Hadronic Matrix Elements Research Articles

New physics effects in leptonic and semileptonic decays

We discuss the possibilities of extracting the constraints on New Physics by using the current data on the leptonic and semileptonic decays of pseudoscalar mesons. In doing so we use a general low energy Lagrangian that besides the vector and axial operators also includes the (pseudo-)scalar and tensor ones. In obtaining constraints on New Physics couplings, we combine the experimental information concerning several decay modes with the accurate and precise lattice QCD results for the hadronic matrix elements. We propose to study new observables that can be extracted from the angular analysis of the semileptonic decays and discuss their values both in the Standard Model and in some specific scenarios of physics beyond the Standard Model.

Role of Bc+→Bs,d(*)ℓ¯νℓ in the Standard Model and in the search for BSM signals

The decays $B_c^+ \to B_{a} \bar \ell \nu_\ell$ and $B_c^+ \to B_{a}^{*}(\to B_a \gamma) \bar \ell \nu_\ell$, with $a=s,d$ and $\ell=e,\mu$, are studied in the Standard Model (SM) and in the extension based on the low-energy Hamiltonian comprising the full set of dimension-$6$ semileptonic $c \to s,d$ operators with left-handed neutrinos. Tests of $\mu/e$ universality are investigated using such modes. The heavy quark spin symmetry is applied to relate the relevant hadronic matrix elements and to exploit lattice QCD results on $B_c$ form factors. Optimized observables are selected, and the pattern of their correlations is studied to identify the effects of the various operators in the extended low-energy Hamiltonian.

CP violation in non-leptonic B_c decays to excited final states

We study the CP violation in two-body nonleptonic decays of B_c meson. We concentrate on the decay channels which contain at least one excited heavy meson in the final states. Specifically, the following channels are considered: B_crightarrow c{bar{c}}(2S, 2P)+{bar{c}}q(1S, 1P), B_crightarrow c{bar{c}}(1S)+{bar{c}}q(2S, 2P), B_crightarrow c{bar{c}}(1P)+{bar{c}}q(2S), B_crightarrow c{bar{c}}(1D)+{bar{c}}q(1S, 1P), and B_crightarrow c{bar{c}}(3S)+{bar{c}}q(1S). The improved Bethe-Salpeter method is applied to calculate the hadronic transition matrix element. Our results show that some decay modes have large branching ratios, which is of the order of 10^{-3}. The CP violation effect in B_c rightarrow eta _c(1S)+D(2S), B_c rightarrow eta _c(1S)+D_0^{*}(2P), and B_c rightarrow J/psi +D^{*}(2S) are most likely to be found. If the detection precision of the CP asymmetry in such channels can reach the 3sigma level, at least 10^7B_c events are needed.

Flavor-diagonal CP violation: the electric dipole moment.

The observed baryon asymmetry in the universe cannot be reconciled with the current form of the Standard Model (SM) of particle physics. The Standard Model breaks charge conjugation parity (CP) symmetry, but not in a sufficient amount to explain the observed matter-antimatter asymmetry. Historically one of the first systems to be studied in the search of symmetry breaking within the Standard Model is the electric dipole moment (EDM) of the neutron. The contribution to the neutron EDM coming from the SM is several order of magnitudes smaller than the current experimental bound, thus providing a unique, background-free window for potential discovery of physics Beyond the Standard Model (BSM). The strong CP-violating theta term can also contribute to the neutron EDM, as can all the CP-violating effective operators describing, at energies below the electro-weak scale, the contributions from BSM. To constrain all these contributions to the neutron EDM we need to precisely determine the hadronic matrix elements of the corresponding renormalized operators. After a brief introduction on baryon asymmetry and baryogenesis, I summarize the current stuatus for experiments in search of a neutron EDM. I then describe in more details the different CP-violating sources, and some results in Chiral Perturbation Theory precede a discussion on the current status of Lattice QCD calculations. I will in particular focus on the 2 main challenges for these type of calculations: the signal-to-noise ratio and the renormalization. I will discuss several improvement techniques trying to improve these two aspects of the calculation and I will conclude with an optimistic view into the future.

