REVIEW
Enhanced CP Violation with $B\to K D^0 (\overline D^0)$ Modes and Extraction of the CKM Angle gamma
High Energy Physics - Phenomenology · Submitted 20 Dec 1996 · 17 references
Pith's verdict: The amplitude-balancing trick and the two-mode solve for gamma are the real contribution; the numerical reach is illustrative and one key D branching ratio is guessed, not measured.
T0 · AI review
Why Pith says this
Highlight any text to comment on it.
Referee report
The paper
The paper claims
Using doubly Cabibbo suppressed D0 decays can make the CP-violating asymmetries in B± → K±D0(D0bar) decays large enough to extract the CKM angle gamma without measuring the hard-to-reach color-suppressed branching ratio.
The reading
What carries the argument
The load-bearing mechanism is amplitude balancing through doubly Cabibbo suppressed $D^0$ decays. In the standard GLW setup the color-suppressed $B^- to K^- overline D^0$ amplitude is roughly ten times smaller than the color-allowed $B^- to K^- D^0$ one, so the interference term $2sqrt{a(K)b(K)c(f)c(bar f)}cos(xi_{Kf} pm gamma)$ in Eq. (3) is a small correction. Selecting $f$ with $D^0 to f$ doubly Cabibbo suppressed and $overline D^0 to f$ Cabibbo allowed reverses which path is small, and the product of the two $D$ branching ratios then compensates the $B$-side mismatch, making the interference term comparable to the two direct terms. The second piece of machinery is the phase bookkeeping: the measured strong phase $xi_{Kf} = zeta_K + delta_f$ splits into a $B$-decay part $zeta_K$ and a $D$-decay part $delta_f$, and the differences $xi_{Kf_1} - xi_{Kf_2} = delta_{f_1} - delta_{f_2}$ tie the $B$ analysis to $D$ decay phase shifts that can be measured separately, for instance at a $psi''$ charm factory. That relation is what lets the system of equations close and, in the two-mode version, lets $gamma$ and $Br(B^- to K^- overline D^0)$ be solved for together.
Extended reading notes
Core claim
The paper's claim is that the small asymmetries of the GLW method come from an avoidable choice of final state, and that replacing CP eigenstates with non-CP-eigenstate modes where $D^0 to f$ is doubly Cabibbo suppressed while $overline D^0 to f$ is Cabibbo allowed restores balance between the interfering amplitudes. The authors estimate the ratio of the two interfering rates in Eq. (1) as $|V_{cb}V_{us}^* / V_{ub}V_{cs}^*|^2 , |a_1/a_2|^2 , Br(D^0 to f)/Br(overline D^0 to f)$, which with $|V_{ub}/V_{cb}| approx 0.08$, $|a_2/a_1| approx 0.26$ and the CLEO value $Br(D^0 to K^+pi^-)/Br(overline D^0 to K^+pi^-) = 0.0077$ comes out near one. With comparable amplitudes the partial rate asymmetry $A(K,f)$ can be of order one rather than the $O(10%)$ ceiling of the GLW case. The paper then gives two extraction schemes: one in which $Br(B^- to K^- D^0)$ is known but $Br(B^- to K^- overline D^0)$ is not, using two distinct modes $f_1, f_2$ to write four equations (Eq. 3) in the four unknowns ${xi_{Kf_1}, xi_{Kf_2}, b(K), gamma}$; and a simpler generalization of GLW using a single non-CP-eigenstate $f$ when both branching ratios are known. A worked estimate for $B^- to K^{*-}[K^+rho^-]$ gives $R approx 0.99$, $A approx 50%$ and about $5.9 times 10^7$ charged $B$'s for a $3sigma$ observation, against roughly $3.1 times 10^8$ for a single GLW CP-eigenstate mode such as $K_Spi^0$.
Load-bearing premise
The argument needs the strong phase differences in the chosen $D^0$ decays to be large and to differ appreciably between modes, so that $sin(zeta_K + delta_f)$ is sizeable for at least some $f$; the paper supports this only by pointing to some experimental evidence for final-state interactions and to the sheer number of available modes.
Editorial extensions
If this is right
- If the enhancement is real, a single non-CP-eigenstate mode such as $B^- to K^{*-}[K^+rho^-]$ reaches a $3sigma$ asymmetry measurement with roughly $6 times 10^7$ charged $B$'s, comparable to or better than the full set of GLW CP-eigenstate modes combined.
- Because the two-mode scheme determines $Br(B^- to K^- overline D^0)$ from data rather than from a semileptonic tag, the experimentally difficult measurement singled out in the paper is no longer on the critical path to $gamma$.
- The relation $xi_{Kf_1} - xi_{Kf_2} = delta_{f_1} - delta_{f_2}$ runs in both directions: $D$ decay phase shifts constrain the $B$ analysis, and a measured CP-violating phase difference yields information about strong phases in $D$ decays.
- Extending the treatment point-by-point across the $Kpipi$ Dalitz plot, where each point carries its own strong phase, turns the single-mode measurement into a binned fit for $gamma$.
- The same construction carries over from $K^-$ to $K^{*-}$ and from $D^0$ to $D^{*0}$ or higher $D$ resonances that cascade to a $D^0$, provided the spin-zero case is used or the partial waves are separated.
Reading between the lines
- The paper's reach numbers are quoted for assumed phases ($sinxi sin gamma = 1/2$, $cosxi cos gamma = 0$); a reader should expect the real sensitivity to sit somewhere between the GLW case and the quoted $50%$, depending on what the $D$ strong phases turn out to be.
