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Gorazd Cvetic

Publications and source records attributed to Gorazd Cvetic.

At least 19 recordsLinked to original sources
arXiv2026

Renormalon-based resummation for B(D) Mesons

We apply a previously developed method of renormalon-based resummation of spacelike and timelike QCD observables, to evaluate of the values of the pole masses $m_q$ of $q=b$ and $c$ quarks, using as input the knowledge of the values of the corresponding ${\overline{\rm MS}}$ masses ${\overline m}_q \equiv {\overline m}_q({\overline m}_q^2)$. The evaluation also uses the knowledge of the first few coefficients of the perturbation expansion of $m_q$ (i.e., of $m_q/{\overline m}_q$), as well as the known renormalon structure of that expansion. In the evaluation, we use the timelike QCD running coupling based on a specific holomorphic spacelike QCD coupling, in order to avoid additional ambiguities due to the Landau poles of the usual perturbative coupling. The principal IR regulator parameter of the coupling is varied in an expected range. We also reevaluate the chromomagnetic Wilson coefficient of heavy quark ${\hat C}(m_q^2)$, and extract values of several corresponding hadronic parameters.

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arXiv2024

Towards unifying perturbative and Holographic Light-Front QCD via holomorphic coupling

We construct a QCD coupling ${\mathcal{A}}(Q^2)$ in the Effective Charge (ECH) scheme of the canonical part $d(Q^2)$ of the (inelastic) polarised Bjorken Sum Rule (BSR) ${\overline Γ}_1^{\rm p-n}(Q^2)$. In the perturbative domain, the coupling ${\mathcal{A}}(Q^2)$ practically coincides with the perturbative coupling $a(Q^2)$ [$\equiv α_s(Q^2)/π$] in the four-loop ECH renormalisation scheme. In the deep infrared (IR) regime, ${\mathcal{A}}(Q^2)$ behaves as suggested by the Holographic Light-Front QCD up to the second derivative. Furthermore, in contrast to its perturbative counterpart $a(Q^2)$, the coupling ${\mathcal{A}}(Q^2)$ is holomorphic in the entire complex $Q^2$-plane with the exception of the negative semiaxis, reflecting the holomorphic properties of the BSR observable $d(Q^2)$ [or: ${\overline Γ}_1^{\rm p-n}(Q^2)$] as dictated by the general principles of the Quantum Field Theory. It turns out that the obtained coupling, used as ECH, reproduces quite well the experimental data for ${\overline Γ}_1^{\rm p-n}(Q^2)$ in the entire $N_f=3$ regime $0 < Q^2 \lesssim 5 \ {\rm GeV}^2$.

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arXiv2024

Rare tau decays via exchange of on-shell almost degenerate Majorana neutrinos, $τ^{\mp} \to π^{\mp} N_j \to π^{\mp} μ^{\mp} π^{\pm}$ and $τ^{\mp} \to π^{\mp} N_j \to π^{\mp} μ^{\pm} π^{\mp}$

We investigate rare decays of tau leptons that occur via exchange of heavy on-shell neutrinos $N_j$ ($j=1,2$). These neutrinos can be either Dirac or Majorana, and are considered to be almost degenerate in mass. The decays can thus be either lepton number conserving (LNC), $τ^{\mp} \to π^{\mp} N_j \to π^{\mp} μ^{\mp} π^{\pm}$, or lepton number violating (LNV), $τ^{\mp} \to π^{\mp} N_j \to π^{\mp} μ^{\pm} π^{\mp}$. If neutrinos are Dirac, only LNC decays are possible. If they are Majorana, both LNC and LNV are possible. We derive the corresponding expressions for the effective decay widths $Γ_{{\rm eff},\mp}^{\rm (X)}$ (X=LNC, LNV) of these rare decays, where we account for $N_1$-$N_2$ overlap and oscillation effects and for the finite detector length effects. We then numerically evaluate these decay widths as well as the related CP violation asymmetry width $ΔΓ_{\rm CP}^{\rm (X)} = (Γ_{{\rm eff},-}^{\rm (X)} - Γ_{{\rm eff},+}^{\rm (X)})$. We conclude that for certain, presently allowed, ranges of the heavy-light neutrino mixing parameters, such decays and asymmetries could be observed in Belle II experiment.

