arXiv subjects

Gerhard Buchalla

Publications and source records attributed to Gerhard Buchalla.

At least 19 recordsLinked to original sources

arXiv2025

Anomalous Couplings from the Electroweak Chiral Lagrangian for Off-Shell Higgs in $gg\to Z_L Z_L$

We investigate the production of (longitudinal) $Z$-boson pairs in gluon fusion as a probe of anomalous Higgs couplings. Of particular interest is the kinematic region of large center-of-mass energy, where the Higgs-boson is highly off-shell. We employ the electroweak chiral Lagrangian with a light Higgs, which is the most natural effective field theory (EFT) for this process. We demonstrate this by a detailed analysis of the leading and next-to-leading EFT contributions to the amplitude, at leading order in QCD, emphasizing the role of power counting for a systematic application of the EFT. We show that at leading order the new-physics contributions are described by only two parameters, which depend on three EFT couplings. Subleading effects can be expected to be small within the range of validity of the EFT. Phenomenological implications are briefly discussed.

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arXiv2023

$h\to gg$ and $h\toγγ$ with Anomalous Couplings at Next-to-Leading Order in QCD

We generalize the next-to-leading order QCD calculations for the decay rates of $h\to gg$ and $h\toγγ$ to the case of anomalous couplings of the Higgs boson. We demonstrate how this computation can be done in a consistent way within the framework of an electroweak chiral Lagrangian, based on a systematic power counting. It turns out that no additional coupling parameters arise at NLO in QCD beyond those already present at leading order. The impact of QCD is large for $h\to gg$ and the uncertainties from QCD are significantly reduced at NLO. $h\toγγ$ is only mildly affected by QCD; here the NLO treatment practically eliminates the uncertainties. Consequently, our results will allow for an improved determination of anomalous Higgs couplings from these processes. The relation of our framework to a treatment in Standard Model effective field theory is also discussed.

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arXiv2019

Complete One-Loop Renormalization of the Higgs-Electroweak Chiral Lagrangian

The electroweak sector of the Standard Model can be formulated in a way similar to Chiral Perturbation Theory (ChPT), but extended by a singlet scalar. The resulting effective field theory (EFT) is called Higgs-Electroweak Chiral Lagrangian (EWCh$\mathcal{L}$) and is the most general approach to new physics in the Higgs sector. It solely assumes the pattern of symmetry breaking leading to the three electroweak Goldstone bosons (i.e. massive $W$ and $Z$) and the existence of a Higgs-like scalar particle. The power counting of the EWCh$\mathcal{L}$ is given by a generalization of the momentum expansion of ChPT. It is connected to a loop expansion, making the theory renormalizable order by order in the EFT. I will briefly review the construction of the EWCh$\mathcal{L}$ and its power counting. Then, I will discuss the complete one-loop renormalization of the EWCh$\mathcal{L}$ employing the background-field method and the super-heat-kernel expansion. This computation confirms the power counting assumptions, is consistent with the completeness of the operator basis, and reproduces known results of subsectors in the appropriate limits.

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arXiv2019

Master formula for one-loop renormalization of bosonic SMEFT operators

Using background-field method and super-heat-kernel expansion, we derive a master formula for the one-loop UV divergences of the bosonic dimension-6 operators in Standard Model Effective Field Theory (SMEFT). This approach reduces the calculation of all the UV divergences to algebraic manipulations. Using this formula we corroborate results in the literature for the one-loop anomalous dimension matrix of SMEFT obtained via diagrammatic methods, considering contributions from the operators $X^3, ϕ^6, ϕ^4 D^2, X^2 ϕ^2$ of the Warsaw basis. The formula is derived in a general way and can be applied to other quantum field theories as well.

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arXiv2018

Higher order and top mass effects in Higgs boson pair production beyond the Standard Model

We discuss the interplay between NLO QCD corrections and anomalous couplings in Higgs boson pair production via gluon fusion, within the framework of a non-linearly realised Effective Field Theory, described by the electroweak chiral Lagrangian. We study how the NLO corrections with full top quark mass dependence affect the total cross sections as well as distributions in the Higgs boson pair invariant mass. For a large part of the parameter space, significant and non-homogeneous K-factors arise.

