arXiv subjects

Roman Zwicky

Publications and source records attributed to Roman Zwicky.

At least 37 records · Page 2Linked to original sources

arXiv2022

Charged and Neutral $\bar B_{u,d,s} \to γ$ Form Factors from Light Cone Sum Rules at NLO

We present the first analytic ${\cal O}(α_s)$-computation at twist-$1$,$2$ of the $\bar B_{u,d,s} \to γ$ form factors within the framework of sum rules on the light-cone. These form factors describe the charged decay $\bar B_u \to γ\ell^- \barν$, contribute to the flavour changing neutral currents $\bar B_{d,s} \to γ\ell^+ \ell^-$ and serve as inputs to more complicated processes. We provide a fit in terms of a $z$-expansion with correlation matrix and extrapolate the form factors to the kinematic endpoint by using the $g_{BB^*γ}$ couplings as a constraint. Analytic results are available in terms of multiple polylogarithms as ancillary files. We give binned predictions for the $\bar B_u \to γ\ell^- \barν$ branching ratio along with the associated correlation matrix. By comparing with three SCET-computations we extract the inverse moment $B$-meson distribution amplitude parameter $λ_B = 360 (110) \text{MeV}$. The uncertainty thereof could be improved by a more dedicated analysis. In passing, we extend the photon distribution amplitude to include quark mass corrections with a prescription for the magnetic vacuum susceptibility, $χ_q$, compatible with the twist-expansion. The values $χ_q = 3.21 (15) \text{GeV}^{-2}$ and $χ_s = 3.79 (17) \text{GeV}^{-2}$ are obtained.

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arXiv2022

Notes on QED Corrections in Weak Decays

In these lecture notes the basics of QED corrections to hadronic decays are reviewed with special emphasis on conceptual (e.g. counting and tracking of infrared sensitive logs) rather than numerical aspects. General matters are illustrated for the cases of increased complexity and decreased inclusiveness: $e^+ e^- \to hadrons$, the leptonic decay $π^+ \to \ell^+ \bar ν$ and the semileptonic decay $B \to π\ell^+ \bar ν$. The non-trivial and ongoing efforts of including structure dependence are very briefly outlined.

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arXiv2022

Endpoint Symmetries of Helicity Amplitudes

We investigate helicity amplitudes (HAs) of $A \to B C$-type decays for arbitrary spin towards the kinematic endpoint. We show that they are proportional to product of Clebsch-Gordan coefficients (CGC) and the velocity to some positive power. The latter can be zero in which case the HA is non-vanishing at the endpoint. In essence the spatial rotational symmetry, broken by the relative spatial momenta of the particles, is restored at the kinematic endpoint. Therefore SO(3) and SU(2), for bosons and fermion in the decay, act like a global internal symmetry groups. Some of our results can be understood in terms of the Wigner- Eckart theorem. The findings are useful for i) checking theoretical computations and ii) the case where there is a sequence of decays, say $B \to B_1B_2$ with the pair $(B_1B_2)$ not interacting (significantly) with the $C$-particle. An example is $H \to Z Z^* \to 4\ell$ where our findings might be of use for experimentally determining the Higgs quantum numbers. Angular observables, which are essentially ratios of HAs, are given by ratios of CGC at the endpoint. We briefly discuss power corrections in the velocity to the leading order.

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arXiv2021

Endpoint Relations for Baryons

Following our earlier work we establish kinematic endpoint relations for baryon decays using the Wigner-Eckart theorem and apply them to $\frac{1}{2} \to \frac{1}{2}$ and $\frac{1}{2} \to \frac{3}{2}$ baryon transitions. We provide angular distributions at the kinematic endpoint which hold for the generic $d=6$ model-independent effective Hamiltonian. Moreover, we explicitly verify the endpoint relations using an explicit form factor parametrisation and clarify constraints on helicity based form factors to evidence endpoint relations. Our results provide guidance for phenomenological parameterisations, consistency checks for theory computations and experiment. Results are applicable to ongoing and future new physics searches at LHCb, BES III and Belle II with rare semileptonic-, dineutrino-and charged-modes, which include $Λ_b \to Λ^{(*)} \ell \ell, Λ_b \to Λ^{(*)} νν$, $Ω_b \to Ω\ell \ell$, $Λ_c \to p \ell \ell$, $Σ\to p \ell \ell$ and $Λ_b \to Λ_c^{(*)} \ell ν$

