lattice qcd for the intensity frontier - indico-fnal (indico) · 2013. 5. 7. · doe annual...

Lattice QCD forthe Intensity Frontier

Ruth Van de Waterfor the USQCD Collaboration

DOE Annual Progress Review of LQCD-Ext and LQCD-ARRAMay 9, 2013

R. Van de Water Lattice QCD for the intensity frontier

The experimental high-energy physics community is presently searching for new physics with two complimentary approaches

(1) Production of new particles at high-energycolliders (the “Energy frontier”)

E.g., the LHC has already discovered a~125 GeV particle that may be the SM Higgs

(2) Precise measurements of Standard Model parameters and processes(the “Intensity frontier”)

E.g., heavy flavor factories have been pouring out datato pin down CKM matrix elements & the CP-violating phase

Search for processes that are extremely rare in the StandardModel and look for tiny deviations from SM expectations

Upcoming experiments will improve existingmeasurements and observe some rare decayprocesses for the first time

Beyond-the-Standard-Model search strategies

2


The experimental high-energy physics community is presently searching for new physics with two complimentary approaches

(1) Production of new particles at high-energycolliders (the “Energy frontier”)

E.g., the LHC has already discovered a~125 GeV particle that may be the SM Higgs

(2) Precise measurements of Standard Model parameters and processes(the “Intensity frontier”)

E.g., heavy flavor factories have been pouring out datato pin down CKM matrix elements & the CP-violating phase

Search for processes that are extremely rare in the StandardModel and look for tiny deviations from SM expectations

Upcoming experiments will improve existingmeasurements and observe some rare decayprocesses for the first time

Beyond-the-Standard-Model search strategies

2

Lattice-QCD calculations are needed tointerpret many of their results . . .


Why search at the intensity frontier?Precision measurements probe quantum-mechanical loop effects, e.g.:

Sensitive to physics at higher energy scales than those probed at LHC, in some cases O(1,000 - 10,000 TeV) [Isidori, Nir, Perez, Ann.Rev.Nucl.Part.Sci. 60 (2010) 355]

If new particles are discovered at ATLAS & CMS, precise measurements will still be needed to extract the flavor & CP-violating couplings and determine the underlying structure of the theory

3

u, c, td s sd

g g

sLdL

dRsR

W� W�

s du, c, t s d

K0K0

u, c, td s sd

g g

sLdL

dRsR

W� W�

s du, c, t s d

K0K0

µ� µ�

�

� �

�� µ� µ�

�

neutral kaonmixing

muon g-2


The USQCD program

Comparison between measurements and Standard-Model predictions still limitedin most cases by theoretical uncertainties, often from hadronic matrix elements

Effort since beginning of LQCD project primarily focused on computing weak-matrix elements needed to interpret measurements at flavor factories as determinations of CKM matrix elements

Now that field is more mature, expanding program to more challenging matrix elements needed to interpret past (e.g. ε’K/εK) and upcoming measurements (e.g. rare kaon and B decays, muon g-2, Mu2e, dark-matter searches) as tests of the Standard Model and searches for new physics

Computational strategy to support two streams of ensemble generation with different lattice fermion actions that have different advantages, with several collaborations working on independent physics analyses

4

“The USQCD effort on determining QCD-based quantities needed for measuring ... CKM parameters for precision tests of the Standard Model ... has produced many of the best results available today. The interaction between

the lattice community and the experimental community has been crucial ...” － 2010 hardware review panel

Quark-flavor physics

BK


Lattice-QCD constraints on the CKM matrixCabibbo-Kobayashi-Maskawa matrix elements and phase are fundamental parameters of the Standard Model that enter as parametric inputs to Standard Model predictions for many flavor-changing processes such as neutral kaon mixing and K → πνν decays

Simple matrix elements involving singleparticles enable determinations of allCKM matrix elements except |Vtb|

*Neutral kaon mixing can also be usedto obtain the phase (ρ, η)

6

�

⇧⇧⇧⇧⇧⇧⇧⇧⇧⇧⇤

Vud Vus Vub

⇥ � ⌃� K � ⌃� B � ⌃�K � ⇥⌃� B � ⇥⌃�

Vcd Vcs Vcb

D � ⌃� Ds � ⌃� B � D⌃�D � ⇥⌃� D � K⌃� B � D�⌃�

Vtd Vts Vtb

⇥Bd|Bd⇤ ⇥Bs|Bs⇤

⇥

⌃⌃⌃⌃⌃⌃⌃⌃⌃⌃⌅

Absorb nonperturbative QCD effects into quantities such as decay constants, form factors, and bag-parameters that must be computed numerically with Lattice QCD

(Experiment) = (known) x (CKM factors) × (Hadronic Matrix Element)

✏K ,�m(d,s) ,

d�(B ! ⇡`⌫)dq2

,d�(B ! D(⇤)`⌫)

dw, . . .


