Lorentz violating kinematics: threshold theorems Authors Valentina Baccetti School of Mathematics, Statistics, and Operations Research Victoria University of Wellington Kyle Tate School of Mathematics, Statistics, and Operations Research Victoria University of Wellington Matt Visser School of Mathematics, Statistics, and Operations Research Victoria University of Wellington Article

First Online: 27 March 2012 Received: 06 December 2011 Revised: 23 February 2012 Accepted: 10 March 2012 DOI :
10.1007/JHEP03(2012)087

Cite this article as: Baccetti, V., Tate, K. & Visser, M. J. High Energ. Phys. (2012) 2012: 87. doi:10.1007/JHEP03(2012)087
Abstract Recent tentative experimental indications, and the subsequent theoretical speculations, regarding possible violations of Lorentz invariance have attracted a vast amount of attention. An important technical issue that considerably complicates detailed calculations in any such scenario, is that once one violates Lorentz invariance the analysis of thresholds in both scattering and decay processes becomes extremely subtle, with many new and naively unexpected effects. In the current article we develop several extremely general threshold theorems that depend only on the existence of some energy momentum relation E (p), eschewing even assumptions of isotropy or monotonicity. We shall argue that there are physically interesting situations where such a level of generality is called for, and that existing (partial) results in the literature make unnecessary technical assumptions. Even in this most general of settings, we show that at threshold all final state particles move with the same 3-velocity, while initial state particles must have 3-velocities parallel/anti-parallel to the final state particles. In contrast the various 3-momenta can behave in a complicatedand counter-intuitive manner.

Keywords Space-Time Symmetries Beyond Standard Model Neutrino Physics Global Symmetries

References [1]

OPERA collaboration, T. Adam et al.,

Measurement of the neutrino velocity with the OPERA detector in the CNGS beam ,

arXiv:1109.4897 [

INSPIRE ].

[2]

MINOS collaboration, P. Adamson et al.,

Measurement of neutrino velocity with the MINOS detectors and NuMI neutrino beam ,

Phys. Rev. D 76 (2007) 072005 [

arXiv:0706.0437 ] [

INSPIRE ].

ADS [3]

G. Amelino-Camelia et al.,

OPERA-reassessing data on the energy dependence of the speed of neutrinos ,

Int. J. Mod. Phys. D 20 (2011) 2623 [

arXiv:1109.5172 ] [

INSPIRE ].

MathSciNet ADS [4]

G.F. Giudice, S. Sibiryakov and A. Strumia,

Interpreting OPERA results on superluminal neutrino , Nucl. Phys. B in press,

arXiv:1109.5682 [

INSPIRE ].

[5]

A.G. Cohen and S.L. Glashow,

Pair Creation Constrains Superluminal Neutrino Propagation ,

Phys. Rev. Lett. 107 (2011) 181803 [

arXiv:1109.6562 ] [

INSPIRE ].

ADS CrossRef [6]

G. Dvali and A. Vikman,

Price for Environmental Neutrino-Superluminality ,

JHEP 02 (2012)134 [

arXiv:1109.5685 ] [

INSPIRE ].

ADS CrossRef [7]

J. Alexandre, J. Ellis and N.E. Mavromatos,

On the Possibility of Superluminal Neutrino Propagation ,

Phys. Lett. B 706 (2012) 456 [

arXiv:1109.6296 ] [

INSPIRE ].

ADS [8]

G. Cacciapaglia, A. Deandrea and L. Panizzi,

Superluminal neutrinos in long baseline experiments and SN1987a ,

JHEP 11 (2011) 137 [

arXiv:1109.4980 ] [INSPIRE].

ADS CrossRef [9]

X.-J. Bi, P.-F. Yin, Z.-H. Yu and Q. Yuan,

Constraints and tests of the OPERA superluminal neutrinos ,

Phys. Rev. Lett. 107 (2011) 241802 [

arXiv:1109.6667 ] [

INSPIRE ].

ADS CrossRef [10]

F. Klinkhamer,

Superluminal muon-neutrino velocity from a Fermi-point-splitting model of Lorentz violation ,

arXiv:1109.5671 [

INSPIRE ].

[11]

S.S. Gubser,

Superluminal neutrinos and extra dimensions: Constraints from the null energy condition ,

Phys. Lett. B 705 (2011) 279 [

arXiv:1109.5687 ] [

INSPIRE ].

