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Lorentz invariant quantum field theories (QFTs) in four spacetime dimensions (4D) have a $\mathbb{Z}_4$ symmetry provided there exists a basis of operators in the QFT where all operators have even operator dimension, $d$, including those with $d > 4$. The $\mathbb{Z}_4$ symmetry is the extension of operator dimension parity by fermion number parity. If the $\mathbb{Z}_4$ is anomaly-free, such QFTs can be related to 3D topological superconductors. Additionally, imposing the $\mathbb{Z}_4$ symmetry on the Standard Model effective field theory severely restricts the allowed processes that violate baryon and lepton numbers., Comment: 7 pages + references, 1 figure

In this contribution to the Snowmass 2021 process we review theoretical developments in the Standard Model Effective Field Theory (SMEFT) with a focus on effects at the dimension-8 level and beyond. We review the theoretical advances that led to the complete construction of the operator bases for the dimension-8 and dimension-9 SMEFT Lagrangians. We discuss the possibility of obtaining all-orders results in the $1/\Lambda$ expansion for certain SMEFT observables as well as the current status of renormalization group running and implications for positivity, and briefly present the on-shell approach to constructing SMEFT amplitudes. Finally we present several new phenomenological effects that first arise at dimension-8 and discuss the impact of these terms on experimental analyses., Comment: 37 pages, 6 figures; contribution to Snowmass 2021; new section and additional authors

We construct a complete basis of dimension-8 operators in the Low-Energy Effective Field Theory below the Electroweak Scale (LEFT). We find there are 35058 dimension-8 operators in the LEFT for two generations of up-type quarks and three generations of down-type quarks, charged leptons, and left-handed neutrinos. The existence of this operator basis is a necessary prerequisite for matching to the Standard Model Effective Field Theory at the dimension-8 level., Comment: 29 pages, 20 tables; v3: minor typos corrected

We present a complete basis of dimension-8 operators in the Standard Model Effective Field Theory. Attention is paid to operators that vanish in the absence of flavor structure. There are dimension-8 SMEFT 44,807 operators. We also briefly discuss a few aspects of phenomenology involving dimension-8 operators, including light-by-light scattering and electroweak precision data., Comment: 50 pages, 21 tables; v6: minor update, $\epsilon \tau^I$ ($\tau^I \epsilon$) goes with a pair of $SU(2)_w$ doublet (anti-)fermions

Measurements from the Gaia satellite have greatly increased our knowledge of the dark matter velocity distributions in the Solar neighborhood. There is evidence for multiple cold structures nearby, including a high-velocity stream counterrotating relative to the Sun. This stream could significantly alter the spectrum of recoil energies and increase the annual modulation of dark matter in direct detection experiments such as DAMA/Libra. We reanalyze the experimental limits from Xenon1T, CDMSlite, PICO-60 and COSINE-100, and compare them to the results of the DAMA/Libra experiment. While we find that this new component of the dark matter velocity distribution can greatly improve the fit to the DAMA/Libra data, both spin-independent and spin-dependent interpretations of the DAMA/Libra signal with elastic and inelastic scattering continue to be ruled out by the null results of other experiments, in particular Xenon1T., Comment: 23 pages, 17 figures, updated references. Version published in PRD

A common problem in a high energy physics experiment is extracting a signal from a much larger background. Posed as a classification task, there is said to be an imbalance in the number of samples belonging to the signal class versus the number of samples from the background class. In this work we provide a brief overview of class imbalance techniques in a high energy physics setting. Two case studies are presented: (1) the measurement of the longitudinal polarization fraction in same-sign $WW$ scattering, and (2) the decay of the Higgs boson to charm-quark pairs., Comment: v2: 22 pages, 4 figures, 3 tables, matches journal version

