arXiv subjects

Roman Zwicky

Publications and source records attributed to Roman Zwicky.

At least 19 recordsLinked to original sources

arXiv2025

Gluon Gravitational $ D$-Form Factor: The $\sigma$-Meson as a Dilaton Confronted with Lattice Data II

We investigate the gluon gravitational form factors of the $\pi$, $N$, $\rho$, and $\Delta$ using lattice QCD data at $m_\pi \approx 450 \text{MeV}$ and $m_\pi \approx 170 \text{MeV}$. We base the analysis on fits to a simple $\sigma/f_0(500)$-meson pole, supplemented by a polynomial background term. The fitted residues agree with predictions from dilaton effective theory, in which the $\sigma$-meson acts as the dilaton, the pseudo Goldstone boson of spontaneously broken scale symmetry. We derive new dilaton-based predictions for the $\rho$- and $\Delta$-gravitational form factors, and comment on the $\eta_{c}$- and $\eta_b$-form factors in the context of the dilaton interpretation. These results reinforce our earlier findings, based on lattice total (quark and gluon) gravitational form factors, and provide further evidence that QCD dynamics may be governed by an infrared fixed point.

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arXiv2025

Gravitational $ D$-Form Factor: The $\sigma$-Meson as a Dilaton confronted with Lattice Data

We investigate the nucleon and pion gravitational $D$-form factors, by fitting a $\sigma/f_0(500)$-meson pole, together with a background term, to lattice data at $m_\pi \approx 170\text{MeV}$. We find that the fitted residues are compatible with predictions from dilaton effective theory. In this framework, the $\sigma$-meson takes on the role of the dilaton, the Goldstone boson of spontaneously broken scale symmetry. These results support the idea that QCD may be governed by an infrared fixed point and offer a physical interpretation of the $D$-form factor (or $D$-term) in the soft limit.

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arXiv2025

Soft Theorems and Dilaton Effective Theory

We derive a new model-independent double-soft dilaton theorem, taking into account the spacetime dependence of the dilation commutator $[i Q_D,{\cal O}(x)]= (\Delta_{\cal O} + x \cdot \partial){\cal O}(x)$. The procedure restores positivity in the (pseudo)-Goldstone masses and sets the constraint $\Delta_{\cal O} = d-2\,$ for a single operator ${\cal O}$ responsible for generating a dilaton mass.We discuss gravitational form factors as a tool to probe infrared conformality in field theories with particle content. In a second part we explore to what extent QCD-like gauge theories (in the chiral limit) could fit into this category. We find that the quark bilinear has scaling dimension $\Delta_{\bar qq} = d-2$, therefore satisfying the double-soft theorem. We show that some findings are realised in ${\cal N}=1$ supersymmetric gauge theories and argue that the extension below the conformal window makes sense in that case.

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arXiv2025

Dilaton Physics from Asymptotic Freedom

The dilaton is investigated from first principles in an asymptotically free Gross-Neveu-Yukawa theory in three dimensions. In the limit of many fermion flavours, the theory features a finite line of strongly interacting fixed points with continuous quantum phase transitions and a massless Goldstone boson, the dilaton, following spontaneous scale symmetry breaking at its endpoint. Interestingly, we find that the emergence of a vacuum expectation value and a dilaton can be understood as a double-scaling limit. Exploiting the scalar two-point function, we identify the dilaton in the spectrum, compute its decay constant, and obtain universal expressions for the induced dilaton mass in terms of small perturbations. Consistency of findings with soft dilaton theorems is equally established. Implications for spontaneously broken conformal theories are indicated.

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arXiv2024

Model-independent results on parity violation in the trace anomaly

Anomalous parity violation in four dimensions would be significant for phenomenology (baryogenesis, gravitational waves) and mathematical physics. Over the past decade, there has been a controversy in the literature as to whether free Weyl fermions give rise to (anomalous) parity violation in the trace of the energy momentum tensor; expressed by the Pontryagin densities $R\tilde R$ and $F\tilde F$ in the gravity and the gauge sector respectively. In Ref.$^1$, we have shown, using path integral methods, that the trace anomaly of a free Weyl fermion does not violate parity (i.e the absence of the Pontryagin density). In a subsequent work$^2$ we came to the stronger conclusion that for any theory compatible with dimensional regularisation, the Pontryagin-terms are equally absent. It is the \textit{finiteness} of the diffeomorphism, the Lorentz and the gauge anomalies that prevents anomalous parity violation.

