Review of lattice results concerning low-energy particle physics

LHC lifetime frontier and visible decay searches in composite asymmetric dark matter models

The LHC lifetime frontier will probe dark sector in near future, and the visible decay searches at fixed-target experiments have been exploring dark sector. Composite asymmetric dark matter with dark photon portal is a promising framework explaining the coincidence problem between dark matter and visible matter. Dark strong dynamics provides rich structure in the dark sector: the lightest dark nucleon is the dark matter, while strong annihilation into dark pions depletes the symmetric components of the dark matter. Dark photons alleviate cosmological problems. Meanwhile, dark photons make dark hadrons long-lived in terrestrial experiments. Moreover, the dark hadrons are produced through the very same dark photon. In this study, we discuss the visible decay searches for composite asymmetric dark matter models. For a few GeV dark nucleons, the LHC lifetime frontier, MATHUSLA and FASER, has a potential to discover their decay when kinetic mixing angle of dark photon is ϵ ≳ 10 ^-4. On the other hand, fixed-target experiments, in particular SeaQuest, will have a great sensitivity to dark pions with a mass below GeV and with kinetic mixing ϵ ≳ 10 ^-4 in addition to the LHC lifetime frontier. These projected sensitivities to dark hadrons in dark photon parameter space are comparable with the future sensitivities of dark photon searches, such as Belle-II and LHCb.

Ruling Out the Massless Up-Quark Solution to the Strong CP Problem by Computing the Topological Mass Contribution with Lattice QCD

The infamous strong CP problem in particle physics can in principle be solved by a massless up quark. In particular, it was hypothesized that topological effects could substantially contribute to the observed nonzero up-quark mass without reintroducing CP violation. Alternatively to previous work using fits to chiral perturbation theory, in this Letter, we bound the strength of the topological mass contribution with direct lattice QCD simulations, by computing the dependence of the pion mass on the dynamical strange-quark mass. We find that the size of the topological mass contribution is inconsistent with the massless up-quark solution to the strong CP problem.

A per-cent-level determination of the nucleon axial coupling from quantum chromodynamics

The axial coupling of the nucleon, g_A, is the strength of its coupling to the weak axial current of the standard model of particle physics, in much the same way as the electric charge is the strength of the coupling to the electromagnetic current. This axial coupling dictates the rate at which neutrons decay to protons, the strength of the attractive long-range force between nucleons and other features of nuclear physics. Precision tests of the standard model in nuclear environments require a quantitative understanding of nuclear physics that is rooted in quantum chromodynamics, a pillar of the standard model. The importance of g_A makes it a benchmark quantity to determine theoretically-a difficult task because quantum chromodynamics is non-perturbative, precluding known analytical methods. Lattice quantum chromodynamics provides a rigorous, non-perturbative definition of quantum chromodynamics that can be implemented numerically. It has been estimated that a precision of two per cent would be possible by 2020 if two challenges are overcome^1,2: contamination of g_A from excited states must be controlled in the calculations and statistical precision must be improved markedly^2-10. Here we use an unconventional method ¹¹ inspired by the Feynman-Hellmann theorem that overcomes these challenges. We calculate a g_A value of 1.271 ± 0.013, which has a precision of about one per cent.

CLS 2+1 flavor simulations at physical light-and strange-quark masses

We report recent efforts by CLS to generate an ensemble with physical lightand strange-quark masses in a lattice volume of 192 × 963 at β = 3:55 corresponding to a lattice spacing of 0:064 fm. This ensemble is being generated as part of the CLS 2+1 flavor effort with improved Wilson fermions. Our simulations currently cover 5 lattice spacings ranging from 0:039 fm to 0:086 fm at various pion masses along chiral trajectories with either the sum of the quark masses kept fixed, or with the strange-quark mass at the physical value. The current status of simulations is briefly reviewed, including a short discussion of measured autocorrelation times and of the main features of the simulations. We then proceed to discuss the thermalization strategy employed for the generation of the physical quark-mass ensemble and present first results for some simple observables. Challenges encountered in the simulation are highlighted.

