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 collaboration enquête 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/
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̴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
where Q and m are the charge and mass of the particle. µ 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
where Q and m are the charge and mass of the particle. µ 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 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 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= P featureM ofu the+ setM ofu octet+ M baryons,d P 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. • The new names are NOT given to these particles but to distinguish them, ’ it is sometimes called (Ξc1, Ξc2) or (Ξc, Ξc ).
J=3/2 J=1/2 totally-symmetric mixed-symmetry decuplet octet
8 Feasibility of measuring the magnetic dipole moments of the charm baryons at the LHC using bent crystals
1, 2, 3, 2, 3, 1, 4 1 2, 3 A.S. Fomin, ⇤ A.Yu. Korchin, † A. Stocchi, ‡ O.A. Bezshyyko, L. Burmistrov, S.P. Fomin, I.V. Kirillin,2, 3 L. Massacrier,5 A. Natochii,4, 1 P. Robbe,1 W. Scandale,1, 6, 7 and N.F. Shul’ga2, 3 1LAL (Laboratoire de l’Acc´el´erateur Lin´eaire), Universit´eParis-Sud/IN2P3, Orsay, France 2NSC Kharkiv Institute of Physics and Technology, 61108 Kharkiv, Ukraine 3V.N. Karazin Kharkiv National University, 61022 Kharkiv, Ukraine 4Taras Shevchenko National University of Kyiv, 01601 Kyiv, Ukraine 5IPNO (Institut de Physique Nucl´eaire),Λ Universit´eParis-Sud/IN2P3,C MAGNETIC MOMENT Orsay, France 6CERN, European Organization for Nuclear Research, CH-1211 Geneva 23, Switzerland 7INFN Sezione• We dicompute Roma, Piazzale the Λc Aldo (udc, Moro spin 2, anti-symmetric 00185 Rome, Italy state) magnetic moment in the quark(Dated: model. May The 9, result 2017) turns out that Λc magnetic moment is equal to In this paper we revisit thethe idea charm of measuring quark magnetic the magnetic moment. dipole moments of the charm baryons and, in particular, of ⇤+ by studying the spin precession induced by the strong e↵ective magnetic c µ⇤ = ⇤ Mu + Md + Mc ⇤ field inside the channels of a bent crystal. We presentc h ac detailed| sensitivity study| showingc i the feasibility of such an experiment at the LHC in the= comingµc years. PACS numbers: 13.30.Eg,• 13.40.Em,Using 13.88+e,the definition 14.20.Lq, 61.85.+p
g⇤c e Qc gc e Qc µ⇤c = | | = µc = | | I. INTRODUCTION µN 2 e~2/m(2Pmpc)[1], where2mp2misc the proton mass and e ✓is the⌘ elementary◆ charge.✓ ◆ the measurement of g /2 can be translated to the charm quark magnetic The magnetic dipole moment (MDM) of a particle is ΛItc would be very important to measure the MDM of + + moment gc/2 the charm baryons ⇤ (udc) and ⌅ (usc), which have not its fundamental characteristic that determines the torque g⇤c m⇤c cgc c which particle experiences in an external magnetic field. been measured= so far because of their very short lifetime 2 mc13 2 The MDMs of many particles are presently known [1]. of the order of 10 s. For electron the QED prediction agrees• If the with measured experimen- gΛc/2 isThere far from has been mΛc/m manyc~1.3-1.9 calculations (mc=1.2-1.8GeV) of the MDM then, of the tally measured value up to very high precision. For muon charm baryons in various models of their structure [5– that is an indication of large anomalous+ magnetic moment of charm quark. the measurement of the BNL E821 experiment [2]dis- 21]. As for the ⇤c baryon, majority of the calculations agrees with the Standard Model prediction• Nevertheless, by 3–4 stan- the quantitativepredict the statement MDM and g is-factor model-dependent. in the ranges dard deviations, which may