Searcharxiv⌕ Search

arXiv subjects

Christoph Greub

Publications and source records attributed to Christoph Greub.

At least 19 recordsLinked to original sources
arXiv2024

Three-loop contributions to $b\to s\gamma$ associated with the current-current operators

In a recent work, we calculated all three-loop diagrams contributing to the decay amplitude for $b \to s \gamma$ where none of the gluons touch the $b$-leg. In the present paper, we complete the calculation by working out all remaining three-loop diagrams (of order $\alpha_s^2$) associated with the current-current operators $O_1$ and $O_2$ at the physical value of the charm-quark mass $m_c$. Using the programs AMFlow and DiffExp to solve the differential equations for the master integrals, we obtained precise numerical results at 23 values for $z=m_c^2/m_b^2$, ranging from $z=1/1000$ to $z=1/5$, along with asymptotic expansions around $z=0$. For certain diagrams, the asymptotic expansion breaks down in the physical $z$-range, necessitating a Taylor expansion (which we do around $z=1/10$). In all expansions, we retained power terms up to $z^{20}$ and included the accompanying $\log(z)$ terms to all powers for asymptotic expansions. Numerical results for the sum of all diagrams (including those calculated in the previous paper) are presented in tabular form, while the mentioned expansions of individual diagram classes are provided electronically. We note that our results for the asymptotic expansions around $z=0$ are in good agreement with those recently published by Fael et al. and Czaja et al..

hep-ph↗
arXiv2023

Specific three-loop contributions to $b\to s\gamma$ associated with the current-current operators

We work out a specific class of three-loop diagrams (of order $\alpha_s^2$) contributing to the decay amplitude for $b \to s \gamma$ associated with the current-current operators $O_1$ and $O_2$ at the physical value of the charm-quark mass $m_c$. For many of the considered diagrams we were able to solve the master integrals using differential equations in the canonical form. For some diagrams we did not find a transformation to canonical form and therefore calculated the corresponding master integral directly as an expansion around $z=m_c^2/m_b^2=0$, retaining power terms up to $z^{10}$ and keeping the accompanying $\log(z)$ terms to all powers. The results for the sum of all considered diagrams are given in tabular form, while contributions of individual diagrams (or combinations thereof) are given in electronic form.

hep-ph↗
arXiv2021

Scalar Leptoquarks in Leptonic Processes

Leptoquarks are hypothetical new particles, which couple quarks directly to leptons. They experienced a renaissance in recent years as they are prime candidates to explain the so-called \textit{flavor anomalies}, i.e. the deviations between the Standard Model predictions and measurements in $b\to s\ell^{+}\ell^{-}$ and $b\to cτν$ processes and in the anomalous magnetic moment of the muon. At the one-loop level these particles unavoidably generate effects in the purely leptonic processes like $Z\to\ell^{+}\ell^{-}$, $Z\toν\barν$, $W\to\ellν$ and $h\to\ell^{+}\ell^{-}$ and can even generate non-zero rates for lepton flavor violating processes such as $\ell\to \ell^{\prime}γ$, $Z\to\ell^+\ell^{\prime -}$, $h\to\ell^+\ell^{\prime -}$ and $\ell\to 3\ell^\prime$. In this article we calculate these processes for all five representations of scalar Leptoquarks. We include their most general interaction terms with the Standard Model Higgs boson, which leads to Leptoquark mixing after the former acquires a vacuum expectation value. In our phenomenological analysis we investigate the effects in modified lepton couplings to electroweak gauge bosons, we study the correlations of the anomalous magnetic moment of the muon with $h\toμ^{+}μ^{-}$ and $Z\toμ^{+}μ^{-}$ as well as the interplay between different lepton flavor violating decays.

hep-ph↗
arXiv2019

Exact NLO Matching and Analyticity in $b\to s\ell\ell$

Exclusive rare decays mediated by $b\to s\ell\ell$ transitions receive contributions from four-quark operators that cannot be naively expressed in terms of local form factors. Instead, one needs to calculate a matrix element of a bilocal operator. In certain kinematic regions, this bilocal operator obeys some type of Operator Product Expansion, with coefficients that can be calculated in perturbation theory. We review the formalism and, focusing on the dominant SM operators ${\cal O}_{1,2}$, we perform an improved calculation of the NLO matching for the leading dimension-three operators. This calculation is performed completely analytically in the two relevant mass scales (charm-quark mass $m_c$ and dilepton squared mass $q^2$), and we pay particular attention to the analytic continuation in the complex $q^2$ plane. This allows for the first time to study the analytic structure of the non-local form factors at NLO, and to calculate the OPE coefficients far below $q^2=0$, say $q^2 \lesssim -10\,{\rm GeV}^2$. We also provide explicitly the contributions proportional to different charge factors, which obey separate dispersion relations.

