# Presentation: 487604

## Charm Review

- Update on charm mixing
- Charm semileptonic decay
- Analysis of DK*
- Analysis of Ds
- Charm 3 body hadronic decay
- Isobar model versus K- matrix
- Dalitz analysis as probes of new physics
- Excited charm spectroscopy
- cu and cd results from Belle and Focus
- cs results from Babar/Cleo/Belle/ Focus
- The future of charm physics
- B-Factories / Cleo-c / Bes III

- Jim Wiss Univ of IllinoisAPS meetingMay 2 , 2004

- Apologies for all the important and fascinating results that I had to skip

**Notes:**
There has been significant progress in charm physics in the last few years.  I only have time for a few topics unfortunately

## charm mixing circa 2000

**Notes:**
This was the situation just about 4 years ago.  CLEO has obtained intriguing evidence for mixing through looking at the time evolution of wrong sign D*+ decays which is dominated by doubly Cabibbo suppressed – mixing interference.  Later Focus published their direct measurement of CP eigenstate ifetimes. Both effects were roughly 2 sigma.  Here was the summary of allowed measurements in the x (mass difference) versus y (lifetime difference) plane.  The black and whide hash were mapped out by E791.  Intriguing but not conclusive.

## Mixing  circa 2003

- Things have come a long way since those heady days...

- It will be interesting to see if mixing does occur at the percent level.

**Notes:**
Information on mixing is massively improving due to the advent of new very high statistics data from Belle and Babar both through mixing-DCDS interference, direct lifetime measurement and mixing through semileptonic decay.

## Dvector   decays

- H0(q2), H+(q2), H-(q2) are helicity-basis form factors computable by LQCD...

- right-handed +

- left-handed +

- Two amplitude sums over W polarization using D-matrices

- Helicity FF are combinations of vector and axial FF

- Two numbers parameterize the decay

**Notes:**
Here is a diagram showing the internal angles in terms of which the decay rate is expressed.  We call these the weak decay angle, the vector or strong decay angle, and the acoplanarity angle.  You get a fairly scary looking expression for the decay intensity but when written in this amplitude form all of the pieces are easy to understand in terms of “helicity” basis form factors that describe the  amplitude for the W to be in each of its three allowed spin states. These helicity basis form factors are combinations axial and vector pole forms shown here.  The form factors are traditionally fit two just two “form factor ratios”.

## Interference in D+ K* 

**Yield **** 31,254**

**Data****MC**

** ****K********* interferes with S- wave K******** and creates a forward-backward asymmetry in the K* decay angle with a  mass variation** **due to the varying BW phase**

- (2002)

**The S-wave amplitude is about 7% of the K* BW with a 45****o**** relative phase**

**Focus “K*” signal**

**The same relative phase as LASS**

**Notes:**
Are these isodoublet phase differences from LASS
One interesting complication to semileptonic decay was published by Focus in 2002.  Although the Kpi mass peak of focus looked pretty much like a pure K*, there was an interesting asymmetry on the K* decay angle below and above the K* peak The forward backward asymmetry as a function of kpi mass was consistent with s-wave amplitude interfering with the K* breit wigner which of course changes phase as a function of mass. This interference also created a previously unobserved  asymmetry in the acoplanarity between the K* and virtual W decay planes.

##  K*form factors

- acoplanarity

- Results are getting very precise and more calculations are needed.

**Notes:**
The s-wave interference was discovered in the process of measuring the K*munu form factor ratios.  Here are is a comparison of these measurements for RV and R2 compared quark model and lattice gauge theory.   On the right we probe some neat features of the model by showing how the acoplanarity distribution changes as a function of the K* decay angle.

## Ds form factors

- Theoretically the **Ds********l******form factor should be within 10% of  **D ********K*l****** The rV values were consistent but r2 for **Ds********l******was **** 2 higher than  **D ********K*l******

**Notes:**
Here is another result from FOCUS which bears a long standing enigma concerning the Ds to phi mu nu decay. One always expected that these form factors should lie within 10% of those for K* mu nu.  If we look at the older data we find the Rv values were consistent but the r2 values for phi mu nu (red averages) were a factor of two larger than the for D+ to K*munu (blue averages).  New precise measurements from focus changes this picture. They get an R2 for phimunu which is very consistent with K*munu.

## Dalitz plots

**“****...consistent with a phase space Dalitz distribution.”**

**Same state but higher statistics**
**Lots of structure!**

**Notes:**
Here is the earliest charm dalitz plot I am aware of.  It was for the D+ to K- pi+ pi+ and appeared in my thesis. Here is a somewhat more detailed analysis of the same state form E791 where considerable structure is evident. And a lovely K- pi+ pi0 Dalitz plot from cleo with nearly no background where considerable interference is evident between K* and rho channels.

