Quarkonia spectroscopy at CDF

Quarkonia spectroscopy at CDF

Ulrich Kerzel, University of Karlsruhefor the CDF collaboration

Heavy Quarkonia 2006Content:• X(3872)

• m(+ -) mass spectrum • quantum numbers JPC

• search for b

June 2006 U.Kerzel, University of Karlsruhe ---- Workshop on Heavy Quarkonia 2

• huge inelastic cross-section:¼ 5000 times bigger than for) triggers are essential!

• events “polluted” by fragmentation tracks, underlying event, pile-up

) need precise tracking and good resolution

Heavy quark physics at the Tevatron

• dedicated trigger for • J/ ! + -: m(+-) around m(J/) ) high quality J/ events with large statistics (channel

J/ ! e+e- much more challenging in hadronic environment)

• lepton + track with large IP (semi-leptonic B decay) • two tracks with large IP (hadronic B decay)

bb


The X(3872)

) what is the X(3872)? charmonium? exotic?! determine quantum numbers JPC

• m(+ -) sensitive to JPC

• use distribution of angles between decay particles to measure JPC

2S) ! J/ + -

known resonancecc

• discovered 2003 by Belle in search for charmonium states• m(+ -) spectrum compatible with 0

CDF PRL 96,102002 (2006)

• mass: m = 3871.3 § 0.7 § 0.4 MeV/c2 CDF PRL 93,072001 (2004) , width compatible with detector resolution

< 2.3 MeV/c2 Belle PRL 91,26001 (2003)

• No X++ or X– -- CDF PRL 93,072001 (2004)

• No iso-partner X§ BaBar PRD 71, 031501 (2005)

• Evidence for X ! J/ , J/ Belle hep-ex/0505037


m(+ -) mass spectrum for (2S)

• (2S) in same exclusive final state

• m(+-) spectrum known:

s-wave with small d-wave contribution

e.g. model byNovikov-Shifman

) high precision data by CDF) allows to discriminate between models


The m(+ -) mass spectrum

if (+-) in s-wave state:shape needs to be modellede.g. multipole expansions for

if (+-) in p-wave state:shape follows Breit-Wignere.g. decay via 0 ! + -

• m(+-) favours high end of mass spectrum ) compatible with intermediate 0 ! + - resonance

• also 3S1 multipole-expansion for charmonium possible• no charmonium candidate at that mass• 3S1 also has JPC = 1- - ) non-observation by BES

((e+e-)B(+-J/) < 10 eV @90% C.L. )

notation: n2s+1LJ (JPC)

Phys.Lett.B579:74-78 (2004)

cc

Mass spectrum sensitive to JPC


The m(+ -) mass spectrum

Possible 0 - mixing:• mass contribution far from pole position

• interference 0 $ possible

) L=0 and L=1 both compatible with m(+-) spectrum) mixing phase of 95± describes data

for broad resonances (0):• kinematic quantities vary across width• introduce form-factor

e.g. Blatt-Weisskopfdepends on ang. momentum L,effective range R

) affects shape for L=0, L=1


example: JPC assumptions

Determination of JPC (1)definition of angular variables:


Determination of JPC (2)

• Predictions for kinematic decay quantities from helicity formalism: ) decay chain as sequential 2-body decays

X(3872) ! J/ (+-)s,p ! + - + -

need:• one matrix element per decay vertex• propagators to connect vertices

matrix elements: angular part A and kinetic part T

assume state with lowest L dominates, neglect others• dedicated simulation for each JPC hypothesis

(including detector effects)• compare to angular distributions measured in data via 2

M / M X £³PJ =Ã ¢M J =Ã

´£ P¼¼¢M ¼¼

M A J i;¸ iµ;Á ¢T j~pj; L


Determination of JPC (3)

Limitations from helicity formalism:• no model-independent description of +- in s-wave• Breit-Wigner for 0 ! +- depends on form-factor details

) fix m distribution to match the data ) analyse angular distributions only

N.B. 0 and have both JPC = 1- -

) angular distributions not affected by potential interference

• JPC = 1-+ and 2-+: multiple sub-states with same L contribute

) Can an arbitrary mixture describe the data?