suggest physics beyond the + µ(⇤c ) + Standard Model. The disagreement for the muon g 2 =0.37–0.42,g(⇤c )=1.80–2.05. (2) µN is the subject of many studies (see, e.g.,review[3]). The 9 MDM of the ⌧-lepton has not been measured so far and is Thus, an experimental study of the MDM of heavy of great interest for testing calculations in the Standard baryons can be useful to distinguish between di↵erent Model [4]. theoretical approaches. For hadrons, the MDMs are measured for the baryon One of the motivations for measurement of the MDM + of the heavy baryons is also studying the MDM of the octet with J P = 1 . Historically, reasonable agree- 2 charm quark. If this quark behaves as a point-like Dirac ment between the measured MDM and predictions of particle, then the corresponding gyromagnetic factor g the quark model was important to substantiate the con- c is equal or close to 2, while if the charm quark has a stituent quark models of the hadrons. composite structure we can expect a sizable deviation In general, the MDM of the spin- 1 particle is expressed 2 from this value. as In the quark model the MDM of the heavy baryon is expressed in terms of the MDMs of the heavy and light 2µ ~ q~ g µ~ = S, µ = , (1) quarks. In particular, for the charm baryons, the spin ~ 2mc 2 + and flavor structure of the ground-state baryons ⇤c and + ~ ~ ⌅ implies that (see, e.g.,Ref.[5]) where S = 2 ~ , m is the particle mass, q is the c arXiv:1705.03382v4 [hep-ph] 31 Aug 2017 particle electric charge, g is the gyromagnetic factor. 1 µ(⇤+)=µ ,µ(⌅+)= (2µ +2µ µ ) . (3) The value g = 2 corresponds to a Dirac particle with- c c c 3 u s c out magnetic moment anomaly. Usually, the MDM of MDMs in Eqs. (3) depend on the MDM of the charm baryons is measured in units of the nuclear magneton + quark. Let us consider ⇤c and take “e↵ective” mass of the c-quark mc =1.6 GeV as suggested from the char- monia spectroscopy [5]. Keeping explicitly the g-factor of the charm quark we can write ⇤ [email protected] [email protected] + † µ(⇤c ) gc + gc ‡ [email protected] =0.39 ,g(⇤c )=1.91 . (4) µN 2 2 Thus, the ratio of the proton and the neutron magnetic moments is quark mass free µ /µ = 3/2, which can be compared to the experimental value 1.460 ,inavery P N ··· good agreement. Although these results are very convincing, since it is known that the proton spin is actually carried mostly by the gluons, the relation between proton magnetic moment and the quark magnetic moment might be more complex. At least, such a problem can be avoided in the case of heavy baryons: at the infinite mass limit, the heavy baryon spin is carried by the heavy quark. Nevertheless, the quark mass dependence would remain and the certain uncertainty is unavoidable. Let us first see the the magnetic moment of ⇤c in the naive quark model: e µ 2 mP µ⇤c = µc = | | = µM (12) 3mc 3 mc If we choose the charm quark mass as the ”constituent quark mass“, i.e. m = m c ⇤c 2mq(1/3 GeV) = 1.7 GeV, we find µ⇤c =0.39 n.m.. This value is higher than the value found by BESIII in Eq. (). However, if we use the constituent quark mass obtained from charmonium, e.g. from J/ , mc = mJ/ /2=1.5 GeV, we find µ⇤c =0.44 n.m.,whichis closer to the value in Eq. (). One can also derive the charm quark mass independent relation with di↵erent charmed baryons. It turned out that the other two triplet (spin 1/2, anti-symmetric) charmed 0 + baryon, ⌅c and ⌅c have the same magnetic moment in the quark model: OTHER CHARMED BARYON MAGNETIC MOMENT µ 0,+ = µc = µ⇤ (13) ⌅c c • Spin anti-symmetric state ~0.39N.M. 0,+ µ 0,+ = µ Thus, if a measurement of the magnetic moment of ⌅c⌅c can playc an important role to test the quark model description.which is the same as Λc