Radiative corrections to neutral pion-pair production

We calculate the one-photon loop radiative corrections to the neutral pion-pair photoproduction process $\pi^-\gamma \to \pi^-\pi^0\pi^0$. At leading order this reaction is governed by the chiral pion-pion interaction. Since the chiral $\pi^+\pi^-\to\pi^0\pi^0$ contact-vertex depends only on the final-state invariant-mass it factors out of all photon-loop diagrams. We give analytical expressions for the multiplicative correction factor $R\sim \alpha/2\pi$ arising from eight classes of contributing one-photon loop diagrams. An electromagnetic counterterm has to be included in order to cancel the ultraviolet divergences generated by the photon-loops. Infrared finiteness of the virtual radiative corrections is achieved (in the standard way) by including soft photon radiation below an energy cut-off $\lambda$. The radiative corrections to the total cross section vary between $+2\%$ and $-2\%$ for center-of-mass energies from threshold up to $7m_\pi$. The finite part of the electromagnetic counterterm gives an additional constant contribution of about $1\%$, however with a large uncertainty.Comment: 10 pages, 6 figures, submitted to Eur. Phys. J.

Two-loop representations of low-energy pion form factors and pi-pi scattering phases in the presence of isospin breaking

Dispersive representations of the pi-pi scattering amplitudes and pion form factors, valid at two-loop accuracy in the low-energy expansion, are constructed in the presence of isospin-breaking effects induced by the difference between the charged and neutral pion masses. Analytical expressions for the corresponding phases of the scalar and vector pion form factors are computed. It is shown that each of these phases consists of the sum of a "universal" part and a form-factor dependent contribution. The first one is entirely determined in terms of the pi-pi scattering amplitudes alone, and reduces to the phase satisfying Watson's theorem in the isospin limit. The second one can be sizeable, although it vanishes in the same limit. The dependence of these isospin corrections with respect to the parameters of the subthreshold expansion of the pi-pi amplitude is studied, and an equivalent representation in terms of the S-wave scattering lengths is also briefly presented and discussed. In addition, partially analytical expressions for the two-loop form factors and pi-pi scattering amplitudes in the presence of isospin breaking are provided.Comment: 57 pages, 12 figure

Soft-photon corrections in multi-body meson decays

The effects due to soft-photon emission (and the related virtual corrections) in multi-body decays of B, D, and K mesons are analysed. We present analytic expressions for the universal O(alpha) correction factors which can be applied to all multi-body decay modes where a tight soft-photon energy cut in the decaying-particle rest-frame is applied. All-order resummations valid in the limit of small and large velocities of the final-state particles are also discussed. The phenomenological implications of these correction factors in the distortion of Dalitz-plot distributions of K -> 3 pi decays are briefly analysed.Comment: 8 pages, 2 figures (v2: minor modifications - published version

K^+ -> pi^+pi^0e^+e^-: a novel short-distance probe

We study the decay K^+ -> pi^+ pi^0 e^+ e^-, currently under analysis by the NA62 Collaboration at CERN. In particular, we provide a detailed analysis of the Dalitz plot for the long-distance, gamma^*-mediated, contributions (Bremsstrahlung, direct emission and its interference). We also examine a set of asymmetries to isolate genuine short-distance effects. While we show that charge asymmetries are not required to test short distances, they provide the best environment for its detection. This constitutes by itself a strong motivation for NA62 to study K^- decays in the future. We therefore provide a detailed study of different charge asymmetries and the corresponding estimated signals. Whenever possible, we make contact with the related processes K^+ -> pi^+ pi^0 gamma and K_L -> pi^+ pi^- e^+ e^- and discuss the advantages of K^+ -> pi^+ pi^0 e^+ e^- over them.Comment: 25 pages, 6 figure

Couplings of light I=0 scalar mesons to simple operators in the complex plane

The flavour and glue structure of the light scalar mesons in QCD are probed by studying the couplings of the I=0 mesons $\sigma(600)$ and $f_0(980)$ to the operators $\bar{q}q$, $\alpha_s G^2$ and to two photons. The Roy dispersive representation for the $\pi\pi$ amplitude $t_0^0(s)$ is used to determine the pole positions as well as the residues in the complex plane. On the real axis, $t_0^0$ is constrained to solve the Roy equation together with elastic unitarity up to the K\Kbar threshold leading to an improved description of the $f_0(980)$. The problem of using a two-particle threshold as a matching point is discussed. A simple relation is established between the coupling of a scalar meson to an operator $j_S$ and the value of the related pion form-factor computed at the resonance pole. Pion scalar form-factors as well as two-photon partial-wave amplitudes are expressed as coupled-channel Omn\`es dispersive representations. Subtraction constants are constrained by chiral symmetry and experimental data. Comparison of our results for the $\bar{q}q$ couplings with earlier determinations of the analogous couplings of the lightest I=1 and $I=1/2$ scalar mesons are compatible with an assignment of the $\sigma$, $\kappa$, $a_0(980)$, $f_0(980)$ into a nonet. Concerning the gluonic operator $\alpha_s G^2$ we find a significant coupling to both the $\sigma$ and the $f_0(980)$.Comment: 31 pages, 5 figure