R(D) from unquenched lattice QCD

B→D(*)τν decays sensitive to new-physics contributions such as from charged Higgs bosons

Recently BaBar measured the ratios R(D) = BR(B → Dτν)/BR(B → Dlν), R(D*) = BR(B → D*τν)/BR(B → D*lν) and observed excesses in both channels that disagree with the Standard Model by 3.4σ [PRL 109 (2012) 101802]

7

2012Highlight:

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5

R(D

)

tanβ/MH+ (GeV

-1)

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5

R(D

)

tanβ/MH+ (GeV

-1)

1 σ2 σ

BaBar ’12

2HDM II (This work)

Fermilab Lattice and MILC Collaborations quickly followed with first Standard-Model calculation of R(D) from ab initio lattice-QCD [PRL 109 (2012) 071802]

Uncertainty smaller than previous modelestimate from dispersive bounds, heavy-quark symmetry, and quenched lattice QCD

Lattice calculation of R(D*) in progress...


K→πlυ form factor can be combined with experimentally-measured branching fractionto obtain |Vus| in the Standard Model:

Fermilab Lattice and MILC recentlyobtained the first three-flavorresult for the K→πlυ form factorat zero momentum transferwith two lattice spacings and acontrolled continuum extrapolation[Bazavov et al. PRD87, 073012 (2013)]

Single most precise result for f+(0)enables 0.5% determination of |Vus|

0 0.2 0.4 0.6

aml /(ams )physical

0.97

0.98

0.99

1

f + (q

2 =

0)a = 0.12 fm, moving πa = 0.12 fm, moving Ka = 0.09 fm, moving πa = 0.09 fm, moving Kcontinuum NLOcontinuum NNLO (fit)a = 0.12 fm (fit)a = 0.09 fm (fit)

χ2/dof = 0.81, p = 0.62

K→πlυ form factor in the continuum

8

2012Highlight:

�(K � ⇤⌅⇥) =G2

Fm5K

192⇤3C2

KSEW|Vus|2|fK0��

+ (0)|2IK⇥

⇣1 + �K⇥

EM + �K�SU(2)

⌘2

f+Kπ(0) = 0.9667(23)stat(33)sys

|Vus| = 0.2238(9)theo(5)exp


2013 Highlight: fK/fπ at the physical point

The SU(3) flavor-breaking ratio fK/fπ allows a determination of |Vud| /|Vus| [Marciano]

MILC collaboration recently obtained thefirst lattice-QCD determination of fK/fπ (1) including dynamical charm and(2) at the physical pion mass withhighly-improved staggered (HISQ) quarks[Bazavov et al. PRL110, 172003]

Eliminate error from extrapolationto physical u- and d-quark masses

Combined with |Vud| from nuclearβ-decay, enables sub-percent test ofunitarity of 1st row of CKM matrix

9

�(K ! l⌫l)�(⇡ ! l⌫l)

=✓

|Vus||Vud|

◆2 ✓fK

f⇡

◆2 mK

⇣1� m2

l

m2K

⌘2

m⇡

⇣1� m2

lm2

⇡

⌘2

h1 +

↵

⇡(CK � C⇡)

i

Source fK+/f⇡+

Monte-Carlo statistics 0.22%

Continuum extrapolation 0.28%

Finite-volume corrections 0.14%

EM corrections 0.02%

Total 0.38%

1 − |Vud|2 − |Vus|2 − |Vub|2 = 0.0003(6)


Coming soon: K→ππ decay

Direct CP-violation in K→π π decays (ε’K/εK) sensitive to new physics because it receives contributions from EW penguins

Measured experimentally to <10%precision, but utility for testingStandard Model handicapped bylarge uncertainty in correspondingweak matrix elements

In the past two years, the RBC-UKQCD Collaboration made significant progress in resolving theoretical issues associated with computing K→ππ amplitudes

Computed ΔI=3/2 matrix elements with nearly physical pion and kaon masses, and obtained Re(A2) & Im(A2) with ~20% errors [PRL 108 (2012) 141601]

