Sophie Hollitt Ross Young, James Zanotti, and QCDSF LATTICE2018, - - PowerPoint PPT Presentation

Sophie Hollitt

Ross Young, James Zanotti, and QCDSF LATTICE2018, Wednesday 25th July

Why B decay constants?

 New experiments and the CKM matrix:

 Need to reduce error in theoretical calculations

to reduce error on CKM matrix elements ahead

• f new experimental results from Belle II

 Decay constant fB could be used alongside

measurement of B →τν to pinpoint |Vub|

 fB, fBs also important to |Vtd|,|Vts| through B0B0

• scillations

Sophie Hollitt SU(3) breaking of B meson decay constant

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 We want to learn more about the way SU(3) breaking in

the lightest quarks affects heavy B mesons

 Need a strategy for studying SU(3) breaking effects in u,d,s

quarks on the lattice

2007

2014

Choosing light and strange quarks

 We choose to study SU(3) breaking in a controlled way, by

keeping the average mass of these three lightest quarks constant.

 Lattice configurations for this method are produced by the

QCDSF Collaboration. These configurations are simplified with mu = md , (called mlight)

Sophie Hollitt SU(3) breaking of B meson decay constant

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 Choose constant average mass

matching the physical average mass

 Produces controlled breaking of

SU(3) symmetry

 Flavour singlet quantities remain

• approx. constant (O(δm) removed)

m = ( 2ml + ms )

⅓

Choosing light and strange quarks

 We choose to study SU(3) breaking in a controlled way, by

keeping the average mass of these three lightest quarks constant.

 Lattice configurations for this method are produced by the

QCDSF Collaboration. These configurations are simplified with mu = md , (called mlight)

Sophie Hollitt SU(3) breaking of B meson decay constant

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 Choose constant average mass

matching the physical average mass

 Produces controlled breaking of

SU(3) symmetry

 Flavour singlet quantities remain

• approx. constant (O(δm) removed)

m = ( 2ml + ms )

⅓

Light flavour singlets on QCDSF configurations, including:

Choosing light and strange quarks

 We choose to study SU(3) breaking in a controlled way, by

keeping the average mass of these three lightest quarks constant.

 Lattice configurations for this method are produced by the

QCDSF Collaboration. These configurations are simplified with mu = md , called mlight

Sophie Hollitt SU(3) breaking of B meson decay constant

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m = ( 2ml + ms )

⅓

0.5 1

ms = constant

Breaking ratio mπ

2 / Xπ 2

mπ

2

mK

2

The kaon is light + strange, so its mass still changes when ms is constant SU(3) breaking effects and effects from simulating a heavier vacuum

• ccur together

The average quark mass in the vacuum is constant

Choosing light and strange quarks

 We choose to study SU(3) breaking in a controlled way, by

keeping the average mass of these three lightest quarks constant.

 Lattice configurations for this method are produced by the

QCDSF Collaboration. These configurations are simplified with mu = md , called mlight

Sophie Hollitt SU(3) breaking of B meson decay constant

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m = ( 2ml + ms )

⅓

0.5 1

ms = constant

Breaking ratio mπ

2 / Xπ 2

mB

2

mBs

2 The kaon is light + strange, so its mass still changes when ms is constant SU(3) breaking effects and effects from simulating a heavier vacuum

• ccur together

The average quark mass in the vacuum is constant

mBX

2

Generating b-quarks

 b-quarks are heavy and “fall through” the lattice if a

standard quark action is used.

 We use an anisotropic, clover-improved action

(Relativistic Heavy Quark Action), and then tune the free parameters to physical quantities for the B meson.

1

Aoki, Y et al (2012). “Nonperturbative tuning of an improved relativistic heavy-quark action with application to bottom spectroscopy.” Physical Review D, 86(11), 116003. doi:10.1103/PhysRevD.86.116003

1 spin-averaged meson mass dispersion relation hyperfine splitting between B* and B bare mass anisotropy clover coefficient

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SU(3) breaking of B meson decay constant Sophie Hollitt

Generating b-quarks

1.

On every set of configurations, generate

• ne “central” b-quark and six other b-

quarks in a “parameter star” by changing our three free variables.

2.

Make a Blight and Bstrange meson for each b quark

3.

Calculate the “singlet” B meson, BX = (2/3) Bl + (1/3) Bs for each of our seven b-quarks.

4.

Compare the calculated BX mesons to the physical BX meson, and find the set

• f parameters matching the physical B.