magnetic moment Corrections to the relation For the sextet (spin 1/2, symmetric) charmed baryons, the situation is verySavage di↵ eterent. al PLB326 (’94) radiatively to the former. Whether these observed two states (massBanuls et eigenstates) al PRD61 (‘00) are the We can find: pure anti-symmetric• Spin symmetric and symmetric state states (flavour eigenstate) is not known though it can1 o↵er an4 excellent test of1 the heavy2 quark2 limit. In the1 following,4 we show that the µ ++ = µc + µu,µ+ = µc + µu + µd,µ⌃0 = µc + µd (14) ⌃c magnetic 3 moment3 measurement,⌃c 3 which3 are3 the mostc sensitive 3 to3 the flavour symmetry of the constituent quarks, can be used to answer this question. which leads to the value (with mc = m⌃ 2mq(1/3 GeV) = 1.8 GeV) µ ++ =2.54 n.m., Let us compute the magneticc moment of@SU(3) another limit sextet (spin⌃c 1/2, symmetric) charmed +,0 ~0.54N.M. ~—1.46N.M. µ + =0.54 n.m., µ⌃0 = 1.46 n.m. Even though this numericalµ c=µ c’ value su↵ers from the ⌃c baryonc⌅c0 : Σ Ξ 0 quark mass uncertainty, the sign for ⌃c seems to be opposite to the one of ⇤c, and the 1++ 2 2 1 2 2 magnetic moment of doubly-charmedµ + = ⌃ µ is+ muchµ + largerµ ,µ than0 ⇤= , whichµ + wouldµ + beµ also (15) ⌅0 c c u s ⌅c0 c c d s c 3 3 3 +3 3 3 interesting to be tested. Note that the main decay channel of ⌃c is ⇤c ⇡. +,0 Finally, letwhich us discuss leads the to µ another+ = µ sextet+ ,µ (spin0 = 1/2,µ 0 at symmetric) the SU(3) charmed limit. The baryon theoretical⌅c0 . uncertainty If⌅ c0heavy quark⌃c limit⌅c0 is correct⌃c and Ξc (Ξc’) state is purely anti-symmetric 0,++,0 These baryonsmight have be the larger same than quark the content case(symmetric) of as⌃⌅c c due butstate, to their weSU would(3) wave however, observe function we are would SU(3) still expect the flavour symmetric.magnetic Since moment these states of the have⌅ 0 to the have same an quarkopposite0 contents sign0 comparing and the same to the spin, ones of ⌅0.This +,0 c0 µΛc=µΞc ≫µΞc ’ c they can mix withresult the implies triplet that⌅c thestates. magnetic At the moment infinite measurements mass10 limit, though, are very this sensitive mixing to resolve the +,0 +,0 is zero, i.e. ⌅c deviationis the pure between anti-symmetric the flavour and and⌅ thec0 massis the eigenstate pure symmetric of ⌅c’s. state. In particular, Indeed, the equality two states areof observed, the magnetic one at moment2468 MeVof ⌅+, and0 and the⇤ otherin Eq.2577 (13) does GeV. not The depend latter on decays the quark masses ⇠ c c ⇠ and the most precise test can be performed. Thus, we will investigate in the following section, this equality in more detail.7
3.2 Magnetic moment beyond the quark model There are various models to compute the magnetic moment beyond the quark model. For example, the so-called Heavy Hadron Chiral Perturbation Theory (HHCPT) is devel- oped [1, 2, 3, 4], which combine the heavy quark e↵ective theory and the chiral perturbation theory of light hadrons. It allows to improve theoretical prediction in a systematic manner. The next to leading order Lagrangian for the magnetic moment of triplet and sextet baryons have been given in [5, 6]. At the order (1/m )(m is the heavy quark mass), O Q Q we have two extra contributions. First, it is the heavy quark magnetic moment, i.e. the interaction of the photons and the heavy quark constituent inside of the hadrons, which also induces M1 transition. This term induces the contribution of the quark model. The second contribution is the photon interacting with the light brown mock inside of the heavy +,0 hadrons. However, the anti-symmetric baryons (⇤c, ⌅c ), whose light degree of freedom is spinless, do not receive any contribution from this interaction