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Magnetic Moment of Charmed Baryon Μλc BLEU du CAc 03/03/2017 _______________________________________________________________________________________________ ! I. Préambule général Ce « Bleu du CAc » présente une synthèse (QCM et questionnaire ouvert 1 menée par le Conseil Académique (CAc) auprès de la communauté (personnels MAGNETIC MOMENT OFpermanents , sous contrat et étudiants) sur les orientations (objectifs / structure / organisation) qui devraient prévaloir au sein de la future Université cible « Paris-Saclay ». Cette synthèse est découpée en six items majeurs qui, nt diverses recommandations. Elle constitue donc un socle de propositions solides issues réflexion collective de la communauté des personnels et usagers de Paris- CHARMED BARYON Saclay, sur lequel le « GT des sept » pourrait/devrait cette communauté autour des futures bases de université cible. Emi KOU (LAL) Présentation de : for charm g-2 collaborationenquête réalisée par le CAc du 15 décembre 2016 au 7 février 2017 comportait un questionnaire (informatique) S. Barsuk, O. Fomin, L. Henri, A. Korchin, M. Liul,en deuxE. Niel,parties : P. Robbe, A. Stocchi I. Based on arXiv:1812.#### mble des personnels. pas été partout le cas : le -Saclay la garantie de distribution des messages officiels du Conseil Académique à personnel. II. Une partie ouverte destinée à tout collectif (Conseil de Laboratoire, par exemple). Tau-Charm factory workshop, 3-6 DecemberLa synthèse 2018 présentée at ciLAL-dessous prend en compte ces deux . Analyse des réponses reçues : I. Partie QCM 2135 réponses dont 2021 complètes : 1. Nombre de réponses comparable au nombre des participants aux élections de 2015 au CA et au CAc. 2. ~33% des réponses proviennent des étudiants, avec un taux de participation plus fort pour les étudiants des Grandes Ecoles. 3. Bonne participation des chercheurs et enseignants chercheurs de rang A mais plus faible taux de réponses dans la catégorie B. 4. La plupart des réponses ont été analysées en fonction du profil des répondants. II. Partie ouverte : 1. 28 réponses reçues, 19 venant de es, moyennes et grosses), artie venant de collectifs représe(Conseil de département, Conseil ). 2. 1 https://indico.lal.in2p3.fr/event/3400/ 1/8 ̴MAGNETIC MOMENT OF ELEMENTARY PARTICLES LEPTON, PROTON AND QUARK • The spin 1/2 particle such as leptons (electron, muon…) have a magnetic moment of the form g e Q gelectron=2.00231930436182 ± (2.6×10−13) µ = | | 2 2m γ where Q and m are the charge and mass of the particle. µ γ µ • The g factor is 2 at the classic level while it is slightly modified by the quantum effect. This correction is called anomalous magnetic moment and defined as a=g-2/2. • There is a longstanding question of muon anomalous magnetic moment: the experiment is 3.6 sigma away from experiment (hint of exp. 11 new physics?) a� =116592091(54)(33) × 10− . 3.6σ effect! the. -11 a� =116591803(1)(42)(26) x 10 ̴MAGNETIC MOMENT OF ELEMENTARY PARTICLES LEPTON, PROTON AND QUARK • The spin 1/2 particle such as leptons (electron, muon…) have a magnetic moment of the form g e Q gelectron=2.00231930436182 ± (2.6×10−13) µ = | | 2 2m γ where Q and m are the charge and mass of the particle. µ γ µ • The g factor is 2 at the classic level while it is slightly modified by the quantum effect. This correction is called anomalous magnetic moment and defined as a=g-2/2. • There is a longstanding question of muon anomalous magnetic moment: the experiment is 3.6 sigma away from experiment (hint of exp. 11 new physics?) a� =116592091(54)(33) × 10− . 3.6σ effect! the. -11 a� =116591803(1)(42)(26) x 10 ̴MAGNETIC MOMENT OF ELEMENTARY PARTICLES LEPTON, PROTON AND QUARK • The proton magnetic moment is also measured very precisely. But how do we interpret this result? gproton=5.585694702(17) • If we consider the proton to be a fundamental particle, the γ magnetic moment can be written as g e p g p µ = P | | 2 2mP • g>>2 can be understood by a large strong interaction effect? • The proton is not a fundamental particle. So this may not be the solution… µM=|e|/2MP is called the nuclear magneton PROTON MAGNETIC MOMENT IN QUARK MODEL • In quark model, magnetic moment of proton is a sum of the magnetic moment of the constituent quark (up-up-down) with fully symmetric spin configuration. e M = M M = µ q σ Particles and Symmetriesq q CHAPTERq 5. QUARKSµ=|e|/2M AND HADRONSq q e X where q is the Oneconstituent may write this wavefunctionquark and more σ explicitly is the with spin the various operator terms multiplied out, proton = 2 u u d u u d u u d spin+flavor " " # # " " " # " +2⇥ u d u u d u u d u " # " # " " " " # +2d u u d u u d u u /p18 , (5.5.9) # " " " # " " " # (where we have also normalized the result). You can, and