SU(3) Yang Mills theory at small distances and fine lattices

We investigate the SU(3) Yang Mills theory at small gradient flow time and at short distances. Lattice spacings down to a = 0.015 fm are simulated with open boundary conditions to allow topology to flow in and out. We study the behaviour of the action density E(t) close to the boundaries, the feasibility of the small flow-time expansion and the extraction of the Λ-parameter from the static force at small distances. For the latter, significant deviations from the 4-loop perturbative β-function are visible at α ≈ 0.2. We still can extrapolate to extract roΛ.

Local-duality QCD sum rules for strong isospin breaking in the decay constants of heavy-light mesons

We discuss the leptonic decay constants of heavy-light mesons by means of Borel QCD sum rules in the local-duality (LD) limit of infinitely large Borel mass parameter. In this limit, for an appropriate choice of the invariant structures in the QCD correlation functions, all vacuum-condensate contributions vanish and all nonperturbative effects are contained in only one quantity, the effective threshold. We study properties of the LD effective thresholds in the limits of large heavy-quark mass [Formula: see text] and small light-quark mass [Formula: see text]. In the heavy-quark limit, we clarify the role played by the radiative corrections in the effective threshold for reproducing the pQCD expansion of the decay constants of pseudoscalar and vector mesons. We show that the dependence of the meson decay constants on [Formula: see text] arises predominantly (at the level of 70-80%) from the calculable [Formula: see text]-dependence of the perturbative spectral densities. Making use of the lattice QCD results for the decay constants of nonstrange and strange pseudoscalar and vector heavy mesons, we obtain solid predictions for the decay constants of heavy-light mesons as functions of [Formula: see text] in the range from a few to 100 MeV and evaluate the corresponding strong isospin-breaking effects: [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text].

Non-leptonic kaon decays at large Nc

We study the scaling with the number of colors Nc of the weak amplitudes mediating kaon mixing and decay, in the limit of light charm masses (mu = md = ms = mc). The amplitudes are extracted directly on the lattice for Nc = 3 - 7 (with preliminar results for Nc = 8 and 17) using twisted mass QCD. It is shown that the (sub-leading) 1 /Nc corrections to [see formula in PDF] are small and that the naive Nc → ∞ limit, [see formula in PDF] = 3/4, seems to be recovered. On the other hand, the O (1/Nc) corrections in K → ππ amplitudes (derived from K → π matrix elements) are large and fully anti-correlated in the I = 0 and I = 2 channels. This may have some implications for the understanding of the ΔI = 1/2 rule.

On flavourful Easter eggs for New Physics hunger and lepton flavour universality violation

Within the standard approach of effective field theory of weak interactions for Δ B = 1 transitions, we look for possibly unexpected subtle New Physics effects, here dubbed "flavourful Easter eggs". We perform a Bayesian global fit using the publicly available HEPfit package, taking into account state-of-the-art experimental information concerning these processes, including the suggestive measurements from LHCb of R K and R K ∗ , the latter available only very recently. We parametrise New Physics contributions to b → s transitions in terms of shifts of Wilson coefficients of the electromagnetic dipole and semileptonic operators, assuming CP-conserving effects, but allowing in general for violation of lepton flavour universality. We show how optimistic/conservative hadronic estimates can impact quantitatively the size of New Physics extracted from the fit. With a conservative approach to hadronic uncertainties we find nonzero New Physics contributions to Wilson coefficients at the level of ∼ 3 σ , depending on the model chosen. Furthermore, given the interplay between hadronic contributions and New Physics effects in the leptonic vector current, a scenario with nonstandard leptonic axial currents is comparable to the more widely advocated one with New Physics in the leptonic vector current.

CP violation in the B system

The phenomenon of CP violation is crucial to understand the asymmetry between matter and antimatter that exists in the Universe. Dramatic experimental progress has been made, in particular in measurements of the behaviour of particles containing the b quark, where CP violation effects are predicted by the Kobayashi-Maskawa mechanism that is embedded in the standard model. The status of these measurements and future prospects for an understanding of CP violation beyond the standard model are reviewed.