## What do  you learn from Dalitz plots?

- Bands indicate resonance contributions
- For spinless parents, the number of nodes in the band give you the resonance spin
- Look at the ****band
- Interference pattern gives relative phases and amplitudes
- Look at the D+ K* band pattern of asymmetry

**Nearly all charm analyses use the isobar model:**

**Notes:**
Here is a particularly simple looking Dalitz plot for Ds to KK pi from E698 where the Ds appears essentially completely dominated by a phi pi and K*K.

## Why study charm Dalitz plots?

**Notes:**
the bj/aj exp(i phi) is a first order piece that parmeterizes the difference in amplitude or phase?  This is the form they use but can’t defend the form.

## Although used frequently, the isobar model has problems ...

- When broad resonances overlap you just can’t add Breit-Wigners and respect QM!

**The K and T descriptions are equivalent for a single pole but what happens when several poles contribute??**

**Notes:**
Check the algebra f2(1560) and f2(1240) about 200 MeV 

## FOCUS  D  ++- analysis

- Yield Ds+ = 1475 50
- S/N Ds+ = 3.41

- Several broad and overlapping resonances contribute
- Can they fit it using K- matrix based on fits to other data??

**Yield D****+**** = 1527 ********51**
**S/N  D****+**** = 3.64**

## “K-matrix analysis of the 00++-wave in the mass region below 1900  MeV’’ V.V Anisovich and A.V.Sarantsev  Eur.Phys.J.A16 (2003) 229

- An impressive amount of data is well described in terms of 5 poles

## K-matrix picture

***K*****-matrix picture**

- The Focus amplitude was written as a sum
- F term models S-wave using _five _virtual states ’
- An isobar BW sum represents higher spin resonances
- A coherent non –resonant piece is included

**known from scattering data ****(A&S)**

- describes coupling of
- resonances to D (_fit for couplings_)

- vector and tensor contributions

## First K matrix fits to charm Dalitz plots

**Reasonable fits with **_**no retuning**_** of the A&S K-matrix and no need to invoke new resonances (such as**** ********(400)) and **_**no**_** NR term**

## L=1 charm mesons

- One of few “good” applications of HQET to charm

- Q spin decouples leaving leaving j = LS**q** as a “good” Q-num(L=1) (Sq=1/2)  j=3/2 and 1/2

- The S**Q **acts as a perturbation and creates additional splitting

- Of course alternative splitting patterns are possible...

- The axial states might switch

## Pion transitions to D and D* 

**Notes:**
Both Belle an Focus have interesting new data that bears on the broad s-wave states and new measurements of the D1 and D2* state. I borrowed this plot from the Belle paper who have information on all three states.  The spin of this system is remarkably constrained and a great source of problems in a Jr. Level QM course.  Basically the parity of all 4 states is plus which means the decay pion must be in an even wave such as s-wave or d-wave. Assuming that the charm quark spectates The jq = 3/2 states jump to the D or D* (jq=1/2) via a Dwave while the jq = 1⁄2 states go via an S-wave. The angular momentum barrier causes the Dwave states to proceed slowly.

## Analysis of mass D spectra

**Notes:**
Let me start with the focus analys. The upper rows show the focus fit to the D pi mass spectra where an exponential like background term is included along with the PDG values of the j=3/2 D2* and D1 masses and widths.  You can see some real problem regions. The lower two plots include a broad s-wave contribution and the D2* width and centroid have been adjusted as well. In particular you can see that the D2* width that Focus prefers is significantly broader than the PDG value. These fits are quite good.  (Why weren’t the D1 parameters adjusted?) 

## Belle measured the spin 1 states as well

**Notes:**
Belle looks for the broad states by fitting the Dpipi and D*pipi Dalitz plots.  The D pi pi decay can only contain the Ds* and D*0; wile the D* pipi is accessible to all but the D0*. They thus have spin information as well as spectroscopic information.  You can see for example a lovely 2 node structure that corresponds to the (narrow) D2*and (with a bit of imagination) the one node structure corresponding to the narrow D1. The Belle numbers on the D1 state are in good agreement.

## L=1 cu and cd results

**Notes:**
Why didn’t focus fit for the D1 state?

## So on to  L=1 cs states.

- Naively expects the same spectroscopy and same pattern of decays to D and D*  pion****kaon

- Two narrow states were seen in DK and D*K transitions. Presumably the jq=3/2 spin 1 and spin 2 states.

- You then expect to see two broad states which were expected to lie above the kaon threshold and decay via s-wave

**Are  two broad states there???**
**Ask the experts?**

## New excited Ds states

- This was confirmed by CLEO and a new state was discovered D**sJ** (2463) again with a very small width

- These _could be_ the jq=1/2 states but are unexpectedly low in mass.

