arXiv subjects

Roman Zwicky

Publications and source records attributed to Roman Zwicky.

At least 55 records · Page 3Linked to original sources

arXiv2016

$B\to V\ell^+\ell^-$ in the Standard Model from Light-Cone Sum Rules

We present $B_q\toρ$, $B_q\toω$, $B_q\to K^*$, $B_s\to K^*$ and $B_s\to ϕ$ form factors from light-cone sum rules (LCSR) at $\mathcal{O}(α_s)$ for twist-2 and 3 and $\mathcal{O}(α_s^0)$ for twist-4 with updated hadronic input parameters. Three asymptotic light-cone distribution amplitudes of twist-$4$ (and $5$) are determined, necessary for the form factors to obey the equations of motion. It is argued that the latter constrain the uncertainty of tensor-to-vector form factor ratios thereby improving the prediction of zeros of helicity amplitudes of major importance for $B\to K^*\ell\ell$ angular observables. We provide easy-to-use fits to the LCSR results, including the full error correlation matrix, in all modes at low $q^2$ as well as combined fits to LCSR and lattice results covering the entire kinematic range for $B_q\to K^*$, $B_s\to K^*$ and $B_s\to ϕ$. The error correlation matrix avoids the problem of overestimating the uncertainty in phenomenological applications. Using the new form factors and recent computations of non-factorisable contributions we provide Standard Model predictions for $B\to K^*γ$ as well as $B\to K^*\ell^+\ell^-$ and $B_s\toϕμ^+μ^-$ at low dilepton invariant mass. Employing our $B \to (ρ,ω) $ form factor results we extract the CKM element $|V_\mathrm{ub}|$ from the semileptonic decays $B\to(ρ,ω) \ellν$ and find good agreement with other exclusive determinations.

hep-ph↗

arXiv2016

A brief Introduction to Dispersion Relations and Analyticity

In these lectures we provide a basic introduction into the topic of dispersion relation and analyticity. The properties of 2-point functions are discussed in some detail from the viewpoint of the Källén-Lehmann and general dispersion relations. The Weinberg sum rules figure as an application. The analytic structure of higher point functions in perturbation theory are analysed through the Landau equations and the Cutkosky rules.

hep-ph↗

arXiv2016

Generalised helicity formalism, higher moments and the $B \to K_{J_K}(\to K π) \bar{\ell}_1 \ell_2$ angular distributions

We generalise the Jacob-Wick helicity formalism, which applies to sequential decays, to effective field theories of rare decays of the type $B \to K_{J_K}(\to K π) \bar{\ell}_1 \ell_2$. This is achieved by reinterpreting local interaction vertices $\bar b Γ'_{μ_1 ..μ_n} s \bar \ell Γ^{μ_1 ..μ_n} \ell$ as a coherent sum of $1 \to 2$ processes mediated by particles whose spin ranges between zero and $n$. We illustrate the framework by deriving the full angular distributions for $B \to K\bar{\ell}_1 \ell_2$ and $B \to K^*(\to K π) \bar{\ell}_1 \ell_2$ for the complete dimension-six effective Hamiltonian for non-equal lepton masses. Amplitudes and decay rates are expressed in terms of Wigner rotation matrices, leading naturally to the method of moments in various forms. We discuss how higher-spin operators and QED corrections alter the standard angular distribution used throughout the literature, potentially leading to differences between the method of moments and the likelihood fits. We propose to diagnose these effects by assessing higher angular moments. These could be relevant in investigating the nature of the current LHCb anomalies in $R_K = {\cal B}( B \to K μ^+μ^-) /{\cal B}( B \to K e^+e^-)$ as well as angular observables in $B \to K^* μ^+μ^-$.

