Subleading Terms Research Articles

Linear power corrections to single top production processes at the LHC

We discuss the linear power corrections to the electroweak production of top quarks at the LHC using renormalon calculus. We show how such non-perturbative corrections can be obtained using the Low-Burnett-Kroll theorem, which provides the first subleading term to the expansion of the real-emission amplitudes around the soft limit. We demonstrate that there are no linear power corrections to the total cross sections of arbitrary processes of a single top production type provided that these cross sections are expressed in terms of a short-distance top quark mass. We also derive a universal formula for the linear power corrections to generic observables that involve the top-quark momentum.

On the Emergence of Quantum Boltzmann Fluctuation Dynamics near a Bose–Einstein Condensate

In this work, we study the quantum fluctuation dynamics in a Bose gas on a torus $$\Lambda =(L{\mathbb {T}})^3$$ that exhibits Bose–Einstein condensation, beyond the leading order Hartree–Fock–Bogoliubov (HFB) theory. Given a Bose–Einstein condensate (BEC) with density $$N\gg 1$$ surrounded by thermal fluctuations with density 1, we assume that the system dynamics is generated by a Hamiltonian with mean-field scaling. We derive a quantum Boltzmann type dynamics from a second-order Duhamel expansion upon subtracting both the BEC dynamics and the HFB dynamics, with rigorous error control. Given a quasifree initial state, we determine the time evolution of the centered correlation functions $$\langle a\rangle $$ , $$\langle aa\rangle -\langle a\rangle ^2$$ , $$\langle a^+a\rangle -|\langle a\rangle |^2$$ at mesoscopic time scales $$t\sim \lambda ^{-2}$$ , where $$0<\lambda \ll 1$$ is the coupling constant determining the HFB interaction, and a, $$a^+$$ denote annihilation and creation operators. While the BEC and the HFB fluctuations both evolve at a microscopic time scale $$t\sim 1$$ , the Boltzmann dynamics is much slower, by a factor $$\lambda ^2$$ . For large but finite N, we consider both the case of fixed system size $$L\sim 1$$ , and the case $$L\sim \lambda ^{-2-}$$ . In the case $$L\sim 1$$ , we show that the Boltzmann collision operator contains subleading terms that can become dominant, depending on time-dependent coefficients assuming particular values in $${\mathbb {Q}}$$ ; this phenomenon is reminiscent of the Talbot effect. For the case $$L\sim \lambda ^{-2-}$$ , we prove that the collision operator is well approximated by the expression predicted in the literature. In either of those cases, we have $$\lambda \sim \Big (\frac{\log \log N}{\log N}\Big )^{\alpha }$$ , for different values of $$\alpha >0$$ .

Probing RG flows, symmetry resolution and quench dynamics through the capacity of entanglement

We compare the capacity of entanglement with the entanglement entropy by considering various aspects of these quantities for free bosonic and fermionic models in one spatial dimension, both in the continuum and on the lattice. Substantial differences are observed in the subleading terms of these entanglement quantifiers when the subsystem is made by two disjoint intervals, in the massive scalar field and in the fermionic chain. We define c-functions based on the capacity of entanglement similar to the one based on the entanglement entropy, showing through a numerical analysis that they display a monotonic behaviour under the renormalisation group flow generated by the mass. The capacity of entanglement and its related quantities are employed to explore the symmetry resolution. The temporal evolutions of the capacity of entanglement and of the corresponding contour function after a global quench are also discussed.

Entanglement islands in generalized two-dimensional dilaton black holes

The Fabbri--Russo model is a generalized model of a two-dimensional dilaton gravity theory with various parameters ``$n$'' describing various specific gravities. Particularly, the Russo--Susskind--Thorlacius gravity model fits the case $n=1$. In the Fabbri--Russo model, we investigate Page curves and the entanglement island. Islands are considered in eternal and evaporating black holes. Surprisingly, in any black hole, the emergence of islands causes the rise of the entanglement entropy of the radiation to decelerate after the Page time, satisfying the principle of unitarity. For eternal black holes, the fine-grained entropy reaches a saturation value that is twice the Bekenstein--Hawking entropy. For evaporating black holes, the fine-grained entropy finally reaches zero. At late times and large distance limit, the impact of the parameter ``$n$'' is a subleading term and is exponentially suppressed. As a result, the shape of Page curves is ``$n$'' independent in the leading order, which also indicates the universality of the Page curve in generalized two-dimensional models. Furthermore, we discuss the relationship between islands and firewalls. We show that the island is a better candidate than firewalls for encountering the quantum entanglement-monogamy problem. Finally, we briefly review the gravity/ensemble duality as a possible resolution to the state paradox resulting from the island formula.