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arXiv2021

Radiative Decays of Heavy-light Mesons and the $f_{H,H^*,H_1}^{(T)}$ Decay Constants

The on-shell matrix elements, or couplings $g_{H H^*(H_1)γ}$, describing the $B(D)_q^* \to B(D)_q γ$ and $B_{1 q} \to B_q γ$ ($q = u,d,s$) radiative decays, are determined from light-cone sum rules at next-to-leading order for the first time. Two different interpolating operators are used for the vector meson, providing additional robustness to our results. For the $D^*$-meson, where some rates are experimentally known, agreement is found. The couplings are of additional interest as they govern the lowest pole residue in the $B(D) \to γ$ form factors which in turn are connected to QED-corrections in leptonic decays $B(D) \to \ell \bar ν$. Since the couplings and residues are related by the decay constants $f_{H^*(H_1)}$ and $f^T_{H^*(H_1)}$ respectively, we determine them at next-leading order as a by-product. The quantities $\{ f_{H^*}^T, f_{H_1},f_{H_1}^T\}$ have not previously been subjected to a QCD sum rule determination. All results are compared with the existing experimental and theoretical literature.

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arXiv2021

Probing flavoured Axions in the Tail of $B_q \to μ^+μ^-$

We discuss how LHC di-muon data collected to study $B_q \to μμ$ can be used to constrain light particles with flavour-violating couplings to $b$-quarks. Focussing on the case of a flavoured QCD axion, $a$, we compute the decay rates for $B_q \to μμa$ and the SM background process $B_q \to μμγ$ near the kinematic endpoint. These rates depend on non-perturbative $B_q \to γ^{(*)}$ form factors with on- or off-shell photons. The off-shell form factors -- relevant for generic searches for beyond-the-SM particles -- are discussed in full generality and computed with QCD sum rules for the first time. With these results, we analyse available LHCb data to obtain the sensitivity on $B_q \to μμa$ at present and future runs. We find that the full LHCb dataset alone will allow to probe axion-coupling scales of the order of $10^6$ GeV for both $b\to d$ and $b \to s$ transitions.

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arXiv2021

QED Corrections in $\bar{B} \to \bar{K} \ell^+ \ell^-$ at the Double-Differential Level

We present a detailed analysis of QED corrections to $\bar{B} \to \bar{K} \ell^+ \ell^-$ decays at the double-differential level. Cancellations of soft and collinear divergences are demonstrated analytically using the phase space slicing method. Whereas soft divergences are found to cancel at the differential level, the cancellation of the hard-collinear logs $\ln m_\ell$ require, besides photon-inclusiveness, a specific choice of kinematic variables. In particular, hard-collinear logs in the lepton-pair invariant mass distribution ($q^2$), are sizeable and need to be treated with care when comparing with experiment. Virtual and real amplitudes are evaluated using an effective mesonic Lagrangian. Crucially, we show that going beyond this approximation does not introduce any further infrared sensitive terms. All analytic computations are performed for generic charges and are therefore adaptable to semileptonic decays such as $B \to D \ell \bar ν$.

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arXiv2020

Three Exceptions to the Grossman-Nir Bound

We show that the Grossman-Nir (GN) bound, $\text{Br}(K_L\to π^0ν\barν)\leq 4.3 \, \text{Br}(K^+\to π^+ν\barν)$, can be violated in the presence of light new physics with flavor violating couplings. We construct three sample models in which the GN bound can be violated by orders of magnitude, while satisfying all other experimental bounds. In the three models the enhanced branching ratio $\text{Br}(K_L\to π^0+{\rm inv})$ is due to $K_L\to π^0ϕ_1$, $K_L\to π^0ϕ_1ϕ_1$, $K_L\to π^0ψ_1\bar ψ_1$ transitions, respectively, where $ϕ_1 (ψ_1)$ is a light scalar (fermion) that escapes the detector. In the three models $\text{Br}(K^+\to π^++{\rm inv})$ remains very close to the SM value, while $\text{Br}(K_L\to π^0+{\rm inv})$ can saturate the present KOTO bound. Besides invisible particles in the final state (which may account for dark matter) the models require additional light mediators around the GeV-scale.