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arXiv2015

${\cal N} = 1$ Euler Anomaly Flow from Dilaton Effective Action

We consider ${\cal N} =1$ supersymmetric gauge theories in the conformal window. The running of the gauge coupling is absorbed into the metric by applying a suitable matter superfield- and Weyl-transformation. The computation becomes equivalent to one of a free theory in a curved background carrying the information of the renormalisation group flow. We use the techniques of conformal anomaly matching and dilaton effective action, by Komargodski and Schwimmer, to rederive the difference of the Euler anomaly coefficient $Δa \equiv a_{\rm UV} - a_{\rm IR} $ for the ${\cal N} =1$ theory. The structure of $Δa $ is therefore in one-to-one correspondence with the Wess-Zumino dilaton action.

hep-th↗

arXiv2015

Isospin asymmetries in $B\to (K^*,ρ) γ/ l^+ l^-$ and $B \to K l^+ l^-$ in and beyond the Standard Model

We compute the isospin asymmetries in $B \to (K^*,ρ) γ$ and $B\to (K,K^*,ρ) l^+l^-$ for low lepton pair invariant mass $q^2$, within the Standard Model (SM) and beyond the SM (BSM) in a generic dimension six operator basis. Within the SM the CP-averaged isospin asymmetries for $B \to (K,K^*,ρ) ll$, between $1{\rm GeV}^2 \leq q^2 \leq 4m_c^2$, are predicted to be small (below 1.5%) though with significant cancellation. In the SM the non-CP averaged asymmetries for $B \to ρll$ deviate by $\approx \pm 5%$ from the CP-averaged ones. We provide physical arguments, based on resonances, of why isospin asymmetries have to decrease for large $q^2$ (towards the endpoint). Two types of isospin violating effects are computed: ultraviolet (UV) isospin violation due to differences between operators coupling to up and down quarks, and infrared (IR) isospin violation where a photon is emitted from the spectator quark and is hence proportional to the difference between the up- and down-quark charges. These isospin violating processes may be subdivided into weak annihilation (WA), quark loop spectator scattering (QLSS) and a chromomagnetic contribution. Furthermore we discuss generic selection rules based on parity and angular momentum for the $B \to Kll$ transition as well as specific selection rules valid for WA at leading order in the strong coupling constant. We clarify that the relation between the $K$ and the longitudinal part of the $K^*$ only holds for leading twist and for left-handed currents. In general the $B \to ρll$ and $B \to K^*ll$ isospin asymmetries are structurally different yet the closeness of $α_{\rm CKM}$ to ninety degrees allows us to construct a (quasi) null test for the SM out of the respective isospin symmetries. We provide an update on ${\cal B}(B^0 \to K^{*0}γ)/{\cal B}(B_s \to ϕγ)$ which is sensitive to WA.

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arXiv2014

Renormalization group, trace anomaly and Feynman-Hellmann theorem

We show that the logarithmic derivative of the gauge coupling on the hadronic mass and the cosmological constant term of a gauge theory are related to the gluon condensate of the hadron and the vacuum respectively. These relations are akin to Feynman-Hellmann relations whose derivation for the case at hand are complicated by the construction of the gauge theory Hamiltonian. We bypass this problem by using a renormalisation group equation for composite operators and the trace anomaly. The relations serve as possible definitions of the gluon condensates themselves which are plagued in direct approaches by power divergences. In turn these results might help to determine the contribution of the QCD phase transition to the cosmological constant and test speculative ideas.

hep-ph↗

arXiv2014

Resonances gone topsy turvy - the charm of QCD or new physics in $b \to s \ell^+ \ell^-$?

We investigate the interference pattern of the charm-resonances $Ψ(3370,4040,4160,4415)$ with the electroweak penguin operator $O_9$ in the branching fraction of $B^+\to K^+μμ$. For this purpose we extract the charm vacuum polarisation via a standard dispersion relation from BESII-data on $e^+e^-\to hadrons$. In the factorisation approximation (FA) the vacuum polarisation describes the interference fully non-perturbatively. The observed interference pattern by the LHCb collaboration is opposite in sign and and significantly enhanced as compared to the FA. A change of the FA-result by a factor of -2.5, which correspond to a 350%-corrections, results in a reasonable agreement with the data. This raises the question on the size of non-factorisable corrections which are colour enhanced but loop-suppressed. In the parton picture it is found that the corrections are of relative size ~-0.5 when averaged over the open charm-region which is far below -3.5 needed to explain the observed effect. We present combined fits to the BESII- and the LHCb-data, testing for effects beyond the Standard Model (SM)-FA. We cannot find any significant evidence of the parton estimate being too small due to cancellations between the individual resonances. It seems difficult to accommodate the LHCb-result in the standard treatment of the SM or QCD respectively. In the SM the effect can be described in a $q^2$-dependent shift of the Wilson coefficient combination $C^{eff}_9 + C^{' eff}_9$. We devise strategies to investigate the microscopic structure in future measurements. We show that the charm-resonance effects can accommodate the $B \to K^* ll$-anomalies (e.g. $P_5'$). Hence our findings indicate that the interpretation of the anomaly through a $Z'$-boson, mediating between $bs$ and $ll$ fields, is disfavoured. More generally our results motivate investigations into $b \to s\bar cc$-physics.

