From general analyticity and unitarity requirements on the UV theory, positivity bounds on the Wilson coefficients of the dimension-8 operators composed of 4 fermions and two derivatives appearing in the Standard Model Effective Field Theory have been derived recently. We explore the fate of these bounds in the context of models endowed with a Minimal Flavor Violation (MFV) structure, models in which the flavor structure of higher dimensional operators is inherited from the one already contained in the Yukawa sector of the Standard Model Lagrangian. Our goal is to check whether the general positivity bounds translate onto bounds on the Yukawa coefficients and/or on elements of the CKM matrix. MFV fixes the coefficients of dimension-8 operators up to some multiplicative flavor-blind factors and we find that, in the most generic setup, the freedom left by those unspecified coefficients is enough as not to constrain the parameters of the renormalizable Yukawa sector. On the contrary, the latter shape the allowed region for the former. Requiring said overall coefficients to take natural $\mathcal{O}(1)$ values could give rise to bounds on the Yukawa couplings. Remarkably, at leading order in an expansion in powers of the Yukawa matrices, no bounds on the CKM entries can be retrieved.
The positivity bound for the transverse asymmetry $A_2$ may be improved and applied for each quark flavor separately. We use it to test the consistency of twist-two approximation for the transverse spin-dependent ($g_T$) and the longitudinal spin-averaged ($F_L$) structure functions. While it is satisfied in the case of $u$ quarks, it might be violated for $d$ quarks in a region of moderate $x$ because of its negative polarization. We attribute this inconsistency to a stronger twist-three contribution, whose existence found by the QCD sum rule method is a long-standing puzzle.
Both lattice simulations and theoretical studies show that the spectral function of the gluon propagator of QCD (in various gauges, as well as for the gauge-invariant Pinch Technique, or PT, propagator) is not non-negative everywhere, although it should be if it has a physical interpretation as in QED. Theory says moreover that the non-positive spectral function of the Landau-gauge or of the PT gluon propagator is further constrained to obey a superconvergence relation (the integral of the spectral function vanishes). We review the theoretical and lattice evidence for violation of positivity a…
We study the minimal flavor violation in the context of string effective field theory. Stringy selection rules indicate that $n$-point couplings among fermionic zero-modes and lightest scalar modes in the string effective action are given by a product of Yukawa couplings which are regarded as spurion fields of stringy and geometrical symmetries. Hence, Yukawa couplings determine the dynamics of flavor and CP violations. This observation strongly supports the hypothesis of minimal flavor violation in the Standard Model effective field theory.
We study the spontaneous $CP$ violation through the stabilization of the modulus $τ$ in modular invariant flavor models. The $CP$-invaraiant potentential has the minimum only at ${\rm Re}[τ] = 0$ or 1/2. From this prediction, we study $CP$ violation in modular invariant flavor models. The physical $CP$ phase is vanishing. The important point for the $CP$ conservation is the $T$ transformation in the modular symmetry. One needs the violation of $T$ symmetry to realize the spontaneous $CP$ violation.
We calculate the quark self-energy at one-loop level at high temperature, taking into account contributions from both the (chromo)electric scale $gT$ and the (chromo)magnetic scale $g^2T$. While reproducing standard massive excitations due to the electric scale, we uncover a novel massless excitation ascribable to the magnetic scale. The residue of this massless excitation is nonpositive at all temperatures, which consequently gives rise to positivity violation in the quark spectral functions. This demonstrates the profound impact of confinement effects on thermal quark collective excitations,…
We address several aspects of gluon propagation at zero and finite temperature. In particular, we study the violation of spectral positivity, we discuss a method to extract the Källén-Lehmann spectral density of a particle (be it elementary or bound state) propagator and apply it to compute gluon spectral densities from lattice data. Furthermore, we also consider the interpretation of the Landau gauge gluon propagator at finite temperature as a massive type bosonic propagator.
