Non-perturbative Contributions Research Articles

Supersymmetric indices factorize

The extent to which quantum mechanical features of black holes can be understood from the Euclidean gravity path integral has recently received significant attention. In this paper, we examine this question for the calculation of the supersymmetric index. For concreteness, we focus on the case of charged black holes in asymptotically flat four-dimensional mathcal{N} = 2 ungauged supergravity. We show that the gravity path integral with supersymmetric boundary conditions has an infinite family of Kerr-Newman classical saddles with different angular velocities. We argue that fermionic zero-mode fluctuations are present around each of these solutions making their contribution vanish, except for a single saddle that is BPS and gives the expected value of the index. We then turn to non-perturbative corrections involving spacetime wormholes and show that a fermionic zero mode is present in all these geometries, making their contribution vanish once again. This mechanism works for both single- and multi-boundary path integrals. In particular, only disconnected geometries without wormholes contribute to the gravitational path integral which computes the index, and the factorization puzzle that plagues the black hole partition function is resolved for the supersymmetric index. Finally, we classify all other single-centered geometries that yield non-perturbative contributions to the gravitational index of each boundary.

Asymptotics in an asymptotic CFT

In this work we illustrate the resurgent structure of the λ-deformation; a two-dimensional integrable quantum field theory that has an RG flow with an SU(N)k Wess-Zumino-Witten conformal fixed point in the UV. To do so we use modern matched asymptotic techniques applied to the thermodynamic Bethe ansatz formulation to compute the free energy to 38 perturbative orders in an expansion of large applied chemical potential. We find numerical evidence for factorial asymptotic behaviour with both alternating and non-alternating character which we match to an analytic expression. A curiosity of the system is that the leading non-alternating factorial growth vanishing when k divides N. The ambiguities associated to Borel resummation of this series are suggestive of non-perturbative contributions. This is verified with an analytic study of the TBA system demonstrating a cancellation between perturbative and non-perturbative ambiguities.

Constraints on lepton universality violation from rare B decays

The LHCb Collaboration has recently released a new study of ${B}^{+}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ and $B\ensuremath{\rightarrow}{K}^{*0}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ ($\ensuremath{\ell}=e$, $\ensuremath{\mu}$) decays, testing lepton universality with unprecedented accuracy using the whole Run 1 and 2 dataset. In addition, the CMS Collaboration has reported an improved analysis of the branching ratios ${B}_{(d,s)}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. While these measurements offer, per se, a powerful probe of new physics, global analyses of $b\ensuremath{\rightarrow}s{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ transitions also rely on the assumptions about nonperturbative contributions to the decay matrix elements. In this work, we perform a global Bayesian analysis of new physics in (semi)leptonic rare $B$ decays, paying attention to the role of charming penguins which are difficult to evaluate from first principles. We find data to be consistent with the Standard Model once rescattering from intermediate hadronic states is included. Consequently, we derive stringent bounds on lepton universality violation in $|\mathrm{\ensuremath{\Delta}}B|=|\mathrm{\ensuremath{\Delta}}S|=1$ (semi)leptonic processes.

On the prompt contribution to the atmospheric neutrino flux

The prompt contribution to the atmospheric neutrino flux is analyzed. We demonstrate that the corresponding theoretical uncertainties related to perturbative treatment of charm production, notably, the ones stemming from the low- and high-$x$ behavior of parton distribution functions, can be conveniently studied at the level of charm quark production. Additionally, we discuss the nonperturbative contribution to the prompt neutrino flux, related to the intrinsic charm content of the proton and analyze its main features.