ADS [12]

A. Kehagias,

Relativistic Superluminal Neutrinos ,

arXiv:1109.6312 [

INSPIRE ].

[13]

P. Wang, H. Wu and H. Yang,

Superluminal neutrinos and domain walls ,

arXiv:1109.6930 [

INSPIRE ].

[14]

E.N. Saridakis,

Superluminal neutrinos in Ho ř

ava-Lifshitz gravity ,

arXiv:1110.0697 [

INSPIRE ].

[15]

W. Winter,

Constraints on the interpretation of the superluminal motion of neutrinos at OPERA ,

Phys. Rev. D 85 (2012) 017301 [

arXiv:1110.0424 ] [

INSPIRE ].

ADS [16]

J. Alexandre,

Lifshitz-type Quantum Field Theories in Particle Physics ,

Int. J. Mod. Phys. A 26 (2011) 4523 [

arXiv:1109.5629 ] [

INSPIRE ].

ADS [17]

F. Klinkhamer and G. Volovik,

Superluminal neutrino and spontaneous breaking of Lorentz invariance ,

Pisma Zh. Eksp. Teor. Fiz. 94 (2011) 731 [

arXiv:1109.6624 ] [

INSPIRE ].

[18]

R. Cowsik, S. Nussinov and U. Sarkar,

Superluminal Neutrinos at OPERA Confront Pion Decay Kinematics ,

Phys. Rev. Lett. 107 (2011) 251801 [

arXiv:1110.0241 ] [

INSPIRE ].

ADS CrossRef [19]

L. Maccione, S. Liberati and D.M. Mattingly,

Violations of Lorentz invariance in the neutrino sector after OPERA ,

arXiv:1110.0783 [

INSPIRE ].

[20]

N. Dass,

OPERA, SN1987a and energy dependence of superluminal neutrino velocity ,

arXiv:1110.0351 [

INSPIRE ].

[21]

J. Carmona and J. Cortes,

Constraints from Neutrino Decay on Superluminal Velocities ,

arXiv:1110.0430 [

INSPIRE ].

[22]

S.R. Coleman and S.L. Glashow,

Cosmic ray and neutrino tests of special relativity ,

Phys. Lett. B 405 (1997) 249 [

hep-ph/9703240 ] [

INSPIRE ].

ADS [23]

S.R. Coleman and S.L. Glashow,

High-energy tests of Lorentz invariance ,

Phys. Rev. D 59 (1999)116008 [

hep-ph/9812418 ] [

INSPIRE ].

ADS [24]

S. Liberati, T. Jacobson and D. Mattingly,

High-energy constraints on Lorentz symmetry violations ,

hep-ph/0110094 [

INSPIRE ].

[25]

T. Jacobson, S. Liberati and D. Mattingly,

TeV astrophysics constraints on Planck scale Lorentz violation ,

Phys. Rev. D 66 (2002) 081302 [

hep-ph/0112207 ] [

INSPIRE ].

ADS [26]

T. Jacobson, S. Liberati and D. Mattingly,

Threshold effects and Planck scale Lorentz violation: Combined constraints from high-energy astrophysics ,

Phys. Rev. D 67 (2003) 124011 [

hep-ph/0209264 ] [

INSPIRE ].

ADS [27]

D. Mattingly, T. Jacobson and S. Liberati,

Threshold configurations in the presence of Lorentz violating dispersion relations ,

Phys. Rev . D 67 (2003) 124012 [

hep-ph/0211466 ] [

INSPIRE ].

ADS [28]

T. Jacobson, S. Liberati and D. Mattingly,

A Strong astrophysical constraint on the violation of special relativity by quantum gravity ,

Nature 424 (2003) 1019 [

astro-ph/0212190 ] [

INSPIRE ].

ADS CrossRef [29]

T. Jacobson, S. Liberati and D. Mattingly,

Comments on ’

Improved limit on quantum space-time modifications of Lorentz symmetry from observations of gamma-ray blazars ’,

gr-qc/0303001 [

INSPIRE ].

[30]

T.A. Jacobson, S. Liberati, D. Mattingly and F. Stecker,

New limits on Planck scale Lorentz violation in QED ,

Phys. Rev. Lett. 93 (2004) 021101 [

astro-ph/0309681 ] [

INSPIRE ].

ADS CrossRef [31]

T. Jacobson, S. Liberati and D. Mattingly,

Quantum gravity phenomenology and Lorentz violation ,

Springer Proc. Phys. 98 (2005) 83 [

gr-qc/0404067 ] [

INSPIRE ].