Performed pilot study of ΔI=1/2 matrix elements with ~330 MeV pions [PRD 84 (2011) 114503]

Simulations with physical pions on BG/Q at ALCF should yield first ab initio QCD calculation of ΔI=1/2 rule and ε’K/εK with ~20-30% precision in one or two years

With projected lattice improvements, combining the pattern of results for ε’K/εK with K→πνν decays can help distinguish between new-physics scenarios [Buras et al., NPB 566 (2000)]

10

K

π

π

s

etc...

d

uu

BK

Lattice QCD for the Intensity Frontier


Project X@ FermilabK0 → π0νν

(Select) Upcoming experiments

12

NOW 20142013 2020+

Belle IIsin(2β), B →τ(µ)ν,

B→π(ρ)lν, B→D(*)lν,rare b→sγ & b→sll decays, ...

E14 “KOTO” @ J-PARC K0 → π0νν

NA62 @ CERN SPSK+ → π+νν

ATLAS/CMSΔms, Bs→µ+µ-, ...

LHCbrare b→sγ & b→sll decays,

Bs→µ+µ-, D-mixing...

2016

newmuon g-2

ORKAK+ → π+νν

2019

Mu2e

LBNEneutrino mixing &

mass hierarchy,proton decay, ...


Scientific goals and 5-year plan

USQCD aims to support the US HEP experimental intensity-physics program by “improv[ing] the accuracy of QCD calculations to the point where they no longer limit what can be learned from high precision experiments that seek to test the Standard Model” — USQCD HEP SciDAC-3 proposal

2013 White Paper “Lattice QCD at the Intensity Frontier” outlines a program of calculations matched to experimental priorities

(1) “Improve the calculation of the matrix elements needed for the CKM unitarity fit”

(2) “Calculate ... new, more computationally demanding, matrix elements that are needed for the interpretation of planned (and in some cases old) experiments”

Target quantities and precision goals developed with input from experimentalists and phenomenologists (primarily quark-flavor and muon g-2)

Currently in discussions with neutrino and charged-lepton communities to expand lattice-QCD portfolio relevant for LBNE, Mu2e, etc...

13


Rare B decaysStandard Model branching fraction predictions for many b→s processes limited by hadronic form factor uncertainties

E.g., hadronic uncertainties are dominant error for B→K*l+l - decay observables over all q2

Lattice QCD calculations are underway of B→Kl+l -

[Zhou et al.(Fermilab/MILC), arXiv:1111.0981]and of B→K*l+l - & B→K*γ[Liu et al., arXiv:1101.2726]

Expect first lattice-QCD results for B→Kl+l - by the end of the year with few-percent errors in the high-q2 region

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12 14 16 18

dB

/dq

2 [10

-7/G

eV

2]

q2 [GeV2]

J/ψ ψ’

Differential branching fraction

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10 12 14 16 18

AF

B(q

2)

q2 [GeV2]

J/ψ ψ’

Blue = form factor uncertainty

Forward-backward asymmetry

[Bobeth,Hiller, & van Dyk, JHEP 1007 (2010) 098]

14


Muon anomalous magnetic momentSensitive probe of heavy mass scales in the several hundred GeV range

New particles can generate significant non-Standard Model contributions in well-motivated models such as Supersymmetry or warped extra dimensions

Muon g-2 currently measured experimentally to 0.54 ppm

A >3σ discrepancy with the Standard Model, assuming you trust the SM prediction...

New Muon g-2 experiment will reduce error by a factor of four to 0.14 ppm

Reduction in theoretical uncertainty on SM prediction to the same level(with more reliable error estimate!) needed to conclusively establish the presence of new physics with the planned measurement

15

aμexp = 116 592 089(54)(33) x 10-11 [E821] aμexp -aμSM =287(80) x 10-11 [3.6σ]

SM SUSY

aSUSYµ /

✓mµ

MSUSY

◆2

tan(�) sign(µ)�

�� µ� µ�µ� µ�

�


Standard-Model contributions to g-2

16

[1] Davier, Hoecker, Malaescu, Zhang, Eur.Phys.J. C71 (2011) 1515[2] Prades, de Rafael, Vainshtein, arXiv:0901.030

Contribution Result (�1011) ErrorQED (leptons) 116 584 718 ± 0.14 ± 0.04� 0.00 ppmHVP(lo) [1] 6 923 ± 42 0.36 ppmHVP(ho) -98 ± 0.9exp ± 0.3rad 0.01 ppmHLbL [2] 105 ± 26 0.22 ppmEW 154 ± 2 ± 1 0.02 ppmTotal SM 116 591 802 ± 49 0.42 ppm

+

QED (4 loops) & EW (2 loops)

+ +

Hadronic vacuum polarization (HVP):

from experimental result for e+e-→ hadrons plus

dispersion relation

+ ...

