D-Dbar mixing and new physics: general considerations and constraints on the MSSM

D. Guadagnoli; E. Franco; L. Silvestrini; M. Ciuchini; M. Pierini; V. Lubicz; V. Porretti

REVIEW

D-Dbar mixing and new physics: general considerations and constraints on the MSSM

M. Ciuchini, E. Franco, D. Guadagnoli, V. Lubicz, M. Pierini, V. Porretti, L. Silvestrini

High Energy Physics - Phenomenology · Submitted 19 Mar 2007 · 24 references

Pith's verdict: A timely, careful letter that turns the 2007 D-mixing evidence into real bounds on up-type squark mixing — the flat A_SM prior is conservative, not fragile, so the δ limits hold up better than the reader thinks.

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arXiv IDhep-ph/0703204 (version 3)

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CitationD. Guadagnoli, E. Franco, L. Silvestrini, M. Ciuchini, M. Pierini, V. Lubicz, V. Porretti. "D-Dbar mixing and new physics: general considerations and constraints on the MSSM." arXiv:hep-ph/0703204 (2007). https://pith.science/paper/NKR3UNJT

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Editor's note

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This is the paper that took the first BaBar/Belle D–Dbar mixing evidence and made it do work. Two things are genuinely new: a model-independent fit of the mixing amplitude and its CP phase that allows CP violation in mixing (unlike the HFAG averages of the day), and the translation of that into 95% bounds on the up-type squark mass insertions (δ^u_12)_AB. The headline number — |(δ^u_12)_LL| < 0.033 at 350 GeV — is about a factor of three tighter than Nir–Raz, and the conclusion that quark–squark alignment models (δ_LL ~ 0.2) need squarks and gluinos above ~2 TeV, likely past LHC reach, is a real narrowing of the discovery window. The machinery is standard and correctly assembled: MIA, published NLO gluino Wilson coefficients, RGE down to 2.8 GeV, lattice B parameters in Table IV. Nothing is oversold, and the inputs and correlations are all in Table I, so anyone can redo the fit. Credit where due: they also state plainly that the unknown long-distance SM piece dilutes the φ_NP bound. That honesty is worth noting, not penalizing. On the reader's weakest link: I think the flat A_SM ∈ [−0.02, 0.02] ps⁻¹ prior is being over-weighted as a vulnerability. It is wider than the measured 95% range of |M12| and much wider than typical SM estimates, so it dilutes A_NP and makes the δ bounds conservative upper limits. A better long-distance calculation would tighten them, not break them. The stress-test note is right on this. What does deserve more attention is that the 95% A_NP bound (0.02 ps⁻¹) is essentially the full prior range, so the 68% number (0.006) is the one carrying real information; the paper could say so more clearly. The other loose end is the assumed real Γ12 — stated, never quantified — and the MIA extrapolation from the tabulated δ ≲ 0.1 up to δ ~ 0.2 for the 2 TeV claim. Neither is fatal, but both are worth a referee question. Overall: a solid, useful, appropriately short letter from people who know this calculation. It is the reference for D-mixing constraints on up-type squarks and will be cited as such. Send it out; the referees will have a short list of questions, not a long one.

Referee report

Significance

The paper is a timely and useful Letter: it is among the first to convert the 2007 D-mixing evidence into quantitative constraints on the up-type squark flavour structure, a sector that had been only weakly bounded. The strengths are real and should be credited. The experimental inputs and their correlations are tabulated transparently (Table I), the fit allows for CP violation in mixing rather than assuming it away, and the mass-insertion calculation uses published NLO Wilson coefficients and lattice B parameters rather than ad hoc estimates. The resulting bounds in Table V are falsifiable and directly comparable to model predictions, and the choice of a deliberately wide A_SM prior makes the quoted limits conservative upper bounds rather than fragile ones. The conclusion that alignment models are pushed to the multi-TeV regime is a physically important, testable statement.