A reduced inner product for kink states

Solitons in classical field theories correspond to states in quantum field theories. If the spatial dimension is infinite, then momentum eigenstates are not normalizable. This leads to infrared divergences, which are generally regularized via wave packets or by compactification. However, in some applications both possibilities are undesirable. In the present note, we introduce a finite inner product on translation-invariant kink states that allows us to compute probabilities involving these nonnormalizable states. Essentially, it is the quotient of the usual inner product by the translation group. We present a surprisingly simple formula for the reduced inner product, which requires no knowledge of the zero-mode dependence of the states but includes a correction which accounts for the mixing between zero modes and normal modes as the kink moves. As an application, we show that initial and final state corrections to meson multiplication vanish. However, we find that the pole of the subleading term in the initial state requires an infinitesimal imaginary shift.

Mutual information of generalized free fields

We study generalized free fields (GFF) from the point of view of information measures. We first review conformal GFF, their holographic representation, and the ambiguities in the assignation of algebras to regions that arise in these theories. Then we study the mutual information (MI) in several geometric configurations. The MI displays unusual features at the short distance limit: a leading volume term rather than an area term, and a logarithmic term in any dimensions rather than only for even dimensions as in ordinary CFT's. We find the dependence of some subleading terms on the conformal dimension $\Delta$ of the GFF. We study the long distance limit of the MI for regions with boundary in the null cone. The pinching limit of these surfaces show the GFF behaves as an interacting model from the MI point of view. The pinching exponents depend on the choice of algebra. The entanglement wedge algebra choice allows these models to ``fake'' causality, giving results consistent with its role in the description of large $N$ models.

Higher derivative corrections and AdS5 black holes

The authors investigate the precise holography between a 5d gauged supergravity and the dual superconformal field theory (CFT) on the 4d boundary. They show that four-derivative contributions to the action of supersymmetric black holes on the supergravity site matches precisely with certain subleading terms in the CFT index which are determined by anomalies.

Three-body recombination in a single-component Fermi gas with p -wave interaction

We study the three-body recombination of identical fermionic atoms. Using a zero-range model for the $p$-wave interaction, we show that the rate constant of three-body recombination into weakly bound $p$-wave dimers can be written as $\alpha_{\rm rec} \propto v^{5/2}R^{1/2} k_T^4 (1+ C k_T^2 l_{\rm d}^2)$ for large and positive scattering volume $v$. Here $R$ is the $p$-wave effective range, $k_T^2$ gives the average thermal kinetic energy of the colliding atoms, and $l_{\rm d}$ is the size of the $p$-wave dimer. The leading term is different from the usually stated $v^{8/3}$-scaling law, but is consistent with an earlier two-channel calculation. For the subleading term, we compute the constant $C$ by solving the relevant three-body problem perturbatively when the parameter $\gamma\equiv R/v^{1/3}$ is small. The additional $C k_T^2 l_{\rm d}^2$ term provides important corrections for the temperature and interaction dependence of $\alpha_{\rm rec}$, especially close to resonance when $k_T l_{\rm d}$ is relatively large.

Complete SMEFT predictions for four top quark production at hadron colliders

We study four top quark production at hadron colliders in the Standard Model Effective Field Theory (SMEFT). We perform an analysis at the tree-level, including all possible QCD- and EW-coupling orders and relevant dimension-six operators. We find several cases where formally subleading terms give rise to significant contributions, potentially providing sensitivity to a broad class of operators. Inclusive and differential predictions are presented for the LHC and a future pp circular collider operating at 100 TeV. We estimate the sensitivity of different operators and perform a simplified chi-square fit to set limits on SMEFT Wilson coefficients. In so doing, we assess the importance of including subleading terms and differential information in constraining new physics contributions. Finally, we compute the SMEFT predictions for the double insertion of dimension-six operators and scrutinise the possible enhancements to the sensitivity induced by a specific class of higher order terms in the EFT series.

