Asymptotic limits and the structure of the pion form factor

We use dispersive techniques to address the behavior of the pion form factor as Q2 → ∞ and Q2 → 0. We perform the matching with the constraints of perturbative QCD and chiral perturbation theory in the high energy and low energy limits, leading to four sum rules. We present a version of the dispersive input which is consistent with the data and with all theoretical constraints. The results indicate that the asymptotic perturbative QCD limit is approached relatively slowly, and give a model independent determination of low energy chiral parameters

K-L-\u3epi(0)gamma e(+)e(-) and its relation to CP and chiral tests

The decay KL→π0γe+e- occurs at a higher rate than the nonradiative process KL→π0e+e-, and hence can be a background to CP violation studies using the latter reaction. It also has interest in its own right in the context of chiral perturbation theory, through its relation to the decay KL→π0γγ. The leading order chiral loop contribution to KL→π0γe+e-, including the (qe++qe-)2/mπ2 dependence, is completely calculable. We present this result and also include the higher order modifications which are required in the analysis of KL→π0γγ

Towards pp -> VVjj at NLO QCD: Bosonic contributions to triple vector boson production plus jet

In this work, some of the NLO QCD corrections for pp -> VVjj + X are presented. A program in Mathematica based on the structure of FeynCalc which automatically simplifies a set of amplitudes up to the hexagon level of rank 5 has been created for this purpose. We focus on two different topologies. The first involves all the virtual contributions needed for quadruple electroweak vector boson production, i.e. pp -> VVVV + X. In the second, the remaining "bosonic" corrections to electroweak triple vector boson production with an additional jet (pp -> VVV j + X) are computed. We show the factorization formula of the infrared divergences of the bosonic contributions for VVVV and VVVj production with V=(W,Z,gamma). Stability issues associated with the evaluation of the hexagons up to rank 5 are studied. The CPU time of the FORTRAN subroutines rounds the 2 milliseconds and seems to be competitive with other more sophisticated methods. Additionally, in Appendix A the master equations to obtain the tensor coefficients up to the hexagon level in the external momenta convention are presented including the ones needed for small Gram determinants.Comment: 48 pages,16 figure

Quantum corrections to Schwarzschild black hole

Using effective field theory techniques, we compute quantum corrections to spherically symmetric solutions of Einstein’s gravity and focus in particular on the Schwarzschild black hole. Quantum modifications are covariantly encoded in a non-local effective action. We work to quadratic order in curvatures simultaneously taking local and non-local corrections into account. Looking for solutions perturbatively close to that of classical general relativity, we find that an eternal Schwarzschild black hole remains a solution and receives no quantum corrections up to this order in the curvature expansion. In contrast, the field of a massive star receives corrections which are fully determined by the effective field theory

Dimension-eight operators in the weak OPE

We argue that there is a potential flaw in the standard treatment of weak decay amplitudes, including that of ǫ′/ǫ. We show that (contrary to conventional wisdom) dimension-eight operators do contribute to weak amplitudes, at order GFαs and without 1/M2W suppression. We demonstrate the existence of these operators through the use of a simple weak hamiltonian. Their contribution appears in different places depending on which scheme is adopted in performing the OPE. If one performs a complete separation of short and long distance physics within a cutoff scheme, dimension-eight operators occur in the weak hamiltonian at order GFαs/μ2, μ being the separating scale. However, in an MS renormalization scheme for the OPE the dimension-eight operators do not appear explicitly in the hamiltonian at order GFαs. In this case, matrix elements must include physics above the scale μ, and it is here that dimension eight effects enter. The use of a cutoff scheme (especially quark model methods) for the calculation of the matrix elements of dimension-six operators is inconsistent with MS unless there is careful matching including dimension-eight operators. The contribution of dimension-eight operators can be minimized by working at large enough values of the scale μ. We find from sum rule methods that the contribution of dimension-eight operators to the dimension-six operator Q(6) 7 is at the 100% level for μ = 1.5 GeV. This suggests that presently available values of μ are too low to justify the neglect of these effects. Finally, we display the dimension-eight operators which appear within the Standard Model at one loop

K -\u3epi pi phenomenology in the presence of electromagnetism

We describe the influence of electromagnetism on the phenomenology of $K \to \pi\pi$ decays. This is required because the present data were analyzed without inclusion of electromagnetic radiative corrections, and hence contain several ambiguities and uncertainties which we describe in detail. Our presentation includes a full description of the infrared effects needed for a new experimental analysis. It also describes the general treatment of final state interaction phases, needed because Watson\u27s theorem is no longer valid in the presence of electromagnetism. The phase of the isospin-two amplitude ${\cal A}_2$ may be modified by $50 \to 100\%$. We provide a tentative analysis using present data in order to illustrate the sensitivity to electromagnetic effects, and also discuss how the standard treatment of $\epsilon\u27 /\epsilon$ is modified

Final state rescattering as a contribution to B-\u3erho gamma

We provide a new estimate of the long-distance component to the radiative transition $B \to \rho \gamma$. Our mechanism involves the soft-scattering of on-shell hadronic products of nonleptonic $B$ decay, as in the chain $B \to \rho\rho \to \rho\gamma$. We employ a phenomenological fit to scattering data to estimate the effect. The specific intermediate states considered here modify the $B \to \rho \gamma$ decay rate at roughly the $5 \to 8$ level, although the underlying effect has the potential to be larger. Contrary to other mechanisms of long distance physics which have been discussed in the literature, this yields a non-negligible modification of the $B^0 \to \rho^0 \gamma$ channel and hence will provide an uncertainty in the extraction of $V_{td}$. This mechanism also affects the isospin relation between the rates for $B^- \to \rho^-\gamma$ and $B^0 \to \rho^0 \gamma$ and may generate CP asymmetries at experimentally observable levels

Electromagnetic corrections to K -\u3epi pi. I. Chiral perturbation theory

An analysis of electromagnetic corrections to the (dominant) octet K → ππ hamiltonian using chiral perturbation theory is carried out. Relative shifts in amplitudes at the several per cent level are found

SU(3) baryon chiral perturbation theory and long distance regularization

The use of SU(3) chiral perturbation theory in the analysis of low energy meson-baryon interactions is discussed. It is emphasized that short distance effects, arising from propagation of Goldstone bosons over distances smaller than a typical hadronic size, are modeldependent and can lead to a lack of convergence in the SU(3) chiral expansion if they are included in loop diagrams. In this paper we demonstrate how to remove such effects in a chirally consistent fashion by use of a cutoff and demonstrate that such removal ameliorates problems which have arisen in previous calculations due to large loop effects

Electromagnetic corrections to K -\u3epi pi. II. Dispersive matching

We express the leading electromagnetic corrections in K → ππ as integrals over the virtual photon squared-momentum Q2. The high Q2 behavior is obtained via the operator product expansion. The low Q2 behavior is calculated using chiral perturbation theory. We model the intermediate Q2 region using resonance contributions in order to enforce the matching of these two regimes. Our results confirm our previous estimates that the electromagnetic corrections provide a reasonably small shift in the I = 3/2 amplitude