arXiv subjects
Publications and source records attributed to Tobias Hurth.
We consider the stochastic heat equation on the integer lattice $\mathbb{Z}^d$ in dimension $d \geq 3$ and with small coupling constant. We show uniqueness of global solutions within the class of positive functions that are stationary in time and whose asymptotic growth in space is subexponential. Our proof relies on a factorization formula for the point-to-point partition function in the associated polymer model.
We consider a continuous-time simple symmetric random walk on the integer lattice $\mathbb{Z}^d$ in dimension $d \geq 3$, subject to a random potential given by a field of two-sided Wiener processes. In the high-temperature regime, we prove the existence of the $L^2$- and almost sure limits of the partition function as time $t \to \pm \infty$, and show that these limiting partition functions are positive almost surely. Our main result is a factorization formula for the point-to-point partition function, which is shown to be valid up to any sub-ballistic scale.
In all previous calculations of the non-local sub-leading contribution to the inclusive penguin decay $\bar B \to X_s \gamma$ due to the interference of the electroweak operators ${O}_1^c$ - ${O}_{7\gamma}$ the local Voloshin term was subtracted. In view of the ongoing analysis at order $\alpha_s$, we present a calculation of the complete non-local contribution which takes into account the high correlation between the uncertainties of the local Voloshin and the non-local term of the previous analyses. The new calculation has a high impact on the range of the non-local contribution.
We report on progress towards including next-to-leading order (NLO) radiative corrections to the subleading-power factorization formula for the $Q_1^{q}-Q_{7γ}$ interference contribution in $\bar{B}\to X_sγ$ at large photon energies, $m_b - 2E_γ= \mathcal{O}(Λ_{\rm QCD})$. The novel ingredients for a NLO analysis are the one-loop anomalous dimension of the subleading shape function $g_{17}(ω,ω_1;μ)$, which was recently computed by us, and the two-loop corrections to the jet function with an internal charm loop. Here we summarize the renormalization of $g_{17}(ω,ω_1;μ)$, and further discuss that our insights allow for a simplified renormalization of a specific generalization of a three-particle $B$-meson light-cone distribution amplitude, but with non-aligned light-like separations of the fields.
This paper is devoted to the study of a stochastic process obtained by random switching between a finite collection of vector fields. Such processes have recently been the focus of much attention in the case where the switching times are exponentially distributed, i.e., Markovian switching. In this contribution, we admit any distribution on $\mathbb{R}_+$ as a law for the switching times. We show that whenever this law is not singular with respect to the Lebesgue measure, the stochastic process obtained from the random switching is Feller. More importantly, we give conditions on the switching and on the vector fields ensuring that the Lie bracket condition considered in the Markovian case in Bakhtin and Hurth (2012) and Benaïm, Le Borgne, Malrieu and Zitt (2015) still imply ergodicity of the process.
We present theoretical predictions for observables in inclusive $\bar{B}\to X_s \ell^+\ell^-$ suitable for measurements at hadron colliders through a sum-over-exclusive approach. At low $q^2$ we calculate the branching ratio and three angular observables. At high $q^2$ we provide the branching ratio and the ratio of the $\bar B \to X_s \ell^+\ell^-$ rate with respect to the inclusive $\bar B \to X_u \ell \barν$ rate with the same phase-space cut. We compare our predictions to the $B$ factory measurements and also to an extraction of the experimental rate through a sum-over-exclusive method using branching ratios of the exclusive $\bar B \to K^{(*)}μ^+μ^-$ modes measured at LHCb. We find a consistent picture comparing Standard Model theory and experiment. As such, our analysis does not support a recent claim about a deficit in the inclusive branching ratio in the high-$q^2$ region. Finally, we present current model-independent bounds on new physics and emphasize the potential of complementary analyses of $\bar{B}\to X_s \ell^+\ell^-$ at Belle II and the LHC.
We derive and solve the renormalisation-group (RG) equation of the shape function $g_{17}(ω,ω_1;μ)$, which appears at subleading power in the factorization of the inclusive decays $\bar{B} \to X_s γ$ and $\bar B \to X_s \ell^+\ell^-$. Our results provide the first ingredient for a next-to-leading order analysis of the respective resolved-photon ${Q}^{c}_{1} - {Q}_{7γ}$ interference contribution, whose current uncertainties are among the largest ones in both inclusive penguin modes. As a by-product of our study, we find that the analytic properties of the soft anomalous dimension as well as the jet functions in a factorization theorem allow for a simplified renormalisation of operators in Heavy-Quark Effective Theory that are composed of fields smeared along distinct light-cone directions. Their hadronic matrix elements become relevant in various inclusive and exclusive $B$-decays beyond leading power in the heavy-quark and large-energy expansion. Using these insights, we derive and solve a simpler ``reduced'' RG equation of an amplitude-level soft function that describes the long-distance QCD dynamics for penguin contributions to exclusive $\bar{B}_{d,s} \to γγ$ decays, and which has recently been discussed in the literature.
The hadronic mass spectrum of inclusive $\bar{B} \to X_s \ell^+ \ell^-$ is investigated at next to leading order in the heavy quark expansion. For mild cuts on the hadronic mass, the expansion, which applies when the cut is released, remains convergent. However, the cuts used at BaBar and Belle to reduce backgrounds from charged current semileptonic processes are too severe for a description in terms of matrix elements of local operators to apply. Strategies for interpolating between the two regions are discussed.
Global analyses in the Standard Model Effective Field Theory (SMEFT) framework serve as a tool to probe potential directions of new physics. To break degeneracies between the Wilson coefficients of the SMEFT, it is essential to combine observables from various experiments. Since different observables entering global fits may be measured at different energy scales, it becomes increasingly important to account for this fact through the renormalisation group evolution (RGE) of the Wilson coefficients. In this work, we investigate the effects of the RGE on a global SMEFT fit under the assumption of a $U(3)^5$ symmetry within the minimal flavour violation framework. We comment on the role of next-to-leading order SMEFT predictions for breaking potential degeneracies between Wilson coefficients arising as a result of RGE effects.