M ¡ reiÁ M ¡ S reiÁM ¡

S reiÁM ¡ S

M ¡ reiÁ M ¡ S reiÁM ¡

S


Result for (2S)

obtain expected result:

JPC = 1- -

Exploit correlations between angles via 3D fit:• 3 bins in • 2 bins in J/

• 2 bins in


Result for X(3872)

Only JPC = 1++ or 2-+ compatible with data!All other tested hypotheses excluded by > 3

J P C Â ¡ ¡ ¡ ¡ ¢ ¡

¡ ¢ ¡

¡ ¡ ¢ ¡

¡ ¢ ¡

¡ ¡ ¢ ¡

¢ ¡

¡ ¢ ¡

¡ ¢¡

¡ <¢¡

<¢¡


What is the X(3872) ?? Charmonium ?

potential candidates:

but: decay via 0: isospin violating mass predictions from potential models ¼ 50-100 MeV/c2 off

exotic? m(X) ¼ m(D0) + m(D0*) ! coincidence? charmed molecule ? ( or or ...)

hybrid state, i.e. ? (but expected above ¼ 4 GeV/c2)

mainly charmonium - but interaction with ? ccg

notation: 2s+1LJ (JPC)

Â0c P J P C

´c D J P C ¡

D D ¤e.g. M. Suzuki hep-ph/0508258

D D ¤ccqq


X(3872) with neural networks

Use sophisticated neural networks for“next generation” X(3872) analyses:

• exploit correlations between variables ! improved candidate selection

• train networks for multiple JPC assignments• further handle to test hypotheses:

“good” hypotheses ! higher significanceto be used in likelihood analyses

• strong suppression of combinatorial BG ! to be used in search for

partner of X(3872) in B system:X b ! S¼ ¼¡


Search for b (1)• ground state of system• test NRQCD:

~30-160 MeV/c2 lighter than • not yet observed, searches:

• LEP ! b

• CLEO • 2 evidence from CDF RunI

bb

• search in exclusive final state:b ! J/ J/ ! +- +-

JPC: 0-+ ! 1- - 1- -

BR( ! ¼ 40%

Rc ! ) ¼ 3¢ 10-3

expect BR ¼ 7¢ 10-5 – 7¢ 10-3

Phys. Rev. D 63, 094006 (2001)

S

nS ! ´b°


Search for b (2)

• use 1.1 fb-1 data from J/ ! +- trigger• candidate selection:b ! J/ J/2 of vertex fit < 18.5|| < 0.6pt (b) > 3 GeV/c

J/ (1): J/ ! +- trigger || < 0.6pt (J/ ) > 3 GeV/cpt (§) > 2.0 GeV/c

J/ (2): + trackpt(J/) > 3 GeV/cpt(§) > 2 GeV/c (||<0.6) or

> 3.5GeV/c (0.6 < || < 1.0)pt(track) > 1.5 GeV/cdE/dx residual < 3.7(track)

pt(J/) > 50 GeV/c


Search for b (3)

after cuts:3 candidates observed in 9.0 – 9.5 GeV/c2,expect 3.6 background events

) no significant evidence of b

) upper limit on b production cross-section

¾pp! ´bX ¢Br´b! J =ÃJ =Ã¾pp! b! J =ÃX < ¢ ¡


Conclusions & Outlook Tevatron and CDF performing well, rich B physics

programme New results on X(3872):

3D angular analysis: JPC = 1++ or 2-+

m(+-): both L=0 or L=1 transition via 0 compatible with data

) cannot exclude J hypotheses from m(+ -)

possibly 0 $ interference with =95±

) both charmonium and exotic interpretation still “in the game” further analyses using neural networks started ongoing search for

in molecular picture: expect further states similar to X(3872), e.g.

Search for b ! J/ J/ no signal observed, upper limit on production cross section

B B ¤X b ! S¼ ¼¡


BACKUP


• • • 1 fb-1 delivered June 2005• 15-20 pb-1/week delivered

before spring 2006 shutdown

Tevatron Run 2 ppp

s :

1 fb-1 delivered • analyses presented use 0.3 – 1.0 fb-1 (“good data”)


CDF D0

Tevatron

Main injectorand recycler

RunI: 1992 – 1996data taking period at

RunII: 2001 – 2009major upgrades tocollider anddetectors

ps :

The Tevatron

ps :

pp


Tevatron performance

Running well - both peak luminosity and integrated luminositybefore spring 2006 shutdown: ~15-20 pb-1 / week delivered

1 fb-1 delivered in beginning of June 2005 .

1 fb-1


• precise tracking: silicon vertex detector and drift chamber

• important for B physics: direct trigger for displaced vertices, J/ ! +-

The CDF detector


Physics at the Tevatron• large b production rates:

) 103 times bigger than !