Reflected entropy in random tensor networks. Part II. A topological index from canonical purification

In ref. [1], we analyzed the reflected entropy (SR) in random tensor networks motivated by its proposed duality to the entanglement wedge cross section (EW) in holographic theories, {S}_R=2frac{EW}{4G} . In this paper, we discover further details of this duality by analyzing a simple network consisting of a chain of two random tensors. This setup models a multiboundary wormhole. We show that the reflected entanglement spectrum is controlled by representation theory of the Temperley-Lieb algebra. In the semiclassical limit motivated by holography, the spectrum takes the form of a sum over superselection sectors associated to different irreducible representations of the Temperley-Lieb algebra and labelled by a topological index k ∈ ℤ>0. Each sector contributes to the reflected entropy an amount 2kfrac{EW}{4G} weighted by its probability. We provide a gravitational interpretation in terms of fixed-area, higher-genus multiboundary wormholes with genus 2k – 1 initial value slices. These wormholes appear in the gravitational description of the canonical purification. We confirm the reflected entropy holographic duality away from phase transitions. We also find important non-perturbative contributions from the novel geometries with k ≥ 2 near phase transitions, resolving the discontinuous transition in SR. Along with analytic arguments, we provide numerical evidence for our results. We finally speculate that signatures of a non-trivial von Neumann algebra, connected to the Temperley-Lieb algebra, will emerge from a modular flowed version of reflected entropy.

Cardy expansion of 3d superconformal indices and corrections to the dual black hole entropy

We consider the superconformal index of three-dimensional mathcal{N} = 2 supersymmetric field theories computed via localization on S1 × S2. We systematically develop an expansion where the ratio of the radius of S1 to the radius of S2 is taken very small — a Cardy-like expansion. We emphasize the sub-leading structures in this Cardy-like expansion as well as their interplay with the large-N limit for theories with gauge group of the form product of U(N) factors. We demonstrate that taking the large-N limit first leads to an expression for the effective action yielding the index that only includes terms proportional to 1/β and powers of βi=0,1,2 where β is the ratio of radii. As we depart from the β → 0 limit for finite N, we find indications of non-perturbative contributions of the form e−1/β. We present an explicit evaluation of the superconformal index for the ABJM theory in the large-N limit that is exact in β up to non-perturbative corrections. For the ABJM theory we explore the implications of the Cardy-like expansion for corrections to the entropy of the rotating, electricallly charged, asymptotically AdS4 dual black hole. Interestingly, we find a closed form for the entropy that includes all perturbative corrections in β and takes the form of the leading order expression but with shifted charges.

Schwinger-Dyson equations and mass generation for an axion theory with a [formula omitted] symmetric Yukawa fermion interaction

A nonperturbative Schwinger-Dyson analysis of mass generation is presented for a non-Hermitian PT -symmetric field theory in four dimensions of an axion coupled to a Dirac fermion. The model is motivated by phenomenological considerations. The axion has a quartic self-coupling λ and a Yukawa coupling g to the fermion. The Schwinger-Dyson equations are derived for the model with generic couplings. In the non-Hermitian case there is an additional nonperturbative contribution to the scalar mass. In a simplified rainbow analysis the solutions for the SD equations, are given for different regimes of the couplings g and λ.

Nonperturbative effects in neutrino magnetic moments

In this paper, we calculate the QCD nonperturbative contributions of the neutrino-quark tensor operators to the neutrino magnetic moments by matching onto the chiral perturbation theory at low energies. These nonperturbative contributions can be compared to the perturbative ones, which are induced from one-loop mixing when performing the renormalization group evolutions from $\mu=m_W$ down to $\mu=2~\mathrm{GeV}$. We then constrain the dipole and tensor Wilson coefficients of the low-energy neutrino effective field theory (LNEFT) separately from the neutrino-electron scattering with Borexino data and coherent elastic neutrino-nucleus scattering (CE$\nu$NS) with COHERENT data to show the competition between these two contributions, at the renormalization scales $\mu=2~\mathrm{GeV}$ and $\mu=m_W$ in the $\bar{\mathrm{MS}}$ scheme. In the neutrino-electron scattering, it is found that the nonperturbative contributions dominate for the coefficients involving up and down quarks, while they are expected to be of the same order of magnitude as the perturbative contributions for the coefficients involving strange quark. As for constraints in the CE$\nu$NS, the tensor operators can contribute to the process through either direct or indirect way. As a result, the indirect contributions including nonperturbative and perturbative parts for all couplings become negligible in comparison with the direct ones. As the nonperturbative contributions crucially depend on the value of $c_T$, its inputs will affect the extraction of limits on the tensor LNEFT Wilson coefficients. We compute the upper bounds on these coefficients with $c_T$ quoting from the model and lattice estimates.