Hadronic light-by-light (HLbL):

estimated from models such as large

Nc, vector meson dominance, χPT,

etc...


Recent lattice-QCD progressLattice QCD can provide calculations of the hadronic contributions from QCD first principles with controlled uncertainties that are systematically improvable

USQCD research and development efforts on both hadronic contributions are ongoing

Hadronic vacuum polarization

Aubin et al.,[Phys.Rev. D86 (2012) 054509] introduced model-independent fitting approach based on analytic structure of Π(Q2) using Padé approximants to eliminate potentially hidden systematic associated with vector-meson dominance fits

Theoretical improvements + increased computing resources should enable a lattice-QCD determination with few-percent error on the timescale of New g-2

Hadronic light-by-light

RBC Collaboration [Hayakawa et al., PoS LAT2005 (2006) 353] developed a promising method using QCD + QED lattice simulations that is simpler and cleaner than the correlation function of 4 currents, but calculation still in early stages

Over the next few years, US lattice-QCD community will increase both human and computing resources devoted to this high-priority calculation

17

http://inspirebeta.net/author/Hayakawa%2C%20Masashi?recid=691579&ln=en



Muon-to-electron conversionCharged-lepton flavor violation highly suppressed in the Standard Model

➡ Observation of CLFV would be unambiguous evidence of new physics

Many new-physics models allow for CLFV and predict rates close to current limits

Mu2e Experiment @ Fermilab (with Project X) aims to search for μN → eN with a sensitivity four orders of magnitude below the current best limit

MEG@PSI searching for μ → eɣ, while Mu3e proposes improved search for μ → eee

Combining measured rates of µ → eɣ and µ → e conversion on different target nuclei can distinguish between models and reveal information on underlying theory

18

q e

µ q

LQ

q q

µ e

γ

µ e

χ0

SUSY Leptoquarks

q q

µ e

γ

W W

N

Type-I Seesaw


0.00 0.05 0.10

fs

Feyn

man

-Hel

lman

n

0.053(19) present work0.134(63) [27] nf = 2 + 1, SU(3)0.022(+47

�6 ) [26] nf = 2 + 1, SU(3)0.023(22) [25] nf = 2 + 1, SU(3)0.075(73) [24] nf = 2 + 10.036(+33

�29) [23] nf = 2 + 10.033(17) [13] nf = 2 + 1, SU(3)0.023(40) [19] nf = 2 + 10.058(09) [22] nf = 2 + 10.046(11) [20] nf = 2 + 10.009(22) [19] nf = 2 + 10.048(15) [18] nf = 2 + 10.014(06) [17] nf = 2 + 1 + 10.012(+17

�14) [16] nf = 20.032(25) [14] nf = 20.063(11) [21] nf = 2 + 1

fs

0.043(11) lattice average (see text)

Dire

ctE

xclu

ded

Model discrimination in CLFVModel predictions for μ → e conversion rate off target nucleus depend upon the light- and strange-quark contents of the nucleon

(Same quark scalar density matrix elements also needed to interpret dark-matter detection experiments in which the DM particle scatters off a nucleus)

Lattice-QCD can nonperturbativelydetermine the pion-nucleon sigma termand strangeness content of the nucleonwith controlled uncertainties

Calculations improved significantly inrecent years, and already rule out muchlarger values of fs=ms⟨N|ss|N⟩/mN

favored by early non-lattice estimates

Even greater precision is needed for Mu2eand dark-matter searches

Realistic goal for next five years is to pindown values with ~10-20% errors

19

[Junnarkar & Walker-Loud,arXiv:1301.1114]


Proton decayProton decay forbidden in the Standard Model, but a natural prediction of grand unification

➡ Observation of proton decay would be unambiguous evidence of new physics

Proton-decay matrix elementsessential to interpret limits on(or a measurement of) theproton lifetime as constraints onGUT scenarios

Lattice QCD can compute nonperturbative hadronic matrixelements ⟨π,K,η,... | ONP |p⟩of new-physics operators

RBC/UKQCD recently obtained first three-flavor result for proton-decay matrix elements with a complete systematic error assessment [Aoki,Shintani,Soni, arXiv:1304.7424]

Errors range from 20-40%, but use of finer lattice spacings and lighter quark masses will improve the precision of these matrix elements in the next five years

20

Outlook


Project goals: how are we doing?