• spectrum quickly falling with pt

• Heavy and excited states not produced at B factories:

• enormous inelastic cross-section:

) triggers are essential

• events “polluted” by fragmentation tracks, underlying events

) need precise tracking and good resolution!

S

Bc; Bs; B¤¤; b; b; : : :

¾pp;j´j < : ¼ ¹


Dedicated trigger J/ ! + -

trigger events where m(-) around m(J/ ) • high quality J/ events• large statistics available

N.B. channel J/ ! e+e- much more challenging in complex hadronic environment!

Evaluate muon chamber info on trigger level:


X(3872) with J/ ! e+ e-

Reconstruction of J/ ! e+e- very difficult in complex hadronic environment

• dedicated J/ ! e+e- trigger• use neural-network based approach to

identify soft e§ (pt > 2GeV/c)• reject e§ from conversions based on neural network approach• add at J/ vertex to accommodate Bremsstrahlung• X(3872) reconstructions follows

J/ ! +- case

) able to reconstruct X(3872) in this channel!

strong radiative tail


) X(3872) behaves similarly to the (2S)

(with given uncertainties)

X(3872) production fraction from B

fraction from B decays:

2S): 28.3 § 1.0 (stat.) § 0.7 (syst.) %

X(3872): 16.1 § 4.9 (stat.) § 1.0 (syst.)%


The m(+ -) mass spectrumDistribution of m(+-) constrains quantum numbers JPC

shape depends on:• decay of (+-) sub-system: (+-) in s or p wave

(i.e. intermediate sub-resonance or not)• relative angular momentum between (+-) and (+-) • (and detector acceptance, efficiency, etc.)

e.g. for decay chain: X ! J/ 0; 0 ! +-

d Xdm¼¼

m¼¼ X ! J = ½m¼¼¢m½ ½! ¼¼m¼¼

m¼¼¡ m

½ m½ ½m¼¼

for broad resonances (kinematic factors vary across width)

form-factor

A! BC ;A! BC

µk¤

k¤

¶L µf k¤f k¤

¶ ³mm

´

spectrum described byBreit – Wigner function


The m(+ -) mass spectrum2

Ca

nd

ida

tes

/ 5

Me

V/c

0

100

200

300

400

500

3.8 3.9

-1CDF II Preliminary, 360 pb

38 (stat.) X's102

2) < 650 MeV/c625 < M(

3.8 3.9 4

]2

Mass [GeV/cJ/

35 (stat.) X's165

2) < 710 MeV/c690 < M(

3.9 4

30 (stat.) X's182

2) < 765 MeV/c750 < M(

Challenge: Large background, rather low X(3872) yield ) sideband-subtraction difficult, instead:

“slicing technique”• impose bin borders in m(+-) as additional cuts• fit resulting (+-+-) mass spectrum• obtained yield shows variation with m(+-)

need to be careful at kinematic borders


Influence of form-factor on m(+ -)

use: model from Blatt-Weiskopf:parameter “R” determines effective size, no unique choice


Mixing phase between and

good fit probability foundfor relative phase 95

Relatively small influenceof 0 form-factor radius,large effect from X(3872)form-factor radius.


Effect of 0- mixing

) Neither L=0 nor L=1 can be ruled out from m(+-) alone


Illustration of angular correlation

example for JPC = 1++


Sample fit for X(3872) angular analysis


Helicity matrix element

J P ! J P

J P

• treat initial and final state in respective rest-frame• two body decay:

• are back-to-back• common quantisation axis ) final state helicity = 1 - 2

~p ;~p

M / D JJ z;¸ µ;Á ¢T j~pj;L

D JJ z;¸ eiÁ J z¡ ¸dJ

J z;¸using Wigner D functions

assume lowest angular momentum L is dominant


Transition weight from Helicity matrix element

mean over initial state

incoherent sum overfinal states

coherent sum overintermediate states

M / M X £³PJ =Ã ¢M J =Ã

´£ P¼¼¢M ¼¼

in case of several substates:coherent sum contains a priori unknown mixing constant gLS

¯¯¯P

L S

P¸ J =Ã

P¸ ¼ ¼¡

gL SM¯¯¯

w / J X

PJ z

µP

¸ ¹

P¸ ¹ ¡

P¸¼

P¸¼¡

¯¯¯P

¸ J =Ã

P¸ ¼ ¼¡

M¯¯¯¶


X(3872) fit results Â Â

¡ ¡ ¡ ¡ ¢¡

¡ ¢¡

¡ ¡ ¢¡

¡ ¢¡

¡ ¡ ¢¡

¢¡

¡ ¢¡

¡ ¢¡

¡ <¢¡

<¢¡


Systematics for X(3872)systematics:13 – 17:details of MC

12:use phase-spaceto describe m()

