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Controllable text-to-image generation synthesizes visual text and objects in images with certain conditions, which are frequently applied to emoji and poster generation. Visual text rendering and layout-to-image generation tasks have been popular in controllable text-to-image generation. However, each of these tasks typically focuses on single modality generation or rendering, leaving yet-to-be-bridged gaps between the approaches correspondingly designed for each of the tasks. In this paper, we combine text rendering and layout-to-image generation tasks into a single task: layout-controllable text-object synthesis (LTOS) task, aiming at synthesizing images with object and visual text based on predefined object layout and text contents. As compliant datasets are not readily available for our LTOS task, we construct a layout-aware text-object synthesis dataset, containing elaborate well-aligned labels of visual text and object information. Based on the dataset, we propose a layout-controllable text-object adaptive fusion (TOF) framework, which generates images with clear, legible visual text and plausible objects. We construct a visual-text rendering module to synthesize text and employ an object-layout control module to generate objects while integrating the two modules to harmoniously generate and integrate text content and objects in images. To better the image-text integration, we propose a self-adaptive cross-attention fusion module that helps the image generation to attend more to important text information. Within such a fusion module, we use a self-adaptive learnable factor to learn to flexibly control the influence of cross-attention outputs on image generation. Experimental results show that our method outperforms the state-of-the-art in LTOS, text rendering, and layout-to-image tasks, enabling harmonious visual text rendering and object generation.

Future colliders aim to provide highly precise experimental measurements of the properties of the Higgs boson. In order to benefit from these precision machines, theoretical errors in the Higgs sector observables have to match at least the experimental uncertainties. The theoretical uncertainties in the Higgs sector observables can be reduced by including missing higher-order terms in their perturbative calculations. In this direction, we compute the mixed QCD-electroweak corrections at ${\mathcal O}(\alpha \alpha_s)$ to the Higgs decay into four charged leptons by considering the golden decay channel, $ H \to e^+e^-\mu^+\mu^-$. Due to color conservation, these corrections receive contributions only from the two-loop virtual diagrams. In the complex mass scheme, we find that the mixed QCD-electroweak corrections to the partial decay width, relative to the leading order predictions, are positive and about $0.27\%$ for $\alpha_s(M_Z)$. Relative to the next-to-leading order electroweak corrections, the mixed QCD-electroweak corrections are found to be approximately $18\%$ for $\alpha_s(M_Z)$. With respect to the leading order, we observe a flat effect of the mixed QCD-electroweak corrections on the invariant mass distribution of the lepton pairs with fixed QCD coupling. The $\phi$ distribution, due to the mixed QCD-electroweak corrections, follows a $(1-\cos \phi)$ dependence., Comment: 21 pages, 10 figures

A muon collider would enable the big jump ahead in energy reach that is needed for a fruitful exploration of fundamental interactions. The challenges of producing muon collisions at high luminosity and 10~TeV centre of mass energy are being investigated by the recently-formed International Muon Collider Collaboration. This Review summarises the status and the recent advances on muon colliders design, physics and detector studies. The aim is to provide a global perspective of the field and to outline directions for future work., Comment: 118 pages, 103 figures

Motivated by the recent rare B decays measurements, we study the matching procedure of operators $O_9, O_{10}$ in the low energy effective Hamiltonian and operators in the Standard Model effective theory (SMEFT). It is noticed that there are more related operators in the SMEFT whose coefficients can not be determined only from the low-energy data from B physics. We demonstrate how to determine these coefficients with some new physics models, like $Z^\prime$ model and leptoquark models, and then consider how to probe these operators of SMEFT at high energy by using the process $\mu^+\mu^-\to tc$ at future muon colliders, which can provide complementary information except for $\mu^+ \mu^- \to b s$ on the underlying models which lead to rare B decay processes. We perform a Monte Carlo study (a hadron level analysis) to show how to separate the signal events from the SM background events and estimate the sensitivity to the Wilson coefficients for different models., Comment: 29 pages, 8 figures, 3 tables, added references, publication version

