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Hadronic B/D decays in factorization assisted topology

diagram approach

Cai-Dian Lü(吕才典) CFHEP, Institute of High Energy Physics, Beijing

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Based on work collaborated with Hsiang-nan Li, Ying Li, F-S. Yu, Qin Qin, X.-X. Wang, S-H. Zhou, Y.-B. Wei arXiv:1101.4714, PRD84 (2011) 074019 arXiv:1203.3120, PRD86 (2012) 036012 arXiv:1305.7021, PRD89 (2014) 054006 arXiv:1509.04060, PRD92 (2015) 094016

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Outline n  Introduction/Motivation n  Factorization assisted topological diagram

approach for hadronic B/D decays n  Use hadronic parameters fixed by data of BRs Predict

BRs of other channels and direct CP asymmetries in SM

n  Summary

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Flavor physics is important

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CKM triangle measurement

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b W u B π d(s) π (K) W

b t B π

In experiments, we can only observe hadrons

The standard model describes interactions amongst quarks and leptons

π (K)

Rich physics in hadronic B decays

How can we test the standard model without solving QCD? 40

Perturbative calculations n  In principle, all hadronic physics should be

calculated by QCD n  In fact, you can always use QCD to calculate

any process, provided you can renormalize the infinities and

do all order calculations.

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Divergences n  Perturbation calculation means order by order n  Involving loop diagrams n  Therefore divergences unavoidable n  Ultraviolet divergences à renormalization n  Infrared divergences ? Infrared divergence in

virtual corrections should be canceled by real emission

n  In exclusive QCD processes à factorization

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Factorization can only be proved in power expansion by operator product expansion. To

achieve that, we need a hard scale Q

•  In the certain order of 1/Q expansion, the hard dynamics characterized by Q and the soft dynamic factorize

•  The former into hard kernel H and the latter into distribution amplitude ϕ

•  Factorization theorem holds up to all orders in αs, but to certain power in 1/Q

•  H is process-dependent, but calculable •  ϕ are universal (process-independent) predictive

power of factorization theorem •  In B decays the hard scale Q is just the b quark mass

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✤  QCD-methods based on factorization work well for many processes Perturbative QCD approach based on kT factorization [Keum, Li, Sanda, 00’; Lu, Ukai, Yang, 00’] collinear QCD Factorization approach [Beneke, Buchalla, Neubert, Sachrajda, 99’] Soft-Collinear Effective Theory [Bauer, Pirjol, Stewart, 01’]

Unavailable for 1/mb power corrections

✤  Topological diagrammatic approach

[Chau, Cheng, et al, 91’; Chiang, Rosner, et al, 04’]

✤  Work well for most of charmless B decays, except for pi K puzzle etc.

Hadronic matrix elements calculations

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n  High precision measurements of B/D decays already by BaBar, Belle, BESIII and LHCb, and to be pushed by LHCb upgrade and Belle-II.

n  High precision in theoretical calculation is urged

n  Theore&cally,itisnotsa&sfied,sincetherearemostlymodelcalcula/ons,someQCDsumrulescalcula/onorrelyonLa6ceQCD:anul/matetoolbutaformidabletasknow

n  Charmquarkmassisnotlargeenoughforheavyquarkexpansion

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Hadronic decays with charm quark in the final states or initial state

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Topological diagrammatic approach

n  Distinct by weak interaction and flavor flows with all

strong interaction encoded, including non-perturbative ones. Model-independent

n  Based on flavor SU(3) symmetry. Amplitudes with strong phases extracted from data. SU(3) breaking was lost.

n  DP, D*P and DV fitted separately, 5 parameters for each category of decay modes. Less predictive.

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[Chiang, Senaha, 07’]

T C E A

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Ø Effective Hamiltonian: For the color favored diagram (T), it is proved factorization to all order of αs expansion in soft-collinear effective theory, The decay amplitudes is just the decay constants and form factors times Wilson coeficients of four quark operators. The SU(3) breaking effect is automatically kept

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No free parameter

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Ø Effective Hamiltonian: For other diagrams, we extract the amplitude and strong phase from experimental data by χ2 fit We factorize out the decay constants and form factor to keep the SU(3) breaking effect

