results for au:Zwicky_R in:hep-ph

- Precision measurements of flavour observables provide powerful tests of many extensions of the Standard Model. This contribution covers a range of flavour measurements of $b\to s\ell^+\ell^-$ transitions, several of which are in tension with the Standard Model of particle physics, as well as their theoretical interpretation. The basics of the theoretical background are discussed before turning to the main question of the field: whether the anomalies can be explained by QCD effects or whether they may be indicators of effects beyond the Standard Model.
- We investigate a recently proposed UV-complete composite Higgs scenario in the light of the first LHC runs. The model is based on a SU(4) gauge group with global flavour symmetry breaking SU(5)$\to$ SO(5), giving rise to pseudo Nambu-Goldstone bosons in addition to the Higgs doublet. This includes a real and a complex electroweak triplet with exotic electric charges. Including these, as well as constraints on other exotic states, we show that LHC measurements are not yet sensitive enough to significantly constrain the model's low energy constants. The Higgs potential is described by two parameters which are on the one hand constrained by the LHC measurement of the Higgs mass and Higgs decay channels and on the other hand can be computed from correlation functions in the UV-complete theory. Hence to exclude the model at least one constant needs to be determined and to validate the Higgs potential both constants need to be reproduced by the UV-theory. Because the model is based on a UV-complete theory, the low energy constants can be computed from first principle numerical simulations of the theory formulated on a lattice, which can help in establishing the validity of this model. We assess the potential impact of lattice calculations for phenomenological studies, as a preliminary step towards Monte Carlo simulations.
- An important aspect of Weyl anomalies is that they encode information on the irreversibility of the renormalisation group flow. We consider, $\Delta \bar b = \bar{b}^{\textrm{UV}} - \bar{b}^{\textrm{IR}}$, the difference of the ultraviolet and infrared value of the $\Box R$-term of the Weyl anomaly. The quantity is related to the fourth moment of the trace of the energy momentum tensor correlator for theories which are conformal at both ends. Subtleties arise for non-conformal fixed points as might be the case for infrared fixed points with broken chiral symmetry. Provided that the moment converges, $\Delta \bar{b}$ is then automatically positive by unitarity. Written as an integral over the renormalisation scale, flow-independence follows since its integrand is a total derivative. Furthermore, using a momentum subtraction scheme (MOM) the 4D Zamolodchikov- metric is shown to be strictly positive beyond perturbation theory and equivalent to the metric of a conformal manifold at both ends of the flow. In this scheme $\bar{b}(\mu)$ can be extended outside the fixed point to a monotonically decreasing function. The ultraviolet finiteness of the fourth moment enables us to define a scheme for the $\delta {\cal L} \sim b_0 R^2$-term, for which the $R^2$-anomaly vanishes along the flow. In the MOM- and the $R^2$-scheme, $\bar{b}(\mu)$ is shown to satisfy a gradient flow type equation. We verify our findings in free field theories, higher derivative theories and extend $\Delta \bar{b}$ and the Euler flow $\Delta \beta_a$ for a Caswell-Banks-Zaks fixed point for QCD-like theories to next-to-next-to leading order using a recent $\langle G^2G^2 \rangle$-correlator computation.
- Several UV complete models of physics beyond the Standard Model are currently under scrutiny, their low-energy dynamics being compared with the experimental data from the LHC. Lattice simulations can play a role in these studies by providing a first principles computations of the low-energy constants that describe this low-energy dynamics. In this work, we study in detail a specific model recently proposed by Ferretti, and discuss the potential impact of lattice calculations.
- We consider ${\cal N}=1$ supersymmetric gauge theories in the conformal window. By applying a suitable matter superfield rescaling and a Weyl-transformation the renormalisation group running (matter and gauge field $Z$-factors) are absorbed into the metric. The latter becomes a function of the $Z$-factors. The Euler flow $\Delta a \equiv a_{\rm UV} - a_{\rm IR} |_{{\cal N}=1}$ is then obtained by free field theory computation with the non-trivial dynamics coming from expanding the Euler invariant in the flow dependent metric. The result is therefore directly obtained in terms of the infrared anomalous dimension confirming an earlier result using the matching of conserved currents.