as photon can not interact with spinless component. As a result, even at this order, the quark model limit results given in the previous section hold. The lack of contributions from light degree of freedom seems to be generic and theoretical predictions using di↵erent models show that the magnetic +,0 moment of ⇤c, ⌅c is close to the one predicted by the quark model, thus the relation Eq. 13 still holds (see e.g. [11]). In [8] and [7], further corrections are discussed. The reference [8] discusses the so- called spin-symmetry breaking e↵ect, which typically induces the ⌃c⇤ ⌃c. mass splitting. ( ) It comes form a loop diagram with ⌃c⇤ and ⇡,K in the loop. This contribution leads to
8 PREDICTING ΛC MAGNETIC MOMENT WITH BESIII RESULT Karl et al PR D13 ‘76 ~r ~v C ( , , ~ 1) 2 2 — + -→ψ → γ γ ~r ~v e e (2S) �cJ (@ c.m.s) C ( , , ~ 2) 2 2 θ’ e- e+ The charm quark magnetic moment can be determined by the charmonium radiative decays
�cJ ψ(2S)→�cJγ’→J/ψγγ’ γ (@ �cJ r.f)
- + - �cJ →J/ψγ→l l γ �cJ ψ(2s) θγ’γ l+ γ’ (@ �cJ r.f) θ γ (@ cJ r.f) J/ψ �cJ � J/ψ
5 angles to disentangle different contributions θ ϕ θ ϕ θ l- ( , , ’, ’, γ’γ) which is in BESIII/CLEO paper
(θ3, ϕ3, θ1, ϕ1, θ2) 11 10
1 mass and width of χc0,1,2 with 1σ of the world average val- the most precise measurement of the M2 amplitudes a2 and ± 2 ues [17] for the signal MC shape. To estimate the uncertainty by taking mc =1.5 0.3 GeV/c ,theanomalousmagnetic due to the background of ψ(3686) π0J/ψ, π0π0J/ψ and moment κ can be obtained± from Eq. (1), → the ratio of Nℓ+ℓ−γγ/Nℓ+ℓ−γ for Bhabha and dimuon back- grounds, alternative fits are performed in which the numbers 4mc 1 1+κ = a2 of expected background events (see Table II) and the ratio of − Eγ2 [χc1 γ2J/ψ] (9) → Nγγℓ+ℓ− /Nγℓ+ℓ− are varied by 1σ.Forχc0,1,2,thelargest =1.140 0.051 0.053 0.229, differences in the signal yields from± the nominal values are ± ± ± taken as the systematic uncertainty. For the ηc(2S) case, to where the first uncertainty is statistical, the second uncertainty be conservative, the one corresponding to the largest upper is systematic, and the third uncertainty is from mc =1.5 limit is taken as the final result. All systematic uncertainties 0.3 GeV/c2. ± of the different sources are summarized in Table IV. The total Based on the multipole analysis, we measure the product systematic uncertainties are obtained by adding the individ- branching fractions for ψ(3686) γχc0,1,2 γγJ/ψ to be ual ones in quadrature, thereby assuming all these sources are (15.8 0.3 0.6) 10−4, (351→.8 1.0 →12.0) 10−4, independent. and (199± .6 ± 0.8 ×7.0) 10−4,respectively,wherethe± ± × first uncertainty± is statistical± × and the second is systematic. In Fig. 5, the product branching fractions are compared to pre- TABLE IV. Summary of all systematic uncertainties for the branch- ing fractions measurement. vious results from BESIII [18], CLEO [36], and the world average [17]. The world average refers to the product of the Source χ (%) χ (%) χ (%) η (2S) (%) c0 c1 c2 c average branching fraction of ψ(3686) γ χ and the av- N 0.9 0.9 0.9 0.9 1 cJ ψ(3686) erage branching fraction of χ γ J/→ψ,wheretheresults Trackingefficiency 0.2 0.2 0.2 0.2 cJ → 2 Photon detection 2.0 2.0 2.0 2.0 of BESIII and CLEO are not included in the world average Kinematic fit 0.6 0.5 0.5 0.4 values. For all χcJ ,ourresultsexceedtheprecisionofthe J/ψ mass window 0.6 0.6 0.6 0.6 previous measurements. Compared to the previous BESIII re- Other selection 2.4 2.2 2.3 2.4 sult, the results are consistent within 1σ,butwehaveconsid- − − (J/ψ e+e /µ+µ ) 0.6 0.6 0.6 0.6 ered the higher-order multipole amplitudes and improved the InterferenceB → 0.7 - - - systematic uncertainty due to a