Renormalization of higher-dimensional operators from on-shell amplitudes

An analysis of the Fermi gamma-ray space telescope data has recently revealed a resolved gamma-ray feature close to the galactic center which is consistent with monochromatic photons at an energy of about 130 GeV. If interpreted in terms of dark matter (DM) annihilating into $\ensuremath{\gamma}\ensuremath{\gamma}$ ($\ensuremath{\gamma}Z$, $\ensuremath{\gamma}h$), this would correspond to a DM particle mass of roughly 130 GeV (145 GeV, 155 GeV). The rate for these loop-suppressed processes, however, is larger than typically expected for thermally produced DM. Correspondingly, one would generically expect even larger tree-level production rates of standard model fermions or gauge bosons. Here, we quantify this expectation in a rather model-independent way by relating the tree level and loop amplitudes with the help of the optical theorem. As an application, we consider bounds from continuum gamma rays, radio, and antiproton data on the tree-level amplitudes and translate them into constraints on the loop amplitudes. We find that, independently of the DM production mechanism, any DM model aiming at explaining the line signal in terms of charged standard model particles running in the loop is in rather strong tension with at least one of these constraints, with the exception of loops dominated by top quarks. We stress that attempts to explain the 130 GeV feature with internal bremsstrahlung do not suffer from such difficulties.

The field theoretic renormalization group technique together with the operator product expansion in the second order of the perturbation theory (in the two-loop approximation) is used for the investigation of the influence of the finite time correlations of the velocity field on the anomalous dimensions of the leading set of composite operators, which drive the anomalous scaling of correlation functions of a weak magnetic field in the framework of the kinematic Kazantsev–Kraichnan model in the presence of a large scale anisotropy. The system of possible scaling regimes of the model is found and two important special limits of the model are briefly discussed. The general two-loop expressions for the anomalous and critical dimensions of the leading composite operators are found as functions of the spatial dimension d and of the renormalization group fixed point value of the parameter u, which drives the presence of the finite time correlations of the velocity field in the model. The anisotropic hierarchies among various anomalous dimensions are investigated and it is shown that, regardless of the fixed point value of the parameter u as well as regardless of the spatial dimension of the system, the leading role in the anomalous scaling properties of the model is played by the anomalous dimensions of the composite operators near the isotropic shell, in accordance with the Kolmogorov’s local isotropy restoration hypothesis. The properties of the anomalous dimensions of the leading composite operators in the Kazantsev–Kraichnan model with finite time correlations of the velocity field are compared to the properties of the corresponding anomalous dimensions of the composite operators relevant in the framework of the Kraichnan model of passively advected scalar field with finite time correlations. It is shown that, regardless of the fixed point value of the parameter u, the two-loop corrections to the anomalous dimensions are much more important in the framework of the Kazantsev–Kraichnan vector model than in the Kraichnan model of a passive scalar advection. At the same time, again regardless of the strength of time correlations, the two-loop values of the leading anomalous dimensions in the Kazantsev–Kraichnan model of the passive magnetic field are significantly more negative than the corresponding two-loop values of the relevant anomalous dimensions in the framework of the Kraichnan model. It means that the anomalous scaling of the correlation functions of the passive magnetic field, deep inside the inertial interval of the turbulent environment with finite time correlations of the velocity field, must be much more pronounced than in the case of the correlation functions of the passively advected scalar field.

We introduce the computer code Recola for the recursive generation of tree-level and one-loop amplitudes in the Standard Model. Tree-level amplitudes are constructed using off-shell currents instead of Feynman diagrams as basic building blocks. One-loop amplitudes are represented as linear combinations of tensor integrals whose coefficients are calculated similarly to the tree-level amplitudes by recursive construction of loop off-shell currents. We introduce a novel algorithm for the treatment of colour, assigning a colour structure to each off-shell current which enables us to recursively construct the colour structure of the amplitude efficiently. Recola is interfaced with a tensor-integral library and provides complete one-loop Standard Model amplitudes including rational terms and counterterms. As a first application we consider Z+2jets production at the LHC and calculate with Recola the next-to-leading-order electroweak corrections to the dominant partonic channels.