Major objections (3)

[Text following Table V (alignment prediction and 2 TeV conclusion)] The strongest phenomenological statement of the paper — that alignment models with (δ^u_12)_LL ∼ 0.2 require squark and gluino masses above ∼2 TeV and 'probably lie beyond the reach of the LHC' — rests on extrapolating the mass-insertion result beyond the regime in which it was computed. The bounds in Table V are quoted for δ values at most 0.14, and the MIA is a perturbative expansion in δ; the paper's own justification ('the lowest non-vanishing order ... gives an excellent approximation ... given the tight experimental constraints') applies precisely where δ is small, not at δ ∼ 0.2. The authors should either qualify the 2 TeV sentence explicitly as an extrapolation of the MIA scaling, or support it with a check against the full (non-MIA) amplitude at δ ∼ 0.2. As written, the headline corollary is less controlled than the bounds themselves.
[Table III and Table V (95% bounds)] The 95% upper bound on A_NP in Table III is 0.02 ps^−1, which is exactly the upper edge of the assumed flat prior [−0.02, 0.02] ps^−1; the 95% A_NP bound is therefore prior-saturated and carries essentially no information beyond the choice of prior. Since the 95% δ bounds in Table V are derived from this prior-saturated A_NP limit, they are correspondingly weak, and the informative constraint is the 68% bound (0.006 ps^−1). The paper should quote the 68% δ bounds alongside the 95% ones, or justify why only the 95% column is presented, because the comparison 'a factor of ∼3 more stringent than ref. [6]' depends on which probability level is being compared.
[Table I (cos δ_Kπ input)] The input cos δ_Kπ = 1.09 ± 0.66 in Table I is unphysical, since the cosine of a phase cannot exceed unity; the Gaussian spills well outside the kinematic range. Because this input is used to rotate (x′, y′) into (x, y), the treatment of the boundary can affect the extracted mixing parameters and hence the downstream A_NP bounds. The authors should either fit δ_Kπ directly as a bounded parameter or state explicitly how the unphysical region is handled in the likelihood.

Minor objections (6)

[Abstract and text after Table II] The abstract advertises 'model-independent information' on the mixing amplitude and phase, but the A_NP and φ_NP ranges in Table III depend on the flat A_SM prior and on the assumption of no accidental cancellations. The |M12| and Φ12 extraction is model-independent; the new-physics bounds are not. A short qualification in the abstract or introduction would align the wording with the body.
[Text before Table I] The assumption that Γ12 is real is stated but its quantitative impact on the fit is not shown. A brief estimate of how the |M12|, Φ12 ranges shift if a small imaginary part of Γ12 is allowed would strengthen confidence in the quoted errors.
[Table II (Φ12)] The fit returns two branches, Φ12 = (2 ± 14)° ∪ (179 ± 14)°, but the second branch is not discussed in the text. The reader would benefit from a sentence on its origin and on whether it affects the A_NP/φ_NP ranges.
[Table II] Only 68% and 95% ranges are given for the fitted parameters, with no correlation matrix. Since the δ bounds depend on the joint A_NP–φ_NP distribution, providing at least the leading correlations would make the propagation to Table V reproducible.
[Table IV and Table V] The uncertainties on the B parameters in Table IV are not propagated into the bounds of Table V. A statement of the resulting theoretical error on the δ limits would help the reader judge how much of the quoted bound is robust.
[Table I versus Table II (y)] The fitted y = (5.5 ± 1.4)×10^−3 in Table II sits noticeably above the direct input y = (3.4 ± 2.8)×10^−3 in Table I, driven by y_CP. A comment on this pull and on consistency with the direct Belle/CLEO determination would be useful.

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The paper

The paper claims

New D-meson mixing data turns into hard limits on the squark partners of the up and charm quarks, with aligned supersymmetry pushed toward the TeV scale.

