# ${{\boldsymbol W}_{{R}}}$ (Right-Handed ${{\boldsymbol W}}$ Boson) MASS LIMITS INSPIRE search

Assuming a light right-handed neutrino, except for BEALL 1982 , LANGACKER 1989B, and COLANGELO 1991 . ${{\mathit g}_{{R}}}$ = ${{\mathit g}_{{L}}}$ assumed. [Limits in the section MASS LIMITS for ${{\mathit W}^{\,'}}$ below are also valid for ${{\mathit W}_{{R}}}$ if ${\mathit m}_{{{\mathit \nu}_{{R}}}}{}\ll$ ${\mathit m}_{{{\mathit W}_{{R}}}}$.] Some limits assume manifest left-right symmetry, $\mathit i.e.$, the equality of left- and right Cabibbo-Kobayashi-Maskawa matrices. For a comprehensive review, see LANGACKER 1989B. Limits on the ${{\mathit W}_{{L}}}-{{\mathit W}_{{R}}}$ mixing angle $\zeta$ are found in the next section. Values in brackets are from cosmological and astrophysical considerations and assume a light right-handed neutrino.
VALUE (GeV) CL% DOCUMENT ID TECN  COMMENT
$> 592$ 90 1
 2011
TWST ${{\mathit \mu}}$ decay
$\bf{>715}$ 90 2
 1999
RVUE Electroweak
• • • We do not use the following data for averages, fits, limits, etc. • • •
$>235$ 90 3
 2014
PIE3 ${{\mathit \mu}}$ decay
$> 245$ 90 4
 2010
CNTR ${}^{60}\mathrm {Co}{{\mathit \beta}}$ decay
$> 2500$ 5
 2008
THEO ${\mathit m}_{{{\mathit K}_L^0} }−{\mathit m}_{{{\mathit K}_S^0} }$
$> 180$ 90 6
 2007
CNTR ${}^{37}\mathrm {K}{{\mathit \beta}^{+}}$ decay
$> 290.7$ 90 7
 2007
CNTR Polarized neutron decay
$\text{[> 3300]}$ 95 8
 2005
COSM Nucleosynthesis; light ${{\mathit \nu}_{{R}}}$
$>310$ 90 9
 2001
CNTR ${{\mathit \beta}^{+}}$ decay
$>137$ 95 10
 1999 D
OPAL ${{\mathit \tau}}$ decay
$>1400$ 68 11
 1998
RVUE Electroweak, ${{\mathit Z}}-{{\mathit Z}^{\,'}}$ mixing
$>549$ 68 12
 1997
RVUE ${{\mathit \mu}}$ decay
$>220$ 95 13
 1997
RVUE ${{\mathit \tau}}$ decay
$>220$ 90 14
 1996
CNTR ${{\mathit \beta}^{+}}$ decay
$>281$ 90 15
 1995
CNTR Polarized neutron decay
$>282$ 90 16
 1994 B
CNTR Polarized neutron decay
$>439$ 90 17
 1993
RVUE ${{\mathit Z}}-{{\mathit Z}^{\,'}}$ mixing
$>250$ 90 18
 1993
CNTR ${{\mathit \beta}^{+}}$ decay
19
 1992
CNTR ${{\mathit K}^{+}}$ decay
$>475$ 90 20
 1992 B
RVUE ${{\mathit \mu}}$ decay
$>240$ 90 21
 1991
RVUE Neutron decay
$>496$ 90 21
 1991
RVUE Neutron and muon decay
$>700$ 22
 1991
THEO ${\mathit m}_{{{\mathit K}_L^0} }–{\mathit m}_{{{\mathit K}_S^0} }$
$>477$ 90 23
 1991
RVUE ${{\mathit \mu}}$ decay
$\text{[none 540 - 23000]}$ 24
 1989 B
ASTR SN 1987A; light ${{\mathit \nu}_{{R}}}$
$>300$ 90 25
 1989 B
RVUE General
$>160$ 90 26
 1988
CNTR ${{\mathit \mu}}$ $\rightarrow$ ${{\mathit e}}{{\mathit \nu}}{{\overline{\mathit \nu}}}$
$>406$ 90 27
 1986
ELEC Any $\zeta$
$>482$ 90 27
 1986
ELEC $\zeta$ = 0
$>800$
 1986
RVUE SU(2)$_{\mathit L}{\times }SU(2)_{\mathit R}{\times }$U(1)
$>400$ 95 28
 1985
ELEC Any $\zeta$
$>475$ 95 28
 1985
ELEC $\zeta$ $<$0.041
29
 1983
CHRM ${{\mathit \nu}_{{\mu}}}$ ${{\mathit e}}$ $\rightarrow$ ${{\mathit \mu}}{{\mathit \nu}_{{e}}}$
$>380$ 90 30
 1983
ELEC ${{\mathit \mu}^{+}}$ decay
$>1600$ 31
 1982
THEO ${\mathit m}_{{{\mathit K}_L^0} }–{\mathit m}_{{{\mathit K}_S^0} }$
1  The quoted limit is for manifest left-right symmetric model.
2  CZAKON 1999 perform a simultaneous fit to charged and neutral sectors.
3  PRIEELS 2014 limit is from ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}}{{\overline{\mathit \nu}}}$ decay parameter ${{\mathit \xi}^{''}}$, which is determined by the positron polarization measurement.