- Two and three point functions of composite operators are analysed with regard to (logarithmically) divergent contact terms. Using the renormalisation group of dimensional regularisation it is established that the divergences are governed by the anomalous dimensions of the operators and the leading UV-behaviour of the $1/\epsilon$-coefficient. Explicit examples are given by the $<G^2G^2>$-, $<\Theta \Theta>$-trace of the energy momentum tensor) and $<\bar q q \bar q q>$- correlators in QCD-like theories. The former two are convergent when all orders are taken into account but divergent at each order in perturbation theory implying that the latter and the the $\epsilon \to 0$ limit do not generally commute. Finite correlation functions obey unsubtracted dispersion relations which is of importance when they are directly related to physical observables. As a byproduct the $R^2$-anomaly is extended to NNLO ($O(\alpha^5)$) using a recent $<G^2G^2>$-computation.
- 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.
- Jun 15 2015 hep-ph arXiv:1506.03970v3We generalise the Jacob-Wick helicity formalism, which applies to sequential decays, to effective field theories of rare decays of the type $B \to K_{J_K}(\to K \pi) \bar{\ell}_1 \ell_2$. This is achieved by reinterpreting local interaction vertices $\bar b \Gamma'_{\mu_1 ..\mu_n} s \bar \ell \Gamma^{\mu_1 ..\mu_n} \ell$ 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 $B \to K^*(\to K \pi) \bar{\ell}_1 \ell_2$ 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 $R_K = {\cal B}( B \to K \mu^+\mu^-) /{\cal B}( B \to K e^+e^-)$ as well as angular observables in $B \to K^* \mu^+\mu^-$.
- Mar 19 2015 hep-ph arXiv:1503.05534v3We present $B_q\to\rho$, $B_q\to\omega$, $B_q\to K^*$, $B_s\to K^*$ and $B_s\to \phi$ form factors from light-cone sum rules (LCSR) at $\mathcal{O}(\alpha_s)$ for twist-2 and 3 and $\mathcal{O}(\alpha_s^0)$ 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 $B_s\to \phi$. 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 $B\to K^*\gamma$ as well as $B\to K^*\ell^+\ell^-$ and $B_s\to\phi\mu^+\mu^-$ at low dilepton invariant mass. Employing our $B \to (\rho,\omega) $ form factor results we extract the CKM element $|V_\mathrm{ub}|$ from the semileptonic decays $B\to(\rho,\omega) \ell\nu$ and find good agreement with other exclusive determinations.
- Jun 04 2014 hep-ph arXiv:1406.0566v1We investigate the interference pattern of the charm-resonances $\Psi(3370,4040,4160,4415)$ with the electroweak penguin operator $O_9$ in the branching fraction of $B^+\to K^+\mu\mu$. 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.
- 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).
- 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 \emphexact 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 $B \to V \ell^+ \ell^-$, $V=K^*,\phi, \rho$ and $B \to V \ell \nu$, $V=\rho,D^*$ is straightforward. For hadronic modes of the types $B \to V p \bar p, V \Lambda \bar \Lambda, ..$ and $B \to V \pi \pi, V \pi K, .. $ endpoint relations apply as long as they are not overwhelmed by sizeable final state interactions between the $V$ and the hadron pair.
- We investigate helicity amplitudes (HAs) of $A \to B C$-type decays for arbitrary spin towards the kinematic endpoint. We show that they are proportional to product of Clebsch-Gordan coefficients (CGC) and the velocity to some positive power. The latter can be zero in which case the HA is non-vanishing at the endpoint. In essence the spatial rotational symmetry, broken by the relative spatial momenta of the particles, is restored at the kinematic endpoint. Therefore SO(3) and SU(2), for bosons and fermion in the decay, act like a global internal symmetry groups. Some of our results can be understood in terms of the Wigner- Eckart theorem. The findings are useful for i) checking theoretical computations and ii) the case where there is a sequence of decays, say $B \to B_1B_2$ with the pair $(B_1B_2)$ not interacting (significantly) with the $C$-particle. An example is $H \to Z Z^* \to 4\ell$ where our findings might be of use for experimentally determining the Higgs quantum numbers. Angular observables, which are essentially ratios of HAs, are given by ratios of CGC at the endpoint. We briefly discuss power corrections in the velocity to the leading order.
