We calculate the renormalisation group running of the bosonic Standard Model (SM) effective operators at one loop and to order $v^4/Λ^4$, with $v\sim 246$ GeV being the electroweak scale and $Λ$ the unknown new physics threshold. We focus on contributions driven by one dimension-eight term and SM couplings, thus extending (and completing) the effort initiated in arXiv:2106.05291, in which quantum corrections from pairs of dimension-six interactions were considered. We highlight some interesting consequences, including the renormalisation of loop-induced interactions by tree-level generated terms and, more importantly, the validity of positivity bounds on different operators inducing anomalous gauge quartic couplings.
We compute the one-loop renormalisation group running of the bosonic Standard Model effective operators to order $v^4/Λ^4$, with $v\sim 246$ GeV being the electroweak scale and $Λ$ the unknown new physics threshold. We concentrate on the effects triggered by pairs of the leading dimension-six interactions, namely those that can arise at tree level in weakly-coupled ultraviolet completions of the Standard Model. We highlight some interesting consequences, including the interplay between positivity bounds and the form of the anomalous dimensions; the non renormalisation of the $S$ and $U$ parame…
The details of the recent calculation of the two-loop bosonic corrections to the muon lifetime in the Standard Model are presented. The matching on the Fermi theory is discussed. Renormalisation in the on-shell and in the MS scheme is studied and transition between the schemes is shown to lead to identical results. High precision numerical methods are compared with mass difference and large mass expansions.
We present a basis of dimension-eight Green's functions involving Standard Model (SM) bosonic fields, consisting of 86 new operators. Rather than using algebraic identities and integration by parts, we prove the independence of these interactions in momentum space, including a discussion on evanescent bosonic operators. Our results pave the way for renormalising the SM effective field theory (SMEFT), as well as for performing matching of ultraviolet models onto the SMEFT, to higher order. To demonstrate the potential of our construction, we have implemented our basis in matchmakereft and used …
The functional renormalisation group is used for the BCS-BEC crossover in gases of ultracold fermionic atoms. In a simple truncation, we see how universality and an effective theory with composite bosonic di-atom states emerge. We obtain a unified picture of the whole phase diagram. The flow reflects different effective physics at different scales. In the BEC limit as well as near the critical temperature, it describes an interacting bosonic theory.
We consider here in a toy model an approach to bound state problem in a nonperturbative manner using equal time algebra for the interacting field operators. Potential is replaced by offshell bosonic quanta inside the bound state of nonrelativistic particles. The bosonic dressing is determined through energy minimisation, and mass renormalisation is carried out in a nonperturbative manner. Since the interaction is through a scalar field, it does not include spin effects. The model however nicely incorporates an intuitive picture of hadronic bound states in which the gluon fields dress the quark…
Focusing on four-Higgs interactions, we analyse the robustness of tree-level-derived positivity bounds on Standard Model effective field theory (SMEFT) operators under quantum corrections. Among other results, we demonstrate that: (i) Even in the simplest extensions of the Standard Model, e.g. with one new scalar singlet or with a neutral triplet, some positivity bounds are strictly violated; (ii) the mixing of the dimension-eight operators under renormalisation, which we compute here for the first time, can drive them out of their positivity region; (iii) the running of the dimension-eight in…
In this publication we present an extension of the Standard Model within the framework of Connes' noncommutative geometry [1]. The model presented here is based on a minimal spectral triple [7] which contains the Standard Model particles, new vectorlike fermions and a new U(1) gauge subgroup. Additionally a new complex scalar field appears that couples to the right-handed neutrino, the new fermions and the standard Higgs particle. The bosonic part of the action is given by the spectral action [1] which also determines relations among the gauge couplings, the quartic scalar couplings and the Yu…
We study the bosonic excitations in the favorite cubic three flavor crystalline LOFF phases of QCD. We calculate in the Ginzburg-Landau approximation the masses of the eight pseudo Nambu-Goldstone Bosons (NGB) present in the low energy theory. We also compute the decay constants of the massless NGB Goldstones associated to superfluidity as well as those of the eight pseudo NGB. Differently from the corresponding situation in the Color-Flavor-Locking phase, we find that meson condensation phases are not expected in the present scenario.