Review of lattice results concerning low-energy particle physics: Flavour Lattice Averaging Group (FLAG)

We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the determination of the light-quark masses, the form factor [Formula: see text], arising in the semileptonic [Formula: see text] transition at zero momentum transfer, as well as the decay constant ratio [Formula: see text] and its consequences for the CKM matrix elements [Formula: see text] and [Formula: see text]. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of [Formula: see text] and [Formula: see text] Chiral Perturbation Theory. We review the determination of the [Formula: see text] parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. The latter quantities are an addition compared to the previous review. For the heavy-quark sector, we provide results for [Formula: see text] and [Formula: see text] (also new compared to the previous review), as well as those for D- and B-meson-decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. Finally, we review the status of lattice determinations of the strong coupling constant [Formula: see text].

Precision measurement and interpretation of inclusive W+ , W- and Z/γ∗ production cross sections with the ATLAS detector

High-precision measurements by the ATLAS Collaboration are presented of inclusive W+→ℓ+ν , W-→ℓ-ν¯ and Z/γ∗→ℓℓ ( ℓ=e,μ ) Drell-Yan production cross sections at the LHC. The data were collected in proton-proton collisions at s=7TeV with an integrated luminosity of 4.6fb-1 . Differential W+ and W- cross sections are measured in a lepton pseudorapidity range |ηℓ|<2.5 . Differential Z/γ∗ cross sections are measured as a function of the absolute dilepton rapidity, for |yℓℓ|<3.6 , for three intervals of dilepton mass, mℓℓ , extending from 46 to 150GeV . The integrated and differential electron- and muon-channel cross sections are combined and compared to theoretical predictions using recent sets of parton distribution functions. The data, together with the final inclusive e±p scattering cross-section data from H1 and ZEUS, are interpreted in a next-to-next-to-leading-order QCD analysis, and a new set of parton distribution functions, ATLAS-epWZ16, is obtained. The ratio of strange-to-light sea-quark densities in the proton is determined more accurately than in previous determinations based on collider data only, and is established to be close to unity in the sensitivity range of the data. A new measurement of the CKM matrix element |Vcs| is also provided.

Determination of the QCD Λ Parameter and the Accuracy of Perturbation Theory at High Energies

We discuss the determination of the strong coupling α_{MS[over ¯]}(m_{Z}) or, equivalently, the QCD Λ parameter. Its determination requires the use of perturbation theory in α_{s}(μ) in some scheme s and at some energy scale μ. The higher the scale μ, the more accurate perturbation theory becomes, owing to asymptotic freedom. As one step in our computation of the Λ parameter in three-flavor QCD, we perform lattice computations in a scheme that allows us to nonperturbatively reach very high energies, corresponding to α_{s}=0.1 and below. We find that (continuum) perturbation theory is very accurate there, yielding a 3% error in the Λ parameter, while data around α_{s}≈0.2 are clearly insufficient to quote such a precision. It is important to realize that these findings are expected to be generic, as our scheme has advantageous properties regarding the applicability of perturbation theory.

The Standard Model: how far can it go and how can we tell?

The Standard Model of particle physics encapsulates our current best understanding of physics at the smallest distances and highest energies. It incorporates quantum electrodynamics (the quantized version of Maxwell's electromagnetism) and the weak and strong interactions, and has survived unmodified for decades, save for the inclusion of non-zero neutrino masses after the observation of neutrino oscillations in the late 1990s. It describes a vast array of data over a wide range of energy scales. I review a selection of these successes, including the remarkably successful prediction of a new scalar boson, a qualitatively new kind of object observed in 2012 at the Large Hadron Collider. New calculational techniques and experimental advances challenge the Standard Model across an ever-wider range of phenomena, now extending significantly above the electroweak symmetry breaking scale. I will outline some of the consequences of these new challenges, and briefly discuss what is still to be found.This article is part of the themed issue 'Unifying physics and technology in light of Maxwell's equations'.

Supersymmetric Explanation of CP Violation in K→ππ Decays

Recent progress in the determination of hadronic matrix elements has revealed a tension between the measured value of ε_{K}^{'}/ε_{K}, which quantifies direct CP violation in K→ππ decays, and the standard-model prediction. The well-understood indirect CP violation encoded in the quantity ε_{K} typically precludes large new-physics contributions to ε_{K}^{'}/ε_{K} and challenges such an explanation of the discrepancy. We show that it is possible to cure the ε_{K}^{'}/ε_{K} anomaly in the minimal supersymmetric standard model with squark masses above 3 TeV without overshooting ε_{K}. This solution exploits two features of supersymmetry: the possibility of large isospin-breaking contributions (enhancing ε_{K}^{'}) and the Majorana nature of gluinos (permitting a suppression of ε_{K}). Our solution involves no fine-tuning of CP phases or other parameters.