Dark Matter is a necessary ingredient for a complete theory of Nature, which has so far remained elusive in laboratory searches for new particles. Searches at current and future colliders are in principle a promising way to search for electroweak charged dark matter particles, but the sensitivity of experiments at the LHC and future $pp$ colliders falls short to fully probe the whole mass range allowed for electroweak charged dark matter particles, which extends in principle up to the O(0.1) PeV. In this work we examine the effect of on-shell and off-shell propagation of electroweak charged thermal dark matter particles on integrated and differential rates of several Standard Model final states at the muon collider, considering candidates from weak 2-plet at the TeV scale up to 7-plet and 9-plet in the O(0.1) PeV ballpark. For fermionic WIMPs we find that all dark matter candidates with $n\leq 5$, corresponding to a thermal mass up to 14~TeV, can be excluded at the high-energy muon collider for some center-of-mass energy at or below 14~TeV. For the $n>5$ WIMPs our results show that higher energy muon colliders offer a route to conclusively probe both scalar and fermionic WIMPs off-shell production all the way up to the perturbativity bound for WIMP dark matter at O(0.1)~PeV. Our results bring WIMPs over the whole allowed mass range in the realm of collider searches and motivate research and development for the realization of a high energy muon collider., Comment: 11 pages, 9 figures

We compute the QCD corrections at next-to-leading order for the process $gg \rightarrow ZH$, including both the virtual two-loop terms and real-emission contributions. The two-loop box diagrams in the virtual corrections are approximated analytically over the complete phase space, combining the results of an expansion in the limit of small transverse momentum and an expansion in the regime of high energy. We obtain both inclusive and differential results for the cross section. We find that the NLO QCD corrections are of the same size as the LO contribution up to $ZH$ invariant masses close to 1 TeV, but they increase significantly when higher energies are considered, due to a class of real-emission diagrams in which the $Z$ boson is radiated from an open quark line. Finally, we estimate the uncertainty due to the renormalization scheme used for the top-quark mass both on the total and differential cross section., Comment: 19 pages, 6 figures; references added

We study the application of BCFW recursion relations to the QED processes $0\to e^- e^+ n \gamma$. Based on 6-point amplitudes (both MHVA and NMHVA) computed from Feynman diagrams in the Berends-Giele gauge, we conduct a comprehensive study on all different shifts. Then we propose a new shift (LLYZ shift) which can lead to the full amplitudes for these processes and can have some realistic computation advantages. We compare the number of terms and the independent amplitudes of this novel shift with a few typical shifts., Comment: Version accepted by CPC

In the path towards a muon collider with center of mass energy of 10 TeV or more, a stage at 3 TeV emerges as an appealing option. Reviewing the physics potential of such muon collider is the main purpose of this document. In order to outline the progression of the physics performances across the stages, a few sensitivity projections for higher energy are also presented. There are many opportunities for probing new physics at a 3 TeV muon collider. Some of them are in common with the extensively documented physics case of the CLIC 3 TeV energy stage, and include measuring the Higgs trilinear coupling and testing the possible composite nature of the Higgs boson and of the top quark at the 20 TeV scale. Other opportunities are unique of a 3 TeV muon collider, and stem from the fact that muons are collided rather than electrons. This is exemplified by studying the potential to explore the microscopic origin of the current $g$-2 and $B$-physics anomalies, which are both related with muons., Comment: 73 pages, 28 figures; Contribution to Snowmass 2021

The perspective of designing muon colliders with high energy and luminosity, which is being investigated by the International Muon Collider Collaboration, has triggered a growing interest in their physics reach. We present a concise summary of the muon colliders potential to explore new physics, leveraging on the unique possibility of combining high available energy with very precise measurements., Comment: 21 pages, 7 figures; Contribution to Snowmass 2021

MadGraph5_aMC@NLO is a software package that allows one to simulate processes of arbitrary complexity, at both the leading and the next-to-leading order perturbative accuracy, with or without matching and multi-jet merging to parton showers. It has been designed for, and so far primarily employed in the context of, hadronic collisions. In this note, we document the implementation of a few technical features that are necessary to extend its scope to realistic ee collider environments. We limit ourselves to discussing the unpolarized beam case, but we point out that the treatment of polarized beams is conceptually identical, and that the structure we set up can easily be extended to carry out simulations at muon colliders.