The reading

For years the charm sector was the one place where new physics could hide almost unconstrained, because no one had seen a $D^0$ meson turn into its antiparticle. The paper takes the first combined evidence for that oscillation from BaBar and Belle, fits it for the mixing amplitude $|M_{12}|$, the width difference $|Γ_{12}|$ and the CP-violating phase $Φ_{12}$, and then asks how much of the measured mixing could come from something other than the Standard Model. The answer is: not much, and certainly not with a large CP-odd phase. That leftover room is then translated, through the standard mass-insertion expansion of supersymmetric flavour physics, into upper bounds on the off-diagonal entries of the up-type squark mass matrix connecting the up and charm flavours. The payoff is a concrete statement about model building: mechanisms that align quark and squark mass matrices, which naturally predict a mixing of order $0.2$, now require squark and gluino masses above roughly $2$ TeV, plausibly out of the LHC's reach.

What carries the argument

The argument runs on two machines. The first is a global fit that writes every charm mixing and CP observable in terms of just three quantities, $|M_{12}|$, $|Γ_{12}|$ and the phase $Φ_{12}$, so that the experimental inputs collapse onto a small parameter space; a flat prior on the Standard Model amplitude $A_{SM}$ over $[-0.02, 0.02]$ ps$^{-1}$ then converts the fitted $|M_{12}|$ into a probability distribution for the new-physics amplitude and phase. The second is the mass-insertion approximation in the super-CKM basis, where the off-diagonal squark mass terms $(δ^u_{12})_{AB}$ are treated as perturbations connecting up and charm squarks of helicity $A$ and $B$, divided by the average squark mass. Because the experimental bounds force these insertions to be small, the leading order of that expansion is an excellent approximation, and the translation from $A_{NP}$ to $(δ^u_{12})_{AB}$ is a one-loop calculation. Chirality-flipping insertions are punished by renormalization-group running, which is why the $LR$ and $LL=RR$ bounds come out an order of magnitude below the $LL$ one.

Extended reading notes

Core claim

The paper's central claim is that the newly reported $D-⁻D$ mixing evidence, combined with earlier charm measurements, is already sharp enough to constrain new physics in the up-quark sector. Fitting the world data on $x$, $y$, $|q/p|$, $y_{CP}$, $A_Γ$, $R_M$ and the strong phase $δ_{Kπ}$ simultaneously, the authors obtain $|M_{12}| = (7.7 ± 2.4) × 10^{-3}$ ps$^{-1}$ and $Φ_{12} = (2 ± 14)°$ (with a mirror solution near $180°$), and $|Γ_{12}| = (13.6 ± 3.5) × 10^{-3}$ ps$^{-1}$. Treating the full amplitude as a real Standard Model piece plus a new-physics piece $A_{NP} e^{iφ_{NP}}$, they find $A_{NP} < 0.006$ ps$^{-1}$ at 68% probability and $A_{NP} < 0.02$ ps$^{-1}$ at 95%, with $φ_{NP}$ restricted to bands near $0°$ and near $180°$. Feeding these into gluino-exchange box diagrams with next-to-leading-order Wilson coefficients and lattice $B$ parameters, they quote 95% bounds such as $|(δ^u_{12})_{LL}| < 0.033$ for $350$ GeV squarks and gluinos, tightening to $0.0020$ when left- and right-handed insertions are switched on together. These are roughly a factor of three stronger than the previous bounds in the literature.

Load-bearing premise

The Standard Model's own charm mixing amplitude is taken as a flat guess spread over $-0.02$ to $0.02$ ps$^{-1}$ rather than calculated, and that chosen range alone decides how much room is left for new physics and therefore sets every bound in the paper.