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SU(3) breaking of B meson decay constant Sophie Hollitt

METHOD:

Tuning B mesons

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SU(3) breaking of B meson decay constant Sophie Hollitt

Tuning B mesons

Central b value

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SU(3) breaking of B meson decay constant Sophie Hollitt

Tuning B mesons

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SU(3) breaking of B meson decay constant Sophie Hollitt

Tuning B mesons

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SU(3) breaking of B meson decay constant Sophie Hollitt

Tuning B mesons

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SU(3) breaking of B meson decay constant Sophie Hollitt

Tuning B mesons

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SU(3) breaking of B meson decay constant Sophie Hollitt

Calculating the decay constant fBq

 Once we have chosen the appropriate quarks, the

decay constant is calculated mostly using two point functions

Lattice decay constant: 2 point functions with different operators in the quark propagators, and mass of B Improvement term: 2 point correlators & coefficient cA Currently take cA=0, Exact value can be calculated using perturbative QCD Renormalisation factor: Ratio of 2 point and 3 point functions with constant coefficient ρ=1

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SU(3) breaking of B meson decay constant Sophie Hollitt

Calculating the decay constant fBq

1.

Calculate ΦB and ΦBs for each of the b-quarks in the tuning “star”

2.

For each set of lattice configurations, collect the “best” tuning parameters matching the physical properties of the BX meson (as seen earlier)

3.

Use these parameters to interpolate to a “best” ΦB and thus calculate “best” fB

4.

Repeat at other light quark masses and lattice spacings!

fB at symmetric point ml = ms

fB for b in tuning star Interpolated best fB

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SU(3) breaking of B meson decay constant Sophie Hollitt

Configurations used

Sophie Hollitt SU(3) breaking of B meson decay constant

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0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 110 160 210 260 310 360 410 460 510

a2 mπ

QCDSF Configurations

Part of this analysis (systematic error in average mass) New configurations

0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 110 160 210 260 310 360 410 460 510

a2 mπ

QCDSF Configurations

Part of this analysis (systematic error in average mass) New configurations

Configurations used

Sophie Hollitt SU(3) breaking of B meson decay constant

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BLUE configurations have a systematic error in the SU(3) symmetric point value compared to the physical point, so we need a more careful approach

SU(3) breaking of fBq

 On each configuration,

calculate fBl and fBs and the average fBx to cancel most systematic errors from calculation method

 Visible errors are

almost entirely from extrapolation to best B meson  Linear fit is not

sufficient! 19

SU(3) breaking of B meson decay constant Sophie Hollitt

a = 0.082 fm a = 0.074 fm a = 0.068 fm a = 0.059 fm

SU(3) symmetric point

fBs fB

Toward physical fB and fBs

 If we take an SU(3) expansion of fBq / fBX to NLO, and include quenched

light quarks (q) and ignore the b quark in the SU(3) breaking, we can write: with a similar equation governing the mass of the B mesons.

 By using lattice data to fit the coefficients for both f and M, we can:

 Extrapolate to a value of fBq at the physical point for each lattice

spacing

 Perform a continuum extrapolation for each fBq

Difference between valence quark mass and SU(3) quark mass ( δμb = 0, not part of SU(3) )

2

Based on equation in Bornyakov, V. G. et al (2017). “Flavour breaking effects in the pseudoscalar meson decay constants.” Physics Letters B, 767(3), 366–373. doi:10.1016/j.physletb.2017.02.018

2

Sophie Hollitt SU(3) breaking of B meson decay constant

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Differences between sea quark masses and SU(3) quark mass

Toward physical fB and fBs

 Fits should be performed for

each lattice spacing separately…

 … but for now we have an

• verview of the data

collected so far  Fits to the mass and decay

constant for each lattice spacing are waiting for more lattice configurations to be processed.

 Next: extrapolate from finite

lattice spacing to continuum QCD

Sophie Hollitt SU(3) breaking of B meson decay constant

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δmq change in quark mass from SU(3) symmetric point(s)

SU(3) symmetric point

fBs fB

a = 0.082 fm a = 0.082 fm a = 0.074 fm a = 0.068 fm a = 0.059 fm

(partially-quenched)

Summary and future work

 fB and fBs calculated for a large number of lattice

spacings and SU(3) splittings

 Additional configurations to be included soon  Adding more partially-quenched light quarks  Improvement coefficients

 Future plans include

 Measurement of fB*  Semileptonic form factors B→D(*)lv  Studies of Λb

Sophie Hollitt SU(3) breaking of B meson decay constant

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