We shall proceed to discuss the significance of charm dynamics in an era when
the Standard Model is well established in its degrees of freedom but little
understood in quite a few of its different parts. The study of decays and
asymmetries in the decays of mesons with charm quantum numbers provide us
possible insights into the yet uncharted dynamics of the Standard Model at the
GeV scale. We will discuss some interesting channels with hadrons and/or
leptons in the final state, the shortcomings of theoretical structures
currently advocated and future experimental prospects.Comment: Proceedings of XII IFAE, Cittadella Universitaria di Monserrato,
  Cagliari. 3rd - 5th April 2013. 5 page

Paul, Ayan

English

arXiv

We shall proceed to discuss the significance of charm dynamics in an era when the Standard Model is well established in its degrees of freedom but little understood in quite a few of its different parts. The study of decays and asymmetries in the decays of mesons with charm quantum numbers provides us with possible insights into the yet uncharted dynamics of the Standard Model at the GeV scale. We will discuss some interesting channels with hadrons and/or leptons in the final state, the shortcomings of theoretical structures currently advocated and future

experimental prospects

Paul, A.

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2014-11671-0Colloquia: IFAE 2013IL NUOVO CIMENTO Vol. 37 C, N. 1 Gennaio-Febbraio 2014Lessons from charm dynamicsA. PaulINFN, Sezione di Roma - I-00185 Roma, Italyricevuto l’1 Ottobre 2013Summary. — We shall proceed to discuss the significance of charm dynamicsin an era when the Standard Model is well established in its degrees of freedombut little understood in quite a few of its different parts. The study of decays andasymmetries in the decays of mesons with charm quantum numbers provides us withpossible insights into the yet uncharted dynamics of the Standard Model at the GeVscale. We will discuss some interesting channels with hadrons and/or leptons in thefinal state, the shortcomings of theoretical structures currently advocated and futureexperimental prospects.PACS 13.20.Fc – Charmed mesons, leptonic and semileptonic decays.PACS 13.25.Ft – Charmed mesons, hadronic decays.PACS 11.30.Er – CP invariance.1. – IntroductionAfter more than a century of rigorous experimentations, all the “fundamental” degreesof freedom of the Standard Model (SM) have been discovered with the final saga beingthe discovery of the Higgs Boson. The stage now lies open for dynamics beyond what wehave grown to understand as Standard. Yet, our understanding of a significant part of SMdynamics lacks solid grounding and leads the lack of predictability in many arenas thathave been somewhat neglected in the race to discover theoretically established resonances.Charm dynamics is one such important arena which stands on the threshold that canbe, at best, called “pseudo-perturbative” dynamics. Not only is it capable of givingus important insights into the workings of the SM in an area which is, and has alwaysbeen, gray, but also serves as a testing ground for innovations in theoretical technologiesbeyond what is well established.Testing for the presence of new dynamics (ND) is now the central theme of our studyof Particle Physics or High Energy Physics. Dynamics beyond the SM is very wellmotivated by various arguments such as:– addressing the challenges of scale separation between electroweak and Planck scale,– finding the key to the observed matter anti-matter asymmetry,– explaining the flavour hierarchy in the SM,c© Societa` Italiana di Fisica 9596 A. PAUL– explaining the presence of massive neutrinos and their oscillation(1),– contemplations on the existence and representations of dark matter and dark en-ergy,– various arguments revolving around the statement: “this cannot be all”,to name a few. However, it is becoming increasingly obvious that ND will appear notwith great fanfare but with great subtlety. While we continue on our quest to discovernew degrees of freedom, it is becoming more and more important to focus on precisionmeasurements in the flavour sector as the scales of dynamics probed is well known to be“loop-enhanced” and hence several orders of magnitude larger than what direct detectiontechniques can probe.Charm dynamics serves as an interesting testing ground for the existence of relativelylarge ND effects because the signatures left by SM dynamics are tiny due to a veryeffective GIM/CKM suppression and the lack of a large hierarchy in the down typequark masses. However, when it is necessary to study percentage effects of ND, oneneeds a good handle on SM predictions, something that is lacking in general in charmdynamics. Hence the study of charm dynamics not only allows us to probe ND but alsogain a more concrete understanding of the SM at the GeV scale. This, to say the least,has been an unsurmountable challenge in the past few decades due to the breakdown(2)of our work-horses, the perturbation technologies, at the GeV