We derive model-independent bounds on the form factors for the decay $B_c^+ \to \eta_c\, \ell^+\, \nu$ including full mass effects, i.e. $\ell = e,\, \mu, \text{ and } \tau$. The bounds are obtained by using the BGL parameterization for the form factors, and fitting to the preliminary lattice data of the HPQCD Collaboration. Our main result after bounding the form factors is the Standard Model (SM) prediction for the ratio of branching fractions $R(\eta_c) = \mathcal{B}(B_c^+ \to \eta_c\, \tau^+\, \nu_{\tau}) / \mathcal{B}(B_c^+ \to \eta_c\, \mu^+\, \nu_{\mu})$. We find $R(\eta_c)|_{\text{SM}} = 0.31^{+0.04}_{-0.02}$, and argue that a measurement of $R(\eta_c)$ is within the reach of LHCb during the high luminosity run of the LHC. In addition, using the heavy-quark spin symmetry of the $B_c$ meson we relate our results for $B_c^+ \to \eta_c\, \ell^+\, \nu$ to those for $B_c^+ \to J/\psi\, \ell^+\, \nu$ yielding the estimate $R(J/\psi)|_{\text{SM}} = 0.26 \pm 0.02$ in good agreement with other determinations., Comment: v3: 9 pages, 2 figures, 2 tables, journal version

We study theoretical constraints on a model whose scalar sector contains one color octet and one or two color singlet $SU(2)_L$ doublets. Using the unitarity of the theory, we constrain the parameters of the scalar potential for the first time at next-to-leading order in perturbation theory. We also derive new conditions guaranteeing the stability of the potential. We use the HEPfit package to single out the viable parameter regions at the electroweak scale and test the stability of the renormalization group evolution up to the multi-TeV region. Additionally, we set upper limits on the scalar mass splittings. All results are given for both cases, with and without a second scalar color singlet., Comment: 17 pages, 5 figures, to be published in Chinese Physics C

The ATLAS and CMS collaborations have recently released significant new data on Higgs and diboson production in LHC Run 2. Measurements of Higgs properties have improved in many channels, while kinematic information for $h \to \gamma\gamma$ and $h \to ZZ$ can now be more accurately incorporated in fits using the STXS method, and $W^+ W^-$ diboson production at high $p_T$ gives new sensitivity to deviations from the Standard Model. We have performed an updated global fit to precision electroweak data, $W^+W^-$ measurements at LEP, and Higgs and diboson data from Runs 1 and 2 of the LHC in the framework of the Standard Model Effective Field Theory (SMEFT), allowing all coefficients to vary across the combined dataset, and present the results in both the Warsaw and SILH operator bases. We exhibit the improvement in the constraints on operator coefficients provided by the LHC Run 2 data, and discuss the correlations between them. We also explore the constraints our fit results impose on several models of physics beyond the Standard Model, including models that contribute to the operator coefficients at the tree level and stops in the MSSM that contribute via loops., Comment: 28 pages plus references, 8 figures, 8 tables; v2: journal version, Moriond results included, references and 1 table added, additional smaller changes

We perform a parameter fit in the Standard Model Effective Field Theory (SMEFT) with an emphasis on using regularized linear regression to tackle the issue of the large number of parameters in the SMEFT. In regularized linear regression a positive definite function of the parameters of interest is added to the usual cost function. A cross-validation is performed to try to determine the optimal value of the regularization parameter to use, but it selects the Standard Model (SM) as the best model to explain the measurements. Nevertheless as proof of principle of this technique we apply it to fitting Higgs boson signal strengths in SMEFT, including the latest Run-2 results. Results are presented in terms of the eigensystem of the covariance matrix of the least squares estimators as it has a degree model-independent to it. We find several results in this initial work: the SMEFT predicts the total width of the Higgs boson to be consistent with the SM prediction; the ATLAS and CMS experiments at the LHC are currently sensitive to non-resonant double Higgs boson production. Constraints are derived on the viable parameter space for electroweak baryogenesis in the SMEFT, reinforcing the notion that a first order phase transition requires fairly low scale Beyond the SM physics. Finally, we study which future experimental measurements would give the most improvement on the global constraints on the Higgs sector of the SMEFT., Comment: 11 + 8 pages, 8 figures, 4 tables; v2: references added, 2 figures added, version to appear in PRD