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arXiv2024

Structure-dependent QED in $B^- \to \ell^- \bar \nu (\gamma)$

Based on explicitly gauge invariant interpolating operators we compute complete next-leading order QED-corrections for leptonic decays. These are sizeable since the helicity-suppression in V-A interactions allows for structure-dependent collinear logs. We have explicitly checked that these logs are absent for helicity-unsuppressed Yukawa-type transitions. Based on $B \to \gamma$ form factors we present the rates for $B^- \to (\mu^-,\tau^-) \bar \nu (\gamma)$ in differential and integrated form as a function of the photon energy cut-off $E_\gamma^{\text{cut}}$. The effect of the virtual structure-dependent corrections are approximately $+5\%$ and $+3\%$ for the $\mu$- and $\tau$-channel respectively. The structure dependence of the real radiation exceeds that of the virtual one for $E_\gamma^{\text{cut}}|_{\mu} > 0.18(3)$ GeV and is subdominant for the tau channel even when fully inclusive.

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arXiv2023

QCD with an Infrared Fixed Point and a Dilaton

Following previous work we further explore the possibility that the chirally broken phase of gauge theories admits an infrared fixed point interpretation. The slope of the $\beta$ function, $\beta'_*$, is found to vanish at the infrared fixed point which has several attractive features such as logarithmic running. We provide a more in-depth analysis of our previous result that the mass anomalous assumes $\gamma_* = 1$ at the fixed point. The results are found to be consistent with ${\cal N}=1$ supersymmetric gauge theories. In a second part the specific properties of a dilaton, the (pseudo) Goldstone, due to spontaneous symmetry breaking are investigated. Dilaton soft theorems indicate that a soft dilaton mass can only originate from an operator of scaling dimension two. In the gauge theory this role is taken on by the $\bar qq$-operator. The QCD dilaton candidate, the $\sigma = f_0(500)$ meson is investigated. Singlet-octet mixing is found to be important. We briefly discuss the dilaton as a candidate for the Higgs boson, which relies on the ratio of dilaton to pion decay constant being close to unity. In QCD this is approximately satisfied but it is remains unclear if this is accidental or whether there is unknown reason behind it.

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arXiv2023

Gravity-gauge Anomaly Constraints on the Energy-momentum Tensor

We derive constraints on the four dimensional energy-momentum tensor from gravitational and gauge anomalies. Our work can be considered an extension of Duff's analysis [1] to include parity-odd terms and explicit symmetry breaking. The constraints imply the absence of the parity-odd $R\tilde R$ and $F\tilde F$ terms, for theories whose symmetries are compatible with dimensional regularisation, in a model-independent way. Remarkably, even in the case of explicit symmetry breaking the $\Box R$-anomaly is found to be finite and unambiguous after applying the symmetry constraints. We compute mixed gravity-gauge anomalies at leading order and deduce phenomenological consequences for vector bosons associated with global chiral symmetries.

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arXiv2023

Relating $\beta'_$ and $\gamma'_{Q}$ in the ${\cal N}=1$ SQCD Conformal Window

In this note we show that $\beta'_*$, the $\beta$-function slopes in the electric and magnetic theories are equal at the corresponding infrared fixed points. This follows from the scaling of the correlators of the trace of the energy momentum tensors. The slopes $\beta'_*$ determine the scaling dimensions. Our paper can be considered as a commentary to Anselmi et al. [1] -- it proposes an improved derivation not based on a rather contrived construction by Kutasov et al. [2]. As a byproduct we note that $\gamma'_{Q^*}$ -- the slopes of the matter superfield anomalous dimension -- vanish at both edges of the conformal window where one of the dual theories is strongly coupled. Finally, we determine the two-coupling magnetic fixed point at weak coupling correcting the result of [3]}.