- Aug 21 2013 hep-ph arXiv:1308.4379v2Sufficient 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.
- 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 $\langle r_H^2 \rangle \sim m^{-2/(1+\gamma^*_m)}$ 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 $M_H \sim m^{1/(1+\gamma_m^*)}$ 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.
- 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.
- May 24 2013 hep-ph arXiv:1305.5332v1We 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.
- We compute the isospin asymmetries in $B \to (K^*,\rho) \gamma$ and $B\to (K,K^*,\rho) l^+l^-$ 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 $B \to (K,K^*,\rho) ll$, 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 $B \to \rho ll$ 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 $B \to \rho ll$ and $B \to K^*ll$ isospin asymmetries are structurally different yet the closeness of $\alpha_{\rm CKM}$ 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 ${\cal B}(B^0 \to K^{*0}\gamma)/{\cal B}(B_s \to \phi \gamma)$ which is sensitive to WA.
- Dec 12 2012 hep-ph arXiv:1212.2242v2We 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.
- A large CP-asymmetry $\Delta A_{\rm CP}$ has been reported in the $D^0 \to \pi^+\pi^-/K^+K^-$ system. At present it remains unclear whether this is due to incalculable strong interaction matrix elements or genuine new physics (NP). Amongst the latter a new weak phase in the chromomagnetic operator ${\cal O}_8$ has emerged as a promising candidate. Extending earlier ideas we show that the interference of long-distance (LD) terms with the ${\cal O}_8$ matrix element, which has a large strong phase, gives rise to direct CP-violation at the level of a few percent in $D^0 \to (\rho^0,\omega) \gamma$ and $D^+_{(d,s)} \to (\rho^+,K^{*+}) \gamma$ for reference values $ {\rm Im}[C_8^{NP}] \simeq 0.4 \cdot 10^{-2}$. This is two orders of magnitude above a Standard Model (SM) estimate. The contribution of $ {\rm Im}[C_7^{NP}]$, which is dependent on the model of NP, is governed by the LD strong phase which vanishes in the chiral limit at leading order. The question of whether this is significantly changed by radiative corrections is an open and interesting question that we discuss. Furthermore we point out that the relative size of left- and right-handed (photon polarisation)-LD amplitudes can be measured, in principle, through time-dependent CP (TDCP) asymmetries in the case where they are both sizeable which is supported by SM estimates. Thus determination of the latter provides interesting information on the LD-chirality independent of NP. We comment on the origin of the LD contribution, which we believe to be dominated by weak annihilation (WA), in the appendix.
- Oct 24 2012 hep-ph arXiv:1210.6239v2These are the proceedings of the 2nd Workshop on Flavor Symmetries and Consequences in Accelerators and Cosmology, held 30 June 2012 - 4 July 2012, Dortmund, Germany.
- 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 ∆(3n^2), ∆(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]-, ∆(3n^2)-, ∆(6n^2)-series and for all crystallographic groups \Sigma(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.
- 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 $gg \to h_0 h_0 \to \bar b b \gamma \gamma$ 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.
- 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^\eta_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 m̃^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.
- 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> ∼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+\gamma*)$ as a function of the mass anomalous dimension gamma* at the IRFP. The arguments can be generalized to other condensates such as <G^2> ~ 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.
- Oct 06 2009 hep-ph arXiv:0910.0823v1We investigate the consequences of replacing the continuous flavour symmetry of minimal flavour violation by a discrete group. Goldstone bosons, resulting from the breaking of the continuous flavour symmetry, generically lead to bounds on new flavour structure by many orders of magnitude above the TeV-scale. The absence of Goldstone bosons for discrete symmetries constitutes the primary motivation of our work. The four crystal-like groups Sigma(168), Sigma(72phi), Sigma(216phi) and Sigma(360phi)$ provide enough protection for a discrete TeV-scale MFV scenario in the case where Delta F = 2 processes are generated by two subsequent Delta F = 1 transitions.