Exact Toverline{T} deformation of two-dimensional Yang-Mills theory on the sphere

We study the Toverline{T} deformation of two-dimensional Yang-Mills theory at genus zero by carrying out the analysis at the level of its instanton representation. We first focus on the perturbative sector by considering its power expansion in the deformation parameter μ. By studying the resulting asymptotic series through resurgence theory, we determine the nonperturbative contributions that enter the result for μ < 0. We then extend this analysis to any flux sector by solving the relevant flow equation. Specifically, we impose boundary conditions corresponding to two distinct regimes: the quantum undeformed theory and the semiclassical limit of the deformed theory. The full partition function is obtained as a sum over all magnetic fluxes. For any μ > 0, only a finite portion of the quantum spectrum survives and the partition function reduces to a sum over a finite set of representations. For μ < 0, nonperturbative contributions regularize the partition function through an intriguing mechanism that generates nontrivial subtractions.

Running coupling and non-perturbative corrections for O(N) free energy and for disk capacitor

We reconsider the complete solution of the linear TBA equation describing the energy density of finite density states in the O(N) nonlinear sigma models by the Wiener-Hopf method. We keep all perturbative and non-perturbative contributions and introduce a running coupling in terms of which all asymptotic series appearing in the problem can be represented as pure power series without logs. We work out the first non-perturbative contribution in the O(3) case and show that (presumably because of the instanton corrections) resurgence theory fails in this example. Using the relation of the O(3) problem to the coaxial disks capacitor problem we work out the leading non-perturbative terms for the latter and show that (at least to this order) resurgence theory, in particular the median resummation prescription, gives the correct answer. We demonstrate this by comparing the Wiener-Hopf results to the high precision numerical solution of the original integral equation.

Systematics of perturbatively flat flux vacua for CICYs

In this paper, we extend the analysis of scanning the perturbatively flat flux vacua (PFFV) for the type IIB orientifold compactifications on the mirror of the projective complete intersection Calabi-Yau (pCICY) 3-folds, which are realized as hypersurfaces in the product of complex projective spaces. The main objective of this scan is to investigate the behaviour of PFFV depending on the nature of CY 3-folds in the light of the observations made in [1] where it has been found that K3-fibered CY 3-folds have significantly large number of physical vacua as compared to other geometries. For this purpose, we present the PFFV statistics for all the 36 pCICYs with h1,1 = 2 and classify them into two categories of being K3-fibered model and non K3-fibered model. We subsequently confirm that all the K3-fibered models have a significantly large number of PFFV leading to physical vacua by fixing the axio-dilaton by non-perturbative effects, while only a couple of non K3-fibered models have such physical vacua. For h1,1 = 2 case, we have found that there are five pCICY 3-folds with the suitable exchange symmetry leading to the so-called exponentially flat flux vacua (EFFV) which are protected against non-perturbative prepotential effects as well. By exploring the underlying exchange symmetries in the favorable CY 3-folds with h1,1 ≥ 3 in the dataset of 7820 pCICYs, we have found that there are only 13 spaces which can result in EFFV configurations, and therefore most of the CY 3-folds are a priory suitable for fixing the dilaton valley of the flat vacua using the non-perturbative prepotential contributions.

Energy dependence of intrinsic charm production: Determining the best energy for observation

