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Register a new userComplex angular momenta approach for scattering problems in the presence of both monopoles and short range potentials
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Authors
Fabrizio Canfora
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It is analyzed the quantum mechanical scattering off a topological defect (such as a Dirac monopole) as well as a Yukawa-like potential(s) representing the typical effects of strong interactions. This system, due to the presence of a short-range potential, can be analyzed using the powerful technique of the complex angular momenta which, so far, has not been employed in the presence of monopoles (nor of other topological solitons). Due to the fact that spatial spherical symmetry is achieved only up to internal rotations, the partial wave expansion becomes very similar to the Jacob-Wick helicity amplitudes for particles with spin. However, since the angular-momentum operator has an extra internal contribution, fixed cuts in the complex angular momentum plane appear. Correspondingly, the background integral in the Regge formula does not decrease for large values of cos(Theta) (namely, large values of the Mandelstam variable s). Hence, the experimental observation of this kind of behavior could be a direct signal of non-trivial topological structures in strong interactions. The possible relations of these results with the soft Pomeron are shortly analyzed.
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We apply renormalisation-group methods to two-body scattering by a combination of known long-range and unknown short-range potentials. We impose a cut-off in the basis of distorted waves of the long-range potential and identify possible fixed points of the short-range potential as this cut-off is lowered to zero. The expansions around these fixed points define the power countings for the corresponding effective field theories. Expansions around nontrivial fixed points are shown to correspond to distorted-wa
We report a complete calculation of the quark and glue momenta and angular momenta in the proton. These include the quark contributions from both the connected and disconnected insertions. The calculation is carried out on a $16^3 times 24$ quenched lattice at $beta = 6.0$ and for Wilson fermions with $kappa = 0.154, 0.155,$ and 0.1555 which correspond to pion masses at 650, 538, and 478 MeV. The quark loops are calculated with $Z_4$ noise and signal-to-noise is improved further with unbiased subtractions. The glue operator is comprised of gauge-field tensors constructed from the overlap operator. The $u$ and $d$ quark momentum/angular momentum fraction is 0.66(5)/0.72(5), the strange momentum/angular momentum fraction is 0.024(6)/0.023(7), and that of the glue is 0.31(6)/0.25(8). The orbital angular momenta of the quarks are obtained from subtracting the angular momentum component from its corresponding spin. As a result, the quark orbital angular momentum constitutes 0.50(2) of the proton spin, with almost all it coming from the disconnected insertion. The quark spin carries a fraction 0.25(12) and glue carries a fraction 0.25(8) of the total proton spin.
We report a complete calculation of the quark and glue momenta and angular momenta in the proton. These include the quark contributions from both the connected and disconnected insertions. The quark disconnected insertion loops are computed with $Z_4$ noise, and the signal-to-noise is improved with unbiased subtractions. The glue operator is comprised of gauge-field tensors constructed from the overlap operator. The calculation is carried out on a $16^3 times 24$ quenched lattice at $beta = 6.0$ for Wilson fermions with $kappa=0.154, 0.155$, and $0.1555$ which correspond to pion masses at $650, 538$, and $478$~MeV, respectively. The chirally extrapolated $u$ and $d$ quark momentum/angular momentum fraction is found to be $0.64(5)/0.70(5)$, the strange momentum/angular momentum fraction is $0.024(6)/0.023(7)$, and that of the glue is $0.33(6)/0.28(8)$. The previous study of quark spin on the same lattice revealed that it carries a fraction of $0.25(12)$ of proton spin. The orbital angular momenta of the quarks are then obtained from subtracting the spin from their corresponding angular momentum components. We find that the quark orbital angular momentum constitutes $0.47(13)$ of the proton spin with almost all of it coming from the disconnected insertions.
Three nucleon short range correlations~(SRCs) are one of the most elusive structures in nuclei. Their observation and the subsequent study of their internal makeup will have a significant impact on our understanding of the dynamics of super-dense nuclear matter which exists at the cores of neutron stars. We discuss the kinematic conditions and observables that are most favorable for probing 3N-SRCs in inclusive electro-nuclear processes and make a prediction for a quadratic dependence of the probabilities of finding a nucleon in 2N- and 3N- SRCs. We demonstrate that this prediction is consistent with the limited high energy experimental data available, suggesting that we have observed, for the first time, 3N-SRCs in electro-nuclear processes. Our analysis enables us to extract $a_3(A,Z)$, the probability of finding 3N-SRCs in nuclei relative to the A=3 system.
Having in mind present uncertainty of the experimental situation in respect to exotic hadrons, it is important to discuss any possible theoretical arguments, pro and contra. Up to now, there are no theoretical ideas which could forbid existence of the exotic states. Theoretical proofs for their existence are also absent. However, there are some indirect arguments for the latter case. It will be shown here, by using the complex angular momenta approach, that the standard assumptions of analyticity and unitarity for hadronic amplitudes lead to a non-trivial conclusion: the S-matrix has infinitely many poles in the energy plane (accounting for all its Riemann sheets). This is true for any arbitrary quantum numbers of the poles, exotic or non-exotic. Whether some of the poles may provide physical (stable or resonance) states, should be determined by some more detailed dynamics.
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