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arXiv2023

Analytical solution to DGLAP integro-differential equation in a simple toy-model with a fixed gauge coupling

We consider a simple model for QCD dynamics in which DGLAP integro-differential equation may be solved analytically. This is a gauge model which possesses dominant evolution of gauge boson (gluon) distribution and in which the gauge coupling does not run. This may be ${\cal N} =4$ supersymmetric gauge theory with softly broken supersymmetry, other finite supersymmetric gauge theory with lower level of supersymmetry, or topological Chern-Simons field theories. We maintain only one term in the splitting function of unintegrated gluon distribution and solve DGLAP analytically for this simplified splitting function. The solution is found by use of the Cauchy integral formula. The solution restricts form of the unintegrated gluon distribution as function of momentum transfer and of Bjorken $x$. Then we consider an almost realistic splitting function of unintegrated gluon distribution as an input to DGLAP equation and solve it by the same method which we have developed to solve DGLAP equation for the toy-model. We study a result obtained for the realistic gluon distribution and find a singular Bessel-like behaviour in the vicinity of the point $x=0$ and a smooth behaviour in the vicinity of the point

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arXiv2023

Borel-Laplace Sum Rules with $τ$ decay data, using OPE with improved anomalous dimensions

We perform numerical analysis of double-pinched Borel-Laplace QCD sum rules for the strangeless semihadronic $τ$-decay data. The $D=0$ contribution to the theoretical contour integral in the sum rules is evaluated by the (truncated) Fixed Order perturbation theory method (FO) and by the Principal Value (PV) of the Borel integration. We use for the full Adler function the Operator Product Expansion (OPE) with the terms $\sim \langle O_D \rangle$ of dimension $D=2 n$ where $2 \leq n \leq 5$ for the (V+A)-channel, and $2 \leq n \leq 7$ for the V-channel data. In our previous works [1,2], only the (V+A)-channel data was analysed. In this work, the analysis of a new set of V-channel data is performed as well. Further, a renormalon-motivated construction of the $D=0$ part of the Adler function is improved in the $u=3$ infrared renormalon sector, by involving the recently known information on the two principal noninteger values $k^{(j)}=γ^{(1)}(O_6^{(j)})/β_0$ of the effective leading-order anomalous dimensions. Additionally, the OPE of the Adler function has now the D=6 contribution with the principal anomalous dimension ($\sim α_s^{k^{(1)}}$), and terms of higher dimension (with zero anomalous dimension). Cross-checks of the obtained extracted values of $α_s$ and of the condensates were performed by reproduction of the (central) experimental values of several double-pinched momenta $a^{(2,n)}$. The averaged final extracted values of the (MSbar) coupling are: $α_s(m_τ^2) = 0.3169^{+0.0070}_{-0.0096}$, corresponding to $α_s(M_Z^2)=0.1183^{+0.0009}_{-0.0012}$.

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arXiv2022

Using improved Operator Product Expansion in Borel-Laplace Sum Rules with ALEPH $τ$ decay data, and determination of pQCD coupling

We use improved truncated Operator Product Expansion (OPE) for the Adler function, involving two types of terms with dimension $D=6$, in the double-pinched Borel-Laplace Sum Rules and Finite Energy Sum Rules for the V+A channel strangeless semihadronic $τ$ decays. The generation of the higher order perturbative QCD terms of the $D=0$ part of the Adler function is carried out using a renormalon-motivated ansatz incorporating the leading UV renormalon and the first two leading IR renormalons. The trunacted $D=0$ part of the Sum Rules is evaluated by two variants of the fixed-order perturbation theory (FO), by Principal Value of the Borel resummation (PV), and by contour-improved perturbation theory (CI). For the experimental V+A channel spectral function we use the ALEPH $τ$-decay data. We point out that the truncated FO and PV evaluation methods account correctly for the renormalon structure of the Sum Rules, while this is not the case for the truncated CI evaluation. We extract the value of the ${\overline {\rm MS}}$ coupling $α_s(m_τ^2) = 0.3235^{+0.0138}_{-0.0126}$ [$α_s(M_Z^2)=0.1191 \pm 0.0016$] for the average of the two FO methods and the PV method, which we consider as our main result. If we included in the average also CI extraction, the value would be $α_s(m_τ^2) = 0.3299^{+0.0232}_{-0.0225}$ [$α_s(M_Z^2)=0.1199^{+0.0026}_{-0.0028}$]. This work is an extension and improvement of our previous work [Eur.Phys.J.C81 (2021) 10, 930] where we used for the truncated OPE a more naive (and widely used) form and where the extracted values for $α_s(M_Z^2)$ were somewhat lower.