A bstract The precise measurement of the Higgs boson properties requires a robust framework to parametrize possible deviations from Standard Model (SM) predictions in the most model-independent way possible. The Effective Field Theory (EFT) framework has become the most widely used since it offers a broad scope and a consistent path to increase the precision of the computations. Two prominent EFTs are the Standard Model Effective Field Theory (SMEFT) and the Higgs Effective Field Theory (HEFT). While similar in many aspects, their phenomenological differences are nowhere more pronounced than in multi-Higgs production. To precisely chart the separation between both EFTs, we study gluon-fusion double and triple Higgs production using bootstrapped on-shell amplitudes. This allows us to get the kinematic dependence of the gauge-invariant amplitude without field-redefinition ambiguities. As part of our study, we develop a technique that allows to build tree-level five-point on-shell amplitudes from lower-point on-shell amplitudes and bootstrapped contact terms. We then match the bootstrapped on-shell scattering amplitudes to the amplitudes computed in SMEFT (up to order 1/Λ 4 ) and HEFT (at NNLO) and analyze the EFT order at which each kinematic structure appears. We also show how certain structures in gg → hhh appear only at dimension-12 in SMEFT or N 3 LO in HEFT.

The search for dark matter (DM) at colliders is founded on the idea of looking for something invisible. There are searches based on production and decay processes where DM may reveal itself as missing energy. If nothing is found, our best tool to constrain the parameter space of many extensions of the Standard Model (SM) with a DM candidate is the Higgs boson. As the measurements of the Higgs couplings become increasingly precise, higher-order corrections will start to play a major role. The tree-level contribution to the invisible decay width provides information about the portal coupling. Higher-order corrections also give us access to other parameters from the dark sector of the Higgs potential that are not present in the tree-level amplitude. In this work we will focus on the complex singlet extension of the SM in the phase with a DM candidate. We calculate the one-loop electroweak corrections to the decay of the Higgs boson into two DM particles. We find that the corrections are stable and of the order of a few percent. The present measurement of the Higgs invisible branching ratio, $\mathrm{BR}(H\ensuremath{\rightarrow}\text{ }\mathrm{invisible})<0.11$, already constrains the parameter space of the model at leading order. We expect that by the end of the LHC the experimental measurement will require the inclusion of the electroweak corrections to the decay in order to match the experimental accuracy. Furthermore, the only competing process, which is direct detection, is shown to have a cross section below the neutrino floor.

The observation of lepton number violation would provide strong evidence for physics beyond the Standard Model, with neutrinoless double beta decay ($0\nu\beta\beta$) serving as one of the most sensitive experimental probes. In the context of the Standard Model Effective Field Theory (SMEFT), our analysis demonstrates that one-loop corrections can considerably enhance the constraints on new physics scales that are set at tree level for several dimension-7 operators. Through specific ultraviolet (UV) model scenarios, we explore how contributions to $0\nu\beta\beta$ from both dimension-7 and loop-generated dimension-5 SMEFT operators can compete and interplay.

In this work we propose improved holographic hard wall (HW) models by the inclusion of anomalous dimensions in the dual operators that describe glueballs inspired by the AdS/CFT correspondence. The anomalous dimensions come from well known semiclassical gauge/string duality analysis showing a dependence with the logarithm of spin S of the boundary states. We show that these logarithm anomalous dimensions of the high spin operators combined with the usual HW model allow us to match the pomeron trajectory and give glueball masses that are better than that of the original HW and soft wall models in comparison with lattice data. We also build up other anomalous HW models considering that the logarithm anomalous dimensions can be approximated by a truncated series of odd powers of the difference S−1/S. These models also fit the pomeron trajectory and produce good glueball masses. Then, we consider an anomalous dimension that is proportional to S, providing reasonable results. Finally, we propose an asymptotic linear anomalous HW model that effective dimensions for high spins operators are of the form Δ=aS+b, where a and b are constants to be fixed by comparison with the soft pomeron trajectory. In this last model, the Regge trajectory is asymptotically linear even for very high spins (J∼100) matching the soft pomeron trajectory accurately and generates glueball masses with deviations with respect to the lattice data better than the original HW and soft wall models. Published by the American Physical Society 2024

We study the scattering amplitudes of mass-deformed Chern-Simons theories and Yang-Mills-Chern-Simons theories with $\mathcal{N}=2$ supersymmetry in three dimensions. In particular, we derive the on-shell supersymmetry algebras which underlie the scattering matrices of these theories. We then compute various 3 and 4-point on-shell tree-level amplitudes in these theories. For the mass-deformed Chern-Simons theory, odd-point amplitudes vanish and we find that all of the 4-point amplitudes can be encoded elegantly in superamplitudes. For the Yang-Mills-Chern-Simons theory, we obtain all of the 4-point tree-level amplitudes using a combination of perturbative techniques and algebraic constraints and we comment on difficulties related to computing amplitudes with external gauge fields using Feynman diagrams. Finally, we propose a Britto-Cachazo-Feng-Witten recursion relation for mass-deformed theories in three dimensions and discuss the applicability of this proposal to mass-deformed $\mathcal{N}=2$ theories.