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arXiv2015

Complete Electroweak Chiral Lagrangian with a Light Higgs at NLO

We consider the Standard Model, including a light scalar boson $h$, as an effective theory at the weak scale $v=246\,{\rm GeV}$ of some unknown dynamics of electroweak symmetry breaking. This dynamics may be strong, with $h$ emerging as a pseudo-Goldstone boson. The symmetry breaking scale $Λ$ is taken to be at $4πv$ or above. We review the leading-order Lagrangian within this framework, which is nonrenormalizable in general. A chiral Lagrangian can then be constructed based on a loop expansion. A systematic power counting is derived and used to identify the classes of counterterms that appear at one loop order. With this result the complete Lagrangian is constructed at next-to-leading order, ${\cal O}(v^2/Λ^2)$. This Lagrangian is the most general effective description of the Standard Model containing a light scalar boson, in general with strong dynamics of electroweak symmetry breaking. Scenarios such as the SILH ansatz or the dimension-6 Lagrangian of a linearly realized Higgs sector can be recovered as special cases.

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arXiv2015

A Systematic Approach to the SILH Lagrangian

We consider the electroweak chiral Lagrangian, including a light scalar boson, in the limit of small $ξ=v^2/f^2$. Here $v$ is the electroweak scale and $f$ is the corresponding scale of the new strong dynamics. We show how the conventional SILH Lagrangian, defined as the effective theory of a strongly-interacting light Higgs (SILH) to first order in $ξ$, can be obtained as a limiting case of the complete electroweak chiral Lagrangian. The approach presented here ensures the completeness of the operator basis at the considered order, it clarifies the systematics of the effective Lagrangian, guarantees a consistent and unambiguous power counting, and it shows how the generalization of the effective field theory to higher orders in $ξ$ has to be performed. We point out that terms of order $ξ^2$, which are usually not included in the SILH Lagrangian, are parametrically larger than terms of order $ξ/16π^2$ that are retained, as long as $ξ> 1/16π^2$. Conceptual issues such as custodial symmetry and its breaking are also discussed. For illustration, the minimal composite Higgs model based on the coset $SO(5)/SO(4)$ is considered at next-to-leading order in the chiral expansion. It is shown how the effective Lagrangian for this model is contained as a special case in the electroweak chiral Lagrangian based on $SU(2)_L\otimes SU(2)_R/SU(2)_V$.

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arXiv2013

On the Power Counting in Effective Field Theories

We discuss the systematics of power counting in general effective field theories, focussing on those that are nonrenormalizable at leading order. As an illuminating example we consider chiral perturbation theory gauged under the electromagnetic $U(1)$ symmetry. This theory describes the low-energy interactions of the octet of pseudo-Goldstone bosons in QCD with photons and has been discussed extensively in the literature. Peculiarities of the standard approach are pointed out and it is shown how these are resolved within our scheme. The presentation follows closely our recent discussion of power counting for the electroweak chiral Lagrangian. The systematics of the latter is reviewed and shown to be consistent with the concept of chiral dimensions. The results imply that naive dimensional analysis (NDA) is incomplete in general effective field theories, while still reproducing the correct counting in special cases.

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arXiv2013

Nonstandard Higgs Couplings from Angular Distributions in $h\to Z \ell^+\ell^-$

We compute the fully differential rate for the Higgs-boson decay $h\to Z\ell^+\ell^-$, with $Z\to\ell^{'+}\ell^{'-}$. For these processes we assume the most general matrix elements within an effective Lagrangian framework. The electroweak chiral Lagrangian we employ assumes minimal particle content and Standard Model gauge symmetries, but is otherwise completely general. We discuss how information on new physics in the decay form factors may be obtained that is inaccessible in the dilepton-mass spectrum integrated over angular variables. The form factors are related to the coefficients of the effective Lagrangian, which are used to estimate the potential size of new-physics effects.