We investigate lepton flavor violation in the context of intersecting D-brane models. We point out that these models have a source to generate flavor violation in the trilinear scalar couplings while the geometry of the construction leads to degenerate soft scalar masses for different generations (as in the minimal supergravity model) at the string scale. The trilinear scalar couplings are not proportional to the Yukawa couplings when the F-term of the U-moduli contribution is non-zero. Consequently, the lepton flavor violating decay processes are generated. Only other sources of flavor violat…
As with parton distributions, flexible phenomenological parameterizations of generalized parton distributions (GPDs) are essential for their extraction from data. The large number of constraints imposed on GPDs make simple Lorentz covariant models viable; but, such models are often incomplete in that they employ the impulse approximation. Using the GPD of the pion as a test case, we show that the impulse approximation can lead to violation of the positivity bound required of GPDs. We focus on a particular model of the pion bound-state vertex that was recently proposed and demonstrate that sati…
Spectral positivity is known to be violated by some forms of lattice gauge fixing. The most notable example is lattice Landau gauge, where the effective gluon mass is observed to rise rather than fall with increasing distance. We trace this violation to the use of quenched auxiliary fields in the lattice gauge fixing process, and show that violation of spectral positivity is a general feature of quenching. We illustrate this with a simple quenched mass-mixing model in continuum field theory, and with a quenched form of the Ising model. For lattice gauge fixing associated with Abelian projectio…
We present explicit numerical evidence of reflection-positivity violation for the lattice Landau gluon propagator in three-dimensional pure SU(2) gauge theory. We use data obtained at very large lattice volumes (V = 80^3, 140^3) and for three different lattice couplings in the scaling region (beta = 4.2, 5.0, 6.0). In particular, we observe a clear oscillatory pattern in the real-space propagator C(t). We also verify that the (real-space) data show good scaling in the range t \in [0,3] fm and can be fitted using a Gribov-like form. The violation of positivity is in contradiction with a stable-…
We elaborate on previous results concerning the positivity of the Euclidean path integral measure for low-energy modes in dense fermionic matter. We show that the sign problem usually associated with fermions is absent if one considers only low-energy degrees of freedom. We describe a method for simulating dense QCD on the lattice and give a proof using rigorous inequalities that the color-flavor locked (CFL) phase is the true vacuum of three flavor, massless QCD. We also discuss applications to electronic systems in condensed matter, such as generalized Hubbard models.
We show there is a non-null probability to produce neutrinos of the ``wrong'' type in general decays, within the SM augmented by the known three massive neutrinos and nontrivial mixing. Such effect is equivalent to an intrinsic flavor violation (lepton flavor violation) at creation without requiring neutrino propagation. The exact amount of flavor violation depends on the neutrino flavor state to be detected. For realistic conditions, the violation is tiny but much larger than other indirect lepton flavor violation processes not involving neutrinos as final states. For neutrinos produced in a …
We show that in supersymmetric models with explicit flavor lepton number violation due to soft supersymmetry breaking terms there must be flavor lepton number violation in slepton decays. We propose to look for flavor lepton number violation in righthanded selectron and smuon decays. For selectron and smuon lighter than 80 Gev flavor lepton number violation in slepton decays could be discovered at LEP2 provided the mixing betwen selectron and smuon is not small. We also estimate NLC discovery potential of the lepton flavor number violation in slepton decays.
We extend the notion of Minimal Flavor Violation to the lepton sector. We introduce a symmetry principle which allows us to express lepton flavor violation in the charged lepton sector in terms of neutrino masses and mixing angles. We explore the dependence of the rates for flavor changing radiative charged lepton decays (ell(i) -> ell(j) + gamma) and mu-to-e conversion in nuclei on the scales for total lepton number violation, lepton flavor violation and the neutrino masses and mixing angles. Measurable rates are obtained when the scale for total lepton number violation is much larger than th…
We show that in supersymmetric models with explicit flavor lepton number violation due to soft supersymmetry breaking mass terms there could be detectable flavor lepton number violation in slepton decays. We estimate LHC discovery potential of the lepton flavor number violation in slepton decays.
In this paper we study flavor violation in supersymmetric models with gauged flavor symmetries. There are several sources of flavor violation in these theories. The dominant flavor violation is the tree-level $D$-term contribution to scalar masses generated by flavor symmetry breaking. We present a new approach for suppressing this phenomenologically dangerous effects by separating the flavor-breaking sector from supersymmetry-breaking one. The separation can be achieved in geometrical setups or in a dynamical way. We also point out that radiative corrections from the gauginos of gauged flavor…
Models of minimal lepton flavor violation where the seesaw scale is higher than the relevant flavor scale predict that all lepton flavor violation is proportional to the charged lepton Yukawa matrix. If extra vector-like leptons are within the reach of the LHC, it will be possible to test the resulting predictions in ATLAS/CMS.
