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Hadronic decay modes of b

Yu Jia

Institute of High Energy Physics, CAS, Beijing

(based on hep-ph/0611130)

5th International Workshop on Heavy Quarkonia,17-20 October 2007, DESY

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Outline

1. Current experimental status of the b

2. Peculiarity about the decay mode b J/ + J/ Calculation of the decay rate in the NRQCD factoriz

ation framework.

Discovery potential of this very clean decay mode at Tevatron Run II and LHC

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Outline (cont’)

3. Estimates of branching ratios for other hadronic decay modes of b

b VV, VP (e.g. , D*D* and D*D) b 3 P (e.g. KS K )

4. Summary

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What is special about b ?

The missing pseudoscalar ground state of bottomonium family

Its existence is a solid prediction of QCD

After 30 years extensive searches, still NO conclusive evidence about its existence

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Mass of b

Various models estimated the mass splitting between (1S) and b about 20-140 GeV

Latest model-independent estimation (exploiting pNRQCD RG technique) Kniehl et al (PRL 04) M(b ) = 9.421 0.013 GeV

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Why it is so difficult to observe b

Because of its heavy mass, many hadronic decay channels of b partition the branching ratio

For a given decay channel, the branching ratio is diluted at least by a factor (mc/mb)

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In general, clean modes have rather small branching ratios, overshadowed by copious background events at hadron collider.

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One candidate event found in collision at LEP2 ALEPH (PLB 02)

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b KS K¯ ¯ + +

A fit gives: M(b) = 9.30 0.03 GeV

Lower than most theoretical predictions!

Most probably due to background

fluctuation or/ probably missing a 0

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b J/+J/: An ideal searching

mode?? Inspired by relatively large branching

ratios of c , , one may argue the analogous double J/ decay channel

b J/ + J/ 4

may have bright chance to be observed at Tevatron Run II

Braaten, Fleming, Leibovich (PRD

01)

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Estimate based on simple counting

From experimental value (PDG 06 edition) :

Br[c ] = 0.0027 0.0009

Assuming Br ~ 1/mb4 scaling, one gets

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CDF Run I preliminary (Tseng, 02)

7 events are seen, 1.8 expected from background A fit gives M(b ) = 9.445 0.006 (stat) GeV

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Potential pitfall of this analogy

Reminder: cVV is very suppressed in pQCD

e.g., light-cone approach generates vanishing amplitude even when light quark mass is kept nonzero

Anselmino, Murgia and Caruso (PRD 90) or very small in constituent quark model approach Y. J., Ms thesis (98), Jia & Zhao (HP&NP, 99) Therefore, the large experimental branching ratio se

ems to arise from nonperturbative mechanism

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Analogy between cVV and b J/ J/ may be superficial

One should not draw straightforward analogy from c to b -- the major mechanism governing exclusive decay can be rather different

b J/J/ is not expected to have room to accommodate large nonperturbative effect

PQCD is expected to be reliable in this case

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Some light shed by inclusive 4-

charm decay rate of b

Maltoni’s talk

Maltoni and Polosa (PRD, 04)

Even the low end of the simple estimate based on Br ~ 1/mb

4 assumption for Br[b J/ J/] is

larger than the inclusive 4-charm rate

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Our goal: calculate the decay rate from NRQCD factorization

QCD diagram

fragmentation-type QED diagram

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Angular Momentum Conservation requires: = ̃

The favorable decay is through (, ̃ ) = (0,0)

However, the helicity-conserving decay is strictly forbidden in such an “unnatural” process.

Chernyak and Zhitnitsky (NPB, 82)

Hadron Helicity Selection Rule Brodsky and Lepage (PRD 81)

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(, ̃ ) = (0,0) helicity state strictly forbidden: a quick proof

No enough number of independent Lorentz vectors to contract with anti-symmetric tensor for (0,0) state.

Equivalently, because of <10|10;10>=0 Y. J., MS thesis (98)

Two J/ must be transversely polarized

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Keeping transverse momentum of c plays a crucial role

LO NRQCD amplitude vanishes

Should go to NLO in v expansion Keep transverse momentum of c inside J/ is essen

tial to generate a nonzero amplitude. Helicity selection rule is violated by two units, th

erefore Br ~ 1/mb8 (power correction)

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NRQCD (color-singlet model) calculation

QCD contribution QED contribution

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Phenomenological Input

Using ee = 5.55 0.14 keV to extract (0)

I borrow the input of <v2>J/ from Bodwin et al (PRD 06)

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Numerical result

About 3 orders of magnitude smaller than the estimatebased on naive scaling assumption!

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Consistency check of my prediction

The color-singlet model prediction

Perfectly compatible with the inclusive bound set by the decay ratio to 4 charm quark

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Can we find 4 mode of b at Tevatron?

The J/ can be cleanly reconstructed through decay to muon pair.