Revisiting the role of grooming in DIS

We introduce a novel grooming procedure, which is an extension of the modified MassDrop tagging algorithm, tailored to the needs of deep inelastic scattering (DIS). The new algorithm, which grooms the event as a whole, takes advantage of the natural separation of current and target fragmentation in the Breit frame, in order to eliminate radiation in the beam and central rapidity regions. We study the groomed invariant mass in DIS and within soft-collinear effective theory we construct a factorization theorem for the cross-section in the back-to-back limit. In this limit we show that, up to a normalization factor, the cross-section does not depend on the incoming hadronic matrix element and we propose this measurement at HERA and the future electron-ion collider (EIC) as a probe to hadronization, precision QCD, and cold nuclear matter effects. We also give an event based definition of the Winner-Take-All axis and comment on possible applications.

Non-local matrix elements in B(s) \u2192 {K(*), \u03d5}\u2113+\u2113\u2212

We revisit the theoretical predictions and the parametrization of non-local matrix elements in rare {overline{B}}_{(s)}to left{{overline{K}}^{left(ast right)},phi right}{mathrm{ell}}^{+}{mathrm{ell}}^{-} and {overline{B}}_{(s)}to left{{overline{K}}^{ast },phi right}gamma decays. We improve upon the current state of these matrix elements in two ways. First, we recalculate the hadronic matrix elements needed at subleading power in the light-cone OPE using B-meson light-cone sum rules. Our analytical results supersede those in the literature. We discuss the origin of our improvements and provide numerical results for the processes under consideration. Second, we derive the first dispersive bound on the non-local matrix elements. It provides a parametric handle on the truncation error in extrapolations of the matrix elements to large timelike momentum transfer using the z expansion. We illustrate the power of the dispersive bound at the hand of a simple phenomenological application. As a side result of our work, we also provide numerical results for the Bs → ϕ form factors from B-meson light-cone sum rules.

Natural interpretation on the data of Λc→Σπ

Even though the Standard Model (SM) has achieved great success, its application to the field of low energies still lacks solid foundation due to our limited knowledge on non-perturbative QCD. Practically, all theoretical calculations of the hadronic transition matrix elements are based various phenomenological models. There indeed exist some anomalies in the field which are waiting for interpretations. The goal of this work is trying to solve one of the anomalies: the discrepancy between the theoretical prediction on the sign of the up-down asymmetry parameter of $\Lambda_c\to\Sigma\pi$ and the experimental measurement. In the literatures several authors calculated the rate and determined the asymmetry parameter within various schemes, but there exist obvious loopholes in those adopted scenarios. To solve the discrepancy between theory and data, we suggest that not only the direct transition process contributes to the observed $\Lambda_c\to\Sigma\pi$, but also other portals such as $\Lambda_c\to \Lambda\rho$ also play a substantial role via an isospin-conserving re-scattering $\Lambda\rho\to\Sigma\pi$. Taking into account of the effects induced by the final state interaction, we re-evaluate the relevant quantities. Our numerical results indicate that the new theoretical prediction based on this scenario involving an interference between the direct transition of $\Lambda_c\to\Sigma\pi$ and the portal $\Lambda_c\to\Lambda\rho\to\Sigma\pi$ can make both the decay rate and sign of the asymmetry parameter to be consistent with data.

Another SMEFT story: Z\u2032 facing new results on \u03b5\u2032/\u03b5, \u2206MK and K \u2192 pi nu overline{nu}

Recently the RBC-UKQCD lattice QCD collaboration presented new results for the hadronic matrix elements relevant for the ratio ε′/ε in the Standard Model (SM) albeit with significant uncertainties. With the present knowledge of the Wilson coefficients and isospin breaking effects there is still a sizable room left for new physics (NP) contributions to ε′/ε which could both enhance or suppress this ratio to agree with the data. The new SM value for the K0 − {overline{K}}^0 mass difference ∆MK from RBC-UKQCD is on the other hand by 2σ above the data hinting for NP required to suppress ∆MK. Simultaneously the most recent results for K+ → {pi}^{+}nu overline{nu} from NA62 and for KL → {pi}^0nu overline{nu} from KOTO still allow for significant NP contributions. We point out that the suppression of ∆MK by NP requires the presence of new CP-violating phases with interesting implications for K → pi nu overline{nu} , KS → μ+μ− and KL → π0ℓ+ℓ− decays. Considering a Z′-scenario within the SMEFT we analyze the dependence of all these observables on the size of NP still allowed by the data on ε′/ε. The hinted ∆MK anomaly together with the εK constraint implies in the presence of only left-handed (LH) or right-handed (RH) flavour-violating Z′ couplings strict correlation between K+ → {pi}^{+}nu overline{nu} and KL → {pi}^0nu overline{nu} branching ratios so that they are either simultaneously enhanced or suppressed relative to SM predictions. An anticorrelation can only be obtained in the presence of both LH and RH couplings. Interestingly, the NP QCD penguin scenario for ε′/ε is excluded by SMEFT renormalization group effects in εK so that NP effects in ε′/ε are governed by electroweak penguins. We also investigate for the first time whether the presence of a heavy Z′ with flavour violating couplings could generate through top Yukawa renormalization group effects FCNCs mediated by the SM Z-boson. The outcome turns out to be very interesting.