Editorial extensions

If this is right

Any extension of the Standard Model that generates $D-⁻D$ mixing must keep its new-physics amplitude below about $0.006$ ps$^{-1}$ at 68% probability, with a CP-violating phase clustered near $0°$ or $180°$.
In the Minimal Supersymmetric Standard Model with gluino mediation, the up-charm squark mixing entries obey 95% bounds of order $10^{-2}$ to $10^{-3}$ depending on helicity structure, for squark and gluino masses of a few hundred GeV.
Supersymmetric models built on quark-squark alignment, which generically predict $(δ^u_{12})_{LL} \sim 0.2$, survive only if squark and gluino masses exceed roughly $2$ TeV.
If the mixing amplitude turns out to be dominated by new physics, the measured phase $Φ_{12}$ becomes a direct experimental handle on the new-physics CP phase $φ_{NP}$.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The charm sector has now joined the down-type sector as a place where flavour models can be checked, so alignment-type constructions face constraints from both up-type and down-type squarks at once; that squeeze is likely tighter than either bound applied separately.
Because the quoted bounds scale roughly linearly with the assumed new-physics amplitude, a future lattice determination of the long-distance Standard Model charm mixing contribution would shift every number in the mass-insertion table, in either direction.
The bound is quoted for gluino exchange only; extending the same fit to neutralino or chargino boxes, or to non-degenerate squark spectra, would test whether the factor-of-three improvement over earlier work survives when the mediator changes.
The $2$ TeV conclusion is a statement about the simplest alignment ansatz; a model that aligns squarks only in the down sector, or that suppresses the up-charm entry by an additional flavour symmetry, would evade it without contradicting the data.

Original abstract

Combining the recently available experimental evidence of D-Dbar mixing, we extract model-independent information on the mixing amplitude and on its CP-violating phase. Using this information, we present new constraints on the flavour structure of up-type squark mass matrices in supersymmetric extensions of the Standard Model.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,272 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.09 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.13 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

Combining the recently available experimental evidence of D-Dbar mixing, we extract model-independent information on the mixing amplitude and on its CP-violating phase. Using this information, we present new constraints on the flavour structure of up-type squark mass matrices in supersymmetric extensions of the Standard Model.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Combining the recently available experimental evidence of D-Dbar mixing, we extract model-independent information on the mixing amplitude and on its CP-violating phase.	result 0.67	0.86	0.18	asserted 1.00
s1	Using this information, we present new constraints on the flavour structure of up-type squark mass matrices in supersymmetric extensions of the Standard Model.	contribution 0.60	0.93	0.60	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.95 · evidence from analysis of existing data 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** FIG. 1: Probability density functions of the combined fit fro

**Figure 2.** FIG. 2: Probability density functions of the combined fit fro

**Figure 3.** FIG. 3: Selected regions in the Re(

Figures reproduced from arXiv:hep-ph/0703204 by the authors.

References

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Forward citations

Cited by 14 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

D-Dbar Mixing in the Standard Model and Beyond from Nf=2 Twisted Mass QCD
hep-lat 2014-03 conditional novelty 6.0 of 10

First unquenched lattice QCD determination of the full set of D-meson mixing bag parameters, used to set lower bounds on the new-physics scale and on squark mass terms.
Observation of D0-D0bar oscillations
hep-ex 2012-11 accept novelty 6.0 of 10

The LHCb experiment observes D0-D0bar oscillations at 9.1 standard deviations in a single measurement, with y' = (7.2 +/- 2.4) x 10^-3 and x'^2 = (-0.9 +/- 1.3) x 10^-4.
Hierarchical Soft Terms and Flavor Physics
hep-ph 2008-12 conditional novelty 6.0 of 10

Making the first two squark generations heavy produces a specific, testable pattern of flavor violation in which the d-to-s transition is fixed by the product of d-to-b and b-to-s transitions, allowing a B_s mixing ph...
\Delta S=2 and \Delta C=2 bag parameters in the SM and beyond from Nf=2+1+1 twisted-mass LQCD
hep-lat 2015-05 accept novelty 5.0 of 10

