# Λ_{b}→pl⁻ν¯_{l} form factors from lattice QCD with static b quarks

## Abstract

We present a lattice QCD calculation of form factors for the decay Λ_{b}→pμ⁻ν¯_{μ}, which is a promising channel for determining the Cabibbo-Kobayashi-Maskawa matrix element |V_{ub}| at the Large Hadron Collider. In this initial study we work in the limit of static b quarks, where the number of independent form factors reduces to two. We use dynamical domain-wall fermions for the light quarks, and perform the calculation at two different lattice spacings and at multiple values of the light-quark masses in a single large volume. Using our form factor results, we calculate the Λ_{b}→pμ⁻ν¯_{μ} differential decay rate in the range 14 GeV²≤q²≤q²_{max}, and obtain the integral ∫^{q²max} _{14 GeV²}[dΓ/dq²]dq²/|V_{ub}|²=15.3±4.2 ps⁻¹. Combined with future experimental data, this will give a novel determination of |V_{ub}| with about 15% theoretical uncertainty. The uncertainty is dominated by the use of the static approximation for the b quark, and can be reduced further by performing the lattice calculation with a more sophisticated heavy-quark action.

- Authors:

- Publication Date:

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1104294

- Resource Type:
- Publisher's Accepted Manuscript

- Journal Name:
- Physical Review. D, Particles, Fields, Gravitation and Cosmology

- Additional Journal Information:
- Journal Name: Physical Review. D, Particles, Fields, Gravitation and Cosmology Journal Volume: 88 Journal Issue: 1; Journal ID: ISSN 1550-7998

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Detmold, William, Lin, C.-J. David, Meinel, Stefan, and Wingate, Matthew. Λb→pl⁻ν¯l form factors from lattice QCD with static b quarks. United States: N. p., 2013.
Web. doi:10.1103/PhysRevD.88.014512.
```

```
Detmold, William, Lin, C.-J. David, Meinel, Stefan, & Wingate, Matthew. Λb→pl⁻ν¯l form factors from lattice QCD with static b quarks. United States. doi:10.1103/PhysRevD.88.014512.
```

```
Detmold, William, Lin, C.-J. David, Meinel, Stefan, and Wingate, Matthew. Tue .
"Λb→pl⁻ν¯l form factors from lattice QCD with static b quarks". United States. doi:10.1103/PhysRevD.88.014512.
```

