16 November 1994
UTPT-94-33





Is there a Vector Boson Coupling to Baryon Number?





David Bailey

Physics Department,

University of Toronto, Toronto, Ontario M5S 1A7, Canada

E-mail: dbailey@physics.utoronto.ca



Sacha Davidson

Center for Particle Astrophysics,

301 LeConte Hall, UC Berkeley, CA 94720, USA

E-mail: sacha@physics.berkeley.edu





 21 Nov 1994

Abstract

Discrepancies in measurements of the QCD running coupling constant are

consistent with a new vector gauge boson coupling to baryon number with

strength ~0.1. Upsilon decays constrain such a boson to have a mass greater
B

than about 35 GeV. It is difficult to observe such a boson in Z decays, e+e

annihilation, or hadronic interactions.





1


1. Introduction

Baryon number (B) and the lepton family number (Li) are the only exact

symmetries which are not known to couple to a gauge boson. Anomaly

cancellation suggests that only the combination BL could be a gauge

symmetry, but this constraint can be avoided by adding additional heavy (e.g.

mirror) fermions. Many authors [1-6] have suggested extensions to the

Standard Model in which BL, B, or L are gauged symmetries, but such

extensions usually predict few low energy consequences [7]. In this paper we

consider bounds on a gauge boson coupled to baryon number.


Relatively good limits exist on new forces coupling to L [8] or B-L [9]. The

constraints on forces coupling only to B are much weaker, except in the "fifth

force" limit of very light bosons.


Since the only known fundamental particles carrying baryon number are

quarks, searches for a new baryonic force must be made by studying the

interactions of quarks. These are, however, dominated by their strong

interactions, so new baryonic forces can only be found by looking for differences

between the expected Quantum Chromodynamic colour interactions and the

actual interactions of the quarks. Small discrepancies in recent measurements

of the running coupling of QCD has led to wide speculation [10-13] that light

gluinos might exist. In this paper we study the possibility that the discrepancy

is due to a new vector force coupled to baryon number.


The simplest gauge hypothesis for baryon number is that it is a U(1)

symmetry, with a "B" gauge boson coupling to the vector quark current with
strength 2
g /3 ( /4
B B gB ). It would also be possible, in more complicated




2


models, to couple a B boson to the axial, scalar, or pseudoscalar currents [14].

In the limit of a massless gauge boson, this vector theory would be analogous to

quantum electrodynamics. There are, however, significant constraints on such

a boson for masses MB ~< m [9, 15-21]. We therefore assume the U(1)B
symmetry is broken and the B gauge boson is massive.


2. Running of S

Figure 1 shows current data [22, 23] on the running of the strong coupling

constant S(Q). Also shown is the expected QCD evolution for S(MZ)=0.12.

There is some question as to whether the values for S extracted from low

energy data are fully corrected for all non-perturbative low energy effects. At

higher energies the data are consistent with QCD, but the slope of the data is

less than expected. It is this slight difference which may suggest that either

new coloured particles (e.g. gluinos) modify the evolution of S, or that an

additional force exists between quarks.


A U(1)B force would increase in strength with increasing Q in exactly the
same manner as QED, and modify the observed slope of S(Q). If we naively

treat the observed values for S as the sum of the true QCD coupling plus a

new baryonic coupling, then we can estimate the necessary strength of the new
(M
coupling. The expected evolution for B Z)
S(MZ)=0.1 and 32 = 0.02 with M =0
B
1
is also shown in Figure 1. (The factor of " 32 " makes explicit that a quark has
baryon number 1/3.) This value of /9=0.02 is, of course, not a precise estimate
B

since the actual determinations of S all assume that only QCD exists. The

effect of a B gauge boson will vary from process to process and on the

experimental cuts. Since the U(1)B coupling is small, it should not appreciably
change the QCD anomalous dimensions, but in any given matrix element gS


3


and g will not appear multiplied by exactly the same terms because the
B B

boson is colourless.


Is such a new boson consistent with other data on quark interactions?

Relevant data include detailed studies of heavy vector meson decays, Z0 decays,

e+e annihilations, and high energy quark scattering.