4  WAUTERS 2010 limit is from a measurement of the asymmetry parameter of polarized ${}^{60}\mathrm {Co}{{\mathit \beta}}$ decays. The listed limit assumes no mixing.
5  ZHANG 2008 limit uses a lattice QCD calculation of the relevant hadronic matrix elements, while BEALL 1982 limit used the vacuum saturation approximation.
6  MELCONIAN 2007 measure the neutrino angular asymmetry in ${{\mathit \beta}^{+}}$-decays of polarized ${}^{37}\mathrm {K}$, stored in a magneto-optical trap. Result is consistent with SM prediction and does not constrain the ${{\mathit W}_{{L}}}$ ${{\mathit W}_{{R}}}$ mixing angle appreciably.
7  SCHUMANN 2007 limit is from measurements of the asymmetry $\langle \overrightarrow{{\mathit p}}_{{{\mathit \nu}}}\cdot{}{{\mathit \sigma}_{{n}}}\rangle$ in the $\beta$ decay of polarized neutrons. Zero mixing is assumed.
8  CYBURT 2005 limit follows by requiring that three light ${{\mathit \nu}_{{R}}}$'s decouple when ${{\mathit T}_{{{dec}}}}$ $>$ 140 MeV. For different ${{\mathit T}_{{{dec}}}}$, the bound becomes ${{\mathit M}}_{{{\mathit W}_{{R}}}}$ $>$ 3.3 TeV (${{\mathit T}_{{{dec}}}}$ $/$ 140 MeV)${}^{3/4}$.
9  THOMAS 2001 limit is from measurement of ${{\mathit \beta}^{+}}$ polarization in decay of polarized ${}^{12}\mathrm {N}$. The listed limit assumes no mixing.
10  ACKERSTAFF 1999D limit is from ${{\mathit \tau}}$ decay parameters. Limit increase to 145 GeV for zero mixing.
11  BARENBOIM 1998 assumes minimal left-right model with Higgs of SU(2)$_{\mathit R}$ in SU(2)$_{\mathit L}$ doublet. For Higgs in SU(2)$_{\mathit L}$ triplet, ${\mathit m}_{{{\mathit W}_{{R}}}}>$1100 GeV. Bound calculated from effect of corresponding ${{\mathit Z}_{{LR}}}$ on electroweak data through ${{\mathit Z}}-{{\mathit Z}_{{LR}}}$ mixing.
12  The quoted limit is from ${{\mathit \mu}}$ decay parameters. BARENBOIM 1997 also evaluate limit from ${{\mathit K}_{{L}}}-{{\mathit K}_{{S}}}$ mass difference.
13  STAHL 1997 limit is from fit to ${{\mathit \tau}}$-decay parameters.
14  ALLET 1996 measured polarization-asymmetry correlation in ${}^{12}\mathrm {N}$ ${{\mathit \beta}^{+}}$ decay. The listed limit assumes zero $\mathit L-\mathit R$ mixing.
15  KUZNETSOV 1995 limit is from measurements of the asymmetry $\langle{}\overrightarrow{{\mathit p}}_{{{\mathit \nu}}}\cdot{}{{\mathit \sigma}_{{n}}}\rangle{}$ in the $\beta$ decay of polarized neutrons. Zero mixing assumed. See also KUZNETSOV 1994B.
16  KUZNETSOV 1994B limit is from measurements of the asymmetry $\langle{}\overrightarrow{{\mathit p}}_{{{\mathit \nu}}}\cdot{}{{\mathit \sigma}_{{n}}}\rangle{}$ in the $\beta$ decay of polarized neutrons. Zero mixing assumed.
17  BHATTACHARYYA 1993 uses ${{\mathit Z}}-{{\mathit Z}^{\,'}}$ mixing limit from LEP '90 data, assuming a specific Higgs sector of SU(2)$_{\mathit L}{\times }SU(2)_{\mathit R}{\times }$U(1) gauge model. The limit is for ${\mathit m}_{{{\mathit t}}}$=200 GeV and slightly improves for smaller ${\mathit m}_{{{\mathit t}}}$.
