analyticity
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A. Khodjamirian
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I discuss recent applications of QCD light-cone sum rules to various form factors of pseudoscalar mesons. In this approach both soft and hard contributions to the form factors are taken into account. Combining QCD calculation with the analyticity of the form factors, one enlarges the region of accessible momentum transfers.
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Applying the vacuum-to-$B$-meson correlation functions with an interpolating current for the light vector meson we construct the light-cone sum rules (LCSR) for the effective form factors $xi_{parallel}(n cdot p)$, $xi_{perp}(n cdot p)$, $Xi_{parallel}(tau, n cdot p)$ and $Xi_{perp}(tau, n cdot p)$, defined by the corresponding hadronic matrix elements in soft-collinear effective theory (SCET), entering the leading-power factorization formulae for QCD form factors responsible for $B to V ell bar u_{ell}$ and $B to V ell bar ell$ decays at large hadronic recoil at next-to-leading-order in QCD. The light-quark mass effect for the local SCET form factors $xi_{parallel}(n cdot p)$ and $xi_{perp}(n cdot p)$ is also computed from the LCSR method with the $B$-meson light-cone distribution amplitude $phi_B^{+}(omega, mu)$ at ${cal O}(alpha_s)$. Furthermore, the subleading power corrections to $B to V$ form factors from the higher-twist $B$-meson light-cone distribution amplitudes are also computed with the same method at tree level up to the twist-six accuracy. Having at our disposal the LCSR predictions for $B to V$ form factors, we further perform new determinations of the CKM matrix element $|V_{ub}|$ from the semileptonic $B to rho , ell , bar u_{ell}$ and $B to omega , ell , bar u_{ell}$ decays, and predict the normalized differential branching fractions and the $q^2$-binned $K^{ast}$ longitudinal polarization fractions of the exclusive rare $B to K^{ast} , u_{ell} , bar u_{ell}$ decays.
We update QCD calculations of $B to pi, K$ form factors at large hadronic recoil by including the subleading-power corrections from the higher-twist $B$-meson light-cone distribution amplitudes (LCDAs) up to the twist-six accuracy and the strange-quark mass effects at leading-power in $Lambda/m_b$ from the twist-two $B$-meson LCDA $phi_B^{+}(omega, mu)$. The higher-twist corrections from both the two-particle and three-particle $B$-meson LCDAs are computed from the light-cone QCD sum rules (LCSR) at tree level. In particular, we construct the local duality model for the twist-five and -six $B$-meson LCDAs, in agreement with the corresponding asymptotic behaviours at small quark and gluon momenta, employing the QCD sum rules in heavy quark effective theory at leading order in $alpha_s$. The strange quark mass effects in semileptonic $B to K$ form factors yield the leading-power contribution in the heavy quark expansion, consistent with the power-counting analysis in soft-collinear effective theory, and they are also computed from the LCSR approach due to the appearance of the rapidity singularities. We further explore the phenomenological aspects of the semileptonic $B to pi ell u$ decays and the rare exclusive processes $B to K u u$, including the determination of the CKM matrix element $|V_{ub}|$, the normalized differential $q^2$ distributions and precision observables defined by the ratios of branching fractions for the above-mentioned two channels in the same intervals of $q^2$.
The nucleon electromagnetic form factors are calculated in light cone QCD sum rules framework using the most general form of the nucleon interpolating current. Using two forms of the distribution amplitudes (DAs), predictions for the form factors are presented and compared with existing experimental data. It is shown that our results describe remarkably well the existing experimental data.
Lattice simulations of QCD have produced precise estimates for the masses of the lowest-lying hadrons which show excellent agreement with experiment. By contrast, lattice results for the vector and axial vector form factors of the nucleon show significant deviations from their experimental determination. We present results from our ongoing project to compute a variety of form factors with control over all systematic uncertainties. In the case of the pion electromagnetic form factor we employ partially twisted boundary conditions to extract the pion charge radius directly from the linear slope of the form factor near vanishing momentum transfer. In the nucleon sector we focus specifically on the possible contamination from contributions of higher excited states. We argue that summed correlation functions offer the possibility of eliminating this source of systematic error. As an illustration of the method we discuss our results for the axial charge, gA, of the nucleon.
Precision computation of hadronic physics with lattice QCD is becoming feasible. The last decade has seen percent-level calculations of many simple properties of mesons, and the last few years have seen calculations of baryon masses, including the nucleon mass, accurate to a few percent. As computational power increases and algorithms advance, the precise calculation of a variety of more demanding hadronic properties will become realistic. With this in mind, I discuss the current lattice QCD calculations of generalized parton distributions with an emphasis on the prospects for well-controlled calculations for these observables as well. I will do this by way of several examples: the pion and nucleon form factors and moments of the nucleon parton and generalized-parton distributions.
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