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Charm quark

The charm quark (denoted by the symbol c) is a fundamental elementary particle and one of the six quarks in the Standard Model of particle physics, classified as a second-generation up-type quark with a flavor quantum number C = +1.^[1] It possesses an electric charge of +2/3 e, a spin-parity of J^P = 1/2⁺, and is a fermion with isospin I = 0.^[1] The charm quark has a mass of 1.2730 ± 0.0046 GeV/c² in the \overline{MS} scheme evaluated at the charm mass scale μ = m_c, making it significantly heavier than the first-generation up quark but lighter than the third-generation top quark.^[2] Theoretically predicted in 1970 by Sheldon Glashow, John Iliopoulos, and Luciano Maiani through the GIM mechanism—which introduced a fourth quark to suppress flavor-changing neutral currents in weak interactions while preserving the symmetry between quarks and leptons—the charm quark resolved key puzzles in kaon decays and enabled a consistent electroweak theory for hadrons. Its experimental discovery came independently in November 1974: Burton Richter's SPEAR team at SLAC observed a new resonance at 3.1 GeV, identified as the J/ψ meson (a charm-anticharm bound state), while Samuel Ting's group at Brookhaven detected the same particle using the proton beam on a beryllium target. This breakthrough, dubbed the "November Revolution," confirmed the existence of a new quark generation, earned Richter and Ting the 1976 Nobel Prize in Physics, and catalyzed the development of quantum chromodynamics (QCD) as the theory of strong interactions.^[3] The charm quark plays a crucial role in understanding CP violation and the Cabibbo-Kobayashi-Maskawa (CKM) matrix, which governs quark mixing in weak decays, as its inclusion expands the three-quark model to six flavors and allows for the observed matter-antimatter asymmetry in the universe. It forms a variety of hadrons, including charmonium states like J/ψ and ψ(2S), open-charm mesons such as D and D_s, and charmed baryons like Λ_c⁺, whose production and decay properties are studied extensively at accelerators like the LHC to probe QCD dynamics, heavy-ion collisions, and potential new physics beyond the Standard Model. Recent experiments, including those at LHCb and Belle II, have revealed exotic charm-containing pentaquarks and tetraquarks, further highlighting the quark's versatility in multiquark configurations.

Properties

Basic attributes

The charm quark, denoted as c, is a fundamental constituent of matter in the Standard Model of particle physics, classified as the up-type quark in the second generation of quarks.^[4] It is a spin-\frac{1}{2} fermion, obeying the Fermi-Dirac statistics, and participates in all three fundamental interactions: strong, weak, and electromagnetic.^[4] Like all quarks, the charm quark carries a color charge, belonging to the fundamental triplet representation of the SU(3)_C color gauge group, with possible states labeled red, green, or blue; this confines it within color-neutral hadrons via quantum chromodynamics.^[4] Its electric charge is +\frac{2}{3} e, where e is the elementary charge magnitude.^[4] In the approximate SU(3) flavor symmetry of strong interactions, the charm quark has isospin quantum numbers I = 0 and I_z = 0, in contrast to the first-generation up and down quarks, which form an isospin doublet with I = \frac{1}{2} (I_z = \pm \frac{1}{2}), while the strange quark also has I = 0.^[4] The second-generation quarks (charm and strange) extend the flavor symmetry beyond the light quarks (up, down, strange), introducing heavier flavors that break the SU(3) symmetry more severely.^[4] The charm quark is distinguished by its flavor quantum number, the charm number C = +1, with all other flavor numbers zero: strangeness S = 0, bottomness B = 0, and topness T = 0.^[4] These additive quantum numbers are conserved in strong and electromagnetic interactions but violated in weak processes. In the electroweak sector, the left-handed charm quark forms part of the SU(2)_L doublet (c_L, s_L) with weak isospin T = \frac{1}{2} and third component T_3 = +\frac{1}{2} for the charm, while the doublet carries hypercharge Y = \frac{1}{3}; the right-handed charm quark c_R is an SU(2)_L singlet with T = 0 and Y = \frac{4}{3}.^[5] The following table summarizes the key quantum numbers of the charm quark compared to the lighter quarks:

Quark	Generation	Type	Spin	Charge Q	Isospin I (I_z)	Charm C	Color
u	1st	up	1/2	+2/3	1/2 (+1/2)	0	Triplet
d	1st	down	1/2	-1/3	1/2 (-1/2)	0	Triplet
s	2nd	down	1/2	-1/3	0 (0)	0	Triplet
c	2nd	up	1/2	+2/3	0 (0)	+1	Triplet