We study the observability of new interactions which modify Higgs-pair production via vector-boson fusion processes at the LHC and at future proton-proton colliders. In an effective-Lagrangian approach, we explore in particular the effect of the operator $h^2 W_{\mu\nu}^a W^{a,\mu\nu}$, which describes the interaction of the Higgs boson with transverse vector-boson polarization modes. By tagging highly boosted Higgs bosons in the final state, we determine projected bounds for the coefficient of this operator at the LHC and at a future 27 TeV or 100 TeV collider. Taking into account unitarity constraints, we estimate the new-physics discovery potential of Higgs pair production in this channel., Comment: 27 pages, 11 figures, 14 tables, added references

High-energy lepton colliders with a centre-of-mass energy in the multi-TeV range are currently considered among the most challenging and far-reaching future accelerator projects. Studies performed so far have mostly focused on the reach for new phenomena in lepton-antilepton annihilation channels. In this work we observe that starting from collider energies of a few TeV, electroweak (EW) vector boson fusion/scattering (VBF) at lepton colliders becomes the dominant production mode for all Standard Model processes relevant to studying the EW sector. In many cases we find that this also holds for new physics. We quantify the size and the growth of VBF cross sections with collider energy for a number of SM and new physics processes. By considering luminosity scenarios achievable at a muon collider, we conclude that such a machine would effectively be a "high-luminosity weak boson collider," and subsequently offer a wide range of opportunities to precisely measure EW and Higgs coupling as well as to discover new particles., Comment: 58 pages, 17 figures, 9 tables. A contribution to Snowmass 2021

Measuring the shape of the Higgs boson potential is of paramount importance and will be a challenging task at current as well as future colliders. While the expectations for the measurement of the trilinear Higgs self-coupling are rather promising, an accurate measurement of the quartic self-coupling interaction is presently considered extremely challenging even at a future 100 TeV proton-proton collider. In this work we explore the sensitivity that a muon collider with a center of mass energy in the multi-TeV range, and luminosities of the order of 10^35cm^-2s^-1, as presently under discussion, might provide thanks to a rather large three Higgs-boson production and to a limited background. By performing a first and simple analysis, we find a clear indication that a muon collider could provide a determination of the quartic Higgs self-coupling that is significantly better than what is currently considered attainable at other future colliders., Comment: Table 3 and figs.14-18 added. Matches version published on JHEP

At hadron colliders, the leading production mechanism for a pair of photons is from quark-anti-quark annihilation at the tree level. However, due to large gluon-gluon luminosity, the loop-induced process $gg\to \gamma \gamma$ provides a substantial contribution. In particular, the amplitudes mediated by the top quark become important at the $t \bar t$ threshold and above. In this letter we present the first complete computation of the next-to-leading order (NLO) corrections (up to $\alpha_S^3$) to this process, including contributions from the top quark. These entail two-loop diagrams with massive propagators whose analytic expressions are unknown and have been evaluated numerically. We find that the NLO corrections to the top-quark induced terms are very large at low diphoton invariant mass $m(\gamma \gamma)$ and close to the $t \bar t$ threshold. The full result including five massless quarks and top quark contributions at NLO displays a much more pronounced change of slope in the $m(\gamma \gamma)$ distribution at $t \bar t$ threshold than at LO and an enhancement at high invariant mass with respect to the massless calculation.

