Heavy quark jet production near threshold

In this paper, we study the fragmentation of a heavy quark into a jet near threshold, meaning that final state jet carries most of the energy of the fragmenting heavy quark. Using the heavy quark fragmentation function, we simultaneously resum large logarithms of the jet radius R and 1 − z, where z is the ratio of the jet energy to the initiating heavy quark energy. There are numerically significant corrections to the leading order rate due to this resummation. We also investigate the heavy quark fragmentation to a groomed jet, using the soft drop grooming algorithm as an example. In order to do so, we introduce a collinear-ultrasoft mode sensitive to the grooming region determined by the algorithm’s zcut parameter. This allows us to resum large logarithms of zcut/(1 − z), again leading to large numerical corrections near the endpoint. A nice feature of the analysis of the heavy quark fragmenting to a groomed jet is the heavy quark mass m renders the algorithm infrared finite, allowing a perturbative calculation. We analyze this for EJR ∼ m and EJR » m, where EJ is the jet energy. To do the latter case, we introduce an ultracollinear-soft mode, allowing us to resum large logarithms of EJR/m. Finally, as an application we calculate the rate for e+e− collisions to produce a heavy quark jet in the endpoint region, where we show that grooming effects have a sizable contribution near the endpoint.

Local stability of cooperation in a continuous model of indirect reciprocity

Reputation is a powerful mechanism to enforce cooperation among unrelated individuals through indirect reciprocity, but it suffers from disagreement originating from private assessment, noise, and incomplete information. In this work, we investigate stability of cooperation in the donation game by regarding each player’s reputation and behaviour as continuous variables. Through perturbative calculation, we derive a condition that a social norm should satisfy to give penalties to its close variants, provided that everyone initially cooperates with a good reputation, and this result is supported by numerical simulation. A crucial factor of the condition is whether a well-reputed player’s donation to an ill-reputed co-player is appreciated by other members of the society, and the condition can be reduced to a threshold for the benefit-cost ratio of cooperation which depends on the reputational sensitivity to a donor’s behaviour as well as on the behavioural sensitivity to a recipient’s reputation. Our continuum formulation suggests how indirect reciprocity can work beyond the dichotomy between good and bad even in the presence of inhomogeneity, noise, and incomplete information.

3D Yang-Mills glueballs vs closed effective strings

Recent lattice results strongly support the Axionic String Ansatz (ASA) for quantum numbers of glueballs in 3D Yang-Mills theory. The ASA treats glueballs as closed bosonic strings. The corresponding worldsheet theory is a deformation of the minimal Nambu-Goto theory. In order to understand better the ASA strings and as a first step towards a perturbative calculation of the glueball mass splittings we compare the ASA spectrum to the closed effective string theory. Namely, we model glueballs as excitations around the folded rotating rod solution with a large angular momentum J. The resulting spectrum agrees with the ASA in the regime of validity of the effective theory, i.e., in the vicinity of the leading Regge trajectory. In particular, closed effective string theory correctly predicts that only glueballs of even spin J show up at the leading Regge trajectory. Interestingly though, the closed effective string theory overestimates the number of glueball states far above the leading Regge trajectory.

Relativistic fermions: Introduction

Some basic concepts needed for the discussion of Fermi fields have been introduced earlier, as in quantum mechanics (QM) with Grassmann variables, a representation by field integrals of the statistical operator e<συπ>−βH</συπ> for the non-relativistic Fermi gas in the formalism of second quantization, and an expression for the evolution operator. Here, it is first recalled how relativistic fermions transform under the spin group. The free action for Dirac fermions is analysed, the relation between fields and particles explained, an expression for the scattering matrix obtained, and the non-relativistic limit of a model of self-coupled massive Dirac fermions derived. A formalism of Euclidean relativistic fermions is then introduced. In the Euclidean formalism: fermions transform under the fundamental representation of the spin group Spin(d) associated with the SO(d) rotation group (spin 1/2 fermions for d = 4). As for the scalar field theory, the Gaussian integral, which corresponds to a free field theory is calculated. Then the generating functional of correlation functions is obtained by adding a source term to the action. The field integral corresponding to a general action with an interaction expandable in powers of the field, can be expressed in terms of a series of Gaussian integrals, which can be calculated, for example, with the help of Wick's theorem. The connection between spin and statistics is verified by a simple perturbative calculation. The appendix describes a few additional properties of the spin group, the algebra of γ matrices, and the corresponding spinors for Euclidean fermions.

Entropy linear response theory with non-Markovian bath

We developed a perturbative calculation for entropy dynamics, which considers a sudden coupling between a system and a bath. The theory we developed can work in a general environment without Markovian approximation. A perturbative formula is given for bosonic environments and fermionic environments, respectively. We find the Rényi entropy response is only related to the spectral functions of the system and the environment, together with a statistical kernel distribution function. We find a t2 growth/decay in the short time limit and a linear t growth/decay in a longer time scale for the second Rényi entropy response. A non-monotonic behavior of Rényi entropy for fermionic systems is found to be quite general when the environmental temperature is the lower one. A Fourier’s law in heat transport is obtained when two systems’ temperatures are close to each other. A consistency check is made for Sachdev-Ye-Kitaev model coupling to free fermions, a Page curve alike dynamics is found in a process dual to black hole evaporation. An oscillation of Rényi entropy is found for an environment with a gapped spectrum.