more precise measurement of Signal shape 0.7 0.9 1.0 - the total number of produced ψ(3686) [19]. In addition, our Background 0.1 0.1 0.1 - measurement for the χc0 channel is 3σ larger than the result Total 3.6 3.4 3.5 3.4 from CLEO and 3σ larger than the world average value, while for the χc1,2,ourresultsareconsistentwithpreviousmea- surements. There are theoretical predictions for the branch- ing fraction ψ(3686) γχc0,1,2 by several different mod- VII. RESULT AND SUMMARY els [14–16] without consideration→ of higher-order multipole amplitudes, which agree with each other poorly. The results Based on 106 million ψ(3686) decays, we measure the in this measurement will provide a guidance for the theoretical higher-order multipole amplitudes for the decays ψ(3686) calculations. PREDICTING Λ MAGNETIC MOMENT WITH→ BESIII RESULT γ χ γC γ J/ψ channels. The statistical significance of We also search for the decay ηc(2S) γJ/ψ through 1 c1,2 → 1 2 → nonpure E1 transition is 24.3σ and 13.4σ for the χ and χ ψ(3686) γηc(2S).Nostatisticallysignificantsignalis arXiv:c 11701.01197c2 (also see→ CLEO 0910.0046)6 channels, respectively. The normalized M2 contribution for observed. Considering the systematic uncertainty, an upper χc1,2 and the normalized E3 contributions for χc2 are listed in limit on the product branching fraction is determined to be J J −6 TABLE I. Fit results for a and b for the process of ψ(3686) γ1χc1,2 γ1γ2J/ψ;thefirstuncertaintyisstatistical,andthesecondis(ψ(3686) γη (2S)) (η (2S) γJ/ψ) < 9.7 10 Table2,3 I. Figure2,3 4 shows a comparison→ of our→ results with pre- c c systematic. The J are the correlation coefficients between J and J . B → ×B → × ρa2,3viouslyb2,3 published measurements anda2,3 withb theoretical2,3 predic- at the 90% C.L., where the systematic uncertainty is incor- 1 2 1 tions with mca2=1= .50.0740GeV/c0.0033and κ 0=0.0034.Theresultsarecon-, b2 =0.0229 0.0039 0.0027porated by a factor 1/(1 σsyst.) for conservative. Com- χc1 − ± ± ± ± − sistent with and more precise thanρ those1 =0 obtained.133 by CLEO- bining the result of B(ψ(3686) γηc(2S)) obtained by a2b2 → 2 2 BESIII [37], the upper limit of the branching fraction for c[5]andconfirmtheoreticalpredictions[1,2].TheM2con-a2 = 0.120 0.013 0.004, b2 =0.017 0.008 0.002 − ± ± 1 ± 1± 2 2 η (2S) γJ/ψ is (η (2S) γJ/ψ) < 0.044 at the 90% tributions for ψa(3686)= 0.013 γ01.χ009c1 (b02.004), χ, bc1= 0.γ0142J/ψ0.007(a2), 0.004 c c χc2 3 2 → 3 → → B → +3.2 2 and − are± found± to be significantly− ± nonzero.± C.L. Using the width of ηc(2S) of 11.3 MeV/c [17], our χc2 γ2J/ψ (aρ22) = 0.605, ρ2 =0.733, ρ2 = 0.095 −2.9 → a2b2 − a2a3 a2b3 − upper limit implies a partial width of The ratios of M2 contributions2 of χc21 to χc2 are2 independent Γ(ηc(2S) γJ/ψ) < ρa3b2 = 0.422, ρb2b3 =0.384, ρa3b3 = 0.024 2 → of the mass mc and the anomalous− magnetic moment κ−of the 0.50 MeV/c .Althoughthisresultagreeswiththeprediction 2 charm quark at leading order in Eγ /mc.Theyaredetermined of LQCD (0.0013 MeV/c )[38],itclearlyhasaverylimited 2 to be sensitivity to rigorously test the theory. for χc1 and χ /ndf =5985.2/5840 = 1.02 for χc2,demon- theirtheory distributions and contributions. With the published strating that the fit gives an excellent representation1 2 of the branching fractions [17], which have been measured precisely b /b =1.35 0.72, ←1.00±0.015 10 data. 2 2 ± by different experiments,(8) the estimated number of events 1 2 for ←ψ(3686) π0π0J/ψ, π0J/ψ and the efficiencyACKNOWLEDGMENTS for a2/a2 =0.617 0.083. 