The computation of Feynman integrals is often the bottleneck of multi-loop calculations. We propose and implement a new method to efficiently evaluate such integrals in the physical region through the numerical integration of a suitable set of differential equations, where the initial conditions are provided in the unphysical region via the sector decomposition method. We present numerical results for a set of two-loop integrals, where the non-planar ones complete the master integrals for $gg\to\gamma\gamma$ and $q\bar{q}\to\gamma\gamma$ scattering mediated by the top quark., Comment: Minor changes, accepted version

We present a sensitivity study on the cubic and quartic self couplings in double Higgs production via gluon fusion at hadron colliders. Considering the relevant operators in the Standard Model Effective Field Theory up to dimension eight, we calculate the dominant contributions up to two-loop level, where the first dependence on the quartic interaction appears. Our approach allows to study the independent variations of the two self couplings and to clearly identify the terms necessary to satisfy gauge invariance and to obtain UV-finite results order by order in perturbation theory. We focus on the $b \bar b \gamma \gamma$ signature for simplicity and provide the expected bounds for the cubic and quartic self couplings at the 14 TeV LHC with 3000 fb$^{-1}$ (HL-LHC) and for a future 100 TeV collider (FCC-100) with 30 ab$^{-1}$. We find that while the HL-LHC will provide very limited sensitivity on the quartic self coupling, precision measurements of double Higgs production at a FCC-100 will offer the opportunity to set competitive bounds. We show that combining information from double and triple Higgs production leads to significantly improved prospects for the determination of the quartic self coupling., Comment: 35 pages, 18 figures, 2 tables

The scattering equations are a set of algebraic equations connecting the kinematic space of massless particles and the moduli space of Riemann spheres with marked points. We present an efficient method for solving the scattering equations based on the numerical algebraic geometry. The cornerstone of our method is the concept of the physical homotopy between different points in the kinematic space, which naturally induces a homotopy of the scattering equations. As a result, the solutions of the scattering equations with different points in the kinematic space can be tracked from each other. Finally, with the help of soft limits, all solutions can be bootstrapped from the known solution for the four-particle scattering., Comment: v2: published version. The code is available at https://github.com/zxrlha/sehomo

We study multi-Higgs final states in vector boson fusion (VBF) processes at the LHC and at future proton-proton colliders, focusing on the prospects for measurements at 27 TeV and at 100 TeV. We use an effective Lagrangian which includes higher-dimensional operators in the mass eigenstates which are relevant to VBF processes and relate this to specific parameterizations and models for new physics in the Higgs sector. We derive theoretical constraints on the parameter space from the unitarity of $2\to n$ scattering amplitudes and apply the results to $V V \to hh$ and $h h h$ processes, where $V=W,Z$. As a result, we present constraints on differential distributions as appropriate to the study of $V V \to hh$ and $h h h$ processes., Comment: 47 pages, 12 figures, 12 tables, major revision. This version focuses on the unitarity discussion of VBF processes

The effective coupling of the Higgs boson to a gluon pair is one of the most important parameters to test the Standard Model and search for the new physics beyond. In this paper, we propose several new observables based on the jet energy profile to extract the effective coupling. The statistical uncertainties of the effective coupling extracted by using new observables are derived and estimated based on the simulation at the future $e^+e^-$ collider for $250$ GeV center-of-mass energy and 5 ab$^{-1}$ integrated luminosity. We found that the statistical uncertainties of effective coupling via the optimized observable can reach about $1.6\%$ in the channels of a $Z$ boson decaying to lepton pairs and is reduced by $52\%$ compared to the relevant uncertainties in the conventional approach. These new observables potentially can be helpful for the measurement of effective coupling at future $e^+e^-$ colliders., Comment: 8 pages, 9 figures