A minimal flavour violation hypothesis for leptons can be implemented essentially in two ways that are compatible with a type-I seesaw structure with three heavy singlet neutrinos $N$, and that satisfy the requirement of being predictive, in the sense that all lepton flavor violating (LFV) effects can be expressed in terms of low energy observables. The first realization is CP conserving and is based on the flavor group $SU(3)_e\times SU(3)_\ell\times O(3)_N$ (being $e$ and $\ell$ the SU(2) singlet and doublet leptons). The second realization allows for CP violation and is based on $SU(3)_e\ti…
Minimal Flavor Violation in the up-type quark sector leads to particularly interesting phenomenology due to the interplay of flavor physics in the charm sector and collider physics from flavor changing processes in the top sector. We study the most general operators that can affect top quark properties and $D$ meson decays in this scenario, concentrating on two CP violating operators for detailed studies. The consequences of these effective operators on charm and top flavor changing processes are generically small, but can be enhanced if there exists a light flavor mediator that is a Standard …
We present a variant of the warped extra dimension, Randall-Sundrum (RS), framework which is based on five dimensional (5D) minimal flavor violation (MFV), in which the only sources of flavor breaking are two 5D anarchic Yukawa matrices. The Yukawa matrices also control the bulk masses, which are responsible for the resulting flavor structure and mass hierarchy in the low energy theory. An interesting result of this set-up is that at low energies the theory flows to next to MFV model where flavor violation is dominantly coming from the third generation. Low energy flavor violation is further s…
Theories of flavor violation beyond the Standard Model typically suppose that the new contributions must be small, for example suppressed by Yukawa couplings, as in Minimal Flavor Violation. We show that this need not be true, presenting a case for flavor violation which maximally mixes the first and third generation flavors. As an example, we realize this scenario via new right-handed gauge bosons, which couple predominantly to the combinations (u,b)_R and (t,d)_R. We show that this new flavor violation could be responsible for several anomalies, focusing in particular on the B_d and B_s syst…
Minimal Flavor Violation is an attractive approach to suppress unacceptably large flavor changing neutral currents from beyond the standard model physics at the TeV scale. It can be used in theories with low energy supersymmetry, multi Higgs doublet theories and other extensions of the minimal standard model. We show how minimal flavor violation can be implemented in Grand Unified theories.
We examine some flavor changing processes such as rare leptonic decays of the long-lived neutral kaon, muon-electron conversion in nuclei and radiative muon decay which are induced by the combined effects of bilinear and trilinear R-parity violations. These processes are used to put strong constraints on certain products of the bilinear and trilinear couplings. We also discuss the constraints on R-parity violation from neutrino masses and compare them with the constraints from flavor changing decay processes. Large range of parameter space satisfying the constraints from neutrino masses can be…
We show that new physics models without new flavor violating interactions can explain the recent anomalies in the $b\to s\ell^+\ell^-$ transitions. The $b\to s\ell^+\ell^-$ arises from a $Z'$ penguin which automatically predicts the $V-A$ structure for the quark currents in the effective operators. This framework can be realized either in a renormalizable $U(1)'$ setup or be due to new strongly interacting dynamics. The di-muon resonance searches at the LHC are becoming sensitive to this scenario since the $Z'$ is relatively light, and could well be discovered in future searches by ATLAS and C…
We present and discuss constraints on supersymmetric type I seesaw models imposed by neutrino data, charged lepton flavor violation and thermal leptogenesis.
The study for lepton flavor violation combined with the neutrino oscillation may provide more information about the lepton flavor structure of the grand unified theory. In this paper, we study two lepton flavor violation processes, $τ\to μγ$ and $Z\to τμ$, in the context of supersymmetric SO(10) grand unified models. We find the two processes are both of phenomenological interest. In particular the latter may be important in some supersymmetric parameter space where the former is suppressed. Thus, Z-dacay may offer another chance for looking for lepton flavor violation.
Recent results from Super Kamiokande suggest $ν_μ-ν_τ$ mixing and hence lepton flavor violation. In supersymmetric models, this flavor violation may have implications for the pattern of slepton masses and mixings. Possible signals for this mixing in the decays of sleptons produced at the LHC are discussed. The sensitivity expected is compared to that of rare decays such as $τ\to μγ$.
I review briefly the notion of minimal flavor violation and its application to supersymmetry, with a special emphasis on a class of operators, so-called Higgs penguins, which can generate new and interesting flavor signals at large tan(beta).