As a valence quark, the charm quark combines with antiquarks or lighter quarks to form hadrons, including pseudoscalar mesons such as the D^0 (c \bar{u}) and D^+ (c \bar{d}), as well as charmed baryons like the \Lambda_c^+ (udc).^[4] These particles exhibit the charm flavor through their quantum numbers, enabling studies of heavy-quark dynamics within the quark model.^[4]

Mass and lifetime

The rest mass of the charm quark is m_c = 1.273 \pm 0.005 GeV/c^2 in the \overline{\text{MS}} scheme at the scale \mu = m_c, as determined from averages of lattice QCD simulations, experimental data on heavy quarkonia, and semileptonic B-meson decays.^[6] This value carries a 90% confidence level uncertainty and represents the current precision benchmark from the Particle Data Group. Early theoretical predictions and initial experimental inferences from the 1970s placed the charm quark mass around 1.5 GeV/c^2, with refinements over decades driven by improved lattice calculations and collider data reducing the uncertainty from tens of percent to the sub-percent level today.^[7] Compared to the strange quark mass of m_s = 93.5 \pm 0.8 MeV/c^2 (in the \overline{\text{MS}} scheme at \mu = 2 GeV), the charm quark's mass is over an order of magnitude larger, classifying it as a heavy quark and enabling its weak decays to dominate over strong interactions, which contributes to its relatively short intrinsic lifetime.^[8] This heaviness suppresses certain decay processes relative to lighter quarks but allows perturbative QCD treatments in many contexts. The intrinsic lifetime of the charm quark, approximated as a free particle, is \tau_c \approx 0.7 \times 10^{-12} s, derived from next-to-leading-order QCD calculations of its total decay width \Gamma_3 \approx 1.4 ps^{-1} within the heavy quark expansion framework.^[9] This lifetime relates to the total decay width via the equation

\tau = \frac{\hbar}{\Gamma},

where \Gamma is the sum of partial widths for weak decays into lighter quarks (primarily strange and down types), neglecting strong and electromagnetic contributions that are absent for free quarks.241) In reality, the charm quark hadronizes rapidly into mesons or baryons, introducing non-perturbative corrections of order 10-20% to the effective lifetime observed in experiments, such as those for D mesons ranging from 0.4 to 1 ps.^[9]

History

Theoretical foundations

The theoretical motivations for introducing a fourth quark flavor emerged in the late 1960s from discrepancies in the standard three-quark model (up, down, strange) and the Cabibbo theory of weak interactions. The Cabibbo model, proposed in 1963, unified semi-leptonic decays of strange and non-strange hadrons by introducing a mixing angle \theta_C between up/down and strange quarks, treating the strange quark effectively as a singlet beyond the (u, d) doublet. However, this framework struggled to explain the observed suppression of flavor-changing neutral currents (FCNC), particularly in K^0 \to \mu^+ \mu^- decays, which were expected to occur at rates comparable to charged current processes but were experimentally absent or highly suppressed. To resolve this, Glashow, Iliopoulos, and Maiani proposed in 1970 the GIM mechanism, which postulated a new quark flavor—later called charm—to form an additional weak doublet (c, s) alongside (u, d), restoring approximate flavor symmetry in the weak charged currents. This extension balanced the Cabibbo structure by pairing the strange quark with a heavier counterpart, ensuring that FCNC processes, mediated by virtual quark loops in second-order weak interactions, interfere destructively due to the mass differences between generations. The mechanism specifically suppressed \Delta S = 1 neutral currents in kaon decays, aligning with experimental limits on their branching ratios below $10^{-9}. Observations of CP violation in K_L^0 \to 2\pi decays further underscored the need for such doublets, as the three-quark model alone could not accommodate the small but nonzero phase in weak interactions without additional structure. The GIM mechanism provided a mathematical basis for FCNC suppression through the difference in squared masses of the up and charm quarks in the loop diagram. The amplitude for processes like K^0 \to \mu^+ \mu^- scales as:

\mathcal{A} \propto \frac{m_c^2 - m_u^2}{M_W^2},

where M_W is the W boson mass; without the charm quark (m_c = m_u), the factor vanishes, naturally yielding the observed suppression on the order of $10^{-10} or smaller. This formulation extended the quark model from three to four flavors, anticipating charmed hadrons as partners to strange ones and paving the way for a generational pattern in weak interactions. Early experimental hints from deep inelastic scattering (DIS) at SLAC in the late 1960s also motivated additional flavors. DIS cross-sections exhibited approximate scaling in the Bjorken x variable, consistent with point-like partons, but the momentum sum rule—requiring the total momentum fraction carried by quarks to equal 1—was only partially satisfied by u, d, and s quarks, accounting for roughly 50% of the proton's momentum and implying undetected sea quarks or extra flavors.^[10] These scaling behaviors, while not directly pinpointing charm, supported the theoretical push beyond three quarks by suggesting a more complex parton content.

Prediction and naming

In 1970, Sheldon Glashow, John Iliopoulos, and Luciano Maiani proposed the existence of a fourth quark flavor, dubbed the charm quark (c), to resolve discrepancies in weak interaction theory by suppressing unobserved strangeness-changing neutral currents through the Glashow-Iliopoulos-Maiani (GIM) mechanism. This mechanism paired the charm quark, with charge +2/3, as the weak isospin partner to the strange quark (s) in a second quark doublet, restoring approximate symmetry between quarks and leptons in the emerging electroweak framework. The charm quark's introduction ensured that neutral currents remained flavor-diagonal at tree level, enabling a renormalizable unified theory of weak and electromagnetic interactions consistent with experimental limits on processes like K_L \to \mu^+ \mu^-. The name "charm" originated from a 1964 speculation by Glashow and James Bjorken, who invoked a fourth quark to maintain lepton-hadron symmetry in weak currents, choosing the term to evoke an "exotic" quality that complemented the "strange" quark while avoiding prosaic sequential labels like "up, down, sidewise." Glashow later emphasized that "charm" symbolized the pleasing symmetry it imparted to the subnuclear world, balancing the known quarks and leptons into parallel doublets.^[11] This nomenclature persisted through the 1970 GIM formulation, distinguishing the charm quark as a heavy, weakly interacting flavor integral to the Standard Model's structure.^[12] The GIM mechanism predicted narrow charmed mesons, such as D mesons composed of a charm quark and a light antiquark, arising from suppressed flavor-changing decays that would otherwise broaden their widths; these decays were expected to proceed via second-order weak processes, yielding lifetimes around $10^{-13} seconds. The charm quark mass was estimated at approximately 1.5 GeV, based on analyses of quadratic divergences in neutral current amplitudes and comparisons with kaon decay data, placing it in the 1–2 GeV range accessible to accelerators of the era yet heavy enough to evade prior detection.^[13] This prediction aligned with the quark's role in the electroweak theory, where its Cabibbo-suppressed couplings to down-type quarks minimized long-distance contributions to rare processes. Concurrently, in 1973, Makoto Kobayashi and Toshihide Maskawa extended the mixing matrix to three quark generations to accommodate CP violation in kaon decays, incorporating the yet-undiscovered charm quark as the fourth flavor while anticipating additional heavier quarks to complete the scheme. Their model reinforced the GIM framework by generalizing quark mixing, emphasizing charm's necessity for consistent weak interactions across generations.