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arXiv2012

Effective Theory of a Dynamically Broken Electroweak Standard Model at NLO

We consider the Standard Model as an effective theory at the weak scale $v$ of a generic new strong interaction that dynamically breaks electroweak symmetry at the energy scale $Λ\sim $ (few) TeV. Assuming only the minimal field content with the Standard Model fermions and gauge bosons, but without a light Higgs particle, we construct the complete Lagrangian through next-to-leading order, that is, including terms of order $v^2/Λ^2$. The systematics behind this expansion is clarified. Although similar to chiral perturbation theory, it is not governed by the dimension of operators alone, but depends in an essential way on the loop expansion. Power-counting formulas are derived that indicate the classes of operators required at the next-to-leading order. The complete set of operators at leading and next-to-leading order is then listed, based on the restrictions implied by the Standard-Model gauge symmetries. We recover the well-known operators discussed in the literature in connection with the electroweak chiral Lagrangian and in similar contexts, but we collect a complete and systematic list of all terms through order $v^2/Λ^2$. This includes some operators not discussed in explicit terms before. We also show that a few of the previously considered operators can be eliminated via the equations of motion. As another important result we confirm the known list of dimension-6 operators in the Standard Model with an elementary Higgs doublet, essentially as a special case of our scenario.

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arXiv2010

Precision flavour physics with $B\to Kν\barν$ and $B\to Kl^+l^-$

We discuss how the combined analysis of $B\to Kν\barν$ and $B\to Kl^+l^-$ can provide us with new physics tests practically free of form factor uncertainties. Residual theory errors are at the level of several percent. This study underlines the excellent motivation for measuring these modes at a Super Flavour Factory, or, in the case of $B\to Kl^+l^-$, also at a hadron collider.

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arXiv2008

B -> V_L V_L Decays at Next-to-Leading Order in QCD

We compute the amplitudes for the two-body decay of $B$ mesons into longitudinally polarized light vector mesons at next-to-leading order in QCD. We give the explicit expressions in QCD factorization for all 34 transitions of a heavy-light $B$ meson into a pair of longitudinal vector mesons $ρ$, $ω$, $ϕ$, $K^*$ within the Standard Model. Decay rates and CP asymmetries are discussed in detail and compared with available data. Exploiting the fact that QCD penguins are systematically smaller for vector mesons in comparison to pseudoscalars in the final state, we investigate several methods to achieve high-precision determinations of CKM parameters and New Physics tests. We propose a method to use V-spin symmetry and data on $\bar B_d\to\bar K^{*0}_L K^{*0}_L$ to constrain the penguin contribution in $\bar B_d\toρ^+_Lρ^-_L$. CP violation in the latter decay together with a measurement of $\sin 2β$ determines the unitarity triangle with high accuracy. We show that CP violation in $\bar B_d\toρ^+_Lρ^-_L$ and $\bar B_d\toψK_S$ alone implies $|V_{ub}|=(3.54\pm 0.17)\cdot 10^{-3}$, presently the most accurate determination of this quantity.

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arXiv2005

The Pattern of CP Asymmetries in $b\to s$ Transitions

New CP violating physics in $b\to s$ transitions will modify the CP asymmetries in B decays into final CP eigenstates ($ϕK_S$, $η^\prime K_S$, $π^0 K_S$, $ωK_S$, $ρ^0 K_S$ and $ηK_S$) from their Standard Model values. In a model independent analysis, the pattern of deviations can be used to probe which Wilson coefficients get a significant contribution from the new physics. We demonstrate this idea using several well-motivated models of new physics, and apply it to current data.

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arXiv2004

Constraining the Unitarity Triangle with B -> V gamma

We discuss the exclusive radiative decays $B\to K^{*}γ$, $B \toργ$, and $B\toωγ$ in QCD factorization within the Standard Model. The analysis is based on the heavy-quark limit of QCD. Our results for these decays are complete to next-to-leading order in QCD and to leading order in the heavy-quark limit. Special emphasis is placed on constraining the CKM-unitarity triangle from these observables. We propose a theoretically clean method to determine CKM parameters from the ratio of the $B\toρlν$ decay spectrum to the branching fraction of $B\toργ$. The method is based on the cancellation of soft hadronic form factors in the large energy limit, which occurs in a suitable region of phase space. The ratio of the $B\toργ$ and $B\to K^{*}γ$ branching fractions determines the side $R_{t}$ of the standard unitarity triangle with reduced hadronic uncertainties. The recent Babar bound on $B(B^0\toρ^0γ)$ implies $R_t < 0.81 (ξ/1.3)$, with the limiting uncertainty coming only from the SU(3) breaking form factor ratio $ξ$. This constraint is already getting competitive with the constraint from $B_{s}$-$\bar B_{s}$ mixing. Phenomenological implications from isospin-breaking effects are briefly discussed.