scale.In the next few sections we will discuss few decay channels and asymmetries in charmdynamics that serve the dual purpose of providing a field for developing new theoreticaltechnologies for dealing with the pseudo-perturbative dynamics of the SM and the studyof ND intervention.2. – Radiative mode: D0 → γγThe branching fraction of the channel D0 → γγ is yet to be measured. The currentbest experimental bound from the BABAR Collaboration [1] and the SM prediction [2-4],respectively, areBRexp(D0 → γγ) < 2.4× 10−6 (90% C.L.),(1)BRSM(D0 → γγ) ∼ (1–3)× 10−8.The primary contribution to this comes from long distance (LD) effects [2, 3]. The SMshort distance (SD) estimate is several orders of magnitude smaller and is estimated atO(10−11)–O(10−12). Hence, it is expected that long distance effects will dominate here.The c → uγ vertex is dominated by SM QCD effects [5] which is quite difficult for NDto overcome with SD dynamics. Moreover, even if this is possible the LD contributiondominates over the c → uγ vertex contribution by a few order of magnitude. Hence,this is not a good testing ground for ND. The measurement of this branching fractionprovides possible validations of models used for estimating LD dynamics [2,3] and is alsoimportant as it gives us an indirect measurement of the long distance contribution toD0 → μ+μ−.(1) This can be argued to be a part of SM.(2) Here “breakdown” is not tantamount to “inapplicable”.LESSONS FROM CHARM DYNAMICS 97BESIII is projecting a reach of 5 × 10−8 within the next 4–5 years [6]. Hadronicmachines are not supposed to be able to reach any reasonable precision in this channeland any further development has to be left to super flavour factories.3. – Leptonic mode: D0 → μ+μ−There can be large new physics intervention in D0 → μ+μ−. Due to a very effectiveGIM suppression the SM short distance contribution is very tiny [3,4] while the dominantcontribution comes from long distance processes, primarily from the two photon unitarycontribution D0 → γγ → μ+μ− [3],BRSDSM(D0 → μ+μ−) ≈ 6× 10−19,(2)BRLDSM(D0 → μ+μ−) = 2.7× 10−5 × BR(D0 → γγ)  2.7–8× 10−13.(3)It should be noted here that this contribution comes from the total branching fractionBR(D0 → γγ) regardless of whether the latter is generated by SM or ND. Hence agood measurement of BR(D0 → γγ) will give us a very good control over the SM LDcontribution in D0 → μ+μ−.ND intervention can be large in this channel [3, 4, 7]. It is also possible to see NDcontribution in this channel even if the analogous channels in the beauty system Bs(d) →μ+μ− yield measurements which are indiscernible from SM predictions [7].LHCb now sets a limit of 6.2(7.6) × 10−9 with 90%(95%) confidence level with0.9 fb−1 [8]. The LHCb reach can be estimated to be another two or three orders of mag-nitude in the future with similar reach at ATLAS and CMS. This channel is measurableat super flavour factories only in the case of orders of magnitude enhancements from ND.4. – Leptonic modes: D → Xul+l−The inclusive mode D → Xul+l− is dominated by resonance contributions from ρ,φ and ω. The exact branching fraction itself depends on the particular inclusive modebut is predicted to be about O(10−6)–O(10−7) [3, 9]. At the charm scales the dualitybetween quarks and hadrons breaks down significantly and hence predictions in exclusivemodes no longer follow from those in inclusive modes. This has been highlighted by therecent LHCb upper bound [10]BRexp(D+ → π+μ+μ−) < 7.3(8.3)× 10−8 at 90%(95%)CL.(4)The dominant long distance contribution is estimated from D+ → π+V : V → μ+μ−,where V is φ, ρ or ω. The short distance c → ul+l− contribution is three orders ofmagnitude smaller [3, 9, 11]:BRSDSM(D → Xul+l−)  3× 10−9.(5)The SM SD contribution is driven by the photon penguins which are no longer strictlylocal operators as they have light quarks running in the loops. It is difficult for mostgeneric ND to contribute to the branching fraction and enhance it by orders of mag-nitude [3, 11], except in very extreme parameter space of certain models [12] which arehighly constrained from other flavour observables.98 A. PAULWhat are significant in this mode for the intervention of ND are the asymmetries,namely, the forward-backward asymmetry AcFB, the CP asymmetry AcCP and the CPasymmetry in the forward-backward asymmetry ACPFB. In the Standard Model theseasymmetries are extremely tiny and are of O(10−6)–O(10−4). These are relatively cleanof long distance dynamics and even more so if the vector resonances are kinematicallyexcluded from the invariant dilepton mass distribution. While generic ND can enhanceboth the AcFB to O(1%)–O(10%) and AcCP to O(1%), they can enhance ACPFB to O(103%)–O(104%), i.e., well beyond the SM reach [11]. An interesting model independent analysisof possibly sizable CP asymmetry is presented in [13] driven by large chromomagneticpenguins, the same source which can drive a CP asymmetry in D0 → K+K−/π+π−.This will also lead to a sizable CP violation in D → V γ [14, 15]With current and projected statistics at the