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arXiv2023

Trace Anomaly of Weyl Fermions via the Path Integral

We compute the trace, diffeomorphism and Lorentz anomalies of a free Weyl fermion in a gravitational background field by path integral methods. This is achieved by regularising the variation of the determinant of the Weyl operator building on earlier work by Leutwyler. The trace anomaly is found to be one half of the one of a Dirac fermion. Most importantly we establish that the potential parity-odd curvature term $R \tilde R$, corresponding to the Pontryagin density, vanishes. This is to the contrary of some recent findings in the literature which gave rise to a controversy. We verify, that the regularisation does not lead to (spurious) anomalies in the Lorentz and diffeomorphism symmetries. We argue that in $d = 2\;(\textrm{mod } 4)$ $P$- and $CP$-odd terms cannot appear and that for $d = 4\;(\textrm{mod } 4)$ they are absent at least at leading order.

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arXiv2023

Dilatons Improve (Non)-Goldstones

Shift symmetry forbids conformal coupling of Goldstone bosons from internal symmetries, but not for spontaneously broken conformal symmetry. Its Goldstone boson, the dilaton $D$, admits and indeed requires, an improvement term $ {\cal L}_R \propto R e^{-2D/F_D}$ as it realises the Goldstone matrix element in the effective theory. The improvement, combined with Weyl-gauging, enables conformal coupling to Goldstone bosons and other particles of arbitrary Weyl-weight. While improvement does not affect scattering amplitudes in flat space, it impacts gravitational form factors decisively, giving rise to the dilaton pole in the spin-zero channel. We compute leading-order scalar, fermion, pion, and dilaton form factors, confirming low-energy constraints. The dilaton decoupling limit further implies that the operator driving spontaneous chiral symmetry breaking has scaling dimension $\Delta= d-2$.

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arXiv2023

QCD with an Infrared Fixed Point -- Pion Sector

The possibility that gauge theories with chiral symmetry breaking below the conformal window exhibit an infrared fixed point is explored. With this assumption three aspects of pion physics are reproduced if the the quark mass anomalous dimension at the infrared fixed point is $\gamma_* = 1$: First, by matching the long-distance scalar adjoint correlation function. Second, by perturbing the fixed point by a small quark mass, the $m_q$-dependence of the pion mass is reproduced by renormalisation group arguments. Third, consistency of the trace anomaly and the Feynman-Hellmann theorem, for small $m_q$, imply the same result once more. This suggests the following picture for the conformal window: close to its upper boundary $\gamma_*$ is zero and grows as the number of fermions is reduced until its lower boundary $\gamma_*=1$ is reached, where chiral symmetry breaking sets in. Below, the strongly coupled gauge theory with $\gamma_*=1$ is infrared dual to the free theory of pions. A possible dilaton sector of the scenario will be addressed in a companion paper.

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arXiv2023

Isospin Mass Differences of the $B$, $D$ and $K$

We compute the electromagnetic mass difference for the $B$-, $D$- and $K$-mesons using QCD sum rules with double dispersion relations. For the $B$- and $D$-mesons we also compute the linear quark mass correction, whereas for the $K$ the standard soft theorems prove more powerful. The mass differences, which have not previously been computed via a double dispersion, are fully consistent with experiment, albeit with large uncertainties.

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arXiv2022

On the $ R_{K} $ Theory Error

To quantify the theory error on $R_K$, essentially means to quantify the uncertainty due to QED corrections since the latter breaks lepton flavour universality through the lepton masses. Since experiment uses photon shower programs, e.g. \texttt{PHOTOS}, to capture QED effects, assessing the uncertainty involves investigating effects not captured by the specific use of these tools. This includes structure-dependent corrections, potentially large non-logarithmic terms and charmonium resonances entering the lower bin by migration of radiation. We are able to close in on these loopholes. For example, using gauge invariance, we show that structure-dependent QED corrections do not lead to additional (sizeable) hard-collinear logs of the form ${\cal O}(\alpha) \ln m_\ell/m_B$. Hence, from the theory point of view $R_K$ is a safe observable.