One of the simplest extensions of the Standard Model is the inclusion of an additional scalar multiplet, and we consider scalars in the $SU(2)_L$ singlet, triplet, and quartet representations. We examine models with heavy neutral scalars, $m_H\sim 1-2$ TeV, and the matching of the UV complete theories to the low energy effective field theory. We demonstrate the agreement of the kinematic distributions obtained in the singlet models for the gluon fusion of a Higgs pair with the predictions of the effective field theory. The restrictions on the extended scalar sectors due to unitarity and precision electroweak measurements are summarized and lead to highly restricted regions of viable parameter space for the triplet and quartet models., Comment: 28 pages, 12 figures, 5 tables; v2: references added, other minor changes, version to appear in PRD

The apparent breakdown of unitarity in low order perturbation theory is often is used to place bounds on the parameters of a theory. In this work we give an algorithm for approximately computing the next-to-leading order (NLO) perturbativity bounds on the quartic couplings of a renormalizable theory whose scalar sector is $\phi^4$-like. By this we mean theories where either there are no cubic scalar interactions, or the cubic couplings are related to the quartic couplings through spontaneous symmetry breaking. The quantity that tests where perturbation theory breaks down itself can be written as a perturbative series, and having the NLO terms allows one to test how well the series converges. We also present a simple example to illustrate the effect of considering these bounds at different orders in perturbation theory. For example, there is a noticeable difference in the viable parameter when the square of the NLO piece is included versus when it is not., Comment: v2: 11 pages, 2 figures, version to appear in PRD

A very light boson of mass $\mathcal{O}(10^{-22})$ eV may potentially be a viable dark matter (DM) candidate which can avoid phenomenological problems associated with cold DM. Such "fuzzy DM (FDM)" may naturally be an axion with a decay constant $f_a \sim 10^{16} \div 10^{18}$ GeV, and a mass $m_a \sim \mu^2/f_a$ with $\mu\sim 10^2$ eV. Here we propose a concrete model where $\mu$ arises as a dynamical scale from infrared confining dynamics, analogous to QCD. Our model is an alternative to the usual approach of generating $\mu$ through string theoretic instanton effects. We outline the features of this scenario that result from various cosmological constraints. We find that those constraints are suggestive of a period of mild of inflation, perhaps from a strong first order phase transition, that reheats the Standard Model (SM) sector only. A typical prediction of our scenario, broadly speaking, is a larger effective number of neutrinos compared to the SM value $N_{\text{eff}} \approx 3$, as inferred from precision measurements of the cosmic microwave background. Some of the new degrees of freedom may be identified as "sterile neutrinos," which may be required to explain certain neutrino oscillation anomalies. Hence, aspects of our scenario could be testable in terrestrial experiments, which is a novelty of our FDM model., Comment: v2: 5 pages, 1 figure; references added, wording improved, matches PRL version

The collection of a few anomalies in semileptonic $B$-decays, especially in $b\rightarrow c \tau \bar{\nu}$, invites to speculate about the emergence of some striking new phenomena, perhaps interpretable in terms of a weakly broken $U(2)^n$ flavor symmetry and of leptoquark mediators. Here we aim at a partial UV completion of this interpretation by generalizing the minimal composite Higgs model to include a composite vector leptoquark as well., Comment: 29 pages, 4 figures, 1 table