Using Nf=2+1+1 twisted-mass lattice QCD, the ETM Collaboration determines the kaon bag parameter B_K^RGI = 0.717(24) and the full set of BSM bag parameters for K and D mixing.
Measurement of D0-D0bar mixing parameters and search for CP violation using D0->K+pi- decays
hep-ex 2013-09 accept novelty 5.0 of 10

With 3 fb^-1 of LHCb data the D0-D0bar mixing parameters are measured to x'^2 = (5.5 ± 4.9)e-5, y' = (4.8 ± 1.0)e-3 and R_D = (3.568 ± 0.066)e-3, with no evidence for CP violation (A_D = (-0.7 ± 1.9)%).

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D-meson lifetimes within the heavy quark expansion
hep-ph 2013-05 conditional novelty 5.0 of 10

Including NLO QCD and 1/m_c^4 corrections, the heavy quark expansion reproduces the D+/D0 and Ds+/D0 lifetime ratios within large hadronic uncertainties, with no sign of breakdown at the charm scale.
New Physics Models of Direct CP Violation in Charm Decays
hep-ph 2012-02 accept novelty 5.0 of 10

A systematic survey finds that only a handful of minimal new-physics models, chiefly those with chirally enhanced chromomagnetic penguins, can explain the LHCb charm CP asymmetry without violating D-meson mixing and c...
Anatomy and Phenomenology of FCNC and CPV Effects in SUSY Theories
hep-ph 2009-09 accept novelty 5.0 of 10

Correlation patterns among B, K, D and lepton observables separate supersymmetric flavour models with right-handed currents from those with left-handed currents, and both from Little-Higgs and Randall-Sundrum alternatives.
On Indirect CP Violation and Implications for D0-\overline{D0} and Bs -\overline{Bs} mixing
hep-ph 2009-07 accept novelty 5.0 of 10

A model-independent relation ties CP violation in mixing to CP violation in decay interference, and a fit to D0 data bounds the mixing phase phi12 at about 0.10 radian at 1 sigma.
The Standard Model and Supersymmetric Flavor Puzzles at the Large Hadron Collider
hep-ph 2007-12 conditional novelty 5.0 of 10

Four explicit supersymmetric models show that TeV-scale new physics need not be minimally flavor violating, and that LHC slepton measurements could distinguish their mixing patterns.
Model-independent constraints on Delta F=2 operators and the scale of New Physics
hep-ph 2007-07 accept novelty 5.0 of 10

Model-independent bounds on all Delta F=2 operators imply that new physics with non-minimal flavor structure must lie above about 60 TeV, beyond LHC reach.
Implications of D^0-\bar D^0 Mixing for New Physics
hep-ph 2007-05 conditional novelty 5.0 of 10

Using the 2007 evidence for D0 mixing, the authors derive upper bounds on new-physics contributions to the charm mass difference for about twenty models, several of which beat competing constraints.
Lessons from Recent Measurements of D-\bar D Mixing
hep-ph 2009-06 conditional novelty 4.0 of 10

Small CP violation in D0 to anti-D0 mixing pushes generic new-physics scales above 10^2 to 10^3 TeV and forces percent-level squark degeneracy or strong flavor suppression for any TeV-scale model.
Flavor Physics Constraints for Physics Beyond the Standard Model
hep-ph 2010-02 accept novelty 3.0 of 10

Existing flavor-changing and CP-violating measurements force TeV-scale new physics to have a highly non-generic flavor structure, and the review catalogs those bounds, the Minimal Flavor Violation escape route, and th...

How the literature uses it

52 arXiv papers cite this in 76 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 46 sentences without a confident label

Uses its method or tool 2 papers

This is performed using the formula ⟨D^0|ℋ_eff^ΔF=2|D^0⟩_i=∑_j=1^5 ∑_r=1^5 ( b_j^(r,i)+ηc_j^(r,i) ) η^a_j C_i(Λ) ⟨D^0|Q_r^cu|D^0⟩and the relevant inputs given in [ref] .

