B Hadron Mixing and Lifetimes

1
B Hadron Mixing and Lifetimes

• Mike Hildreth
• Université de Notre Dame du Lac

2
Overview

• What are we after here?
• b, c Quark Production
• details of QCD, parton luminosities,
  fragmentation functions
• b, c Hadron Masses
• b, c Hadron Lifetimes
• b, c Hadron Decays
• Tevatron and B-Factories Largely Complementary

Tests of, inputs to HQE, CKM
Extraction of CKM Parameters
Heavy Quark Expansion
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Tevatron Collider Detectors
DØ

• Excellent Muon Coverage hlt2
• Excellent Tracking Coverage hlt3
• Impact Parameter Trigger _at_ L2

Central Calorimeter (E/H)
Central Muon
Solenoid
Wall Calorimeter (H)
Plug Calorimeter (E/H)
Forward Muon
CDF

• Excellent Mass Resolution
• Particle ID TOF and dE/dx
• Two-track invariant mass trigger _at_ L1
• Impact Parameter Trigger _at_ L2

Central Tracker
Forward Calorimeter (E)
Silicon
Lumi Monitor
TOF
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B-Factory Detectors
Common Features

• Excellent Mass Resolution
• Excellent EM Energy Resolution
• Excellent Particle ID (TOF/aerogel/DIRC)

1. Silicon Vertex Detector 2. Central Drift
Chamber 3. Aerogel Cerenkov Counter 4. Time of
Flight Counter 5. CsI Calorimeter 6. KLM
Detector 7. Superconducting Solenoid 8.
Superconducting Final Focussing System
U(4s) Running

• Coherent B-B production
• Beam constrained mass ? excellent background
  rejection

5
Datasets

• Tevatron
• gt3 fb-1 delivered to each experiment
• Peak lumi 3x1032/cm2/s
• up to 10 interactions/x-ing
• Summer results include up to 2.4 fb-1

Tevatron Integrated Luminosity

• B-Factories
• Belle 700 fb-1
• Babar 500 fb-1
• ? 1fb-1 106 Bs
• Peak luminosity
• 1.7x1034/cm2/s
• (KEKB)
• 1.2x1034/cm2/s
• (PEPII)

Integrated Luminosity fb-1
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Heavy Flavor Factories

• Tevatron Cross Sections
• central (ylt1) bs at 10kHz
• central charm at 500kHz
• 9x1010 bs already in Run II
• 6x1012 charm hadrons
• ? infinite statistics for some studies
• ? If you can trigger... (S/N .006)
• muon triggers, all-charged modes

• B-Factory Cross Sections
• Bs at 50 Hz
• clean initial state
• E(Y(4S))/2 MB 300MeV
• no extra particles
• easy B selection
• coherent B-B production
• automatic flavor tagging

Belle
CDF
360 pb-1
even works at Y(5S)
MC
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Quarkonia Upsilon Polarization
Cho, Wise, PLB 346, 129 (1995)

• Non-relativistic QCD (NRQCD) predicts significant
  polarization at high pT
• Production described by short distance cross
  sections ? non-perturbative matrix elements for
  evolution to quarkonium state.
• color octet modes required on top of color
  singlet to describe production (demonstrated by
  CDF in Run I)
• New results from DØ ?(1S) and ?(2S) production,
  ???? final state
• measurements of polarization in rest frame of Y

Bodwin, Braaten, Lepage, PRD51, 1125 (1995)
Braaten, Fleming, PRL74, 3327 (1995)
fit cosq distribution in bins of pT to extract a
where
NRQCD prediction
CDF Data (PRL 88 161802 (2002))
DØ Data
NRQCD prediction
kT factorization models
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Belle Y(5S) Studies

• Belle took 23.6 fb-1 at the Y(5S) in 2006
• fs (18 1.3 3.2)
  (earlier results from 1.86fb-1)
• 
  PRL 98 (2007) 052001, PRD 76 (2007)
  012002
• New results on inclusive Bs semi-leptonic decays
• inclusive spectra not accessible at the Tevatron

