arXiv subjects
Publications and source records attributed to Alan R. White.
It is shown that the triangle anomaly is present, as an infra-red divergence, in the six-reggeon triple-regge interaction vertex obtained from a maximally non-planar Feynman diagram in the full triple-regge limit of three-to-three quark scattering. A multi-regge asymptotic dispersion relation formalism can be used to isolate all anomaly contributions and to discuss when and how there is a cancelation.
Reggeized gluon interactions due to a single quark loop are studied in the full triple-regge limit and in closely related helicity-flip helicity-pole limits. Triangle diagram reggeon interactions are generated that include local axial-vector effective vertices. It is shown that the massless quark triangle anomaly is present as a chirality-violating infra-red divergence in the interactions generated by maximally non-planar Feynman diagrams. An asymptotic dispersion relation formalism is developed which provides a systematic counting of anomaly contributions. The asymptotic amplitude is written as a sum over dispersion integrals of triple discontinuities, one set of which is unphysical and can produce chirality transitions. The physical-region anomaly appears in the generalized real parts, determined by multi-regge theory, of the unphysical discontinuities. The amplitudes satisfy a signature conservation rule that implies color parity is not conserved by vertices containing the anomaly. In the scattering of elementary quarks or gluons the signature and color parity of the exchanged reggeon states are such that the anomaly cancels. At lowest-order, it cancels in individual diagrams after the transverse momentum integrations are performed.
Deep-inelastic diffractive scaling violations have provided fundamental insight into the QCD pomeron, suggesting a single gluon inner structure rather than that of a perturbative two-gluon bound state. This paper derives a high-energy, transverse momentum cut-off, confining solution of QCD. The pomeron, in first approximation, is a single reggeized gluon plus a ``wee parton'' component that compensates for the color and particle properties of the gluon. This solution corresponds to a supercritical phase of Reggeon Field Theory. Beginning with the multi-regge behavior of massive quark and gluon amplitudes, reggeon unitarity is used to derive a reggeon diagram description of a wide class of multi-regge amplitudes, including those describing the formation and scattering of bound-state Regge poles. When quark and gluon masses are taken to zero, a logarithmic divergence is produced by helicity-flip reggeon interactions containing the infra-red quark triangle anomaly. With the gauge symmetry partially broken, this divergence selects the bound states and amplitudes of a confining theory. Both the pomeron and hadrons have an anomalous color parity wee-parton component. For the pomeron the wee parton component determines that it carries negative color charge parity and that the leading singularity is an isolated Regge pole.
Workshop presentations on elastic and diffractive scattering and other recent advances in hadron physics are summarized. The role of ``factorization'' in determining parton properties of the pomeron is particularly discussed.
Deep-inelastic diffractive scaling provides fundamental insight into the QCD pomeron. It is argued that single gluon domination of the structure function, together with the well-known Regge pole property, determines that the pomeron carries color-charge parity $ C_c = -1~$ and, at short distances, is in a super-critical phase of Reggeon Field Theory. The main purpose of the talk is to describe the relationship of the super-critical pomeron to QCD.
If dynamical electroweak symmetry breaking is due to a flavor doublet of color sextet quarks, enhanced electroweak scale QCD instanton interactions may produce a large top mass, raise the $η_6$ axion mass, and also explain the excesses in the DIS cross-section at HERA and jet cross-sections at the Tevatron.
Conformally invariant reggeon interactions derived from $t$-channel unitarity are discussed and progress towards understanding the ``physical Pomeron'', via massless quark reggeon interactions, is briefly outlined.
When the Higgs sector of the standard model is replaced by a flavor doublet of color sextet quarks, dynamical electroweak symmetry breaking occurs, with the electroweak scale identified as the sextet chiral scale. Above the electroweak scale QCD is almost scale-invariant, leading to the high-momentum enhancement of both the sextet chiral condensate and instanton interactions. The instanton interactions combine with the sextet condensate to produce electroweak scale chirality violating processes in both the triplet and sextet sectors. If the enhancement is sufficient, an electroweak scale top mass can be produced and the $η_6$ axion mass can be raised, potentially providing a consistent description of both Strong CP conservation and electroweak-scale CP violation. The instanton interactions also produce electroweak scale chirality violating scattering processes for light quarks and additionally modify QCD evolution at the electroweak scale. Such effects could explain the excesses in the DIS cross-section at HERA and jet cross-sections at the Tevatron.
We show that a scale invariant approximation to the next-to-leading order BFKL kernel, constructed via transverse momentum diagrams, has a simple conformally invariant representation in impact parameter space i.e. K(r1,r2,r1',r2') = g^4 N^2 ln^4[(|r1-r1'||r2-r2'|)/(|r1-r2'||r2-r1'|)] That a conformally invariant representation exists is shown first by relating the kernel directly to Feynman diagrams contributing to two photon diffractive dissociation.