hep-ph↗
arXiv2019

Importance of Loop Effects in Explaining the Accumulated Evidence for New Physics in B Decays with a Vector Leptoquark

In recent years experiments revealed intriguing hints for new physics (NP) in $B$ decays involving \bctaunu and $b\to s\ell^+\ell^-$ transitions at the $4\,σ$ and $5\,σ$ level, respectively. In addition, there are slight disagreements in $b\to u τν$ and $b\to dμ^+μ^-$ observables. While not significant on their own, they point in the same direction. Furthermore, $V_{us}$ extracted from $τ$ decays shows a slight tension ($\approx2.5\,σ$) with its value determined from CKM unitarity. Additionally, BELLE found hints for an excess in $B_d\toτ^+τ^-$. Concerning NP explanations, the vector leptoquark $SU(2)$ singlet is of special interest since it is the only single particle extension of the SM which can (in principle) address all the anomalies described above. For this purpose, large couplings to $τ$ leptons are necessary and loop effects, which we calculate in this article, become important. Including them in our phenomenological analysis, we find that neither the tension in $V_{us}$ nor the excess in $B_d\toτ^+τ^-$ can be fully explained without violating bounds from $K\toπν\barν$. However, one can account for $b\to cτν$ and $b\to uτν$ data finding intriguing correlations with $B_{q}\toτ^+τ^-$ and $K\to πν\barν$. Furthermore, the explanation of $b\to cτν$ predicts a positive shift in $C_7$ and a negative one in $C_9$, being nicely in agreement with the global fit to $b\to s\ell^+\ell^-$ data. Finally, we point out that one can fully account for \bctaunu and $b\to s\ell^+\ell^-$ without violating bounds from $τ\to ϕμ$, $Υ\toτμ$ or $b\to sτμ$ processes.

hep-ph↗
arXiv2018

QCD Improved Matching for Semi-Leptonic B Decays with Leptoquarks

Leptoquarks (LQs) provide very promising solutions to the tensions between the experimental measurements and the SM predictions of $b\to s\ell^+\ell^-$ and $b\to cτν$ processes. In this case the LQ masses are in general at the TeV scale and they can thus be produced at high energy colliders and dedicated LHC searches are ongoing. While for LQ production and decay the $O(α_s)$ corrections have been known for a long time, the $O(α_s)$ corrections to the matching on 2-quark-2-lepton operators have not been calculated, yet. In this article we close this gap by computing the QCD corrections to the matching of LQ models on the effective SM Lagrangian for both scalar and vector LQs. We find an enhancement of the Wilson coefficients of vector operators with respect to the tree-level results of around 8 % (13 %) if they originate from scalar (vector) LQs. This softens the LHC bounds and increases the allowed parameter space of LQ models addressing the flavour anomalies.

hep-ph↗
arXiv2018

Matching of gauge invariant dimension 6 operators for $b\to s$ and $b\to c$ transitions

New physics realized above the electroweak scale can be encoded in a model independent way in the Wilson coefficients of higher dimensional operators which are invariant under the Standard Model gauge group. In this article, we study the matching of the $SU(3)_C \times SU(2)_L \times U(1)_Y$ gauge invariant dim-6 operators on the standard $B$ physics Hamiltonian relevant for $b \to s$ and $b\to c$ transitions. The matching is performed at the electroweak scale (after spontaneous symmetry breaking) by integrating out the top quark, $W$, $Z$ and the Higgs particle. We first carry out the matching of the dim-6 operators that give a contribution at tree level to the low energy Hamiltonian. In a second step, we identify those gauge invariant operators that do not enter $b \to s$ transitions already at tree level, but can give relevant one-loop matching effects.

hep-ph↗
arXiv2018

B physics Beyond the Standard Model at One Loop: Complete Renormalization Group Evolution below the Electroweak Scale

General analyses of $B$-physics processes beyond the Standard Model require accounting for operator mixing in the renormalization-group evolution from the matching scale down to the typical scale of $B$ physics. For this purpose the anomalous dimensions of the full set of local dimension-six operators beyond the Standard Model are needed. We present here for the first time a complete and non-redundant set of dimension-six operators relevant for $B$-meson mixing and decay, together with the complete one-loop anomalous dimensions in QCD and QED. These results are an important step towards the automation of general New Physics analyses.

hep-ph↗
arXiv2017

The MSSM without Gluinos; an Effective Field Theory for the Stop Sector

In this article we study the MSSM with stops and Higgs scalars much lighter than gluinos and squarks of the first two generations. In this setup, one should use an effective field theory with partial supersymmetry in which the gluino and heavy squarks are integrated out in order to connect SUSY parameters (given at a high scale) to observables in the stop sector. In the construction of this effective theory, valid below the gluino mass scale, we take into account $O(α_3)$ and $O(Y_{t,b}^2)$ effects and calculate the matching as well as the renormalization group evolution. As a result, the running of the parameters for the stop sector is modified with respect to the full MSSM and SUSY relations between parameters are broken. We show that for some couplings sizable numerical differences exist between the effective field theory approach and the naive calculation based on the MSSM running.