Background: A nonperturbative charm production contribution, known as intrinsic charm, was predicted in the early 1980s. Recent results have provided new evidence for its existence but further confirmation is needed. Purpose: $J/\psi$ and $\bar D$ meson production are calculated with a combination of perturbative QCD and intrinsic charm to determine the best energy range to study intrinsic charm production. Methods: $J/\psi$ and $\bar D$ meson production are calculated in perturbative QCD to next-to-leading order in the cross section. Cold nuclear matter effects, including nuclear modification of the parton densities and $p_T$ broadening by multiple scattering are taken into account in the production of both; absorption by nucleons is also included for the $J/\psi$. Contributions from intrinsic charm are calculated assuming production from a $|uud c \bar c \rangle$ Fock state. Results: The $J/\psi$ and $\bar D$ meson rapidity and $p_T$ distributions are calculated as a function of rapidity and transverse momentum $p_T$ over a wide range of center-of-mass energies with and without intrinsic charm in $p+p$ collisions. The nuclear modification factor, $R_{pA}$, is also calculated for $p+{\rm Pb}$ interactions at appropriate energies. Previous fixed-target data as a function of Feynman $x$, $x_F$, are also compared to calculations within the approach. Good agreement with the data is found when intrinsic charm is included. Conclusions: The intrinsic charm signal may be largest at midrapidity for future low energy fixed target experiments such as the proposed NA60+.

Exclusive production of a pair of high transverse momentum photons in pion-nucleon collisions for extracting generalized parton distributions

We show that exclusive production of a pair of high transverse momentum photons in pion-nucleon collisions can be systematically studied in QCD factorization approach if the photon’s transverse momentum qT with respect to the colliding pion is much greater than ΛQCD. We demonstrate that the leading power non-perturbative contributions to the scattering amplitudes of this exclusive process are process-independent and can be systematically factorized into universal pion’s distribution amplitudes (DAs) and nucleon’s generalized parton distributions (GPDs), which are convoluted with corresponding infrared safe and perturbatively calculable short-distance hard parts. The correction to this factorized expression is suppressed by powers of 1/qT. We demonstrate quantitatively that this new type of exclusive processes is not only complementary to existing processes for extracting GPDs, but also capable of providing an enhanced sensitivity to the dependence of both DAs and GPDs on the active parton’s momentum fraction x. We also introduce additional, but the same type of exclusive observables to enhance our capability to explore GPDs, in particular, their x-dependence.

Disentangling long and short distances in momentum-space TMDs

The extraction of nonperturbative TMD physics is made challenging by prescriptions that shield the Landau pole, which entangle long- and short-distance contributions in momentum space. The use of different prescriptions then makes the comparison of fit results for underlying nonperturbative contributions not meaningful on their own. We propose a model-independent method to restrict momentum-space observables to the perturbative domain. This method is based on a set of integral functionals that act linearly on terms in the conventional position-space operator product expansion (OPE). Artifacts from the truncation of the integral can be systematically pushed to higher powers in ΛQCD/kT. We demonstrate that this method can be used to compute the cumulative integral of TMD PDFs over {k}_Tle {k}_T^{mathrm{cut}} in terms of collinear PDFs, accounting for both radiative corrections and evolution effects. This yields a systematic way of correcting the naive picture where the TMD PDF integrates to a collinear PDF, and for unpolarized quark distributions we find that when renormalization scales are chosen near {k}_T^{mathrm{cut}} , such corrections are a percent-level effect. We also show that, when supplemented with experimental data and improved perturbative inputs, our integral functionals will enable model-independent limits to be put on the non-perturbative OPE contributions to the Collins-Soper kernel and intrinsic TMD distributions.

Exact TT[over ¯] Deformation of Two-Dimensional Maxwell Theory.

We study the partition function of TT[over ¯]-deformed two-dimensional Maxwell theory by solving the relevant flow equation at the level of individual flux sectors. Summing exactly the "instanton" series, we obtain a well-defined expression for the partition function at arbitrary μ. For μ>0, the spectrum of the theory experiences a truncation and the theory undergoes infinite-order quantum phase transitions associated with the vanishing of Polyakov-loop correlators. For μ<0, the appearance of nonperturbative contributions in μ drastically modifies the structure of the partition function.