We argue that deep-inelastic diffractive scaling provides fundamental insight into the QCD Pomeron. The logarithmic scaling violations seen experimentally are in conflict with the scale-invariance of the BFKL Pomeron and with phenomenological two-gluon models. Instead the Pomeron appears as a single gluon at short-distances, indicating the appearance of a Super-Critical phase of Reggeon Field Theory. That the color compensation takes place at a longer distance is consistent with the Pomeron carrying odd color charge parity.
In a non-abelian gauge theory the $t$-channel multiparticle unitarity equations continued in the complex j-plane can be systematically expanded around $j=1$. The combination of Ward identity constraints with unitarity is sufficient to produce directly many results obtained by Regge limit leading-log and next-to-leading log momentum space calculations. The $O(g^2)$ BFKL kernel is completely determined. $O(g^4)$ contributions to the kernel are also determined, including the leading contribution of a new partial-wave amplitude - previously identified as a separate forward component with a holomorphically factorizable spectrum. For this amplitude the only scale ambiguity is the overall normalization and it is anticipated to be a new conformally invariant kernel. The results suggest that all conformally invariant reggeon interactions are determined by $t$-channel unitarity.
We discuss the observed scaling of the small-x diffractive and total deep-inelastic structure functions at HERA. We argue that the parton interpretation of Buchmüller and Hebecker can be understood within QCD as the appearance of the Pomeron in a Super-Critical phase. In diffractive hard scattering, the Pomeron appears as reggeized gluon exchange in a color-compensating background field. The formalism can also be applied to diffractive $W$ production at the Tevatron. If the scaling is a true asymptotic property then it should anticipate the appearance of a further massive sector of QCD and associated asymptotic Critical Pomeron behaviour.
Unitarity corrections to the BFKL evolution at next to leading order determine a new component of the evolution kernel which is shown to possess conformal invariance properties. Expressions for the complete spectrum of the new component and the correction to the intercept of the pomeron trajectory are presented.
We study the scale-invariant $O(g^4)$ kernel which appears as an infra-red contribution in the BFKL evolution equation and is constructed via multiparticle $t$-channel unitarity. We detail the variety of Ward identity constraints and infra-red cancellations that characterize its infrared behaviour. We give an analytic form for the full non-forward kernel. For the forward kernel controlling parton evolution at small-x, we give an impact parameter representation, derive the eigenvalue spectrum, and demonstrate a holomorphic factorisation property related to conformal invariance. The results show that, at next-to-leading-order, the transverse momentum infra-red region may produce a strong reduction of the BFKL small-x behavior.
The scale-invariant $O(g^4)$ Lipatov kernel has been determined by t-channel unitarity. The forward kernel responsible for parton evolution is evaluated and its eigenvalue spectrum determined. In addition to a logarithmic modification of the $O(g^2)$ kernel a distinct new kinematic component appears. This component is infra-red finite without regularization and has the holomorphic factorization property necessary for conformal invariance. It gives a reduction (of ~$\sim 65α_s^2/π^2\sim 0.15$) in the power growth of parton distributions at small-x.
Theoretical arguments for a new higher-color quark sector, based on Pomeron physics in QCD, are briefly described. The electroweak symmetry-breaking, Strong CP conservation, and electroweak scale CP violation, that is naturally produced by this sector is also outlined. A further consequence is that above the electroweak scale there will be a radical change in the strong interaction. Electroweak states, in particular multiple $W$'s and $Z$'s, and new, semi-stable, very massive , baryons, will be commonly produced. The possible correlation of expected phenomena with a wide range of observed Cosmic Ray effects at and above the primary spectrum knee is described. Related phenomena that might be seen in the highest energy hard scattering events at the Fermilab Tevatron, some of which could be confused with top production, are also briefly discussed.
Three closely related topics are covered. The derivation of $O(g^4)$ Lipatov kernels in pure glue QCD. The significance of quarks for the physical Pomeron in QCD. The possible inter-relation of Pomeron dynamics with Electroweak symmetry breaking.
Leading plus next-to leading log results for the Regge limit of massless Yang-Mills theories are reproduced by reggeon diagrams in which the Regge slope $α' \to 0$ and reggeon amplitudes satisfy Ward identity constraints at zero transverse momentum. Using reggeon unitarity together with multiple discontinuity theory a complete set of such diagrams can be constructed. The resulting two-two, one-three and two-four kernels which generalise the Lipatov equation at $O(g^4)$ are determined uniquely.