Discovery experiments

The discovery of the charm quark was first indicated by the observation of the J/ψ meson, a bound state of a charm quark and its antiquark (c\bar{c}), in November 1974 by two independent experiments. At Brookhaven National Laboratory, Samuel C. C. Ting's team used a high-intensity proton beam from the Alternating Gradient Synchrotron (AGS) incident on a beryllium target to produce hadronic collisions, detecting dilepton (electron-positron or muon-antimuon) events with a magnetic spectrometer. They observed a narrow resonance peak at a mass of 3.105 GeV/c^2 with a width of approximately 70 keV, far narrower than expected for known hadrons, suggesting a new flavor quantum number to suppress decays. Simultaneously, at the Stanford Linear Accelerator Center (SLAC), Burton Richter's team utilized the SPEAR electron-positron collider to scan for resonances in e^+ e^- annihilation, identifying the same narrow peak at 3.097 GeV/c^2 using the Mark I detector, confirming the particle's production in clean quarkonium-like events. The matching mass and narrow width of this particle, named J/ψ after the Greek letter psi used by the SLAC group and J by Ting's group, provided compelling evidence for a fourth quark flavor, resolving anomalies in weak interaction parity violation. The significance of the J/ψ discovery was recognized with the 1976 Nobel Prize in Physics awarded jointly to Ting and Richter for their pioneering work in revealing this heavy elementary particle of a new kind.^[3] Confirmation of "naked" charm—charmed hadrons containing a single charm quark—followed in 1976 through observations of D mesons at SLAC and Fermilab. At SLAC's SPEAR collider, the SLAC-LBL collaboration detected charged (D^\pm, containing c\bar{d} or \bar{c}d) and neutral (D^0, containing c\bar{u}) D mesons with masses around 1.865 GeV/c^2 and 1.869 GeV/c^2, respectively, via their hadronic decays such as D^0 \to K^- \pi^+ and evidence for D^* excited states decaying to D \pi. At Fermilab, the initial evidence emerged from 1975 dimuon events in high-energy proton collisions using the 15-ft bubble chamber, attributed to semileptonic decays of charmed mesons produced in hadron beams, with subsequent confirmation of D signals in 1976 data. Between 1976 and 1977, charmed baryons were observed, further validating the quark model with charm incorporation. At Fermilab, the Λ_c^+ baryon (udc) was identified in neutrino interactions with masses near 2.285 GeV/c^2, appearing in decays like Λ_c^+ \to p K^- \pi^+. The Σ_c baryons (uuc, ddc) were also detected there in hadronic production. At DESY's DORIS e^+ e^- collider, the PLUTO collaboration confirmed charmed baryon signals in inclusive lepton events, solidifying the existence of charmed hadrons beyond mesons. These discoveries relied on complementary techniques: e^+ e^- colliders like SPEAR and DORIS provided resonant production of c\bar{c} pairs for clean spectroscopy of J/ψ and D mesons, while hadron and neutrino beams at Brookhaven and Fermilab enabled production of open-charm states via strong interactions, with dilepton events crucial for identifying weak decays suppressed by the heavy charm mass.^[14]

Post-discovery confirmations

Following the initial discoveries of the J/ψ and D mesons in 1974–1976, subsequent experiments in the late 1970s and 1980s focused on charm spectroscopy to map out the spectrum of charmonium and open-charm states, providing strong confirmation of the charm quark's existence and properties. The ψ′ (3770), identified as the first radial excitation of the c\bar{c} bound state, was observed in 1975 at the SPEAR e⁺e⁻ collider by the SLAC-MIT collaboration through its decay to e⁺e⁻, with a mass of 3.770 GeV and width consistent with electromagnetic transitions in charmonium. In the open-charm sector, the vector D* mesons (D*⁺ and D⁰) were identified in 1979 at energies near the ψ″(3770) resonance by the MARK I detector at SLAC, via their decays to Dπ with masses around 2.01 GeV, establishing the spin-1 partners to the pseudoscalar D mesons and supporting the quark model predictions for heavy-light systems. Further spectroscopy at e⁺e⁻ colliders like CESR (CLEO) and DORIS (MARK III) in the 1980s revealed orbitally excited P-wave states, such as the D₁(2420) and D₂(2460), observed by CLEO in 1985 through inclusive production and decays to D*π, with masses and widths aligning with potential models incorporating QCD effects. Fixed-target experiments at CERN's Super Proton Synchrotron and Fermilab's Tevatron also contributed, with photoproduction data from the WA75 collaboration in 1984 confirming radial excitations like the D(2550) through vertex reconstruction of decay vertices. Confirmation of the charm quark's weak interactions came through observations of semileptonic and hadronic decays of D mesons, particularly the Cabibbo-favored channel D⁰ → K⁻π⁺, which proceeds via c → sūd̅ and suppresses ΔC = 1 transitions relative to lighter quarks. This decay was first clearly observed in 1979 by the SLAC-LBL collaboration using the MARK I detector at SPEAR, with a branching fraction of (3.9 ± 1.6)% and kinematic reconstruction showing the expected V_cs dominance in the CKM matrix. Subsequent measurements at higher statistics by the CLEO experiment in 1980 refined the rate to (3.7 ± 0.4 ± 0.6)%, establishing the short lifetime of ~10⁻¹² s for neutral D mesons and validating the GIM mechanism's role in flavor-changing neutral currents. These results ruled out non-standard weak models and confirmed the charmed nature of the decays through the absence of significant backgrounds from lighter quark states. In the 1980s, experiments also verified indirect charm production via b-quark decays, linking the charm and bottom sectors. The MARK III detector at SPEAR reported in 1987 evidence for B → Dℓν decays, with a semileptonic branching fraction of (9.3 ± 1.5 ± 1.6)% and D⁰ reconstruction in B events, indicating b → c transitions dominate B decays as predicted by the spectator model. Similarly, the ARGUS collaboration at DORIS observed in 1988 exclusive channels like B⁰ → D*⁻π⁺, with a signal of 12 events and branching fraction (2.1 ± 0.7 ± 0.5) × 10⁻⁴, confirming charm as the primary decay product of b quarks and supporting the three-generation quark structure. A notable puzzle in the late 1980s was the "missing charm" in B decays, where measured inclusive charm yields (n_c ≈ 0.9–1.0) fell short of the spectator model's prediction of ~1.2 charm quarks per B decay, prompting concerns about non-spectator contributions. This was resolved in the early 1990s through QCD-based heavy quark effective theory (HQET), incorporating next-to-leading-order perturbative corrections (α_s ≈ 0.22) and non-perturbative power-suppressed terms like the Darwin operator, yielding n_c = 1.15 ± 0.05 consistent with updated data from CLEO and ARGUS.^[15] Key hadroproduction studies further solidified charm evidence, with the UA1 experiment at CERN's p̄p collider observing charmed particles in 1983 proton-proton collisions at √s = 540 GeV through muonic decays and vertex tags, reporting a cross-section of ~20 μb for open charm near mid-rapidity and confirming QCD parton model expectations for heavy quark pair production.^[16]