We develop the idea of an effective conformal theory describing the low-lying spectrum of the dilatation operator in a CFT. Such an effective theory is useful when the spectrum contains a hierarchy in the dimension of operators, and a small parameter whose role is similar to that of 1/N in a large N gauge theory. These criteria insure that there is a regime where the dilatation operator is modified perturbatively. Global AdS is the natural framework for perturbations of the dilatation operator respecting conformal invariance, much as Minkowski space naturally describes Lorentz invariant perturbations of the Hamiltonian. Assuming that the lowest-dimension single-trace operator is a scalar, O, we consider the anomalous dimensions, gamma(n,l), of the double-trace operators of the form O (del^2)^n (del)^l O. Purely from the CFT we find that perturbative unitarity places a bound on these dimensions of |gamma(n,l)|<4. Non-renormalizable AdS interactions lead to violations of the bound at large values of n. We also consider the case that these interactions are generated by integrating out a heavy scalar field in AdS. We show that the presence of the heavy field "unitarizes" the growth in the anomalous dimensions, and leads to a resonance-like behavior in gamma(n,l) when n is close to the dimension of the CFT operator dual to the heavy field. Finally, we demonstrate that bulk flat-space S-matrix elements can be extracted from the large n behavior of the anomalous dimensions. This leads to a direct connection between the spectrum of anomalous dimensions in d-dimensional CFTs and flat-space S-matrix elements in d+1 dimensions. We comment on the emergence of flat-space locality from the CFT perspective.

The significance of the electroweak phase transition is undeniable, and although initially it was believed that it was second order, it is now believed that it is a first-order transition. However, it is not a strong first-order phase transition in the context of the standard model, and the remedy to this issue is to use the Higgs portal and directly couple the Higgs to a hidden scalar sector. This can result in a strong electroweak phase transition, while the couplings to a hidden scalar are constrained by several phenomenological constraints, such as the sphaleron rate criterion and the branching ratio of the Higgs to invisible channels. In this work, we consider the standard singlet extensions of the standard model, including dimension-six non-renormalizable operators that couple a real singlet scalar field with the Higgs doublet. As a result, we examine the effects of those Higgs-singlet couplings on the electroweak phase transition. The effective theory, where the nonrenormalizable couplings originate from, is considered to be active beyond 15 TeV. As we show, the Universe experiences a two-step electroweak phase transition, a primary phase transition in the singlet sector at a high temperature, and then a subsequent first-order phase transition from the singlet vacuum to the electroweak vacuum. The singlet’s phase transition can either be second order or first order, depending on the singlet mass and its couplings to the Higgs. In particular, we show that the dimension-six operator assists in generating a strong electroweak phase transition in regions of the parameter space that were excluded in the previous singlet extensions of the standard model. This is further apparent for low singlet masses mS&lt;mH/2, which are rarely taken into account in the literature due to the invisible branching ratio of the Higgs boson. In some limited cases in the parameter space, the electroweak phase transition is weakened by the presence of the higher order operator. Published by the American Physical Society 2024

A simple extension of the standard model (SM) with a μ-flavored vector-like lepton (VLL) doublet and a real singlet scalar can have an interesting implication to the h → μ + μ – decay while offering the simplest possible explanation for the dark matter (DM) phenomenology. Assuming the real singlet scalar to be a viable DM candidate, it has been shown that the muon Yukawa coupling can have a negative contribution at the one-loop order if the 2nd generation SM leptons are allowed to couple with the VLL doublet. The stringent direct detection bounds corresponding to a real singlet scalar DM can easily be relaxed if the SM quark sector was augmented with a dimension-6 operator at some new physics (NP) scale Λ NP. Thus, this model presents a significant phenomenological study where the muon Yukawa coupling can be corrected within a real singlet scalar DM framework. The considered parameter space can be tested/constrained through the high luminosity run of the LHC (HL-LHC) and future direct detection experiments.

We present the first calculations of next-to-next-to-next-to-next-to-leading order (N4LO) contributions to anomalous dimensions of spin-N twist-2 operators in perturbative QCD. Specifically, we have obtained the respective non-singlet quark–quark anomalous dimensions at N=2 and N=3 to the fifth order in the strong coupling αs. These results set the scale for the N4LO contributions to the evolution of the non-singlet quark distributions of hadrons outside the small-x region, and facilitate a first approximate determination of the five-loop cusp anomalous dimension. While the N4LO coefficients are larger than expected from the lower-order results, their inclusion stabilizes the perturbative expansions for three or more light flavours at a sub-percent accuracy for αs<0.3.