Relations between b \u2192 c\u03c4\u03bd decay modes in scalar models

As a consequence of the Ward identity for hadronic matrix elements, we find relations between the differential decay rates of semileptonic decay modes with the underlying quark-level transition b → cτν, which are valid in scalar models. The decay-mode dependent scalar form factor is the only necessary theoretical ingredient for the relations. Otherwise, they combine measurable decay rates as a function of the invariant mass-squared of the lepton pair q2 in such a way that a universal decay-mode independent function is found for decays to vector and pseudoscalar mesons, respectively. This can be applied to the decays Bto {D}^{ast}tau v,{B}_sto {D}_s^{ast}tau v,{B}_cto J/psi tau v and B → Dτv, Bs → Dsτv, Bc → ηcτv, with implications for R(D(*)), Rleft({D}_s^{left(ast right)}right) , R(J/ψ), R(ηc), and ℬ(Bc → τv). The slope and curvature of the characteristic q2-dependence is proportional to scalar new physics parameters, facilitating their straight forward extraction, complementary to global fits.

New method for calculating electromagnetic effects in semileptonic beta-decays of mesons

We construct several classes of hadronic matrix elements and relate them to the low-energy constants in Chiral Perturbation Theory that describe the electromagnetic effects in the semileptonic beta decay of the pion and the kaon. We propose to calculate them using lattice QCD, and argue that such a calculation will make an immediate impact to a number of interesting topics at the precision frontier, including the outstanding anomalies in |Vus| and the top-row Cabibbo-Kobayashi-Maskawa matrix unitarity.

Das ist der HAMMER: consistent new physics interpretations of semileptonic decays

Precise measurements of brightarrow ctau bar{nu } decays require large resource-intensive Monte Carlo (MC) samples, which incorporate detailed simulations of detector responses and physics backgrounds. Extracted parameters may be highly sensitive to the underlying theoretical models used in the MC generation. Because new physics (NP) can alter decay distributions and acceptances, the standard practice of fitting NP Wilson coefficients to SM-based measurements of the R(D^{(*)}) ratios can be biased. The newly developed Hammer software tool enables efficient reweighting of MC samples to arbitrary NP scenarios or to any hadronic matrix elements. We demonstrate how Hammer allows avoidance of biases through self-consistent fits directly to the NP Wilson coefficients. We also present example analyses that demonstrate the sizeable biases that can otherwise occur from naive NP interpretations of SM-based measurements. The Hammer library is presently interfaced with several existing experimental analysis frameworks and we provide an overview of its structure.

Non-perturbative renormalization scheme for the C P -odd three-gluon operator

We define a regularization-independent momentum-subtraction scheme for the C P -odd three-gluon operator at dimension six. This operator appears in effective field theories for heavy physics beyond the Standard Model, describing the indirect effect of new sources of C P-violation at low energies. In a hadronic context, it induces permanent electric dipole moments. The hadronic matrix elements of the three-gluon operator are non-perturbative objects that should ideally be evaluated with lattice QCD. We define a non-perturbative renormalization scheme that can be implemented on the lattice and we compute the scheme transformation to overline{mathrm{MS}} at one loop. Our calculation can be used as an interface to future lattice-QCD calculations of the matrix elements of the three-gluon operator, in order to obtain theoretically robust constraints on physics beyond the Standard Model from measurements of the neutron electric dipole moment.