- Aug 31 2009 hep-ph arXiv:0908.4182v4We 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 \emphprimary 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.
- Oct 16 2008 hep-ph arXiv:0810.2686v1We propose a generic framework in which the Higgs and the unparticle are both composite. The underlying theories are four dimensional, asymptotically free, nonsupersymmetric gauge theories with fermionic matter. We sketch a possible uni- fication of these two sectors at a much higher scale resembling extended technicolor models. By construction our extensions are natural, meaning that there is no hierar- chy problem. The coupling of the unparticle sector to the composite Higgs emerges as a four-fermion operator. The bilinear unparticle operator near the electroweak scale has scaling dimension in the range 1 < dU < 3. We investigate, in various ways, the breaking of scale invariance induced by the electroweak scale resulting in an unparticle condensate. The latter acts as a natural infrared cut off or hadronic scale. We give the low-energy effective theory valid near the electroweak scale. The unparticle Higgs mixing is found to be suppressed within our framework.
- Recently two hints for new physics have emerged: The B_s mixing phase phi_s and the rate of D_s -> (mu,tau) nu exposing a discrepancy of ∼3 sigma and 3.8 sigma deviation from the Standard Model respectively. Moreover the difference of the CP asymmetries in B -> K pi between the charged and neutral modes is at the 5.3 sigma level which is somewhat larger than expected. New physics in phi_s or A_CP(B -> K pi) would be in contradiction with the minimal flavour violation hypothesis. The latter has recently attracted attention because of the absence of deviation in CP and flavour violation in the quark sector.
- May 22 2008 hep-ph arXiv:0805.3296v3We investigate the electroweak precision constraints on the recently proposed Lee-Wick Standard Model at tree level. We analyze low energy, Z-pole (LEP1/SLC) and LEP2 data separately. We derive the exact tree level low energy and Z-pole effective Lagrangians from both the auxiliary field and higher derivative formulation of the theory. For the LEP2 data we use the fact that the Lee-Wick Standard Model belongs to the so-called 'universal class' which can be described by seven oblique parameters at leading order in m_W^2/M_1,2^2. At tree level we find that the only non-zero oblique parameters are Y = -m_W^2/M_1^2 and W = -m_W^2/M_2^2, where the negative sign is due to the presence of the negative norm states. The Lee-Wick operators do not violate the SU(2)_L or custodial symmetry at tree level implying S=0 and T=0 respectively. Our results differ substantially from a prior analysis in this respect. We show a plot including all three constraints. The LEP1/SLC constraints are slightly stronger than LEP2 and much stronger than the low energy ones. The LEP1/SLC results exclude gauge boson masses of M_1 ~ M_2 ~ 3 TeV at the 99% confidence level. Somewhat lower masses are possible when one of the masses assumes a large value. Loop corrections to the electroweak observables are suppressed by the standard ~1/(4 \pi)^2 factor and are therefore not expected to change the constraints on M_1 and M_2. This assertion is most transparent from the higher derivative formulation of the theory.
- Feb 08 2008 hep-ph arXiv:0802.0876v1The photon polarization in B -> V gamma is a sensitive probe of right-handed currents. In the time dependent decay rate of B_s -> phi gamma the coefficients S and H in front of the sin(Delta m_s t) and the sinh(Delta Gamma_s /2 t) terms are sensitive to those right-handed currents. As compared to the B_d system there is a sizable width difference in B_s mesons which leads to the additional measurable observable H. We show with a Monte Carlo simulation that the expected resolution on S and H will be about 0.15 at the LHCb experiment for Delta Gamma_s/Gamma_s = 0.15 and a data sample of 2 fb^-1. We also show that the observable H can be measured from the untagged decay rate of B_s mesons which has considerable experimental advantages as no flavour tag will be required. The resolution on H is inversely proportional to the B_s width difference Delta Gamma_s. These experimental prospects have to be compared with the Standard Model predictions S_phi gamma = 0 \pm 0.002 and H_phi \gamma = 0.047 \pm 0.025+0.015 presented in this paper. We also give the Standard Model prediction and the experimental sensitivity for the direct CP asymmetry in B_s -> phi gamma.