Impact of a thermal medium on newly observed Z_{cs}(3985) resonance and its b-partner

Motivated by the very recent discovery of the strange hidden-charm exotic state Z_{cs}(3985) by the BESIII Collaboration, we study the possible interpretation of this exotic state the both at T=0 and Tne 0 . We analytically compute the mass and meson-current coupling constant of this resonance with spin-parity J^{P} = 1^+ at finite temperature approximation up to the sixth order of the thermal operator dimension including non-perturbative contributions. Extracting thermal mass and meson-current coupling constant sum rules, the modifications on properties of the Z_{cs}(3985) state in hot medium are determined. As a by-product, the hadronic parameters of the bottom partner of Z_{cs}(3985) is estimated as well. The search for temperature effects on the hadronic parameters of the hidden-charm meson Z_{cs}(3985) and the bottom partner enable us to understand the phase transitions, chiral symmetry breaking, and the properties of hot-dense matter in QCD. Moreover, the full width of the resonance Z_{cs}(3985) is calculated as (12.0pm 0.8)~{mathrm {MeV}} using the strong decay in the tetraquark picture. Results for width and mass are in reasonable agreement with existing experimental data and results of other theoretical works. The information obtained about the parameters of the considered states is useful for experimental investigations of exotic mesons.

Instanton effects vs resurgence in the O(3) sigma model

We investigate the ground-state energy of the integrable two dimensional O(3) sigma model in a magnetic field. By determining a large number of perturbative coefficients we explore the closest singularities of the corresponding Borel function. We then confront its median resummation to the high precision numerical solution of the exact integral equation and observe that the leading exponentially suppressed contribution is not related to the asymptotics of the perturbative coefficients. By analytically expanding the integral equation we calculate the leading non-perturbative contributions up to fourth order and find complete agreement. These anomalous terms could be attributed to instantons, while the asymptotics of the perturbative coefficients seems to be related to renormalons.

Light baryonium spectrum

We evaluate the light baryonium spectrum, viz. the baryon-antibaryon states, in the framework of QCD sum rules. The nonperturbative contributions up to dimension 12 are taken into account. Numerical results indicate that there might exist eight possible light baryonium states, i.e. $p$-$\bar{p}$, $\Lambda$-$\bar{\Lambda}$, $\Sigma$-$\bar{\Sigma}$, and $\Xi$-$\bar{\Xi}$ with quantum numbers of $0^{-+}$ and $1^{--}$. For the $\Lambda$-$\bar{\Lambda}$, $\Sigma$-$\bar{\Sigma}$, and $\Xi$-$\bar{\Xi}$ states, their masses are found above the corresponding dibaryon thresholds, while the masses of $p$-$\bar{p}$ states are not. The possible baryonium decay modes are analyzed, which are hopefully measurable in BESIII, BELLEII, and LHCb experiments.

Nonperturbative two-pion exchange contributions to the nucleon-nucleon interaction in covariant baryon chiral perturbation theory

We calculate the nonperturbative two-pion exchange (TPE) contributions to the $NN$ interaction in covariant baryon chiral perturbation theory. We study how the nonperturbative resummation affects the $NN$ phase shifts for partial waves with $J \geq 3$ and $L \leq 6$. No significant differences are observed between the nonperturbative phase shifts and perturbative ones for most partial waves except for $^3D_3$, for which the nonperturbative resummation greatly improves the description of the phase shifts. However, a significant cutoff dependence is found for this partial wave and a reasonable description of the phase shifts can only be obtained with a particular cutoff. Furthermore, we compare the so-obtained nonperturbative phase shifts with those obtained in the heavy baryon chiral perturbation theory. We show that the contributions from relativistic nonperturbative TPE are more moderate than those from the nonrelativistic TPE obtained in the dimensional regularization scheme. A proper convergence pattern is observed for most of the partial waves studied except for $^3F_3$, $^3F_4$, and $^3H_6$, for which the subleading TPE contributions are a bit strong. We find that for $H$ and $I$ partial waves, the OPE alone can already describe the phase shifts reasonably well.

Non-perturbative phenomena in jet modification

The interaction of a jet with the medium created in heavy-ion collisions is not yet fully understood from a QCD perspective. This is mainly due to the non-perturbative nature of this interaction which affects both transverse jet momentum broadening and jet quenching. We discuss how lattice simulations of Electrostatic QCD, can be matched to full, four dimensional QCD, to determine non-perturbative contributions to the momentum broadening kernel. We determine the momentum broadening kernel in impact parameter and momentum space and finally show how these results can be used in phenomenological calculations of in-medium splitting rates.