LQCD-ext proposal written in 2007-2008 showed a table of “present status and future prospects for lattice calculations which directly determine elements of the CKM matrix”

Last column is new and shows the current errors in these same quantities

22

Quantity CKM present present 2009 2013

element expt. error lattice error lattice error lattice error

(prediction) (actual)

fK/f⇡ Vus 0.3% 0.9% 0.5% 0.4%

fK⇡(0) Vus 0.4% 0.5% 0.3% 0.4%

D ! ⇡`⌫ Vcd 3% 11% 6% 4.4%

D ! K`⌫ Vcs 1% 11% 5% 2.5%

B ! D⇤`⌫ Vcb 1.8% 2.4% 1.6% 1.8%

B ! ⇡`⌫ Vub 3.2% 14% 10% 8.7%


Project goals: how are we doing?

LQCD-ext proposal written in 2007-2008 showed a table of “present status and future prospects for lattice calculations which directly determine elements of the CKM matrix”

Last column is new and shows the current errors in these same quantities

22

Quantity CKM present present 2009 2013

element expt. error lattice error lattice error lattice error

(prediction) (actual)

fK/f⇡ Vus 0.3% 0.9% 0.5% 0.4%

fK⇡(0) Vus 0.4% 0.5% 0.3% 0.4%

D ! ⇡`⌫ Vcd 3% 11% 6% 4.4%

D ! K`⌫ Vcs 1% 11% 5% 2.5%

B ! D⇤`⌫ Vcb 1.8% 2.4% 1.6% 1.8%

B ! ⇡`⌫ Vub 3.2% 14% 10% 8.7%

We are meeting our goals and are leading the world for all of the quantities shown


Computational developments

Petascale computing resources will enable simulations with increased statistics, lighter pions, finer lattice spacings, and larger volumes, thereby helping most sources of uncertainty

The following improvements will becomewidespread over the next five years

(1)Simulations with physical-mass pions

(2) Systematic inclusion ofisospin-breaking and EM

(3) Dynamical charm quarks

Improved algorithms and analysismethods also being pursued, butdifficult to predict

23

hadronicmatrix

elements

0 50 100 150 200 250 300 350 400M

π [MeV]

0

0.05

0.1

0.15

0.2

a (fm

)

completed ensemblesin progressplannedphysical point

Planned Nf=2+1+1 HISQ Ensembles


Precision measurements at the intensity frontier provide exciting opportunities to discover new physics, and can also be a powerful diagnostic tool to reveal the underlying nature of the new physics

Lattice QCD matrix-element calculations are needed to maximize the scientific output of the current and future worldwide high-intensityphysics program

Already playing a key role in testing the Standard Model in the quark-flavor sector

Lattice community is now expanding our program to meet the needs of current and upcoming experiments:

Increasing precision in simplest quark flavor-changing and nucleon matrix elements

Addressing new challenges such as rare decays, muon g-2, μ → e, long-distance amplitudes, and multi-hadron final states

Given the expected algorithmic improvements and increase in computing power,lattice QCD will continue to systematically and steadily reduce the uncertainties in the needed hadronic parameters over the next several years

Summary

24


Precision measurements at the intensity frontier provide exciting opportunities to discover new physics, and can also be a powerful diagnostic tool to reveal the underlying nature of the new physics

Lattice QCD matrix-element calculations are needed to maximize the scientific output of the current and future worldwide high-intensityphysics program

Already playing a key role in testing the Standard Model in the quark-flavor sector

Lattice community is now expanding our program to meet the needs of current and upcoming experiments:

Increasing precision in simplest quark flavor-changing and nucleon matrix elements

Addressing new challenges such as rare decays, muon g-2, μ → e, long-distance amplitudes, and multi-hadron final states

Given the expected algorithmic improvements and increase in computing power,lattice QCD will continue to systematically and steadily reduce the uncertainties in the needed hadronic parameters over the next several years

Summary

24

With continued support, we look forward to the coming decade’s interplay between

experiment, theory, and lattice QCD

Extras


Sensitivity to new physics

26

[Buras, Acta Phys.Polon.B41:2487-2561,2010]

FFF = sizeable NP e�ectsFF = moderate to small NP e�ectsF = no visable NP e�ects

Complementary measurements probe different new physics scenarios


[A.