Combined Result
c.f. the B0 system
d
(PDG 2007)
(see results on rare Bs decays later...)
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Heavy Quark Expansion Lifetimes
evaluation of LQCD/mQ terms requires knowledge of
light quark dynamics in the presence of the heavy
quark field

• HQE no leading order corrections ? 1/mQ
• General feature of QCD gauge structure
• hadronization and bound state effects given in
  terms of local HQ operators ? Same operators used
  for CKM analyses!
• Precise predictions possible
• verification tests calculational validity of HQE,
  supplies needed input for extraction of CKM
  parameters

Bigi, Shifman, Uraltsev, Vainshtein
mesons vs. baryons, ?(1)
B0 vs. B vs. Bs, ?(3-20)
e.g. Tarantino Gabbiani, Onishchenko, Petrov
e.g. Gabbiani, Onishchenko, Petrov
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Lb Lifetime

• One of the un-solved mysteries of HF lifetime
  measurements
• long-standing discrepancy between theory and
  measurement
• recent HQE calculation refinements
• inclusion of sub-leading spectator
• terms
• inclusion of NLO and 1/mb
• spectator effects
• lowered expected value of
• at time of HFAG 2006, theoretical predictions and
  experimental results agreed within 1.2s
• more accurate results needed for thorough test of
  theory
• ? Updates of precision Lb lifetime measurements
  from CDF, DØ

C. Tarantino hep-ph/0702235
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Lb Lifetime Measurements

• DØ (1.2-1.3 fb-1)
• all-charge decay mode Lb?J/YL
• semi-leptonic mode Lb?Lcmn
• similar topology control modes
• B0?J/Y Ks (all-charged)
• B0?DmnX (semi-leptonic)
• B?D0mnX (semi-leptonic)
• Bs?DsmnX (semi-leptonic)
• Lifetime from mmL or Lcm vertex

• CDF (1 fb-1)
• all-charge decay mode Lb?J/YL
• similar topology control modes
• B0?J/Y Ks
• B0?J/Y K
• B?J/Y K
• Bs?J/Y f
• Lifetime from mm vertex

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Lb?J/YL Lifetime Measurements

• CDF
• reoptimization and detailed study of resolution
  functions for J/Y and vertexing
• Results

• DØ
• extensive studies of non-prompt backgrounds
• Results

N(J/YL) 171
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Lb?Lcmn Lifetime Measurement (DØ)

• main issue huge background after selection of
  the Lcm final state

Likelihood for signal selection developed from
data B0? DmnX, D?Ksp Bs? DsmnX, Ds?KsK
cut

• Global fit uses lifetime pdf to extract Lb
  lifetime from number of signal events/bin

full sample 4437329 events
B0/B/Bs?Dmn, D?Ksp

• c2 fit in bins of proper decay length
• Nsignal, Nbkg, errors determined from mass fits
• mass and width held constant

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Lb Lifetime Summary

• Lifetime Cross Checks

DØ Run II (02-06)
1.5010.0780.050 ps
not in average
PDG 2006
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Lb Lifetime Summary
not in average
not in average
PDG 2006
PDG 2007
more statistics definitely coming...
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B Hadron Mixing

• For neutral B Hadrons, Weak ? Mass ? CP
  eigenstates
• time-dependent evolution
• three observables characterize system
• Dm MH-ML 2M12
• DGCP Geven - Godd 2G12
• f arg(G12/M12)
• f relates mass and CP eigenstates through DGs
  GL-GH DGCPcosfs
• Mixing Measurements in Bd and Bs systems ? access
  to CKM elements

sensitive to New Physics not sensitive sensitive
to New Physics

• Dmd well-measured 0.5090.004 ps-1
• many uncertainties cancel in ratio

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Quantum Entanglement

• Belle EPR tests of quantum coherence of Y(4S)
• measurement of flavor asymmetry vs Dt can
  distinguish between models suggesting different
  degrees of coherence
• true Bells inequality test impossible due to
  short B lifetime, passive nature of flavor
  measurement