0.676±0.071 ± ψ(3686) γγ→J/ψ are obtained as summarized in Table II. mass and width of with of the world average val- the most precise measurement of the M2→ amplitudes 1 and χc0,1,2 1σ V. M E A S U R E M E N T O F The1 second2 majora source2 of background in- ± B → The→ corresponding theory predictions2 are (b /b ) = The BESIII Collaboration thanks the staff of BEPCII and (ψ(3686) γχCJby takingγγJ/ψ) AND SEARCH FOR THEGeV/ cludes,theanomalousmagnetic2 radiative2 th Bhabhaerror and from dimuon charm processes, mass ues [17] for the signal MC shape. To estimate the uncertainty m→c =11.5 2 0.3 c 0 0 0 PROCESS1.000 ηc0(2.015S) andγJ/(aψ2/a2±)th =0.676 0+.071− [5]. By+ using− the Institute of High Energy Physics computing center for due to the background of ψ(3686) π J/ψ, π π J/ψ and moment± κ can be obtained from Eq.±e e (1), ℓ ℓ γISR/FSR(γISRmc=1.5±0.3/FSR) and ψ(3686) GeV Extracting anomalous magnetic moment + − → → → ℓ ℓ γFSR(γFSR)(l = e/µ).Topreciselydescribetheshape, the ratio of Nℓ+ℓ−γγ/Nℓ+ℓ−γ for Bhabha and dimuonWith back- the selected e+e− γ γ J/ψ candidates, we mea- + − → 1 2 the background is divided up into two parts: ℓ ℓ with one grounds, alternative fits are performed in which thesure numbers the product branching fractions of the decay ψ(3686) 4mc 1 + − → radiative photon and ℓ ℓ with two radiative photons. For γ χ γ γ J/ψ and search1+ for theκ = process η (2S) a2 + − of expected background events (see Table II) and the1 ratioc0,1,2 of 1 2 − E c [χ γtheJ/ backgroundψ] from ψ(3686) ℓ ℓ γFSR(γFSR),theratio .Forthe→ + − channel, additionalγ2 require-c1→ 2 →(9) γ2J/ψ J/ψ e e → of event yields between the two parts (N + − /N + − )is − − → gc ℓ ℓ γγ ℓ ℓ γ Nγγℓ+ℓ /Nγℓ+ℓ are varied by 1σ.Forχc0,1,2,thelargestments are applied to suppress the background=1. from140 radiative0.051 obtained0.053 by a0 MC.229 simulation., = For the background from ra- ± + − + − 2 differences in the signal yields from the nominal valuesBhabha events are [e e γISR/FSRe e ,whereγ±ISR/FSR ± ± + − + − → diative Bhabha/dimuon processes, the ratio Nℓ ℓ γγ/Nℓ ℓ γ denotes the initial-/final-state radiative (ISR/FSR) photon(s)]. 12 is obtained by a fit to a 928 pb−1 data sample taken at a taken as the systematic uncertainty. For the ηc(2S) case, to where the first uncertainty is statistical, the second uncertainty Since the electron (positron) from radiative Bhabha tends to center-of-mass energy of 3.773 GeV. After the event selection be conservative, the one corresponding to the largest upper − have a polar angle iscos systematic,θe+(e ) close to and +1 (-1), the wethird apply uncertainty a imposed is on from the data,m thec remaining=1.5 events are mainly radiative + 2 − ± limit is taken as the final result. All systematic uncertaintrequirementies of cos θ0e.3
1, 2, 3, 2, 3, 1, 4 1 2, 3 A.S. Fomin, ⇤ A.Yu. Korchin, † A. Stocchi, ‡ O.A. Bezshyyko, L. Burmistrov, S.P. Fomin, I.V. Kirillin,2, 3 L. Massacrier,5 A. Natochii,4, 1 P. Robbe,1 W. Scandale,1, 6, 7 and N.F. Shul’ga2, 3 1LAL (Laboratoire de l’Acc´el´erateur Lin´eaire), Universit´eParis-Sud/IN2P3, Orsay, France 2NSC Kharkiv Institute of Physics and Technology, 61108 Kharkiv, Ukraine 3V.N. Karazin Kharkiv National University, 61022 Kharkiv, Ukraine 4Taras Shevchenko National University of Kyiv, 01601 Kyiv, Ukraine 5IPNO (Institut de Physique Nucl´eaire), Universit´eParis-Sud/IN2P3, Orsay, France 6CERN, European Organization for Nuclear Research, CH-1211 Geneva 23, Switzerland 7INFN Sezione di Roma, Piazzale Aldo Moro 2, 00185 Rome, Italy (Dated: May 9, 2017) In this paper we revisit the idea of measuring the magnetic dipole moments of the charm baryons + and, in particular, of ⇤c by studying the spin precession induced by the strong e↵ective magnetic field inside the channels of a bent crystal. We present a detailed sensitivity study showing the feasibility of such an experiment at the LHC in the coming years.