3. Upsilon decays

Heavy quark vector mesons normally decay via three gluons, since two

gluon decays are forbidden, and electromagnetic decays are much weaker. A

gauge boson coupling to baryon number would mediate decays of heavy quark

( QQ ) vector mesons into light quark-antiquark pairs. The rate of vector meson
decays into light quarks mediated by a virtual photon or B gauge boson (see

Figure 2) is, to lowest order,
2
2
eQ e 2
q
2  )

e M2
+ Q eq B M 2
V (M2
V B
(V+)
(V
B*,*qq) = Nc 32 (( M2 )2 + 2
V  M2
B B M2)
B
2 (1)
eQ2 q 2
B M4
V
+ 34 ((M2 )2 + 2
V  M2
B B M2)
B
where the sum is over the light quark flavours the vector meson can decay into,

Nc=3 is the colour factor, and eQ is the fractional charge of the heavy quark. MB

and /9 are the mass and decay width of the
B NcNf MB B B gauge boson,

where Nf is the number of light quark flavours the B gauge boson can decay
into. For clarity, the 1-(4m2c/M2) threshold factors for charm production are not
shown. The narrowest of the 
bb resonances, the (1S), eQ=1/3, q=(u,d,s,c), has a

total width is tot=52.51.8 KeV, and a muonic branching ratio of

B.R.((1S)+-) = 2.480.07% [22]. The small value of tot excludes any value



4


of for a
B B boson satisfying the resonance condition MBM. Off resonance

(MBM), equation (1) gives
4.1
M2
 2.0102 V
B
((1S)B*,*qq) M2
V  M2
B (in KeV). (2)
M4
+ 3.1104 V 2
( 2 B
M2
V  M2
B)
Equation(1) implies that a very light gauge boson (MB<<M) with coupling as
small as /9=0.005 would completely saturate the hadronic width of the
B (1S),

leaving no room for any QCD mediated decays. In order to have a coupling as

large as /9= 0.01, the
B B boson must be heavier than about 17 GeV.


Even tighter restrictions on follow from the observed characteristics of
B

(1S) decays. The expected decays into 3 gluons have different characteristics

from decays via a B boson into a quark-antiquark pair.


First, B boson mediated decays into light (u,d,s,c) quarks are expected be

flavour independent, so approximately 1/4 of the decays should be into charm.

The (slightly model dependent) observed upper limit on direct charm

production from the (1S) is only 3.4% [24]. Conservatively assuming no

contribution from gluon fragmentation, this sets an upper limit to any B boson

mediated decays into charm. Applying equation (1) to this upper limit gives

limits on the B boson of /9 < 0.002 for M <<M >
B B , and MB ~ 30 GeV for

/9= 0.01.
B



Secondly, B boson mediated decays into quark-antiquark pairs will have a

2-jet topology different from the event shapes expected for 3-gluon decays. After




5


subtraction of the expected QED contribution, the upper limit on direct 2-jet

decays of the (1S) is 5.3% [25]. This leads to the constraints /9 < 0.0015 for
B

M <<M > /9= 0.01. Newer data [26] could further
B , and MB ~ 35 GeV for B

improve these constraints.

These (1S) data indicate that M >
B ~ 35 GeV if a B gauge boson is to

account for the discrepancy in S(Q). The expected evolution of S(Q)+ '
(
B Q)/9

for M =35 GeV is also shown in Figure 1, using
B S(MZ)=0.11 and
'
(M is the effective value of the
B Z)/9 = 0.01. ( '
B B coupling including the

propagator mass factor.)


4. Other Bounds

There are many other places where on might hope to see evidence for a B

boson with (M
B Z)/9 = 0.01 and MB >
~ 35 GeV. We will review some of the

possibilities here, and briefly discuss why we do not get any interesting bounds.


Although there is no direct coupling between the B and the Z, a B gauge

boson could be produced in two body B + decays of the Z via quark triangle

loops. Current data on exclusive (e.g. Z+ [27]) and inclusive Z+X

decays [28, 29] set limits of B.R.(Z B+) <~ 10-4. There appears, however, to be

some disagreement in the theoretical calculations of the amplitude for such

gauge boson gauge boson + decays (compare references [30] and [31]). We

expect (following the formalism of reference [30] for Z'Z+ decays) the

branching ratio for the decay Z B+ to be less than 10-5 /
B , so the current

data are consistent with /9~0.01. A more restrictive bound from the Z may
B

come in the future from B boson contributions to a "T"-violating asymmetry in

3-jet events at the SLC [32].