Massive Photons: An Infrared Regularization Scheme for Lattice QCD+QED

Standard methods for including electromagnetic interactions in lattice quantum chromodynamics calculations result in power-law finite-volume corrections to physical quantities. Removing these by extrapolation requires costly computations at multiple volumes. We introduce a photon mass to alternatively regulate the infrared, and rely on effective field theory to remove its unphysical effects. Electromagnetic modifications to the hadron spectrum are reliably estimated with a precision and cost comparable to conventional approaches that utilize multiple larger volumes. A significant overall cost advantage emerges when accounting for ensemble generation. The proposed method may benefit lattice calculations involving multiple charged hadrons, as well as quantum many-body computations with long-range Coulomb interactions.

Direct Evaluation of the Quark Content of Nucleons from Lattice QCD at the Physical Point

We evaluate the light, strange, and charm scalar content of the nucleon using one lattice QCD ensemble generated with two degenerate light quarks with mass fixed to their physical value. We use improved techniques to evaluate the disconnected quark loops to sufficient accuracy to determine the strange and charm nucleon σ terms in addition to the light quark content σ_{πN}. We find σ_{πN}=37.2(2.6)(4.7/2.9)  MeV, σ_{s}=41.1(8.2)(7.8/5.8)  MeV, and σ_{c}=79(21)(12/8)  MeV, where the first error is statistical and the second is the systematic error due to the determination of the lattice spacing, the assessment of finite volume, and residual excited state effects.

Searching for the rules that govern hadron construction

Just as quantum electrodynamics describes how electrons are bound in atoms by the electromagnetic force, mediated by the exchange of photons, quantum chromodynamics (QCD) describes how quarks are bound inside hadrons by the strong force, mediated by the exchange of gluons. QCD seems to allow hadrons constructed from increasingly many quarks to exist, just as atoms with increasing numbers of electrons exist, yet such complex constructions seemed, until recently, not to be present in nature. Here we describe advances in the spectroscopy of mesons that are refining our understanding of the rules for predicting hadron structure from QCD.

Lattice Computation of the Nucleon Scalar Quark Contents at the Physical Point

We present a QCD calculation of the u, d, and s scalar quark contents of nucleons based on 47 lattice ensembles with N_{f}=2+1 dynamical sea quarks, 5 lattice spacings down to 0.054 fm, lattice sizes up to 6 fm, and pion masses down to 120 MeV. Using the Feynman-Hellmann theorem, we obtain f_{ud}^{N}=0.0405(40)(35) and f_{s}^{N}=0.113(45)(40), which translates into σ_{πN}=38(3)(3)  MeV, σ_{sN}=105(41)(37)  MeV, and y_{N}=0.20(8)(8) for the sigma terms and the related ratio, where the first errors are statistical and the second errors are systematic. Using isospin relations, we also compute the individual up and down quark contents of the proton and neutron (results in the main text).

Universal Unitarity Triangle 2016 and the tension between [Formula: see text] and [Formula: see text] in CMFV models

Motivated by the recently improved results from the Fermilab Lattice and MILC Collaborations on the hadronic matrix elements entering [Formula: see text] in [Formula: see text]-[Formula: see text] mixing, we determine the universal unitarity triangle (UUT) in models with constrained minimal flavour violation (CMFV). Of particular importance are the very precise determinations of the ratio [Formula: see text] and of the angle [Formula: see text]. They follow in this framework from the experimental values of [Formula: see text] and of the CP-asymmetry [Formula: see text]. As in CMFV models the new contributions to meson mixings can be described by a single flavour-universal variable S(v), we next determine the CKM matrix elements [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] as functions of S(v) using the experimental value of [Formula: see text] as input. The lower bound on S(v) in these models, derived by us in 2006, implies then upper bounds on these four CKM elements and on the CP-violating parameter [Formula: see text], which turns out to be significantly below its experimental value. This strategy avoids the use of tree-level determinations of [Formula: see text] and [Formula: see text], which are presently subject to considerable uncertainties. On the other hand, if [Formula: see text] is used instead of [Formula: see text] as input, [Formula: see text] are found to be significantly above the data. In this manner we point out that the new lattice data have significantly sharpened the tension between [Formula: see text] and [Formula: see text] within the CMFV framework. This implies the presence of new physics contributions beyond this framework that are responsible for the breakdown of the flavour universality of the function S(v). We also present the implications of these results for [Formula: see text], [Formula: see text] and [Formula: see text] within the Standard Model.