Lessons from Recent Measurements of D-\bar D Mixing · Model independent constraints · 0.84
[ref] , in particular their eqs.

TeV Scale Left Right Symmetry and Flavor Changing Neutral Higgs Effects · Numerical Analysis · 0.99

Uses its data or values 11 papers

In our calculation, the following inputs are adopted. $m_t=171.2$GeV, $M_W=80.4$GeV, $α_s(M_Z)=0.118$, and the mass [ref] , decay constants [ref] and the bag parameters [ref] are listed in Table.([ref]).

The Mass Difference of $F-\bar{F}$ with SO(3) Family Gauge Symmetry · Numerical results · 1.00
Finally, concerning $D^0 -D̅^0$ mixing, we use as input the results for the NP amplitude obtained in Ref. [ref] combining the experimental information from Refs. [ref] .

Model-independent constraints on Delta F=2 operators and the scale of New Physics · Experimental input · 0.99
The most stringent constraint in the up-sector comes from $ΔM_D$ [ref] : ΔM_D => |(δ^u_12)_LL|,|(δ^u_12)_RR| 6 ×10^-2 , |(δ^u_12)_LR|,|(δ^u_21)_LR| 10^-2 for $m_q̃ =0.5$ TeV.

Flavor Changing Neutral Higgs Bosons in a Supersymmetric Extension based on a $Q_6$ Family Symmetry · FCNC · 0.96

Compares with it 6 papers

We obtain r/r_30.13, in agreement with previous works [ref] .

Flavor Changing Processes in Supersymmetric Models with Hybrid Gauge- and Gravity-Mediation · Holomorphic zeros · 0.89
Using Eq. ([ref]) above, this results in the constraint on squark and gluino masses of (assuming $m_q̃ ≈m_g̃$ for simplicity) $m_g̃,q̃2$ TeV, which agrees with the results in Refs. [ref] .

Implications of D^0-\bar D^0 Mixing for New Physics · Quark-Squark Alignment Models · 0.94
In this section we compare our bounds with those in the literature, derived from FCNC processes [ref] and vacuum stability (VS) bounds [ref] .

Supersymmetric renormalisation of the CKM matrix and new constraints on the squark mass matrices · Comparison with previous bounds · 1.00

Cites it as support 2 papers

In particular, since $(δ^u_12)_LL$ and $(δ^d_12)_LL$ mass insertions are related to each other and the mass splitting between $d̃_L$ and $s̃_L$ by the Cabibbo angle, it appears less likely that squark and quark masses are merely aligned; rather a near degeneracy of at least the left-chiral squarks of the first two generations is necessary [ref] .

Supersymmetry beyond minimal flavour violation · $D - D̅$ mixing · 0.98
Actually, by combining the constraints from $K^0-K^0$ mixing and $D^0-D^0$ mixing, one can show that this is the case independently of assumptions about the alignment [ref] .

Flavour Physics and CP Violation · The supersymmetric flavor puzzle · 0.98

Cites it as background 8 papers

The highlight of this year's Moriond conference on electroweak interactions and unified theories arguably was the announcement by BaBar and Belle of experimental evidence for $D^0$-$D̅^0$ mixing [ref] , which was quickly followed by a number of theoretical analyses [ref] .

Implication of the D^0 Width Difference On CP-Violation in D^0-\bar D^0 Mixing · Introduction · 0.89
Ref. [ref] has addressed $B$ mixing at NLO, Ref. [ref] contains an update of the constraints from $b→s$ transitions and Ref. [ref] has discussed D mixing.

Chirally enhanced corrections to FCNC processes in the generic MSSM · Introduction · 0.94
It was discussed whether the measured size of the mixing parameters could be interpreted as a hint for physics beyond the standard model [ref] .

Brief Review of Charm Physics · Charm mixing · 0.88

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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