In the standard model cp violation is related to the jarlskog invariant j, which can be obtained. Newest invarianttheory questions mathematics stack. Implications of maximal jarlskog invariant and maximal cp. Please note that some courses are not offered every year. January, 2012 abstract we present a new decomposition of unitary matrices particularly useful for mixing matrices. The most commonly used unitarity triangle arises from vud v. This is a problem about vacuum orbits in an su3 symmetric model, suggested by the penultimate. The breaking of the flavour permutational symmetry. This course introduces the fundamental elements of. Cpsymmetry, often called just cp, is the product of two symmetries. Brief history of flavor physics fermi theory of beta decay e.
Librivox free audiobook chris seits s podcast frecuencia clandestina bigg impact audio experience mickael haller podcast queer as fiction in the name of game a gaming podcast gaming nerds. Volume of the set of unistochastic matrices of order 3 and the mean jarlskog invariant charles dunkl1,a and karol zyczkowski2,b 1department of mathematics, university of virginia. Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on functions. Quark and lepton masses and mixing in the landscape. On the properties of the effective jarlskog invariant for threeflavor. Steven robertson canadian institute of particle physics mcgill university triumf summer institute vancouver b. This presnetation was give at dae symposium in high energy physics at benaras hindu university, varanasi in december 2008 by surender verma, one of my collaborators. Contour plots showing the dependence of jarlskog invariant j. If the only origin of cp violation is the lefthanded lh. Pdf some formulas for invariant phases of unitary matrices by. She is known for her work on cp violation in the electroweak sector of the standard model, introducing what is known as the jarlskog invariant, and for her work on. Pdf cpviolation phase analysis via nontrivial correlation of. Unitary mixing matrices and their parameterizations. The invariant of abiyevs balanced squares and balanced.
The courses are listed by the term in which they are usually offered. Jarlskog invariant and its mathematical origin physics stack. Theory of quark mixing matrix and invariant functions of mass matrices. Some formulas for invariant phases of unitary matrices by. Next, we investigate some formulas for invariant phases of unitary matrices and. This is a full list of courses offered by the department of physics. Simple factorization of the jarlskog invariant for. Index 843 breit frame, 696 breitwigner distribution, 462 brick wall frame, 696 brown muck, 760 brst invariance, 499502 bubbles feynman diagrams, 91.
Jarlskog invariant in turn, observables can only depend on the combination that is invariant under righthanded transformations the simplest cp odd quantity that does not depend on the flavor basis is the jarlskog determinant where j is a rephasing invariant combination of. These relations were proposed by georgi and jarlskog and are known as the gj relations. Nonzero jarlskog invariant impliesthat angles are not 0 or. The jarlskogs invariant the most important property of qaib j that follows from the unitarity of the ckm matrix is. Results for different assumptions concerning the analysis of data from reactor experiments are shown. Planck scale effects on neutrino mixing, we have derived the mixing angles of neutrino flavour due to planck scale effects. Donoghue, koushik dutta and andreas ross department of physics university of massachusetts amherst, ma 01003, usa february 2, 2008 abstract even if quark and lepton masses are. Cecilia jarlskog proposed this invariant already in 1973 and it was. Here is how a proof goes, if you can find an invariant that is in the initial state, and that this invariant persists regardless of any legal transformation applied to the state, then you can prove that if a certain state does not have this invariant then it can never occur, no matter what sequence of transformations are applied to the. It describes our latest reserach on the connection between weak basis.
Quark and lepton masses and mixing in the landscape john f. The decomposition separates the complex phase information from the mixing angle information of the matrices and leads to a new type of parameterization. Invariant approach to flavourdependent cpviolating. The origin of jarlskog invariant and applications sylwester kornowski abstract. However, one is free to rephase any unitary matrix without a. Next, we investigate some formulas for invariant phases of unitary matrices and derive some explicit relations for them. Cecilia jarlskog born in 1941 is a swedish theoretical physicist, working mainly on elementary particle physics jarlskog obtained her doctorate in 1970 in theoretical particle physics at the technical university of lund. In this paper, we show that the ratio of the effective jarlskog invariant j. Unitary mixing matrices and their parameterizations c.