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arXiv2004

CP Violation in B -> pi+ pi- and the Unitarity Triangle

We analyze the extraction of weak phases from CP violation in $B\toπ^+π^-$ decays. We propose to determine the unitarity triangle $(\barρ,\barη)$ by combining the information on mixing induced CP violation in $B\toπ^+π^-$, $S$, with the precision observable $\sin 2β$ obtained from the CP asymmetry in $B\toψK_S$. It is then possible to write down exact analytical expressions for $\barρ$ and $\barη$ as simple functions of the observables $S$ and $\sin 2β$, and of the penguin parameters $r$ and $ϕ$. As an application clean lower bounds on $\barη$ and $1-\barρ$ can be derived as functions of $S$ and $\sin 2β$, essentially without hadronic uncertainty. Computing $r$ and $ϕ$ within QCD factorization yields precise determinations of $\barρ$ and $\barη$ since the dependence on $r$ and $ϕ$ is rather weak. It is emphasized that the sensitivity to the phase $ϕ$ enters only at second order and is extremely small for moderate values of this phase, predicted in the heavy-quark limit. Transparent analytical formulas are further given and discussed for the parameter $C$ of direct CP violation in $B\toπ^+π^-$. We also discuss alternative ways to analyze $S$ and $C$ that can be useful if new physics affects $B_d$--$\bar B_d$ mixing. Predictions and uncertainties for $r$ and $ϕ$ in QCD factorization are examined in detail. It is pointed out that a simultaneous expansion in $1/m_b$ and 1/N leads to interesting simplifications. At first order infrared divergences are absent, while the most important effects are retained. Independent experimental tests of the factorization framework are briefly discussed.

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arXiv2004

QCD and Heavy Hadron Decays

We review recent developments in QCD pertaining to its application to weak decays of heavy hadrons. We concentrate on exclusive rare and nonleptonic B-meson decays, discussing both the theoretical framework and phenomenological issues of current interest.

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arXiv2003

Extracting short-distance physics from K_{L,S} -> pi0 e+ e- decays

We present a new analysis of the rare decay K_L -> pi0 e+ e- taking into account important experimental progress that has recently been achieved in measuring K_L -> pi0 gamma gamma and K_S -> pi0 e+ e-. This includes a brief review of the direct CP-violating component, a calculation of the indirect CP-violating contribution, which is now possible after the measurement of K_S -> pi0 e+ e-, and a re-analysis of the CP conserving part. The latter is shown to be negligible, based on experimental input from K_L -> pi0 gamma gamma, a more general treatment of the form factor entering the dispersive contribution, and on a comparison with the CP violating rate, which can now be estimated reliably. We predict B(K_L -> pi0 e+ e-) = (3.2 +1.2 -0.8) 10^{-11} in the Standard Model, dominated by CP violation with a sizable contribution (~40%) from the direct effect, largely through interference with the indirect one. Methods to deal with the severe backgrounds for K_L -> pi0 e+ e- using Dalitz-plot analysis and time-dependent K_L-K_S interference are also briefly discussed.

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arXiv2003

Model Independent Bound on the Unitarity Triangle from CP Violation in B-> pi+ pi- and B-> psi K_S

We derive model independent lower bounds on the CKM parameters (1-rhobar) and etabar as functions of the mixing-induced CP asymmetry S in B-> pi+ pi- and sin(2 beta) from B->psi K_S. The bounds do not depend on specific results of theoretical calculations for the penguin contribution to B-> pi+ pi-. They require only the very conservative condition that a hadronic phase, which vanishes in the heavy-quark limit, does not exceed 90 degrees in magnitude. The bounds are effective if -sin(2 beta) < S < 1. Dynamical calculations indicate that the limits on rhobar and etabar are close to their actual values.

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