LHCb experiment, these modes mightbe within reach. These measurements are ideal for a flavour factory with its cleanenvironment.5. – Leptonic modes: D0 → h1h2l+l−While there are distinct experimental and theoretical disadvantages of studying fourbody modes, there is also the advantage of having more observables due to differentkinematic combinatorics which can give us additional handles over not only SM dynamicsbut also the nature of ND through distributions and moments.The T-odd correlation leading to CP asymmetry in D0 → h+h−l+l− is driven by theasymmetry in D0 → h+h− (h → K,π). An enhanced asymmetry can be expected inD0 → h+h−l+l− for reasons analogous to the case of KL → π+π−l+l− [16]. Estimatesshow that the asymmetry can be driven up to O(1%) [17] while a more recent work showsthat it can be as high as O(5%) [18].Other modes that can be studied for such T-odd correlations are singly Cabbibo sup-pressed modes with h+ = K+, h− = π−. However, the asymmetries here can be expectedto be smaller as they are driven by indirect CP violation generated by oscillations. Thebranching fraction of all these four body modes are around 10−6 or less [18] and wouldrequire quite a bit of statistics to probe into the asymmetries. A super flavour factorywould have enough statistics to access this. LHCb can possibly explore the final stateswith a pair of charged hadrons and a pair of muons.6. – Hadronic modes: D → h1h2h3h4The invariant mass distributions of different pairs of final state hadrons give a lot ofobservables for the study of SM and ND. The important kind of observables to study hereare the T-odd correlations that are connected to CP violation as in D → h1h2l+l−. Thedifference here is that in the latter channel final state interactions (FSI) can be ignoredto corrections of O(α). However, FSI becomes important in the fully hadronic four bodyfinal state. While T-odd correlations can be generated even without CP violation, thelatter would imply〈h1 · (h2 × h3)〉D = −〈h1 · (h2 × h3)〉D¯,(6)〈h1 · (h2 × h4)〉D = −〈h1 · (h2 × h4)〉D¯,which can be extended to any other triple moment made out of a combination of h1,h2, h3 and h4 which are the kinematic directions of the corresponding hadron. Once acertain set of triple product has been chosen as a test of CP violation, distribution ofanother set can be used to probe the underlying dynamics.LESSONS FROM CHARM DYNAMICS 99It is also possible to study the differential decay rate with respect to the angle Φbetween the K+ −K− plane and the π+ − π− plane in D0 → K+K−π+π− decay. Forthe meson and the anti-meson we have:ddΦΓ(D0(D¯0) → K+K−π+π−) =(7)Γ1(Γ¯1) cos2 Φ + Γ2(Γ¯2) sin2 Φ + Γ3(−Γ¯3) cosΦ sinΦ.Under T transformation, Γ3 is odd as Φ → −Φ. However, Γ3 = 0 is not a clear signalfor CP violation as FSI can produce that too. The unambiguous sign of CP violation isΓ3 = Γ¯3. The CP asymmetry can then be defined asACP =∫ π/20dΦ dΓdΦ −∫ ππ/2dΦ dΓdΦ∫ π0dΦ dΓdΦ=2(Γ3 − Γ¯3)π(Γ1 + Γ2).(8)Similarly, other angles can be defined like Φ between planes containing different pairs ofthe final state mesons from which more information can be gleaned.LHCb can well access D0 → K+K−π+π− and D0 → K+π−π+π− and their conjugatestates. However, in such analysis large statistics is of prime importance as distributionsneed to be studied. A charm factory would definitely have an edge here.∗ ∗ ∗I would like to thank the organizers of IFAE 2013 for their hospitality and, alongwith the participants, for accommodating my inability to speak Italian. My participa-tion in the conference was funded by the European Research Council under the Euro-pean Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreementn. 279972.REFERENCES[1] Lees J. et al., Phys. Rev. D, 85 (2012) 091107.[2] Fajfer S., Singer P. and Zupan J., Phys. Rev. D, 64 (2001) 074008.[3] Burdman G., Golowich E., Hewett J. L. and Pakvasa S., Phys. Rev. D, 66 (2002)014009.[4] Paul A., Bigi I. I. and Recksiegel S., Phys. Rev. D, 82 (2010) 094006.[5] Greub C., Hurth T., Misiak M. and Wyler D., Phys. Lett. B, 382 (1996) 415.[6] Asner D., Barnes T., Bian J., Bigi I., Brambilla N. et al., Int. J. Mod. Phys. A, 24(2009) S1.[7] Paul A., de la Puente A. and Bigi I. I., arXiv:1212.4849 (2012).[8] Aaij R. et al., Phys. Lett. B, 725 (2013) 15, arXiv:1305.5059 (2013).[9] Fajfer S., Prelovsek S. and Singer P., Phys. Rev. D, 64 (2001) 114009.[10] Aaij R. et al., Phys. Lett. B, 724 (2013) 203, arXiv:1304.6365 (2013).[11] Paul A., Bigi I. I. and Recksiegel S., Phys. Rev. D, 83 (2011) 114006.[12] Fajfer S., Kosnik N. and Prelovsek S., Phys. Rev. D, 76 (2007) 074010.[13] Fajfer S. and Kosnik N., Phys. Rev. D, 87 (2013) 054026, arXiv:1208.0759 (2012).[14] Isidori G. and Kamenik J. F., Phys. Rev. Lett., 109 (2012) 171801.[15] Lyon J. and Zwicky R., arXiv:1210.6546 (2012).[16] Sehgal L. and Wanninger M., Phys. Rev. D, 46 (1992) 1035.[17] Bigi I. I. and Paul A., JHEP, 03 (2012) 021.[18] Cappiello L., Cata O. and D’Ambrosio G., JHEP, 04 (2013) 135.

Lessons from charm dynamics

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