We fit the next-to-leading order unitarity conditions to the Two-Higgs-Doublet model with a softly broken $\mathbb{Z}_2$ symmetry. In doing so, we alleviate the existing uncertainty on how to treat higher order corrections to quartic couplings of its Higgs potential. A simplified approach to implementing the next-to-leading order unitarity conditions is presented. These new bounds are then combined with all other relevant constraints, including the complete set of LHC Run I data. The upper $95\%$ bounds we find are $4.2$ on the absolute values of the quartic couplings, and $235$ GeV ($100$ GeV) for the mass degeneracies between the heavy Higgs particles in the type I (type II) scenario. In type II, we exclude an unbroken $\mathbb{Z}_2$ symmetry with a probability of $95\%$. All fits are performed using the open-source code HEPfit., Comment: 33 pages, 13 figures, 5 tables. Comments are welcome

The ATLAS and CMS collaborations recently presented evidence of a resonance decaying to pairs of photons around 750 GeV. In addition, the BaBar, Belle, and LHCb collaborations have evidence of lepton non-universality in the semileptonic decays of $B$ mesons. In this work, we make a first step towards a unified explanation of these anomalies. Specifically, we extend the Standard Model by including vector leptoquarks and a scalar singlet that couples linearly to pairs of the leptoquarks. We find there is parameter space that gives the correct cross section for a putative 750 GeV resonance decaying to photons that is consistent with unitarity, measurements of the properties of the 125 GeV Higgs boson, and direct searches for resonances in other channels. In addition, we also show that constraints can be derived on any Beyond the Standard Model explanation of the 750 GeV resonance where the only new particles are scalars, which are strong enough to rule out certain types of models entirely., Comment: v4: version published in PLB, minor changes from v3

We compute all of the one-loop corrections that are enhanced, $O(\lambda_i \lambda_j / 16 \pi^2)$, in the limit $s \gg |\lambda_i | v^2 \gg M_{W}^2$, $s \gg m_{12}^2$ to all the $2 \to 2$ longitudinal vector boson and Higgs boson scattering amplitudes in the $CP$-conserving two-Higgs doublet model with a softly broken $\mathbb{Z}_2$ symmetry. In the two simplified scenarios we study, the typical bound we find is $|\lambda_i(s)| \lessapprox 4$., Comment: v2: 1 plot corrected, other minor changes, version to appear in JHEP

We derive the decay rate of an unstable phase of a quantum field theory in the presence of an impurity in the thin-wall approximation. This derivation is based on the how the impurity changes the (flat spacetime) geometry relative to case of pure false vacuum. Two examples are given that show how to estimate some of the additional parameters that enter into this heterogeneous decay rate. This formalism is then applied to the Higgs vacuum of the Standard Model (SM), where baryonic matter acts as an impurity in the electroweak Higgs vacuum. We find that the probability for heterogeneous vacuum decay to occur is suppressed with respect to the homogeneous case. That is to say, the conclusions drawn from the homogeneous case are not modified by the inclusion of baryonic matter in the calculation. On the other hand, we show that Beyond the Standard Model physics with a characteristic scale comparable to the scale that governs the homogeneous decay rate in the SM, can in principle lead to an enhanced decay rate., Comment: v3: version published in JHEP, very minor changes from v2

Predictions are made for the forward-backward and charge asymmetries in bottom-quark pair production at hadron colliders. Tree-level exchanges of electroweak (EW) gauge bosons dominate the Standard Model (SM) contribution to the asymmetry near the $Z$-pole. The mixed EW-QCD corrections are computed in an approximate way, and are found to be small in magnitude. These SM predictions are consistent with experimental results from CDF, D0, and LHCb. In particular, CDF and LHCb find that the asymmetry in the invariant mass bin containing the $Z$-pole is larger than in the adjacent bins, as predicted. Several beyond the Standard Model scenarios proposed for the top-quark forward-backward asymmetry, including a 100 GeV axigluon, are disfavored by this combination of SM predictions and measurements. On the other hand, modified $Zb\bar{b}$ couplings can explain the 2$\sigma$ discrepancy in the bottom-quark forward-backward asymmetry at LEP1, while being consistent with the results of CDF and LHCb. It is also shown that $t$-channel $W$ exchange makes a non-negligible contribution to the charm-quark charge asymmetry., Comment: v2: references added, typographical errors corrected, 11 pages, 6 tables, 4 figures, version to appear in PRD

