We consider the stochastic heat equation on the integer lattice ℤ^d in dimension d ≥ 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 ℤ^d in dimension d ≥ 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 →±∞, 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.

A correction to this paper has been published: https://doi.org/10.1007/JHEP11(2024)130

Abstract 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 factorisation of the inclusive decays B ¯ → X s γ $$ \overline{B}\to {X}_s\gamma $$ and B ¯ → X s ℓ + ℓ − $$ \overline{B}\to {X}_s{\ell}^{+}{\ell}^{-} $$ . Our results provide the first ingredient for a next-to-leading order analysis of the respective resolved-photon Q 1 c − Q 7 γ $$ {Q}_1^c-{Q}_{7\gamma } $$ 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 factorisation 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 B ¯ d , s → γγ $$ {\overline{B}}_{d,s}\to \gamma \gamma $$ 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.

We derive and solve the renormalisation-group (RG) equation of the shape function g17(ω, ω1; μ), which appears at subleading power in the factorisation of the inclusive decays B→X_sγ and B→X_sℓ^+ℓ^- . Our results provide the first ingredient for a next-to-leading order analysis of the respective resolved-photon Q_1^c-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 factorisation 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 B_d,s→γγ decays, and which has recently been discussed in the literature.

As Christoph Greub embarks on a well-deserved retirement, we take this opportunity to celebrate his remarkable career and lasting contributions. Over the years, Christoph has been a pillar of excellence, known for his unwavering commitment and expertise in B physics. This tribute reflects on his professional journey, the impact he has had on colleagues, young collaborators and the legacy he leaves behind. With deep appreciation, we honour Christoph’s accomplishments and wish him the best in this exciting new chapter of life.

A correction to this paper has been published: https://doi.org/10.1007/JHEP11(2024)130

We derive and solve the renormalisation-group (RG) equation of the shape function $g_{17}(\omega,\omega_1;\mu)$, which appears at subleading power in the factorization of the inclusive decays $\bar{B} \to X_s \gamma$ 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 ${Q}^{c}_{1} - {Q}_{7\gamma}$ 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 $\bar{B}_{d,s} \to \gamma \gamma$ decays, and which has recently been discussed in the literature.

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 B̅→ X_sγ at large photon energies, m_b - 2E_γ= 𝒪(Λ_ 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 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.

A correction to this paper has been published: https://doi.org/10.1007/JHEP11(2024)130

Abstract We present theoretical predictions for observables in inclusive B ¯ → X s ℓ + ℓ − $$ \overline{B}\to {X}_s{\ell}^{+}{\ell}^{-} $$ 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 B ¯ → X s ℓ + ℓ − $$ \overline{B}\to {X}_s{\ell}^{+}{\ell}^{-} $$ rate with respect to the inclusive B ¯ → X u ℓ ν ¯ $$ \overline{B}\to {X}_u\ell \overline{\nu} $$ 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 B ¯ → K ∗ μ + μ − $$ \overline{B}\to {K}^{\left(\ast \right)}{\mu}^{+}{\mu}^{-} $$ 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 B ¯ → X s ℓ + ℓ − $$ \overline{B}\to {X}_s{\ell}^{+}{\ell}^{-} $$ at Belle II and the LHC.

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 $\bar B \to X_u \ell \bar\nu$ rate with the same phase-space cut. We compare our predictions to an extraction of the experimental rate through a sum-over-exclusive method using branching ratios of the exclusive $\bar B \to K^{(*)}\mu^+\mu^-$ modes measured at LHCb. 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 B̅→ X_s γ and B̅→ X_s ℓ^+ℓ^-. 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 B̅_d,s→γγ decays, and which has recently been discussed in the literature.

We present theoretical predictions for observables in inclusive B→X_sℓ^+ℓ^- suitable for measurements at hadron colliders through a sum-over-exclusive approach. At low q2 we calculate the branching ratio and three angular observables. At high q2 we provide the branching ratio and the ratio of the B→X_sℓ^+ℓ^- rate with respect to the inclusive B→X_uℓν 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 B→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-q2 region. Finally, we present current model-independent bounds on new physics and emphasize the potential of complementary analyses of B→X_sℓ^+ℓ^- at Belle II and the LHC.

Abstract We present comprehensive global fits of the SMEFT under the 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 this flavour assumption 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 dijet 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.

The subleading so-called resolved contributions represent the largest uncertainty in the inclusive decay mode B̅→ 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.