hep-ph↗
arXiv2016

1-Loop Matching of gauge invariant dim-6 operators for B decays

Physics beyond the Standard Model, realized above the electroweak scale, can be incorporated in a model independent way in the Wilson coefficients of higher dimensional gauge invariant operators. In these proceedings we review the matching of the $SU(3)_C\times SU(2)_L\times U(1)_Y$ gauge invariant dimension-six operators on the effective Hamiltonian governing $b\to s$ and $b\to c$ transitions, including the leading 1-loop effects.

hep-ph↗
arXiv2014

1-loop SQCD corrections to the decay of top-squarks to charm and neutralino in the generic MSSM

In this article we calculate the 1-loop supersymmetric QCD (SQCD) corrections to the decay $\tilde u_1\to c \tildeχ^0_1$ in the MSSM with generic flavour structure. This decay mode is phenomenologically important if the mass difference between the lightest squark $\tilde u_1$ (which is assumed to be mainly stop-like) and the neutralino LSP $\tilde χ^0_1$ is smaller than the top mass. In such a scenario $\tilde u_1\to t \tildeχ^0_1$ is kinematically not allowed and searches for $\tilde u_1\to W b \tildeχ^0_1$ and $\tilde u_1\to c \tildeχ^0_1$ are performed. A large decay rate for $\tilde u_1\to c \tildeχ^0_1$ can weaken the LHC bounds from $\tilde u_1\to W b χ^0_1$ which are usually obtained under the assumption ${\rm Br}[\tilde u_1\to W b χ^0_1]=100\%$. We find the SQCD corrections enhance $Γ[\tilde u_1\to c \tildeχ^0_1]$ by approximately 10\% if the flavour-violation originates from bilinear terms. If flavour-violation originates from trilinear terms, the effect can be $\pm 50\%$ or more, depending on the sign of $A^t$. We note that connecting a theory of SUSY breaking to LHC observables, the shift from the $\overline{\rm DR}$ to the on-shell mass is numerically very important for light stop decays.

hep-ph↗
arXiv2013

Flavour-violation in two-Higgs-doublet models

In these proceedings we review the flavour phenomenology of 2HDMs with generic Yukawa structures. We first consider the quark sector and find that despite the stringent constraints from FCNC processes large effects in tauonic B decays are still possible. We then consider lepton flavour observables, show correlations between \mu -> e\gamma and \mu^- -> e^-e^+e^- in the 2HDM of type III and give upper bounds on the lepton flavour violating B decay B_d -> \mu e.

hep-ph↗
arXiv2013

Contributions of the W-boson propagator to muon and tau leptonic decay rates

We derive closed expressions and useful expansions for the contributions of the tree-level W-boson propagator to the the muon and tau leptonic decay rates. Calling M and m the masses of the initial and final charged leptons, our results in the limit m=0 are valid to all orders in M^2/M_W^2. In the terms of O(m_j^2/M_W^2) (m_j=M,m), our leading corrections, of O(M^2/M_W^2), agree with the canonical value (3/5) M^2/M_W^2, while the coefficient of our subleading contributions, of O(m^2/M_W^2), differs from that reported in the recent literature. A possible explanation of the discrepancy is presented. The numerical effect of the O(m_j^2/M_W^2) corrections is briefly discussed. A general expression, valid for arbitrary values of M_W, M and m in the range M_W>M>m, is given in the Appendix. The paper also contains a review of the traditional definition and evaluation of the Fermi constant.

hep-ph↗
arXiv2013

Two-loop SQCD corrections to Higgs-quark-quark couplings in the generic MSSM

In this article we compute the two-loop SQCD corrections to Higgs-quark-quark couplings in the generic MSSM generated by diagrams involving squarks and gluinos. We give analytic results for the two-loop contributions in the limit of vanishing external momenta for general SUSY masses valid in the MSSM with general flavour-structure. Working in the decoupling limit (M_SUSY >> v) we resum all chirally enhanced corrections (related to Higgs-quark-quark couplings) up to order α_s^(n+1) tan(β)^n. This resummation allows for a more precise determination of the Yukawa coupling and CKM elements of the MSSM superpotential necessary for the study of Yukawa coupling unification. The knowledge of the Yukawa couplings of the MSSM superpotential in addition allows us to derive the effective Higgs-quark-quark couplings entering FCNC processes. These effective vertices can in addition be used for the calculation of Higgs decays into quarks as long as M_SUSY > M_Higgs holds. Furthermore, our calculation is also necessary for consistently including the chirally enhanced self-energies contributions into the calculation of FCNC processes in the MSSM beyond leading order. At two-loop order, we find an enhancement of the SUSY threshold corrections, induced by the quark self-energies, of approximately 9% for μ=M_SUSY compared to the one-loop result. At the same time, the matching scale dependence of the effective Higgs-quark-quark couplings is significantly reduced.