should, check⇤ that this does satisfy the • Then the magneticrequired moment condition of symmetry of proton under interchange is computed of spins and as flavors of any pair of quarks. Similar constructions can be performed for all the other members of the spin 1/2 baryon octet. µOnep notable= φP featureM ofu the+ setM ofu octet+ M baryons,d φP shown in Table 5.5 , is the presence of two di↵erent h | | i 0 baryons whose1 quark content is uds, specifically the ⇤ and the ⌃ . This is not inconsistent. When Similar to the previous three= distinct(4 flavors are3(2 involved,eu insteaded)+6 of just two,ed there)µ are more possibilities for constructing result but now, the a spin+flavor18 wavefunction⇥ with− the required symmetry.⇥ A careful examination (left as a problem) denominator is not proton shows that there aree two independent possibilities, completely consistent with the observed list of mass but quark mass! spin= 1/2µ baryons.= | | The mass values2 inm Tableq 5.5 show thatUsing for spin the 1/2 constituent baryons, just asquark for spin mass 3/2 baryons, baryons with strange quarks are heavier thanm thoseq=1/3 with m onlyP, we up andfind down gP=1.86! quarks; each substitution of a strange quark for an up or down raises the energy of the baryon by roughly 120–170 MeV. 5 5.6 Baryon number Baryon number, denoted B, is defined as the total number of baryons minus the number of an- tibaryons, similar to the definition (4.7.1) of lepton number L. Since baryons are bound states of three quarks, and antibaryons are bound states of three antiquarks, baryon number is the same as the number of quarks minus antiquarks, up to a factor of three, B = (# baryons) (# antibaryons) = 1 (# quarks) (# antiquarks) . (5.6.1) − 3 − All known interactions conserve baryon number.9 High⇥ energy scattering processes⇤ can change the number of baryons, and the number of antibaryons, but not the net baryon number. For example, in proton-proton scattering, the reaction p + p p + p + n +¯n can occur, but not p + p p + p + n + n. ! ! 5.7 Hadronic decays Turning to the decays of the various hadrons listed in Tables 5.3–5.6 , it is remarkable how much can be explained using a basic understanding of the quark content of the di↵erent hadrons together with considerations of energy and momentum conservation. As an example, consider the baryons in the spin 3/2 decuplet. The rest energy of the ∆ baryons is larger than that of a nucleon by nearly 300 MeV. This is more than the 140 MeV rest energy of pions, which are the lightest mesons. ⇡ Consequently, a ∆ baryon can decay to a nucleon plus a pion via strong interactions, which do not change the number of quarks minus antiquarks of each quark flavor. (Specifically, a ∆++ can decay 9This is not quite true. As with lepton number, the current theory of weak interactions predicts that there are processes which can change baryon number (while conserving B L). The rate of these processes is so small that baryon − number violation is (so far) completely unobservable. 9 PROTON MAGNETIC MOMENT IN QUARK MODEL • gP is now close to 2 but this result depends on the quark mass. • In addition, since it is known that the large portion of the proton spin is actually carried by the gluons, gluon contributions to the magnetic moment has to be considered. • On the other hand, the quark model can predict the relation of proton and neutron/Lambda magnetic moment without quark mass dependence 2 1 µN = µp,µ⇤ = µp −3 −3 gproton = 5.585694702(17) gneutron= - 3.82608545(90) glambda= - 1.226(8) which is satisfied well by the experiment. • In any case, the proton magnetic moment is an input for various theoretical computations, it is important to measure it very precisely. 6 CHARMED BARYON MAGNETIC MOMENT • An experimental proposal to measure charmed baryon magnetic moment by using precession induced by the VERY strong magnetic field generated by bent crystal (1000T). arXiv:1705.03382 • It will be the first direct measurement of the magnetic moment of the charmed baryon. • Different from light baryon, spin is known to be carried mostly by the heavy quark (charm quark) —> direct connection to the charm quark (anomalous) magnetic moment. • LHCb are producing many new results on charmed baryon (e.g. discovery of doubly charged charmed baryon!) and charmed baryon spectroscopy is becoming very interesting. 7 BARYON SPECTROSCOPY CHARMED BARYONS • Let us now include charm quark. SU(4) symmetry for 3 quark states 4 4 4 = 20 20 20 4 ⌦ ⌦ s ⊕ s ⊕ a ⊕ a • Considering charmed baryons, this results in 6 spin 3/2 baryons and 9 spin 1/2 baryons. • Different from the light baryons, not only Λc (udc) and Σc0 (udc), but also Ξc+ (udc) and Ξc0 (dsc) are no longer degenerated.
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