```
@article{osti_1104294,
```

title = {Λb→pl⁻ν¯l form factors from lattice QCD with static b quarks},

author = {Detmold, William and Lin, C.-J. David and Meinel, Stefan and Wingate, Matthew},

abstractNote = {We present a lattice QCD calculation of form factors for the decay Λb→pμ⁻ν¯μ, which is a promising channel for determining the Cabibbo-Kobayashi-Maskawa matrix element |Vub| at the Large Hadron Collider. In this initial study we work in the limit of static b quarks, where the number of independent form factors reduces to two. We use dynamical domain-wall fermions for the light quarks, and perform the calculation at two different lattice spacings and at multiple values of the light-quark masses in a single large volume. Using our form factor results, we calculate the Λb→pμ⁻ν¯μ differential decay rate in the range 14 GeV²≤q²≤q²max, and obtain the integral ∫q²max 14 GeV²[dΓ/dq²]dq²/|Vub|²=15.3±4.2 ps⁻¹. Combined with future experimental data, this will give a novel determination of |Vub| with about 15% theoretical uncertainty. The uncertainty is dominated by the use of the static approximation for the b quark, and can be reduced further by performing the lattice calculation with a more sophisticated heavy-quark action.},

doi = {10.1103/PhysRevD.88.014512},

journal = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},

number = 1,

volume = 88,

place = {United States},

year = {2013},

month = {7}

}

DOI: 10.1103/PhysRevD.88.014512

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Works referenced in this record:

##
Heavy hadron chiral perturbation theory

journal, June 1994

- Cho, P.
- Nuclear Physics B, Vol. 421, Issue 3

##
Heavy hadron chiral perturbation theory

journal, May 1993

- Cho, Peter
- Nuclear Physics B, Vol. 396, Issue 1

##
Continuum limit physics from $2+1$ flavor domain wall QCD

journal, April 2011

- Aoki, Y.; Arthur, R.; Blum, T.
- Physical Review D, Vol. 83, Issue 7

##
An effective field theory for the calculation of matrix elements involving heavy quarks

journal, January 1990

- Eichten, Estia; Hill, Brian
- Physics Letters B, Vol. 234, Issue 4

##
$B$ meson semileptonic form factors from unquenched lattice QCD

journal, April 2006

- Gulez, Emel; Gray, Alan; Wingate, Matthew
- Physical Review D, Vol. 73, Issue 7

##
Form factors and decay rates for heavy $\Lambda $ semileptonic decays from QCD sum rules

journal, June 1999

- Marques de Carvalho, R. S.; Navarra, F. S.; Nielsen, M.
- Physical Review D, Vol. 60, Issue 3

##
Unitary Symmetry and Leptonic Decays

journal, June 1963

- Cabibbo, Nicola
- Physical Review Letters, Vol. 10, Issue 12

##
Axial symmetries in lattice QCD with Kaplan fermions

journal, April 1995

- Furman, Vadim; Shamir, Yigal
- Nuclear Physics B, Vol. 439, Issue 1-2

##
$B\to \pi l\nu $ semileptonic form factor from three-flavor lattice QCD: A model-independent determination of $|{V}_{\mathrm{ub}}|$

journal, March 2009

- Bailey, Jon A.; Bernard, C.; DeTar, C.
- Physical Review D, Vol. 79, Issue 5

##
Form factors and strong couplings of heavy baryons from QCD light-cone sum rules

journal, September 2011

- Khodjamirian, A.; Klein, Ch.; Mannel, Th.
- Journal of High Energy Physics, Vol. 2011, Issue 9

##
Review of Particle Physics

journal, July 2012

- Beringer, J.; Arguin, J. -F.; Barnett, R. M.
- Physical Review D, Vol. 86, Issue 1

##
Relativistic Heavy Quarks on the Lattice

journal, March 2003

- Aoki, S.; Kuramashi, Y.; Tominaga, S. -i.
- Progress of Theoretical Physics, Vol. 109, Issue 3

##
Relativistic heavy quark effective action

journal, October 2007

- Christ, Norman H.; Li, Min; Lin, Huey-Wen
- Physical Review D, Vol. 76, Issue 7

##
Erratum: Form factors for ${\Lambda}_{b}\to \Lambda $ transitions in the soft-collinear effective theory [Phys. Rev. D **85** , 014035 (2012)]

journal, October 2012

- Feldmann, Thorsten; Yip, Matthew W. Y.
- Physical Review D, Vol. 86, Issue 7

##
Heavy-to-light baryonic form factors at large recoil

journal, December 2011

- Mannel, Thomas; Wang, Yu-Ming
- Journal of High Energy Physics, Vol. 2011, Issue 12

##
Chiral fermions from lattice boundaries

journal, September 1993

- Shamir, Yigal
- Nuclear Physics B, Vol. 406, Issue 1-2

##
Baryon chiral perturbation theory using a heavy fermion lagrangian

journal, February 1991

- Jenkins, Elizabeth; Manohar, Aneesh V.