Knec

ht]

Nonzero particle EDM violates P, T and, (assuming CPT conservation), also CP

New CP-violating interactions could show up in nonzeroEDMs of leptons and nucleons

Standard-Model contribution to neutron EDMfrom CP-odd phase in CKM matrix dN ~10-30 e·cm

Contribution from QCD θ-term could in principle belarger, but experimental limit combined with theoreticalestimates of dN/θ set bounds |θ|<10-10

Lattice-QCD can provide first-principles calculations of dN/θ, as well as matrix elements of non-Standard Model EDM-inducing operators

Test calculations have been carried out for the QCD θ-term contribution to neutron and proton EDMs and statistical errors are ~30%

Calculation of matrix elements of dimension-6 BSM operators also underway

Expect errors at the ~10-20% level in the next five years

Neutron electric dipole moment (EDM)

27


K → πνν decays

K+ → π+νν and KL → π0νν often called “golden” modes because Standard-Model branching ratios known to a precision unmatched by any other quark FCNC processes

➡ Limited by ~10% parametric uncertainty in A4∝|Vcb|4

Within this decade, NA62 @ CERN SPSwill measure O(100) K+ events (assuming the SM),and KOTO @ J-PARC will collect first K0L events

Subsequently, ORKA @ Fermilab proposes to collectO(1000) K+ → π+υῡ events, while a Project Xexperiment could also collect O(1000) KL → π0υῡ events

By 2014, expect to halve error on |Vcb| from latticecalculations of B → D(*)lν, reducing error in the SMbranching fractions to ~6%

➡Theory error in Standard-Model predictions will be commensurate with expected experimental error

28

BR(K+ → π+υῡ)

[Brod & GorbahnPRD83 (2011) 034030]

δPcu9%

mc,mt,αs3%ρ,η

11%

Vcb73%


Room for new physics

Sensitive to Little Higgs models, warped extra dimensions, and 4th generation[Buras, Acta Phys.Polon.B41:2487-2561,2010]

Spectacular deviations from the Standard Model are possible in many new physics scenarios

Correlations between the two channels can help distinguish between models

29

[D. Straub,arXiv:1012.3893(CKM 2010)]


17

ε"/ε Strikes Back

�⌥

0 5 10 15 20 25 30 350

5

10

15

20

25

30

35

Br⇤K� ⌃ ⇧�⌅⌅ ⇤⇤⌅⌅ �10⇥11⇥

Br⇤K L⌃

⇧0⌅⌅⌅�10

⇥11⇥

Gro

ssm

an-N

ir b

ound

E949

✏0/✏ 2 [0.5, 2] (✏0/✏)SM✏0/✏ 2 [0.2, 5] (✏0/✏)SM

|CNP| 2 |�tCSM|

|CNP| |�tCSM||CNP| 0.5|�tCSM|

CNP = |CNP| ei�C

SM

[see S. Jäger, talk at NA62 Physics Handbook Workshop; M. Bauer et al., arXiv:0912.1625 [hep-ph]]

30

With the projected lattice-QCD improvements discussed earlier, combining the pattern of results ε’K/εK with other quantities (such as K→πνν decays) can help further distinguish between new-physics scenarios [Buras et al., Nucl.Phys. B566 (2000)]

[U. Haisch, 2012 Project X Physics Study]


!+

ν!

W+

D(∗)−

cb

B0

dd

|Vcb| from B → Dlν and B → D*lν decays

The B → Dlν and B → D*lνsemileptonic form factorsallow determinations of |Vcb|

hat

hat

Only need one normalization point from lattice-QCD, so choose zero recoil (w=1) because it can be computed most precisely ➡ obtain results with ～2% errors:

31

w ≡ vB·vD}d�(B ⇥ D(�)l�)dw

=G2

F

48⇥3m3

D(mB + mD)2(w2 � 1)3/2|Vcb|2|FB⇥D(�)(w)|2

[Fermilab/MILC, Nucl. Phys.Proc. Suppl.140, 461 (2005)]

[Fermilab/MILC,arXiv:1011.2166]

FB�D(1) = 1.074(18)stat(16)sys FB�D�(1) = 0.9077(51)stat(158)sys


Status of |Vcb|

Also persistent(although smaller)tension between|Vcb|incl. & |Vcb|excl.