- With the advent of the LHC, we will be able to probe New Physics (NP) up to energy scales almost one order of magnitude larger than it has been possible with present accelerator facilities. While direct detection of new particles will be the main avenue to establish the presence of NP at the LHC, indirect searches will provide precious complementary information, since most probably it will not be possible to measure the full spectrum of new particles and their couplings through direct production. In particular, precision measurements and computations in the realm of flavour physics are expected to play a key role in constraining the unknown parameters of the Lagrangian of any NP model emerging from direct searches at the LHC. The aim of Working Group 2 was twofold: on one hand, to provide a coherent, up-to-date picture of the status of flavour physics before the start of the LHC; on the other hand, to initiate activities on the path towards integrating information on NP from high-pT and flavour data.
- Oct 25 2007 hep-ph arXiv:0710.4430v1We give a brief summary of the unparticle scenario proposed by Georgi. The CP-even phase of the propagator is exploited to study the CP-asymmetry in B+ --> tau+ + nu, which is neither experimentally searched for nor predicted by any other model. Furthermore we show that the novel CP-violation is consistent with the CPT theorem by identifying the CP-compensating mode in the unparticle sector.
- Sep 27 2007 hep-ph arXiv:0709.4054v4The process gg -> h_0 -> gamma gamma is studied in the Lee-Wick extension of the Standard Model (LWSM) proposed by Grinstein, O'Connell and Wise. In this model negative norm partners for each SM field are introduced with the aim to cancel quadratic divergences in the Higgs mass. All sectors of the model relevant to gg -> h_0 -> gamma gamma are diagonalized and results are commented on from the perspective of both the Lee-Wick and higher derivative formalisms. Deviations from the SM rate for gg -> h_0 are found to be of the order of 15% - 5% for Lee-Wick masses in the range 500GeV - 1000GeV. Effects on the rate for h_0-> gamma gamma are smaller, of the order of 5% - 1% for Lee-Wick masses in the same range. These comparatively small changes may well provide a means of distinguishing the LWSM from other models such as universal extra dimensions where same-spin partners to Standard Model fields also appear. Corrections to determinations of CKM elements |V_t(b,s,d)| are also considered and are shown to be positive, allowing the possibility of measuring a CKM element larger than unity, a characteristic signature of the ghost-like nature of the Lee-Wick fields.
- Jul 05 2007 hep-ph arXiv:0707.0677v1Coupling the scale invariant unparticle sector to flavour physics and assuming that it remains scale invariant we investigate its consequences in heavy flavour physics. A drastic feature of unparticle physics is an unusual phase leading to novel CP violating phenomena. We consider the CP asymmetry in the leptonic decay B^+ -> tau^+ nu and the hadronic decay B_d -> D^+D^-, taking into account constraints of branching ratios and time dependent CP asymmetries. Generic plots are shown and it turns out that there exist parameters for which the CP violation is maximal. A prediction of a large CP asymmetry in B_d -> D^+D^- is difficult to achieve in other models without contradicting the current data in other channels. The prediction of a CP asymmetry in leptonic decays, such as B^+ -> tau^+ nu, is novel. We identify the CP compensating mode due to the unparticles and show explicitly that it exactly cancels the CP asymmetry of B^+ -> tau^+ nu as demanded by CPT invariance. Building up on earlier works we investigate the breaking of scale invaricance, due to the coupling to the Higgs and the size of the effects in the weak sector resorting to a dimensional analysis. An enhancement is observed on the grounds of the relevance of the unparticle interaction operator as compared to the weak four-Fermi term.
- Dec 08 2006 hep-ph arXiv:hep-ph/0612081v3We calculate the main observables in $B_{u,d}\to (\rho,\omega,K^*)\gamma$ and $B_s\to (\bar K^*,\phi)\gamma$ decays, i.e. branching ratios and CP and isospin asymmetries. We include QCD factorisation results and also the dominant contributions beyond QCD factorisation, namely long-distance photon emission and soft-gluon emission from quark loops. All contributions beyond QCD factorisation are estimated from light-cone sum rules. We devise in particular a method for calculating soft-gluon emission, building on earlier ideas developed for analogous contributions in non-leptonic decays. Our results are relevant for new-physics searches at the $B$ factories, the LHC and a future super-flavour factory. Using current experimental data, we also extract $|V_{td}/V_{ts}|$ and the angle $\gamma$ of the unitarity triangle. We give detailed tables of theoretical uncertainties of the relevant quantities which facilitates future determinations of these CKM parameters from updated experimental results.