hep-ph↗

arXiv2014

Conformal scaling and the size of $m$-hadrons

The scaling laws in an infrared conformal (IR) theory are dictated by the critical exponents of relevant operators. We have investigated these scaling laws at leading order in two previous papers. In this work we investigate further consequences of the scaling laws, trying to identify potential signatures that could be studied by lattice simulations. From the first derivative of the form factor we derive the behaviour of the mean charge radius of the hadronic states in the theory. We obtain $\langle r_H^2 \rangle \sim m^{-2/(1+γ^*_m)}$ which is consistent with $\langle r_H^2 \rangle \sim 1/M_H^{2}$. The mean charge radius can be used as an alternative observable to assess the size of the physical states, and hence finite size effects, in numerical simulations. Furthermore, we discuss the behaviour of specific field correlators in coordinate space for the case of conformal, scale-invariant, and confining theories making use of selection rules in scaling dimensions and spin. We compute the scaling corrections to correlations functions by linearizing the renormalization group equations. We find that these correction are potentially large close to the edge of the conformal window. As an application we compute the scaling correction to the formula $M_H \sim m^{1/(1+γ_m^*)}$ directly through its associated correlator as well as through the trace anomaly. The two computations are shown to be equivalent through a generalisation of the Feynman-Hellmann theorem for the fermion mass, and the gauge coupling.

hep-ph↗

arXiv2014

B -> K^* Form Factors from Flavor Data to QCD and Back

Sufficient control of transition form factors is a vital ingredient for the precision flavor programs including the nearer term searches at the Large Hadron Collider (LHC) and the forthcoming Belle II experiment. We improve on existing methods to extract B -> K^* form factor ratios at low hadronic recoil from B -> K^* l^+ l^- data on the angular observables F_L, A_T^(2) and P'_4 by adding heavy quark symmetry-based constraints and by investigating the cross talk between low and large recoil. The data-extracted form factor ratios i) provide benchmarks for the lattice and light cone sum rule predictions, the latter of which have been updated including improved uncertainty estimations and ii) allow to improve the predictions for benchmark observables. We find that present data on the forward-backward asymmetry A_FB and the angular observable P'_5 at low recoil are in good agreement with the Standard Model.

hep-ph↗

arXiv2014

(A)symmetries of weak decays at and near the kinematic endpoint

At the kinematic endpoint of zero recoil physical momenta are parallel which leads to symmetries in the decay distributions. We implement this observation for decays of the type $A \to (B_1 B_2) C$ by extending the helicity formalism to include an unphysical timelike polarisation. The symmetries of the helicity amplitudes are worked out for a generic dimension six Hamiltonian for a $B \to V \ell \ell$ decay type. We obtain \emph{exact} predictions for angular observables, e.g.,for the fraction of longitudinally polarized vector mesons, $F_L = 1/3$, which may be used to guide experimental analyses. We investigate the vicinity of the endpoint through an expansion in the three momentum of the vector meson. New physics can be searched for in the slope of the observables near the endpoint. Current experimental data on $B \to K^* \ell \ell$ decays are found to be in agreement with our predictions within uncertainties. Application to other semileptonic $B$ and $D$ decays, including $B \to V \ell^+ \ell^-$, $V=K^*,ϕ, ρ$ and $B \to V \ell ν$, $V=ρ,D^*$ is straightforward. For hadronic modes of the types $B \to V p \bar p, V Λ\bar Λ, ..$ and $B \to V ππ, V πK, .. $ endpoint relations apply as long as they are not overwhelmed by sizeable final state interactions between the $V$ and the hadron pair.