Weak Decays of Excited B Mesons

We investigate the decays of the excited (bq[over ¯]) mesons as probes of the short-distance structure of the weak ΔB=1 transitions. These states are unstable under the electromagnetic or strong interactions, although their widths are typically suppressed by phase space. Compared to the pseudoscalar B meson, the purely leptonic decays of the vector B^{*} are not chirally suppressed and are sensitive to different combinations of the underlying weak effective operators. An interesting example is B_{s}^{*}→ℓ^{+}ℓ^{-}, which has a rate that can be accurately predicted in the standard model. The branching fraction is B∼10^{-11}, irrespective of the lepton flavor and where the main uncertainty stems from the unmeasured and theoretically not well known B_{s}^{*} width. We discuss the prospects for producing this decay mode at the LHC and explore the possibility of measuring the B_{s}^{*}→ℓℓ amplitude, instead, through scattering experiments at the B_{s}^{*} resonance peak.

Quark flavour observables in the Littlest Higgs model with T-parity after LHC Run 1

The Littlest Higgs model with T-parity (LHT) belongs to the simplest new physics scenarios with new sources of flavour and CP violation. The latter originate in the interactions of ordinary quarks and leptons with heavy mirror quarks and leptons that are mediated by new heavy gauge bosons. Also a heavy fermionic top partner is present in this model which communicates with the SM fermions by means of standard [Formula: see text] and [Formula: see text] gauge bosons. We present a new analysis of quark flavour observables in the LHT model in view of the oncoming flavour precision era. We use all available information on the CKM parameters, lattice QCD input and experimental data on quark flavour observables and corresponding theoretical calculations, taking into account new lower bounds on the symmetry breaking scale and the mirror quark masses from the LHC. We investigate by how much the branching ratios for a number of rare K and B decays are still allowed to depart from their SM values. This includes [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. Taking into account the constraints from [Formula: see text] processes, significant departures from the SM predictions for [Formula: see text] and [Formula: see text] are possible, while the effects in B decays are much smaller. In particular, the LHT model favours [Formula: see text], which is not supported by the data, and the present anomalies in [Formula: see text] decays cannot be explained in this model. With the recent lattice and large N input the imposition of the [Formula: see text] constraint implies a significant suppression of the branching ratio for [Formula: see text] with respect to its SM value while allowing only for small modifications of [Formula: see text]. Finally, we investigate how the LHT physics could be distinguished from other models by means of indirect measurements and discuss the consequences for quark flavour observables of not finding any LHT state in the coming years.

Form factors of the isovector scalar current and the [Formula: see text] scattering phase shifts

A model for S-wave [Formula: see text] scattering is proposed which could be realistic in an energy range from threshold up to above 1 GeV, where inelasticity is dominated by the [Formula: see text] channel. The T-matrix, satisfying two-channel unitarity, is given in a form which matches the chiral expansion results at order [Formula: see text] exactly for the [Formula: see text], [Formula: see text] amplitudes and approximately for [Formula: see text]. It contains six phenomenological parameters. Asymptotic conditions are imposed which ensure a minimal solution of the Muskhelishvili-Omnès problem, thus allowing one to compute the [Formula: see text] and [Formula: see text] form factor matrix elements of the [Formula: see text] scalar current from the T-matrix. The phenomenological parameters are determined such as to reproduce the experimental properties of the [Formula: see text], [Formula: see text] resonances, as well as the chiral results of the [Formula: see text] and [Formula: see text] scalar radii, which are predicted to be remarkably small at [Formula: see text]. This T-matrix model could be used for a unified treatment of the [Formula: see text] final-state interaction problem in processes such as [Formula: see text], [Formula: see text], or the [Formula: see text] initial-state interaction in [Formula: see text].

