arXiv subjects

Paul Tremper

Publications and source records attributed to Paul Tremper.

5 recordsLinked to original sources

arXiv2018

A Grand-Unified Nelson-Barr Model

We argue that the Nelson-Barr solution to the Strong CP Problem can be naturally realized in an E$_6$ Grand-Unified Theory. The chiral SM fermions reside in three generations of E$_6$ fundamentals together with heavy vectorlike down quarks, leptons doublets and right-handed neutrinos. CP is imposed on the Lagrangian and broken only spontaneously at high scales, leading to a mixing between chiral and vectorlike fields that allows to solve the Strong CP Problem through the Nelson-Barr mechanism. The main benefit of the E$_6$ GUT structure is the predictivity in the SM fermion sector, and a perfect fit to all SM observables can be obtained despite being over-constrained. Definite predictions are made for the neutrino sector, with a Dirac CP phase that is correlated to the CKM phase, allowing to test this model in the near future.

hep-ph↗

arXiv2016

Direct CP violation in $K\to ππ$ decays and supersymmetry

The quantities $ε_K^\prime$ and $ε_K$ measure the amount of direct and indirect CP violation in $K\to ππ$ decays, respectively. Using the recent lattice results from the RBC and UKQCD Collaborations and a new compact implementation of the $ΔS=1$ renormalization group evolution we predict $ \mbox{Re}\, \frac{ε_{K}'}{ε_{K}} = \left(1.06 \pm 5.07 \right) \times 10^{-4}$ in the Standard Model. This value is $2.8\,σ$ below the experimental value of $ \mbox{Re}\, \frac{ε_{K}'}{ε_{K}} = \left(16.6 \pm 2.3 \right) \times 10^{-4}.$ In generic models of new physics the well-understood $ε_K$ precludes large contributions to $ε_K^\prime$, if the new contributions enter at loop level. However, one can resolve the tension in $ε_{K}'/ε_{K}$ within the Minimal Supersymmetric Standard Model. To this end two features of supersymmetry are crucial: First, one can have large isospin-breaking contributions (involving the strong instead of the weak interaction) which enhance $ε_K^\prime$. Second, the Majorana nature of gluinos permits a suppression of the MSSM contribution to $ε_K$, because two box diagrams interfere destructively.

hep-ph↗

arXiv2016

Singularity-free Next-to-leading Order $ΔS= 1$ Renormalization Group Evolution and $ε_{K}^{\prime}/ε_{K}$ in the Standard Model and Beyond

The standard analytic solution of the renormalization group (RG) evolution for the $ΔS = 1$ Wilson coefficients involves several singularities, which complicate analytic solutions. In this paper we derive a singularity-free solution of the next-to-leading order (NLO) RG equations, which greatly facilitates the calculation of $ε_K^{\prime}$, the measure of direct $CP$ violation in $K\to ππ$ decays. Using our new RG evolution and the latest lattice results for the hadronic matrix elements, we calculate the ratio $ε_{K}^{\prime}/ε_{K}$ (with $ε_{K}$ quantifying indirect $CP$ violation) in the Standard Model (SM) at NLO to $ε_{K}^{\prime}/ε_{K} = (1.06 \pm 5.07) \times 10^{-4} $, which is $2.8\,σ$ below the experimental value. We also present the evolution matrix in the high-energy regime for calculations of new physics contributions and derive easy-to-use approximate formulae. We find that the RG amplification of new-physics contributions to Wilson coefficients of the electroweak penguin operators is further enhanced by the NLO corrections: If the new contribution is generated at the scale of 1-10 TeV, the RG evolution between the new-physics scale and the electroweak scale enhances these coefficients by 50-100 %. Our solution contains a term of order $α_{EM}^2/α_s^2$, which is numerically unimportant for the SM case but should be included in studies of high-scale new-physics.

hep-ph↗

arXiv2016

Recent progress on CP violation in $K\to ππ$ decays in the SM and a supersymmetric solution

Using the recent first lattice results of the RBC-UKQCD collaboration for $K \to ππ$ decays, we perform a phenomenological analysis of $ε_K^{\prime}/ε_K$ and find a discrepancy between SM prediction and experiments by $\sim 3\,σ$. We discuss an explanation by new physics. The well-understood value of $ε_K$, which quantifies indirect $CP$ violation, however, typically prevents large new physics contributions to $ε_K^{\prime}/ε_K$. In this talk, we show a solution of the $ε_K^{\prime}/ε_K$ discrepancy in the Minimal Supersymmetric Standard Model with squark masses above 3 TeV without fine-tuning of $CP$ phases. In this solution, the Trojan penguin diagram gives large isospin-breaking contributions which enhance $ε_K^{\prime}$, while the contribution to $ε_K$ is suppressed thanks to the Majorana nature of gluinos.

hep-ph↗

arXiv2016

Supersymmetric Explanation of CP Violation in $K\to ππ$ Decays

Recent progress in the determination of hadronic matrix elements has revealed a tension between the measured value of $ε_K^{\prime}/ε_K$, which quantifies direct $CP$ violation in $K \to ππ$ decays, and the Standard-Model prediction. The well-understood indirect $CP$ violation encoded in the quantity $ε_K$ typically precludes large new-physics contributions to $ε_K^{\prime}/ε_K$ and challenges such an explanation of the discrepancy. We show that it is possible to cure the $ε_K^{\prime}/ε_K$ anomaly in the Minimal Supersymmetric Standard Model with squark masses above 3 TeV without overshooting $ε_K$. This solution exploits two features of supersymmetry: the possibility of large isospin-breaking contributions (enhancing $ε_K^{\prime}$) and the Majorana nature of gluinos (permitting a suppression of $ε_K$). Our solution involves no fine-tuning of $CP$ phases or other parameters.

hep-ph↗