We study probes of neutral triple gauge couplings (nTGCs) at the LHC and the proposed 100 TeV &lt;math display="inline"&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/math&gt; colliders, and compare their sensitivity reaches with those of proposed &lt;math display="inline"&gt;&lt;msup&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;/msup&gt;&lt;/math&gt; colliders. The nTGCs provide a unique window to the new physics beyond the Standard Model (SM) because they can arise from SM effective field theory operators that respect the full electroweak gauge group &lt;math display="inline"&gt;&lt;mrow&gt;&lt;mi&gt;SU&lt;/mi&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi mathvariant="normal"&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo stretchy="false"&gt;⊗&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi mathvariant="normal"&gt;U&lt;/mi&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi mathvariant="normal"&gt;Y&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt; of the SM only at the level of dimension-8 or higher. We derive the neutral triple gauge vertices (nTGVs) generated by these dimension-8 operators in the broken phase and map them onto a newly generalized form factor formulation, which takes into account only the residual &lt;math display="inline"&gt;&lt;mrow&gt;&lt;mi mathvariant="normal"&gt;U&lt;/mi&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;em&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt; gauge symmetry. Using this mapping, we derive new nontrivial relations between the form factors that guarantee a truly consistent form factor formulation of the nTGVs and remove large unphysical energy-dependent terms. We then analyze the sensitivity reaches of the LHC and future 100 TeV hadron colliders for probing the nTGCs via both the dimension-8 nTGC operators and the corresponding nTGC form factors in the reaction &lt;math display="inline"&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mover accent="true"&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo stretchy="false"&gt;¯&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo stretchy="false"&gt;→&lt;/mo&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt; with &lt;math display="inline"&gt;&lt;mrow&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mo stretchy="false"&gt;→&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;ℓ&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;ℓ&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;, &lt;math display="inline"&gt;&lt;mrow&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;mover accent="true"&gt;&lt;mrow&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo stretchy="false"&gt;¯&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;. We compare their sensitivities with the existing LHC measurements of nTGCs and with those of the high-energy &lt;math display="inline"&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt; colliders. In general, we find that the prospective LHC sensitivities are comparable to those of an &lt;math display="inline"&gt;&lt;msup&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;/msup&gt;&lt;/math&gt; collider with center-of-mass energy &lt;math display="inline"&gt;&lt;mrow&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi&gt;TeV&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;, whereas an &lt;math display="inline"&gt;&lt;msup&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;/msup&gt;&lt;/math&gt; collider with center-of-mass energy (3–5) TeV would have greater sensitivities, and a 100 TeV &lt;math display="inline"&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/math&gt; collider could provide the most sensitive probes of the nTGCs.

We study integrability of fishnet-type Feynman graphs arising in planar four-dimensional bi-scalar chiral theory recently proposed in arXiv:1512.06704 as a special double scaling limit of gamma-deformed mathcal{N} = 4 SYM theory. We show that the transfer matrix “building” the fishnet graphs emerges from the R−matrix of non-compact conformal SU(2, 2) Heisenberg spin chain with spins belonging to principal series representations of the four-dimensional conformal group. We demonstrate explicitly a relationship between this integrable spin chain and the Quantum Spectral Curve (QSC) of mathcal{N} = 4 SYM. Using QSC and spin chain methods, we construct Baxter equation for Q−functions of the conformal spin chain needed for computation of the anomalous dimensions of operators of the type tr(ϕ1J) where ϕ1 is one of the two scalars of the theory. For J = 3 we derive from QSC a quantization condition that fixes the relevant solution of Baxter equation. The scaling dimensions of the operators only receive contributions from wheel-like graphs. We develop integrability techniques to compute the divergent part of these graphs and use it to present the weak coupling expansion of dimensions to very high orders. Then we apply our exact equations to calculate the anomalous dimensions with J = 3 to practically unlimited precision at any coupling. These equations also describe an infinite tower of local conformal operators all carrying the same charge J = 3. The method should be applicable for any J and, in principle, to any local operators of bi-scalar theory. We show that at strong coupling the scaling dimensions can be derived from semiclassical quantization of finite gap solutions describing an integrable system of noncompact SU(2, 2) spins. This bears similarities with the classical strings arising in the strongly coupled limit of mathcal{N} = 4 SYM.

We elucidate aspects of the one-loop anomalous dimension of so(6)-singlet multi-trace operators in N=4SU(Nc) SYM at finite Nc. First, we study how 1/Nc corrections lift the large Nc degeneracy of the spectrum, which we call the operator submixing problem. We observe that all large Nc zero modes acquire anomalous dimensions starting at order 1/Nc2 with a non-positive coefficient and they mix only among the operators with the same number of traces at leading order. Second, we study the lowest one-loop dimension of operators of length equal to 2Nc. The dimension of such operators becomes more negative as Nc increases, which will eventually diverge in the double scaling limit. Third, we examine the structure of level-crossing at finite Nc in view of unitarity. Finally we find out a correspondence between the large Nc zero modes and completely symmetric polynomials of Mandelstam variables.