10, 11:vary 0 form-factor radius

6-9:vary X(3872) meanand width

4,5:vary histogram bin width

2,3:vary X(3872) fit window

1: default result


2S) fit results Â Â ¡ ¡

N ovikov ¡ ¡

s

p ¡

s ¢¡

¡ ¡s ¢¡

p < ¢¡

¡s < ¢¡

¡ ¡s < ¢¡

¡s < ¢¡

¡ p <¢¡

¡ p <¢¡

p <¢¡

¡s <¢¡

¡ p <¢¡


Systematics for (2S)systematics:13 – 17:details of MC

6,7 :vary (2S) meanand width

4,5:vary histogram bin width

2,3:vary (2S) fit window

1: default result


Detector effectsDetector acceptance, resolution and cuts affect angular variables:

for JPC = 1++ for JPC = 1--

original

after simulation

left: 1++

right: 1--


J = ½ ; J = ´

possible formation of “molecules”:

decay via:

Charmed molecule?e.g. DeRujula, Georgi, Glashow (1977)

D D;D D¤ D¤D¤

D D¤¤; D¤ D¤¤

?

binding by 0 Törnqvist Phys. Lett. B590, 209-215 (2004)

Swanson Phys. Lett. B588, 189-195 (2004)

0

D¤ Dsimilar to deuteron: small attractive force mediated by 0

predict JPC = 1++ or 0-+

isospin breaking via 0 ! +- allowedSwanson: additional contribution from 0, only JPC = 1++

ccqq


„Deuson“ model (Törnqvist)

0

D¤ DX(3872) similar to deuteron:• composed of two objects• bound by 0 exchange

Prediction:• JPC = 1++ or 0-+

(otherwise potential too weak or repulsive)• small binding energy:

• narrow resonance, big object• isospin breaking:

• X ! J/ 0, 0 ! +- allowed• X ! J/ forbidden for any isoscalar • X ! J/ 0 0 forbidden


Further properties by B-factories

BaBar: search for charged partner X§ ! J/ §

expect twice the rate if X is part of iso-triplett

) no signal found

Belle: 4 evidence for decay X(3872) ! J/ evidence for decay X! J/ +

) Swanson: 1++

has contribution of X ! J/ , ! +

search for X! c1 , X! c2

) no signal found

C = +1

D D¤ (hep-ph/0311229)

(hep-ex/0505037)

(hep-ex/0408083)


Excited B mesons

narrow: ~ 10 MeV/c2

broad : ~ 100 MeV/c2

similar picture for Bs**

Heavy Quark Effective Theory: hydrogen atom like system withheavy + light quark


Exclusive Bd**

experimental observable:Q = m(B**) – m(B) – m()(free remaining kinetic energy)

• focus on narrow states:• B1 ! B* • B2

* ! B • B2

* ! B* ( not reconstructed)

• exclusive analysis ) high resolution• •

B § ! J =ÃK § ; J =Ã ! ¹ ¹ ¡

B § ! D ¼§ ; D ! K ¼¡

mB § stat: § syst:

mB ¤ § stat: § syst:


Exclusive B**

observable:Q = m(B**) – m(B) – m()(free remaining kinetic energy)

focus on narrow states:• B1 , B2

* ! B*

• B2* ! B

mB § stat: § syst:

mB ¤ § stat: § syst:

HQET: hydrogen atom like system withheavy + light quark

B § ! J =ÃK § ; J =Ã ! ¹ ¹ ¡

B § ! D ¼§ ; D ! K ¼¡

Towards Bs¤¤:

• similar to Bd¤¤: Bs

¤¤ ! B§ K¨

• situation much less clear:signal so far from DELPHI, OPAL, D0

• exclusive B§ ! J/ K§ , B§ ! D §

• sophisticated neural networks to suppress background• expect result ~summer


Towards Bs**

Delphi Conf 2005-011 Conf 731

Bs¤ ¤ ! B§ K¨ observed by:

• DELPHI (inclusive)• D0 (exclusive)• OPAL (inclusive)

D0Note 5027-Conf

Rare signal dominated by large background ! deploy sophisticated neural networks

• B§ ! J/ K§ , B§ ! D §

• Bs¤ ¤ resonant signal vs. combinatorial background

) expect CDF result this summer

Z. Phys. C66 (1995) 19

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Quarkonia spectroscopy at CDF

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