Constraints on tensor and scalar couplings from [Formula: see text] and [Formula: see text]

The angular distribution of [Formula: see text] ([Formula: see text]) depends on two parameters, the lepton forward-backward asymmetry, [Formula: see text], and the flat term, [Formula: see text]. Both are strongly suppressed in the standard model and constitute sensitive probes of tensor and scalar contributions. We use the latest experimental results for [Formula: see text] in combination with the branching ratio of [Formula: see text] to derive the strongest model-independent bounds on tensor and scalar effective couplings to date. The measurement of [Formula: see text] provides a complementary constraint to that of the branching ratio of [Formula: see text] and allows us - for the first time - to constrain all complex-valued (pseudo-)scalar couplings and their chirality-flipped counterparts in one fit. Based on Bayesian fits of various scenarios, we find that our bounds even become tighter when vector couplings are allowed to deviate from the standard model and that specific combinations of angular observables in [Formula: see text] are still allowed to be up to two orders of magnitude larger than in the standard model, which would place them in the region of LHCb's sensitivity.

High-Precision Determination of the Pion-Nucleon σ Term from Roy-Steiner Equations

We present a determination of the pion-nucleon (πN) σ term σ_{πN} based on the Cheng-Dashen low-energy theorem (LET), taking advantage of the recent high-precision data from pionic atoms to pin down the πN scattering lengths as well as of constraints from analyticity, unitarity, and crossing symmetry in the form of Roy-Steiner equations to perform the extrapolation to the Cheng-Dashen point in a reliable manner. With isospin-violating corrections included both in the scattering lengths and the LET, we obtain σ_{πN}=(59.1±1.9±3.0)  MeV=(59.1±3.5)  MeV, where the first error refers to uncertainties in the πN amplitude and the second to the LET. Consequences for the scalar nucleon couplings relevant for the direct detection of dark matter are discussed.

CMS and LHCb collaborations. Observation of the rare B(s)(0) →µ+µ− decay from the combined analysis of CMS and LHCb data

The standard model of particle physics describes the fundamental particles and their interactions via the strong, electromagnetic and weak forces. It provides precise predictions for measurable quantities that can be tested experimentally. The probabilities, or branching fractions, of the strange B meson (B(s)(0)) and the B0 meson decaying into two oppositely charged muons (μ+ and μ−) are especially interesting because of their sensitivity to theories that extend the standard model. The standard model predicts that the B(s)(0) →µ+µ− and B(0) →µ+µ− decays are very rare, with about four of the former occurring for every billion mesons produced, and one of the latter occurring for every ten billion B0 mesons. A difference in the observed branching fractions with respect to the predictions of the standard model would provide a direction in which the standard model should be extended. Before the Large Hadron Collider (LHC) at CERN started operating, no evidence for either decay mode had been found. Upper limits on the branching fractions were an order of magnitude above the standard model predictions. The CMS (Compact Muon Solenoid) and LHCb (Large Hadron Collider beauty) collaborations have performed a joint analysis of the data from proton–proton collisions that they collected in 2011 at a centre-of-mass energy of seven teraelectronvolts and in 2012 at eight teraelectronvolts. Here we report the first observation of the B(s)(0) → µ+µ− decay, with a statistical significance exceeding six standard deviations, and the best measurement so far of its branching fraction. Furthermore, we obtained evidence for the B(0) → µ+µ− decay with a statistical significance of three standard deviations. Both measurements are statistically compatible with standard model predictions and allow stringent constraints to be placed on theories beyond the standard model. The LHC experiments will resume taking data in 2015, recording proton–proton collisions at a centre-of-mass energy of 13 teraelectronvolts, which will approximately double the production rates of B(s)(0) and B0 mesons and lead to further improvements in the precision of these crucial tests of the standard model.

Exclusive window onto Higgs Yukawa couplings

We show that both flavor-conserving and flavor-violating Yukawa couplings of the Higgs boson to first- and second-generation quarks can be probed by measuring rare decays of the form h→MV, where M denotes a vector meson and V indicates either γ, W or Z. We calculate the branching ratios for these processes in both the standard model and its possible extensions. We discuss the experimental prospects for their observation. The possibility of accessing these Higgs couplings appears to be unique to the high-luminosity LHC and future hadron colliders, providing further motivation for those machines.