Inflationary reheating via resonant production of non-minimally coupled scalar particles with only gravitational coupling is shown to be extremely strong, exhibiting a negative coupling instability for $ξ< 0$ and a wide resonance decay for $ξ\gg 1$. Since non-minimal fields are generic after renormalisation in curved spacetime, this offers a new paradigm in reheating - one which naturally allows for efficient production of the massive bosons needed for GUT baryogenesis. We also show that both vector and tensor fields are produced resonantly during reheating, extending the previously known corr…
The symmetry breakdown pattern is studied in models containing one fermion flavor multiplet and a multicomponent scalar field, supplemented with a chiral Yukawa-interaction, and in presence of an explicit symmetry breaking source quadratic in the scalar field. In a detailed investigation of the model with $U_L(1) \times U_R(1)$ chiral symmetry it is shown that by diminishing the strength of quadratic explicit symmetry breaking one can still keep stable the mass ratio of the fermionic and the pseudo-Goldstone excitation. At the same time the mass ratio of the two bosonic excitations appears to …
Recently exact results for the complete fermionic two-loop contributions to the prediction for the W-boson mass from muon decay in the electroweak Standard Model have been published [hep-ph/0007091]. This paper illustrates the techniques that have been applied for this calculation, in particular the renormalisation procedure and the treatment of IR-divergent QED contributions. Numerical results are presented in terms of simple parametrisation formulae and compared in detail with a previous result of an expansion up to next-to-leading order in the top-quark mass. An estimate of the remaining th…
$S$-matrix elements are invariant under field redefinitions of the Lagrangian. They are determined by geometric quantities such as the curvature of the field-space manifold of scalar and gauge fields. We present a formalism where scalar and gauge fields are treated together, with a metric on the combined space of both types of fields. Scalar and gauge scattering amplitudes are given by the Riemann curvature $R_{ijkl}$ of this combined space, with indices $i,j,k,l$ chosen to be scalar or gauge indices depending on the type of external particle. One-loop divergences can also be computed in terms…
We derive bounds on couplings in the standard model effective field theory (SMEFT) as a consequence of causality and the analytic structure of scattering amplitudes. In the SMEFT, there are 64 independent operators at mass dimension eight that are quartic in bosons (either Higgs or gauge fields) and that contain four derivatives and/or field strengths, including both CP-conserving and CP-violating operators. Using analytic dispersion relation arguments for two-to-two bosonic scattering amplitudes, we derive 27 independent bounds on the sign or magnitude of the couplings. We show that these bou…
We discuss the implications of dimension-six operators of the Effective Field Theory (EFT) framework in the study of Vector Boson Scattering (VBS) in the $pp \to Z Z j j $ channel. We show that operators of dimension-six should not be neglected in favour of those of dimension-eight. We observe that this process is very sensitive to some of the operators commonly fit using LEP and Higgs data, and that it can be used to improve the bounds on the former. Further we show that other operators than the ones generating anomalous triple and quartic gauge couplings (aTGCs/aQCGs) can have a non-negligib…
CP violation in the standard model originates from the Cabibbo-Kobayashi-Maskawa mixing matrix. Upon integrating all fermions out of the theory, its effects are captured by a series of effective nonrenormalizable operators for the bosonic gauge and Higgs fields. We compute the CP-violating part of the effective action to the leading nontrivial, sixth order in the covariant gradient expansion as a function of temperature. In the limit of zero temperature, our result addresses the discrepancy between two independent calculations existing in the literature [1,2]. We find that CP violation in the …
Let $Θ$ be the Wigner time reversal operator for spin half and let $ϕ$ be a Weyl spinor. Then, for a left-transforming $ϕ$, the construct $ζ_λΘϕ^\ast$ yields a right-transforming spinor. If instead, $ϕ$ is a right-transforming spinor, then the construct $ζ_ρΘϕ^\ast$ results in a left-transforming spinor ($ζ_{λ,ρ}$ are phase factors). This allows us to introduce two sets of four-component spinors. Setting $ζ_λ$ and $ζ_ρ$ to $\pm i$ render all eight spinors as eigenspinor of the charge conjugation operator~$\mathcal{C}$ (called ELKO). This allows us to introduce two quantum fields. A calculation…
We determine complete one-loop beta functions of the multi-scalar four-point couplings in four-dimensional $SU(N)$ gauge theories with $M$ adjoint scalar multiplets. For adjoints scalars, the sign of the one loop gauge coupling beta function depends solely on $M$, vanishing and changing sign precisely at $M=22$. For the multi-scalar potential at fixed gauge coupling we find several fixed points with different stability properties at large $N$. The analysis crucially involves the full set of four $SU(N)$ and $O(M)$ invariant single trace and double trace couplings. Taking the gauge coupling int…
Some time ago Rubakov and Shaposhnikov (RS) suggested that elementary particles might be excitations trapped on a soliton in a flat higher dimensional space. They gave as an example phi-4 theory in five dimensions with a bosonic excitation on a domain wall in the fifth dimension. They also trapped a chiral Dirac particle on the domain wall. We extend the RS field equation for the Dirac particle to eight flat dimensions (M4 X R4) and replace the one-dimensional domain-wall potential with a harmonic- oscillator "potential" in the four higher dimensions. This generates bound states in approximate…