- The proposal effectively converts a $B$-physics measurement of $gamma$ into a joint $B$ and charm program: the precision on $gamma$ is limited by how well $D^0 to K^+pi^-$, $K^+rho^-$ and similar phase differences can be pinned down, which argues for dedicated charm running alongside any $B$ factory.
- Because the method needs no tagging and no time-dependent analysis, it is in principle available at a symmetric $Upsilon(4S)$ machine, so the practical question is whether the relevant $D$ branching ratios and $B$ yields are reachable with existing or near-term data sets.
- The Dalitz-plot version suggests a broader statement the paper only gestures at: any resonance-dominated multibody $D$ final state supplies a continuum of strong phases, so the search for a large asymmetry becomes a scan over phase space rather than a bet on a handful of two-body modes.
Original abstract
The Gronau-London-Wyler (GLW) method extracts the CKM angle $\gamma$ by measuring $B^\pm$ decay rates involving $D^0/\overline D^0$ mesons. Since that method necessitates the interference between two amplitudes that are significantly different in magnitude, the resulting asymmetries tend to be small. CP violation can be greatly enhanced for decays to final states that are common to both D^0 and $\overline D^0$ and that are not CP eigenstates. In particular, large asymmetries are possible for final states f such that $D^0\to f$ is doubly Cabibbo suppressed while $\overline D^0\to f$ is Cabibbo allowed. The measurement of interference effects in two such modes allows the extraction of $\gamma$ without prior knowledge of $Br(B^-\to K^- \overline D^0)$, which may be difficult to determine due to backgrounds.
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.
The abstract, sentence by sentence
The Gronau-London-Wyler (GLW) method extracts the CKM angle $\gamma$ by measuring $B^\pm$ decay rates involving $D^0/\overline D^0$ mesons. Since that method necessitates the interference between two amplitudes that are significantly different in magnitude, the resulting asymmetries tend to be small. CP violation can be greatly enhanced for decays to final states that are common to both D^0 and $\overline D^0$ and that are not CP eigenstates. In particular, large asymmetries are possible for final states f such that $D^0\to f$ is doubly Cabibbo suppressed while $\overline D^0\to f$ is Cabibbo allowed. The measurement of interference effects in two such modes allows the extraction of $\gamma$ without prior knowledge of $Br(B^-\to K^- \overline D^0)$, which may be difficult to determine due to backgrounds.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The Gronau-London-Wyler (GLW) method extracts the CKM angle $\gamma$ by measuring $B^\pm$ decay rates involving $D^0/\overline D^0$ mesons. | background 0.99 | 0.04 | 0.05 | asserted 1.00 |
| s1 | Since that method necessitates the interference between two amplitudes that are significantly different in magnitude, the resulting asymmetries tend to be small. | background 0.87 | 0.07 | 0.04 | asserted 0.87 |
| s2 | CP violation can be greatly enhanced for decays to final states that are common to both D^0 and $\overline D^0$ and that are not CP eigenstates. | background 0.45 | 0.13 | 0.36 | asserted 0.56 |
| s3 | In particular, large asymmetries are possible for final states f such that $D^0\to f$ is doubly Cabibbo suppressed while $\overline D^0\to f$ is Cabibbo allowed. | method 0.46 | 0.11 | 0.15 | hedged possibility 0.94 |
| s4 | The measurement of interference effects in two such modes allows the extraction of $\gamma$ without prior knowledge of $Br(B^-\to K^- \overline D^0)$, which may be difficult to determine due to backgrounds. | contribution 0.62 | 0.28 | 0.49 | asserted 0.79 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
References
How the literature uses it
71 arXiv papers cite this in 83 sentences
Papers citing it · 64 sentences without a confident label
Uses its method or tool 2 papers
-
A solution is to include doubly-Cabibbo-suppressed $D$ meson decays, as first suggested by Atwood, Dunietz and Soni (ADS) [ref] .
Prospects for the Measurement of the Unitarity Triangle Angle gamma from B0 to DK+pi- Decays · Method · 0.83
-
In addition to the above tree-level constraints there exists a direct bound on the CKM angle [equation] It can be extracted via the decays $B →D K,D π$ [ref] .
Less space for a new family of fermions · Tree-level constraints for the CKM parameters · 0.84
Cites it as background 16 papers
-
The measurement of from , →f [ref] (where f represents a multibody final state accessible to both and ) depends on the correct description of the interference between the →f and →f decay amplitudes.[Charged conjugate modes are implied throughout unless stated otherwise.
Model independent determination of the CKM phase $\gamma$ using input from $D^0-\bar{D}^0$ mixing · Introduction · 0.81
-
The types of measurements that dominate $γ$ sensitivity are based on decays where the neutral $D$ meson decays into a $CP$ eigenstate (commonly referred to as the GLW method [ref] ), suppressed $Kπ$ state (ADS method [ref] ), or self-conjugate three-body final state such as (GGSZ or Dalitz plot method [ref] ).
Effect of direct CP violation in charm on gamma extraction from B->DK, D->K0Spi+pi- Dalitz plot analysis · Introduction · 0.91
-
Important examples include the so-called ADS modes [ref] , which are decays to quasi flavour eigenstates such as $D →K^∓π^±$, and the GLW modes [ref] , which are decays to eigenstates such as $D →K^+K^-$.
A study of $CP$ violation in $B^\mp \rightarrow Dh^\mp$ ($h=K,\pi$) with the modes $D \rightarrow K^\mp \pi^\pm \pi^0$, $D \rightarrow \pi^+\pi^-\pi^0$ and $D \rightarrow K^+K^-\pi^0$ · Introduction · 0.96
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.