Quantum Mechanics
Spontaneous Decoherence
Local Realistic Model
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Quantum Coherence

• Fits of flavor asymmetry to different coherence
  models
• spontaneous decoherence disfavored by 18s, local
  reality model disfavored by 5.1s

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Bs Mixing Measurements at the Tevatron

• Time-dependent flavor evolution of Bs measured
  directly
• Three ingredients
• measurement of production flavor
• hardest part of measurement
• various indirect techniques based on properties
  of associated fragmentation and decay products
• measurement of decay flavor
• flavor-specific final state or lepton decay
  flavor
• proper time of decay
• position resolution of tracking system
• momentum resolution critical for
• background suppression

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Bs Mixing Measurements final states

• Semi-leptonic
• most numerous, but missing neutrino spoils proper
  time resolution

• Specific Hadronic Final States
• all-charged final states give excellent vertex
  resolution

2.4 fb-1
CDF Run II
Data Samples
part. rec.
3100
New Analysis
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Bs Mixing Measurements flavor tag

• No luxury of coherent B0-B0 initial state for
  flavor tagging
• need to use as much information as possible in
  the event to determine production flavor
• Figure of Merit ?D2 ? efficiency of tag x
  (dilution factor)2
• 
  final state tags decay flavor

• Kaon flavor b?c?XK-
• lepton flavor b?X?-, but b?c?X?
• jet charge momentum-weighted charge of initial
  fragmentation tracks

• Kaon flavor strange quark not included in Bs
  forms Kaon

CDF achieved ?D2 1.8 (OST) ?D2 3.7
(SSThad), 4.8(SSTlep)
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CDF Results
semi-leptonic
combined
Bs?Dsp
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DØ Results

• Numerous improvements to analysis
• combined event charge flavor tag (?D2 4.49)
• more refined momentum determination for
  semi-leptonic decays
• event-by-event resolution rescaling
• Addition of new tracking layer for Run IIb

DØ Run II Preliminary
DØ Run II Preliminary
3.1s statistical significance
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constraints on new physics in B-mixing
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DGs/Gs and fs

• First Tevatron measurement with direct bearing on
  CP violation in the Bs system (New Physics!)
• define Heavy (H, CP-odd) and Light (L, CP-even)
  Bs states
• GH and GL are partial widths, DGs GL-GH,
  Gs1/2(GHGL)
• Differential decay rate (Lifetime difference!)
• fs ? 0 ? new CP-violation expected SM value is
  very small

CP-even angular configurations (L0, 2)
CP-odd angular configuration (L1)

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DGs/Gs Measurements

• Strategy
• Choose decay with definite CP states Bs?J/??,
  J/??mm-, ??KK-
• Vector mesons in final state are CP-odd (L1) or
  CP-even (L0,2)
• rate depends on relative orientation
• of meson polarization
• time-dependent angular
• distributions allow separation of
• BsLand BsH components
• Simultaneous fit to lifetimes,
• angle space
• modifications of angular distributions
• due to acceptance effects taken
• from MC models

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DGs/Gs Measurements

• New Measurement from CDF
• very loose pre-selection
• Neural Net used to maximize S/?SB 2500 Bs?J/??
  decays

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DGs/Gs Measurements

• CDF Angular projections
• Similar Results from DØ PRL 98 , 121801 (2007)

(Lifetime-enhanced cuts)
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Constraints on fs
hep-ex/0702030
contours

• DØ
• combined constraints from Bs?J/??, semileptonic
  charge assymetry, Dms

• CDF
• allowed region in DG/fs plane determined by
  frequentist method to account for biases at low
  values of DG or fs