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Register a new userMass structure of hadrons and light-front sum rules in t Hooft model
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We study the mass/energy structure of the bound state of hadrons in two-dimensional quantum chromodynamics in the large number of color limit (t Hooft model). We analyze separately the contributions from the traceless and trace part of the energy-momentum tensor, and show that the masses are related to the matrix elements of the scalar charge and Coulomb energy. We derive the light-front sum rules for the scalar charge and Coulomb energy, expressed in terms of the light-front wave functions, and find that they are regular at $x=0$ without the delta function contribution. We also consider the result for the massless Goldstone boson, as well as the structure of the gravitational form factors of the bound meson states.
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Different decompositions of the nucleon mass, in terms of the masses and energies of the underlying constituents, have been proposed in the literature. We explore the corresponding sum rules in quantum electrodynamics for an electron at one-loop order in perturbation theory. To this end we compute the form factors of the energy-momentum tensor, by paying particular attention to the renormalization of ultraviolet divergences, operator mixing and scheme dependence. We clarify the expressions of all the proposed sum rules in the electron rest frame in terms of renormalized operators. Furthermore, we consider the same sum rules in a moving frame, where they become energy decompositions. Finally, we discuss some implications of our study on the mass sum rules for the nucleon.
We present a new calculation of the semileptonic tree-level and flavor-changing neutral current form factors describing $B$-meson transitions to tensor mesons $T=D_2^*,K_2^*,a_2,f_2$ ($J^{P}=2^{+}$). We employ the QCD Light-Cone Sum Rules approach with $B$-meson distribution amplitudes. We go beyond the leading-twist accuracy and provide analytically, for the first time, higher-twist corrections for the two-particle contributions up to twist four terms. We observe that the impact of higher twist terms to the sum rules is noticeable. We study the phenomenological implications of our results on the radiative ${B} to K_2^{*}gamma$ and semileptonic ${B} to D_2^* ell {bar u}_ell$, ${B} to K_2^{*}ell^+ell^-$ decays.
For special kinematic configurations involving a single momentum scale, certain standard relations, originating from the Slavnov-Taylor identities of the theory, may be interpreted as ordinary differential equations for the ``kinetic term of the gluon propagator. The exact solutions of these equations exhibit poles at the origin, which are incompatible with the physical answer, known to diverge only logarithmically; their elimination hinges on the validity of two integral conditions that we denominate ``asymmetric and ``symmetric sum rules, depending on the kinematics employed in their derivation. The corresponding integrands contain components of the three-gluon vertex and the ghost-gluon kernel, whose dynamics are constrained when the sum rules are imposed. For the numerical treatment we single out the asymmetric sum rule, given that its support stems predominantly from low and intermediate energy regimes of the defining integral, which are physically more interesting. Adopting a combined approach based on Schwinger-Dyson equations and lattice simulations, we demonstrate how the sum rule clearly favors the suppression of an effective form factor entering in the definition of its kernel. The results of the present work offer an additional vantage point into the rich and complex structure of the three-point sector of QCD.
The Burkhardt-Cottingham (BC) sum rule connects the twist-3 light-cone parton distribution function (PDF) $g_{T}(x)$ to the twist-2 helicity PDF $g_{1}(x)$. The chiral-odd counterpart of the BC sum rule relates the twist-3 light-cone PDF $h_{L}(x)$ to the twist-2 transversity PDF $h_{1}(x)$. These BC-type sum rules can also be derived for the corresponding quasi-PDFs. We perform a perturbative check of the BC-type sum rules in the quark target model and the Yukawa model, by going beyond the ultra-violet (UV) divergent terms. We employ dimensional regularization (DR) and cut-off schemes to regulate UV divergences, and show that the BC-type sum rules hold for DR, while they are generally violated when using a cut-off. This violation can be traced back to the breaking of rotational invariance. We find corresponding results for the sum rule relating the mass of the target to the twist-3 PDF $e(x)$. Moreover, we supplement our analytical results with numerical calculations.
In this article a systematic quantitative analysis of the isoscalar bosonic states is performed in the framework of supersymmetric light front holographic QCD. It is shown that the spectroscopy of the $eta$ and $h$ mesons can be well described if one additional mass parameter -- which corresponds to the hard breaking of chiral $U(1)$ symmetry in standard QCD -- is introduced. The mass difference of the $eta$ and $eta$ isoscalar mesons is then determined by the strange quark mass content of the $eta$. The theory also predicts the existence of isoscalar tetraquarks which are bound states of diquarks and anti-diquarks. The candidates for these exotic isoscalar tetraquarks are identified. In particular, the $f_0(1500)$ is identified as isoscalar tetraquark; the predicted mass value 1.52 GeV agrees with the measured experimental value within the model uncertainties.
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