PACS numbers: 13.30.Eg, 13.40.Em, 13.88+e, 14.20.Lq, 61.85.+p PREDICTING ΛC MAGNETIC MOMENT
I. INTRODUCTION µN e~/(2mpc)[1], where mp is theBarsuk proton et massal arXiv:1812.### and e is the⌘ elementary charge. • Using the BES III data, we can predict magnetic moment of Λc The magnetic dipole moment (MDM) of a particle is It would be very important to measure the MDM of + + its fundamental characteristic that determines the torqueg⇤c the charm baryons ⇤c (udc) and ⌅c (usc), which have not =1.75 0.13 µ⇤ =0.48 0.04(n.m.) which particle experiences in an external magnetic field.2 been measured± ! so farc because± of their very short lifetime 13 The MDMs of many particles are presently known [1]. of the order of 10 s. For electron the QED prediction agreeswithout with charm experimen- mass ambiguity.There has been many calculations of the MDM of the tally measured value up to very high precision. For muon charm baryons in various models of their structure [5– + the measurement of the BNL E821This experiment value should [2]dis- be compared21]. As for with the theoretical⇤c baryon, majoritypredictions of the (where calculations charm agrees with the Standard Model predictionquark mass by 3–4 is often stan- obtainedpredict thefrom MDM other and observable)g-factor in the ranges dard deviations, which may suggest physics beyond the + µ(⇤c ) + Standard Model. The disagreement for the muon g 2 =0.37–0.42,g(⇤c )=1.80–2.05. (2) µN is the subject of many studies (see, e.g.,review[3]). The MDM of the ⌧-lepton has not been measured so far and is Thus, an experimental study of the MDM of heavy of great interest for testing calculationswhich in implies the Standard a slightlybaryons higher cancharm be anomalous useful to distinguish magnetic between moment di ↵erent Model [4]. (gc>2?). theoretical approaches. For hadrons, the MDMs are measured for the baryon One of the motivations for measurement of the MDM + Higher precision measurementsof the heavy on baryons BOTH at is alsoa few studying % precision the MDMdesired! of the octet with J P = 1 . Historically, reasonable agree- 2 charm quark. If this quark behaves as a point-like Dirac ment between the measured MDM and predictions of magnetic moment of Λc particle, then the corresponding gyromagnetic factor g the quark model was important to substantiate the con- c is equal or close& to 2, while if the charm quark has a stituent quark models of the hadrons. compositecharm structureradiative decays we can expect a sizable deviation In general, the MDM of the spin- 1 particle is expressed 13 2 from this value. as In the quark model the MDM of the heavy baryon is expressed in terms of the MDMs of the heavy and light 2µ ~ q~ g µ~ = S, µ = , (1) quarks. In particular, for the charm baryons, the spin ~ 2mc 2 + and flavor structure of the ground-state baryons ⇤c and + ~ ~ ⌅ implies that (see, e.g.,Ref.[5]) where S = 2 ~ , m is the particle mass, q is the c arXiv:1705.03382v4 [hep-ph] 31 Aug 2017 particle electric charge, g is the gyromagnetic factor. 1 µ(⇤+)=µ ,µ(⌅+)= (2µ +2µ µ ) . (3) The value g = 2 corresponds to a Dirac particle with- c c c 3 u s c out magnetic moment anomaly. Usually, the MDM of MDMs in Eqs. (3) depend on the MDM of the charm baryons is measured in units of the nuclear magneton + quark. Let us consider ⇤c and take “e↵ective” mass of the c-quark mc =1.6 GeV as suggested from the char- monia spectroscopy [5]. Keeping explicitly the g-factor of the charm quark we can write ⇤ [email protected] [email protected] + † µ(⇤c ) gc + gc ‡ [email protected] =0.39 ,g(⇤c )=1.91 . (4) µN 2 2 Towards μΛc measurement Based on arXiv:1812.####
• The magnetic moment is determined by measuring the Λc spin precession which is generated by the strong magnetic field by the bent crystal.