We consider the positivity bounds on dimension-8 four-electron operators and study two related phenomenological aspects at future lepton colliders. First, if positivity is violated, probing such violations will revolutionize our understanding of the fundamental pillars of quantum field theory and the $S$-matrix theory. We observe that positivity violation at scales of 1--10 TeV can potentially be probed at future lepton colliders even if one assumes that dimension-6 operators are also present. Second, the positive nature of the dimension-8 parameter space often allows us to either directly inf…
Lepton flavor violation in various sectors of the theory can bring important effects on neutrino masses and mixing through wave function renormalization. We examine general conditions for flavor structure of radiative corrections producing the atmospheric and solar neutrino mass splittings from degenerate mass patterns. Also obtained are the mixing angle relations consistent with the experimental results.
Supersymmetric theories generally have new flavor violation sources in the squark and slepton mass matrices. If significant lepton flavor violation exists, selectron and smuon should be nearly degenerate. This leads to the phenomenon of slepton oscillations, which is analogous to neutrino oscillations, if sleptons are produced at the Next Linear Collider. The direct slepton production at the Next Linear Collider provides a much more powerful probe of lepton flavor violation than the current bounds from rare processes, such as $μ\to eγ$.
Supersymmetric theories generally have new flavor and CP violation sources in the squark and slepton mass matrices. They will contribute to the lepton flavor violation processes, such as $μ\to e γ$, which can be probed far below the current bound with an intense muon source at the front end of the muon collider. In addition, if sleptons can be produced at the muon collider, the flavor violation can occur at their production and decay, allowing us to probe the flavor mixing structure directly. Asymmetry between numbers of $μ^+ e^-$ and $e^+ μ^-$ events will be a sign for CP violation in supersy…
It is shown that intrinsic neutrino flavor violation invariably occurs when neutrinos are created within the SM augmented by the known massive neutrinos, with mixing and nondegenerate masses. The effects are very small but much greater than the naive estimate $Δm^2/E_ν^2$ or the branching ratio of indirect flavor violating processes such as $μ\to eγ$ within the SM. We specifically calculate the probability (branching ratio) of pion decay processes with flavor violation, such as $π\to μ\barν_e$, showing nonzero results.
Heavy singlet neutrinos admit Majorana masses which are not possible for the Standard Model particles. This suggest new possibilities for generating the masses and mixing angles of light neutrinos. We present a model of neutrino physics which combines the source of lepton number violation with the flavor symmetry responsible for the hierarchy in the charged lepton and quark sector. This is accomplished by giving the scalar field effecting the lepton number violation a nonzero charge under the horizontal flavor symmetry. We find an economical model which is consistent with the measured values o…
The high-energy astrophysical neutrinos recently discovered by IceCube opened a new way to test Lorentz and CPT violation through the astrophysical neutrino mixing properties. The flavor ratio of astrophysical neutrinos is a very powerful tool to investigate tiny effects caused by Lorentz and CPT violation. There are 3 main findings; (1) current limits on Lorentz and CPT violation in neutrino sector are not tight and they allow for any flavor ratios, (2) however, the observable flavor ratio on the Earth is tied with the flavor ratio at production, this means we can test both the presence of ne…
Lepton flavor violation at linear collider experiments is discussed. We show that detectable lepton flavor violation could occur through scalar lepton pair production and decay in the supersymmetric SU(5) grand unified theory in spite of the stringent present experimental constraints by rare process searches. Possible cross sections about 40fb for an e+e- collider and 280fb for an e-e- collider are illustrated.
In a generic supersymmetric extension of the Standard Model, there will be lepton flavor violation at a neutral gaugino vertex due to misalignment between the lepton Yukawa couplings and the slepton soft masses. Sleptons produced at the LHC through the cascade decays of squarks and gluinos can give a sizable number of events with 4 leptons. This channel could give a clean signature of supersymmetric lepton flavor violation under conditions which are identified.
CP violation can be observed in B decays when a given process depends upon interference between two weak amplitudes which have different $CP$-violating phases. Since most weak decay diagrams have quark lines where each has a definite flavor label, neutral mesons which are flavor mixtures are particularly interesting. Different diagrams can contribute to the different flavor components of the meson, and the wave function itself provides interference.