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arXiv2022

Resolving Charged Hadrons in QED -- Gauge Invariant Interpolating Operators

Standard interpolating operators for charged mesons, e.g. $J_{B} = \bar b i \gamma_5 u$ for $B^-$, are not gauge invariant in QED and therefore problematic for perturbative methods. We propose a gauge invariant interpolating operator by adding an auxiliary charged scalar $\Phi_B$, ${\cal J}_{B}^{(0)} = J_B \, \Phi_B$, which reproduces all the universal soft and collinear logs. The modified LSZ-factor is shown to be infrared finite which is a necessary condition for validating the approach. At ${\cal O}(\alpha)$, this is equivalent to a specific Dirac dressing of charged operators. A generalisation thereof, using iterated integrals, establishes the equivalence to all orders and provides a transparent alternative viewpoint. The method is discussed by the example of the leptonic decay $B^- \to \ell^- \bar \nu$ for which a numerical study is to follow. The formalism itself is valid for any spin, flavour and set of final states (e.g. $B^- \to \pi^0 \ell^- \bar \nu$).

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arXiv2022

QED in $\bar B \to \bar K \ell^+\ell^-$ LFU ratios: Theory versus Experiment, a Monte Carlo Study

Using analytic results obtained in a meson effective theory, that includes all infrared sensitive logs, we build a dedicated Monte Carlo framework to describe QED corrections in $\bar B \to \bar K \ell^+\ell^-$ for a generic form factor. For the neutral mode $\bar B^0 \to \bar K^0 \ell^+\ell^-$, we perform a detailed numerical comparison versus those obtained with the general-purpose photon-shower tool PHOTOS. The comparison indicates a good agreement, at the few per-mil level, when focusing on the rare mode only. In addition, our framework allows us to investigate the impact of the charmonium resonances. Interference effects, not described by PHOTOS in the experimental analysis, are found to be small in the dilepton invariant mass region $q^2 < 6 \textrm{GeV}^2$, which is used to determine $R_{K^{(*)}}$. Using a semi-analytic framework we assess the full, rare and resonant, mode. Based thereupon, we discuss strategies to check the subtraction of the resonant mode, which has a sizeable impact at $q^2 \approx 6 \textrm{GeV}^2$ in the electron mode.

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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 $\pi^+ \to \ell^+ \bar \nu$ and the semileptonic decay $B \to \pi \ell^+ \bar \nu$. The non-trivial and ongoing efforts of including structure dependence are very briefly outlined.

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arXiv2021

Dilaton and Massive Hadrons in a Conformal Phase

As the number of fermion fields is increased, gauge theories are expected to undergo a transition from a QCD-like phase, characterised by confinement and chiral symmetry breaking, to a conformal phase, where the theory becomes scale-invariant at large distances. In this paper, we discuss some properties of a third phase, where spontaneously broken conformal symmetry is characterised by its Goldstone boson, the dilaton. In this phase, which we refer to as conformal dilaton phase, the massless pole corresponding to the Goldstone boson guarantees that the conformal Ward identities are satisfied in the infrared despite the other hadrons carrying mass. In particular, using renormalisation group arguments in Euclidean space, we show that for massless quarks the trace of the energy momentum tensor vanishes on all physical states as a result of the fixed point. This implies the vanishing of the gluon condensate and suggests that the scale breaking is driven by the quark condensate which has implications for the cosmological constant. In addition form factors obey an exact constraint for every hadron and are thus suitable probes to identify this phase in the context of lattice Monte Carlo studies. For this purpose we examine how the system behaves under explicit symmetry breaking, via quark-mass and finite-volume deformations. The dilaton mass shows hyperscaling under mass deformation, viz. $m_{D} = {\cal O}(m_q^{1/(1+\gamma^*)})$. This provides another clean search pattern.

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