- Decays to Ds violate strong symmetries

- These states would be narrow if they lie below D K threshold and must decay into Ds

## What are the DsJ* (2317) and DsJ (2463)? 

- States consistent with  JP = 0+ & 1+  given pattern of observed and absent decay modes.  They could be the  j=1/2 cs, But why the low mass?
- DK molecule?  (Barnes/Close/Lipkin)
- 4 quark state
- j=1/2 (1+ , 0+ ) states are chiral partners to the (1-  0- ) or (Ds* Ds)(Bardeen/Eichten/Hill)

- Bardeen/Eichten/Hill predict a Goldberger-Trieman-like splitting  for 1 and 0 states which works for  Ds1’ Ds0*

-  But: 1+  - 1-  0+ - 0-  430 MeV for cu and cd based on Belle measurements

## Some preliminary cs results from Focus

**Notes:**
What are the hashed background Sidebands and WS

## Back to the Future: Charm threshold

**Closing the neutrino in D ********e******** events using energy momentum balance**

**Exploiting quantum coherence**

**Cleo-c and Bes III: Run at  ********(3770) with high luminosity and a modern detector**

**The future of charm is very bright!**

## My Notes

- Cleo98?

- S and D wave required by parity

**Notes:**
Are these theoretical estimates?  Appears to break doublet structure.  Agrees with theory in Bigi paper

## Semileptonic decay as tests of LQCD

- Apart from form factors, these decays can be computed using perturbation theory

## CP violation in the   kspi+pi-  Dalitz plot ?

- 2579 D0

- 2720 D0

- Nov 2003

## Probes of D mixing          

- (assuming CP conservation)

- ,

- Probes of D mixing** **

- Processes which allow               mixing appear in ***H******12*** and* ****H******21***.

- Mass and width differences are parametrized
- by between D1 and D2 are given by

- An alternative probe is to directly compare the lifetime of CP eigenstates or mixed eigenstates.

**Notes:**
Let me now remind the key features of particle-antiparticle mixing this is irrespective of flavour and it applies to pseudoscalar mesons

## New cu cd L=1 spectroscopy

| Mass | D2*0 | D2*+ |  | “D01/2” | “D+1/2” |
| --- | --- | --- | --- | --- | --- |
| Focus03

PDG03
BELLE03 | 2464.5±1.1
±1.9

2458.9±2.0
2461.6± 2.1 ± 3.3 | 2467.6±1.5
±0.76

2459±4 |  | 2407±21±35

2308± 17 ± 32 | 2403±14
±35 |
| Width |  |  |  |  |  |
| Focus03

PDG03
BELLE03 | 38.7±5.3
±2.9
23±5
45.6± 4.4
± 6.6
 | 34.1±6.5
±4.2
25+8-7 |  | 240±55
±59

276±21 
± 66  | 283±24
±34 |

- Results roughly agree (1.8 ) between  BELLE  hep-ex/0307021. FOCUS hep-ex/0312060

| 538 ± 39 |
| --- |
| 564 |
| 509 |
| 563 |
| 699 |
| 520 |
| 520 |
| 489 |
| 259 |
| 374 |

| Focus |
| --- |
| Kalashnikova 02 |
| Di Pierro (2001) |
| Ebert et al. 1998 |
| Isgur (1998) |
| Godfrey and Kokoski (1991) |
| Godfrey & Isgur (1985) |
| Eichten et al. (1980) |
| Barbieri + (76) |
| De Rujula + (76)  |

- <D1/2>-D

**Notes:**
On the left we compare the FOCUS/Belle/and previous PDG values for the mass and width parameters of the broad s-wave resonance as well as the narrow D2* state.  Both Belle and Focus agree the D2* state width is more like 40 MeV rather than the previously thought 23 GeV. Both experiments have consistent widths for the broad s-wave resonance of about 250 MeV.  The Focus value of the centroid is about 1.8 sigma higher. In all cases the errors are reasonably close. I don’t think either experiment can prove that they are observing the broad spin 0 state (D0*) but could easily be measuring a combination of the two and it is possible that the ratio of the two is different so we don’t want to take this centroid difference too seriously. On the right the broad centroid is compared to several theoretical predictions dating from 1976 to 2002. Focus shows the average of the charged and neutral state mass minus the mass of a D0 and makes the comparison assuming they are primarily observing the D0* state. I highlighted in red the theory predictions that lie within one sigma of the Focus measurements.   

## Belle measured the spin 1 states as well

|  | M D1 | D1
 | M D1’ |  D1’
 |
| --- | --- | --- | --- | --- |
| Belle (03) | 2421.4 ± 1.5 ± 0.9 | 23.7 ± 2.7
± 4 | 2427± 6±25 | 384± 91
±74 |
| Cleo (99) |  |  | 2461 ± 45 | 290 ± 110 |
| WA 03 | 2422 ±1.8 | 18.9 ± 4 |  |  |

**Notes:**
Belle looks for the broad states by fitting the Dpipi and D*pipi Dalitz plots.  The D pi pi decay can only contain the Ds* and D*0; wile the D* pipi is accessible to all but the D0*. They thus have spin information as well as spectroscopic information.  You can see for example a lovely 2 node structure that corresponds to the (narrow) D2*and (with a bit of imagination) the one node structure corresponding to the narrow D1. The Belle numbers on the D1 state are in good agreement.