CrossRef [32]

T. Jacobson, S. Liberati and D. Mattingly,

Astrophysical bounds on Planck suppressed Lorentz violation ,

Lect. Notes Phys. 669 (2005) 101 [

hep-ph/0407370 ] [

INSPIRE ].

ADS CrossRef [33]

T. Jacobson, S. Liberati and D. Mattingly,

Lorentz violation at high energy: Concepts, phenomena and astrophysical constraints ,

Annals Phys. 321 (2006) 150 [

astro-ph/0505267 ] [

INSPIRE ].

ADS MATH CrossRef [34]

D. Mattingly,

Modern tests of Lorentz invariance ,

Living Rev. Rel. 8 (2005) 5 [

gr-qc/0502097 ] [

INSPIRE ].

[35]

D. Colladay and V. Kostelecky,

Lorentz violating extension of the standard model ,

Phys. Rev. D 58 (1998) 116002 [

hep-ph/9809521 ] [

INSPIRE ].

ADS [36]

V. Kostelecky and S. Samuel,

Spontaneous Breaking of Lorentz Symmetry in String Theory ,

Phys. Rev. D 39 (1989) 683 [

INSPIRE ].

ADS [37]

V. Kostelecky,

Gravity, Lorentz violation and the standard model ,

Phys. Rev. D 69 (2004) 105009 [

hep-th/0312310 ] [

INSPIRE ].

ADS [38]

V. Kostelecky and R. Lehnert,

Stability, causality and Lorentz and CPT violation ,

Phys. Rev. D 63 (2001) 065008 [

hep-th/0012060 ] [

INSPIRE ].

MathSciNet ADS [39]

V. Kostelecky and M. Mewes,

Signals for Lorentz violation in electrodynamics ,

Phys. Rev. D 66 (2002)056005 [

hep-ph/0205211 ] [

INSPIRE ].

ADS [40]

V. Kostelecky and M. Mewes,

Lorentz and CPT violation in neutrinos ,

Phys. Rev. D 69 (2004)016005 [

hep-ph/0309025 ] [

INSPIRE ].

ADS [41]

V. Kostelecky and C.D. Lane,

Constraints on Lorentz violation from clock comparison experiments ,

Phys. Rev. D 60 (1999) 116010 [

hep-ph/9908504 ] [

INSPIRE ].

ADS [42]

V. Kostelecky and M. Mewes,

Cosmological constraints on Lorentz violation in electrodynamics ,

Phys. Rev. Lett. 87 (2001) 251304 [

hep-ph/0111026 ] [

INSPIRE ].

ADS CrossRef [43]

D. Bear, R. Stoner, R. Walsworth, V. Kostelecky and C.D. Lane,

Limit on Lorentz and CPT violation of the neutron using a two species noble gas maser ,

Phys. Rev. Lett. 85 (2000) 5038 [

Erratum ibid. 89 (2002) 209902] [

physics/0007049 ] [

INSPIRE ].

ADS CrossRef [44]

D. Anselmi, Renormalization And Lorentz Symmetry Violation , PoS(CLAQG08)010.

[45]

D. Anselmi and D. Buttazzo,

Distance Between Quantum Field Theories As A Measure Of Lorentz Violation ,

Phys. Rev. D 84 (2011) 036012 [

arXiv:1105.4209 ] [

INSPIRE ].

ADS [46]

D. Anselmi,

Renormalization of Lorentz violating theories , Prepared for 4th

Meeting on CPT and Lorentz Symmetry , Bloomington, Indiana, 8-11 Aug 2007 [

INSPIRE ].

[47]

D. Anselmi and M. Taiuti,

Vacuum Cherenkov Radiation In Quantum Electrodynamics With High-Energy Lorentz Violation ,

Phys. Rev. D 83 (2011) 056010 [

arXiv:1101.2019 ] [

INSPIRE ].

ADS [48]

D. Anselmi and E. Ciuffoli,

Low-energy Phenomenology Of Scalarless Standard-Model Extensions With High-Energy Lorentz Violation ,

Phys. Rev. D 83 (2011) 056005 [

arXiv:1101.2014 ] [

INSPIRE ].

ADS [49]

D. Anselmi and E. Ciuffoli,

Renormalization Of High-Energy Lorentz Violating Four Fermion Models ,

Phys. Rev. D 81 (2010) 085043 [

arXiv:1002.2704 ] [

INSPIRE ].

