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
1
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
factorization framework.
Discovery potential of this very clean decay
mode at Tevatron Run II and LHC
2
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
3
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
4
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
5
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)4 relative to
c decay.
In general, clean modes have rather small
branching ratios, overshadowed by copious
background events at hadron collider.
6
One candidate event found in 
collision at LEP2
ALEPH (PLB 02)
7
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
8
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)
9
Estimate based on simple counting

From experimental value (PDG 06 edition) :
Br[c  ] = 0.0027  0.0009
Assuming Br ~ 1/mb4 scaling, one gets
10
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
11
Potential pitfall of this analogy

Reminder: cVV 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
seems to arise from nonperturbative mechanism
12
Analogy between cVV 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
13
Some light shed by inclusive 4-charm
decay rate of b
 Maltoni’s
talk
Even the low end of the simple estimate based
on Br ~ 1/mb4 assumption for Br[b J/
J/] is larger than the inclusive 4-charm rate

Maltoni and Polosa (PRD, 04)
14
Our goal: calculate the decay rate
from NRQCD factorization
QCD diagram
fragmentation-type QED diagram
15
Hadron Helicity Selection Rule
Brodsky and Lepage (PRD 81)
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)
16
(, ̃ ) = (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
17
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
essential to generate a nonzero amplitude.
Helicity selection rule is violated by two units,
therefore Br ~ 1/mb8 (power correction)
18
NRQCD (color-singlet model)
calculation
QCD contribution
QED contribution
19
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)
20
Numerical result
About 3 orders of magnitude smaller than the estimate
based on naive scaling assumption!
21
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
22
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
23
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 ]
 (0.050.6) fb
24
The answer is absolutely no for
Tevatron Run I
Tevatron Run I:  100 pb-1 data

0.0050.06 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
25
The answer is still very negative
even for Tevatron Run II
Tevatron Run II: 8.5 fb-1 data by 2009

0.45 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
26
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
1001000 produced events per year
Including acceptance & efficiency for reconstructing
muon pairs (=0.1), we estimate
110 observed events per year
27
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)
28
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
29
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 
30
b decay into VP

SU(3)F + Helicity selection rule

We estimate
31
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
32
b decay into D*D: an estimate



Since b  D*D satisfy helicity conservation,
one then expects Br ~ 1/mb4
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
33
b decay into D*D*: an estimate

Since b  D* D* violates helicity selection rule
maximally, we expect that Br ~ 1/mb8

Again, q is the cause of the violation of selection rule

Therefore I estimate
34
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
35
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.
36
b decay into 3 pseudoscalar


Stimulated by one experimental observation
Largest branching ratios of c come from 3body decays instead of 2-body decays
PDG 06
37
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
38
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.
39
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
40
Summary (cont’)


Very suppressed branching ratio implies that Run I CDF results
(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
41
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
42
Summary (cont’)

Exclusive decay modes with clean signature, not
necessarily to be hadronic, should also be studied
For example, b  J/+ seems much more
efficient than b  J/+J/  Qiao’s talk
43
Backup Slides

44
A possible Nonperturbative Explanation
for large Br[cVV]
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
45