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Global Fit for all BàDP, D*P and DV decays (PRD92, 094016 (2015))

n  31 measured modes induced by b→c transitions

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Topological amplitudes

χ2 is much smaller than previous topology diagram approach

Large strong phase

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BàDP

X

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BàD*P

X

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BàDV

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Nonperturbative parameters 𝜒C, 𝜙C, 𝜒E, 𝜙E

are universal for all the DP, D*P and DV modes

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factorization

SU(3) breaking effects in amplitudes to be 10~20%

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SU(3) breaking effects can be described by decay constants

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SU(3) breaking (I)

CKM suppressed b→u transitions

❖  All modes predicted, with assumptions:n  non-perturbative parameters are the same

as those in the b→c transitionsn  W-annihilation A diagrams calculated in the

pole model

T C E A

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[arXiv:1509.04060]

Vub

CP asymmetries

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FAT predictions LHCb measurement

To be tested in the future

GlobalfitforhadronicDdecays(Phys.Rev. D86 (2012) 036012)

•  12 free parameters are extracted from 28 experimental data of D->PP branching ratios

•  Λ describes the soft momentum in D meson •  The value of Glauber phase is consistent with the

value extracted from B->πK data, resolving the puzzle for direct CP asymmetry in this mode [H.n Li, S. Mishima, 0901.1272]

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EvidenceofCPVinDdecays n  FirstevidenceofCPviola&onincharmedmesondecaysbyLHCb,with3.5σ[arXiv:1112.0938]

n  ConfirmedbyCDF,with2.7σ[CDFnote10784]

n  NaivelyexpectedmuchsmallerintheSM

n  NecessarytopredictmorepreciselyintheSM. 25 40

TopologydiagramsforBRs •  According to weak

interactions and flavor flows •  Include all strong interaction

effects, involving final state interaction (FSI) effects

•  Magnitude and phase are introduced to each topology

•  This is a complete set •  Penguins are neglected for

BRs due to suppression of CKM matrix elements

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Evolu/onscale n  ImportantflavorSU(3)breakingeffectsn  Non-negligiblemassra/osn  SuggestedbythePQCDapproach,thescaleissettotheenergyreleasedependingonmassesoffinalstates

n  :themomentumofsoSdegreesoffreedom,afreeparametertobedetermined

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Singly Cabibbo-suppressed decays (10-3), better agreement with data

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SU(3)breakingeffects

•  In the factorization method •  Large SU(3) breaking effects in W exchange diagram •  Dynamics in the annihilation amplitudes has not yet

been well understood 29 40

30 Phys.Rev. D89 (2014) 5, 054006

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Penguinparameteriza/on n  Usethelong-distancehadronicparametersfixedbythedataofbranchingra/os

n  Trytoformulatepenguincontribu/onwithoutintroducingaddi/onalfreeparameters

n  Thetreeoperatorsareall(V-A)(V-A)n  Forpenguins,thehadronicmatrixelementswith(V-A)(V-A)operatorsarethesameastreeleveloperators

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Predictions of Direct CP asymmetries

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ΔCP =

-1.28 x10-3

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12.03.13 Moriond QCD 2013, La Thuile 17

LHCb combination

● The two measurement are compatible at the 3 % level

● χ2 = 4.85

● Naive average (neglecting indirect CP violation)

LHCb-PAPER-2013-003

LHCb-CONF-2013-003

Semileptonic:

Prompt:(preliminary)

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12.03.13 Moriond QCD 2013, La Thuile 17

LHCb combination

● The two measurement are compatible at the 3 % level

● χ2 = 4.85

● Naive average (neglecting indirect CP violation)

LHCb-PAPER-2013-003

LHCb-CONF-2013-003

Semileptonic:

Prompt:(preliminary)

Current experimental status

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Current experimental status

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Our theoretical prediction in 2012 is -1.28 x 10 -3

Charmless B decays

n  Famous pi K puzzle not well explained n  Tree + penguin contribution, complicated

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Large color suppressed tree diagram contribution together with large strong phase also expected

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Preliminary results

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Summary •  DàPP, PV, B→DP, D*P and DV decays are studied in the

factorization-assisted topological-amplitude approach •  In D decays, we fix hadronic parameters using data of branching

ratios –  Combine short-distance dynamics associated with penguin

operators •  Unambiguous predictions of direct CP asymmetries in Dà PP,

PV decays in the SM n  Only four universal non-perturbative parameters to be fitted for

all B→DP, D*P and DV decays, more predictive than ever n  Results are consistent with data. SU(3) breakings are studied. n  Predictions to be tested by future exp.

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Many Thanks for a wonderful workshop！

Thanks the organizing committee, especially Eung Jin Chun and his team!

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