Interactions

Production processes

Charm quarks are primarily produced in pairs (c\bar{c}) through strong interaction processes governed by quantum chromodynamics (QCD) in high-energy collisions. In hadronic collisions, such as those at proton-proton (pp) colliders like the Large Hadron Collider (LHC), the leading-order (LO) mechanism is gluon fusion, gg → c\bar{c}, which dominates due to the abundance of gluons in the initial state partons.^[17] This process is calculated using tree-level matrix elements, with the parton-level differential cross-section given by

\frac{d\sigma}{dt} \propto \frac{\alpha_s^2}{\hat{s}},

where \alpha_s is the strong coupling constant and \hat{s} is the partonic center-of-mass energy squared.^[18] A secondary LO channel is quark-antiquark annihilation, q\bar{q} → c\bar{c}, though it contributes less owing to the smaller quark densities in protons.^[17] In electron-positron (e^+e^-) annihilation, charm production occurs via electroweak processes, primarily through a virtual photon or Z boson: e^+e^- → γ^*/Z → c\bar{c}. This mechanism is perturbative and free of hadronization complications at leading order, allowing clean probes of the charm sector near thresholds like the Υ(4S) resonance.^[19] Higher-order QCD contributions significantly refine these predictions, including next-to-leading-order (NLO) corrections with real and virtual gluon emissions that account for up to 50% enhancements in some kinematic regions. Flavor excitation processes, such as gq → cq\bar{q}, and gluon splitting into c\bar{c} pairs during fragmentation, become important at higher orders, modeled via fragmentation functions that describe the transition from partons to observable charm hadrons like D mesons.^[18] These effects are incorporated in schemes like the fixed-flavor number scheme (FFNS) or variable-flavor number scheme (VFNS) for accurate simulations.^[17] Production cross-sections for c\bar{c} pairs in pp collisions scale approximately with the center-of-mass energy, increasing roughly as \hat{s}^{0.5} due to gluon luminosity growth at low x, with LHC measurements at √s = 13 TeV yielding inclusive values of order 10-100 μb in central rapidity regions (|y| < 1).^[20] Extrapolations to full phase space using tools like FONLL yield total cross-sections around several millibarns, sensitive to the charm mass and PDFs.^[18] In astrophysical environments, charm production is rarer and occurs mainly through high-energy proton interactions in cosmic rays, where pp-like collisions generate c\bar{c} pairs via similar QCD processes, contributing to atmospheric neutrino fluxes but at rates orders of magnitude below laboratory settings.^[21] Supernovae may also produce charm via proton-induced reactions in dense media, though this remains subdominant compared to lighter particle production.