• The angular distribution of the Λc decay carries information of polarisation ξ, however, it can not be separated from the so-called asymmetry parameter α.
• Note that α is the same in any experiment but ξ has pT dependence. 1 12 g = ↵ ⇠ ! N | | s ⇤c • α and ξ can be separated if i) the subsequent decays are also weak decay ++ (Λc→Λπ→pππ) or ii) there are many resonances interferences (Λc→Δ π→pπK ⊕
Λc→K*p→pπK etc…). • Strategy: we measure α and ξ at LHCb as precise as possible. Then, we
extrapolate ξ to the desired pT value.
±Δg = g - g ±Δg = g - g ±Δg = g - g
Δα=0.3, ΔP=0.05 11 POT Δα=0.1, ΔP=0.05 Δα=0.03, ΔP=0.02 10 0.1 POT 0.1 11 POT 0.1 11 +Δg 13 +Δg 10 +Δg 10 POT 10 1012 POT 13 0 0 10 POT 0
-0.1 -0.1 -Δg -0.1 -Δg
-Δg weak parameter polarisation -0.2 -0.2 -0.2 1.8 1.9 2 2.1 g 1.8 1.9 2 2.1 g 1.8 1.9 2 2.1 g
14 CONCLUSIONS
• Charm quark magnetic moment has never been measured directly.
• A new idea to measure the magnetic moment of charmed baryon µΛc,
using the bent-crystal is proposed (a hight precision expected). µΛc can
be translated to the magnetic moment of charm quark, µc.
• We showed that the measurement of various charmed baryon, such as Ξc
can provide important information on the charmed baryon spectroscopy. • Charmonium radiative decay can indirectly provide the charm quark
magnetic moment. Using BESIII result, we made an estimate on µΛc. We
found that the obtained value of µΛc is slightly higher than the theory predictions.
• Thus, we conclude that a few % level precision for both Λc polarisation and the radiative charmonium decays are desired. • We are currently working on LHCb measurement of polarisation and
weak parameter of Λc, which is a crucial factor for µΛc determination.
15 BARYON SPECTROSCOPY LIGHT BARYONS
• Let us start with the light baryons. SU(3) symmetry for 3 quark states 3 3 3 = 10 8 8 1 ⌦ ⌦ s s a a where s and a corresponds to symmetric and anti-symmetric of flavour, e.g. 1 1 Symmetric : uuu, ddd, [ud + du] u, [us + su] u p2 p2 ··· 1 1 Anti Symmetric : [ud du] u, [us su] u p2 p2 ···
• This results in 10 spin 3/2 baryons and 8 spin 1/2 baryons
J=3/2 J=1/2 totally-symmetric mixed-symmetry decuplet octet 16 BARYON SPECTROSCOPY LIGHT BARYONS
• Let us start with the light baryons. SU(3) symmetry for 3 quark states 3 3 3 = 10 8 8 1 ⌦ ⌦ s s a a where s and a corresponds to symmetric and anti-symmetric of flavour, NOTE ON OCTET STATES: e.g. 1 1 Symmetric : uuu, ddd, [ud + du] u, [us + su] u 8s and 8a statesp2 are mixed.p 2 ··· The qqq’ sates (like proton=uud), 1multiplying with1 the spin symmetry, Anti Symmetric : [ud du] u, [us su] u they turn out to have exactlyp2 the same wavep2 function. ··· For Λ and Σ0 (uds states), the wave function is different: Λ is anti- • This results in 10 spin 3/2 baryons and 8 spin 1/2 baryons symmetric and Σ0 is symmetric.
J=3/2 J=1/2 totally-symmetric mixed-symmetry decuplet octet 17 QUESTION OF TWO ΞC STATES + + Ξ C1 , Ξ C2 ???
At heavy quark limit : + 0 ○: the anti-symmetric 1/2 (Λc,Ξc1 ,Ξc1 ) 0 + 0 ●: the symmetric 1/2 (Σc ,Ξc2 ,Ξc2 ) 0* +* 0* ■: the symmetric 3/2 (Σc ,Ξc ,Ξc )
But this has never been confirmed… The observed state can be a mixture of
Ξc1 and Ξc2. How can we distinguish?
We show below that magnetic moment, which measures directly the quark spin-configuration, is the most powerful tool to distinguish different charmed baryon states!
18