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arXiv2021

Determination of perturbative QCD coupling from ALEPH $τ$ decay data using pinched Borel-Laplace and Finite Energy Sum Rules

We present a determination of the perturbative QCD (pQCD) coupling using the V+A channel ALEPH $τ$-decay data. The determination involves the double-pinched Borel-Laplace Sum Rules and Finite Energy Sum Rules. The theoretical basis is the Operator Product Expansion (OPE) of the V+A channel Adler function in which the higher order terms of the leading-twist part originate from a model based on the known structure of the leading renormalons of this quantity. The applied evaluation methods are contour-improved perturbation theory (CIPT), fixed-order perturbation theory (FOPT), and Principal Value of the Borel resummation (PV). All the methods involve truncations in the order of the coupling. In contrast to the truncated CIPT method, the truncated FOPT and PV methods account correctly for the suppression of various renormalon contributions of the Adler function in the mentioned sum rules. The extracted value of the ${\overline {\rm MS}}$ coupling is $α_s(m_τ^2) = 0.3116 \pm 0.0073$ [$α_s(M_Z^2)=0.1176 \pm 0.0010$] for the average of the FOPT and PV methods, which we regard as our main result. On the other hand, if we include in the average also the CIPT method, the resulting values are significantly higher, $α_s(m_τ^2) = 0.3194 \pm 0.0167$ [$α_s(M_Z^2)=0.1186 \pm 0.0021$].

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arXiv2021

pQCD running couplings finite and monotonic in the infrared: when do they reflect the holomorphic properties of spacelike observables?

We investigate a large class of perturbative QCD (pQCD) renormalization schemes whose beta functions $β(a)$ are meromorphic functions of the running coupling and give finite positive value of the coupling $a(Q^2)$ in the infrared regime ("freezing"), $a(Q^2) \to a_0$ for $Q^2 \to 0$. Such couplings automatically have no singularities on the positive axis of the squared momenta $Q^2$ ($ \equiv -q^2$). Explicit integration of the renormalization group equation (RGE) leads to the implicit (inverted) solution for the coupling, of the form $\ln (Q^2/Q^2_{\rm in}) = {\cal H}(a)$. An analysis of this solution leads us to an algebraic algorithm for the search of the Landau singularities of $a(Q^2)$ on the first Riemann sheet of the complex $Q^2$-plane, i.e., poles and branching points (with cuts) outside the negative semiaxis. We present specific representative examples of the use of such algorithm, and compare the found Landau singularities with those seen after the 2-dimensional numerical integration of the RGE in the entire first Riemann sheet, where the latter approach is numerically demanding and may not always be precise. The specific examples suggest that the presented algebraic approach is useful to find out whether the running pQCD coupling has Landau singularities and, if yes, where precisely these singularities are.

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arXiv2020

Lattice-motivated QCD coupling and hadronic contribution to muon $g-2$

We present an updated version of a QCD coupling which fulfills various physically motivated conditions: at high momenta it practically coincides with the perturbative QCD (pQCD) coupling; at intermediate momenta it reproduces correctly the physics of the semihadronic tau decay; and at very low momenta it is suppressed as suggested by large-volume lattice calculations. An earlier presented analysis is updated here in the sense that the Adler function, in the regime $|Q^2| \lesssim 1 \ {\rm GeV}^2$, is evaluated by a renormalon-motivated resummation method. This Adler function is then used here in the evaluation of the quantities related with the semihadronic (strangeless) $τ$-decay spectral functions, including Borel-Laplace sum rules in the (V+A)-channel. The analysis is then extended to the evaluation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment, $a_μ^{\rm had(1)}$, where we include in the Adler function the V-channel higher-twist OPE terms which are regulated in the infrared (IR) by mass parameters which are expected to be $\lesssim 1$ GeV. The correct value of $a_μ^{\rm had(1)}$ can be reproduced with the mentioned IR-regulating mass parameters if the value of the condensate $\langle O_4 \rangle_{\rm V+A}$ is positive (and thus the gluon condensate value is positive). This restriction and the requirement of the acceptable quality of the fits to the various mentioned sum rules then lead us to the restriction $0.1171 < α_s(M_Z^2;{\overline{MS}}) < 0.1180$.