ADS [50]

D. Anselmi and M. Taiuti,

Renormalization Of High-Energy Lorentz Violating QED ,

Phys. Rev. D 81 (2010) 085042 [

arXiv:0912.0113 ] [

INSPIRE ].

[51]

D. Anselmi,

Standard Model Without Elementary Scalars And High Energy Lorentz Violation ,

Eur. Phys. J. C 65 (2010) 523 [

arXiv:0904.1849 ] [

INSPIRE ].

ADS CrossRef [52]

D. Anselmi,

Weighted power counting, neutrino masses and Lorentz violating extensions of the Standard Model ,

Phys. Rev. D 79 (2009) 025017 [

arXiv:0808.3475 ] [

INSPIRE ].

ADS [53]

D. Anselmi,

Weighted power counting and Lorentz violating gauge theories. II. Classification ,

Annals Phys. 324 (2009) 1058 [

arXiv:0808.3474 ] [

INSPIRE ].

MathSciNet ADS MATH CrossRef [54]

D. Anselmi,

Weighted power counting and Lorentz violating gauge theories. I. General properties ,

Annals Phys. 324 (2009) 874 [

arXiv:0808.3470 ] [

INSPIRE ].

MathSciNet ADS MATH CrossRef [55]

D. Anselmi,

Weighted scale invariant quantum field theories ,

JHEP 02 (2008) 051 [

arXiv:0801.1216 ] [

INSPIRE ].

MathSciNet ADS CrossRef [56]

D. Anselmi and M. Halat,

Renormalization of Lorentz violating theories ,

Phys. Rev. D 76 (2007)125011 [

arXiv:0707.2480 ] [

INSPIRE ].

ADS [57]

P. Hořava,

Quantum Gravity at a Lifshitz Point ,

Phys. Rev. D 79 (2009) 084008 [

arXiv:0901.3775 ] [

INSPIRE ].

ADS [58]

M. Visser,

Lorentz symmetry breaking as a quantum field theory regulator ,

Phys. Rev. D 80 (2009)025011 [

arXiv:0902.0590 ] [

INSPIRE ].

MathSciNet ADS [59]

M. Visser,

Power-counting renormalizability of generalized Ho ř

ava gravity ,

arXiv:0912.4757 [

INSPIRE ].

[60]

T.P. Sotiriou, M. Visser and S. Weinfurtner,

Quantum gravity without Lorentz invariance ,

JHEP 10 (2009) 033 [

arXiv:0905.2798 ] [

INSPIRE ].

MathSciNet ADS CrossRef [61]

T.P. Sotiriou, M. Visser and S. Weinfurtner,

Phenomenologically viable Lorentz-violating quantum gravity ,

Phys. Rev. Lett. 102 (2009) 251601 [

arXiv:0904.4464 ] [

INSPIRE ].

MathSciNet ADS CrossRef [62]

S. Weinfurtner, T.P. Sotiriou and M. Visser,

Projectable Ho ř

ava-Lifshitz gravity in a nutshell ,

J. Phys. Conf. Ser. 222 (2010) 012054 [

arXiv:1002.0308 ] [

INSPIRE ].

ADS CrossRef [63]

M. Visser,

Status of Ho ř

ava gravity: A personal perspective ,

J. Phys. Conf. Ser. 314 (2011) 012002 [

arXiv:1103.5587 ] [

INSPIRE ].

ADS CrossRef [64]

S. Judes and M. Visser,

Conservation laws in ’

Doubly special relativity ’,

Phys. Rev. D 68 (2003)045001 [

gr-qc/0205067 ] [

INSPIRE ].

MathSciNet ADS [65]

S. Liberati, S. Sonego and M. Visser,

Interpreting doubly special relativity as a modified theory of measurement ,

Phys. Rev. D 71 (2005) 045001 [

gr-qc/0410113 ] [

INSPIRE ].

MathSciNet ADS [66]

C. Barcelo, S. Liberati and M. Visser,

Analogue gravity ,

Living Rev. Rel. 8 (2005) 12 [

gr-qc/0505065 ] [

INSPIRE ].

[67]

M. Visser,

Acoustic black holes: Horizons, ergospheres and Hawking radiation ,

Class. Quant. Grav. 15 (1998) 1767 [

gr-qc/9712010 ] [

INSPIRE ].

MathSciNet ADS MATH CrossRef © SISSA, Trieste, Italy 2012