- We calculate the dominant Standard Model contributions to the time-dependent CP asymmetry in B0->K*0 gamma, which is O(1/mb) in QCD factorisation. We find that, including all relevant hadronic effects, in particular from soft gluons, the asymmetry S is very small, S=-0.022\pm 0.015^+0_-0.01, and smaller than suggested recently from dimensional arguments in a 1/mb expansion. Our result implies that any significant deviation of the asymmetry from zero, and in particular a confirmation of the current experimental central value, S_HFAG=-0.28\pm 0.26, would constitute a clean signal for new physics.
- Aug 02 2006 hep-ph arXiv:hep-ph/0608009v2We determine |V_\rm td/V_\rm ts| = 0.192 \pm 0.016_ exp \pm 0.014_th from B -> (K^*,rho) gamma as measured by the B-factories Babar and Belle. This version differs from the original proceedings by the inclusion of the new BaBar measurement of B -> rho(omega) gamma presented at ICHEP 2006, which significantly shifts the results for |V_td/V_ts|.
- The dominant theoretical uncertainty in extracting |V_td/V_ts| from the ratio of branching ratios R=B(B->(rho,omega)gamma)/B(B->K* gamma) is given by the ratio of form factors xi=T_1^B->K*(0)/T_1^B->rho(0). We re-examine xi in the framework of QCD sum rules on the light-cone, taking into account hitherto neglected SU(3)-breaking effects. We find xi=1.17 \pm 0.09. Using QCD factorisation for the branching ratios, and the current experimental average for R quoted by HFAG, this translates into |V_td/V_ts|^HFAG_B->V gamma = 0.192 \pm 0.014(th) \pm 0.016(exp). This result agrees, within errors, with that obtained from the Standard Model unitarity triangle, |V_td/V_ts|_SM = 0.216 \pm 0.029, based on tree-level-only processes, and with |V_td/V_ts|_Delta m = 0.2060^+0.0081_-0.0060(th) \pm 0.0007(exp), from the CDF measurement of B_s oscillations.
- Jan 12 2006 hep-ph arXiv:hep-ph/0601086v1We derive constraints on the asymmetry a1 of the momentum fractions carried by quark and antiquark in K and K* mesons in leading twist. These constraints follow from exact operator identities and relate a1 to SU(3) breaking quark-antiquark-gluon matrix elements which we determine from QCD sum rules. Comparing our results to determinations of a1 from QCD sum rules based on correlation functions of quark currents, we find that, for a1^∥(K*) the central values agree well and come with moderate errors, whereas for a1(K) and a1^\perp(K*) the results from operator relations are consistent with those from quark current sum rules, but come with larger uncertainties. The consistency of results confirms that the QCD sum rule method is indeed suitable for the calculation of a1. We conclude that the presently most accurate predictions for a1 come from the direct determination from QCD sum rules based on correlation functions of quark currents and are given by: a1(K) = 0.06\pm 0.03, a1^∥(K*) = 0.03\pm 0.02, a1^\perp(K*) = 0.04\pm 0.03.
- Nov 15 2005 hep-ph arXiv:hep-ph/0511158v2We address the nonperturbative effects associated with soft charm quarks in inclusive B decays. Such corrections are allowed by the OPE, but have largely escaped attention so far. The related four-quark `double heavy' expectation values of the form <B|\barbc \barcb|B> are computed in the 1/m_c expansion by integrating out the charm field to one and two loops. A significant enhancement of the two-loop coefficients has been noted. A method is suggested for evaluating the expectation values of the higher-order b-quark operators required to calculate charm expectation values, free from the overly large ambiguities of dimensional analyses. The soft-charm effects were found generally at the level of 0.5% in \Gamma_sl(b->c); however, as a result of cancellations the net impact should be smaller. We propose a direct way to search for such effects in the data. Finally, we discuss the relation of the soft charm corrections in inclusive decays with the `Intrinsic Charm' ansatz.