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arXiv2020

Sensitivity bounds on heavy neutrino mixing $|U_{μN}|^2$ and $|U_{τN}|^2$ from LHCb upgrade

Decays of heavy pseudoscalar mesons $B$, $B_c$, $B_s$ and $D_s$ at LHCb upgrade are considered, which produce either two equal sign muons or taus. In addition, we consider the analogous decays with opposite sign muons or taus. All these decays are considered to be mediated by a heavy on-shell neutrino $N$. Such decays of $B$ mesons, if not detected, will give in general stringent upper bounds on the heavy-light mixing parameter $|U_{μN}|^2$ as a function of the neutrino mass $M_N \sim 1$ GeV, principally due to the large expected number of produced mesons $B$. While some of the decays of the other mentioned mesons are attractive due to a weaker CKM-suppression, the expected produced number of such mesons is significantly smaller that that of $B$'s; therefore, the sensitivity bounds from such decays are in general comparable or less restrictive. When $τ$ pairs are produced, only two types of such decays are significant: $B^{\pm}, B_{c}^{\pm} \to τ^{\pm} τ^{\pm} π^{\mp}$ (and $τ^{\pm} τ^{\mp} π^{\pm}$), giving us stringent upper bounds on $|U_{τN}|^2$; the other decays with a pair of $τ$, such as $B^0 \to D^{(*)-} τ^+ τ^+ π^-$ (and $D^{(*)-} τ^+ τ^- π^+$), are prohibited or very suppressed by kinematics.

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arXiv2020

Exploring CP-violation, via heavy neutrino oscillations, in rare B meson decays at Belle II

In this article we study the rare B-meson decay via two on-shell almost-degenerate Majorana Heavy Neutrinos, into two charged leptons and two pseudoscalar mesons ($B^{\pm} \to D^0 \ell^{\pm}_1 \ell^{\pm}_2 π^{\mp}$). We consider the scenario where the heavy neutrino masses are $\sim 2$ GeV and the heavy-light mixing coefficients are $|B_{\ell N}|^2 \sim 10^{-5}$, and evaluate the possibility to measure the CP-asymmetry at Belle II. We present some realistic conditions under which the asymmetry could be detected.

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arXiv2020

Sensitivity limits on heavy-light mixing $|U_{μN}|^2$ from lepton number violating $B$ meson decays

We consider the lepton number violating decays $B \to μ^{\pm} μ^{\pm} π^{\mp}$ and $B \to D^{(*)} μ^{\pm} μ^{\pm} π^{\mp}$ which may be detected at LHCb and Belle-II experiments; and $B \to μ^{\pm} μ^{\pm} e^{\mp} ν$ and $B \to D^{(*)} μ^{\pm} μ^{\pm} e^{\mp} ν$ decays which may be detected at Belle-II experiment. The projected total number of produced $B$ mesons is $4.8 \times 10^{12}$ at LHCb upgrade and $5 \times 10^{10}$ at Belle-II. For the case that the above decays are not detected, we deduce the new upper bounds (sensitivity limits) for the mixing parameter $|U_{μN}|^2$ of heavy sterile neutrino with sub-eV light neutrino, as a function of the sterile neutrino mass in the interval $1.75 \ {\rm GeV} < M_N < 5.0 \ {\rm GeV}$. We take into account the probability of decay of the sterile neutrino $N$ within the detector, taking as the effective detector length $L=2.3 \ m$ at LCHb upgrade and $L=1 \ m$ at Belle-II. In the interval $1.75 \ {\rm GeV} < M_N < 3 \ {\rm GeV}$, the most stringent bounds can be obtained with the decays $B \to μ^{\pm} μ^{\pm} π^{\mp}$ at LHCb upgrade. The sensitivity limits are expected to be in general more stringent at LHCb upgrade than at Belle-II, principally because the number of produced $B$ mesons in LHCb upgrade is expected to be by about two orders of magnitude larger than at Belle-II. We conclude that the LHCb upgrade and Belle-II experiments have the potential to either find a new heavy Majorana neutrino $N$, or to improve significantly the sensitivity limits (upper bounds) on the heavy-light mixing parameter $|U_{μN}|^2$, particularly in the mass range $1.75 \ {\rm GeV} < M_N < 3 \ {\rm GeV}$. This work is a continuation and refinement of our previous work [1] on the subject.