hep-ph↗

arXiv2013

Gluon condensates from the Hamiltonian formalism

We derive recently obtained relations, relating the logarithmic gauge coupling derivative of the hadron mass and the cosmological constant to the matter and vacuum gluon condensates, within a Hamiltonian framework. The key idea is a canonical transformation which brings the relevant part of the Hamiltonian into a suitable form. Furthermore we illustrate the relations within the Schwinger model and ${\cal N}=2$ super Yang Mills theory (Seiberg-Witten theory).

hep-ph↗

arXiv2013

Exclusive Chromomagnetism in heavy-to-light FCNCs

We compute matrix elements of the chromomagnetic operator, often denoted by $ {\cal O}_8$, between $B/D$-states and light mesons plus an off-shell photon by employing the method of light-cone sum rules (LCSR) at leading twist-2. These matrix elements are relevant for processes such as $B \to K^* l^+l^-$ and they can be seen as the analogues of the well-known penguin form factors $T_{1,2,3}$ and $f_T$. We find a large CP-even phase for which we give a long-distance (LD) interpretation. We compare our results to QCD factorisation for which the spectator photon emission is end-point divergent. The analytic structure of the correlation function used in our method admits a complex anomalous threshold on the physical sheet. The meaning and handling within the sum rule approach of the anomalous threshold is discussed.

hep-ph↗

arXiv2013

Heavy-to-light chromomagentic matrix element

We report the computation of the matrix element of the chromomagnetic operator of the flavour changing neutral current (FCNC)-type between a $B$- or $D$-meson state and a light hadron and off-shell photon. The computation is carried out by using the method of light-cone sum rules (LCSR). It is found that the matrix element exhibits a large strong phase for which we give a long distance interpretation. The analytic structure of the correlation function in use admits a complex anomalous threshold on the physical sheet, the meaning and handling of which within the sum rule approach is discussed. We compare our results to QCD factorisation for which spectator photon emission is end-point divergent.

hep-ph↗

arXiv2011

Explicit and spontaneous breaking of SU(3) into its finite subgroups

We investigate the breaking of SU(3) into its subgroups from the viewpoints of explicit and spontaneous breaking. A one-to-one link between these two approaches is given by the complex spherical harmonics, which form a complete set of SU(3)-representation functions. An invariant of degrees p and q in complex conjugate variables corresponds to a singlet, or vacuum expectation value, in a (p,q)-representation of SU(3). We review the formalism of the Molien function, which contains information on primary and secondary invariants. Generalizations of the Molien function to the tensor generating functions are discussed. The latter allows all branching rules to be deduced. We have computed all primary and secondary invariants for all proper finite subgroups of order smaller than 512, for the entire series of groups Δ(3n^2), Δ(6n^2), and for all crystallographic groups. Examples of sufficient conditions for breaking into a subgroup are worked out for the entire T_{n[a]}-, Δ(3n^2)-, Δ(6n^2)-series and for all crystallographic groups Σ(X). The corresponding invariants provide an alternative definition of these groups. A Mathematica package, SUtree, is provided which allows the extraction of the invariants, Molien and generating functions, syzygies, VEVs, branching rules, character tables, matrix (p,q)_{SU(3)}-representations, Kronecker products, etc. for the groups discussed above.