- Oct 27 2005 hep-ph arXiv:hep-ph/0510338v1We review the status of the leptonic decay constants f_K and f_K^∥,\perp of the K and K*, respectively, and the SU(3) breaking quantities a_1(K) and a_1^∥,\perp(K*), the first Gegenbauer-moments of the leading-twist distribution amplitudes of K and K*. We obtain new predictions from QCD sum rules which are relevant for the calculation of K and K* form factors, for instance T_1^B->K*, which determines the decay B -> K* gamma, and for QCD factorisation calculations of nonleptonic B decays into strange mesons, for instance B -> K pi.
- Jul 07 2005 hep-ph arXiv:hep-ph/0507076v1Using new experimental data on the leptonic mass spectrum of B->pi l nu, we simultaneously determine |V_ub| and constrain a_2^pi and a_4^pi, the first two Gegenbauer moments of the pion's leading-twist distribution amplitude. We find |V_ub| = (3.2\pm 0.1\pm 0.1\pm 0.3) 10^-3, where the first error is experimental, the second comes from the shape of the form factor in q^2 and the third is a 8% uncertainty from the normalisation of the form factor. We also find a_2^pi(1 GeV)=0.19\pm 0.19 and a_4^pi(1 GeV)≥-0.07.
- Dec 07 2004 hep-ph arXiv:hep-ph/0412079v1We present an improved calculation of $B\to$ light vector form factors from light-cone sum rules, including one-loop radiative corrections to twist-2 and twist-3 contributions, and leading order twist-4 corrections. The total theoretical uncertainty of our results at zero momentum transfer is typically 10% and can be improved, at least in part, by reducing the uncertainty of hadronic input parameters. We present our results in a way which details the dependence of the form factors on these parameters and facilitates the incorporation of future updates of their values from e.g. lattice calculations. We also give simple and easy-to-inplement parametrizations of the $q^2$-dependence of the form factors which are valid in the full kinematical regime of $q^2$.
- Jun 24 2004 hep-ph arXiv:hep-ph/0406261v1We present an improved calculation of all B -> light pseudoscalar formfactors from light-cone sum rules, including one-loop radiative corrections to twist-2 and twist-3 contributions, and leading order twist-4 corrections. The total theoretical uncertainty of our results at zero momentum transfer is 10 to 13%. The dependence of the formfactors on the momentum transfer q^2 is parametrized in a simple way that is consistent with their analytical properties and is valid for all physical q^2. The uncertainty of the extrapolation in q^2 on the semileptonic decay rate Gamma(B -> pi e nu) is estimated to be 5%.
- Jun 22 2004 hep-ph arXiv:hep-ph/0406232v1We present an improved calculation of $B\to$ light pseudoscalar formfactors from light-cone sum rules, including one-loop radiative corrections to twist-2 and twist-3 contributions, and leading order twist-4 corrections. The total theoretical uncertainty of our results at zero momentum transfer is 10 to 13% and can be improved, at least in part, by reducing the uncertainty of hadronic input parameters, in particular those describing the twist-2 distribution amplitudes of the pi, K and eta. We present our results in a way which details the dependence of the formfactors on these parameters and facilitates the incorporation of future updates of their values from e.g. lattice calculations.
- Oct 10 2001 hep-ph arXiv:hep-ph/0110115v1We present a new calculation of the B->pi form-factor f_+, relevant for the measurement of |V_ub| from semileptonic B->pi transitions, from QCD sum rules on the light-cone. The new element is the calculation of radiative corrections to next-to-leading twist-3 accuracy. We find that these contributions are factorizable at O(alpha_s), which lends additional support to the method of QCD sum rules on the light-cone. We obtain f_+(0) = 0.26\pm 0.06 \pm 0.05, where the first error accounts for the uncertainty in the input-parameters and the second is a guesstimate of the systematic uncertainty induced by the approximations inherent in the method. We also obtain a simple parametrization of the form-factor which is valid in the entire kinematical range of semileptonic decays and consistent with vector-meson dominance at large momentum-transfer.