The subleading so-called resolved contributions represent the largest uncertainty in the inclusive decay mode $\bar B \to X_s γ$. However there had been no complete proof of factorization of these subleading contributions. This failure of factorisation can be traced back to endpoint divergences and cured by recently proposed refactorisation techniques.
We present comprehensive global fits of the SMEFT under the $\textit{minimal}$ minimal flavour violation (MFV) hypothesis, i.e. assuming that only the flavour-symmetric and CP-invariant operators are relevant at the high scale. The considered operator set is determined by theory rather than the used datasets. We establish global limits on these Wilson coefficients using leading order and next-to-leading order SMEFT predictions for electroweak precision observables, Higgs, top, flavour and dijets data as well as measurements from parity violation experiments and lepton scattering. Our investigations reveal an intriguing crosstalk among different observables, underscoring the importance of combining diverse observables from various energy scales in global SMEFT analyses.
We report on recent progress in the field of nonlocal (so-called resolved) contributions to the inclusive penguin decays which presently belong to the largest uncertainties in these inclusive decay modes. There is still a very large scale and a large charm mass dependence in the present leading order results which can in the future be decreased by including the $α_s$ corrections.
We establish refactorisation conditions between the subleading ${O}_8$-${O}_8$ contributions to the inclusive $\bar B \to X_s γ$ decay suffering from endpoint divergences and prove a factorisation theorem for these contributions to all orders in the strong coupling constant. This allows for higher-order calculations of the resolved contributions and consistent summation of large logarithms, consequently reducing the recently found large-scale dependence in these contributions. We implement the concept of refactorisation in a heavy flavour application of SCET, which includes nonperturbative functions as additional subtlety not present in collider applications.
We prove a factorization formula for the point-to-point partition function associated with a model of directed polymers on the space-time lattice $\mathbb{Z}^{d+1}$, subject to an i.i.d. random potential and in the regime of weak disorder. In particular, we show that the error term in the factorization formula is uniformly small for starting and end points $x, y$ in the sub-ballistic regime $\| x - y \| \leq t^σ$, where $σ< 1$ can be arbitrarily close to $1$. This extends a result of Sinai. We also derive asymptotics for spatial and temporal correlations of the field of limiting partition functions.
In this paper, we review several results from singularly perturbed differential equations with multiple small parameters. In addition, we develop a general conceptual framework to compare and contrast the different results by proposing a three-step process. First, one specifies the setting and restrictions of the differential equation problem to be studied and identifies the relevant small parameters. Second, one defines a notion of equivalence via a property/observable for partitioning the parameter space into suitable regions near the singular limit. Third, one studies the possible asymptotic singular limit problems as well as perturbation results to complete the diagrammatic subdivision process. We illustrate this approach for two simple problems from algebra and analysis. Then we proceed to the review of several modern double-limit problems including multiple time scales, stochastic dynamics, spatial patterns, and network coupling. For each example, we illustrate the previously mentioned three-step process and show that already double-limit parametric diagrams provide an excellent unifying theme. After this review, we compare and contrast the common features among the different examples. We conclude with a brief outlook, how our methodology can help to systematize the field better, and how it can be transferred to a wide variety of other classes of differential equations.
We investigate the information that can be gained by including flavour data in fits of the Standard Model Effective Field Theory (SMEFT) with the assumption of Minimal Flavour Violation (MFV), allowing - as initial conditions at the high scale - leading terms in spurionic Yukawas only. Starting therefore from a theory with no tree level flavour changing neutral currents at the scale of new physics, we calculate effects in flavour changing processes at one loop, and the resulting constraints on linear combinations of SMEFT coefficients, consistently parameterising the electroweak parameters and the CKM within the SMEFT. By doing a global fit including electroweak, Higgs and low energy precision measurements among others, we show that flavour observables put strong constraints on previously unconstrained operator directions. The addition of flavour data produces four independent constraints at order TeV or above on otherwise flat directions; reducing to three when complete U(3)^5 flavour symmetry is assumed. Our findings demonstrate that flavour remains a stringent test for models of new physics, even in the most flavourless scenario.
In view of the importance of the nonperturbative resolved contributions for the overall uncertainties of the two inclusive penguin decays $\bar B \to X_s γ$ and $\bar B \to X_{s,d} \ell^+\ell^-$ we reanalyse these contributions using new estimates of moments of the subleading shape functions and of other input parameters. Within a systematic approach we find a significant reduction of the nonperturbative uncertainties in the inclusive decay $\bar B \to X_{s,d} \ell^+\ell^-$, but a much less pronounced reduction in the inclusive decay $\bar B \to X_s γ$ compared to a recent analysis on the resolved contributions to the inclusive decay $\bar B \to X_s γ$. We identify the reasons for this discrepancy.
With the first data being recorded at Belle II, we are at the brink of a new era in quark flavour physics. The many exciting new opportunities for Belle~II include a full angular analysis of inclusive ${\bar B \to X_{s} \, \ell^+\ell^-}$ which has the potential to reveal new physics, in particular by its interplay with the exclusive $b \to s \ell^+\ell^-$ counterparts studied extensively at LHCb. In this paper, we present fully updated Standard Model predictions for all angular observables necessary for this endeavour. These predictions are tailored to Belle II and include an elaborate study of the treatment of collinear photons which become crucial when aiming for the highest precision. In addition, we present a phenomenological study of the potential for Belle II to reveal possible new physics in the inclusive decay channel, both in an independent manner and in combination with exclusive modes.