Decay channels

The charm quark undergoes weak decays dominated by charged-current interactions, with the primary modes involving the transition to a strange or down quark accompanied by a W^+ boson emission. The semileptonic decays, c → s ℓ^+ ν_ℓ (Cabibbo-favored) and c → d ℓ^+ ν_ℓ (Cabibbo-suppressed), proceed via the emission of a charged lepton and neutrino, avoiding hadronic uncertainties. The inclusive branching ratio for the Cabibbo-favored semileptonic decay is measured to be approximately 9.6%, while the suppressed mode has a branching ratio of about 0.5%, reflecting the ratio |V_cd / V_cs|^2 ≈ 0.05 from the CKM matrix elements.^[22] Hadronic decays of the charm quark are predominantly nonleptonic, mediated by the effective four-fermion interaction from W exchange, where the c → s transition pairs with u \bar{d} or similar light quark pairs. Spectator quark diagrams contribute significantly, allowing the accompanying light quark in the charmed hadron to participate without changing flavor. These modes, such as those observed in D meson decays like D^0 → K^- π^+, dominate with a total branching fraction exceeding 80%, governed by selection rules from isospin and color factors. Doubly Cabibbo-suppressed hadronic modes, involving c → d u \bar{d}, occur at rates suppressed by approximately 5% relative to the favored channels due to the small CKM factor |V_cd V_ud / V_cs V_us|^2.^[22] Lifetime differences between charged and neutral charmed mesons arise from interference effects in the decay amplitudes. In the neutral D^0 meson, doubly Cabibbo-suppressed amplitudes interfere destructively with Cabibbo-favored ones in shared final states, shortening its lifetime compared to the D^+ meson, where such interference is absent due to charge conservation; this results in τ(D^+) / τ(D^0) ≈ 2.5.^[22] Rare decays via flavor-changing neutral currents (FCNC), such as c → u transitions (e.g., c → u γ), are forbidden at tree level in the Standard Model and proceed only at loop level, suppressed by the GIM mechanism. The predicted branching ratio for c → u γ is on the order of 10^{-6}, with experimental upper limits around 10^{-5} for inclusive modes, making these sensitive probes for new physics beyond the Standard Model.^[22] In the free quark approximation, the semileptonic decay rate for the Cabibbo-favored mode is given by

\Gamma(c \to s \ell^+ \nu_\ell) \propto |V_{cs}|^2 \frac{G_F^2 m_c^5}{192 \pi^3},

neglecting the strange quark mass and QCD corrections, which provide the leading-order scaling with the charm mass and Fermi constant.

Contemporary research

Experimental measurements

Modern experiments at high-luminosity colliders have provided precise measurements of charm quark properties, advancing our understanding of mixing, CP violation, and production rates. The LHCb experiment at CERN has played a central role in studying charm mixing through D^0 meson oscillations, quantifying the parameters x = \frac{\Delta m}{\Gamma} and y = \frac{\Delta \Gamma}{2\Gamma}, where \Delta m and \Delta \Gamma are mass and width differences between neutral charm eigenstates, and \Gamma is the average width. Recent analyses using proton-proton collision data at \sqrt{s} = 13 TeV yield x = (0.41 \pm 0.05)\% and y = (0.621^{+0.022}_{-0.019})\%, with updates as of 2025 refining these values and providing evidence for CP violation in the mixing process through non-zero asymmetries in decay rates.^[23]^[24]^[25] The Belle II experiment at KEK has contributed high-precision data on semileptonic B decays, while for D mesons, measurements from BESIII and others inform CKM elements. The branching fraction \mathcal{B}(D^0 \to K^- e^+ \nu_e) = (3.51 \pm 0.04)\% , and lattice QCD validations constrain |V_{cs}| to $0.973 \pm 0.006, reducing uncertainties in CKM unitarity tests.^[26]^[27] At the BESIII experiment in Beijing, charmonium spectroscopy has benefited from e^+ e^- collisions near the ψ(2S) threshold, resolving excited states like η_c(2S). The mass of η_c(2S) is $3639.2 \pm 1.3 MeV/c² from decays such as ψ(2S) → γ η_c(2S), with recent analyses confirming this value and clarifying radiative transitions in the charmonium family.^[28] Notable recent results include LHCb searches for direct CP violation in charmed meson decays, with ongoing analyses in modes like D^0 → π^+ π^- π^0 showing no significant deviation from Standard Model expectations as of 2024. Additionally, the total charm production cross-section at the LHC Run 3 energy of 13.6 TeV has been estimated at approximately 7.0 ± 0.4 mb in the forward region (2 < η < 5), combining LHCb data with other experiments to benchmark QCD models.^[29]^[30] These measurements face challenges in high-luminosity environments, where background subtraction from light quark jets requires advanced machine learning techniques, and systematic errors arise from uncertainties in charm fragmentation models, limiting precision to 5-10% in some observables.^[31]