Br[J/ +- ] 6 We get Br[b J/ + J/ 4 ] (0.2-2.4) 10-10

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Can we find 4 mode of b at Tevatron? (cont’)

Using [b] 2.5 b @ Tevatron

Maltoni and Polosa (PRD, 04)

[b] Br[b J/ + J/ 4 ] (0.050.6) fb

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The answer is absolutely no for Tevatron Run I

Tevatron Run I: 100 pb-1 data

0.0050.06 produced events

Not yet taking into account the acceptance and efficiency Will further cut down the number

Therefore, the 7 events observed at CDF Run I (Tseng, 02) must not be identified with the true b signal, merely are statistical fluctuations of continuum background events

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The answer is still very negative even for Tevatron Run II

Tevatron Run II: 8.5 fb-1 data by 2009

0.45 produced events

Acceptance & efficiency of detecting muons, plus kinematical cuts will decrease these numbers by additional two orders of magnitude

The chance for Run II to establish this decay channel seems rather unrealistic

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Can we find 4 decay mode of b at LHC?

Let us guess [b] 15 b @ LHC

LHC design luminosity: 300 fb-1 per year

1001000 produced events per year

Including acceptance & efficiency for reconstructing muon pairs (=0.1), we estimate

110 observed events per year

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The answer is perhaps YES for LHC

However, one worries about that a few signal events are overwhelmed by rather copious background events.

More study on background is welcome. Most important background is through direct double J/ production via gluon fusion: g g J/ J/+X Barger, Fleming, Phillips (PLB 96)

Qiao (PRD 02)

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Other exclusive hadronic decay modes of b

Our NRQCD-based method may be superficially applied to b VV processes.

Equivalent to constitute quark model, hopefully can catch the right order of

magnitude.

Estimating other decay (e.g., b VP, 3P) by resorting to helicity selection rule

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b decay into VV

The NRQCD-based formula may be superficially applied to b VV, hopefully will catch the right order of magnitude.

Taking <v2> 1 to characterize relativistic nature of strange quark inside

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b decay into VP

SU(3)F + Helicity selection rule

We estimate

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b decay to two charmed mesons

Suggestions are made to search for b through decay to D*D or D*D*

Maltoni and Polosa (PRD, 04)

With saturation assumption, they expect

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b decay into D*D: an estimate

Since b D*D satisfy helicity conservation, one then expects Br ~ 1/mb

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The binding probability between a heavy charm and

a light q to form charm meson is ~ QCD/mc

Braaten, Jia and Mehen (PRD,02) Therefore I estimate

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b decay into D*D*: an estimate Since b D* D* violates helicity selection rule maxi

mally, we expect that Br ~ 1/mb8

Again, q is the cause of the violation of selection rule

Therefore I estimate

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Discovery potential of b D*+D- at hadron collider

Br[b D*+D- K+ K¯ + ¯ + ¯ ]

10-8

Therefore, one expects ~ O(100) produced events at Tevatron Run I

~ O(102) produced events at Tevatron Run II

~ O(104) produced events at LHC per year

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b D*D from perturbative QCD calculation

The amplitude vanishes in the exact heavy quark spin symmetry limit.

Y.Y.Charng and Y.J. (work in progress)

So the actual branching ratio receives an

additional QCD/mc symmetry-breaking suppression, its value might be even smaller than the scaling estimate in previous slide.

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b decay into 3 pseudoscalar

Stimulated by one experimental observation Largest branching ratios of c come from 3-b

ody decays instead of 2-body decays

PDG 06

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b decay into 3P (cont’) Since these decay modes are most preferred,

we assume they exhibit leading-twist scaling

Br ~ 1/mb4

Therefore I expect

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b decay into 3P (cont’) A potentially good searching mode is b KS K

b K+ K- 0 is not so useful since ubiquitous 0 events in hadronic collision environment .

This exclusive mode has the largest branching ratio ~10-4 in what so far we have analyzed for b decay.

However, copious combinatorial background events may make the search rather difficult at hadron collider.

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Summary Have performed a pQCD calculation for b J/ + J/ Find the branching ratio is very suppressed.

The LO velocity expansion in NRQCD leads to vanishing amplitude.

Must expand the amplitude to the NLO in v2

Transverse momentum of c inside J/ is the agent to violate the helicity selection rule

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Summary (cont’) Very suppressed branching ratio implies that Run I CDF result

s (Tseng, 02) should be attributed to fluctuations of background events

It also casts doubt on the experimental efforts of searching for b through double J/ channel at Tevatron Run II

For a different point of view Santorelli’s talk

This decay channel might be worth continuing pursuit at LHC

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Summary (cont’)

It is useful to look for other hadronic decay modes which have clean signature

b KS K with a branching ratio of 10-4 may be

worth looking for, but combinatorial background is worrisome

b K* K, D*+ D- with a branching ratio of 10-5 may be difficult to search

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Summary (cont’)

Exclusive decay modes with clean signature, not necessarily to be hadronic, should also be studied

For example, b J/+ seems much more efficie

nt than b J/+J/ Qiao’s talk

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Backup Slides

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A possible Nonperturbative

Explanation for large Br[cVV]

c--’ mixing via anomaly Feldman and Kroll (PRD 00) /or via perturbative box diagram

Zhou, Ping & Zou (PRD 05)

Light quark pair from vacuum to materialize into VV 3P0 model