Extraction of |Vcb| from BR(B→D*lν) problematic because experiments are not consistent (HFAG excludes “outliers” to obtain good confidence level in global fit)

To obtain competitive |Vcb| from B→Dlν must go to nonzero recoil where experimental errors are smaller

32

37 37.5 38 38.5 39 39.5 40 40.5 41 41.5 42 42.5 43

|Vcb

| x 103

B->Dlν: FNAL/MILC ’04B->D*lν: FNAL/MILC ’10

Exclusive Inclusive

∼1.9σ


Work in progress

Fermilab/MILC Collaboration calculating B→Dlν form factor at nonzero recoil[Siwei Qiu et al., arXiv:1211.2247 (Lattice 2012)]

HPQCD Collaboration also working on B→D*lν (with NRQCD bottom & HISQ charm) which will provide a valuable independent calculation

33


Work-in-progress

Lattice QCD calculations are underway of B→Kl+l - [Zhou et al.(Fermilab/MILC), PoS LATTICE2012 (2012) 120 ] and of B→K*l+l - & B→K*γ [Liu et al., arXiv:1101.2726]

Expect few-percent errors in high q2 region in next few years

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0

0.5

1

1.5

2

2.5

3

0 5 10 15 20

f+an

df0

q2(GeV2)

f+f0

Cambridge Group

Preliminary

Preliminary

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20

fT

q2(GeV2)

fTCambridge Group

B→Kl+l - B→Kl+l -


General approach for HVP[Blum, Phys.Rev.Lett. 91 (2003) 052001]

Calculate aμHVP directly in from the Euclidean space vacuum polarization function:

Π(Q2) is a simple correlationfunction of two electromagneticcurrents

In Euclidean space, Π(Q2) hasa smooth Q2 dependence withno resonance structure

Lattice calculation shouldbe easy, right?

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[plot from Dru Renner]

aHVP(LO)µ =

⇣↵

⇡

⌘2Z 1

0dQ2f(Q2)

⇥⇧(Q2)�⇧(0)

⇤

qµ q⌫

i⇧µ⌫(q2) =


Twisted boundary conditions[Della Morte et al., JHEP 1203 (2012) 055]

Because of the finite spatial lattice size (volume=L3), lattice-QCD simulations can only access discrete momentum values in units of (2π/L) [red points]

➡ Lattice-QCD data are sparse and noisy in the low-Q2 region where the contribution to aμHVP is largest

Mainz group introduced use of twisted boundary conditions for the fermion fields to access momenta below (2π/L) [blue points]

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0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5 2 2.5

Π(2)(q2)

q2 [GeV2]

II III IV

periodic bc

twisted bc

Π(2)pert(q

2)

Π(2)fit (q2)

I

IIIII

ahadµ

m2µ

0.2GeV2

Π(2)pert

orange regionwith Q2 < (2π/L)2

only accessible with twisted B.C.


Padé approximants[Aubin et al.,Phys.Rev. D86 (2012) 054509 ]

Even with twisted boundary conditions, aμHVP receives significant contributions from Π(Q2) for momenta below the range directly accessible in current lattice simulations

➡ Must assume functional form for Q2 dependence and extrapolate Q2→0

Most lattice calculations use a forminspired by vector-meson dominance(VMD) which includes the ρ pole,and possibly a few additionalparameters to absorb othercontributions

To eliminate potentially hiddensystematic associated with VMD fits,Aubin et al. introducedmodel-independent fitting approachbased on analytic structure of Π(Q2)using Padé approximants

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Π(Q2) vs. Q2

uncorrelated VMD fit

correlated [1,1] Padé fit


QCD + QED simulations for HLbLMethod introduced by Blum and collaborators in which one computes the full hadronic amplitude, including the muon and photons, nonperturbatively[Hayakawa et al., PoS LAT2005 (2006) 353]

Treat photon field in parallel with gluon field and include in gauge link, so the simulation and analysis follows a conventional lattice-QCD calculation

In practice, must insert a single valence photon connecting the muon line to the quark loop “by hand” into the correlation function, then perform correlated nonperturbative subtraction to remove the dominant O(α2) contamination

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+O(↵4)- =

qcd+qed

qcd+qed

qedµ µ µ µ µ µ



lattice qcd for the intensity frontier - indico-fnal (indico) · 2013. 5. 7. · doe annual...

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