We present a sum rule for Higgs fields in general representations under $SU(2)_L \times U(1)_Y$ that follows from the connection between the Higgs couplings and the mechanism that gives the electroweak bosons their masses, and at the same time restricts these couplings. Sum rules that follow from perturbative unitarity will require us to include singly and doubly charged Higgses in our analysis. We examine the consequences of these sum rules for Higgs phenomenology in both model independent and model specific ways. The relation between our sum rules and other works, based on dispersion relations, is also clarified., Comment: 53 pages, 17 figures. Version 3: expanded references, matched JHEP version

We show that the three-body decays of the resonance recently discovered at the LHC are potentially sensitive to effects of new physics. Even if the fully integrated partial decay widths are consistent with the minimal Standard Model there is information that is lost upon integration, which can be uncovered in the differential decay widths. Concentrating on the decay $h \to Z \ell \bar{\ell}$, we identify the regions in the three-body phase space in which these effects become especially pronounced and could be detected in future experiments., Comment: 20 pages, 5 figures, matches version published in JHEP

We computed the bottom-quark forward-backward asymmetry at the Tevatron in the Standard Model and for several new physics scenarios. Near the $Z$-pole, the SM bottom asymmetry is dominated by tree level exchanges of electroweak gauge bosons. While above the $Z$-pole, next-to-leading order QCD dominates the SM asymmetry as was the case with the top quark forward-backward asymmetry. Light new physics, $M_{NP} \precsim 150$ GeV, can cause significant deviations from the SM prediction for the bottom asymmetry. The bottom asymmetry can be used to distinguish between competing NP explanations of the top asymmetry based on how the NP interferes with s-channel gluon and $Z$ exchange., Comment: v3: Bug found in FeynRules 1.6.1 (not present in current version, 2.0.24) One plot corrected. Conclusions unaffected

Contrary to popular belief conformality does not require zero beta functions. This follows from the work of Jack and Osborn, and examples in non-supersymmetric theories were recently found by some of us. In this note we show that such examples are absent in unitary N=1 supersymmetric four-dimensional field theories. More specifically, we show to all orders in perturbation theory that the beta-function vector field of such theories does not admit limit cycles. A corollary of our result is that unitary N=1 supersymmetric four-dimensional theories cannot be superscale-invariant without being superconformal., Comment: 8 pages, 1 figure. Improved discussion in Section 5

We show that the anomalously large top quark forward-backward asymmetry observed by CDF and D\O\, can naturally be accommodated in models with flavor-violating couplings of a new massive spin-2 state to quarks. Regardless of its origin, the lowest-order couplings of a spin-2 boson to fermions are analogous to the coupling of the graviton to energy/momentum, leading to strong sensitivity of the effects associated with its virtual exchange to the energy scales at hand. Precisely due to this fact, the observed dependence of the asymmetry on the $t\bar t$ invariant mass fits nicely into the proposed framework. In particular, we find a vast parameter space which can lead to the central value for the observed forward-backward asymmetry in the high mass bin, while being in accord with all of the existing experimental constraints., Comment: added discussion of differential observables at the LHC, matches version accepted for publication in JHEP

Electroweak precision data constraints on flavor symmetric vector fields are determined. The flavor multiplets of spin one that we examine are the complete set of fields that couple to quark bi-linears at tree level while not initially breaking the quark global flavor symmetry group. Flavor safe vector masses proximate to, and in some cases below, the electroweak symmetry breaking scale are found to be allowed. Many of these fields provide a flavor safe mechanism to explain the t tbar forward backward anomaly, and can simultaneously significantly raise the allowed values of the Standard Model Higgs mass consistent with electroweak precision data., Comment: Matches version published in JHEP