Covariant extremisation of flavoursymmetric jarlskog. She is known for her work on cp violation in the electroweak sector of the standard model, introducing what is known as the jarlskog invariant, and for her work on grand. We describe a calculation of jarlskogs determinant in the case of n4 in detail. The invariant of abiyevs balanced squares and balanced cubes of odd order 1asker ali abiyev, 2yusif alizada 1institute of radiation problems of anas 9b vakhabzadeh street, baku, azerbaijan republic, az1143. We describe a calculation of jarlskogs determinant in the case of n 4 in detail. The jarlskog invariant 14, j, contains the dependence on the ckm elements. It has been shown that jarlskog determinant remains nearly invariant above the gut scale.
What is called the j jinvariant is an invariant of cubic curves and hence of elliptic curves, partly characterizing them. Matt has given a nice explanation for why one should care about the jinvariant up to a constant, but the precise form of the jinvariant has to do with its numbertheoretic properties and is not easy to explain in an introduction. Leptonic cp violation phases, quarklepton similarity and. Edm free supersymmetric cpviolation with nonuniversal soft terms 2000 nucl. C for charge conjugation, which transforms a particle into its antiparticle, and p for parity, which creates the mirror image of a physical system. Hilario perez ramirez rephasing invariant functions of the ckm matrix.
On the other hand books on elliptic curves dont want to give you the wrong definition. If omitted, invariant will throw regardless of the truthiness of the condition. Invariant approach to flavourdependent cpviolating phases in the mssm. Jarlskog didnt derive it constructively it was a clever guess, a convention were only looking for a quantity that is nonzero when it should be, and the exact value of such a quantity is clearly not unique and there is no canonical generalization of it to larger matrices. Fortunately, the number of free parameters can be greatly reduced by.
Algebraic structure of lepton and quark flavor invariants. Nowosci zaklad optyki atomowej, atomic optics department. The number of invariants of a given degree is encoded in the hilbert series. In our previous paper,4 we proposed a phenomenological formula, md ms mb. The strong interaction and electromagnetic interaction seem to be invariant under the combined cp transformation operation, but this symmetry is slightly. A mathematical model of the quark and lepton mixing angles 2011 update j. Cp odd weak basis invariants free download as powerpoint presentation. In this article we derive the conditions to have hermitian mass matrices which give maximal jarlskog invariant j and maximal cp violating phase phi. The jarlskog s invariant the most important property of qaib j that follows from the unitarity of the ckm matrix is. The normalization of reactor fluxes is left free and data from shortbaseline less than 100 m reactor experiments are included. Invariance of jarlskog determinant above the gut scale. Steven robertson canadian institute of particle physics. Fo example, in the parameterization of wolfenstein the jarlskogs in variant8 j. Implications of maximal jarlskog invariant and maximal cp violation.
In this letter we will show that extremisation of flavoursymmetric jarlskog invariants, leads naturally to jarlskogcovariant constraints. Abstract we explore generic features of the leptonic cp violation in the framework of the seesaw type i mechanism with similarity of the dirac lepton and quarks mass matrices m d. Pdf the existence and mysterious nature of sterile neutrinos are revolutionizing. Over the complex numbers the j jinvariant is a modular function on the upper half plane which serves to characterize most of the properties of the moduli stack of elliptic curves in this case. The results for the amount of cp violation in the lepton sector can be quantified with the jarlskog invariant j cp and the majorana invariants i 1 and i 2 34 see. The different size scales in nature and cp violation lead to very simple our precosmos with lefthanded polarization which has transformed into the lefthanded internal helicity of the baryons it solves the matterantimatter asymmetry. Full list of physics courses physics brown university. Theory of quark mixing matrix and invariant functions of. Rephasing invariants of quark and lepton mixing matrices. For this, we elaborate on the standard parametrization conditions which allow to simultaneously obtain the dirac and majorana phases. August 20, 2015, presusy 2015 abstract this is a set of latexed notes from cornell universitys physics 7661 special topics in theoretical high energy physics course by yuval grossman in fall 2010. This special feature of the jarlskog invariant j and the quark mixing matrix is a clear and precise indication that cp violating phase phi is maximal in order to let nature treat democratically. A mathematical model of the quark and lepton mixing angles.