Theoretical developments

Following the discovery of the charm quark, its incorporation into quantum chromodynamics (QCD) advanced through heavy quark effective theory (HQET), which treats the charm quark as heavy relative to the QCD scale while accounting for threshold effects near the charm mass scale. In HQET, the theory expands around the heavy quark's velocity, with power counting governed by the scaling v^2 \sim \Lambda_{\mathrm{QCD}} / m_c, where \Lambda_{\mathrm{QCD}} \approx 300 MeV and m_c \approx 1.3 GeV, yielding v^2 \approx 0.2 and enabling systematic inclusion of non-perturbative corrections from light degrees of freedom. This framework captures threshold dynamics in heavy-light systems, such as D meson spectroscopy, by resumming soft gluon effects and matching to full QCD perturbatively above the threshold.^[32] Lattice QCD simulations have provided precise predictions for charm quark properties, refining the pole mass m_c to around 1.27 GeV and decay constants like f_D \approx 212 MeV for the D meson, with uncertainties below 1% in recent N_f=2+1 ensembles. These calculations employ twisted-mass or domain-wall fermions to control discretization errors, incorporating continuum extrapolations and chiral symmetry to predict f_{D_s} \approx 248 MeV, aiding validation of HQET at the charm scale. Such results benchmark non-perturbative QCD effects, with lattice inputs improving the accuracy of charm hadron masses by up to 10 MeV compared to earlier quark model estimates. In the Cabibbo-Kobayashi-Maskawa (CKM) matrix, charm quark contributions via loop effects constrain elements like |V_{cb}| and |V_{ub}|, particularly through charm-mediated penguin and box diagrams in B meson decays that probe the unitarity triangle. For instance, charm loops in inclusive B \to X_c \ell \nu decays introduce non-local effects that shift |V_{cb}| determinations by 2-3%, tightening the triangle's apex angle \gamma to within 5° when combined with tree-level inputs.^[33] These loop contributions also test unitarity via \epsilon_K from K^0 mixing, where charm exchange dominates the short-distance phase, aligning with global fits that bound the triangle area to (0.78 \pm 0.08) \times 10^{-5}. Searches for physics beyond the Standard Model using the charm quark focus on enhancements to rare decays, with supersymmetric models contributing to flavor-changing neutral currents like D^0 \to \mu^+ \mu^- through squark-gluino loops that can amplify branching ratios by factors of 10-100 depending on SUSY breaking scales above 1 TeV.^[34] Similarly, leptoquark models, such as scalar leptoquarks coupling to second- and first-generation quarks, enhance c \to u \ell^+ \ell^- transitions in decays like D^+ \to \pi^+ \mu^+ \mu^-, potentially increasing rates by up to O(10^{-6}) while evading constraints from b \to s \ell^+ \ell^- anomalies.^[35] These models are bounded by null results from LHCb, limiting leptoquark masses to above 1 TeV for couplings g_{cq} \sim 0.1. Recent lattice QCD calculations from 2020-2025 have quantified charm CP violation, computing mixing parameters x and y with 5-10% precision using N_f=2+1+1 simulations, yielding \operatorname{Im}(A_{12}) / |A_{12}| \sim 10^{-3} for D^0--\bar{D}^0 mixing that aligns with LHCb's observed direct CP asymmetries \Delta A_{CP} \approx (1.0 \pm 0.2)\%. These simulations incorporate isospin breaking and electromagnetic effects, reducing hadronic uncertainties in \Delta I=1/2 rule violations and supporting Standard Model expectations without invoking new phases. Further advances in ensemble tuning have refined bag parameters B_{12} to $0.85 \pm 0.05, enabling tighter bounds on CP-violating phases in charm loops.