Renormalization Mass Scale and Scheme Dependence in the Perturbative Contribution to Inclusive Semileptonic b Decays

We examine the perturbative calculation of the inclusive semi-leptonic decay rate \Gamma for the b-quark, using mass-independent renormalization. To finite order of perturbation theory the series for \Gamma will depend on the unphysical renormalization scale parameter μ and on the particular choice of mass-independent renormalization scheme; these dependencies will only be removed after summing the series to all orders. In this paper we show that all explicit μ-dependence of \Gamma, through powers of ln(μ), can be summed by using the renormalization group equation. We then find that this explicit μ-dependence can be combined together with the implicit μ-dependence of \Gamma (through powers of both the running coupling a(μ) and the running b-quark mass m(μ)) to yield a μ-independent perturbative expansion for \Gamma in terms of a(μ) and m(μ) both evaluated at a renormalization scheme independent mass scale IM which is fixed in terms of either the ``\overline{MS} mass'' \overline{m}_b of the b quark or its pole mass m_{pole}. At finite order the resulting perturbative expansion retains a degree of arbitrariness associated with the particular choice of mass-independent renormalization scheme. We use the coefficients c_i and g_i of the perturbative expansions of the renormalization group functions \beta(a) and \gamma(a), associated with a(μ) and m(μ) respectively, to characterize the remaining renormalization scheme arbitrariness of \Gamma. We further show that all terms in the expansion of \Gamma can be written in terms of the c_i and g_i coefficients and a set of renormalization scheme independent parameters \tau_i. A second set of renormalization scheme independent parameters \sigma_i is shown to play a very similar role in the perturbative expansion of m_{pole} in terms of m(μ) and a(μ). We illustrate our approach by a perturbative computation of \Gamma using the \overline{MS} renormalization scheme. Two other particular mass independent renormalization schemes are briefly considered.

Nuclear saturation energy in effective chiral model within Fermi liquid theory approach

We calculate the relativistic Fermi liquid parameters (RFLPs) for the description of the nuclear saturation energy using a chiral effective Lagrangian. Analytical expressions of Fermi liquid parameters (FLPs) are presented both for the direct and exchange contributions by retaining the meson masses. We present a comparative study of perturbative calculation with mean field results. The FLPs, so determined, are then used to calculate the chemical potential, energy densities, and binding energy for dense nuclear matter interacting via the exchange of σ, ω, and π mesons. In addition, we also estimate bulk quantities like incompressibility and first sound velocity in terms of RFLPs for dense nuclear matter.

Physics of parameter correlations around the solar-scale enhancement in neutrino theory with unitarity violation

We discuss the physics of the three neutrino flavor transformation with non-unitary mixing matrix, with particular attention to the correlation between the $\nu$SM- and the $\alpha$ parameters which represent the effect of unitarity-violating (UV) new physics. Towards this goal, a new perturbative framework is created to illuminate the effect of non-unitarity in the region of the solar-scale enhanced oscillations. We refute the skepticism about the physical reality of the $\nu$Standard Model CP phase $\delta$–$\alpha$ parameter phase correlation by analysis with the SOL convention of $U_{{\tiny MNS}}$, in which $e^{\pm i \delta}$ is attached to $s_{12}$. Then, a comparative study between the solar- and atmospheric-scale oscillation regions allowed by the framework reveals a dynamical $\delta$–(blobs of the $\alpha$ parameters) correlation in the solar oscillation region, in sharp contrast to the “chiral”-type phase correlation $[e^{- i \delta} \bar{\alpha}_{\mu e},\ e^{- i \delta} \bar{\alpha}_{\tau e},\ \bar{\alpha}_{\tau \mu}]$ in the Particle Data Group convention seen in the atmospheric oscillation region. An explicit perturbative calculation to the first order in the $\nu_{\mu} \rightarrow \nu_{e}$ channel allows us to decompose the UV related part of the probability into the unitary evolution part and the genuine non-unitary part. We observe that the effect of non-unitarity tends to cancel between these two parts, as well as between the different $\alpha_{\beta \gamma}$ parameters.

Calculating the primary Lund Jet Plane density

The Lund-jet plane has recently been proposed as a powerful jet substructure tool with a broad range of applications. In this paper, we provide an all-order single logarithmic calculation of the primary Lund-plane density in Quantum Chromodynamics, including contributions from the running of the coupling, collinear effects for the leading parton, and soft logarithms that account for large-angle and clustering effects. We also identify a new source of clustering logarithms close to the boundary of the jet, deferring their resummation to future work. We then match our all-order results to exact next-to-leading order predictions. For phenomenological applications, we supplement our perturbative calculation with a Monte Carlo estimate of non-perturbative corrections. The precision of our final predictions for the Lund-plane density is 5−7% at high transverse momenta, worsening to about 20% at the lower edge of the perturbative region, corresponding to transverse momenta of about 5 GeV. We compare our results to a recent measurement by the ATLAS collaboration at the Large-Hadron Collider, revealing good agreement across the perturbative domain, i.e. down to about 5 GeV.

Chiral perturbation theory for GR

We describe a new perturbation theory for General Relativity, with the chiral first-order Einstein-Cartan action as the starting point. Our main result is a new gauge-fixing procedure that eliminates the connection-to-connection propagator. All other known first-order formalisms have this propagator non-zero, which significantly increases the combinatorial complexity of any perturbative calculation. In contrast, in the absence of the connection-to-connection propagator, our formalism leads to an effective description in which only the metric (or tetrad) propagates, there are only cubic and quartic vertices, but some vertex legs are special in that they cannot be connected by the propagator. The new formalism is the gravity analog of the well-known and powerful chiral description of Yang-Mills theory.