Varepsilon '/varepsilon in the Standard Model at the Dawn of the 2020s

We reanalyse the ratio varepsilon '/varepsilon in the Standard Model (SM) using most recent hadronic matrix elements from the RBC-UKQCD collaboration in combination with most important NNLO QCD corrections to electroweak penguin contributions and the isospin-breaking corrections. We illustrate the importance of the latter by using their latest estimate from chiral perturbation theory (ChPT) based on the octet approximation for lowest-lying mesons and a very recent estimate in the nonet scheme that takes into account the contribution of eta _0. We find (varepsilon '/varepsilon )^{(8)}_text {SM} = (17.4 pm 6.1) times 10^{-4} and (varepsilon '/varepsilon )^{(9)}_text {SM} = (13.9 pm 5.2) times 10^{-4}, respectively. Despite a very good agreement with the measured value (varepsilon '/varepsilon )_text {exp} = (16.6 pm 2.3) times 10^{-4}, the large error in (varepsilon '/varepsilon )_text {SM} still leaves room for significant new physics (BSM) contributions to this ratio. We update the 2018 master formula for (varepsilon '/varepsilon )_text {BSM} valid in any extension beyond the SM without additional light degrees of freedom. We provide new values of the penguin parameters B_6^{(1/2)}(mu ) and B_8^{(3/2)}(mu ) at the mu -scales used by the RBC-UKQCD collaboration and at lower scales mathcal {O}(1, text {GeV}) used by ChPT and Dual QCD (DQCD). We present semi-analytic formulae for (varepsilon '/varepsilon )_text {SM} in terms of these parameters and hat{Omega }_text {eff} that summarizes isospin-breaking corrections to this ratio. We stress the importance of lattice calculations of the mathcal {O}(alpha _{text {em}}) contributions to the hadronic matrix elements necessary for the removal of renormalization scheme dependence at mathcal {O}(alpha _{text {em}}) in the present analyses of varepsilon '/varepsilon .

Supersymmetric proton decay revisited

Encouraged by the advent of a new generation of underground detectors – JUNO, DUNE and Hyper-Kamiokande – that are projected to improve significantly on the present sensitivities to various baryon decay modes, we revisit baryon decay in the minimal supersymmetric SU(5) GUT. We discuss the phenomenological uncertainties associated with hadronic matrix elements and the value of the strong coupling alpha _s – which are the most important – the weak mixing angle theta _W, quark masses including one-loop renormalization effects, quark mixing and novel GUT phases that are not visible in electroweak interaction processes. We apply our analysis to a variety of CMSSM, super- and sub-GUT scenarios in which soft supersymmetry-breaking parameters are assumed to be universal at, above and below the GUT scale, respectively. In many cases, we find that the next generation of underground detectors should be able to probe models with sparticle masses that are {{mathcal {O}}}(10) TeV, beyond the reach of the LHC.

Renormalization and matching for the Collins-Soper kernel from lattice QCD

The Collins-Soper kernel, which governs the energy evolution of transverse- momentum dependent parton distribution functions (TMDPDFs), is required to accurately predict Drell-Yan like processes at small transverse momentum, and is a key ingredient for extracting TMDPDFs from experiment. Earlier we proposed a method to calculate this kernel from ratios of the so-called quasi-TMDPDFs determined with lattice QCD, which are defined as hadronic matrix elements of staple-shaped Euclidean Wilson line operators. Here we provide the one-loop renormalization of these operators in a regularization-independent momentum subtraction (RI′/MOM) scheme, as well as the conversion factor from the RI′/MOM-renormalized quasi-TMDPDF to the overline{mathrm{MS}} scheme. We also propose a procedure for calculating the Collins-Soper kernel directly from position space correlators, which simplifies the lattice determination.

Lattice QCD Matrix Elements for the B_{s}^{0}-B[over ¯]_{s}^{0} Width Difference beyond Leading Order.

Predicting the B_{s}^{0}-B[over ¯]_{s}^{0} width difference ΔΓ_{s} relies on the heavy quark expansion and on hadronic matrix elements of ΔB=2 operators. We present the first lattice QCD results for matrix elements of the dimension-7 operators R_{2,3} and linear combinations R[over ˜]_{2,3} using nonrelativistic QCD for the bottom quark and a highly improved staggered quark (HISQ) action for the strange quark. Computations use MILC Collaboration ensembles of gauge field configurations with 2+1+1 flavors of sea quarks with the HISQ discretization, including lattices with physically light up or down quark masses. We discuss features unique to calculating matrix elements of these operators and analyze uncertainties from series truncation, discretization, and quark mass dependence. Finally we report the first standard model determination of ΔΓ_{s} using lattice QCD results for all hadronic matrix elements through O(1/m_{b}). The main result of our calculations yields the 1/m_{b} contribution ΔΓ_{1/m_{b}}=-0.022(10) ps^{-1}. Adding this to the leading order contribution, the standard model prediction is ΔΓ_{s}=0.092(14) ps^{-1}.