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arXiv2020

Infrared-suppressed QCD coupling and the hadronic contribution to muon g-2

A variant of QCD with the coupling suppressed in the infrared (IR) regime, as suggested by large-volume lattice calculations of the Landau-gauge gluon and ghost dressing functions, is considered. The coupling is further restricted by the condition of approximate coincidence with perturbative QCD in the high momentum regime, and by the $τ$-lepton semihadronic decay rate in the intermediate momentum regime, the rate which is evaluated by a renormalon-motivated resummation method. The obtained coupling turns out to be free of Landau singularities. The $D=4,6$ condensate values of the Adler function are then extracted by application of the Borel sum rules to the OPAL and ALEPH (V+A)-channel data of $τ$-decay, and the corresponding V-channel condensate values are deduced as well. We then show that the correct value of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment, $a_μ^{\rm had(1)}$, is reproduced by regularizing the $D=4,6$ OPE terms in the V-channel Adler function with IR-regularization masses ${\cal M}_{D/2} \lesssim 1 \ {\rm GeV}$, suggesting the internal consistency of the presented QCD framework.

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arXiv2020

Evaluation of neutrinoless double beta decay: QCD running to sub-GeV scales

We evaluate QCD effects in the neutrinoless double beta ($0νββ$) decay, originating from new physics short-range mechanism in the form of five dimension-9 operators. For this, we employ the one-loop and two-loop renormalization group equations (RGEs) for the corresponding Wilson coefficients, performing the RGE-evolution from the new physics scales (estimated as $Λ~ \sim 10^2$ GeV) to the typical spacelike $0νββ$-scale $Q \sim 0.1$ GeV. Since the latter scale is clearly nonperturbative, we apply various infrared-safe (IR-safe) variants of QCD where the running coupling has no Landau singularities at low spacelike $Q$. We point out that the correct treatment of the IR-safe analogs of the (noninteger) powers of the couplings is important. It turns out that in most cases of the considered operators the resulting QCD effects can be significant in this process, i.e., can be stronger than the effects of the present uncertainties in the nuclear matrix elements.

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arXiv2019

Measuring the heavy neutrino oscillations in rare W boson decays at the Large Hadron Collider

Majorana neutrinos in the seesaw model can have sizable mixings through which they can be produced at the Large Hadron Collider (LHC) and show a remarkable Lepton Number Violating (LNV) signature. In this article we study the LNV decay of the W boson via two almost degenerate heavy on-shell Majorana neutrinos $N_j$, into three charged leptons and a light neutrino. We consider the scenario where the heavy neutrino masses are within $1$ GeV $\leq M_N \leq 10$ GeV. We evaluated the possibility to measure a LNV oscillation process in such a scenario, namely, the modulation of the quantity $d Γ/d L$ for the process at the LHC where $W^{\pm} \to μ^{\pm} N \to μ^{\pm} τ^{\pm} W^{\mp *}$ $ \to μ^{\pm} τ^{\pm} e^{\mp} ν_e$. $L$ is the distance within the detector between the two vertices of the process. We found out some realistic conditions under which such a modulation could be probed at the LHC.

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arXiv2019

Probing heavy neutrino oscillations in rare W boson decays

In this work, we study the lepton number violating W boson and top quark decays via intermediate on-shell Majorana neutrinos Nj into three charged leptons and a light neutrino. We discuss the neutrino oscillation effects present in the decay due to the small mass gap between the heavy neutrino states. We focus on a scenario that contains at least two heavy Majorana neutrinos in the mass range 2-80 GeV. The results indicate that the modulation of the branching ratios as a function of the distance between the vertices may be detected in a future experiment such as High-Luminosity Large Hadron Collider. As a secondary result, the CP-violating phases could be explored.

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arXiv2019

Renormalon-motivated evaluation of QCD observables

A method of evaluation of spacelike QCD observables ${\cal D}(Q^2)$ is developed, motivated by the renormalon structure of these quantities. A related auxiliary quantity ${\widetilde {\cal D}}(Q^2)$ is introduced, which is renomalization scale independent only at the one-loop level, and a large-$β_0$-type renormalon motivated ansatz is made for the Borel transform of this quantity. This leads to a `dressed' Borel transform of the considered observable ${\cal D}(Q^2)$. From there, a Neubert-type distribution is obtained for the observable. The described method is then applied to the massless Adler function and the related decay ratio of the $τ$ lepton semihadronic decays. Comparisons are then made with an evaluation method at higher truncated orders, developed in our earlier works, which is a renormalization scale invariant extension of the diagonal Padé approximants.

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