18  SEVERIJNS 1993 measured polarization-asymmetry correlation in ${}^{107}\mathrm {In}$ ${{\mathit \beta}^{+}}$ decay. The listed limit assumes zero ${{\mathit L}}-{{\mathit R}}$ mixing. Value quoted here is from SEVERIJNS 1994 erratum.
19  IMAZATO 1992 measure positron asymmetry in ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{\mu}}}$ decay and obtain $\xi {{\mathit P}_{{\mu}}}>0.990$ (90$\%$ CL). If ${{\mathit W}_{{R}}}$ couples to ${{\mathit u}}{{\overline{\mathit s}}}$ with full weak strength ($\mathit V{}^{\mathit R}_{ {{\mathit u}} {{\mathit s}} }$=1), the result corresponds to ${\mathit m}_{{{\mathit W}_{{R}}}}>$653 GeV. See their Fig.$~$4 for ${\mathit m}_{{{\mathit W}_{{R}}}}$ limits for general $\vert \mathit V{}^{\mathit R}_{ {{\mathit u}} {{\mathit s}} }\vert ^2=1−\vert \mathit V{}^{\mathit R}_{ {{\mathit u}} {{\mathit d}} }\vert ^2$.
20  POLAK 1992B limit is from fit to muon decay parameters and is essentially determined by JODIDIO 1986 data assuming $\zeta$=0. Supersedes POLAK 1991 .
21  AQUINO 1991 limits obtained from neutron lifetime and asymmetries together with unitarity of the CKM matrix. Manifest left-right symmetry assumed. Stronger of the two limits also includes muon decay results.
22  COLANGELO 1991 limit uses hadronic matrix elements evaluated by QCD sum rule and is less restrictive than BEALL 1982 limit which uses vacuum saturation approximation. Manifest left-right symmetry assumed.
23  POLAK 1991 limit is from fit to muon decay parameters and is essentially determined by JODIDIO 1986 data assuming $\zeta$=0. Superseded by POLAK 1992B.
24  BARBIERI 1989B limit holds for ${\mathit m}_{{{\mathit \nu}_{{R}}}}{}\leq{}$10 MeV.
25  LANGACKER 1989B limit is for any ${{\mathit \nu}_{{R}}}$ mass (either Dirac or Majorana) and for a general class of right-handed quark mixing matrices.
26  BALKE 1988 limit is for ${\mathit m}_{\mathrm {{{\mathit \nu}}_{ {{\mathit e}} {{\mathit R}} }}}$ = 0 and ${\mathit m}_{\mathrm {{{\mathit \nu}}_{ {{\mathit \mu}} {{\mathit R}} }}}{}\leq{}$ 50 MeV. Limits come from precise measurements of the muon decay asymmetry as a function of the positron energy.
27  JODIDIO 1986 is the same TRIUMF experiment as STOKER 1985 (and CARR 1983 ); however, it uses a different technique. The results given here are combined results of the two techniques. The technique here involves precise measurement of the end-point ${{\mathit e}^{+}}$ spectrum in the decay of the highly polarized ${{\mathit \mu}^{+}}$.
28  STOKER 1985 is same TRIUMF experiment as CARR 1983 . Here they measure the decay ${{\mathit e}^{+}}$ spectrum asymmetry above 46 ${\mathrm {MeV}}/\mathit c$ using a muon-spin-rotation technique. Assumed a light right-handed neutrino. Quoted limits are from combining with CARR 1983 .
29  BERGSMA 1983 set limit ${\mathit m}_{{{\mathit W}_{{2}}}}/{\mathit m}_{{{\mathit W}_{{1}}}}$ $>$1.9 at CL = 90$\%$.
30  CARR 1983 is TRIUMF experiment with a highly polarized ${{\mathit \mu}^{+}}$ beam. Looked for deviation from $\mathit V−\mathit A$ at the high momentum end of the decay ${{\mathit e}^{+}}$ energy spectrum. Limit from previous world-average muon polarization parameter is ${\mathit m}_{{{\mathit W}_{{R}}}}$ $>$240 GeV. Assumes a light right-handed neutrino.
31  BEALL 1982 limit is obtained assuming that ${{\mathit W}_{{R}}}$ contribution to ${{\mathit K}_L^0}$ $-{{\mathit K}_S^0}$ mass difference is smaller than the standard one, neglecting the top quark contributions. Manifest left-right symmetry assumed.
