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Register a new userA Charge-Conjugation-Invariance Constrained Pomeron-Quark Coupling
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Lon-chang Liu
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The commonly used $gamma_{mu}} Pomeron-quark coupling changes its sign under charge conjugation, in contradiction to the property of Pomeron. I show that the Pomeron-quark coupling is tensorial and is invariant under the charge conjugation.
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We define gauge theories whose gauge group includes charge conjugation as well as standard $mathrm{SU}(N)$ transformations. When combined, these transformations form a novel type of group with a semidirect product structure. For $N$ even, we show that there are exactly two possible such groups which we dub $widetilde{mathrm{SU}}(N)_{mathrm{I,II}}$. We construct the transformation rules for the fundamental and adjoint representations, allowing us to explicitly build four-dimensional $mathcal{N}=2$ supersymmetric gauge theories based on $widetilde{mathrm{SU}}(N)_{mathrm{I,II}}$ and understand from first principles their global symmetry. We compute the Haar measure on the groups, which allows us to quantitatively study the operator content in protected sectors by means of the superconformal index. In particular, we find that both types of $widetilde{mathrm{SU}}(N)_{mathrm{I,II}}$ groups lead to non-freely generated Coulomb branches.
We calculate twist-3 parton ditribution functions (PDFs) using cut and uncut diagrams. Uncut diagrams lead to a Dirac delta function term. No such term appears when cut diagrams are used. We show that a $delta(x)$ is necessary to satisfy the Lorentz invariance relations of twist-3 PDFs, except for the Burkhardt-Cottingham sum rule in QCD.
We begin the process of unitarizing the Pomeron at large t Hooft coupling. We do so first in the conformal regime, which applies to good accuracy to a number of real and toy problems in QCD. We rewrite the conformal Pomeron in the $J$-plane and transverse position space, and then work out the eikonal approximation to multiple Pomeron exchange. This is done in the context of a more general treatment of the complex $J$-plane and the geometric consequences of conformal invariance. The methods required are direct generalizations of our previous work on single Pomeron exchange and on multiple graviton exchange in AdS space, and should form a starting point for other investigations. We consider unitarity and saturation in the conformal regime, noting elastic and absorptive effects, and exploring where different processes dominate. Our methods extend to confining theories and we briefly consider the Pomeron kernel in this context. Though there is important model dependence that requires detailed consideration, the eikonal approximation indicates that the Froissart bound is generically both satisfied and saturated.
We show that the $1/N_c$ rotational corrections to $g_A$, derived using the semiclassical quantization scheme in the NJL model, possess correct properties under charge conjugation.
A Regge pole model for Pomeron-Pomeron total cross section in the resonance region $sqrt{M^2}le$ 5 GeV is presented. The cross section is saturated by direct-channel contributions from the Pomeron as well as from two different $f$ trajectories, accompanied by the isolated f$_0(500)$ resonance which dominates the $sqrt{M^{2}}lesssim 1$ GeV region. A slowly varying background is taken into account. The calculated Pomeron-Pomeron total cross section cannot be measured directly, but is an essential part of central diffractive processes. In preparation of future calculations of central resonance production at the hadron level, and corresponding measurements at the LHC, we normalize the Pomeron-Pomeron cross section at large masses $sigma_{t}^{PP} (sqrt{M^2}rightarrow infty) approx$ 1 mb as suggested by QCD-motivated estimates.
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