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arXiv2018

On the $a$-theorem in the Conformal Window

We show that for four dimensional gauge theories in the conformal window, the Euler anomaly, known as the $a$-function, can be computed from a $2$-point function of the trace of the energy momentum tensor making it more amenable to lattice simulations. Concretely, we derive an expression for the $a$-function as an integral over the renormalisation scale of quantities related to $2$- and $3$-point functions of the trace of the energy momentum tensor.The crucial ingredients are that the square of the field strength tensor is an exactly marginal operator at the Gaussian fixed point and that the relevant $3$-point correlation function is finite when resummed to all orders. This allows us to define a scheme for which the $3$-point contribution vanishes, thereby explicitly establishing the strong version of the $a$-theorem for this class of theories.

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arXiv2018

Parity Doubling as a Tool for Right-handed Current Searches

The V-A structure of the weak interactions leads to definite amplitude hierarchies in exclusive heavy-to-light decays mediated by $b \to (d,s)γ$ and $b \to (d,s) \ell \bar{\ell}$. However, the extraction of right-handed currents beyond the Standard Model is contaminated by V-A long-distance contributions leaking into right-handed amplitudes. We propose that these quantum-number changing long-distance contributions can be controlled by considering the almost parity-degenerate vector meson final states by exploiting the opposite relative sign of left- versus right-handed amplitudes. For example, measuring the time-dependent rates of a pair of vector $V(J^P=1^-)$ and axial $A(1^+)$ mesons in $B \to (V,A) γ$, up to an order of magnitude is gained on the theory uncertainty prediction, controlled by long-distance ratios to the right-handed amplitude. This renders these decays clean probes to null tests, from the theory side.

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arXiv2018

$B^0_s \to \ell^+ \ell^- γ$ as a Test of Lepton Flavor Universality

We discuss a number of strategies to reduce the $\mathcal B(B^0_s \to \ell^{+} \ell^{-} γ)$ theoretical error, and make such a measurement a new probe of the interactions that are interesting in the light of present-day flavor discrepancies. In particular, for low di-lepton invariant mass we propose to exploit the close parenthood between $\mathcal B(B^0_s \to \ell^{+} \ell^{-} γ)$ and the measured $\mathcal B(B^0_s \to ϕ(\to K^+ K^-) γ)$. For high $q^2$, conversely, we exploit the fact that the decay is dominated by two form-factor combinations, plus contributions from broad charmonium that we model accordingly. We construct the ratio $R_γ$, akin to $R_K$ and likewise sensitive to lepton-universality violation. Provided the two rates in this ratio are integrated in a suitable region that minimises bremsstrahlung contributions while maximising statistics, the ratio is very close to unity and the form-factor dependence cancels to an extent that makes it a new valuable probe of lepton-universality violating contributions in the effective Hamiltonian. We finally speculate on additional ideas to extract short-distance information from resonance regions, which are theoretically interesting but statistically limited at present.

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arXiv2018

Right-handed Currents Searches and Parity Doubling

The extraction of right-handed currents, beyond the Standard Model, faces theoretical challenges from long-distance contributions. We show that these effects can be controlled by combining, for example, studies of $B \to V(1^-) γ$ and $B \to A(1^+) γ$ observables. The sum of the long-distance contributions can be extracted without compromise, and the individual pieces follow from a ratio predicted by theory. This leads to significant reduction in the uncertainty of long-distance contributions. The ideas extend to charm decays and the low $q^2$-region of $B \to V \ell \bar{\ell}$, and open the prospect of checking input affecting the angular $B \to K^* μμ$-anomaly.

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arXiv2017

A UV Complete Compositeness Scenario: LHC Constraints Meet The Lattice

We investigate a recently proposed UV-complete composite Higgs scenario in the light of the first LHC runs. The model is based on a $SU(4)$ gauge group with global flavour symmetry breaking $SU(5) \to SO(5)$, giving rise to pseudo Nambu-Goldstone bosons in addition to the Higgs doublet. This includes a real and a complex electroweak triplet with exotic electric charges. Including these, as well as constraints on other exotic states, we show that LHC measurements are not yet sensitive enough to significantly constrain the model's low energy constants. The Higgs potential is described by two parameters which are on the one hand constrained by the LHC measurement of the Higgs mass and Higgs decay channels and on the other hand can be computed from correlation functions in the UV-complete theory. Hence to exclude the model at least one constant needs to be determined and to validate the Higgs potential both constants need to be reproduced by the UV-theory. Due to its UV-formulation, a certain number of low energy constants can be computed from first principle numerical simulations of the theory formulated on a lattice, which can help in establishing the validity of this model. We assess the potential impact of lattice calculations for phenomenological studies, as a preliminary step towards Monte Carlo simulations.

