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We employ the chirally rotated Schrodinger functional ($chi$SF) to study two-point fermion bilinear correlation functions used in the determination of $Z_{A,V,S,P,T}$ on a series of well-tuned ensembles. The gauge configurations, which span renormalisation scales from 4 to 70~GeV, are generated with $N_{rm f}=3$ massless flavors and Schrodinger Functional (SF) boundary conditions. Valence quarks are computed with $chi$SF boundary conditions. We show preliminary results on the tuning of the $chi$SF Symanzik coefficient $z_f$ and the scaling of the axial current normalization $Z_{rm A}$. Moreover we carry out a detailed comparison with the expectations from one-loop perturbation theory. Finally we outline how automatically $mathrm{O}(a)$-improved $B_{rm K}$ matrix elements, including BSM contributions, can be computed in a $chi$SF renormalization scheme.
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Conventional scenarios of electroweak (EW) baryogenesis are strongly constrained by experimental searches for CP violation beyond the SM. We propose an alternative scenario where the EW phase transition and baryogenesis occur at temperatures of the order of a new physics threshold $Lambda$ far above the Fermi scale, say, in the $100-1000$ TeV range. This way the needed new sources of CP-violation, together with possible associated flavor-violating effects, decouple from low energy observables. The key ingredient is a new CP- and flavor-conserving sector at the Fermi scale that ensures the EW symmetry remains broken and sphalerons suppressed at all temperatures below $Lambda$. We analyze a minimal incarnation based on a linear $O(N)$ model. We identify a specific large-$N$ limit where the effects of the new sector are vanishingly small at zero temperature while being significant at finite temperature. This crucially helps the construction of realistic models. A number of accidental factors, ultimately related to the size of the relevant SM couplings, force $N$ to be above $sim 100$. Such a large $N$ may seem bizarre, but it does affect the simplicity of the model and in fact it allows us to carry out a consistent re-summation of the leading contributions to the thermal effective potential. Extensions of the SM Higgs sector can be compatible with smaller values $Nsim 20-30$. Collider signatures are all parametrically suppressed by inverse powers of $N$ and may be challenging to probe, but present constraints from direct dark matter searches cannot be accommodated in the minimal model. We discuss various extensions that satisfy all current bounds. One of these involves a new gauge force confining at scales between $sim1$ GeV and the weak scale.
The gradient flow provides a new class of renormalized observables which can be measured with high precision in lattice simulations. In principle this allows for many interesting applications to renormalization and improvement problems. In practice, however, such applications are made difficult by the rather large cutoff effects found in many gradient flow observables. At lowest order of perturbation theory we here study the leading cutoff effects in a finite volume gradient flow coupling with SF and SF-open boundary conditions. We confirm that O($a^2$) Symanzik improvement is achieved at tree-level, provided the action, observable and the flow are O($a^2$) improved. O($a^2$) effects from the time boundaries are found to be absent at this order, both with SF and SF-open boundary conditions. For the calculation we have used a convenient representation of the free gauge field propagator at finite flow times which follows from a recently proposed set-up by Luscher and renders lattice perturbation theory more practical at finite flow time and with SF, open, SF-open or open-SF boundary conditions.
In order to study the running coupling in four-flavour QCD, we review the set-up of the Schrodinger functional (SF) with staggered quarks. Staggered quarks require lattices which, in the usual counting, have even spatial lattice extent $L/a$ while the time extent $T/a$ must be odd. Setting $T=L$ is therefore only possible up to ${rm O}(a)$, which introduces different cutoff effects already in the pure gauge theory. We re-define the SF such as to cope with this situation and determine the corresponding classical background field. A perturbative calculation yields the coefficient of the pure gauge ${rm O}(a)$ boundary counterterm to one-loop order.
String theory has no parameter except the string scale, so a dynamically compactified solution to 4 dimensional spacetime should determine both the Planck scale and the cosmological constant $Lambda$. In the racetrack Kahler uplift flux compactification model in Type IIB theory, where the string theory landscape is generated by scanning over discrete values of all the flux parameters, a statistical preference for an exponentially small $Lambda$ is found to be natural (arXiv:1305.0753). Within this framework and matching the median $Lambda$ value to the observed $Lambda$, a mass scale ${bf m}simeq 100$ GeV naturally appears. We explain how the electroweak scale can be identified with this mass scale.
We consider origins of the baryon asymmetry which we observe today. We review the progress of electroweak-scale baryogenesis, and show a new mechanism, string-scale baryogenesis.
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