Entropy variations and light ray operators from replica defects

We study the defect operator product expansion (OPE) of displacement operators in free and interacting conformal field theories using replica methods. We show that as n approaches 1 a contact term can emerge when the OPE contains defect operators of twist d − 2. For interacting theories and general states we give evidence that the only possibility is from the defect operator that becomes the stress tensor in the n → 1 limit. This implies that the quantum null energy condition (QNEC) is always saturated for CFTs with a twist gap. As a check, we show independently that in a large class of near vacuum states, the second variation of the entanglement entropy is given by a simple correlation function of averaged null energy operators as studied by Hofman and Maldacena. This suggests that sub-leading terms in the defect OPE are controlled by a defect version of the spin-3 non-local light ray operator and we speculate about the possible origin of such a defect operator. For free theories this contribution condenses to a contact term that leads to violations of QNEC saturation.

NNLO QCD corrections in full colour for jet production observables at the LHC

Calculations for processes involving a high multiplicity of coloured particles often employ a leading colour approximation, where only the leading terms in the expansion of the number of colours Nc and the number of flavours nf are retained. This approximation of the full colour result is motivated by the 1/ {N}_c^2 suppression of the first subleading terms and by the increasing complexity of including subleading colour contributions to the calculation. In this work, we present the calculations using the antenna subtraction method in the NNLOjet framework for the NNLO QCD corrections at full colour for several jet observables at the LHC. The single jet inclusive cross section is calculated doubly differential in transverse momentum and absolute rapidity and compared with the CMS measurement at 13 TeV. A calculation for dijet production doubly differential in dijet mass and rapidity difference is also performed and compared with the ATLAS 7 TeV data. Lastly, a triply differential dijet cross section in average transverse momentum, rapidity separation and dijet system boost is calculated and compared with the CMS 8 TeV data. The impact of the subleading colour contributions to the leading colour approximation is assessed in detail for all three types of observables and as a function of the jet cone size. The subleading colour contributions play a potentially sizable role in the description of the triply differential distributions, which probe kinematical configurations that are not easily accessed by any of the other observables.

2D Ising Field Theory in a magnetic field: the Yang-Lee singularity

We study Ising Field Theory (the scaling limit of Ising model near the Curie critical point) in pure imaginary external magnetic field. We put particular emphasis on the detailed structure of the Yang-Lee edge singularity. While the leading singular behavior is controlled by the Yang-Lee fixed point (= minimal CFT mathcal{M} 2/5), the fine structure of the subleading singular terms is determined by the effective action which involves a tower of irrelevant operators. We use numerical data obtained through the “Truncated Free Fermion Space Approach” to estimate the couplings associated with two least irrelevant operators. One is the operator Toverline{T} , and we use the universal properties of the Toverline{T} deformation to fix the contributions of higher orders in the corresponding coupling parameter α. Another irrelevant operator we deal with is the descendant L_4 overline{L} _4ϕ of the relevant primary ϕ in mathcal{M} 2/5. The significance of this operator is that it is the lowest dimension operator which breaks integrability of the effective theory. We also establish analytic properties of the particle mass M (= inverse correlation length) as the function of complex magnetic field.

Volume-Law Entanglement Entropy of Typical Pure Quantum States

The entanglement entropy of subsystems of typical eigenstates of quantum many-body Hamiltonians has been recently conjectured to be a diagnostic of quantum chaos and integrability. In quantum chaotic systems it has been found to behave as in typical pure states, while in integrable systems it has been found to behave as in typical pure Gaussian states. In this tutorial, we provide a pedagogical introduction to known results about the entanglement entropy of subsystems of typical pure states and of typical pure Gaussian states. They both exhibit a leading term that scales with the volume of the subsystem, when smaller than one half of the volume of the system, but the prefactor of the volume law is fundamentally different. It is constant (and maximal) for typical pure states, and it depends on the ratio between the volume of the subsystem and of the entire system for typical pure Gaussian states. Since particle-number conservation plays an important role in many physical Hamiltonians, we discuss its effect on typical pure states and on typical pure Gaussian states. We prove that while the behavior of the leading volume-law terms does not change qualitatively, the nature of the subleading terms can change. In particular, subleading corrections can appear that depend on the square root of the volume of the subsystem. We unveil the origin of those corrections. Finally, we discuss the connection between the entanglement entropy of typical pure states and analytical results obtained in the context of random matrix theory, as well as numerical results obtained for physical Hamiltonians.