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arXiv2017

On the Flow of $\Box R$ Weyl-Anomaly

An important aspect of Weyl anomalies is that they encode information on the irreversibility of the renormalisation group flow. We consider, $Δ\bar b = \bar{b}^{\textrm{UV}} - \bar{b}^{\textrm{IR}}$, the difference of the ultraviolet and infrared value of the $\Box R$-term of the Weyl anomaly. The quantity is related to the fourth moment of the trace of the energy momentum tensor correlator for theories which are conformal at both ends. Subtleties arise for non-conformal fixed points as might be the case for infrared fixed points with broken chiral symmetry. Provided that the moment converges, $Δ\bar{b}$ is then automatically positive by unitarity. Written as an integral over the renormalisation scale, flow-independence follows since its integrand is a total derivative. Furthermore, using a momentum subtraction scheme (MOM) the 4D Zamolodchikov- metric is shown to be strictly positive beyond perturbation theory and equivalent to the metric of a conformal manifold at both ends of the flow. In this scheme $\bar{b}(μ)$ can be extended outside the fixed point to a monotonically decreasing function. The ultraviolet finiteness of the fourth moment enables us to define a scheme for the $δ{\cal L} \sim b_0 R^2$-term, for which the $R^2$-anomaly vanishes along the flow. In the MOM- and the $R^2$-scheme, $\bar{b}(μ)$ is shown to satisfy a gradient flow type equation. We verify our findings in free field theories, higher derivative theories and extend $Δ\bar{b}$ and the Euler flow $Δβ_a$ for a Caswell-Banks-Zaks fixed point for QCD-like theories to next-to-next-to leading order using a recent $\langle G^2G^2 \rangle$-correlator computation.

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arXiv2017

On Finiteness of 2- and 3-point Functions and the Renormalisation Group

Two and three point functions of composite operators are analysed with regard to (logarithmically) divergent contact terms. Using the renormalisation group of dimensional regularisation it is established that the divergences are governed by the anomalous dimensions of the operators and the leading UV-behaviour of the $1/ε$-coefficient. Explicit examples are given by the $ $-, $<ΘΘ>$-trace of the energy momentum tensor) and $<\bar q q \bar q q>$- correlators in QCD-like theories. The former two are convergent when all orders are taken into account but divergent at each order in perturbation theory implying that the latter and the the $ε\to 0$ limit do not generally commute. Finite correlation functions obey unsubtracted dispersion relations which is of importance when they are directly related to physical observables. As a byproduct the $R^2$-anomaly is extended to NNLO ($O(α^5)$) using a recent $ $-computation.

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arXiv2017

Flavour Anomalies in $b\to s\ell^+\ell^-$ Processes - a round table Discussion

Precision measurements of flavour observables provide powerful tests of many extensions of the Standard Model. This contribution covers a range of flavour measurements of $b\to s\ell^+\ell^-$ transitions, several of which are in tension with the Standard Model of particle physics, as well as their theoretical interpretation. The basics of the theoretical background are discussed before turning to the main question of the field: whether the anomalies can be explained by QCD effects or whether they may be indicators of effects beyond the Standard Model.

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arXiv2017

Phenomenology of a Composite Higgs Model

Several UV complete models of physics beyond the Standard Model are currently under scrutiny, their low-energy dynamics being compared with the experimental data from the LHC. Lattice simulations can play a role in these studies by providing a first principles computations of the low-energy constants that describe this low-energy dynamics. In this work, we study in detail a specific model recently proposed by Ferretti, and discuss the potential impact of lattice calculations.

hep-lat↗

arXiv2016

${\cal N}$ = $1$ Euler Anomaly from RG-dependent metric-Background

We consider ${\cal N}=1$ supersymmetric gauge theories in the conformal window. By applying a suitable matter superfield rescaling and a Weyl-transformation the renormalisation group running (matter and gauge field $Z$-factors) are absorbed into the metric. The latter becomes a function of the $Z$-factors. The Euler flow $Δa \equiv a_{\rm UV} - a_{\rm IR} |_{{\cal N}=1}$ is then obtained by free field theory computation with the non-trivial dynamics coming from expanding the Euler invariant in the flow dependent metric. The result is therefore directly obtained in terms of the infrared anomalous dimension confirming an earlier result using the matching of conserved currents.

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