- Physics Letters B, Vol. 255, Issue 4

##
Renormalization group improved action for SU(3) lattice gauge theory and the string tension

journal, August 1984

- Iwasaki, Y.; Yoshié, T.
- Physics Letters B, Vol. 143, Issue 4-6

##
Erratum: Heavy-quark symmetry and chiral dynamics [Phys. Rev. D **46** , 1148 (1992)]

journal, May 1997

- Yan, Tung-Mow; Cheng, Hai-Yang; Cheung, Chi-Yee
- Physical Review D, Vol. 55, Issue 9

##
Factorization of heavy-to-light baryonic transitions in SCET

journal, February 2012

- Wang, Wei
- Physics Letters B, Vol. 708, Issue 1-2

##
Improved nonrelativistic QCD for heavy-quark physics

journal, November 1992

- Lepage, G. Peter; Magnea, Lorenzo; Nakhleh, Charles
- Physical Review D, Vol. 46, Issue 9

##
General analysis of weak decay form factors in heavy to heavy and heavy to light baryon transitions

journal, February 1992

- Hussain, F.; Liu, Dongsheng; Krämer, M.
- Nuclear Physics B, Vol. 370, Issue 2

##
On lattice actions for static quarks

journal, August 2005

- Morte, Michele Della; Shindler, Andrea; Sommer, Rainer
- Journal of High Energy Physics, Vol. 2005, Issue 08

##
Massive fermions in lattice gauge theory

journal, April 1997

- El-Khadra, Aida X.; Kronfeld, Andreas S.; Mackenzie, Paul B.
- Physical Review D, Vol. 55, Issue 7

##
Baryons in the heavy quark effective theory

journal, May 1991

- Mannel, Thomas; Roberts, Winston; Ryzak, Zbigniew
- Nuclear Physics B, Vol. 355, Issue 1

##
A method for simulating chiral fermions on the lattice

journal, August 1992

- Kaplan, David B.
- Physics Letters B, Vol. 288, Issue 3-4

##
Flavor physics in the quark sector

journal, September 2010

- Antonelli, M.; Asner, D. M.; Bauer, D.
- Physics Reports, Vol. 494, Issue 3-4

##
Semileptonic ${\Lambda}_{b,c}$ to nucleon transitions in full QCD at light cone

journal, November 2009

- Azizi, K.; Bayar, M.; Sarac, Y.
- Physical Review D, Vol. 80, Issue 9

##
*C* *P* -Violation in the Renormalizable Theory of Weak Interaction

journal, February 1973

- Kobayashi, Makoto; Maskawa, Toshihide
- Progress of Theoretical Physics, Vol. 49, Issue 2

##
On heavy baryon decay form factors

journal, June 1991

- Hussain, F.; K�rner, J. G.; Kr�mer, M.
- Zeitschrift f�r Physik C Particles and Fields, Vol. 51, Issue 2

##
Heavy-quark symmetry and chiral dynamics

journal, August 1992

- Yan, Tung-Mow; Cheng, Hai-Yang; Cheung, Chi-Yee
- Physical Review D, Vol. 46, Issue 3

##
Parameters of heavy quark effective theory from N f = 2 lattice QCD

journal, September 2012

- Blossier, Benoît; Della Morte, Michele; Fritzsch, Patrick
- Journal of High Energy Physics, Vol. 2012, Issue 9

##
${\Lambda}_{b}\to \Lambda {\ell}^{\mathbf{+}}{\ell}^{\mathbf{-}}$ form factors and differential branching fraction from lattice QCD

journal, April 2013

- Detmold, William; Lin, C. -J. David; Meinel, Stefan
- Physical Review D, Vol. 87, Issue 7

##
Form factors for ${\Lambda}_{b}\to \Lambda $ transitions in the soft-collinear effective theory

journal, January 2012

- Feldmann, Thorsten; Yip, Matthew W. Y.
- Physical Review D, Vol. 85, Issue 1

##
Light-cone QCD sum rules for the semileptonic decay ${\Lambda}_{b}\to p\mathcal{l}\overline{\nu}$

journal, May 2004

- Huang, Ming-Qiu; Wang, Dao-Wei
- Physical Review D, Vol. 69, Issue 9

##
Erratum: $B$ meson semileptonic form factors from unquenched lattice QCD [Phys. Rev. D **73** , 074502 (2006)]

journal, June 2007

- Gulez, Emel; Gray, Alan; Wingate, Matthew
- Physical Review D, Vol. 75, Issue 11

##
${\Lambda}_{b}\to p$ , $\Lambda $ transition form factors from QCD light-cone sum rules

journal, October 2009

- Wang, Yu-Ming; Shen, Yue-Long; Lü, Cai-Dian
- Physical Review D, Vol. 80, Issue 7

##
Renormalization of heavy-light bilinears and fB for Wilson fermions

journal, April 1990

- Eichten, Estia; Hill, Brian
- Physics Letters B, Vol. 240, Issue 1-2

##
One-loop operator matching in the static heavy and domain-wall light quark system with O(a) improvement

journal, May 2011

- Ishikawa, Tomomi; Aoki, Yasumichi; Flynn, Jonathan M.
- Journal of High Energy Physics, Vol. 2011, Issue 5

##
Non-Lagrangian Models of Current Algebra

journal, March 1969

- Wilson, Kenneth G.
- Physical Review, Vol. 179, Issue 5

##
The Chroma Software System for Lattice QCD

journal, March 2005

- Edwards, Robert G.; Joó, Bálint
- Nuclear Physics B - Proceedings Supplements, Vol. 140