Flavor mixing and the quark mass spectrum are intimately related. In view of the observed strong hierarchy of the quark and lepton masses and of the flavor mixing angles it is argued that the description of flavor mixing must take this into account. One particular interesting way to describe the flavor mixing emerges, which is particularly suited for models of quark mass matrices based on flavor symmetries. We conclude that the unitarity triangle important for $B$ physics should be close to or identical to a rectangular triangle. $CP$ violation is maximal in this sense.
The mixing between third and second (or first) generation squarks is very small in supersymmetric models with minimal flavor violation such as gauge-, anomaly- or gaugino-mediation. An opportunity to measure this mixing will arise if the lightest stop is close enough in mass to the lightest neutralino, so that the decays into third generation quarks are kinematically forbidden. We analyze under which circumstances it might become possible to measure at the Large Hadron Collider (LHC) the rate of the flavor changing stop decays.
If new physics is called upon to explain away fine tunings, like the hierarchy problem, then, we argue, the principle of Minimal Flavor Violation is inescapable. We review the principle and recent extensions to the lepton sector and to Grand-Unified theories.
I study many higgs doublet supersymmetric model with spontaneous CP violation. The damaging flavor changing interactions and large CP violation are brought under control simultaneously by an approximate PQ symmetry. I relate the smallness of the CP violating parameter in the kaon system to the small ${m_b \over m_t}$ ratio.
We discuss flavor charges and states for interacting mixed neutrinos in QFT. We show that the Pontecorvo states are not eigenstates of the flavor charges. This implies that their use in describing the flavor neutrinos produces a violation of lepton charge conservation in the production/detection vertices. The flavor states defined as eigenstates of the flavor charges give the correct representation of mixed neutrinos in charged current weak interaction processes.
Neutrino oscillation experiments suggest existence of new flavor-violating interactions in high energy scale. It may be possible to probe them by the flavor- and CP-violating processes in leptons and hadrons in the supersymmetric (SUSY) models. In this article the third-generation flavor violation is reviewed in the SUSY seesaw model and SUSY SU(5) GUT with the right-handed neutrinos.
Lepton flavor and CP violation in supersymmetric models are briefly reviewed. After a short motivation and an introduction to the phenomenology, model independent constraints on mass insertions, predictions of SUSY GUT models and rates for several LFV and CPV processes are presented.
Lectures on flavor physics presented at the 2012 CERN HEP Summer School. Content: 1) flavor physics within the Standard Model, 2) phenomenology of B and D decays, 3) flavor physics beyond the Standard Model.
Working within the context of the minimal supersymmetric standard model, we compare current bounds from quark flavor changing processes with current and upcoming bounds on lepton flavor violation. We assume supersymmetry breaking approximately respects CP invariance. Under the further assumption that flavor violating insertions in the quark and lepton scalar masses are comparable, we explore when lepton flavor violation provides the strongest probe of new physics. We quote results both for spectra with all superpartners near the TeV scale and where scalars are multi-TeV. Constraints from quark…
Models of extended gauge mediation, in which large A-terms arise through direct messenger-MSSM superpotential couplings, are well-motivated by the discovery of the 125 GeV Higgs. However, since these models are not necessarily MFV, the flavor constraints could be stringent. In this paper, we perform the first detailed and quantitative study of the flavor violation in these models. To facilitate our study, we introduce a new tool called FormFlavor for computing precision flavor observables in the general MSSM. We validate FormFlavor and our qualitative understanding of the flavor violation in t…
Lepton flavor violation may be a signature of "GUT scale" physics, if the messenger scale for SUSY breaking is above the "GUT scale." We elaborate on the details of this simple statement in the following talk.
We discuss the impact of fermion mass matrices on some lepton number violating processes, namely baryogenesis via leptogenesis and neutrinoless double beta decay, and on some lepton flavor violating processes, namely radiative lepton decays in supersymmetric seesaw models.
We discuss charged lepton flavor violation in supersymmetric models with extended leptonic sectors at low energies. Contrary to the usual high-scale realizations of the seesaw mechanism, these non-minimal supersymmetric models have new superfields and/or interactions at the supersymmetric scale. As a consequence of this, the resulting lepton flavor violating phenomenology may be very different from that of minimal models.
Two short introductory lectures on Flavor Physics delivered at CLASHEP 2015. Among included topics: The KM matrix and the KM model of CP-violation, Determination of KM Elements, FCNC and GIM, New Physics and Flavor, Neutral Meson Mixing and CP Asymmetries. Many problems for the student, and solutions to selected problems, included.