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Charm and synthesis - CERN Courier
Jan 27, 2025 · Sheldon Glashow recalls the events surrounding a remarkable decade of model building and discovery between 1964 and 1974.
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[PDF] GLASHOW Lecture - Nobel Prize
Again, in 1970, Iliopoulos and I showed that a wide class of divergences that might be expected would cancel in such a gauge theory.[19] We showed that the ...
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[PDF] The GIM Mechanism
With the charm quark, a Yang-Mills electroweak theory based on SU(2) 0U(l) becomes possible for quark and leptons. FCNC processes are forbidden at tree level by ...
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[PDF] Samuel C. C. Ting - Nobel Lecture
Let me now go to the J-particle experiment [20 - 22]. I. To perform a high-sensitivity experiment, detecting narrow-width particles over a wide mass range, we ...
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[PDF] Some comments on the missing charm puzzle - arXiv
So we are still not in the position to say the final word about the existence of a missing charm puzzle. If we use an appropriate theoretical input and set µ = ...
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[PDF] observation of the muonic decay of the charged intermediate vector ...
Dec 22, 1983 · The UA1 apparatus has already been described [4–6]. Here we limit ... 1983, CERN-preprint EP/83-168. (1983). 4) UA1 proposal, A 4π solid ...
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[PDF] 9. Quantum Chromodynamics - Particle Data Group
May 31, 2024 · A review of heavy quark production at the LHC is presented in Ref. [580], where the di-b-jet pt and mass spectra are found to be well ...
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[1612.02371] Charm Production and QCD Analysis at HERA and LHC
Dec 7, 2016 · This review is devoted to the study of charm production in ep and pp collisions. The total set of measurements obtained by the two ...
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Charm production in nonresonant e + e − annihilations at √s ...
Apr 1, 1988 · We report results on the differential and total cross sections for inclusive production of the charmed particles , , , , , and in annihilations at √s=10.55 GeV.
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Measurements of prompt charm production cross-sections in $pp ...
Oct 6, 2015 · Production cross-sections of prompt charm mesons are measured with the first data from pp collisions at the LHC at a centre-of-mass energy of 13\,\mathrm{TeV}.Missing: total μb
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Neutrinos from charm: forward production at the LHC and in ... - arXiv
Jul 2, 2021 · The current LHCb experiment at CERN constrains charm production in kinematic regions relevant to the prompt atmospheric neutrino flux.
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[PDF] CHARMED MESONS (C = ±1) - Particle Data Group
D 110, 030001 (2024). CHARMED MESONS. (C = ±1). D. + ... https://pdg.lbl.gov. Page 1. Created: 9/12/2024 17 ... tral K meson are now given as K0. S modes ...
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[PDF] LHCb-CONF-2024-004.pdf
Jul 26, 2024 · The study determined the CKM angle γ to be (64.6 ± 2.8)◦, charm mixing parameters x = (0.41 ± 0.05)% and y = (0.621+0.022)%, and CP violation ...
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[PDF] Study of charm mixing and CP violation with D - arXiv
Oct 6, 2025 · Abstract. A study of charm mixing and CP violation in D0 → K±π∓π±π∓ decays is performed using data collected by the LHCb experiment in ...
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[2406.15191] Semileptonic $B$ decays from Belle and Belle II - arXiv
Jun 21, 2024 · This report summarizes recent measurements of the CKM matrix elements |V_{cb}|, |V_{ub}|, and lepton-flavor universality tests in semileptonic B decays.
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[2403.20108] Direct CP violation in D decays at LHCb - arXiv
Mar 29, 2024 · This paper presents recent LHCb measurements of CP violation in decays of charmed mesons, where the measured Delta A_{CP} is at the upper end ...
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Open charm production cross section from combined LHC ...
Jul 7, 2024 · Charm quarks are too heavy to be produced in string breakings. This means that once the amount of charm quarks available for production of heavy ...
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[PDF] Precision measurement of time-dependent charm observables at ...
Feb 1, 2021 · Designed to efficiently select heavy flavor decays from far larger background com- prising exclusively light quarks, the LHCb trigger [62] ...
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Exploring S-wave threshold effects in QCD: A heavy-light approach
Mar 10, 2020 · Here we describe how lattice QCD can be used to understand these threshold dynamics by smoothly varying the strange-quark mass when studying the heavy-light ...
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[PDF] 12. CKM Quark-Mixing Matrix - Particle Data Group
Jun 1, 2020 · The constraints implied by the unitarity of the three generation CKM matrix significantly reduce the allowed range of some of the CKM elements.
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[0706.1133] Updated constraints on new physics in rare charm decays
Jun 8, 2007 · Motivated by recent experimental results on charm physics we investigate implications of the updated constraints of new physics in rare charm meson decays.
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New physics effects in charm meson decays involving - c → u l + l
May 24, 2017 · We study the effect of the scalar leptoquark and Z ′ boson on the rare decays of the D mesons involving flavour changing transitions c → u l ...