6


In addition to direct observation in Z decays, the existence of a B gauge

boson would modify the effective colour factors observed in Z 4-jets events.

We would expect the observed colour factors to have contributions from both

SU(3)QCD (TF/CF=9/4, NC/CF=3/8) and the new U(1)B (TF/CF=0, NC/CF=1). For
~0.01 and
B S~0.11, we would naively expect the observed values to be

TF/CF=2.06, NC/CF=0.43. The best measurements [33] are

TF/CF=2.240.320.24, NC/CF=0.580.170.23, which are easily compatible
with ~0.01, even without considering the suppression factor due to a finite
B B

boson mass.


Below the Z resonance, one could hope to see the B boson as a peak in the
total cross section for 
e+eBqq. The B does not couple at tree level to

electrons in the fundamental Lagrangian, but a coupling is induced at one loop

via vacuum polarization diagrams that mix the B with the photon [34]. We

assume that at sufficiently high energies the U(1)'s are orthogonal, so the

mixing amplitude is finite. One expects [14, 32] that B.R.(Be+e) ~ 2/162.
Thus even at the peak of any 
B resonance, the contribution from e+eBqq
is only of the order of a few percent of the 
e+e *qq rate, where the

uncertainty comes from the vacuum polarization integral. Such a small peak

might be observable, but only with difficulty. For /9 ~ 0.01, the resonance
B

would be quite broad ( ~ 0.1M ) and could only be observed as a peak above
B B

background by scanning an energy range larger than has been typically

scanned with good relative normalization by a single experiment. (For example,

a small excess of events above 56 GeV has been reported [35], but the data do

not reach high enough energies to show if it is a unexpected broad peak.)

Normalization uncertainties are typically 510% (see data of Fig. 32.11 of




7


reference [22]), so it is difficult to search for such a peak by combining data

from different experiments.


Another place to look for a new force coupling only to quarks is in hadronic

interactions. The obvious channel for observation of a B boson would be its
direct  
s-channel production and 2-jet decay qq B qq. The mass range of

interest here (30 GeV <~ M <
B ~ MZ) is, however, too high for ISR data [36] with

negligible high mass 
qq scattering, and somewhat low for collider experiments

with thresholds of Mjj > 40 to 140 GeV [37-39]. The collider limits on massive B

gauge bosons will be discussed elsewhere [14]. We only mention here that the

published dijet mass limits are for M ~> 80 GeV [40], and the dijet data are
inconsistent with any very massive B boson (MB > MZ) with coupling large

enough to make an effective contribution of '
~0.01 at
B Q~MZ.


Finally, a B gauge boson could also affect tchannel hadron scattering. In

particular, a B gauge boson would mediate a colour neutral force which would

produce "rapidity gap" events with no intermediate hadronization between jets.
2
The rate of such events would be R B
gap<
~ . The observed rate [41] in deep
9
S

inelastic (10< Q2<100 GeV2) electron-proton collisions is ~5% , which would

require /9 ~0.03. The stringent limits from
B (1S) decays rule out any B

bosons with a low enough mass and large enough coupling to explain these

rapidity gap events. More massive bosons could contribute to rapidity events in

collider experiments observed at higher Q2 [42], but they could probably only be
identified if they produce an observable threshold effect above Q2 >~ M2 .
B





8


This work was partially supported by the Natural Sciences and

Engineering Research Council of Canada. While this work was in preparation,

we learned of similar work in progress by Carone and Murayama [43].





9


Figure Captions


Figure 1: The values extracted from data [22, 23] for the running coupling

constant S(Q), compared with the expected evolution for QCD with

S(MZ)=0.12, and QCD plus a new U(1)B gauge boson coupling to

baryon number (for either M =0 or M =35 GeV, with /9=0.12
B B S+ '
B

at Q=MZ).


Figure 2: Heavy quark vector boson decay into light quark-antiquark pairs

mediated by (a) a B boson coupled to baryon number, or (b) a

photon.





10


Figure 1





0.5

QCD

0.4
QCD+U(1)
S B
(M = 35 GeV)
0.3 B




0.2


QCD + U(1)
0.1 B
(M = 0)
B


0 1 10 100
Q (GeV)





11


Figure 2





(a)

q
Q
1 B 1
B
32   B
32
--
Q --
q





(b)
f
Q
e2
Q   e2f
 
Q f





12


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