K -> 3 pi Final State Interactions at NLO in CHPT and Cabibbo's Proposal to Measure a_0-a_2

We present the analytical results for the K -> 3 pi final state interactions at next-to-leading order (NLO) in CHPT. We also study the recent Cabibbo's proposal to measure the pi-pi scattering lenghts combination a_0-a_2 from the cusp effect in the pi^0-pi^0 energy spectrum at threshold for K^+ -> pi^0 pi^0 pi^+ and K_L -> pi^0 pi^0 pi^0$, and give the relevant formulas to describe it at NLO. For that, we use the NLO CHPT expression to fit the real part of K -> 3 pi to data while the pi-pi scattering lenghts are treated non-perturbatively. Using them, we make a quantitative estimate of the theoretical uncertaintity of the a_0-a_2 determination at NLO in our approach and obtain that it is not smaller than 5 % if added quadratically and 7 % if linearly for K^+ -> pi^0 pi^0 pi^+. One gets similar theoretical uncertainties if the neutral K_L -> pi^0 pi^0 pi^0 decay data below threshold are used instead. For this decay, there are very large theoretical uncertainties above threshold due to cancellations and data above threshold cannot be used to get the scattering lenghts. All the numbers we present are in the isospin limit apart of two-pion phase space factors which are physical. We compare our results for the cusp effect with Cabibbo and Isidori's results and discuss the differences and agreements. We also comment on the apperance of the singularity at the K -> 3 pi pseudo-threshold s=(m_K-m_pi)^2 in the discontinuity that defines the cusp.Comment: 31 pages, 8 figures. v2=v3 Added the full contributions to the cusp from the real part of the discontinuity. v4 Improved text. Matches published versio

Final state interaction in kaons decays

The kaons decays to the pairs of charged and neutral pions are considered in the framework of the non-relativistic quantum mechanics. The general expressions for the decay amplitudes to the two different channels accounting for the strong interaction between pions are obtained. The developed approach allows one to estimate the contribution of terms of any order in strong interaction and correctly takes into account the electromagnetic interaction between the pions in the final state.Comment: 8 page

Bremsstrahlung simulation in K to pi l^pm nu_l (gamma) decays

In physics simulation chains, the PHOTOS Monte Carlo program is often used to simulate QED effects in decays of intermediate particles and resonances. The program is based on an exact multiphoton phase space. In general, the matrix element is obtained from iterations of a universal kernel and approximations are involved. To evaluate the program precision, it is necessary to formulate and implement within the generator the exact matrix element, which depends on the decay channel. Then, all terms necessary for non-leading logarithms are taken into account. In the present letter we focus on the decay K to pi l^pm nu_l and tests of the PHOTOS Monte Carlo program. We conclude a 0.2% relative precision in the implementation of the hard photon matrix element into the emission kernel, including the case where approximations are used.Comment: 1+20 pages, 8 figure

Contributions from SUSY-FCNC couplings to the interpretation of the HyperCP events for the decay \Sigma^+ \to p \mu^+ \mu^-

The observation of three events for the decay $\Sigma^+ \to p \mu^+ \mu^-$ with a dimuon invariant mass of $214.3\pm0.5$MeV by the HyperCP collaboration imply that a new particle X may be needed to explain the observed dimuon invariant mass distribution. We show that there are regions in the SUSY-FCNC parameter space where the $A^0_1$ in the NMSSM can be used to explain the HyperCP events without contradicting all the existing constraints from the measurements of the kaon decays, and the constraints from the $K^0-\bar{K}^0$ mixing are automatically satisfied once the constraints from kaon decays are satisfied.Comment: 18 pages, 7 figure

Empirical parameterization of the K+- -> pi+- pi0 pi0 decay Dalitz plot

As first observed by the NA48/2 experiment at the CERN SPS, the \p0p0 invariant mass (M00) distribution from \kcnn decay shows a cusp-like anomaly at M00=2m+, where m+ is the charged pion mass. An analysis to extract the pi pi scattering lengths in the isospin I=0 and I=2 states, a0 and a2, respectively, has been recently reported. In the present work the Dalitz plot of this decay is fitted to a new empirical parameterization suitable for practical purposes, such as Monte Carlo simulations of K+- -> pi+- pi0 pi0 decays.Comment: 9 pages, 3 figures