hep-ph↗

arXiv2011

The other Higgses, at resonance, in the Lee-Wick extension of the Standard Model

Within the framework of the Lee Wick Standard Model (LWSM) we investigate Higgs pair production $gg \to h_0 h_0$, $gg \to h_0 \tilde p_0$ and top pair production $gg \to \bar tt$ at the Large Hadron Collider (LHC), where the neutral particles from the Higgs sector ($h_0$, $\tilde h_0$ and $\tilde p_0$) appear as possible resonant intermediate states. We investigate the signal $gg \to h_0 h_0 \to \bar b b γγ$ and we find that the LW Higgs, depending on its mass-range, can be seen not long after the LHC upgrade in 2012. More precisely this happens when the new LW Higgs states are below the top pair threshold. In $gg \to \bar tt$ the LW states, due to the wrong-sign propagator and negative width, lead to a dip-peak structure instead of the usual peak-dip structure which gives a characteristic signal especially for low-lying LW Higgs states. We comment on the LWSM and the forward-backward asymmetry in view of the measurement at the TeVatron. Furthermore, we present a technique which reduces the hyperbolic diagonalization to standard diagonalization methods. We clarify issues of spurious phases in the Yukawa sector.

hep-ph↗

arXiv2011

Scaling relations for the entire spectrum in mass-deformed conformal gauge theories

We consider mass-deformed conformal gauge theories (mCGT) and investigate the scaling behaviour of hadronic observables as a function of the fermion mass. Applying renormalization group arguments directly to matrix elements, we find m_H ~ m^{1/(1+gamma*)} and F ~ m^{η_F(gamma*)} for the decay constants, thereby generalizing our results from a previous paper to the entire spectrum. We derive the scaling law m_H m^{1/(1+gamma*)} using the Hellmann-Feynman theorem, and thus provide a derivation which does not rely on renormalization group arguments. Using the new results we reiterate, on the phenomenologically important, S-parameter. Finally, we discuss how spectral representations can be used to relate the mass and decay constant trajectories.

hep-ph↗

arXiv2011

On discrete Minimal Flavour Violation

We investigate the consequences of replacing the global flavour symmetry of Minimal Flavour Violation (MFV) SU(3)_QxSU(3)_UxSU(3)_Dx..., by a discrete D_QxD_UxD_Dx.. symmetry. Goldstone bosons resulting from the breaking of the flavour symmetry generically lead to bounds on new flavour structure many orders of magnitude above the TeV-scale. The absence of Goldstone bosons for discrete symmetries constitute the \emph{primary} motivation of our work. Less symmetry implies further invariants and renders the mass flavour basis transformation observable in principle and calls for a hierarchy in the Yukawa matrix expansion. We show, through the dimension of the representations, that the (discrete) symmetry in principle does allow for additional Delta F = 2 operators. If though the Delta F = 2 transitions are generated by two subsequent Delta F = 1 processes, as for example in the Standard Model, then the four crystal-like groups Sigma(168) ~ PSL(2,7), Sigma(72phi), Sigma(216phi) and especially Sigma(360phi) do provide enough protection for a TeV-scale discrete MFV scenario. Models where this is not the case have to be investigated case by case. Interestingly Sigma(216phi) has a (non-faithful) representation corresponding to an A4-symmetry. Moreover we argue that the, apparently often omitted, (D)-groups are subgroups of an appropriate Delta(6g^2). We would like to stress that we do not provide an actual model that realizes the MFV scenario nor any other theory of flavour.

hep-ph↗

arXiv2010

Hyperscaling relations in mass-deformed conformal gauge theories

We present a number of analytical results which should guide the interpretation of lattice data in theories with an infra-red fixed point (IRFP) deformed by a mass term deltaL = - m \bar qq. From renormalization group (RG) arguments we obtain the leading scaling exponent, F ~ m^(eta_F), for all decay constants of the lowest lying states other than the ones affected by the chiral anomaly and the tensor ones. These scaling relations provide a clear cut way to distinguish a theory with an IRFP from a confining theory with heavy fermions. Moreover, we present a derivation relating the scaling of <\bar qq> \sim m^(eta_qq) to the scaling of the density of eigenvalues of the massless Dirac operator rho(lambda) ~ lambda^(eta_qq) RG arguments yield eta_qq = (3-gamma*)/(1+γ*)$ as a function of the mass anomalous dimension gamma* at the IRFP. The arguments can be generalized to other condensates such as ~ m^(4/(1+gamma*)). We describe a heuristic derivation of the result on the condensates, which provides interesting connections between different approaches. Our results are compared with existing data from numerical studies of SU(2) with two adjoint Dirac fermions.

hep-ph↗