We study the sensitivity to the shape of the Higgs potential of single, double, and triple Higgs production at future $e^+e^-$ colliders. Physics beyond the Standard Model is parameterised through the inclusion of higher-dimensional operators $(\Phi^\dagger \Phi- v^2/2)^n/\Lambda^{(2n-4)}$ with $n=3,4$, which allows a consistent treatment of independent deviations of the cubic and quartic self couplings beyond the tree level. We calculate the effects induced by a modified potential up to one loop in single and double Higgs production and at the tree level in triple Higgs production, for both $Z$ boson associated and $W$ boson fusion production mechanisms. We consider two different scenarios. First, the dimension six operator provides the dominant contribution (as expected, for instance, in a linear effective-field-theory(EFT)); we find in this case that the corresponding Wilson coefficient can be determined at $\mathcal{O}(10\%)$ accuracy by just combining accurate measurements of single Higgs cross sections at $\sqrt{\hat s}=$240-250 GeV and double Higgs production in $W$ boson fusion at higher energies. Second, both operators of dimension six and eight can give effects of similar order, i.e., independent quartic self coupling deviations are present. Constraints on Wilson coefficients can be best tested by combining measurements from single, double and triple Higgs production. Given that the sensitivity of single Higgs production to the dimension eight operator is presently unknown, we consider double and triple Higgs production and show that combining their information colliders at higher energies will provide first coarse constraints on the corresponding Wilson coefficient., Comment: minor changes, version accepted for publication in JHEP

We study one-loop effects induced by an anomalous Higgs trilinear coupling on total and differential rates for the $H\to 4\ell$ decay and some of the main single-Higgs production channels at the LHC, namely, VBF, $VH$, $t\bar tH$ and $tHj$. Our results are based on a public code that calculates these effects by simply reweighting samples of Standard-Model-like events for a given production channel. For $VH$ and $t\bar tH$ production, where differential effects are particularly relevant, we include Standard Model electroweak corrections, which have similar sizes but different kinematic dependences. Finally, we study the sensitivity of future LHC runs to determine the trilinear coupling via inclusive and differential measurements, considering also the case where the Higgs couplings to vector bosons and the top quark is affected by new physics. We find that the constraints on the couplings and the relevance of differential distributions critically depend on the expected experimental and theoretical uncertainties., Comment: 31 pages, 15 figures, 5 tables; Matches the journal version

We explore the potential for the discovery of the triple-Higgs signal in the $2b2l^{\pm}4j+E\!\!\!/$ decay channel at a $100$ TeV hadron collider. We consider both the Standard Model and generic new-physics contributions, described by an effective Lagrangian that includes higher-dimensional operators. The selected subset of operators is motivated by composite-Higgs and Higgs-inflation models. In the Standard Model, we perform both a parton-level and a detector-level analysis. Although the parton-level results are encouraging, the detector-level results demonstrate that this mode will be really challenging. However, sizable contributions from new effective operators can largely increase the cross section and/or modify the kinematics of the Higgs bosons in the final state. Taking into account the projected constraints from single and double Higgs-boson production, we propose benchmark points in the new physics models for the measurement of the triple-Higgs boson final state for future collider projects., Comment: 47 pages, 19 figures, 19 tables, added references, improved text, corrected typos

Since the discovery of the Higgs boson at the Large Hadron Collider, a future electron-position collider has been proposed for precisely studying its properties. We investigate the production of the Higgs boson at such an $e^+e^-$ collider associated with a $Z$ boson, and calculate for the first time the mixed QCD-electroweak corrections to the total cross sections. We provide an approximate analytic formula for the cross section and show that it reproduces the exact numeric results rather well for collider energies up to 350 GeV. We also provide numeric results for $\sqrt{s}=500$ GeV, where the approximate formula is no longer valid. We find that the $\mathcal{O}(\alpha\alpha_s)$ corrections amount to a 1.3% increase of the cross section for a center-of-mass energy around 240 GeV. This is significantly larger than the expected experimental accuracy and has to be included for extracting the properties of the Higgs boson from the measurements of the cross sections in the future., Comment: Version published in Phys.Rev.D