hep-ph↗
arXiv2013

Flavor-phenomenology of two-Higgs-doublet models with generic Yukawa structure

We perform an extensive study of flavor observables in a 2HDM with generic Yukawa structure (the decoupling limit of the MSSM). We examine the effects in flavor physics and constrain the model both from tree-level processes and loop-observables. The free parameters of the model are the heavy Higgs mass, tan(β) and the "non-holomorphic" Yukawa couplings ε^f_ij (f=u,d,\ell). In our analysis we constrain the elements ε^f_ij in various ways: In a first step we give order of magnitude constraints on ε^f_ij from 't Hooft's naturalness criterion. Then we constrain the Yukawa structure of the type-III 2HDM from tree-level FCNC processes (B_s,d->μ^+μ^-, τ^-->μ^-μ^+μ^-, etc.) and observe that all flavor off-diagonal elements except ε^u_32,31 and ε^u_23,13 must be very small in order to satisfy the experimental bounds. In a third step, we consider Higgs mediated loop contributions to FCNC processes (b->s,dγ, μ->eγ, etc.) finding that also ε^u_13 and ε^u_23 must be very small, while the bounds on ε^u_31 and ε^u_32 are especially weak. Taking into account the constraints from FCNC processes we study the possible size of contributions from tree-level charged Higgs exchange. Interestingly, the unconstrained elements ε^u_{32,31} enter directly the branching ratios for B->τν, B->Dτνand B->D*τνand we show that the deviations from the SM predictions in these processes can be explained simultaneously. We give upper limits on the branching ratios of the lepton flavor-violating neutral B meson decays and correlate the radiative lepton decays to the corresponding neutral current lepton decays (τ^- ->μ^-μ^+μ^-, τ^- ->e^-μ^+μ^- and μ^- ->e^-e^+e^-). A detailed appendix contains all relevant information for the considered processes for general scalar-fermion-fermion couplings.

hep-ph↗
arXiv2012

Explaining B->Dτν, B->D*τνand B->τνin a 2HDM of type III

Recently, the BaBar collaboration reported first evidence for new physics in B->Dτνand B->D*τν. Combining both processes the significance is 3.4σ. This result cannot be explained in a two Higgs doublet model of type II. Furthermore, the CKMfitter group finds a 2.9σdiscrepancy between the Standard Model prediction for Br[B->τν] (using Vub from a global fit to the unitary triangle) and the measurements of the B factories. Altogether, these measurements are strong indications for physics beyond the SM in B meson decays to taus. We show that in a two Higgs doublet model of type III it is possible to simultaneously explain \bdtau and \bdstau using a single free parameter ε^u_32. Also Br[B->τν] can be brought into agreement with experiment using ε^u_31. Furthermore, for Higgs (A^0, H^0, H^+) masses around 500 GeV, as suggested by recent CMS results, all bounds from FCNC processes are satisfied and B->Dτν, B->D*τνand B->τνcan be explained without a significant degree of fine-tuning.

hep-ph↗
arXiv2011

Complete next-to-leading order gluino contributions to b--> s gamma and b--> s g

We present the first complete order alpha_s corrections to the Wilson coefficients (at the high scale) of the various versions of magnetic and chromomagnetic operators which are induced by a squark-gluino exchange. For this matching calculation, we work out the on-shell amplitudes b--> s gamma and b --> s g, both in the full and in the effective theory up to order alpha_s^2. The most difficult part of the calculation is the evaluation of the two-loop diagrams in the full theory; these can be split into two classes: a) diagrams with one gluino and a virtual gluon; b) diagrams with two gluinos or with one gluino and a four-squark vertex. Accordingly, the Wilson coefficients can be split into a part a) and a part b). While part b) of the Wilson coefficients is presented in this paper for the first time, part a) was given in (Bobeth et al.). We checked their results for the coefficients of the magnetic operators and found perfect agreement. Moreover, we work out the renormalization procedure in great detail. Our results for the complete next-to-leading order Wilson coefficients are fully analytic, but far too long to be printed. We therefore publish them in the form of a C++ program. They constitute a crucial building block for the phenomenological next-to-leading logarithmic analysis of the branching ratio Bbar --> X_s gamma in a supersymmetric model beyond minimal flavor violation.

hep-ph↗