On the importance of NNLO QCD and isospin-breaking corrections in varepsilon '/varepsilon

Following the 1999 analysis of Gambino, Haisch and one of us, we stress that all the recent NLO analyses of varepsilon '/varepsilon in the Standard Model (SM) suffer from the renormalization scheme dependence present in the electroweak penguin contributions as well as from scale uncertainties in them related to the matching scale mu _W and in particular to mu _t in m_t(mu _t). We also reemphasize the important role of isospin-breaking and QED effects in the evaluation of varepsilon '/varepsilon . Omitting all these effects, as done in the 2015 analysis by RBC-UKQCD collaboration, and choosing as an example the QCD penguin (Q_6) and electroweak penguin (Q_8) parameters B_6^{(1/2)} and B_8^{(3/2)} to be B_6^{(1/2)}= 0.80 pm 0.08 and B_8^{(3/2)}= 0.76 pm 0.04 at mu = m_c=1.3,, text {GeV}, we find (varepsilon '/varepsilon )_mathrm{SM} = (9.4 pm 3.5) times 10^{-4}, whereas including them results in (varepsilon '/varepsilon )_mathrm{SM} = (5.6pm 2.4)times 10^{-4}. This is an example of an anomaly at the 3.3,sigma level, which would be missed without these corrections. NNLO QCD contributions to QCD penguins are expected to further enhance this anomaly. We provide a table for varepsilon '/varepsilon for different values of B_6^{(1/2)} and the isospin-breaking parameter {widehat{Omega }}_text {eff}, that should facilitate monitoring the values of varepsilon '/varepsilon in the SM when the RBC-UKQCD calculations of hadronic matrix elements including isospin-breaking corrections and QED effects will improve with time.

Patterns of flavor symmetry breaking in hadron matrix elements involving u , d , and s quarks

By considering a flavour expansion about the SU(3)-flavour symmetric point, we investigate how flavour-blindness constrains octet baryon matrix elements after SU(3) is broken by the mass difference between quarks. Similarly to hadron masses we find the expansions to be constrained along a mass trajectory where the singlet quark mass is held constant, which provides invaluable insight into the mechanism of flavour symmetry breaking and proves beneficial for extrapolations to the physical point. Expansions are given up to third order in the expansion parameters. Considering higher orders would give no further constraints on the expansion parameters. The relation of the expansion coefficients to the quark-line-connected and quark-line disconnected terms in the 3-point correlation functions is also given. As we consider Wilson clover-like fermions, the addition of improvement coefficients is also discussed and shown to be included in the formalism developed here. As an example of the method we investigate this numerically via a lattice calculation of the flavour-conserving matrix elements of the vector first class form factors.

The heavy quark expansion for inclusive semileptonic charm decays revisited

The Heavy Quark Expansion (HQE) has become an extremely powerful tool in flavor physics. For charm decays, where the expansion parameters αs(mc) and ΛQCD/mc are bigger than for bottom decays, it remains to be seen if the HQE can be applied with similar success. Nevertheless, to make optimal use of the plethora of data already available and coming in the near future, a better understanding of HQE for charm decays is crucial. This paper discusses in detail how the HQE for charm decays is set up, what is the role of four-quark (weak annihilation) operators and how this compares to the well understood bottom decays. Subtleties concerning radiative corrections and the charm mass scheme are briefly discussed. An experimental study of the relevant HQE hadronic matrix elements will then show if the HQE expansion for charm converges well enough. Besides serving as an important cross check for inclusive B decays, in the end, this study might open the road for inclusive |Vcs| and |Vcd| extractions.

Sum rules for CP-violating operators of Weinberg type

We estimate the size of the hadronic matrix elements of CP-violating three-gluon and four-gluon Weinberg operators using sum-rule techniques. In the three-gluon case, we are able to reproduce the expressions given in earlier works, while the four-gluon results obtained in this article are new. Our paper therefore represents the first systematic study of contributions to the electric dipole moment of the neutron due to CP-violating dimension-six and dimension-eight operators. We provide many details on both the derivation of the sum rules as well as the analysis of the uncertainties that plague our final predictions.