Universal logarithmic correction to Rényi (Shannon) entropy in generic systems of critical quadratic fermions

The R\'enyi (Shannon) entropy, i.e., $R{e}_{\ensuremath{\alpha}}(Sh)$, of the ground state of quantum systems in local bases normally show a volume-law behavior. For a subsystem of quantum chains at a critical point there is an extra logarithmic subleading term with a coefficient which is universal. In this paper we study this coefficient for generic time-reversal translational invariant quadratic critical free fermions. These models can be parametrized by a complex function which has zeros on the unit circle. When the zeros on the unit circle do not have degeneracy and there is no zero outside of the unit circle we are able to classify the coefficient of the logarithm. In particular, we numerically calculate the R\'enyi (Shannon) entropy in a configuration basis for a wide variety of these models and show that there are two distinct classes. For systems with $U(1)$ symmetry the coefficient is proportional to the central charge, i.e., one half of the number of points that one can linearize the dispersion relation of the system; for all the values of $\ensuremath{\alpha}$ with transition point at $\ensuremath{\alpha}=4$. For systems without this symmetry, when $\ensuremath{\alpha}&gt;1$, this coefficient is again proportional to the central charge. However, the coefficient for $\ensuremath{\alpha}\ensuremath{\le}1$ is a new universal number. Finally, by using the discrete version of the Bisognano-Wichmann modular Hamiltonian of the Ising chain we show that these coefficients are universal and dependent on the underlying CFT.

Entanglement entropy and negativity in the Ising model with defects

Defects in two-dimensional conformal field theories (CFTs) contain signatures of their characteristics. In this work, we analyze entanglement properties of subsystems in the presence of energy and duality defects in the Ising CFT using the density matrix renormalization group (DMRG) technique. In particular, we compute the entanglement entropy (EE) and the entanglement negativity (EN) in the presence of defects. For the EE, we consider the cases when the defect lies within the subsystem and at the edge of the subsystem. We show that the EE for the duality defect exhibits fundamentally different characteristics compared to the energy defect due to the existence of localized and delocalized zero energy modes. Of special interest is the nontrivial ‘finite-size correction’ in the EE obtained recently using free fermion computations [1]. These corrections arise when the subsystem size is appreciable compared to the total system size and lead to a deviation from the usual logarithmic scaling characteristic of one-dimensional quantum-critical systems. Using matrix product states with open and infinite boundary conditions, we numerically demonstrate the disappearance of the zero mode contribution for finite subsystem sizes in the thermodynamic limit. Our results provide further support to the recent free fermion computations, but clearly contradict earlier analytical field theory calculations based on twisted torus partition functions. Subsequently, we compute the logarithm of the EN (log-EN) between two disjoint subsystems separated by a defect. We show that the log-EN scales logarithmically with the separation of the subsystems. However, the coefficient of this logarithmic scaling yields a continuously-varying effective central charge that is different from that obtained from analogous computations of the EE. The defects leave their fingerprints in the subleading term of the scaling of the log-EN. Furthermore, the log-EN receives similar ‘finite size corrections’ like the EE which leads to deviations from its characteristic logarithmic scaling.

Vortex lattices in binary Bose–Einstein condensates: collective modes, quantum fluctuations, and intercomponent entanglement

We study binary Bose–Einstein condensates subject to synthetic magnetic fields in mutually parallel or antiparallel directions. Within the mean-field theory, the two types of fields have been shown to give the same vortex-lattice phase diagram. We develop an improved effective field theory to study properties of collective modes and ground-state intercomponent entanglement. Here, we point out the need to introduce renormalized coupling constants for coarse-grained densities. We show that the low-energy excitation spectra for the two types of fields are related to each other by suitable rescaling with the renormalized coupling constants. By calculating the entanglement entropy, we find that for an intercomponent repulsion (attraction), the two components are more strongly entangled in the case of parallel (antiparallel) fields, in qualitative agreement with recent studies for a quantum (spin) Hall regime. We also find that the entanglement spectrum exhibits an anomalous square-root dispersion relation, which leads to a subleading logarithmic term in the entanglement entropy. All of these are confirmed by numerical calculations based on the Bogoliubov theory with the lowest-Landau-level approximation. Finally, we investigate the effects of quantum fluctuations on the phase diagrams by calculating the correction to the ground-state energy due to zero-point fluctuations in the Bogoliubov theory. We find that the boundaries between rhombic-, square-, and rectangular-lattice phases shift appreciably with a decrease in the filling factor.