SU(2)×U(1) gauge invariance and the shape of new physics in rare B decays

New physics effects in B decays are routinely modeled through operators invariant under the strong and electromagnetic gauge symmetries. Assuming the scale for new physics is well above the electroweak scale, we further require invariance under the full standard model gauge symmetry group. Retaining up to dimension-six operators, we unveil new constraints between different new physics operators that are assumed to be independent in the standard phenomenological analyses. We illustrate this approach by analyzing the constraints on new physics from rare B(q) (semi-)leptonic decays.

QCD and strongly coupled gauge theories: challenges and perspectives

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.

Review of lattice results concerning low-energy particle physics

We review lattice results related to pion, kaon, [Formula: see text]- and [Formula: see text]-meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the determination of the light-quark masses, the form factor [Formula: see text], arising in semileptonic [Formula: see text] transition at zero momentum transfer, as well as the decay-constant ratio [Formula: see text] of decay constants and its consequences for the CKM matrix elements [Formula: see text] and [Formula: see text]. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of [Formula: see text] and [Formula: see text] Chiral Perturbation Theory and review the determination of the [Formula: see text] parameter of neutral kaon mixing. The inclusion of heavy-quark quantities significantly expands the FLAG scope with respect to the previous review. Therefore, we focus here on [Formula: see text]- and [Formula: see text]-meson decay constants, form factors, and mixing parameters, since these are most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. In addition we review the status of lattice determinations of the strong coupling constant [Formula: see text].

[Formula: see text] rule, [Formula: see text] and [Formula: see text] in [Formula: see text] and [Formula: see text] models with FCNC quark couplings

The experimental value for the isospin amplitude [Formula: see text] in [Formula: see text] decays has been successfully explained within the standard model (SM), both within the large [Formula: see text] approach to QCD and by QCD lattice calculations. On the other hand within the large [Formula: see text] approach the value of [Formula: see text] is by at least [Formula: see text] below the data. While this deficit could be the result of theoretical uncertainties in this approach and could be removed by future precise QCD lattice calculations, it cannot be excluded that the missing piece in [Formula: see text] comes from new physics (NP). We demonstrate that this deficit can be significantly softened by tree-level FCNC transitions mediated by a heavy colourless [Formula: see text] gauge boson with a flavour-violating left-handed coupling [Formula: see text] and an approximately universal flavour diagonal right-handed coupling [Formula: see text] to the quarks. The approximate flavour universality of the latter coupling assures negligible NP contributions to [Formula: see text]. This property, together with the breakdown of the GIM mechanisms at tree level, allows one to enhance significantly the contribution of the leading QCD-penguin operator [Formula: see text] to [Formula: see text]. A large fraction of the missing piece in the [Formula: see text] rule can be explained in this manner for [Formula: see text] in the reach of the LHC, while satisfying the constraints from [Formula: see text], [Formula: see text], [Formula: see text], LEP-II and the LHC. The presence of a small right-handed flavour-violating coupling [Formula: see text] and of enhanced matrix elements of [Formula: see text] left-right operators allows one to satisfy simultaneously the constraints from [Formula: see text] and [Formula: see text], although this requires some fine-tuning. We identify the quartic correlation between [Formula: see text] contributions to [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. The tests of this proposal will require much improved evaluations of [Formula: see text] and [Formula: see text] within the SM, of [Formula: see text] as well as precise tree-level determinations of [Formula: see text] and [Formula: see text]. We present correlations between [Formula: see text], [Formula: see text] and [Formula: see text] with and without the [Formula: see text] rule constraint and generalise the whole analysis to [Formula: see text] with colour ([Formula: see text]) and [Formula: see text] with FCNC couplings. In the latter case no improvement on [Formula: see text] can be achieved without destroying the agreement of the SM with the data on [Formula: see text]. Moreover, this scenario is very tightly constrained by [Formula: see text]. On the other hand, in the context of the [Formula: see text] rule [Formula: see text] is even more effective than [Formula: see text]: it provides the missing piece in [Formula: see text] for [Formula: see text]-[Formula: see text].