References:
 PRIEELS 2014
PR D90 112003 Measurement of the Parameter ${{\mathit \xi}^{\,'}}{}^{'}$ in Polarized Muon Decay and Implications on Exotic Couplings of the Leptonic Weak Interaction
 BUENO 2011
PR D84 032005 Precise Measurement of Parity Violation in Polarized Muon Decay
 WAUTERS 2010
PR C82 055502 Precision Measurements of the ${}^{60}\mathrm {Co}$ $\beta$-Asymmetry Parameter in Search for Tensor Currents in Weak Interactions
 ZHANG 2008
NP B802 247 General $\mathit CP$ Violation in Minimal Left-Right Symmetric Model and Constraints on the Right-Handed Scale
 MELCONIAN 2007
PL B649 370 Measurement of the Neutrino Asymmetry in the ${{\mathit \beta}}$ Decay of Laser-Cooled, Polarized ${}^{37}\mathrm {K}$
 SCHUMANN 2007
PRL 99 191803 Measurement of the Neutrino Asymmetry Parameter $\mathit B$ in Neutron Decay
 CYBURT 2005
ASP 23 313 New BBN Limits on Physics Beyond the Standard Model from ${}^{4}\mathrm {He}$
 THOMAS 2001
NP A694 559 Positron Polarization in the Decay of Polarized ${}^{12}\mathrm {N}$: a Precision Test of the Standard Model
 ACKERSTAFF 1999D
EPJ C8 3 Measurement of the Michel Parameters in Leptonic ${{\mathit \tau}}$ Decays
 CZAKON 1999
PL B458 355 Low-Energy Physics and Left-Right Symmetry: Bounds on the Model Parameters
 BARENBOIM 1998
EPJ C1 369 Electroweak Precision Data and Righthanded Gauge Bosons
 BARENBOIM 1997
PR D55 4213 Constraints on the W$_{R}$ Mass and $\mathit CP$ Violation in Left $−$ Right Models
 STAHL 1997
ZPHY C74 73 Testing the Lorentz Structure of the Charged Weak Current in ${{\mathit \tau}}$ Decays
 ALLET 1996
PL B383 139 Search for Right Handed Weak Currents in the $\beta$ Asymmetry Polarization Correlation from ${}^{12}\mathrm {N}$ Decay
 KUZNETSOV 1995
PRL 75 794 Measurements of the Antineutrino Spin Asymmetry in $\beta$ Decay of the Neutron and Restrictions on the Mass of a Right Handed Gauge Boson
 KUZNETSOV 1994B
JETPL 60 315 New Measurement of the Antineutrino Spin Asymmetry in $\beta$ Decay of the Neutron and Restriction for Mass of ${{\mathit W}_{{R}}}$
 BHATTACHARYYA 1993
PR D47 3693 New Bound on Righthanded Charged Gauge Boson Mass
 SEVERIJNS 1993
PRL 70 4047 Limits on Right Handed Charged Weak Currents from a Polarization Asymmetry Correlation Experiment with ${}^{107}\mathrm {In}$
 IMAZATO 1992
PRL 69 877 Search for Right Handed Currents in the Decay Chain ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}}$ , ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}}{{\overline{\mathit \nu}}}$
 POLAK 1992B
PR D46 3871 Left-Right Symmetric Model Parameters: Updated Bounds
 AQUINO 1991
PL B261 280 Bounds on Manifest Left-Right Symmetry from Neutron $\beta$ Decay
 COLANGELO 1991
PL B253 154 Improved Bound on $\mathit W_{R}$ Mass in Left-Right Symmetric Models from ${{\mathit K}^{0}}$ $−$ ${{\overline{\mathit K}}^{0}}$ Mixing
 POLAK 1991
NP B363 385 Updated Constraints on the Neutral Current Parameters in Left-Right Symmetric Model
 BARBIERI 1989B
PR D39 1229 Limits on Righthanded Interactions from SN1987a Observations
 LANGACKER 1989B
PR D40 1569 Bounds on the Mass of $\mathit W_{R}$ and the $\mathit W_{L}$ $−$ $\mathit W_{R}$ Mixing Angle $\xi$ in General SU(2)$_{\mathit L}$ $⊗$ SU(2)$_{\mathit R}$ $⊗$ U(1) Models
 BALKE 1988
PR D37 587 Precise Measurement of the Asymmetry Parameter $\delta$ in Muon Decay
 JODIDIO 1986
PR D34 1967 Search for Right Handed Currents in Muon Decay
 MOHAPATRA 1986
PR D34 909 Limits on the Mass of the Righthanded Majorana Neutrino
 STOKER 1985
PRL 54 1887 Search for Right Handed Currents by Means of Muon Spin Rotation
 BERGSMA 1983
PL 122B 465 Experimental Study of the Reaction ${{\mathit \nu}_{{\mu}}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \mu}^{-}}{{\mathit \nu}_{{e}}}$
 CARR 1983
PRL 51 627 Search for Right Handed Currents in Muon Decay
 BEALL 1982
PRL 48 848 Constraint on the Mass Scale of a Left-right Symmetric Electroweak Theory from the ${{\mathit K}_L^0}$ ${{\mathit K}_S^0}$ Mass Difference