B → Dℓνℓ form factors beyond leading power and extraction of |Vcb| and R(D)

We investigate the subleading-power corrections to the exclusive B → Dℓνℓ form factors at mathcal{O} ( {alpha}_s^0 ) in the light-cone sum rules (LCSR) framework by including the two- and three-particle higher-twist contributions from the B-meson light-cone distribution amplitudes up to the twist-six accuracy, by taking into account the subleading terms in expanding the hard-collinear charm-quark propagator, and by evaluating the hadronic matrix element of the subleading effective current . Employing further the available leading-power results for the semileptonic B → D form factors at the next-to- leading-logarithmic level and combining our improved LCSR predictions with the recent lattice determinations, we then carry out a comprehensive phenomenological analysis on the semi-leptonic B → Dℓνℓ decay. We extract left|{V}_{cb}right|=left({40.2}_{-0.5}^{+0.6}{left|{{}_{mathrm{th}}}_{-1.4}^{+1.4}right|}_{mathrm{exp}}right)times {10}^{-3}left(left|{V}_{cb}right|=left({40.9}_{-0.5}^{+0.6}{left|{{}_{mathrm{th}}}_{-1.0}^{+1.0}right|}_{mathrm{exp}}right)times {10}^{-3}right) using the BaBar (Belle) experimental data, and particularly obtain for the gold-plated ratio R(D) = 0.302 ± 0.003.

Universal Behavior beyond Multifractality of Wave Functions at Measurement-Induced Phase Transitions.

We investigate the structure of many-body wave functions of 1D quantum circuits with local measurements employing the participation entropies. The leading term in system size dependence of participation entropy indicates a model-dependent multifractal scaling of the wave functions at any nonzero measurement rate. The subleading term contains universal information about measurement-induced phase transitions and plays the role of an order parameter, being constant nonzero in the error-correcting phase and vanishing in the quantum Zeno phase. We provide robust numerical evidence investigating a variety of quantum many-body systems and provide an analytical interpretation of this behavior expressing the participation entropy in terms of partition functions of classical statistical models in 2D.

High-precision QED initial state corrections for e+e−→ γ∗/Z∗ annihilation

The precise knowledge of the QED initial state corrections is of instrumental importance in studying high-luminosity measurements in [Formula: see text] annihilation at facilities like LEP, the International Linear Collider ILC, CLIC, a Giga-[Formula: see text] facility, and the planned FCC_ee. Logarithmic corrections of up to [Formula: see text] are necessary with various subleading terms taken into account. This applies to both the inclusive measurement of processes like [Formula: see text] and also the forward–backward asymmetry. As has been shown recently, techniques from massive QCD, such as the computation of massive on-shell operator matrix elements, can be used for these calculations. We give an introduction to this topic and present both the calculation methods and the numerical corrections having been reached so far.

Entanglement Entropy in the Ising Model with Topological Defects.

Entanglement entropy (EE) contains signatures of many universal properties of conformal field theories (CFTs), especially in the presence of boundaries or defects. In particular, topological defects are interesting since they reflect internal symmetries of the CFT and have been extensively analyzed with field-theoretic techniques with striking predictions. So far, however, no lattice computation of EE has been available. Here, we present an abinitio analysis of EE for the Ising model in the presence of a topological defect. While the behavior of the EE depends, as expected, on the geometric arrangement of the subsystem with respect to the defect, we find that zero-energy modes give rise to crucial finite-size corrections. Importantly, contrary to the field-theory predictions, the universal subleading term in the EE when the defect lies at the edge of the subsystem arises entirely due to these zero-energy modes and is not directly related to the modular S matrix of the Ising CFT.